%PDF-1.1 %쏢 8 0 obj <> stream q 1 0 0 1 0 0 cm q q 1 0 0 1 0 0 cm BT /R6 10.9091 Tf 118.2 704 Td (Memoirs)Tj 52.0034 0 Td (on)Tj 17.4978 0 Td (Dieren)Tj 43.6038 0 Td (tial)Tj 22.0361 0 Td (Equations)Tj 58.5815 0 Td (and)Tj 24.207 0 Td (Mathematical)Tj 79.7888 0 Td (Ph)Tj 15.0981 0 Td (ysics)Tj /R12 9.96264 Tf -205.177 -14.76 Td (V)Tj 7.91919 0 Td (olume)Tj 34.175 0 Td (47,)Tj 17.9963 0 Td (2009,)Tj 28.9148 0 Td (123{132)Tj ET Q 1 i 122 674 334.68 0.47998 re f q 1 0 0 1 0 0 cm BT /R15 9.96264 Tf 138.6 578.24 Td (G.)Tj 16.0737 0 Td (Berik)Tj 26.9775 0 Td (elash)Tj 24.5764 0 Td (vili,)Tj 22.5486 0 Td (O.)Tj 15.5952 0 Td (Jokhadze,)Tj 53.3645 0 Td (S.)Tj 13.314 0 Td (Kharib)Tj 35.498 0 Td (egash)Tj 27.0972 0 Td (vili,)Tj 22.5486 0 Td (and)Tj -257.594 -12 Td (B.)Tj 15.1172 0 Td (Mido)Tj 26.6311 0 Td (dash)Tj 22.4246 0 Td (vili)Tj /R6 10.9091 Tf -64.1729 -68.6401 Td (FINITE-DIFFERENCE)Tj 135.534 0 Td (METHOD)Tj 61.8542 0 Td (OF)Tj 21.5781 0 Td (SOL)Tj 22.5271 0 Td (VING)Tj -241.494 -14.04 Td (THE)Tj 30.927 0 Td (D)Tj 9.229 0 Td (ARBOUX)Tj 60.5342 0 Td (PR)Tj 17.4983 0 Td (OBLEM)Tj 50.3452 0 Td (F)Tj 7.54907 0 Td (OR)Tj 22.8979 0 Td (THE)Tj 31.0471 0 Td (NONLINEAR)Tj -230.028 -14.04 Td (KLEIN{GORDON)Tj 108.109 0 Td (EQUA)Tj 35.7163 0 Td (TION)Tj ET Q Q Q endstream endobj 9 0 obj 1239 endobj 18 0 obj <> stream q 1 0 0 1 0 0 cm q q 1 0 0 1 0 0 cm BT /R15 9.96264 Tf 138.6 716 Td (Abstract.)Tj /R22 9.96264 Tf 51.1938 0 Td (The)Tj 19.9053 0 Td (rst)Tj 19.905 0 Td (Darb)Tj 22.2971 0 Td (oux)Tj 18.3403 0 Td (problem)Tj 38.1367 0 Td (for)Tj 14.6248 0 Td (cubic)Tj 25.4246 0 Td (nonlinear)Tj 43.0476 0 Td (Klein{Gordon)Tj -264.755 -12 Td (equation)Tj 40.2795 0 Td (is)Tj 9.71436 0 Td (considered,)Tj 51.3184 0 Td (with)Tj 22.4272 0 Td (a)Tj 8.03076 0 Td (nonhomogeneous)Tj 76.6128 0 Td (condition)Tj 43.4082 0 Td (on)Tj 13.55 0 Td (the)Tj 16.908 0 Td (c)Tj 4.19336 0 Td (haracter-)Tj -286.443 -11.8801 Td (istic)Tj 22.0632 0 Td (line.)Tj 26.0313 0 Td (Solv)Tj 17.9805 0 Td (abilit)Tj 22.4248 0 Td (y)Tj 9.58984 0 Td (and)Tj 20.3894 0 Td (con)Tj 14.7437 0 Td (v)Tj 5.03003 0 Td (ergence)Tj 36.3188 0 Td (of)Tj 12.4697 0 Td (the)Tj 18.228 0 Td (prop)Tj 20.2649 0 Td (er)Tj 12.7083 0 Td (dierence)Tj 45.5649 0 Td (sc)Tj 8.14844 0 Td (heme)Tj 26.9846 0 Td (is)Tj -318.94 -12 Td (in)Tj 8.03882 0 Td (v)Tj 5.03003 0 Td (estigated)Tj 41.9541 0 Td (in)Tj 11.6387 0 Td (Sob)Tj 16.3096 0 Td (olev)Tj 20.7344 0 Td (spaces.)Tj /R15 9.96264 Tf -91.8257 -17.6399 Td (2000)Tj 26.7534 0 Td (Mathematics)Tj 68.7065 0 Td (Sub)Tj 19.6682 0 Td (ject)Tj 22.0515 0 Td (Classication.)Tj /R22 9.96264 Tf 73.6299 0 Td (65M06,)Tj 35.1196 0 Td (35L70.)Tj /R15 9.96264 Tf -245.929 -11.8801 Td (Key)Tj 24.5837 0 Td (w)Tj 7.91895 0 Td (ords)Tj 25.6597 0 Td (and)Tj 22.5513 0 Td (phrases.)Tj /R22 9.96264 Tf 46.0376 0 Td (Klein{Gordon)Tj 64.6206 0 Td (equation,)Tj 43.999 0 Td (dierence)Tj 44.9651 0 Td (sc)Tj 8.14844 0 Td (heme,)Tj -300.364 -12 Td (con)Tj 14.7437 0 Td (v)Tj 5.03003 0 Td (ergence,)Tj 37.9983 0 Td (Sob)Tj 16.3096 0 Td (olev)Tj 20.7344 0 Td (space.)Tj /A 1 Tf 1 0 0 -1 139 621 Tm ( )Tj 7 0 Td ()Tj 5 0 Td ()Tj 6 0 Td ()Tj 5 0 Td ()Tj 6 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 8 0 Td ()Tj 5 0 Td ()Tj 5 0 Td ( )Tj 5 0 Td ()Tj 5 0 Td (\n)Tj 7 0 Td ()Tj 7 0 Td ()Tj 5 0 Td (\n)Tj 7 0 Td ()Tj 4 0 Td (\r)Tj 5 0 Td (\n)Tj 7 0 Td ()Tj 6 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 7 0 Td ( )Tj 4 0 Td ()Tj 5 0 Td ()Tj 7 0 Td ()Tj 4 0 Td ()Tj 4 0 Td ()Tj 7 0 Td ()Tj 4 0 Td ()Tj 7 0 Td ()Tj 4 0 Td ()Tj 8 0 Td ()Tj 3 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 5 0 Td ()Tj 5 0 Td ()Tj 6 0 Td (\n)Tj 7 0 Td ()Tj 7 0 Td ()Tj 6 0 Td ()Tj 4 0 Td ()Tj 4 0 Td ()Tj 8 0 Td ()Tj 5 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 6 0 Td ()Tj 7 0 Td ()Tj 7 0 Td ()Tj 4 0 Td ( )Tj 4 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 5 0 Td ()Tj 6 0 Td ()Tj -322 12 Td ()Tj 4 0 Td ()Tj 5 0 Td ()Tj 7 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 4 0 Td ()Tj 4 0 Td ()Tj 5 0 Td ()Tj 7 0 Td ()Tj 6 0 Td ()Tj 7 0 Td ()Tj 4 0 Td ()Tj 7 0 Td ()Tj 7 0 Td ()Tj 4 0 Td (\n)Tj 7 0 Td ( )Tj 5 0 Td ()Tj 5 0 Td ()Tj 7 0 Td ()Tj 5 0 Td ()Tj 4 0 Td (\n)Tj 7 0 Td ()Tj 4 0 Td ()Tj 4 0 Td ()Tj 7 0 Td ()Tj 8 0 Td ()Tj 4 0 Td ()Tj 4 0 Td ()Tj 6 0 Td ()Tj 7 0 Td ()Tj 4 0 Td ()Tj 4 0 Td ()Tj 7 0 Td ()Tj 4 0 Td (\n)Tj 7 0 Td ()Tj 4 0 Td ()Tj 4 0 Td (\n)Tj 7 0 Td ()Tj 7 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 4 0 Td (\n)Tj 7 0 Td ()Tj 7 0 Td ()Tj 4 0 Td ()Tj 5 0 Td ()Tj 3 0 Td ()Tj 8 0 Td ()Tj 4 0 Td ()Tj 6 0 Td ()Tj 4 0 Td ()Tj 4 0 Td ()Tj 7 0 Td ()Tj 3 0 Td ()Tj 4 0 Td ()Tj 5 0 Td ()Tj 9 0 Td ()Tj 4 0 Td ()Tj 4 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj -322 12 Td ()Tj 4 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 7 0 Td ()Tj 3 0 Td ( )Tj 5 0 Td ()Tj 4 0 Td ()Tj 11 0 Td (\r)Tj 6 0 Td ()Tj 4 0 Td (\n)Tj 7 0 Td ( )Tj 5 0 Td ()Tj 4 0 Td (!)Tj 10 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 4 0 Td ()Tj 7 0 Td ()Tj 4 0 Td ()Tj 5 0 Td ()Tj 7 0 Td ()Tj 4 0 Td ()Tj 5 0 Td ()Tj 7 0 Td ()Tj 5 0 Td ()Tj 8 0 Td (")Tj 5 0 Td ()Tj 4 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ( )Tj 5 0 Td ()Tj 4 0 Td ()Tj 4 0 Td ()Tj 4 0 Td ()Tj 5 0 Td ()Tj 8 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 7 0 Td ( )Tj 4 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 4 0 Td ()Tj 8 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 3 0 Td ()Tj 4 0 Td ()Tj 5 0 Td ()Tj 8 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 6 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 4 0 Td ()Tj 4 0 Td ()Tj 7 0 Td ()Tj 7 0 Td ( )Tj 4 0 Td ()Tj -321 12 Td ()Tj 6 0 Td ()Tj 8 0 Td ()Tj 5 0 Td (\n)Tj 6 0 Td ()Tj 4 0 Td ( )Tj 4 0 Td ()Tj 5 0 Td ()Tj 6 0 Td ()Tj 7 0 Td ( )Tj 5 0 Td ()Tj 7 0 Td ()Tj 5 0 Td ()Tj 6 0 Td ( )Tj 5 0 Td ()Tj 6 0 Td ()Tj 8 0 Td ()Tj 3 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 8 0 Td ()Tj 5 0 Td ()Tj 4 0 Td ()Tj 4 0 Td ()Tj 7 0 Td ()Tj 3 0 Td ()Tj 4 0 Td ( )Tj 5 0 Td (")Tj 5 0 Td ()Tj 4 0 Td (!)Tj ET Q Q Q endstream endobj 19 0 obj 4554 endobj 65 0 obj <> stream q 1 0 0 1 0 0 cm q q 1 0 0 1 0 0 cm BT /R63 6.97385 Tf 126.72 739.88 Td (Klein{Gor)Tj 37.1663 0 Td (don)Tj 15.95 0 Td (Equation)Tj /R69 6.97385 Tf 260.85 0 Td (125)Tj /R22 9.96264 Tf -191.206 -23.8799 Td (1.)Tj /R12 9.96264 Tf 12.7107 0 Td (Intr)Tj 21.8271 0 Td (oduction)Tj /R22 9.96264 Tf -145.418 -18 Td (W)Tj 9.35181 0 Td (e)Tj 8.0332 0 Td (consider)Tj 38.9663 0 Td (the)Tj 17.3879 0 Td (cubic)Tj 26.2646 0 Td (nonlinear)Tj 43.8877 0 Td (Klein{Gordon)Tj 64.5005 0 Td (equation.)Tj 45.0791 0 Td (This)Tj 23.0269 0 Td (equation)Tj -288.378 -11.8801 Td (arises)Tj 28.7695 0 Td (in)Tj 13.1987 0 Td (the)Tj 18.708 0 Td (quan)Tj 21.0999 0 Td (tum)Tj 22.5537 0 Td (theory)Tj 32.8445 0 Td (of)Tj 12.8296 0 Td (eld)Tj 23.1514 0 Td ([1],)Tj 18.5898 0 Td (solid)Tj 24.8247 0 Td (and)Tj 20.9895 0 Td (high)Tj 23.6292 0 Td (energy)Tj 33.4424 0 Td (ph)Tj 10.7986 0 Td (ysics)Tj -305.429 -12 Td ([2],)Tj 17.1499 0 Td (radiation)Tj 43.0417 0 Td (theory)Tj 31.6445 0 Td ([3],)Tj 17.1499 0 Td (in)Tj 8.03882 0 Td (v)Tj 5.03003 0 Td (estigation)Tj 45.7915 0 Td (of)Tj 11.7498 0 Td (thermal)Tj 37.533 0 Td (equilibrium)Tj 53.2542 0 Td (prop)Tj 20.2649 0 Td (erties)Tj 26.9722 0 Td (of)Tj -317.62 -11.8799 Td (solitary)Tj 35.7175 0 Td (w)Tj 6.95288 0 Td (a)Tj 4.79102 0 Td (v)Tj 5.03003 0 Td (e)Tj 7.55322 0 Td (solutions)Tj 41.606 0 Td (\(\\kinks"\))Tj 43.6279 0 Td (in)Tj 11.6387 0 Td (the)Tj 17.1479 0 Td (classical)Tj /R72 9.96264 Tf 38.238 0 Td ()Tj /R69 6.97385 Tf 6.09668 3.59985 Td (4)Tj /R22 9.96264 Tf 7.91992 -3.59985 Td (eld)Tj 21.5913 0 Td (theory)Tj 31.2847 0 Td ([4].)Tj -267.316 -12 Td (Man)Tj 19.426 0 Td (y)Tj 8.86987 0 Td (w)Tj 6.95288 0 Td (orks)Tj 21.6917 0 Td (are)Tj 16.8994 0 Td (dedicated)Tj 45.0842 0 Td (to)Tj 12.5867 0 Td (the)Tj 17.3879 0 Td (in)Tj 8.03882 0 Td (v)Tj 5.03003 0 Td (estigation)Tj 45.6716 0 Td (of)Tj 11.6296 0 Td (b)Tj 5.75928 0 Td (oundary)Tj 39.4453 0 Td (v)Tj 4.67017 0 Td (alue)Tj 21.3433 0 Td (prob-)Tj -302.367 -12 Td (lems)Tj 23.2668 0 Td (for)Tj 15.7048 0 Td (these)Tj 26.0166 0 Td (equations,)Tj 47.9543 0 Td (among)Tj 32.6116 0 Td (whic)Tj 19.6653 0 Td (h)Tj 9.35913 0 Td (w)Tj 6.95288 0 Td (e)Tj 8.27319 0 Td (men)Tj 17.9915 0 Td (tion)Tj 20.8655 0 Td ([5]{[9].)Tj 34.7715 0 Td (The)Tj 20.9854 0 Td (dierence)Tj -284.418 -11.8801 Td (sc)Tj 8.14844 0 Td (hemes)Tj 30.1001 0 Td (of)Tj 11.6296 0 Td (some)Tj 25.1785 0 Td (problems)Tj 43.0518 0 Td (for)Tj 15.4648 0 Td (nonlinear)Tj 44.0078 0 Td (w)Tj 6.95288 0 Td (a)Tj 4.79102 0 Td (v)Tj 5.03003 0 Td (e)Tj 7.79321 0 Td (equations)Tj 44.9546 0 Td (ha)Tj 10.3103 0 Td (v)Tj 5.03003 0 Td (e)Tj 7.79321 0 Td (b)Tj 5.75928 0 Td (een)Tj 18.106 0 Td (studied)Tj -294.102 -12 Td (in)Tj 11.5188 0 Td ([10]{[13].)Tj 0.361084 -12 Td (F)Tj 5.63574 0 Td (or)Tj 12.106 0 Td (the)Tj 17.1479 0 Td (men)Tj 17.9915 0 Td (tioned)Tj 30.3381 0 Td (equation)Tj 40.5195 0 Td (w)Tj 6.95288 0 Td (e)Tj 7.55322 0 Td (consider)Tj 38.7263 0 Td (the)Tj 17.0281 0 Td (rst)Tj 20.5051 0 Td (Darb)Tj 22.2971 0 Td (oux)Tj 18.9404 0 Td (problem)Tj 38.7368 0 Td (with)Tj -306.359 -11.8799 Td (a)Tj 9.47095 0 Td (non-homogeneous)Tj 81.5303 0 Td (condition)Tj 44.9683 0 Td (on)Tj 15.1101 0 Td (the)Tj 18.3479 0 Td (c)Tj 4.19336 0 Td (haracteristic)Tj 58.2573 0 Td (line.)Tj 26.5112 0 Td (Note)Tj 25.292 0 Td (that)Tj 22.9014 0 Td (suc)Tj 13.6677 0 Td (h)Tj -320.25 -12 Td (problems)Tj 42.0918 0 Td (arise)Tj 22.894 0 Td (in)Tj 11.0386 0 Td (mathematical)Tj 61.9875 0 Td (mo)Tj 13.55 0 Td (deling)Tj 28.9021 0 Td (of)Tj 10.7896 0 Td (v)Tj 4.67017 0 Td (arious)Tj 28.8914 0 Td (ph)Tj 10.7986 0 Td (ysical)Tj 26.9688 0 Td (pro)Tj 14.7454 0 Td (cesses,)Tj 30.6848 0 Td (e.g.,)Tj -308.013 -11.8801 Td (in)Tj 11.2786 0 Td (the)Tj 16.908 0 Td (study)Tj 27.2195 0 Td (of)Tj 11.0295 0 Td (harmonic)Tj 43.5276 0 Td (oscillations)Tj 50.7104 0 Td (of)Tj 11.1497 0 Td (a)Tj 8.03076 0 Td (c)Tj 4.19336 0 Td (ho)Tj 10.7903 0 Td (c)Tj 4.19336 0 Td (k)Tj 8.1499 0 Td (in)Tj 11.3987 0 Td (a)Tj 8.03076 0 Td (sup)Tj 15.2336 0 Td (ersonic)Tj 33.0869 0 Td (\ro)Tj 10.3103 0 Td (w)Tj 10.1926 0 Td ([14],)Tj 21.3408 0 Td (as)Tj -316.775 -12 Td (w)Tj 6.95288 0 Td (ell)Tj 13.0725 0 Td (as)Tj 12.2261 0 Td (in)Tj 11.5188 0 Td (in)Tj 8.03882 0 Td (v)Tj 5.03003 0 Td (estigation)Tj 45.1914 0 Td (of)Tj 11.2698 0 Td (oscillation)Tj 46.9951 0 Td (of)Tj 11.2698 0 Td (a)Tj 8.15088 0 Td (string)Tj 28.1758 0 Td (with)Tj 22.6672 0 Td (a)Tj 8.15088 0 Td (piston)Tj 29.8601 0 Td (b)Tj 5.75928 0 Td (eaded)Tj 28.1763 0 Td (on)Tj 13.7903 0 Td (it,)Tj -316.296 -12 Td (whic)Tj 19.6653 0 Td (h)Tj 8.75928 0 Td (is)Tj 10.0745 0 Td (immersed)Tj 44.8538 0 Td (in)Tj 11.6387 0 Td (a)Tj 8.271 0 Td (cylinder)Tj 37.8899 0 Td (lled)Tj 24.3511 0 Td (with)Tj 22.6672 0 Td (viscous)Tj 34.1638 0 Td (liquid)Tj 27.9475 0 Td ([15].)Tj -209.242 -24.5999 Td (2.)Tj /R12 9.96264 Tf 12.7107 0 Td (St)Tj 11.2749 0 Td (a)Tj 5.39697 0 Td (tement)Tj 40.3035 0 Td (of)Tj 15.4661 0 Td (the)Tj 21.2341 0 Td (Pr)Tj 13.1895 0 Td (oblem)Tj 33.9365 0 Td (and)Tj 22.1907 0 Td (Main)Tj 28.9058 0 Td (Resul)Tj 28.5303 0 Td (ts)Tj /R22 9.96264 Tf -262.299 -18 Td (Consider)Tj 41.606 0 Td (the)Tj 17.1479 0 Td (nonlinear)Tj 43.6477 0 Td (Klein{Gordon)Tj 64.2605 0 Td (equation)Tj /R72 9.96264 Tf -79.062 -16.6802 Td (@)Tj /R69 6.97385 Tf 5.87988 3.6001 Td (2)Tj /R72 9.96264 Tf 4.43994 -3.6001 Td (u)Tj ET Q 1 i 226 479 16.0798 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 227.28 469.76 Td (@)Tj 5.86987 0 Td (t)Tj /R69 6.97385 Tf 3.61011 2.88013 Td (2)Tj /R75 9.96264 Tf 8.88013 3.84009 Td ( )Tj /R72 9.96264 Tf 11.1599 6.83984 Td (@)Tj /R69 6.97385 Tf 5.88013 3.6001 Td (2)Tj /R72 9.96264 Tf 4.43994 -3.6001 Td (u)Tj ET Q 257 479 16.0798 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 256.8 469.76 Td (@)Tj 5.86987 0 Td (x)Tj /R69 6.97385 Tf 5.65015 2.88013 Td (2)Tj /R22 9.96264 Tf 7.92017 3.84009 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (m)Tj /R69 6.97385 Tf 8.76929 4.19995 Td (2)Tj /R72 9.96264 Tf 4.43994 -4.19995 Td (u)Tj /R22 9.96264 Tf 7.91821 0 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (u)Tj /R69 6.97385 Tf 11.531 4.19995 Td (3)Tj /R22 9.96264 Tf 7.19995 -4.19995 Td (=)Tj 10.5505 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf 80.5193 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (1\))Tj -317.007 -20.4001 Td (where)Tj /R72 9.96264 Tf 28.7742 0 Td ()Tj 8.51807 0 Td (>)Tj /R22 9.96264 Tf 10.5505 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj 7.07935 0 Td (m)Tj /R75 9.96264 Tf 11.5168 0 Td ()Tj /R22 9.96264 Tf 10.5505 0 Td (0)Tj 8.271 0 Td (are)Tj 16.6594 0 Td (constan)Tj 33.085 0 Td (ts.)Tj -128.156 -12 Td (Let)Tj /R72 9.96264 Tf 17.8652 0 Td (D)Tj /R78 6.97385 Tf 8.29468 -1.43994 Td ()Tj /R22 9.96264 Tf 7.68018 1.43994 Td (:=)Tj /R81 9.96264 Tf 13.3198 8.16016 Td ()Tj /R22 9.96264 Tf 5.76001 -8.16016 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (x;)Tj 10.0784 0 Td (t)Tj /R22 9.96264 Tf 3.59644 0 Td (\))Tj /R75 9.96264 Tf 3.83545 0 Td (j)Tj /R22 9.96264 Tf 5.6394 0 Td (0)Tj /R72 9.96264 Tf 7.79077 0 Td (<)Tj 10.5505 0 Td (x)Tj 8.39844 0 Td (<)Tj 10.5505 0 Td (t;)Tj /R22 9.96264 Tf 10.7959 0 Td (0)Tj /R72 9.96264 Tf 7.6709 0 Td (<)Tj 10.5505 0 Td (t)Tj 6.3562 0 Td (<)Tj 10.5505 0 Td ()Tj /R81 9.96264 Tf 5.48071 8.16016 Td ( )Tj /R22 9.96264 Tf 5.87988 -8.16016 Td (,)Tj 6 0 Td ( )Tj /R78 6.97385 Tf 6.24048 -1.43994 Td ()Tj /R22 9.96264 Tf 7.80005 1.43994 Td (:=)Tj /R81 9.96264 Tf 13.3201 8.16016 Td ()Tj /R22 9.96264 Tf 5.76001 -8.16016 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (x;)Tj 10.0784 0 Td ()Tj /R22 9.96264 Tf 5.39355 0 Td (\))Tj /R75 9.96264 Tf 3.83545 0 Td (j)Tj /R22 9.96264 Tf 5.75928 0 Td (0)Tj /R72 9.96264 Tf 7.6709 0 Td (<)Tj 10.5505 0 Td (x)Tj 8.39844 0 Td (<)Tj 10.5505 0 Td ()Tj /R81 9.96264 Tf 5.44751 8.16016 Td ( )Tj /R22 9.96264 Tf 5.87988 -8.16016 Td (.)Tj -291 -11.8799 Td (In)Tj 11.8755 0 Td (the)Tj 16.5479 0 Td (domain)Tj /R72 9.96264 Tf 34.8992 0 Td (D)Tj /R78 6.97385 Tf 8.31763 -1.44019 Td (T)Tj /R22 9.96264 Tf 9 1.44019 Td (for)Tj 14.6248 0 Td (the)Tj 16.5479 0 Td (equation)Tj 40.0396 0 Td (\(2.1\))Tj 23.2527 0 Td (consider)Tj 38.1262 0 Td (the)Tj 16.668 0 Td (rst)Tj 19.905 0 Td (Darb)Tj 22.2971 0 Td (oux)Tj 18.4604 0 Td (prob-)Tj -302.442 -12 Td (lem)Tj 18.7119 0 Td (with)Tj 22.7874 0 Td (the)Tj 17.1479 0 Td (follo)Tj 18.3403 0 Td (wing)Tj 23.6228 0 Td (b)Tj 5.75928 0 Td (oundary)Tj 39.0854 0 Td (conditions)Tj /R72 9.96264 Tf -66.6152 -17.6401 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\(0)Tj /R72 9.96264 Tf 8.8667 0 Td (;)Tj 4.43945 0 Td (t)Tj /R22 9.96264 Tf 3.59644 0 Td (\))Tj 6.59521 0 Td (=)Tj 10.4307 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj 12.7195 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (t;)Tj 8.03589 0 Td (t)Tj /R22 9.96264 Tf 3.59644 0 Td (\))Tj 6.59521 0 Td (=)Tj /R72 9.96264 Tf 10.4307 0 Td (')Tj /R22 9.96264 Tf 6.47559 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (t)Tj /R22 9.96264 Tf 3.59644 0 Td (\))Tj /R72 9.96264 Tf 3.83545 0 Td (;)Tj /R22 9.96264 Tf 10.0793 0 Td (0)Tj /R75 9.96264 Tf 7.79077 0 Td ()Tj /R72 9.96264 Tf 10.5505 0 Td (t)Tj /R75 9.96264 Tf 6.3562 0 Td ()Tj /R72 9.96264 Tf 10.4307 0 Td (T)Tj 6.71777 0 Td (:)Tj /R22 9.96264 Tf 61.0793 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (2\))Tj -305.023 -17.6399 Td (By)Tj /R72 9.96264 Tf 15.7034 0 Td (W)Tj /R78 6.97385 Tf 10.8167 3.59985 Td (q)Tj -1.43994 -6.11987 Td (p)Tj /R22 9.96264 Tf 5.76001 2.52002 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (D)Tj /R22 9.96264 Tf 8.5188 0 Td (\))Tj 7.19531 0 Td (w)Tj 6.95288 0 Td (e)Tj 7.79321 0 Td (denote)Tj 32.012 0 Td (the)Tj 17.1479 0 Td (Sob)Tj 16.3096 0 Td (olev)Tj 20.7344 0 Td (space)Tj 26.6123 0 Td (with)Tj 22.6672 0 Td (the)Tj 17.1479 0 Td (norm)Tj 26.0244 0 Td (dened)Tj 34.3037 0 Td (b)Tj 5.2793 0 Td (y)Tj /R75 9.96264 Tf -224.094 -27.48 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R78 6.97385 Tf 5.05078 -2.04004 Td (W)Tj /R84 4.98132 Tf 8.52002 3.35986 Td (q)Tj -1.08008 -4.43994 Td (p)Tj /R69 6.97385 Tf 4.91992 1.08008 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (D)Tj /R69 6.97385 Tf 6.71851 0 Td (\))Tj /R22 9.96264 Tf 6.36426 2.04004 Td (:=)Tj /R81 9.96264 Tf 13.3201 11.04 Td ()Tj /R78 6.97385 Tf 12.8401 1.91992 Td (q)Tj /R81 9.96264 Tf -5.28003 -3.47998 Td (X)Tj /R78 6.97385 Tf 21.48 TL (k)' /R69 6.97385 Tf 4.31812 0 Td (=0)Tj /R75 9.96264 Tf 11.8818 12 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R78 6.97385 Tf 2.76221 4.80005 Td (p)Tj 8.40015 TL (W)' /R84 4.98132 Tf 8.52002 2.04004 Td (k)Tj -1.08008 -4.08008 Td (p)Tj /R69 6.97385 Tf 5.40015 2.04004 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (D)Tj /R69 6.97385 Tf 6.71851 0 Td (\))Tj /R81 9.96264 Tf 3.60425 14.6401 Td ()Tj /R69 6.97385 Tf 6 -2.04004 Td (1)Tj /R78 6.97385 Tf 3.9541 0 Td (=p)Tj /R72 9.96264 Tf 8.64575 -9 Td (;)Tj /R75 9.96264 Tf -133.68 -32.1602 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R78 6.97385 Tf 2.76221 -2.03979 Td (W)Tj /R84 4.98132 Tf 8.52002 2.03979 Td (k)Tj -1.08008 -3.95996 Td (p)Tj /R69 6.97385 Tf 5.52002 1.92017 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (D)Tj /R69 6.97385 Tf 6.71851 0 Td (\))Tj /R22 9.96264 Tf 6.36426 2.03979 Td (:=)Tj /R81 9.96264 Tf 13.3201 11.04 Td ()Tj 13.6799 -1.56006 Td (X)Tj /R78 6.97385 Tf -6.11987 -21.48 Td ()Tj /R69 6.97385 Tf 5.15356 0 Td (+)Tj /R78 6.97385 Tf 6.11597 0 Td ()Tj /R69 6.97385 Tf 4.91357 0 Td (=)Tj /R78 6.97385 Tf 6.11597 0 Td (k)Tj /R81 9.96264 Tf 6.021 23.52 Td (\r)Tj 6 TL (\r)' (\r)' /R72 9.96264 Tf 8.63989 7.2002 Td (@)Tj /R78 6.97385 Tf 5.87988 3.59985 Td ()Tj /R69 6.97385 Tf 5.15356 0 Td (+)Tj /R78 6.97385 Tf 6.11597 0 Td ()Tj /R72 9.96264 Tf 5.41064 -3.59985 Td (u)Tj ET Q 298 328 32.0398 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 298.2 318.44 Td (@)Tj 5.86987 0 Td (x)Tj /R78 6.97385 Tf 5.65015 2.87988 Td ()Tj /R72 9.96264 Tf 5.76001 -2.87988 Td (@)Tj 5.86987 0 Td (t)Tj /R78 6.97385 Tf 3.61011 2.87988 Td ()Tj /R81 9.96264 Tf 6.47998 15.48 Td (\r)Tj 6 TL (\r)' (\r)' /R78 6.97385 Tf 5.52002 9.47998 Td (p)Tj 15.96 TL (L)' /R84 4.98132 Tf 5.52002 -0.959961 Td (p)Tj /R69 6.97385 Tf 4.19995 0.959961 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (D)Tj /R69 6.97385 Tf 6.71851 0 Td (\))Tj /R81 9.96264 Tf 3.60425 18 Td ()Tj /R69 6.97385 Tf 5.87988 -2.04004 Td (1)Tj /R78 6.97385 Tf 3.9541 0 Td (=p)Tj /R72 9.96264 Tf 8.76611 -9 Td (:)Tj /R22 9.96264 Tf -252 -29.1599 Td (In)Tj 12.3557 0 Td (particular,)Tj 48.7991 0 Td (for)Tj /R72 9.96264 Tf 15.2249 0 Td (q)Tj /R22 9.96264 Tf 7.55322 0 Td (=)Tj 10.5505 0 Td (0)Tj 8.271 0 Td (w)Tj 6.95288 0 Td (e)Tj 7.67334 0 Td (ha)Tj 10.3103 0 Td (v)Tj 5.03003 0 Td (e)Tj /R72 9.96264 Tf 7.55322 0 Td (W)Tj /R69 6.97385 Tf 10.9258 3.6001 Td (0)Tj /R78 6.97385 Tf -1.43994 -6 Td (p)Tj /R22 9.96264 Tf 8.76001 2.3999 Td (=)Tj /R72 9.96264 Tf 10.4307 0 Td (L)Tj /R78 6.97385 Tf 6.84912 -1.43994 Td (p)Tj /R22 9.96264 Tf 4.56006 1.43994 Td (.)Tj 7.19946 0 Td (Moreo)Tj 27.3264 0 Td (v)Tj 5.03003 0 Td (er,)Tj 14.1479 0 Td (let)Tj /R75 9.96264 Tf -179.584 -30 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R69 6.97385 Tf 2.76221 4.08008 Td (2)Tj /R78 6.97385 Tf 7.19995 TL (W)' /R87 4.98132 Tf 8.51978 2.3999 Td (1)Tj -1.07983 -4.56006 Td (2)Tj /R69 6.97385 Tf 4.91992 2.16016 Td (\( )Tj /R84 4.98132 Tf 8.04004 -0.960205 Td ()Tj /R69 6.97385 Tf 4.56006 0.960205 Td (\))Tj /R22 9.96264 Tf 6.35986 3.11987 Td (:=)Tj /R78 6.97385 Tf 18.24 15.48 Td ()Tj /R81 9.96264 Tf -5.04004 -1.91992 Td (Z)Tj /R69 6.97385 Tf 0.840088 -28.3201 Td (0)Tj /R81 9.96264 Tf 10.8 28.8 Td ()Tj 7.32007 -3 Td ()Tj /R72 9.96264 Tf 7.19995 -4.32007 Td (@)Tj 5.86987 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (x;)Tj 10.0784 0 Td ()Tj /R22 9.96264 Tf 5.39355 0 Td (\))Tj ET Q 263 268 34.9199 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 274.8 259.28 Td (@)Tj 5.86987 0 Td (x)Tj /R81 9.96264 Tf 18.6101 17.8801 Td ()Tj /R69 6.97385 Tf 5.88013 -2.15991 Td (2)Tj /R22 9.96264 Tf 6.71997 -8.88013 Td (+)Tj /R81 9.96264 Tf 9.95996 11.04 Td ()Tj /R72 9.96264 Tf 7.19995 -4.32007 Td (@)Tj 5.86987 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (x;)Tj 10.0784 0 Td ()Tj /R22 9.96264 Tf 5.39355 0 Td (\))Tj ET Q 329 268 34.9199 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 341.76 259.28 Td (@)Tj 5.86987 0 Td (t)Tj /R81 9.96264 Tf 17.4102 17.8801 Td ()Tj /R69 6.97385 Tf 6 -2.15991 Td (2)Tj /R81 9.96264 Tf 4.44019 5.15991 Td ()Tj /R72 9.96264 Tf 9 -14.04 Td (dx:)Tj /R22 9.96264 Tf -245.88 -30.6001 Td (As)Tj 14.147 0 Td (in)Tj 11.1587 0 Td ([16],)Tj 21.1008 0 Td (one)Tj 17.7434 0 Td (can)Tj 17.6235 0 Td (pro)Tj 14.2654 0 Td (v)Tj 5.03003 0 Td (e)Tj 7.07324 0 Td (that)Tj 20.9812 0 Td (if)Tj /R72 9.96264 Tf 8.51807 0 Td (')Tj /R75 9.96264 Tf 9.35547 0 Td (2)Tj /R72 9.96264 Tf 9.35498 0 Td (C)Tj /R69 6.97385 Tf 7.92822 3.6001 Td (1)Tj /R22 9.96264 Tf 4.56006 -3.6001 Td (,)Tj 5.6394 0 Td (then)Tj 22.0671 0 Td (the)Tj 16.668 0 Td (problem)Tj 38.1367 0 Td (\(2.1\),)Tj 24.9326 0 Td (\(2.2\))Tj 23.2527 0 Td (has)Tj -311.417 -12 Td (a)Tj 8.03076 0 Td (classical)Tj 37.998 0 Td (solution.)Tj 41.4902 0 Td (In)Tj 12.2356 0 Td (the)Tj 16.908 0 Td (in)Tj 8.03882 0 Td (v)Tj 5.03003 0 Td (estigation)Tj 45.0715 0 Td (of)Tj 11.1497 0 Td (the)Tj 16.908 0 Td (dierence)Tj 44.365 0 Td (sc)Tj 8.14844 0 Td (heme)Tj 25.6646 0 Td (w)Tj 6.95288 0 Td (e)Tj 7.43311 0 Td (require)Tj -295.425 -11.8799 Td (that)Tj 21.4614 0 Td (the)Tj 17.1479 0 Td (solution)Tj 37.7708 0 Td (of)Tj 11.2698 0 Td (the)Tj 17.1479 0 Td (problem)Tj 38.7368 0 Td (\(2.1\),)Tj 24.9326 0 Td (\(2.2\))Tj 23.7329 0 Td (b)Tj 5.75928 0 Td (elongs)Tj 29.9697 0 Td (to)Tj 12.2266 0 Td (the)Tj 17.0281 0 Td (space)Tj /R72 9.96264 Tf 26.6123 0 Td (W)Tj /R69 6.97385 Tf 11.0437 3.6001 Td (2)Tj -1.43994 -6.12012 Td (2)Tj /R22 9.96264 Tf 6 2.52002 Td (.)Tj -287.52 -12 Td (Denote)Tj /R72 9.96264 Tf 34.8843 0 Td (h)Tj /R22 9.96264 Tf 9.59814 0 Td (:=)Tj /R72 9.96264 Tf 14.3901 0 Td (T)Tj 6.95776 0 Td (=n)Tj /R22 9.96264 Tf 11.0286 0 Td (.)Tj 9.11938 0 Td (Using)Tj 28.6572 0 Td (the)Tj 17.748 0 Td (straigh)Tj 29.8472 0 Td (t)Tj 7.67529 0 Td (lines)Tj /R72 9.96264 Tf 23.5068 0 Td (t)Tj /R75 9.96264 Tf 6.23633 0 Td ()Tj /R72 9.96264 Tf 10.3105 0 Td (x)Tj /R22 9.96264 Tf 9.59863 0 Td (=)Tj 11.6306 0 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (ih)Tj /R22 9.96264 Tf 9.23535 0 Td (,)Tj /R72 9.96264 Tf 6.83936 0 Td (i)Tj /R22 9.96264 Tf 7.31665 0 Td (=)Tj 11.6306 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf 4.43945 0 Td (1)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf 4.43945 0 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj /R22 9.96264 Tf 2.51953 0 Td (,)Tj -322.932 -12.24 Td (let)Tj 15.3484 0 Td (us)Tj 13.6743 0 Td (co)Tj 9.22437 0 Td (v)Tj 5.03003 0 Td (er)Tj ET Q 183 195 8.63989 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 182.465 187.4 Td (D)Tj /R78 6.97385 Tf 8.57446 -1.43994 Td (T)Tj /R22 9.96264 Tf 10.5601 1.43994 Td (b)Tj 5.2793 0 Td (y)Tj 9.58984 0 Td (a)Tj 9.23096 0 Td (mesh)Tj ET Q 252 195 7.91992 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 252.207 187.4 Td (Q)Tj /R78 6.97385 Tf 7.83325 -2.52002 Td (n)Tj /R22 9.96264 Tf 5.52002 2.52002 Td (.)Tj 10.0793 0 Td (Denote)Tj 35.1243 0 Td (b)Tj 5.2793 0 Td (y)Tj /R72 9.96264 Tf 9.46997 0 Td (Q)Tj /R78 6.97385 Tf 7.96729 -1.43994 Td (n)Tj /R22 9.96264 Tf 9.71997 1.43994 Td (the)Tj 18.1079 0 Td (set)Tj 16.5439 0 Td (of)Tj 12.2297 0 Td (in)Tj 8.03882 0 Td (ternal)Tj 29.7341 0 Td (no)Tj 10.7903 0 Td (des)Tj ET Q Q Q endstream endobj 66 0 obj 17512 endobj 90 0 obj <> stream q 1 0 0 1 0 0 cm q q 1 0 0 1 0 0 cm BT /R69 6.97385 Tf 126.72 739.88 Td (126)Tj /R63 6.97385 Tf 68.1421 0 Td (G.)Tj 11.7505 0 Td (Berikelashvili,)Tj 53.8267 0 Td (O.)Tj 11.7517 0 Td (Jokhadze,)Tj 37.6526 0 Td (S.)Tj 10.071 0 Td (Kharib)Tj 24.1042 0 Td (e)Tj 3.47559 0 Td (gashvili,)Tj 32.1294 0 Td (and)Tj 16.0701 0 Td (B.)Tj 11.2705 0 Td (Mido)Tj 17.8696 0 Td (dashvili)Tj /R22 9.96264 Tf -298.114 -23.8799 Td (\(including)Tj 48.2161 0 Td (the)Tj 18.468 0 Td (no)Tj 10.7903 0 Td (des)Tj 18.4675 0 Td (lying)Tj 25.8997 0 Td (on)Tj 15.1101 0 Td (the)Tj 18.3479 0 Td (line)Tj /R72 9.96264 Tf 20.1519 0 Td (t)Tj /R22 9.96264 Tf 8.39624 0 Td (=)Tj /R72 9.96264 Tf 12.7107 0 Td (T)Tj /R22 9.96264 Tf 7.31787 0 Td (\),)Tj 11.395 0 Td (and)Tj 20.6294 0 Td (b)Tj 5.2793 0 Td (y)Tj /R72 9.96264 Tf 9.82983 0 Td (\r)Tj /R78 6.97385 Tf 5.31006 -1.44019 Td (i)Tj /R22 9.96264 Tf 7.92017 1.44019 Td (the)Tj 18.3479 0 Td (set)Tj 16.9041 0 Td (of)Tj 12.5896 0 Td (the)Tj -312.082 -12 Td (in)Tj 8.03882 0 Td (ternal)Tj 28.7742 0 Td (no)Tj 10.7903 0 Td (des)Tj 17.1477 0 Td (lying)Tj 24.5798 0 Td (on)Tj 13.7903 0 Td (the)Tj 17.1479 0 Td (la)Tj 7.55078 0 Td (y)Tj 5.03003 0 Td (ers)Tj /R72 9.96264 Tf 15.4634 0 Td (t)Tj /R22 9.96264 Tf 6.3562 0 Td (=)Tj /R72 9.96264 Tf 10.5505 0 Td (ih;)Tj 23.5146 0 Td (i)Tj /R22 9.96264 Tf 6.23657 0 Td (=)Tj 10.4307 0 Td (3)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf 4.43945 0 Td (4)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj /R22 9.96264 Tf 2.63965 0 Td (:)Tj /R72 9.96264 Tf -203.941 -17.52 Td (\r)Tj /R69 6.97385 Tf 5.15991 -1.44019 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td (k)Tj /R22 9.96264 Tf 7.68604 1.44019 Td (:=)Tj /R81 9.96264 Tf 13.3198 8.03979 Td ()Tj /R22 9.96264 Tf 5.76001 -8.03979 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (x)Tj /R69 6.97385 Tf 5.64453 -1.44019 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td ()Tj /R72 9.96264 Tf 5.88599 1.44019 Td (;)Tj 4.43945 0 Td (t)Tj /R69 6.97385 Tf 3.60059 -1.44019 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td (k)Tj /R22 9.96264 Tf 4.80591 1.44019 Td (\))Tj /R75 9.96264 Tf 3.83545 0 Td (j)Tj /R72 9.96264 Tf 5.6394 0 Td ()Tj /R22 9.96264 Tf 9.11572 0 Td (=)Tj 10.5505 0 Td (1)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf 4.43945 0 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.19946 0 Td (;)Tj 4.43945 0 Td (k)Tj /R75 9.96264 Tf 7.79053 0 Td ( )Tj /R22 9.96264 Tf 9.95068 0 Td (1)Tj /R81 9.96264 Tf 5.09888 8.03979 Td ( )Tj /R72 9.96264 Tf 5.76001 -8.03979 Td (;)Tj -176.4 -16.5601 Td (\r)Tj /R69 6.97385 Tf 5.15991 -1.43994 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td (k)Tj /R94 6.97385 Tf 4.31812 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R22 9.96264 Tf 7.33325 1.43994 Td (:=)Tj /R81 9.96264 Tf 13.3198 8.04004 Td ()Tj /R22 9.96264 Tf 5.76001 -8.04004 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (x)Tj /R69 6.97385 Tf 5.64453 -1.43994 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td ()Tj /R94 6.97385 Tf 5.15356 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R72 9.96264 Tf 4.69775 1.43994 Td (;)Tj 4.43945 0 Td (t)Tj /R69 6.97385 Tf 3.60059 -1.43994 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td (k)Tj /R94 6.97385 Tf 4.31812 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R22 9.96264 Tf 4.45313 1.43994 Td (\))Tj /R75 9.96264 Tf 3.83545 0 Td (j)Tj /R72 9.96264 Tf 5.6394 0 Td ()Tj /R22 9.96264 Tf 9.11572 0 Td (=)Tj 10.5505 0 Td (1)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf 4.43945 0 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.19946 0 Td (;)Tj 4.43945 0 Td (k)Tj /R75 9.96264 Tf 7.79053 0 Td ( )Tj /R22 9.96264 Tf 9.95068 0 Td (1)Tj /R81 9.96264 Tf 5.09912 8.04004 Td ( )Tj /R72 9.96264 Tf 5.76001 -8.04004 Td (;)Tj 9.95947 0 Td (x)Tj /R78 6.97385 Tf 5.64038 -1.43994 Td (i)Tj /R22 9.96264 Tf 6.12012 1.43994 Td (=)Tj /R72 9.96264 Tf 10.4307 0 Td (ih;)Tj 19.1948 0 Td (t)Tj /R78 6.97385 Tf 3.6145 -1.43994 Td (j)Tj /R22 9.96264 Tf 6.95996 1.43994 Td (=)Tj /R72 9.96264 Tf 10.5505 0 Td (j)Tj 4.67456 0 Td (h:)Tj /R22 9.96264 Tf -295.665 -17.52 Td (Let)Tj /R72 9.96264 Tf 8.63989 -17.52 Td (\r)Tj /R69 6.97385 Tf 5.76001 4.08008 Td (+)Tj /R22 9.96264 Tf 9.36011 -4.08008 Td (:=)Tj /R81 9.96264 Tf 13.2 8.04004 Td ()Tj /R22 9.96264 Tf 5.87988 -8.04004 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (j)Tj 4.67456 0 Td (h;)Tj 10.1978 0 Td (j)Tj 4.67456 0 Td (h)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj /R75 9.96264 Tf 3.83545 0 Td (j)Tj /R72 9.96264 Tf 5.51929 0 Td (j)Tj /R22 9.96264 Tf 7.43457 0 Td (=)Tj 10.4307 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf 4.43945 0 Td (1)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.31934 0 Td (;)Tj 4.43945 0 Td (n)Tj /R81 9.96264 Tf 6.06079 8.04004 Td ( )Tj /R72 9.96264 Tf 5.76001 -8.04004 Td (;)Tj 12.7195 0 Td (\r)Tj /R94 6.97385 Tf 5.7605 4.08008 Td ( )Tj /R22 9.96264 Tf 9.47998 -4.08008 Td (:=)Tj /R81 9.96264 Tf 13.3201 8.04004 Td ()Tj /R22 9.96264 Tf 5.76001 -8.04004 Td (\(0)Tj /R72 9.96264 Tf 8.8667 0 Td (;)Tj /R22 9.96264 Tf 4.43945 0 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (j)Tj 4.67456 0 Td (h)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj /R75 9.96264 Tf 3.83545 0 Td (j)Tj /R72 9.96264 Tf 5.39941 0 Td (j)Tj /R22 9.96264 Tf 7.43457 0 Td (=)Tj 10.5505 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf 4.43945 0 Td (1)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.31934 0 Td (;)Tj /R22 9.96264 Tf 4.43945 0 Td ([)Tj /R72 9.96264 Tf 2.75952 0 Td (n=)Tj /R22 9.96264 Tf 11.0286 0 Td (2])Tj /R81 9.96264 Tf 7.8833 8.04004 Td ( )Tj /R72 9.96264 Tf 5.64014 -8.04004 Td (;)Tj /R22 9.96264 Tf -314.52 -17.6399 Td (where)Tj 28.7742 0 Td ([)Tj /R75 9.96264 Tf 5.51929 0 Td ()Tj /R22 9.96264 Tf 4.43945 0 Td (])Tj 6 0 Td (denotes)Tj 36.0869 0 Td (the)Tj 17.1479 0 Td (in)Tj 8.03882 0 Td (teger)Tj 24.8083 0 Td (part)Tj 21.5811 0 Td (of)Tj 11.3896 0 Td (a)Tj 8.271 0 Td (n)Tj 5.2793 0 Td (um)Tj 13.5581 0 Td (b)Tj 5.75928 0 Td (er.)Tj ET Q Q q 145.2 292.765 m 145.2 600.2 l 433.915 600.2 l 433.915 292.765 l 145.2 292.765 l W n q 288.716 0 0 -307.435 145.2 600.2 cm /R95 Do Q Q q q 1 0 0 1 0 0 cm BT /R12 9.96264 Tf 248.16 268.88 Td (Figure)Tj 37.9021 0 Td (1.)Tj /R22 9.96264 Tf 13.677 0 Td (Meshes)Tj -161.139 -23.3999 Td (F)Tj 5.63574 0 Td (or)Tj 12.2261 0 Td (summing)Tj 42.7021 0 Td (up)Tj 14.3984 0 Td (on)Tj 13.7903 0 Td (subsets)Tj 34.4131 0 Td (of)Tj /R72 9.96264 Tf 11.3896 0 Td (Q)Tj /R78 6.97385 Tf 8.00464 -1.44019 Td (n)Tj /R22 9.96264 Tf 5.3999 1.44019 Td (,)Tj 6.11938 0 Td (w)Tj 6.95288 0 Td (e)Tj 7.67334 0 Td (use)Tj 17.1477 0 Td (the)Tj 17.1479 0 Td (iden)Tj 17.9915 0 Td (tities)Tj /R81 9.96264 Tf -186.313 -17.8801 Td (X)Tj /R78 6.97385 Tf 0.120117 -21.3599 Td (Q)Tj /R87 4.98132 Tf 6.23999 -1.08008 Td (2)Tj /R84 4.98132 Tf 3.35718 0 Td (k)Tj /R72 9.96264 Tf 6.24292 12.96 Td (f)Tj /R22 9.96264 Tf 8.75122 0 Td (=)Tj /R78 6.97385 Tf 10.5686 12.48 Td (k)Tj /R94 6.97385 Tf 4.31812 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R81 9.96264 Tf -10.4326 -3 Td (X)Tj /R78 6.97385 Tf 0.23999 -21.24 Td (j)Tj /R69 6.97385 Tf 3.5957 0 Td (=1)Tj 12.2441 24.72 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td (k)Tj /R94 6.97385 Tf 4.31812 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td (j)Tj /R81 9.96264 Tf -14.5007 -3.47998 Td (X)Tj /R78 6.97385 Tf 0.719971 -21.24 Td (i)Tj /R69 6.97385 Tf 2.75464 0 Td (=1)Tj /R72 9.96264 Tf 16.5652 11.76 Td (f)Tj /R78 6.97385 Tf 6 4.80005 Td (i)Tj /R69 6.97385 Tf 2.75464 0 Td (+2)Tj /R78 6.97385 Tf 10.0701 0 Td (j)Tj -13.9045 -7.56006 Td (i)Tj /R72 9.96264 Tf 18.1199 2.76001 Td (;)Tj /R81 9.96264 Tf 18.6001 9.47998 Td (X)Tj /R78 6.97385 Tf -4.19995 -21.3599 Td (Q)Tj /R87 4.98132 Tf 6.23999 -1.08008 Td (2)Tj /R84 4.98132 Tf 3.35718 0 Td (k)Tj /R98 4.98132 Tf 3.83594 0 Td ( )Tj /R87 4.98132 Tf 5.39966 0 Td (1)Tj /R72 9.96264 Tf 5.64722 12.96 Td (f)Tj /R22 9.96264 Tf 8.63135 0 Td (=)Tj /R78 6.97385 Tf 10.5686 12.48 Td (k)Tj /R94 6.97385 Tf 4.31812 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R81 9.96264 Tf -10.4329 -3 Td (X)Tj /R78 6.97385 Tf 0.240234 -21.24 Td (j)Tj /R69 6.97385 Tf 3.5957 0 Td (=1)Tj 12.2441 24.72 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td (k)Tj /R94 6.97385 Tf 4.31812 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R81 9.96264 Tf -19.1711 -3.47998 Td (X)Tj /R78 6.97385 Tf 0.719971 -21.24 Td (i)Tj /R69 6.97385 Tf 2.75464 0 Td (=1)Tj /R72 9.96264 Tf 21.6052 11.76 Td (f)Tj /R78 6.97385 Tf 6 4.80005 Td (i)Tj /R69 6.97385 Tf 2.75464 0 Td (+2)Tj /R78 6.97385 Tf 10.0701 0 Td (j)Tj -13.9045 -7.56006 Td (i)Tj /R72 9.96264 Tf 18.1199 2.76001 Td (:)Tj /R22 9.96264 Tf -264.72 -30.72 Td (F)Tj 5.63574 0 Td (or)Tj 12.2261 0 Td (mesh)Tj 25.5466 0 Td (functions)Tj 42.9314 0 Td (w)Tj 6.95288 0 Td (e)Tj 7.67334 0 Td (use)Tj 17.1477 0 Td (the)Tj 17.1479 0 Td (notation)Tj /R72 9.96264 Tf 39.8027 0 Td (U)Tj /R78 6.97385 Tf 8.05566 4.80005 Td (j)Tj -1.08008 -7.56006 Td (i)Tj /R22 9.96264 Tf 8.04004 2.76001 Td (:=)Tj /R72 9.96264 Tf 13.3101 0 Td (U)Tj /R22 9.96264 Tf 7.91406 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (x)Tj /R78 6.97385 Tf 5.6604 -1.43994 Td (i)Tj /R72 9.96264 Tf 3.35986 1.43994 Td (;)Tj 4.43945 0 Td (t)Tj /R78 6.97385 Tf 3.60059 -1.43994 Td (j)Tj /R22 9.96264 Tf 4.19995 1.43994 Td (\))Tj /R72 9.96264 Tf 3.83545 0 Td (:)Tj ET Q Q Q endstream endobj 91 0 obj 9435 endobj 102 0 obj <> stream q 1 0 0 1 0 0 cm q q 1 0 0 1 0 0 cm BT /R63 6.97385 Tf 126.72 739.88 Td (Klein{Gor)Tj 37.1663 0 Td (don)Tj 15.95 0 Td (Equation)Tj /R69 6.97385 Tf 260.85 0 Td (127)Tj /R22 9.96264 Tf -302.086 -23.8799 Td (Let)Tj 17.8652 0 Td (us)Tj 12.8342 0 Td (appro)Tj 24.8159 0 Td (ximate)Tj 32.6086 0 Td (the)Tj 17.1479 0 Td (problem)Tj 38.8567 0 Td (\(2.1\),)Tj 24.8125 0 Td (\(2.2\))Tj 23.7329 0 Td (b)Tj 5.2793 0 Td (y)Tj 8.62988 0 Td (the)Tj 17.1479 0 Td (dierence)Tj 44.4851 0 Td (sc)Tj 8.14844 0 Td (heme)Tj /R75 9.96264 Tf -232.085 -19.3201 Td (L)Tj /R72 9.96264 Tf 6.83423 0 Td (U)Tj /R22 9.96264 Tf 10.6741 0 Td (:=)Tj /R75 9.96264 Tf 13.1902 0 Td (L)Tj /R69 6.97385 Tf 6.86157 -1.43994 Td (0)Tj /R72 9.96264 Tf 4.55981 1.43994 Td (U)Tj /R22 9.96264 Tf 10.0742 0 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (m)Tj /R69 6.97385 Tf 8.77515 4.07983 Td (2)Tj /R75 9.96264 Tf 4.44019 -4.07983 Td (L)Tj /R78 6.97385 Tf 6.83984 -1.43994 Td (m)Tj /R72 9.96264 Tf 7.67993 1.43994 Td (U)Tj /R22 9.96264 Tf 10.0742 0 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td ()Tj /R75 9.96264 Tf 5.7583 0 Td (L)Tj /R78 6.97385 Tf 6.85693 -1.43994 Td ()Tj /R72 9.96264 Tf 5.28003 1.43994 Td (U)Tj /R22 9.96264 Tf 10.6741 0 Td (=)Tj 10.4307 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf 9.95947 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (x;)Tj 10.0784 0 Td (t)Tj /R22 9.96264 Tf 3.59644 0 Td (\))Tj /R75 9.96264 Tf 6.71533 0 Td (2)Tj /R72 9.96264 Tf 9.35498 0 Td (Q)Tj /R78 6.97385 Tf 7.96411 -1.43994 Td (n)Tj /R72 9.96264 Tf 5.40015 1.43994 Td (;)Tj /R22 9.96264 Tf 38.3994 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (3\))Tj /R72 9.96264 Tf -204.106 -22.2 Td (U)Tj /R81 9.96264 Tf 7.91992 8.52002 Td ()Tj 6 TL ()' /R78 6.97385 Tf 3.23999 -6.48022 Td (\r)Tj /R87 4.98132 Tf 4.68018 1.92017 Td (+)Tj /R22 9.96264 Tf 8.87988 2.04004 Td (=)Tj 10.4307 0 Td ()Tj /R72 9.96264 Tf 7.19287 0 Td (;)Tj 14.3994 0 Td (U)Tj /R81 9.96264 Tf 7.93701 8.52002 Td ()Tj ()' /R78 6.97385 Tf 3.36011 -6.48022 Td (\r)Tj /R98 4.98132 Tf 4.67993 1.92017 Td ( )Tj /R22 9.96264 Tf 9.12012 2.04004 Td (=)Tj 10.4307 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf 95.1594 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (4\))Tj -317.007 -18.3601 Td (where)Tj 3.71997 -19.2 Td (\()Tj /R75 9.96264 Tf 3.83545 0 Td (L)Tj /R69 6.97385 Tf 6.84448 -1.43994 Td (0)Tj /R72 9.96264 Tf 4.56006 1.43994 Td (U)Tj /R22 9.96264 Tf 7.91406 0 Td (\))Tj /R78 6.97385 Tf 3.84595 4.80005 Td (j)Tj 7.56006 TL (i)' /R22 9.96264 Tf 6.95996 2.76001 Td (:=)Tj 13.1902 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (U)Tj /R78 6.97385 Tf 7.93433 4.80005 Td (j)Tj -1.08008 -7.56006 Td (i)Tj /R22 9.96264 Tf 7.56006 2.76001 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (U)Tj /R78 6.97385 Tf 7.92944 4.80005 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (2)Tj /R78 6.97385 Tf -10.9104 -7.56006 Td (i)Tj /R75 9.96264 Tf 17.6399 2.76001 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (U)Tj /R78 6.97385 Tf 7.92944 4.80005 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R78 6.97385 Tf -10.9104 -7.56006 Td (i)Tj /R94 6.97385 Tf 2.75464 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R75 9.96264 Tf 8.65088 2.76001 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (U)Tj /R78 6.97385 Tf 7.9292 4.80005 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R78 6.97385 Tf -10.9104 -7.56006 Td (i)Tj /R69 6.97385 Tf 2.75464 0 Td (+1)Tj /R22 9.96264 Tf 12.7253 2.76001 Td (\))Tj /R72 9.96264 Tf 3.83545 0 Td (=h)Tj /R69 6.97385 Tf 10.8047 4.08008 Td (2)Tj /R72 9.96264 Tf 4.43994 -4.08008 Td (;)Tj /R22 9.96264 Tf 12.7195 0 Td (\()Tj /R75 9.96264 Tf 3.83545 0 Td (L)Tj /R78 6.97385 Tf 6.84521 -1.43994 Td (m)Tj /R72 9.96264 Tf 7.67993 1.43994 Td (U)Tj /R22 9.96264 Tf 7.91406 0 Td (\))Tj /R78 6.97385 Tf 3.84595 4.80005 Td (j)Tj (i)' /R22 9.96264 Tf 6.95996 2.76001 Td (:=)Tj 13.1902 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (5\()Tj /R72 9.96264 Tf 8.8667 0 Td (U)Tj /R78 6.97385 Tf 7.95264 4.80005 Td (j)Tj -1.08008 -7.56006 Td (i)Tj /R22 9.96264 Tf 7.43994 2.76001 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (U)Tj /R78 6.97385 Tf 7.92944 4.80005 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (2)Tj /R78 6.97385 Tf -10.9104 -7.56006 Td (i)Tj /R22 9.96264 Tf 15.48 2.76001 Td (\))Tj /R72 9.96264 Tf 3.83545 0 Td (;)Tj /R22 9.96264 Tf -290.515 -17.52 Td (\()Tj /R75 9.96264 Tf 3.83545 0 Td (L)Tj /R78 6.97385 Tf 6.84448 -1.43994 Td ()Tj /R72 9.96264 Tf 5.28003 1.43994 Td (U)Tj /R22 9.96264 Tf 7.91406 0 Td (\))Tj /R78 6.97385 Tf 3.84595 4.80005 Td (j)Tj (i)' /R22 9.96264 Tf 6.95996 2.76001 Td (:=)Tj 13.3101 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (U)Tj /R78 6.97385 Tf 7.93457 4.80005 Td (j)Tj -1.08008 -7.56006 Td (i)Tj /R22 9.96264 Tf 7.43994 2.76001 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (U)Tj /R78 6.97385 Tf 7.92944 4.80005 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (2)Tj /R78 6.97385 Tf -10.9104 -7.56006 Td (i)Tj /R22 9.96264 Tf 15.48 2.76001 Td (\))Tj /R81 9.96264 Tf 3.84009 8.15991 Td ( )Tj /R22 9.96264 Tf 4.56006 -8.15991 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (U)Tj /R78 6.97385 Tf 7.92456 4.80005 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R78 6.97385 Tf -10.9104 -7.56006 Td (i)Tj /R94 6.97385 Tf 2.75464 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R22 9.96264 Tf 6.49072 2.76001 Td (\))Tj /R69 6.97385 Tf 3.84009 4.19995 Td (2)Tj /R22 9.96264 Tf 6.71997 -4.19995 Td (+)Tj 9.95068 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (U)Tj /R78 6.97385 Tf 7.93384 4.80005 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R78 6.97385 Tf -10.9104 -7.56006 Td (i)Tj /R69 6.97385 Tf 2.75464 0 Td (+1)Tj /R22 9.96264 Tf 12.7253 2.76001 Td (\))Tj /R69 6.97385 Tf 3.84009 4.19995 Td (2)Tj /R81 9.96264 Tf 4.56006 3.95996 Td ()Tj /R72 9.96264 Tf 4.56006 -8.15991 Td (=)Tj /R22 9.96264 Tf 5.03101 0 Td (4)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf 12.5994 0 Td ()Tj /R78 6.97385 Tf 7.21851 -1.43994 Td (i)Tj /R22 9.96264 Tf 6.12012 1.43994 Td (:=)Tj /R72 9.96264 Tf 13.1902 0 Td (')Tj /R22 9.96264 Tf 6.47559 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (ih)Tj /R22 9.96264 Tf 9.23535 0 Td (\))Tj /R72 9.96264 Tf 3.83545 0 Td (:)Tj /R22 9.96264 Tf -282.212 -19.2 Td (Denote)Tj 34.1643 0 Td (b)Tj 5.2793 0 Td (y)Tj /R72 9.96264 Tf 8.51001 0 Td (@)Tj /R69 6.97385 Tf 5.32642 -1.44019 Td (1)Tj /R22 9.96264 Tf 4.43994 1.44019 Td (,)Tj /R72 9.96264 Tf 6.11938 0 Td (@)Tj /R69 6.97385 Tf 5.28076 -1.44019 Td (2)Tj /R22 9.96264 Tf 4.43994 1.44019 Td (,)Tj /R72 9.96264 Tf 6.11938 0 Td (@)Tj /R78 6.97385 Tf 5.28052 -1.44019 Td (t)Tj /R22 9.96264 Tf 6.71997 1.44019 Td (dierence)Tj 44.605 0 Td (quotien)Tj 32.1284 0 Td (ts)Tj 11.0308 0 Td (along)Tj 26.4922 0 Td (lines)Tj /R72 9.96264 Tf 22.667 0 Td (x)Tj /R75 9.96264 Tf 7.91846 0 Td ( )Tj /R72 9.96264 Tf 9.83057 0 Td (t)Tj /R22 9.96264 Tf 6.3562 0 Td (=)Tj 10.5505 0 Td (0,)Tj /R72 9.96264 Tf 11.0308 0 Td (x)Tj /R22 9.96264 Tf 7.79858 0 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (t)Tj /R22 9.96264 Tf 6.3562 0 Td (=)Tj 10.5505 0 Td (0)Tj -320.826 -11.8801 Td (and)Tj /R72 9.96264 Tf 19.3096 0 Td (t)Tj /R22 9.96264 Tf 3.59644 0 Td (,)Tj 6.11938 0 Td (resp)Tj 18.1028 0 Td (ectiv)Tj 20.4922 0 Td (ely:)Tj -37.6204 -23.3999 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (@)Tj /R69 6.97385 Tf 5.28442 -1.43994 Td (1)Tj /R72 9.96264 Tf 4.43994 1.43994 Td (U)Tj /R22 9.96264 Tf 7.91406 0 Td (\))Tj /R78 6.97385 Tf 3.84595 4.80005 Td (j)Tj (i)' /R22 9.96264 Tf 6.95996 2.76001 Td (:=)Tj 21.6001 6.83984 Td (1)Tj ET Q 1 i 204 567 19.0798 0.47998 re f q 1 0 0 1 0 0 cm BT /R75 9.96264 Tf 203.52 565.28 Td (p)Tj ET Q 212 565 5.03979 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 211.799 557 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (h)Tj /R81 9.96264 Tf 8.53027 16.0798 Td ( )Tj /R72 9.96264 Tf 4.56006 -8.15991 Td (U)Tj /R78 6.97385 Tf 7.91992 4.80005 Td (j)Tj -1.08008 -7.56006 Td (i)Tj /R75 9.96264 Tf 7.56006 2.76001 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (U)Tj /R78 6.97385 Tf 7.92944 4.80005 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R78 6.97385 Tf -10.9104 -7.56006 Td (i)Tj /R94 6.97385 Tf 2.75464 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R81 9.96264 Tf 6.37085 10.9199 Td ()Tj /R72 9.96264 Tf 4.55981 -8.15991 Td (;)Tj /R22 9.96264 Tf 14.3994 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (@)Tj /R69 6.97385 Tf 5.28516 -1.43994 Td (2)Tj /R72 9.96264 Tf 4.56006 1.43994 Td (U)Tj /R22 9.96264 Tf 7.91406 0 Td (\))Tj /R78 6.97385 Tf 3.84595 4.80005 Td (j)Tj 7.56006 TL (i)' /R22 9.96264 Tf 6.95996 2.76001 Td (:=)Tj 21.48 6.83984 Td (1)Tj ET Q 342 567 19.0798 0.47998 re f q 1 0 0 1 0 0 cm BT /R75 9.96264 Tf 342.36 565.28 Td (p)Tj ET Q 351 565 5.03979 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 350.639 557 Td (2)Tj /R72 9.96264 Tf 4.91113 0 Td (h)Tj /R81 9.96264 Tf 8.65015 16.0798 Td ( )Tj /R72 9.96264 Tf 4.55981 -8.15991 Td (U)Tj /R78 6.97385 Tf 7.92017 4.80005 Td (j)Tj -1.08008 -7.56006 Td (i)Tj /R75 9.96264 Tf 7.43994 2.76001 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (U)Tj /R78 6.97385 Tf 7.92944 4.80005 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R78 6.97385 Tf -10.9104 -7.56006 Td (i)Tj /R69 6.97385 Tf 2.75464 0 Td (+1)Tj /R81 9.96264 Tf 12.7253 10.9199 Td ()Tj /R72 9.96264 Tf 4.56006 -8.15991 Td (;)Tj /R22 9.96264 Tf -189.12 -26.4001 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (@)Tj /R78 6.97385 Tf 5.28467 -1.43994 Td (t)Tj /R72 9.96264 Tf 3.47998 1.43994 Td (U)Tj /R22 9.96264 Tf 7.91406 0 Td (\))Tj /R78 6.97385 Tf 3.84595 4.80005 Td (j)Tj 7.56006 TL (i)' /R22 9.96264 Tf 6.95996 2.76001 Td (:=)Tj 17.4001 6.84009 Td (1)Tj ET Q 277 541 10.7998 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 276.6 531.68 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (h)Tj /R81 9.96264 Tf 8.52905 15 Td ( )Tj /R72 9.96264 Tf 4.56006 -8.16016 Td (U)Tj /R78 6.97385 Tf 7.91992 4.80005 Td (j)Tj -1.08008 -7.56006 Td (i)Tj /R75 9.96264 Tf 7.43994 2.76001 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (U)Tj /R78 6.97385 Tf 7.92944 4.80005 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (2)Tj /R78 6.97385 Tf -10.9104 -7.56006 Td (i)Tj /R81 9.96264 Tf 15.48 10.9202 Td ()Tj /R72 9.96264 Tf 4.56006 -8.16016 Td (:)Tj /R22 9.96264 Tf -219.12 -21.8398 Td (Let)Tj /R75 9.96264 Tf 63.72 -26.52 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (U)Tj /R75 9.96264 Tf 7.91406 0 Td (j)Tj /R69 6.97385 Tf 2.76636 4.19995 Td (2)Tj /R78 6.97385 Tf 7.19995 TL (W)' /R87 4.98132 Tf 8.52002 2.3999 Td (1)Tj -1.08008 -4.55981 Td (2)Tj /R69 6.97385 Tf 5.04004 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R87 4.98132 Tf 4.20288 -1.08008 Td (2)Tj /R84 4.98132 Tf 3.35718 0 Td (k)Tj /R69 6.97385 Tf 4.32275 1.08008 Td (\))Tj /R22 9.96264 Tf 6.47998 3 Td (:=)Tj /R72 9.96264 Tf 13.1902 0 Td (h)Tj /R78 6.97385 Tf 12.8499 12.48 Td (k)Tj /R81 9.96264 Tf -4.91992 -3 Td (X)Tj /R78 6.97385 Tf -0.47998 -21.1201 Td ()Tj /R69 6.97385 Tf 5.15356 0 Td (=1)Tj /R22 9.96264 Tf 10.0864 11.6401 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (@)Tj /R69 6.97385 Tf 5.28442 -1.43994 Td (1)Tj /R72 9.96264 Tf 4.56006 1.43994 Td (U)Tj /R69 6.97385 Tf 7.91992 4.19995 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td (k)Tj /R69 6.97385 Tf -5.03394 -6.6001 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td ()Tj /R22 9.96264 Tf 6.00586 2.40015 Td (\))Tj /R69 6.97385 Tf 3.83984 4.19995 Td (2)Tj /R22 9.96264 Tf 6.6001 -4.19995 Td (+)Tj /R72 9.96264 Tf 10.0706 0 Td (h)Tj /R78 6.97385 Tf 7.68945 12.48 Td (k)Tj /R94 6.97385 Tf 4.31812 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R81 9.96264 Tf -10.4329 -3 Td (X)Tj /R78 6.97385 Tf -0.359863 -21.1201 Td ()Tj /R69 6.97385 Tf 5.15356 0 Td (=0)Tj /R22 9.96264 Tf 9.96631 11.6401 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (@)Tj /R69 6.97385 Tf 5.28467 -1.43994 Td (2)Tj /R72 9.96264 Tf 4.56006 1.43994 Td (U)Tj /R69 6.97385 Tf 7.91992 4.19995 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td (k)Tj /R69 6.97385 Tf -5.03418 -6.6001 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td ()Tj /R22 9.96264 Tf 6.00586 2.40015 Td (\))Tj /R69 6.97385 Tf 3.84009 4.19995 Td (2)Tj /R72 9.96264 Tf 4.43994 -4.19995 Td (;)Tj /R75 9.96264 Tf -227.04 -34.9199 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (U)Tj /R75 9.96264 Tf 7.91406 0 Td (j)Tj /R69 6.97385 Tf 2.7666 4.19995 Td (2)Tj /R78 6.97385 Tf (W)' /R87 4.98132 Tf 8.52002 2.3999 Td (1)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 5.04004 2.16016 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R87 4.98132 Tf 4.20288 -1.08008 Td (2)Tj /R84 4.98132 Tf 3.35718 0 Td (k)Tj /R98 4.98132 Tf 3.83594 0 Td ( )Tj /R87 4.98132 Tf 5.39966 0 Td (1)Tj /R69 6.97385 Tf 3.96704 1.08008 Td (\))Tj /R22 9.96264 Tf 6.36011 3 Td (:=)Tj /R72 9.96264 Tf 13.1902 0 Td (h)Tj /R78 6.97385 Tf 12.8499 12.48 Td (k)Tj /R81 9.96264 Tf -4.92017 -3 Td (X)Tj /R78 6.97385 Tf -0.47998 -21 Td ()Tj /R69 6.97385 Tf 5.15356 0 Td (=1)Tj /R22 9.96264 Tf 10.0864 11.52 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (@)Tj /R69 6.97385 Tf 5.28467 -1.44019 Td (1)Tj /R72 9.96264 Tf 4.56006 1.44019 Td (U)Tj /R69 6.97385 Tf 7.91992 4.31982 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td (k)Tj /R94 6.97385 Tf 4.31812 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj -15.5869 -6.95996 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td ()Tj /R94 6.97385 Tf 5.15356 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R22 9.96264 Tf 4.81787 2.64014 Td (\))Tj /R69 6.97385 Tf 3.83984 4.19995 Td (2)Tj /R22 9.96264 Tf 6.71997 -4.19995 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (h)Tj /R78 6.97385 Tf 7.68945 12.48 Td (k)Tj /R94 6.97385 Tf 4.31812 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R81 9.96264 Tf -10.4329 -3 Td (X)Tj /R78 6.97385 Tf -0.359863 -21 Td ()Tj /R69 6.97385 Tf 5.15356 0 Td (=1)Tj /R22 9.96264 Tf 9.96631 11.52 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (@)Tj /R69 6.97385 Tf 5.28467 -1.44019 Td (2)Tj /R72 9.96264 Tf 4.56006 1.44019 Td (U)Tj /R69 6.97385 Tf 7.91992 4.31982 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td (k)Tj /R94 6.97385 Tf 4.31812 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj -15.5869 -6.95996 Td (2)Tj /R78 6.97385 Tf 3.9541 0 Td ()Tj /R94 6.97385 Tf 5.15356 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R22 9.96264 Tf 4.81787 2.64014 Td (\))Tj /R69 6.97385 Tf 3.83984 4.19995 Td (2)Tj /R72 9.96264 Tf 4.43994 -4.19995 Td (;)Tj 9.95947 0 Td (k)Tj /R75 9.96264 Tf 8.27051 0 Td ()Tj /R22 9.96264 Tf 10.5505 0 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf -208.052 -27 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (U;)Tj 11.2739 0 Td (V)Tj /R22 9.96264 Tf 7.91821 0 Td (\))Tj /R78 6.97385 Tf 3.85254 -1.44019 Td (Q)Tj /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R22 9.96264 Tf 7.19995 2.40015 Td (:=)Tj /R72 9.96264 Tf 13.3101 0 Td (h)Tj /R69 6.97385 Tf 5.77002 4.07983 Td (2)Tj /R81 9.96264 Tf 14.6399 5.40015 Td (X)Tj /R69 6.97385 Tf -8.52002 -21.8401 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (x;t)Tj /R69 6.97385 Tf 9.95166 0 Td (\))Tj /R94 6.97385 Tf 3.11719 0 Td (2)Tj /R78 6.97385 Tf 5.39771 0 Td (Q)Tj /R84 4.98132 Tf 6.25635 -0.959961 Td (s)Tj /R72 9.96264 Tf 5.3999 13.3201 Td (U)Tj /R22 9.96264 Tf 7.91406 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (x;)Tj 10.0784 0 Td (t)Tj /R22 9.96264 Tf 3.59644 0 Td (\))Tj /R72 9.96264 Tf 3.83545 0 Td (V)Tj /R22 9.96264 Tf 8.03809 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (x;)Tj 10.0784 0 Td (t)Tj /R22 9.96264 Tf 3.59644 0 Td (\))Tj /R72 9.96264 Tf 3.83545 0 Td (;)Tj /R75 9.96264 Tf -169.404 -27.7202 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (U)Tj /R75 9.96264 Tf 7.91406 0 Td (k)Tj /R69 6.97385 Tf 5.05493 4.08008 Td (2)Tj /R78 6.97385 Tf 6.59985 TL (Q)' /R84 4.98132 Tf 6.23999 -0.960205 Td (s)Tj /R22 9.96264 Tf 7.08008 3.47998 Td (:=)Tj 13.1902 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (U;)Tj 11.2739 0 Td (U)Tj /R22 9.96264 Tf 7.91406 0 Td (\))Tj /R78 6.97385 Tf 3.86646 -1.43994 Td (Q)Tj /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R72 9.96264 Tf 4.32007 2.3999 Td (;)Tj /R75 9.96264 Tf 12.8394 0 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (U)Tj /R75 9.96264 Tf 7.91406 0 Td (k)Tj /R78 6.97385 Tf 5.05542 -1.7998 Td (C)Tj /R69 6.97385 Tf 6.2334 0 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (Q)Tj /R69 6.97385 Tf 6.23462 0 Td (\))Tj /R22 9.96264 Tf 6.13477 1.7998 Td (:=)Tj 13.3101 0 Td (max)Tj /R78 6.97385 Tf 6.13013 -6.47998 Td (Q)Tj /R75 9.96264 Tf 14.0398 6.47998 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (U)Tj /R75 9.96264 Tf 7.91406 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (:)Tj /R22 9.96264 Tf -240.353 -24.48 Td (Let)Tj /R72 9.96264 Tf 17.7454 0 Td (Z)Tj /R22 9.96264 Tf 10.3142 0 Td (:=)Tj /R72 9.96264 Tf 13.3101 0 Td (u)Tj /R75 9.96264 Tf 7.7981 0 Td ( )Tj /R72 9.96264 Tf 9.83057 0 Td (U)Tj /R22 9.96264 Tf 7.91406 0 Td (,)Tj 6 0 Td (where)Tj /R72 9.96264 Tf 28.6541 0 Td (u)Tj /R22 9.96264 Tf 8.99829 0 Td (is)Tj 9.95459 0 Td (the)Tj 17.1479 0 Td (exact)Tj 26.1235 0 Td (solution)Tj 37.6509 0 Td (of)Tj 11.2698 0 Td (the)Tj 17.0281 0 Td (problem)Tj 38.7368 0 Td (\(2.1\),)Tj 24.8125 0 Td (\(2.2\))Tj -305.168 -11.8799 Td (and)Tj /R72 9.96264 Tf 20.2695 0 Td (U)Tj /R22 9.96264 Tf 12.2341 0 Td (is)Tj 10.9146 0 Td (the)Tj 18.1079 0 Td (solution)Tj 38.6108 0 Td (of)Tj 12.3496 0 Td (the)Tj 18.1079 0 Td (nite)Tj 26.387 0 Td (dierence)Tj 45.5649 0 Td (sc)Tj 8.14844 0 Td (heme)Tj 26.8647 0 Td (\(2.3\),)Tj 24.9326 0 Td (\(2.4\).)Tj 30.5725 0 Td (F)Tj 5.63574 0 Td (or)Tj 13.186 0 Td (the)Tj -311.886 -12 Td (discretization)Tj 61.3813 0 Td (error)Tj /R72 9.96264 Tf 24.4497 0 Td (Z)Tj /R22 9.96264 Tf 10.7942 0 Td (w)Tj 6.95288 0 Td (e)Tj 7.67334 0 Td (obtain)Tj 31.0559 0 Td (the)Tj 17.1479 0 Td (follo)Tj 18.3403 0 Td (wing)Tj 23.6228 0 Td (problem)Tj /R75 9.96264 Tf -123.779 -19.2 Td (L)Tj /R69 6.97385 Tf 6.84009 -1.44019 Td (0)Tj /R72 9.96264 Tf 4.55981 1.44019 Td (Z)Tj /R22 9.96264 Tf 9.71411 0 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (m)Tj /R69 6.97385 Tf 8.77539 4.07983 Td (2)Tj /R75 9.96264 Tf 4.43994 -4.07983 Td (L)Tj /R78 6.97385 Tf 6.84009 -1.44019 Td (m)Tj /R72 9.96264 Tf 7.55981 1.44019 Td (Z)Tj /R22 9.96264 Tf 10.3142 0 Td (=)Tj /R72 9.96264 Tf 10.5505 0 Td ()Tj /R22 9.96264 Tf 5.7583 0 Td (\()Tj /R75 9.96264 Tf 3.83545 0 Td (L)Tj /R78 6.97385 Tf 6.86157 -1.44019 Td ()Tj /R72 9.96264 Tf 5.28003 1.44019 Td (U)Tj /R75 9.96264 Tf 10.0742 0 Td ( )Tj 9.95068 0 Td (L)Tj /R78 6.97385 Tf 6.85498 -1.44019 Td ()Tj /R72 9.96264 Tf 5.28003 1.44019 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj 6.11523 0 Td (+)Tj /R75 9.96264 Tf 9.95068 0 Td (L)Tj /R72 9.96264 Tf 6.83423 0 Td (u:)Tj /R22 9.96264 Tf 65.6377 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (5\))Tj /R15 9.96264 Tf -305.122 -24.8401 Td (Theorem)Tj 49.7517 0 Td (2.1.)Tj /R106 9.96264 Tf 25.3123 0 Td (F)Tj 5.75562 0 Td (or)Tj 13.6653 0 Td (the)Tj 17.5012 0 Td (err)Tj 12.4614 0 Td (or)Tj 13.7852 0 Td (of)Tj 12.5896 0 Td (the)Tj 17.5012 0 Td (solution)Tj 38.4822 0 Td (of)Tj 12.7097 0 Td (the)Tj 17.3813 0 Td (dier)Tj 22.4141 0 Td (enc)Tj 14.2646 0 Td (e)Tj 9.11255 0 Td (scheme)Tj /R22 9.96264 Tf -294.568 -11.8799 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (3\))Tj /R106 9.96264 Tf 8.8667 0 Td (,)Tj /R22 9.96264 Tf 4.67847 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (4\))Tj /R106 9.96264 Tf 12.3467 0 Td (the)Tj 16.5413 0 Td (fol)Tj 11.0203 0 Td (lowing)Tj 31.1672 0 Td (estimate)Tj /R81 9.96264 Tf -0.113037 -10.8 Td ()Tj 5.88013 TL ()' /R72 9.96264 Tf 3.35986 -2.52002 Td (U)Tj /R75 9.96264 Tf 10.0742 0 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (u)Tj /R81 9.96264 Tf 5.77515 8.40015 Td ()Tj ()' /R78 6.97385 Tf 3.23999 -6.47998 Td (W)Tj /R87 4.98132 Tf 8.52002 2.40015 Td (1)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 5.04004 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R84 4.98132 Tf 4.20288 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.83984 0.959961 Td (\))Tj /R75 9.96264 Tf 6.36011 3.95996 Td ()Tj /R72 9.96264 Tf 10.5505 0 Td (c)Tj /R75 9.96264 Tf 4.31372 0 Td (kL)Tj /R72 9.96264 Tf 11.8655 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R78 6.97385 Tf 5.07202 -1.43994 Td (Q)Tj /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R22 9.96264 Tf 91.4399 2.3999 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (6\))Tj /R106 9.96264 Tf -317.026 -21.3599 Td (is)Tj 10.6731 0 Td (valid,)Tj 26.9629 0 Td (wher)Tj 19.8936 0 Td (e)Tj 8.15259 0 Td (the)Tj 16.5413 0 Td (c)Tj 4.07275 0 Td (onstant)Tj /R72 9.96264 Tf 35.6094 0 Td (c)Tj 7.07349 0 Td (>)Tj /R22 9.96264 Tf 10.5505 0 Td (0)Tj /R106 9.96264 Tf 8.51099 0 Td (do)Tj 9.58228 0 Td (es)Tj 12.2273 0 Td (not)Tj 17.6272 0 Td (dep)Tj 14.135 0 Td (end)Tj 18.8228 0 Td (on)Tj /R72 9.96264 Tf 14.2698 0 Td (h)Tj /R106 9.96264 Tf 5.7583 0 Td (.)Tj /R15 9.96264 Tf -228.583 -17.52 Td (Theorem)Tj 49.6316 0 Td (2.2.)Tj /R106 9.96264 Tf 25.0723 0 Td (The)Tj 21.0974 0 Td (solution)Tj 38.4822 0 Td (of)Tj 12.5896 0 Td (the)Tj 17.3813 0 Td (dier)Tj 22.4141 0 Td (enc)Tj 14.2646 0 Td (e)Tj 8.99268 0 Td (scheme)Tj /R22 9.96264 Tf 35.4836 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (3\))Tj /R106 9.96264 Tf 8.8667 0 Td (,)Tj /R22 9.96264 Tf 4.67847 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (4\))Tj /R106 9.96264 Tf 13.1865 0 Td (c)Tj 4.07275 0 Td (on-)Tj -311.346 -12 Td (ver)Tj 12.8201 0 Td (ges)Tj 16.4204 0 Td (to)Tj 11.7483 0 Td (the)Tj 16.1814 0 Td (solution)Tj 37.4021 0 Td (of)Tj 11.3896 0 Td (the)Tj 16.3013 0 Td (pr)Tj 8.74536 0 Td (oblem)Tj /R22 9.96264 Tf 28.1667 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (1\))Tj /R106 9.96264 Tf 8.8667 0 Td (,)Tj /R22 9.96264 Tf 4.79834 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (2\))Tj /R106 9.96264 Tf 12.1067 0 Td (and)Tj 19.0608 0 Td (the)Tj 16.1814 0 Td (fol)Tj 11.0203 0 Td (lowing)Tj 30.9272 0 Td (estimates)Tj /R75 9.96264 Tf -274.109 -19.3201 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (U)Tj /R75 9.96264 Tf 10.0742 0 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R78 6.97385 Tf 2.77734 -2.15991 Td (W)Tj /R87 4.98132 Tf 8.52002 2.3999 Td (1)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 5.04004 2.16016 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R84 4.98132 Tf 4.20288 -0.959961 Td (n)Tj /R69 6.97385 Tf 4.80005 0.959961 Td (\))Tj /R75 9.96264 Tf 6.35986 2.15991 Td ()Tj /R72 9.96264 Tf 10.5505 0 Td (ch)Tj /R69 6.97385 Tf 10.0896 4.08008 Td (2)Tj /R75 9.96264 Tf 4.43994 -4.08008 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R78 6.97385 Tf 5.05078 -2.15991 Td (W)Tj /R87 4.98132 Tf 8.52002 2.3999 Td (2)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 4.80005 2.16016 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (Q)Tj /R84 4.98132 Tf 6.24268 -0.959961 Td (T)Tj /R69 6.97385 Tf 5.52002 0.959961 Td (\))Tj /R72 9.96264 Tf 3.71997 2.15991 Td (;)Tj /R75 9.96264 Tf 14.5193 0 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (U)Tj /R75 9.96264 Tf 10.0742 0 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R78 6.97385 Tf 5.06665 -1.80005 Td (C)Tj /R69 6.97385 Tf 6.2334 0 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (Q)Tj /R84 4.98132 Tf 6.24927 -0.959961 Td (n)Tj /R69 6.97385 Tf 4.80005 0.959961 Td (\))Tj /R75 9.96264 Tf 6.36011 1.80005 Td ()Tj /R72 9.96264 Tf 10.4307 0 Td (ch)Tj /R69 6.97385 Tf 10.0894 4.08008 Td (2)Tj /R75 9.96264 Tf 4.55981 -4.08008 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R78 6.97385 Tf 5.05078 -2.15991 Td (W)Tj /R87 4.98132 Tf 8.52002 2.3999 Td (2)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 4.80005 2.16016 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (Q)Tj /R84 4.98132 Tf 6.24292 -0.959961 Td (T)Tj /R69 6.97385 Tf 5.52002 0.959961 Td (\))Tj /R22 9.96264 Tf 14.8799 2.15991 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (7\))Tj /R106 9.96264 Tf -317.026 -19.4399 Td (ar)Tj 8.74536 0 Td (e)Tj 8.15259 0 Td (valid,)Tj 26.9629 0 Td (wher)Tj 19.8936 0 Td (e)Tj 8.15259 0 Td (the)Tj 16.5413 0 Td (c)Tj 4.07275 0 Td (onstant)Tj /R72 9.96264 Tf 35.6094 0 Td (c)Tj 7.07349 0 Td (>)Tj /R22 9.96264 Tf 10.5505 0 Td (0)Tj /R106 9.96264 Tf 8.51099 0 Td (do)Tj 9.58228 0 Td (es)Tj 12.2273 0 Td (not)Tj 17.6272 0 Td (dep)Tj 14.135 0 Td (end)Tj 18.8228 0 Td (on)Tj /R72 9.96264 Tf 14.2698 0 Td (h)Tj /R106 9.96264 Tf 5.7583 0 Td (.)Tj ET Q Q Q endstream endobj 103 0 obj 24244 endobj 109 0 obj <> stream q 1 0 0 1 0 0 cm q q 1 0 0 1 0 0 cm BT /R69 6.97385 Tf 126.72 739.88 Td (128)Tj /R63 6.97385 Tf 68.1421 0 Td (G.)Tj 11.7505 0 Td (Berikelashvili,)Tj 53.8267 0 Td (O.)Tj 11.7517 0 Td (Jokhadze,)Tj 37.6526 0 Td (S.)Tj 10.071 0 Td (Kharib)Tj 24.1042 0 Td (e)Tj 3.47559 0 Td (gashvili,)Tj 32.1294 0 Td (and)Tj 16.0701 0 Td (B.)Tj 11.2705 0 Td (Mido)Tj 17.8696 0 Td (dashvili)Tj /R22 9.96264 Tf -187.354 -23.8799 Td (3.)Tj /R12 9.96264 Tf 12.7107 0 Td (A)Tj 7.91919 0 Td (uxiliar)Tj 34.7769 0 Td (y)Tj 9.83691 0 Td (Resul)Tj 28.5303 0 Td (ts)Tj /R15 9.96264 Tf -192.654 -18 Td (Lemma)Tj 41.8516 0 Td (3.1.)Tj /R106 9.96264 Tf 25.5522 0 Td (F)Tj 5.75562 0 Td (or)Tj 13.7852 0 Td (any)Tj 20.1418 0 Td (mesh)Tj 26.3779 0 Td (function)Tj /R72 9.96264 Tf 40.176 0 Td (V)Tj /R106 9.96264 Tf 12.5981 0 Td (dene)Tj 24.9346 0 Td (d)Tj 9.71094 0 Td (on)Tj ET Q 1 i 375 706 7.91992 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 374.714 698 Td (Q)Tj /R78 6.97385 Tf 8.08618 -2.40015 Td (s)Tj /R106 9.96264 Tf 8.76001 2.40015 Td (and)Tj 20.3809 0 Td (satisfying)Tj /R72 9.96264 Tf -285.221 -11.8801 Td (V)Tj /R75 9.96264 Tf 7.91821 0 Td (j)Tj /R78 6.97385 Tf 2.76172 -1.91992 Td (\r)Tj /R98 4.98132 Tf 4.67993 2.04004 Td ( )Tj /R22 9.96264 Tf 9.12012 -0.120117 Td (=)Tj 10.5505 0 Td (0)Tj /R106 9.96264 Tf 5.03101 0 Td (,)Tj 6.59839 0 Td (the)Tj 16.5413 0 Td (fol)Tj 11.0203 0 Td (lowing)Tj 31.1672 0 Td (identity)Tj /R22 9.96264 Tf -44.5488 -26.3999 Td (\()Tj /R75 9.96264 Tf 3.83545 0 Td (L)Tj /R69 6.97385 Tf 6.84473 -1.44019 Td (0)Tj /R72 9.96264 Tf 4.55981 1.44019 Td (V)Tj 6.35815 0 Td (;)Tj 4.43945 0 Td (@)Tj /R78 6.97385 Tf 5.28247 -1.44019 Td (t)Tj /R72 9.96264 Tf 3.47998 1.44019 Td (V)Tj /R22 9.96264 Tf 8.03809 0 Td (\))Tj /R78 6.97385 Tf 3.84204 -1.44019 Td (Q)Tj /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R22 9.96264 Tf 7.19995 2.40015 Td (=)Tj 10.5505 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (5)Tj /R75 9.96264 Tf 5.03101 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (V)Tj /R75 9.96264 Tf 7.91821 0 Td (j)Tj /R69 6.97385 Tf 2.79004 4.07983 Td (2)Tj /R78 6.97385 Tf 7.19995 TL (W)' /R87 4.98132 Tf 8.52002 2.40015 Td (1)Tj -1.07983 -4.56006 Td (2)Tj /R69 6.97385 Tf 5.03979 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R84 4.98132 Tf 4.20288 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.71997 0.959961 Td (\))Tj /R75 9.96264 Tf 5.88013 3.12012 Td ( )Tj /R22 9.96264 Tf 9.95068 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (5)Tj /R72 9.96264 Tf 5.03101 0 Td (h)Tj /R78 6.97385 Tf 12.6277 12.3599 Td (s)Tj /R81 9.96264 Tf -5.28003 -2.87988 Td (X)Tj /R78 6.97385 Tf 0.719971 -21.24 Td (i)Tj /R69 6.97385 Tf 2.75464 0 Td (=1)Tj /R22 9.96264 Tf 10.9255 11.76 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (@)Tj /R69 6.97385 Tf 5.28442 -1.44019 Td (1)Tj /R72 9.96264 Tf 4.43994 1.44019 Td (V)Tj /R78 6.97385 Tf 8.04004 4.07983 Td (i)Tj -2.28003 -6.59985 Td (i)Tj /R22 9.96264 Tf 5.64014 2.52002 Td (\))Tj /R69 6.97385 Tf 3.84009 4.07983 Td (2)Tj /R106 9.96264 Tf -260.52 -30.48 Td (is)Tj 10.6731 0 Td (valid.)Tj /R15 9.96264 Tf 1.20679 -17.6399 Td (Lemma)Tj 41.8516 0 Td (3.2.)Tj /R106 9.96264 Tf 25.5522 0 Td (F)Tj 5.75562 0 Td (or)Tj 13.7852 0 Td (any)Tj 20.1418 0 Td (mesh)Tj 26.3779 0 Td (function)Tj /R72 9.96264 Tf 40.176 0 Td (V)Tj /R106 9.96264 Tf 12.5981 0 Td (dene)Tj 24.9346 0 Td (d)Tj 9.71094 0 Td (on)Tj ET Q 375 624 7.91992 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 374.714 615.68 Td (Q)Tj /R78 6.97385 Tf 8.08618 -2.40015 Td (s)Tj /R106 9.96264 Tf 8.76001 2.40015 Td (and)Tj 20.3809 0 Td (satisfying)Tj /R72 9.96264 Tf -285.221 -12 Td (V)Tj /R75 9.96264 Tf 7.91821 0 Td (j)Tj /R78 6.97385 Tf 2.76172 -1.92017 Td (\r)Tj /R98 4.98132 Tf 4.67993 2.04004 Td ( )Tj /R22 9.96264 Tf 9.12012 -0.119873 Td (=)Tj 10.5505 0 Td (0)Tj /R106 9.96264 Tf 5.03101 0 Td (,)Tj 6.59839 0 Td (the)Tj 16.5413 0 Td (fol)Tj 11.0203 0 Td (lowing)Tj 31.1672 0 Td (ine)Tj 12.7104 0 Td (quality)Tj /R22 9.96264 Tf -36.1392 -27.8401 Td (\()Tj /R75 9.96264 Tf 3.83545 0 Td (L)Tj /R78 6.97385 Tf 6.84448 -1.43994 Td (m)Tj /R72 9.96264 Tf 7.56006 1.43994 Td (V)Tj 6.35815 0 Td (;)Tj 4.43945 0 Td (@)Tj /R78 6.97385 Tf 5.28223 -1.43994 Td (t)Tj /R72 9.96264 Tf 3.48022 1.43994 Td (V)Tj /R22 9.96264 Tf 8.03809 0 Td (\))Tj /R78 6.97385 Tf 3.8418 -1.43994 Td (Q)Tj /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R75 9.96264 Tf 7.19995 2.3999 Td ()Tj 10.5505 0 Td ( )Tj /R72 9.96264 Tf 9.00952 6.71997 Td (h)Tj ET Q 291 578 5.75977 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 291.72 569 Td (4)Tj /R78 6.97385 Tf 8.3999 19.2 Td (s)Tj /R94 6.97385 Tf 3.71704 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (2)Tj /R81 9.96264 Tf -10.1917 -3 Td (X)Tj /R78 6.97385 Tf 0.719971 -21.1201 Td (i)Tj /R69 6.97385 Tf 2.75464 0 Td (=1)Tj /R22 9.96264 Tf 10.9253 11.76 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (V)Tj /R78 6.97385 Tf 8.04468 4.08008 Td (i)Tj -2.28003 -6.6001 Td (i)Tj /R22 9.96264 Tf 5.63989 2.52002 Td (\))Tj /R69 6.97385 Tf 3.84009 4.08008 Td (2)Tj /R72 9.96264 Tf 4.43994 -4.08008 Td (;)Tj 9.95947 0 Td (s)Tj /R75 9.96264 Tf 7.43213 0 Td ()Tj /R22 9.96264 Tf 10.5505 0 Td (3)Tj /R106 9.96264 Tf -239.022 -26.3999 Td (is)Tj 10.6731 0 Td (valid.)Tj /R15 9.96264 Tf 1.20679 -17.6401 Td (Lemma)Tj 40.6516 0 Td (3.3.)Tj /R106 9.96264 Tf 22.1924 0 Td (If)Tj /R72 9.96264 Tf 10.4341 0 Td (V)Tj /R75 9.96264 Tf 8.03809 0 Td (j)Tj /R78 6.97385 Tf 2.80396 -1.91992 Td (\r)Tj /R98 4.98132 Tf 4.67993 2.04004 Td ( )Tj /R22 9.96264 Tf 9.11987 -0.120117 Td (=)Tj 10.5505 0 Td (0)Tj /R106 9.96264 Tf 5.03101 0 Td (,)Tj 6.47852 0 Td (then)Tj /R22 9.96264 Tf -44.5 -27.96 Td (\()Tj /R75 9.96264 Tf 3.83545 0 Td (L)Tj /R78 6.97385 Tf 6.84448 -1.43994 Td ()Tj /R72 9.96264 Tf 5.28003 1.43994 Td (V)Tj 6.35815 0 Td (;)Tj 4.43945 0 Td (@)Tj /R78 6.97385 Tf 5.28247 -1.43994 Td (t)Tj /R72 9.96264 Tf 3.47998 1.43994 Td (V)Tj /R22 9.96264 Tf 8.03809 0 Td (\))Tj /R78 6.97385 Tf 3.84204 -1.43994 Td (Q)Tj /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R75 9.96264 Tf 7.19995 2.3999 Td ()Tj 10.5505 0 Td ( )Tj /R72 9.96264 Tf 9.00952 6.71997 Td (h)Tj ET Q 294 506 5.75977 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 294.84 497 Td (8)Tj /R78 6.97385 Tf 8.40015 19.3198 Td (s)Tj /R94 6.97385 Tf 3.71704 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R81 9.96264 Tf -10.1919 -3 Td (X)Tj /R78 6.97385 Tf 0.720215 -21.24 Td (i)Tj /R69 6.97385 Tf 2.75464 0 Td (=2)Tj /R22 9.96264 Tf 10.9253 11.76 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (V)Tj /R78 6.97385 Tf 8.04443 4.08008 Td (i)Tj -2.28003 -6.47998 Td (i)Tj /R72 9.96264 Tf 5.64014 2.3999 Td (V)Tj /R78 6.97385 Tf 7.91992 4.32007 Td (i)Tj /R94 6.97385 Tf 2.75464 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R78 6.97385 Tf -11.1492 -7.08008 Td (i)Tj /R94 6.97385 Tf 2.75464 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R22 9.96264 Tf 6.73071 2.76001 Td (\))Tj /R69 6.97385 Tf 3.84009 4.08008 Td (2)Tj /R72 9.96264 Tf 4.55981 -4.08008 Td (:)Tj /R15 9.96264 Tf -223.92 -32.6399 Td (Lemma)Tj 40.7717 0 Td (3.4.)Tj /R106 9.96264 Tf 22.5522 0 Td (F)Tj 5.75562 0 Td (or)Tj 12.9453 0 Td (the)Tj 16.6614 0 Td (solutions)Tj 41.8369 0 Td (of)Tj 11.7498 0 Td (the)Tj 16.6614 0 Td (dier)Tj 22.4141 0 Td (enc)Tj 14.2646 0 Td (e)Tj 8.39258 0 Td (scheme)Tj /R22 9.96264 Tf 34.6438 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (3\))Tj /R106 9.96264 Tf 8.8667 0 Td (,)Tj /R22 9.96264 Tf 4.67847 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (4\))Tj /R106 9.96264 Tf 12.5867 0 Td (and)Tj -309.914 -11.8801 Td (the)Tj 16.5413 0 Td (pr)Tj 8.74536 0 Td (oblem)Tj /R22 9.96264 Tf 28.4067 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (1\))Tj /R106 9.96264 Tf 8.8667 0 Td (,)Tj /R22 9.96264 Tf 4.79834 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (2\))Tj /R106 9.96264 Tf 8.8667 0 Td (,)Tj 6.47852 0 Td (the)Tj 16.5413 0 Td (fol)Tj 11.0203 0 Td (lowing)Tj 31.2874 0 Td (estimates)Tj /R75 9.96264 Tf -68.325 -17.76 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (U)Tj /R75 9.96264 Tf 7.91406 0 Td (k)Tj /R78 6.97385 Tf 5.05493 -1.80005 Td (C)Tj /R69 6.97385 Tf 6.2334 0 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (Q)Tj /R84 4.98132 Tf 6.24927 -0.959961 Td (n)Tj /R69 6.97385 Tf 4.68018 0.959961 Td (\))Tj /R75 9.96264 Tf 6.35986 1.80005 Td ()Tj /R72 9.96264 Tf 10.5505 0 Td ()Tj 4.31348 0 Td (;)Tj /R75 9.96264 Tf 14.5193 0 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R78 6.97385 Tf 5.06738 -3 Td (C)Tj /R69 6.97385 Tf 6.2334 0 Td (\()Tj ET Q 322 444 6.83984 0.359863 re f q 1 0 0 1 0 0 cm BT /R78 6.97385 Tf 322.43 438.56 Td (D)Tj /R84 4.98132 Tf 6.4895 -0.959961 Td (T)Tj /R69 6.97385 Tf 5.52002 0.959961 Td (\))Tj /R75 9.96264 Tf 6.35986 3 Td ()Tj /R72 9.96264 Tf 10.5505 0 Td ()Tj /R106 9.96264 Tf -224.63 -22.6799 Td (ar)Tj 8.74536 0 Td (e)Tj 7.55249 0 Td (valid,)Tj 26.363 0 Td (wher)Tj 19.8936 0 Td (e)Tj /R72 9.96264 Tf 7.67261 0 Td ()Tj /R22 9.96264 Tf 7.55322 0 Td (:=)Tj /R81 9.96264 Tf 13.2996 8.04004 Td ( )Tj /R22 9.96264 Tf 4.56006 -8.04004 Td (\(1)Tj 9.70654 0 Td (+)Tj /R72 9.96264 Tf 8.63062 0 Td (m)Tj /R69 6.97385 Tf 8.78296 3.6001 Td (2)Tj /R72 9.96264 Tf 4.43994 -3.6001 Td (T)Tj /R69 6.97385 Tf 7.32007 3.6001 Td (2)Tj /R22 9.96264 Tf 5.27979 -3.6001 Td (+)Tj 8.63062 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf 4.43945 0 Td (5)Tj /R72 9.96264 Tf 5.03101 0 Td (T)Tj /R69 6.97385 Tf 13.1079 3.6001 Td (3)Tj /R72 9.96264 Tf 4.2002 -3.6001 Td (')Tj /R94 6.97385 Tf 6.47998 -1.43994 Td ()Tj /R22 9.96264 Tf 4.67993 1.43994 Td (\))Tj /R72 9.96264 Tf 3.83545 0 Td (T)Tj 7.31787 0 Td (')Tj /R94 6.97385 Tf 6.48657 -1.43994 Td ()Tj /R81 9.96264 Tf 4.44019 9.47998 Td ()Tj /R69 6.97385 Tf 4.55981 -2.04004 Td (1)Tj /R78 6.97385 Tf 3.9541 0 Td (=)Tj /R69 6.97385 Tf 4.07959 0 Td (2)Tj /R106 9.96264 Tf 4.56641 -6 Td (,)Tj /R72 9.96264 Tf 6.11841 0 Td (')Tj /R94 6.97385 Tf 6.48169 -1.43994 Td ()Tj /R22 9.96264 Tf 7.31982 1.43994 Td (:=)Tj /R81 9.96264 Tf 13.3201 8.04004 Td (R)Tj /R78 6.97385 Tf 6.6001 -2.52002 Td (T)Tj /R69 6.97385 Tf -1.92017 -9.12012 Td (0)Tj /R81 9.96264 Tf 9.96021 11.6401 Td ( )Tj /R72 9.96264 Tf 4.55981 -8.04004 Td (')Tj /R94 6.97385 Tf 6.47998 3.6001 Td (0)Tj /R22 9.96264 Tf 2.76001 -3.6001 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (t)Tj /R22 9.96264 Tf 3.59644 0 Td (\))Tj /R81 9.96264 Tf 3.84814 8.04004 Td ()Tj /R69 6.97385 Tf 4.67993 -2.04004 Td (2)Tj /R72 9.96264 Tf 6.12012 -6 Td (dt:)Tj /R15 9.96264 Tf -302.52 -19.0801 Td (Lemma)Tj 40.7717 0 Td (3.5.)Tj /R106 9.96264 Tf 22.6724 0 Td (F)Tj 5.75562 0 Td (or)Tj 12.9453 0 Td (any)Tj 19.1819 0 Td (function)Tj /R72 9.96264 Tf 39.3362 0 Td (V)Tj /R106 9.96264 Tf 11.7581 0 Td (dene)Tj 24.9346 0 Td (d)Tj 8.75098 0 Td (on)Tj ET Q 339 408 7.91992 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 339.096 399.8 Td (Q)Tj /R78 6.97385 Tf 7.94336 -2.3999 Td (n)Tj /R106 9.96264 Tf 9.12012 2.3999 Td (and)Tj 19.5408 0 Td (satisfying)Tj /R72 9.96264 Tf 44.3577 0 Td (V)Tj /R75 9.96264 Tf 8.03809 0 Td (j)Tj /R78 6.97385 Tf 2.82349 -1.7998 Td (\r)Tj /R98 4.98132 Tf 4.67993 1.91992 Td ( )Tj /R22 9.96264 Tf 9.36011 -0.120117 Td (=)Tj /R72 9.96264 Tf -318.24 -11.8799 Td (V)Tj /R75 9.96264 Tf 7.91821 0 Td (j)Tj /R78 6.97385 Tf 2.76172 -1.91992 Td (\r)Tj /R87 4.98132 Tf 4.67993 2.03979 Td (+)Tj /R22 9.96264 Tf 8.88013 -0.119873 Td (=)Tj 10.5505 0 Td (0)Tj /R106 9.96264 Tf 5.03101 0 Td (,)Tj 6.47852 0 Td (the)Tj 16.5413 0 Td (fol)Tj 11.0203 0 Td (lowing)Tj 31.1672 0 Td (ine)Tj 12.7104 0 Td (quality)Tj /R75 9.96264 Tf -47.4194 -26.4001 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (@)Tj /R78 6.97385 Tf 5.28906 -1.43994 Td (t)Tj /R72 9.96264 Tf 3.36011 1.43994 Td (V)Tj /R75 9.96264 Tf 8.03809 0 Td (k)Tj /R69 6.97385 Tf 5.04175 4.08008 Td (2)Tj /R78 6.97385 Tf 6.59985 TL (Q)' /R84 4.98132 Tf 6.23999 -0.960205 Td (s)Tj /R75 9.96264 Tf 7.08008 3.47998 Td ()Tj /R72 9.96264 Tf 10.5505 0 Td (h)Tj /R78 6.97385 Tf 12.7295 12.3601 Td (s)Tj /R81 9.96264 Tf -5.28003 -3 Td (X)Tj /R78 6.97385 Tf 0.840088 -21.3601 Td (l)Tj /R69 6.97385 Tf 2.51733 0 Td (=3)Tj /R75 9.96264 Tf 12.6025 12 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (V)Tj /R75 9.96264 Tf 8.03809 0 Td (j)Tj /R69 6.97385 Tf 2.76245 4.08008 Td (2)Tj /R78 6.97385 Tf 7.19995 TL (W)' /R87 4.98132 Tf 8.52002 2.3999 Td (1)Tj -1.08008 -4.55981 Td (2)Tj /R69 6.97385 Tf 5.04004 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R84 4.98132 Tf 4.20288 -1.08008 Td (l)Tj /R69 6.97385 Tf 2.87988 1.08008 Td (\))Tj /R75 9.96264 Tf 5.88013 3.11987 Td ( )Tj /R22 9.96264 Tf 9.95068 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (5)Tj /R72 9.96264 Tf 5.03101 0 Td (h)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (V)Tj /R75 9.96264 Tf 7.7981 0 Td (j)Tj /R69 6.97385 Tf 2.79175 4.08008 Td (2)Tj /R78 6.97385 Tf (W)' /R87 4.98132 Tf 8.52002 2.3999 Td (1)Tj -1.08008 -4.55981 Td (2)Tj /R69 6.97385 Tf 5.04004 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R84 4.98132 Tf 4.20288 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.84009 0.959961 Td (\))Tj /R106 9.96264 Tf -252 -23.52 Td (is)Tj 10.6731 0 Td (valid.)Tj /R15 9.96264 Tf 1.20679 -17.6399 Td (Lemma)Tj 41.8516 0 Td (3.6)Tj /R22 9.96264 Tf 19.0745 0 Td (\(Discrete)Tj 43.6328 0 Td (Gron)Tj 22.0564 0 Td (w)Tj 6.95288 0 Td (all's)Tj 21.4651 0 Td (lemma\))Tj /R15 9.96264 Tf 32.6177 0 Td (.)Tj /R106 9.96264 Tf 10.7976 0 Td (L)Tj 5.75659 0 Td (et)Tj /R72 9.96264 Tf 12.47 0 Td (w)Tj /R78 6.97385 Tf 7.24487 -1.44019 Td (s)Tj /R106 9.96264 Tf 4.32007 1.44019 Td (,)Tj /R72 9.96264 Tf 7.79834 0 Td (g)Tj /R78 6.97385 Tf 4.80176 -1.44019 Td (s)Tj /R106 9.96264 Tf 8.87988 1.44019 Td (b)Tj 4.07275 0 Td (e)Tj 9.11255 0 Td (nonne)Tj 26.0205 0 Td (gative)Tj -300.806 -12 Td (se)Tj 8.14746 0 Td (quenc)Tj 24.2173 0 Td (es)Tj 12.1074 0 Td (of)Tj 11.6296 0 Td (numb)Tj 23.2708 0 Td (ers)Tj 16.3018 0 Td (and)Tj /R72 9.96264 Tf 19.4209 0 Td (g)Tj /R78 6.97385 Tf 4.90479 -1.44019 Td (s)Tj /R106 9.96264 Tf 7.67993 1.44019 Td (b)Tj 4.07275 0 Td (e)Tj 8.15259 0 Td (nonde)Tj 25.4128 0 Td (cr)Tj 8.26709 0 Td (e)Tj 4.07275 0 Td (asing.)Tj 30.0947 0 Td (Then)Tj 25.8962 0 Td (fr)Tj 6.71289 0 Td (om)Tj 16.7903 0 Td (the)Tj 16.5413 0 Td (ine)Tj 12.7104 0 Td (qualities)Tj /R72 9.96264 Tf -255.684 -26.6401 Td (w)Tj /R78 6.97385 Tf 7.07983 -1.43994 Td (s)Tj /R75 9.96264 Tf 7.08008 1.43994 Td ()Tj /R72 9.96264 Tf 10.5505 0 Td (c)Tj /R78 6.97385 Tf 6.24951 12.48 Td (s)Tj /R94 6.97385 Tf 3.71704 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R81 9.96264 Tf -10.1917 -3 Td (X)Tj /R78 6.97385 Tf 0.47998 -21.3599 Td (i)Tj /R69 6.97385 Tf 2.75464 0 Td (=)Tj /R78 6.97385 Tf 6.11597 0 Td (k)Tj /R72 9.96264 Tf 6.72949 11.8799 Td (w)Tj /R78 6.97385 Tf 7.07983 -1.43994 Td (i)Tj /R22 9.96264 Tf 5.52002 1.43994 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (g)Tj /R78 6.97385 Tf 4.80933 -1.43994 Td (s)Tj /R72 9.96264 Tf 4.19995 1.43994 Td (;)Tj 9.95947 0 Td (s)Tj /R22 9.96264 Tf 7.43213 0 Td (=)Tj /R72 9.96264 Tf 10.5505 0 Td (k)Tj /R22 9.96264 Tf 7.67041 0 Td (+)Tj 9.95068 0 Td (1)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj 4.43945 0 Td (k)Tj /R22 9.96264 Tf 7.67041 0 Td (+)Tj 9.95068 0 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.31934 0 Td (;)Tj 4.43945 0 Td (n;)Tj 15.957 0 Td (w)Tj /R78 6.97385 Tf 7.16016 -1.43994 Td (k)Tj /R75 9.96264 Tf 7.67993 1.43994 Td ()Tj /R72 9.96264 Tf 10.5505 0 Td (g)Tj /R78 6.97385 Tf 4.80957 -1.43994 Td (k)Tj /R72 9.96264 Tf 4.7998 1.43994 Td (;)Tj 9.95947 0 Td (c)Tj 7.07349 0 Td (>)Tj /R22 9.96264 Tf 10.5505 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R106 9.96264 Tf -292.414 -26.52 Td (it)Tj 9.83594 0 Td (fol)Tj 11.0203 0 Td (lows)Tj /R72 9.96264 Tf 50.0637 -13.5601 Td (w)Tj /R78 6.97385 Tf 7.08008 -1.43994 Td (s)Tj /R75 9.96264 Tf 7.07983 1.43994 Td ()Tj /R72 9.96264 Tf 10.4307 0 Td (g)Tj /R78 6.97385 Tf 4.80933 -1.43994 Td (s)Tj /R22 9.96264 Tf 5.88013 1.43994 Td (exp\()Tj /R72 9.96264 Tf 19.0583 0 Td (c)Tj /R22 9.96264 Tf 4.31372 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (s)Tj /R75 9.96264 Tf 6.95215 0 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (k)Tj /R22 9.96264 Tf 5.5105 0 Td (\)\))Tj /R72 9.96264 Tf 7.67114 0 Td (;)Tj 9.95947 0 Td (s)Tj /R22 9.96264 Tf 7.43213 0 Td (=)Tj /R72 9.96264 Tf 10.5505 0 Td (k)Tj 5.5105 0 Td (;)Tj 4.43945 0 Td (k)Tj /R22 9.96264 Tf 7.67041 0 Td (+)Tj 9.95068 0 Td (1)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.31934 0 Td (;)Tj 4.43945 0 Td (n:)Tj /R15 9.96264 Tf -234.233 -21.24 Td (Lemma)Tj 39.6917 0 Td (3.7.)Tj /R106 9.96264 Tf 21.9524 0 Td (L)Tj 5.75659 0 Td (et)Tj /R72 9.96264 Tf 10.6699 0 Td (u)Tj /R106 9.96264 Tf 8.51807 0 Td (b)Tj 4.07275 0 Td (e)Tj 7.3125 0 Td (the)Tj 15.8213 0 Td (exact)Tj 24.9265 0 Td (solution)Tj 36.9221 0 Td (of)Tj 10.9097 0 Td (the)Tj 15.8213 0 Td (pr)Tj 8.74536 0 Td (oblem)Tj /R22 9.96264 Tf 27.6868 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (1\))Tj /R106 9.96264 Tf 8.8667 0 Td (,)Tj /R22 9.96264 Tf 4.67847 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (2\))Tj /R106 9.96264 Tf 11.6265 0 Td (and)Tj /R72 9.96264 Tf 18.5808 0 Td (U)Tj /R106 9.96264 Tf -317.692 -12 Td (b)Tj 4.07275 0 Td (e)Tj 7.79272 0 Td (the)Tj 16.3013 0 Td (solution)Tj 37.4021 0 Td (of)Tj 11.3896 0 Td (the)Tj 16.3013 0 Td (nite)Tj 25.4268 0 Td (dier)Tj 22.4141 0 Td (enc)Tj 14.2646 0 Td (e)Tj 7.9126 0 Td (scheme)Tj /R22 9.96264 Tf 34.4038 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (3\))Tj /R106 9.96264 Tf 8.8667 0 Td (,)Tj /R22 9.96264 Tf 4.67847 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (4\))Tj /R106 9.96264 Tf 8.8667 0 Td (.)Tj 7.55835 0 Td (Then)Tj 25.6563 0 Td (the)Tj 16.1814 0 Td (e)Tj 4.07275 0 Td (quality)Tj /R75 9.96264 Tf -174.415 -17.76 Td (kL)Tj /R78 6.97385 Tf 11.8799 -1.43994 Td ()Tj /R72 9.96264 Tf 5.16016 1.43994 Td (U)Tj /R75 9.96264 Tf 10.1941 0 Td ( )Tj 9.95068 0 Td (L)Tj /R78 6.97385 Tf 6.85522 -1.43994 Td ()Tj /R72 9.96264 Tf 5.15991 1.43994 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R69 6.97385 Tf 5.04175 4.08008 Td (2)Tj /R78 6.97385 Tf 6.59985 TL (Q)' /R84 4.98132 Tf 6.23999 -0.960205 Td (s)Tj /R75 9.96264 Tf 7.08008 3.47998 Td ()Tj ET Q Q Q endstream endobj 110 0 obj 18241 endobj 113 0 obj <> stream q 1 0 0 1 0 0 cm q q 1 0 0 1 0 0 cm BT /R63 6.97385 Tf 126.72 739.88 Td (Klein{Gor)Tj 37.1663 0 Td (don)Tj 15.95 0 Td (Equation)Tj /R69 6.97385 Tf 260.85 0 Td (129)Tj /R75 9.96264 Tf -292.606 -31.9199 Td ()Tj /R72 9.96264 Tf 10.5505 0 Td (c)Tj /R69 6.97385 Tf 4.32959 -1.44019 Td (1)Tj /R72 9.96264 Tf 4.43994 1.44019 Td (h)Tj /R78 6.97385 Tf 7.56006 12.48 Td (s)Tj /R94 6.97385 Tf 3.71704 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R81 9.96264 Tf -10.1917 -3 Td (X)Tj /R78 6.97385 Tf 0.959961 -21.3601 Td (l)Tj /R69 6.97385 Tf 2.51733 0 Td (=3)Tj /R75 9.96264 Tf 12.6025 11.8801 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (U)Tj /R75 9.96264 Tf 10.0742 0 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R69 6.97385 Tf 2.77734 4.19995 Td (2)Tj /R78 6.97385 Tf 7.19995 TL (W)' /R87 4.98132 Tf 8.52002 2.3999 Td (1)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 5.04004 2.16016 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R84 4.98132 Tf 4.20288 -1.08008 Td (l)Tj /R69 6.97385 Tf 2.87988 1.08008 Td (\))Tj /R22 9.96264 Tf 5.76001 3 Td (+)Tj 9.95068 0 Td (\(2)Tj /R72 9.96264 Tf 8.8667 0 Td (=)Tj /R69 6.97385 Tf 10.8228 4.19995 Td (2)Tj /R22 9.96264 Tf 4.43994 -4.19995 Td (\))Tj /R75 9.96264 Tf 3.83545 0 Td (kL)Tj /R72 9.96264 Tf 11.8655 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R69 6.97385 Tf 5.06079 4.19995 Td (2)Tj /R78 6.97385 Tf 6.6001 TL (Q)' /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R72 9.96264 Tf 4.32007 3.36011 Td (;)Tj 9.95947 0 Td (s)Tj /R75 9.96264 Tf 7.43213 0 Td ()Tj /R22 9.96264 Tf 10.4307 0 Td (4)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj 9.95947 0 Td (c)Tj /R69 6.97385 Tf 4.34717 -1.44019 Td (1)Tj /R22 9.96264 Tf 7.19995 1.44019 Td (:=)Tj 13.3101 0 Td (18)Tj /R72 9.96264 Tf 10.0623 0 Td ()Tj /R69 6.97385 Tf 4.82764 4.19995 Td (4)Tj /R22 9.96264 Tf 4.32007 -4.19995 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (sh)Tj /R22 9.96264 Tf 10.4307 0 Td (\))Tj /R69 6.97385 Tf 3.854 4.19995 Td (2)Tj /R106 9.96264 Tf -300 -29.52 Td (is)Tj 10.6731 0 Td (valid.)Tj /R22 9.96264 Tf 86.7668 -21 Td (4.)Tj /R12 9.96264 Tf 12.7107 0 Td (Pr)Tj 13.1895 0 Td (oof)Tj 21.7024 0 Td (of)Tj 15.4661 0 Td (Main)Tj 28.7859 0 Td (Resul)Tj 28.5303 0 Td (ts)Tj /R106 9.96264 Tf -217.825 -17.8801 Td (Pr)Tj 10.429 0 Td (o)Tj 4.55103 0 Td (of)Tj 11.6296 0 Td (of)Tj 11.6296 0 Td (The)Tj 16.1775 0 Td (or)Tj 8.74536 0 Td (em)Tj /R22 9.96264 Tf 16.312 0 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (1)Tj /R72 9.96264 Tf 5.03101 0 Td (:)Tj /R22 9.96264 Tf 6 0 Td (Multiplying)Tj 54.0891 0 Td (the)Tj 17.0281 0 Td (equation)Tj 40.6396 0 Td (\(2.5\))Tj 23.7329 0 Td (b)Tj 5.2793 0 Td (y)Tj /R72 9.96264 Tf 8.38989 0 Td (@)Tj /R78 6.97385 Tf 5.50586 -1.43994 Td (t)Tj /R72 9.96264 Tf 3.59985 1.43994 Td (Z)Tj /R22 9.96264 Tf 10.6741 0 Td (and)Tj 19.3096 0 Td (summing)Tj -286.543 -12 Td (up)Tj 14.3984 0 Td (on)Tj /R72 9.96264 Tf 13.7903 0 Td (Q)Tj /R78 6.97385 Tf 7.93115 -1.43994 Td (s)Tj /R22 9.96264 Tf 4.19995 1.43994 Td (,)Tj 6.11938 0 Td (w)Tj 6.95288 0 Td (e)Tj 7.67334 0 Td (obtain)Tj -37.9055 -16.3198 Td (\()Tj /R75 9.96264 Tf 3.83545 0 Td (L)Tj /R69 6.97385 Tf 6.84448 -1.43994 Td (0)Tj /R72 9.96264 Tf 4.56006 1.43994 Td (Z)Tj /R22 9.96264 Tf 9.71411 0 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (m)Tj /R69 6.97385 Tf 8.77515 4.07983 Td (2)Tj /R75 9.96264 Tf 4.43994 -4.07983 Td (L)Tj /R78 6.97385 Tf 6.84009 -1.43994 Td (m)Tj /R72 9.96264 Tf 7.67993 1.43994 Td (Z)Tj 6.9541 0 Td (;)Tj 4.43945 0 Td (@)Tj /R78 6.97385 Tf 5.28662 -1.43994 Td (t)Tj /R72 9.96264 Tf 3.47998 1.43994 Td (Z)Tj /R22 9.96264 Tf 7.5542 0 Td (\))Tj /R78 6.97385 Tf 3.8457 -1.43994 Td (Q)Tj /R84 4.98132 Tf 6.23999 -0.960205 Td (s)Tj /R22 9.96264 Tf 7.08008 2.40015 Td (=)Tj 10.5505 0 Td (\()Tj /R75 9.96264 Tf 3.83545 0 Td (L)Tj /R72 9.96264 Tf 6.83423 0 Td (u;)Tj 10.1978 0 Td (@)Tj /R78 6.97385 Tf 5.302 -1.43994 Td (t)Tj /R72 9.96264 Tf 3.47998 1.43994 Td (Z)Tj /R22 9.96264 Tf 7.5542 0 Td (\))Tj /R78 6.97385 Tf 3.8457 -1.43994 Td (Q)Tj /R84 4.98132 Tf 6.24023 -0.960205 Td (s)Tj /R22 9.96264 Tf 6.59985 2.40015 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td ()Tj /R22 9.96264 Tf 5.7583 0 Td (\()Tj /R75 9.96264 Tf 3.83545 0 Td (L)Tj /R78 6.97385 Tf 6.85571 -1.43994 Td ()Tj /R72 9.96264 Tf 5.27979 1.43994 Td (U)Tj /R75 9.96264 Tf 10.1941 0 Td ( )Tj 9.95068 0 Td (L)Tj /R78 6.97385 Tf 6.85522 -1.43994 Td ()Tj /R72 9.96264 Tf 5.16016 1.43994 Td (u;)Tj 10.1978 0 Td (@)Tj /R78 6.97385 Tf 5.28223 -1.43994 Td (t)Tj /R72 9.96264 Tf 3.47998 1.43994 Td (Z)Tj /R22 9.96264 Tf 7.5542 0 Td (\))Tj /R78 6.97385 Tf 3.8457 -1.43994 Td (Q)Tj /R84 4.98132 Tf 6.23999 -0.960205 Td (s)Tj /R72 9.96264 Tf 4.32007 2.40015 Td (;)Tj /R22 9.96264 Tf -299.88 -16.5601 Td (whence)Tj 34.7717 0 Td (using)Tj 26.0244 0 Td (Lemmas)Tj 39.574 0 Td (3.1,)Tj 18.7014 0 Td (3.2)Tj 16.0618 0 Td (and)Tj 19.4294 0 Td (the)Tj 17.1479 0 Td (equalit)Tj 29.3689 0 Td (y)Tj /R72 9.96264 Tf 8.38989 0 Td (Z)Tj /R78 6.97385 Tf 7.73047 3.71997 Td (i)Tj -0.719971 -6.23999 Td (i)Tj /R22 9.96264 Tf 6.83984 2.52002 Td (=)Tj 10.4307 0 Td (0,)Tj 11.1506 0 Td (w)Tj 6.95288 0 Td (e)Tj 7.67334 0 Td (receiv)Tj 25.0452 0 Td (e)Tj -274.613 -19.5601 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (5)Tj /R75 9.96264 Tf 5.03101 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (j)Tj /R69 6.97385 Tf 2.78467 4.08008 Td (2)Tj /R78 6.97385 Tf 7.19995 TL (W)' /R87 4.98132 Tf 8.52002 2.3999 Td (1)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 4.80005 2.16016 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R84 4.98132 Tf 4.20288 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.83984 0.959961 Td (\))Tj /R75 9.96264 Tf 6.36011 3.11987 Td ()Tj 10.5505 0 Td (kL)Tj /R72 9.96264 Tf 11.8655 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R78 6.97385 Tf 5.06567 -1.43994 Td (Q)Tj /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R75 9.96264 Tf 4.19995 2.3999 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (@)Tj /R78 6.97385 Tf 5.28906 -1.43994 Td (t)Tj /R72 9.96264 Tf 3.47998 1.43994 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (k)Tj /R78 6.97385 Tf 5.0459 -1.43994 Td (Q)Tj /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R22 9.96264 Tf 6.47998 2.3999 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td ()Tj /R75 9.96264 Tf 5.7583 0 Td (kL)Tj /R78 6.97385 Tf 11.8909 -1.43994 Td ()Tj /R72 9.96264 Tf 5.28003 1.43994 Td (U)Tj /R75 9.96264 Tf 10.0742 0 Td ( )Tj 9.95068 0 Td (L)Tj /R78 6.97385 Tf 6.85522 -1.43994 Td ()Tj /R72 9.96264 Tf 5.28003 1.43994 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R78 6.97385 Tf 5.0415 -1.43994 Td (Q)Tj /R84 4.98132 Tf 6.24023 -0.959961 Td (s)Tj /R75 9.96264 Tf 4.19995 2.3999 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (@)Tj /R78 6.97385 Tf 5.28882 -1.43994 Td (t)Tj /R72 9.96264 Tf 3.48022 1.43994 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (k)Tj /R78 6.97385 Tf 5.04565 -1.43994 Td (Q)Tj /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R75 9.96264 Tf 6.95996 2.3999 Td ()Tj -241.56 -24.1199 Td ()Tj /R72 9.96264 Tf 11.6399 6.71997 Td (")Tj /R69 6.97385 Tf 4.67993 -1.43994 Td (1)Tj ET Q 1 i 171 557 9.11987 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 173.28 548.36 Td (2)Tj /R75 9.96264 Tf 8.16016 6.84009 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (@)Tj /R78 6.97385 Tf 5.28882 -1.44019 Td (t)Tj /R72 9.96264 Tf 3.48022 1.44019 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (k)Tj /R69 6.97385 Tf 5.04565 4.19995 Td (2)Tj /R78 6.97385 Tf 6.6001 TL (Q)' /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R22 9.96264 Tf 6.47998 3.36011 Td (+)Tj 15.72 6.71997 Td (1)Tj ET Q 232 557 14.1599 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 231.72 548.36 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (")Tj /R69 6.97385 Tf 4.68896 -1.43994 Td (1)Tj /R75 9.96264 Tf 5.63989 8.28003 Td (kL)Tj /R72 9.96264 Tf 11.8655 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R69 6.97385 Tf 5.05615 4.19995 Td (2)Tj /R78 6.97385 Tf 6.6001 TL (Q)' /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R22 9.96264 Tf 6.36011 3.36011 Td (+)Tj /R72 9.96264 Tf 11.1599 6.71997 Td (")Tj /R69 6.97385 Tf 4.68018 -1.43994 Td (2)Tj ET Q 294 557 9.11987 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 295.56 548.36 Td (2)Tj /R75 9.96264 Tf 8.28003 6.84009 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (@)Tj /R78 6.97385 Tf 5.28906 -1.44019 Td (t)Tj /R72 9.96264 Tf 3.47998 1.44019 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (k)Tj /R69 6.97385 Tf 5.0459 4.19995 Td (2)Tj /R78 6.97385 Tf 6.6001 TL (Q)' /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R22 9.96264 Tf 6.47998 3.36011 Td (+)Tj /R72 9.96264 Tf 13.0798 6.71997 Td ()Tj /R69 6.97385 Tf 5.76001 3.71997 Td (2)Tj ET Q 354 557 14.1599 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 354.12 548.36 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (")Tj /R69 6.97385 Tf 4.68896 -1.43994 Td (2)Tj /R75 9.96264 Tf 5.52002 8.28003 Td (kL)Tj /R78 6.97385 Tf 11.8801 -1.44019 Td ()Tj /R72 9.96264 Tf 5.27979 1.44019 Td (U)Tj /R75 9.96264 Tf 10.0742 0 Td ( )Tj 9.95068 0 Td (L)Tj /R78 6.97385 Tf 6.85522 -1.44019 Td ()Tj /R72 9.96264 Tf 5.28003 1.44019 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R69 6.97385 Tf 5.04175 4.19995 Td (2)Tj /R78 6.97385 Tf 6.6001 TL (Q)' /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R72 9.96264 Tf 4.19995 3.36011 Td (:)Tj /R22 9.96264 Tf -313.2 -21.24 Td (Cho)Tj 17.9834 0 Td (ose)Tj /R72 9.96264 Tf 16.5393 0 Td (")Tj /R69 6.97385 Tf 4.71729 -1.44019 Td (1)Tj /R22 9.96264 Tf 7.19995 1.44019 Td (=)Tj 10.5505 0 Td (4)Tj /R72 9.96264 Tf 5.03101 0 Td (=)Tj /R22 9.96264 Tf 5.03101 0 Td (\(3)Tj /R72 9.96264 Tf 8.8667 0 Td (T)Tj /R22 9.96264 Tf 7.31787 0 Td (\),)Tj /R72 9.96264 Tf 9.71509 0 Td (")Tj /R69 6.97385 Tf 4.72778 -1.44019 Td (2)Tj /R22 9.96264 Tf 7.19995 1.44019 Td (=)Tj 10.5505 0 Td (8)Tj /R72 9.96264 Tf 5.03101 0 Td (=)Tj /R22 9.96264 Tf 5.03101 0 Td (\(3)Tj /R72 9.96264 Tf 8.8667 0 Td (T)Tj /R22 9.96264 Tf 7.31787 0 Td (\))Tj 6.83521 0 Td (and)Tj 19.4294 0 Td (use)Tj 17.1477 0 Td (Lemma)Tj 35.6187 0 Td (3.7:)Tj -199.708 -25.8 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (5)Tj /R75 9.96264 Tf 5.03101 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (j)Tj /R69 6.97385 Tf 2.78467 4.08008 Td (2)Tj /R78 6.97385 Tf 7.2002 TL (W)' /R87 4.98132 Tf 8.52002 2.40015 Td (1)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 4.80005 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R84 4.98132 Tf 4.20288 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.83984 0.959961 Td (\))Tj /R75 9.96264 Tf 6.36011 3.12012 Td ()Tj /R22 9.96264 Tf 11.76 6.71997 Td (3)Tj /R72 9.96264 Tf 5.03101 0 Td (T)Tj ET Q 215 510 12.24 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 218.76 501.32 Td (4)Tj /R75 9.96264 Tf 9.72021 6.84009 Td (kL)Tj /R72 9.96264 Tf 11.8655 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R69 6.97385 Tf 5.05615 4.08008 Td (2)Tj /R78 6.97385 Tf 6.6001 TL (Q)' /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R22 9.96264 Tf 6.47998 3.47998 Td (+)Tj 12.24 6.71997 Td (2)Tj ET Q 275 510 7.31982 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 275.04 501.32 Td (T)Tj /R75 9.96264 Tf 8.40015 6.84009 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (@)Tj /R78 6.97385 Tf 5.28882 -1.43994 Td (t)Tj /R72 9.96264 Tf 3.48022 1.43994 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (k)Tj /R69 6.97385 Tf 5.04565 4.08008 Td (2)Tj /R78 6.97385 Tf 6.6001 TL (Q)' /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R22 9.96264 Tf 6.47998 3.47998 Td (+)Tj 11.1602 6.71997 Td (3)Tj /R72 9.96264 Tf 5.03101 0 Td (T)Tj 7.31787 0 Td ()Tj /R69 6.97385 Tf 5.771 3.6001 Td (2)Tj /R72 9.96264 Tf 4.32007 -3.6001 Td (c)Tj /R69 6.97385 Tf 4.32007 -1.43994 Td (1)Tj /R72 9.96264 Tf 4.43994 1.43994 Td (h)Tj ET Q 334 510 37.0798 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 347.16 501.32 Td (16)Tj /R78 6.97385 Tf 26.6399 19.3201 Td (s)Tj /R94 6.97385 Tf 3.71704 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R81 9.96264 Tf -10.1917 -3 Td (X)Tj /R78 6.97385 Tf 0.840088 -21.48 Td (l)Tj /R69 6.97385 Tf 2.51733 0 Td (=3)Tj /R75 9.96264 Tf 12.7227 12 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (j)Tj /R69 6.97385 Tf 2.76636 4.08008 Td (2)Tj /R78 6.97385 Tf 7.2002 TL (W)' /R87 4.98132 Tf 8.52002 2.40015 Td (1)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 4.91992 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R84 4.98132 Tf 4.20288 -1.07983 Td (l)Tj /R69 6.97385 Tf 2.87988 1.07983 Td (\))Tj /R72 9.96264 Tf 3.6001 3.12012 Td (:)Tj /R22 9.96264 Tf -302.16 -25.3201 Td (Due)Tj 20.864 0 Td (to)Tj 12.1067 0 Td (Lemma)Tj 35.6187 0 Td (3.5,)Tj 18.7014 0 Td (w)Tj 6.95288 0 Td (e)Tj 7.79321 0 Td (ha)Tj 10.3103 0 Td (v)Tj 5.03003 0 Td (e)Tj 13.7827 -16.3201 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (5)Tj /R75 9.96264 Tf 5.03101 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (j)Tj /R69 6.97385 Tf 2.78467 4.08008 Td (2)Tj /R78 6.97385 Tf (W)' /R87 4.98132 Tf 8.52002 2.3999 Td (1)Tj -1.07983 -4.55981 Td (2)Tj /R69 6.97385 Tf 4.91992 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R84 4.98132 Tf 4.20288 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.83984 0.959961 Td (\))Tj /R75 9.96264 Tf 6.36011 3.11987 Td ()Tj -174.84 -27.24 Td ()Tj /R81 9.96264 Tf 10.4399 11.04 Td ()Tj /R22 9.96264 Tf 7.2002 -4.31982 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (h)Tj ET Q 156 442 10.7998 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 158.28 432.44 Td (T)Tj /R22 9.96264 Tf 12.3601 6.83984 Td (+)Tj 11.1599 6.72021 Td (3)Tj /R72 9.96264 Tf 5.03101 0 Td (T)Tj 7.31787 0 Td ()Tj /R69 6.97385 Tf 5.77124 3.59985 Td (2)Tj /R72 9.96264 Tf 4.32007 -3.59985 Td (c)Tj /R69 6.97385 Tf 4.31982 -1.44019 Td (4)Tj /R72 9.96264 Tf 4.43994 1.44019 Td (h)Tj ET Q 182 442 37.0798 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 195.24 432.44 Td (16)Tj /R81 9.96264 Tf 24.72 17.8799 Td ()Tj /R78 6.97385 Tf 7.7998 1.43994 Td (s)Tj /R94 6.97385 Tf 3.71704 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R81 9.96264 Tf -10.1917 -3 Td (X)Tj /R78 6.97385 Tf 0.960205 -21.48 Td (l)Tj /R69 6.97385 Tf 2.51733 0 Td (=3)Tj /R75 9.96264 Tf 12.6025 12 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (j)Tj /R69 6.97385 Tf 2.76636 4.08008 Td (2)Tj /R78 6.97385 Tf 7.19995 TL (W)' /R87 4.98132 Tf 8.52002 2.3999 Td (1)Tj -1.08008 -4.55981 Td (2)Tj /R69 6.97385 Tf 5.04004 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R84 4.98132 Tf 4.20288 -1.08008 Td (l)Tj /R69 6.97385 Tf 2.87988 1.08008 Td (\))Tj /R22 9.96264 Tf 5.76001 3.11987 Td (+)Tj /R72 9.96264 Tf 11.8799 6.72021 Td (h)Tj ET Q 296 442 7.31982 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 296.28 432.44 Td (T)Tj /R75 9.96264 Tf 8.40015 6.83984 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (j)Tj /R69 6.97385 Tf 2.76611 4.08008 Td (2)Tj /R78 6.97385 Tf 7.19995 TL (W)' /R87 4.98132 Tf 8.52002 2.3999 Td (1)Tj -1.07983 -4.55981 Td (2)Tj /R69 6.97385 Tf 5.04004 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R84 4.98132 Tf 4.20264 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.71997 0.959961 Td (\))Tj /R22 9.96264 Tf 5.88013 3.11987 Td (+)Tj 11.1599 6.72021 Td (3)Tj /R72 9.96264 Tf 5.03101 0 Td (T)Tj ET Q 358 442 12.24 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 361.92 432.44 Td (4)Tj /R75 9.96264 Tf 9.71997 6.83984 Td (kL)Tj /R72 9.96264 Tf 11.8655 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R69 6.97385 Tf 5.05615 4.08008 Td (2)Tj /R78 6.97385 Tf 6.47998 TL (Q)' /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R72 9.96264 Tf 4.32007 3.35986 Td (;)Tj 9.95947 0 Td (s)Tj /R75 9.96264 Tf 7.43213 0 Td ()Tj /R22 9.96264 Tf 10.4307 0 Td (4)Tj /R72 9.96264 Tf 5.03101 0 Td (:)Tj /R22 9.96264 Tf -311.013 -25.9199 Td (Since)Tj /R72 9.96264 Tf 25.9048 0 Td (h=T)Tj /R22 9.96264 Tf 20.7473 0 Td (=)Tj /R72 9.96264 Tf 10.4307 0 Td (h=)Tj /R22 9.96264 Tf 10.7893 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (nh)Tj /R22 9.96264 Tf 11.7559 0 Td (\))Tj /R75 9.96264 Tf 6.59521 0 Td ()Tj /R22 9.96264 Tf 10.5505 0 Td (1)Tj /R72 9.96264 Tf 5.03101 0 Td (=)Tj /R22 9.96264 Tf 5.03101 0 Td (4)Tj 8.15088 0 Td (for)Tj 15.2249 0 Td (4)Tj /R75 9.96264 Tf 7.79077 0 Td ()Tj /R72 9.96264 Tf 10.4307 0 Td (s)Tj /R75 9.96264 Tf 7.43213 0 Td ()Tj /R72 9.96264 Tf 10.5505 0 Td (n)Tj /R22 9.96264 Tf 5.99731 0 Td (,)Tj 6 0 Td (w)Tj 6.95288 0 Td (e)Tj 7.79321 0 Td (nd)Tj /R75 9.96264 Tf -59.4739 -16.4399 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (j)Tj /R69 6.97385 Tf 2.76611 4.08008 Td (2)Tj /R78 6.97385 Tf 7.2002 TL (W)' /R87 4.98132 Tf 8.52002 2.40015 Td (1)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 5.04004 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R84 4.98132 Tf 4.20288 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.84009 0.959961 Td (\))Tj /R75 9.96264 Tf 6.35986 3.12012 Td ()Tj -163.56 -28.9199 Td ()Tj /R81 9.96264 Tf 10.5601 11.1599 Td ()Tj /R22 9.96264 Tf 8.28003 -4.32007 Td (8)Tj ET Q 161 370 7.31982 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 161.4 361.16 Td (T)Tj /R22 9.96264 Tf 10.6799 6.84009 Td (+)Tj 11.1602 6.83984 Td (3)Tj /R72 9.96264 Tf 5.03101 0 Td (T)Tj 7.31787 0 Td ()Tj /R69 6.97385 Tf 5.771 3.6001 Td (2)Tj /R72 9.96264 Tf 4.32007 -3.6001 Td (c)Tj /R69 6.97385 Tf 4.31982 -1.43994 Td (1)Tj ET Q 183 370 31.3198 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 196.32 361.16 Td (4)Tj /R81 9.96264 Tf 19.3201 18 Td ()Tj /R72 9.96264 Tf 6 -11.1599 Td (h)Tj /R78 6.97385 Tf 7.56006 12.48 Td (s)Tj /R94 6.97385 Tf 3.71704 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R81 9.96264 Tf -10.1917 -3 Td (X)Tj /R78 6.97385 Tf 0.959961 -21.3601 Td (l)Tj /R69 6.97385 Tf 2.51733 0 Td (=3)Tj /R75 9.96264 Tf 12.6025 11.8801 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (j)Tj /R69 6.97385 Tf 2.76636 4.19995 Td (2)Tj /R78 6.97385 Tf 7.19995 TL (W)' /R87 4.98132 Tf 8.52002 2.3999 Td (1)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 5.04004 2.16016 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R84 4.98132 Tf 4.20288 -1.08008 Td (l)Tj /R69 6.97385 Tf 2.87988 1.08008 Td (\))Tj /R22 9.96264 Tf 5.76001 3 Td (+)Tj 9.95068 0 Td (3)Tj /R72 9.96264 Tf 5.03101 0 Td (T)Tj /R75 9.96264 Tf 7.31787 0 Td (kL)Tj /R72 9.96264 Tf 11.8655 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R69 6.97385 Tf 5.07666 4.19995 Td (2)Tj /R78 6.97385 Tf 6.6001 TL (Q)' /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R72 9.96264 Tf 4.08008 3.36011 Td (;)Tj 9.95947 0 Td (s)Tj /R22 9.96264 Tf 7.43213 0 Td (=)Tj 10.5505 0 Td (4)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf 4.43945 0 Td (5)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.19946 0 Td (;)Tj 4.43945 0 Td (n:)Tj /R22 9.96264 Tf 25.7969 0 Td (\(4)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (1\))Tj -305.104 -23.1602 Td (No)Tj 12.2231 0 Td (w)Tj 10.4329 0 Td (let)Tj 14.3884 0 Td (us)Tj 12.8342 0 Td (sho)Tj 14.2654 0 Td (w)Tj 10.4329 0 Td (that)Tj /R75 9.96264 Tf 25.623 -16.4399 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (j)Tj /R69 6.97385 Tf 2.76636 4.19995 Td (2)Tj /R78 6.97385 Tf 7.19995 TL (W)' /R87 4.98132 Tf 8.52002 2.3999 Td (1)Tj -1.08008 -4.55981 Td (2)Tj /R69 6.97385 Tf 4.92017 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R87 4.98132 Tf 4.20264 -0.959961 Td (3)Tj /R69 6.97385 Tf 3.95996 0.959961 Td (\))Tj /R75 9.96264 Tf 6.36011 3 Td ()Tj /R22 9.96264 Tf 10.4307 0 Td (3)Tj /R72 9.96264 Tf 5.03101 0 Td (T)Tj /R75 9.96264 Tf 7.31787 0 Td (kL)Tj /R72 9.96264 Tf 11.8655 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R69 6.97385 Tf 5.07666 4.19995 Td (2)Tj /R78 6.97385 Tf 6.59985 TL (Q)' /R87 4.98132 Tf 6.23999 -0.960205 Td (3)Tj /R72 9.96264 Tf 4.19995 3.36011 Td (:)Tj /R22 9.96264 Tf 94.3193 0 Td (\(4)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (2\))Tj -305.146 -18.72 Td (Indeed,)Tj 34.6606 0 Td (rst)Tj 19.905 0 Td (note)Tj 21.5791 0 Td (that)Tj /R75 9.96264 Tf 20.9812 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (j)Tj /R69 6.97385 Tf 2.84033 3.59985 Td (2)Tj /R78 6.97385 Tf 7.19995 TL (W)' /R87 4.98132 Tf 8.52002 2.40015 Td (1)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 4.92017 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R87 4.98132 Tf 4.20264 -0.959961 Td (3)Tj /R69 6.97385 Tf 3.84009 0.959961 Td (\))Tj /R22 9.96264 Tf 6.35986 3.6001 Td (=)Tj 10.5505 0 Td (\(1)Tj /R72 9.96264 Tf 8.8667 0 Td (=h)Tj /R22 9.96264 Tf 10.7893 0 Td (\)\()Tj /R72 9.96264 Tf 7.67114 0 Td (Z)Tj /R69 6.97385 Tf 7.60254 3.59985 Td (3)Tj -0.720215 -6.11987 Td (1)Tj /R22 9.96264 Tf 5.16016 2.52002 Td (\))Tj /R69 6.97385 Tf 3.83984 3.59985 Td (2)Tj /R72 9.96264 Tf 4.44019 -3.59985 Td (:)Tj /R22 9.96264 Tf 5.51929 0 Td (The)Tj 19.7854 0 Td (equation)Tj 40.0396 0 Td (\(2.5\))Tj 23.2527 0 Td (on)Tj 13.1902 0 Td (the)Tj -312.027 -14.28 Td (grid)Tj /R72 9.96264 Tf 20.385 0 Td (Q)Tj /R69 6.97385 Tf 7.93481 -1.43994 Td (3)Tj /R22 9.96264 Tf 7.80005 1.43994 Td (\(consisting)Tj 49.875 0 Td (from)Tj 23.5039 0 Td (one)Tj 18.3435 0 Td (grid)Tj 20.385 0 Td (p)Tj 5.75928 0 Td (oin)Tj 13.0701 0 Td (t)Tj 7.19531 0 Td (only\))Tj 25.7756 0 Td (can)Tj 18.2236 0 Td (b)Tj 5.75928 0 Td (e)Tj 7.79321 0 Td (rewritten)Tj 43.1602 0 Td (as)Tj 12.2261 0 Td (follo)Tj 18.3403 0 Td (ws)Tj /R81 9.96264 Tf -212.65 -11.6399 Td ()Tj /R22 9.96264 Tf 9.71997 -4.32007 Td (1)Tj ET Q 227 275 10.3198 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 226.8 265.88 Td (h)Tj /R69 6.97385 Tf 5.76001 2.88013 Td (2)Tj /R22 9.96264 Tf 7.80005 3.95996 Td (+)Tj /R72 9.96264 Tf 11.1599 6.71997 Td (m)Tj /R69 6.97385 Tf 8.76001 3.59985 Td (2)Tj ET Q 252 275 13.3198 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 255.6 265.88 Td (2)Tj 12.6001 6.84009 Td (+)Tj /R72 9.96264 Tf 11.1599 6.71997 Td ()Tj ET Q 279 275 5.87988 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 279.72 265.88 Td (4)Tj 6.59985 6.84009 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R69 6.97385 Tf 5.76465 4.07983 Td (2)Tj 6.59985 TL (2)' /R22 9.96264 Tf 4.43994 2.52002 Td (\))Tj /R69 6.97385 Tf 3.84009 4.07983 Td (2)Tj /R81 9.96264 Tf 4.55981 6.96021 Td ()Tj /R72 9.96264 Tf 5.88013 -11.04 Td (Z)Tj /R69 6.97385 Tf 7.56006 4.07983 Td (3)Tj -0.719971 -6.59985 Td (1)Tj /R22 9.96264 Tf 7.91992 2.52002 Td (=)Tj /R75 9.96264 Tf 10.5505 0 Td (L)Tj /R72 9.96264 Tf 6.83423 0 Td (u)Tj /R69 6.97385 Tf 5.77515 4.07983 Td (3)Tj (1)' /R72 9.96264 Tf 4.43994 2.52002 Td (;)Tj /R22 9.96264 Tf -230.28 -20.4001 Td (whence)Tj 34.7717 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (Z)Tj /R69 6.97385 Tf 7.59277 3.6001 Td (3)Tj -0.719971 -6.12012 Td (1)Tj /R22 9.96264 Tf 5.15991 2.52002 Td (\))Tj /R69 6.97385 Tf 3.84009 3.6001 Td (2)Tj /R75 9.96264 Tf 7.31982 -3.6001 Td ()Tj /R72 9.96264 Tf 10.5505 0 Td (h)Tj /R69 6.97385 Tf 5.76953 3.6001 Td (4)Tj /R22 9.96264 Tf 4.43994 -3.6001 Td (\()Tj /R75 9.96264 Tf 3.83545 0 Td (L)Tj /R72 9.96264 Tf 6.83423 0 Td (u)Tj /R69 6.97385 Tf 5.77051 3.6001 Td (3)Tj 6.12012 TL (1)' /R22 9.96264 Tf 4.43994 2.52002 Td (\))Tj /R69 6.97385 Tf 3.83984 3.6001 Td (2)Tj /R72 9.96264 Tf 4.44019 -3.6001 Td (:)Tj /R22 9.96264 Tf -99.8401 -12 Td (Therefore)Tj /R75 9.96264 Tf 74.04 -12.1199 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (j)Tj /R69 6.97385 Tf 2.76636 4.07983 Td (2)Tj /R78 6.97385 Tf 7.19995 TL (W)' /R87 4.98132 Tf 8.52002 2.40015 Td (1)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 5.04004 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R87 4.98132 Tf 4.20264 -0.959961 Td (3)Tj /R69 6.97385 Tf 3.84009 0.959961 Td (\))Tj /R75 9.96264 Tf 6.36011 3.12012 Td ()Tj /R72 9.96264 Tf 10.5505 0 Td (h)Tj /R75 9.96264 Tf 5.7583 0 Td (kL)Tj /R72 9.96264 Tf 11.8655 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R69 6.97385 Tf 5.06738 4.07983 Td (2)Tj /R78 6.97385 Tf 6.59985 TL (Q)' /R87 4.98132 Tf 6.23999 -0.959961 Td (3)Tj /R75 9.96264 Tf 6.95996 3.47998 Td ()Tj /R22 9.96264 Tf 10.5505 0 Td (3)Tj /R72 9.96264 Tf 5.03101 0 Td (T)Tj /R75 9.96264 Tf 7.31787 0 Td (kL)Tj /R72 9.96264 Tf 11.8655 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R69 6.97385 Tf 5.07666 4.07983 Td (2)Tj /R78 6.97385 Tf (Q)' /R87 4.98132 Tf 6.23999 -0.959961 Td (3)Tj /R72 9.96264 Tf 4.08008 3.47998 Td (:)Tj /R22 9.96264 Tf -237.12 -16.0801 Td (Applying)Tj 42.8103 0 Td (Lemma)Tj 35.2585 0 Td (3.6)Tj 15.7017 0 Td (to)Tj 11.8665 0 Td (the)Tj 16.908 0 Td (inequalities)Tj 52.0356 0 Td (\(4.1\),)Tj 26.2524 0 Td (\(4.2\),)Tj 26.3726 0 Td (w)Tj 6.95288 0 Td (e)Tj 7.43311 0 Td (obtain)Tj 30.6958 0 Td (the)Tj 16.7878 0 Td (estimate)Tj -289.075 -12.8401 Td (\(2.6\))Tj 24.2129 0 Td (with)Tj /R72 9.96264 Tf 23.2673 0 Td (c)Tj /R22 9.96264 Tf 7.91357 0 Td (=)Tj /R81 9.96264 Tf 11.446 8.52002 Td (p)Tj ET Q 204 208 95.2798 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 203.512 199.28 Td (3)Tj /R72 9.96264 Tf 5.03101 0 Td (T)Tj /R22 9.96264 Tf 8.87769 0 Td (exp\(8)Tj 26.2495 0 Td (+)Tj 9.95068 0 Td (14)Tj /R72 9.96264 Tf 10.0623 0 Td ()Tj /R69 6.97385 Tf 5.83618 2.87988 Td (2)Tj /R72 9.96264 Tf 4.44019 -2.88013 Td (T)Tj /R69 6.97385 Tf 7.31982 2.88013 Td (4)Tj /R72 9.96264 Tf 4.32007 -2.88013 Td ()Tj /R69 6.97385 Tf 4.80005 2.88013 Td (4)Tj /R22 9.96264 Tf 4.43994 -2.88013 Td (\))Tj 3.95532 0 Td (,)Tj 6.71948 0 Td (where)Tj /R72 9.96264 Tf 29.2542 0 Td ()Tj /R22 9.96264 Tf 8.75317 0 Td (is)Tj 10.4346 0 Td (dened)Tj 34.9038 0 Td (in)Tj 12.1187 0 Td (Lemma)Tj 36.0986 0 Td (3.4.)Tj /R117 9.96264 Tf 7.88232 -11.8799 Td ()Tj ET Q Q Q endstream endobj 114 0 obj 25210 endobj 120 0 obj <> stream q 1 0 0 1 0 0 cm q q 1 0 0 1 0 0 cm BT /R69 6.97385 Tf 126.72 739.88 Td (130)Tj /R63 6.97385 Tf 68.1421 0 Td (G.)Tj 11.7505 0 Td (Berikelashvili,)Tj 53.8267 0 Td (O.)Tj 11.7517 0 Td (Jokhadze,)Tj 37.6526 0 Td (S.)Tj 10.071 0 Td (Kharib)Tj 24.1042 0 Td (e)Tj 3.47559 0 Td (gashvili,)Tj 32.1294 0 Td (and)Tj 16.0701 0 Td (B.)Tj 11.2705 0 Td (Mido)Tj 17.8696 0 Td (dashvili)Tj /R106 9.96264 Tf -298.114 -23.8799 Td (Pr)Tj 10.429 0 Td (o)Tj 4.55103 0 Td (of)Tj 11.6296 0 Td (of)Tj 11.7498 0 Td (The)Tj 16.1775 0 Td (or)Tj 8.74536 0 Td (em)Tj /R22 9.96264 Tf 16.4321 0 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (:)Tj /R22 9.96264 Tf 6 0 Td (Let)Tj /R72 9.96264 Tf 6.10449 -21.4802 Td (l)Tj /R22 9.96264 Tf 3.23853 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj 6.47534 0 Td (:=)Tj 19.6924 6.72021 Td (1)Tj ET Q 1 i 265 697 15.24 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 265.2 687.68 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (h)Tj /R69 6.97385 Tf 5.7688 2.87988 Td (2)Tj /R81 9.96264 Tf 7.32007 17.52 Td (Z)Tj /R78 6.97385 Tf -2.28003 -28.2 Td (e)Tj /R84 4.98132 Tf 3.71997 -0.959961 Td (ij)Tj /R72 9.96264 Tf 10.3201 15.5999 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (x;)Tj 10.0784 0 Td (t)Tj /R22 9.96264 Tf 3.59644 0 Td (\))Tj /R72 9.96264 Tf 5.51538 0 Td (dx)Tj 12.4692 0 Td (dt:)Tj /R22 9.96264 Tf -197.733 -30.48 Td (By)Tj 15.7034 0 Td (in)Tj 8.03882 0 Td (tro)Tj 13.0618 0 Td (ducing)Tj 32.022 0 Td (the)Tj 17.1479 0 Td (notation)Tj /R72 9.96264 Tf -2.21387 -17.3999 Td ( )Tj /R69 6.97385 Tf 6.47998 -1.43994 Td (1)Tj /R22 9.96264 Tf 4.43994 1.43994 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj 6.59521 0 Td (:=)Tj /R72 9.96264 Tf 13.3101 0 Td (l)Tj /R22 9.96264 Tf 3.23853 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj /R75 9.96264 Tf 5.99536 0 Td ( )Tj /R22 9.96264 Tf 9.95068 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (5\()Tj /R72 9.96264 Tf 8.8667 0 Td (u)Tj /R78 6.97385 Tf 5.82544 4.80005 Td (j)Tj 7.56006 TL (i)' /R22 9.96264 Tf 6.23999 2.76001 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (u)Tj /R78 6.97385 Tf 5.76929 4.80005 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (2)Tj /R78 6.97385 Tf -9.83032 -7.56006 Td (i)Tj /R22 9.96264 Tf 14.4001 2.76001 Td (\))Tj /R72 9.96264 Tf 3.83545 0 Td (;)Tj -137.035 -18.6001 Td ( )Tj /R69 6.97385 Tf 6.47998 -1.43994 Td (2)Tj /R22 9.96264 Tf 4.56006 1.43994 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj 6.59521 0 Td (:=)Tj /R72 9.96264 Tf 13.1902 0 Td (l)Tj /R22 9.96264 Tf 3.23853 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj /R75 9.96264 Tf 5.99536 0 Td ( )Tj /R22 9.96264 Tf 9.95068 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (5\()Tj /R72 9.96264 Tf 8.8667 0 Td (u)Tj /R78 6.97385 Tf 5.8252 4.80005 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R78 6.97385 Tf -9.83032 -7.56006 Td (i)Tj /R94 6.97385 Tf 2.75464 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R22 9.96264 Tf 7.5708 2.76001 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (u)Tj /R78 6.97385 Tf 5.76929 4.80005 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R78 6.97385 Tf -9.83032 -7.56006 Td (i)Tj /R69 6.97385 Tf 2.75464 0 Td (+1)Tj /R22 9.96264 Tf 11.5254 2.76001 Td (\))Tj /R72 9.96264 Tf 3.83545 0 Td (;)Tj -165.835 -18.72 Td ( )Tj /R69 6.97385 Tf 6.47998 -1.43994 Td (3)Tj /R22 9.96264 Tf 4.43994 1.43994 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj 6.71533 0 Td (:=)Tj /R72 9.96264 Tf 13.1902 0 Td (l)Tj /R22 9.96264 Tf 3.23853 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R69 6.97385 Tf 5.78687 4.19995 Td (2)Tj /R22 9.96264 Tf 4.43994 -4.19995 Td (\))Tj /R72 9.96264 Tf 3.83545 0 Td ( )Tj /R69 6.97385 Tf 6.48462 -1.43994 Td (1)Tj /R22 9.96264 Tf 4.43994 1.43994 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj 6.11523 0 Td (+)Tj 9.95068 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (5\()Tj /R72 9.96264 Tf 8.8667 0 Td (u)Tj /R78 6.97385 Tf 5.80298 4.80005 Td (j)Tj (i)' /R22 9.96264 Tf 6.23999 2.76001 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (u)Tj /R78 6.97385 Tf 5.76929 4.80005 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (2)Tj /R78 6.97385 Tf -9.83032 -7.56006 Td (i)Tj /R22 9.96264 Tf 14.4001 2.76001 Td (\))Tj /R72 9.96264 Tf 3.83545 0 Td ( )Tj /R69 6.97385 Tf 6.48462 -1.43994 Td (2)Tj /R22 9.96264 Tf 4.43994 1.43994 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R69 6.97385 Tf 5.7644 4.19995 Td (2)Tj /R22 9.96264 Tf 4.44019 -4.19995 Td (\))Tj /R72 9.96264 Tf 3.83545 0 Td (;)Tj /R22 9.96264 Tf 49.0845 19.0801 Td (\(4)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (3\))Tj -317.026 -35.52 Td (w)Tj 6.95288 0 Td (e)Tj 7.67334 0 Td (write)Tj 25.4167 0 Td (the)Tj 17.1479 0 Td (truncation)Tj 48.6794 0 Td (error)Tj 24.4497 0 Td (in)Tj 11.6387 0 Td (the)Tj 17.1479 0 Td (form)Tj /R75 9.96264 Tf -100.547 -17.04 Td (L)Tj /R72 9.96264 Tf 6.83423 0 Td (u)Tj /R22 9.96264 Tf 8.51807 0 Td (=)Tj /R75 9.96264 Tf 10.5505 0 Td ( )Tj /R72 9.96264 Tf 7.79077 0 Td (m)Tj /R69 6.97385 Tf 8.78638 4.08008 Td (2)Tj /R72 9.96264 Tf 4.44019 -4.08008 Td ( )Tj /R69 6.97385 Tf 6.47998 -1.43994 Td (1)Tj /R22 9.96264 Tf 4.43994 1.43994 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj /R75 9.96264 Tf 5.99536 0 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td ()Tj /R81 9.96264 Tf 5.78027 8.04004 Td ( )Tj /R72 9.96264 Tf 4.67993 -8.04004 Td (l)Tj /R22 9.96264 Tf 3.23853 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R69 6.97385 Tf 5.76611 4.08008 Td (3)Tj /R22 9.96264 Tf 4.31982 -4.08008 Td (\))Tj /R75 9.96264 Tf 6.11523 0 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (l)Tj /R22 9.96264 Tf 3.23853 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj /R72 9.96264 Tf 3.83545 0 Td (l)Tj /R22 9.96264 Tf 3.23853 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R69 6.97385 Tf 5.79248 4.08008 Td (2)Tj /R22 9.96264 Tf 4.32007 -4.08008 Td (\))Tj 6.11523 0 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td ( )Tj /R69 6.97385 Tf 6.4939 -1.43994 Td (3)Tj /R22 9.96264 Tf 4.44019 1.43994 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj /R81 9.96264 Tf 3.84619 8.04004 Td ()Tj /R72 9.96264 Tf 4.56006 -8.04004 Td (:)Tj /R22 9.96264 Tf 40.9194 0 Td (\(4)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (4\))Tj -305.146 -16.9199 Td (The)Tj 20.5054 0 Td (expressions)Tj 51.9067 0 Td (for)Tj /R72 9.96264 Tf 15.2249 0 Td ( )Tj /R78 6.97385 Tf 6.56299 -1.43994 Td ()Tj /R22 9.96264 Tf 5.64014 1.43994 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\),)Tj /R72 9.96264 Tf 9.95508 0 Td ()Tj /R22 9.96264 Tf 9.23584 0 Td (=)Tj 10.4307 0 Td (1)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf 4.43945 0 Td (2,)Tj 11.0308 0 Td (can)Tj 18.2236 0 Td (b)Tj 5.75928 0 Td (e)Tj 7.79321 0 Td (rewritten)Tj 43.1602 0 Td (as)Tj 12.2261 0 Td (follo)Tj 18.3403 0 Td (ws:)Tj /R72 9.96264 Tf -266.979 -26.4001 Td ( )Tj /R78 6.97385 Tf 6.47998 -1.43994 Td ()Tj /R22 9.96264 Tf 5.63989 1.43994 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj 6.59521 0 Td (=)Tj 16.811 6.72021 Td (1)Tj ET Q 177 535 15.24 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 176.76 525.68 Td (4)Tj /R72 9.96264 Tf 5.03101 0 Td (h)Tj /R69 6.97385 Tf 5.76904 2.87988 Td (2)Tj /R81 9.96264 Tf 7.32007 17.52 Td (Z)Tj /R78 6.97385 Tf -2.28003 -28.0798 Td (e)Tj /R84 4.98132 Tf 3.71997 -0.960205 Td (ij)Tj /R81 9.96264 Tf 10.3201 29.52 Td ()Tj /R22 9.96264 Tf 7.32007 -14.04 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (x)Tj /R75 9.96264 Tf 7.91846 0 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (x)Tj /R78 6.97385 Tf 5.65527 -1.43994 Td (i)Tj /R69 6.97385 Tf 2.75464 0 Td (+)Tj /R78 6.97385 Tf 6.11597 0 Td ()Tj /R94 6.97385 Tf 5.15356 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (2)Tj /R22 9.96264 Tf 4.5813 1.43994 Td (\)\()Tj /R72 9.96264 Tf 7.67114 0 Td (x)Tj /R75 9.96264 Tf 8.03857 0 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (x)Tj /R78 6.97385 Tf 5.65967 -1.43994 Td (i)Tj /R94 6.97385 Tf 2.75464 0 Td ( )Tj /R78 6.97385 Tf 6.23462 0 Td ()Tj /R69 6.97385 Tf 5.15356 0 Td (+2)Tj /R22 9.96264 Tf 10.697 1.43994 Td (\))Tj /R72 9.96264 Tf 5.04004 6.72021 Td (@)Tj /R69 6.97385 Tf 5.88013 3.71997 Td (2)Tj /R72 9.96264 Tf 4.43994 -3.71997 Td (u)Tj ET Q 327 535 16.0798 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 328.44 525.68 Td (@)Tj 5.86987 0 Td (t)Tj /R69 6.97385 Tf 3.61011 2.87988 Td (2)Tj /R22 9.96264 Tf 6.71997 3.95996 Td (+)Tj -175.56 -36.3599 Td (+)Tj 9.95068 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (t)Tj /R75 9.96264 Tf 5.75635 0 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (t)Tj /R78 6.97385 Tf 3.62695 -1.43994 Td (j)Tj /R69 6.97385 Tf 3.5957 0 Td (+)Tj /R78 6.97385 Tf 6.11597 0 Td ()Tj /R94 6.97385 Tf 5.15356 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (2)Tj /R22 9.96264 Tf 4.58008 1.43994 Td (\)\()Tj /R72 9.96264 Tf 7.67114 0 Td (t)Tj /R75 9.96264 Tf 5.87622 0 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (t)Tj /R78 6.97385 Tf 3.62183 -1.43994 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R78 6.97385 Tf 6.23462 0 Td ()Tj /R22 9.96264 Tf 5.76978 1.43994 Td (\))Tj /R72 9.96264 Tf 5.04004 6.71997 Td (@)Tj /R69 6.97385 Tf 5.87988 3.71997 Td (2)Tj /R72 9.96264 Tf 4.56006 -3.71997 Td (u)Tj ET Q 276 498 16.0798 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 275.64 489.32 Td (@)Tj 5.86987 0 Td (x)Tj /R69 6.97385 Tf 5.65015 2.88013 Td (2)Tj /R22 9.96264 Tf 8.04004 3.95996 Td (+)Tj 9.95068 0 Td (2\()Tj /R72 9.96264 Tf 8.8667 0 Td (x)Tj /R75 9.96264 Tf 7.79858 0 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (x)Tj /R78 6.97385 Tf 5.67334 -1.43994 Td (i)Tj /R22 9.96264 Tf 3.35986 1.43994 Td (\)\()Tj /R72 9.96264 Tf 7.67114 0 Td (t)Tj /R75 9.96264 Tf 5.87622 0 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (t)Tj /R78 6.97385 Tf 3.62207 -1.43994 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (1)Tj /R22 9.96264 Tf 4.56958 1.43994 Td (\))Tj /R72 9.96264 Tf 7.56006 6.71997 Td (@)Tj /R69 6.97385 Tf 5.87988 3.71997 Td (2)Tj /R72 9.96264 Tf 4.44019 -3.71997 Td (u)Tj ET Q 387 498 20.9998 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 387.36 489.32 Td (@)Tj 5.86987 0 Td (x@)Tj 11.5088 0 Td (t)Tj /R81 9.96264 Tf 4.82129 20.8801 Td ()Tj /R72 9.96264 Tf 9 -14.04 Td (dx)Tj 12.4692 0 Td (dt:)Tj /R22 9.96264 Tf -304.309 -22.3201 Td (Hence)Tj 29.4915 0 Td (it)Tj 9.95508 0 Td (follo)Tj 18.3403 0 Td (ws)Tj /R75 9.96264 Tf -23.5869 -20.8799 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td ( )Tj /R78 6.97385 Tf 6.48047 -1.44019 Td ()Tj /R22 9.96264 Tf 5.63989 1.44019 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj /R75 9.96264 Tf 3.83545 0 Td (j)Tj 5.51929 0 Td ()Tj /R22 9.96264 Tf 11.7715 6.71997 Td (1)Tj ET Q 207 455 5.03979 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 206.52 446.12 Td (4)Tj /R81 9.96264 Tf 7.92017 20.3999 Td (Z)Tj /R78 6.97385 Tf -2.28003 -28.2 Td (e)Tj /R84 4.98132 Tf 3.71997 -0.959961 Td (ij)Tj /R81 9.96264 Tf 10.3201 29.6401 Td ()Tj 7.31982 -2.64014 Td ()Tj 6 TL ()' 5.87988 TL ()' /R72 9.96264 Tf 4.56006 7.19995 Td (@)Tj /R69 6.97385 Tf 5.88013 3.59985 Td (2)Tj /R72 9.96264 Tf 4.43994 -3.59985 Td (u)Tj ET Q 238 455 16.0798 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 239.16 446.12 Td (@)Tj 5.86987 0 Td (t)Tj /R69 6.97385 Tf 3.61011 2.88013 Td (2)Tj /R81 9.96264 Tf 6.6001 15.3599 Td ()Tj 6 TL ()' 5.87988 TL ()' /R22 9.96264 Tf 5.51978 0.47998 Td (+)Tj /R81 9.96264 Tf 9.96021 11.3999 Td ()Tj 6 TL ()' 5.87988 TL ()' /R72 9.96264 Tf 4.55981 7.19995 Td (@)Tj /R69 6.97385 Tf 5.88013 3.59985 Td (2)Tj /R72 9.96264 Tf 4.43994 -3.59985 Td (u)Tj ET Q 275 455 16.0798 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 275.28 446.12 Td (@)Tj 5.86987 0 Td (x)Tj /R69 6.97385 Tf 5.65015 2.88013 Td (2)Tj /R81 9.96264 Tf 5.64014 15.3599 Td ()Tj 6 TL ()' 5.87988 TL ()' /R22 9.96264 Tf 5.52002 0.47998 Td (+)Tj 9.95068 0 Td (2)Tj /R81 9.96264 Tf 5.04932 11.3999 Td ()Tj 6 TL ()' 5.87988 TL ()' /R72 9.96264 Tf 6.95996 7.19995 Td (@)Tj /R69 6.97385 Tf 5.87988 3.59985 Td (2)Tj /R72 9.96264 Tf 4.44019 -3.59985 Td (u)Tj ET Q 318 455 20.9998 0.47998 re f q 1 0 0 1 0 0 cm BT /R72 9.96264 Tf 317.52 446.12 Td (@)Tj 5.86987 0 Td (x@)Tj 11.5088 0 Td (t)Tj /R81 9.96264 Tf 4.70142 18.24 Td ()Tj 6 TL ()' 5.87988 TL ()' 3.36011 14.52 Td ()Tj /R72 9.96264 Tf 9 -14.04 Td (dxdt;)Tj 29.6162 0 Td ()Tj /R22 9.96264 Tf 9.11572 0 Td (=)Tj 10.5505 0 Td (1)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf 4.43945 0 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf -289.024 -30.48 Td (whence,)Tj 37.291 0 Td (using)Tj 25.7842 0 Td (the)Tj 16.7878 0 Td (Cauc)Tj 21.9368 0 Td (h)Tj 5.2793 0 Td (y{Sc)Tj 20.0139 0 Td (h)Tj 5.2793 0 Td (w)Tj 6.95288 0 Td (artz)Tj 19.895 0 Td (inequalit)Tj 37.6477 0 Td (y)Tj 8.26978 0 Td (and)Tj 19.0693 0 Td (the)Tj 16.7878 0 Td (algebraic)Tj 41.8337 0 Td (inequalit)Tj 37.6477 0 Td (y)Tj -320.476 -12 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (a)Tj /R22 9.96264 Tf 7.42993 0 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (b)Tj /R22 9.96264 Tf 6.47363 0 Td (+)Tj 9.95068 0 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (c)Tj /R22 9.96264 Tf 4.31372 0 Td (\))Tj /R69 6.97385 Tf 3.89478 3.71997 Td (2)Tj /R75 9.96264 Tf 7.19995 -3.71997 Td ()Tj /R22 9.96264 Tf 10.5505 0 Td (4\()Tj /R72 9.96264 Tf 8.8667 0 Td (a)Tj /R69 6.97385 Tf 5.30273 3.71997 Td (2)Tj /R22 9.96264 Tf 6.6001 -3.71997 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (b)Tj /R69 6.97385 Tf 4.32935 3.71997 Td (2)Tj /R22 9.96264 Tf 6.71997 -3.71997 Td (+)Tj 9.95068 0 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (c)Tj /R69 6.97385 Tf 4.33838 3.71997 Td (2)Tj /R22 9.96264 Tf 4.31982 -3.71997 Td (\),)Tj 9.95508 0 Td (w)Tj 6.95288 0 Td (e)Tj 7.79321 0 Td (ha)Tj 10.3103 0 Td (v)Tj 5.03003 0 Td (e)Tj /R75 9.96264 Tf -123.681 -22.0801 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td ( )Tj /R69 6.97385 Tf 6.48047 -1.43994 Td (1)Tj /R22 9.96264 Tf 4.56006 1.43994 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj /R75 9.96264 Tf 3.83545 0 Td (j)Tj 5.51929 0 Td ()Tj /R72 9.96264 Tf 15.4915 6.71997 Td (h)Tj ET Q 222 391 13.3198 0.47998 re f q 1 0 0 1 0 0 cm BT /R75 9.96264 Tf 221.52 388.64 Td (p)Tj ET Q 230 389 5.03979 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 229.92 380.36 Td (2)Tj /R75 9.96264 Tf 7.80005 8.04004 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R78 6.97385 Tf 2.76196 -2.15991 Td (W)Tj /R87 4.98132 Tf 8.52002 2.3999 Td (2)Tj -1.07983 -4.67993 Td (2)Tj /R69 6.97385 Tf 4.91992 2.28003 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (e)Tj /R84 4.98132 Tf 3.7229 -0.960205 Td (ij)Tj /R69 6.97385 Tf 6.47998 0.960205 Td (\))Tj /R72 9.96264 Tf 3.59985 2.15991 Td (;)Tj /R75 9.96264 Tf 12.7195 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td ( )Tj /R69 6.97385 Tf 6.4812 -1.43994 Td (2)Tj /R22 9.96264 Tf 4.43994 1.43994 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R69 6.97385 Tf 5.7644 4.08008 Td (2)Tj /R22 9.96264 Tf 4.44019 -4.08008 Td (\))Tj /R75 9.96264 Tf 3.83545 0 Td (j)Tj 5.6394 0 Td ()Tj /R72 9.96264 Tf 15.4851 6.71997 Td (h)Tj ET Q 340 391 13.3198 0.47998 re f q 1 0 0 1 0 0 cm BT /R75 9.96264 Tf 339.96 388.64 Td (p)Tj ET Q 348 389 5.03979 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 348.239 380.36 Td (2)Tj /R75 9.96264 Tf 6.12109 8.03979 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R69 6.97385 Tf 5.7605 4.08008 Td (2)Tj /R75 9.96264 Tf 4.43994 -4.08008 Td (j)Tj /R78 6.97385 Tf 2.76001 -2.15991 Td (W)Tj /R87 4.98132 Tf 8.52002 2.3999 Td (2)Tj -1.08008 -4.67993 Td (2)Tj /R69 6.97385 Tf 5.04004 2.28003 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (e)Tj /R84 4.98132 Tf 3.7229 -0.960205 Td (ij)Tj /R69 6.97385 Tf 6.35986 0.960205 Td (\))Tj /R72 9.96264 Tf 3.72021 2.15991 Td (:)Tj /R22 9.96264 Tf 32.6394 0 Td (\(4)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (5\))Tj -317.026 -22.0801 Td (Since)Tj /R72 9.96264 Tf 60.3599 -12.8398 Td (l)Tj /R22 9.96264 Tf 3.23853 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R69 6.97385 Tf 5.76611 4.07983 Td (2)Tj /R22 9.96264 Tf 4.32007 -4.07983 Td (\))Tj /R75 9.96264 Tf 6.59521 0 Td ()Tj 10.5505 0 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R69 6.97385 Tf 5.06494 4.07983 Td (2)Tj /R78 6.97385 Tf 8.04004 TL (C)' /R69 6.97385 Tf 6.2334 0 Td (\()Tj ET Q 247 355 6.83984 0.359863 re f q 1 0 0 1 0 0 cm BT /R78 6.97385 Tf 246.591 349.52 Td (D)Tj /R84 4.98132 Tf 6.48926 -0.959961 Td (T)Tj /R69 6.97385 Tf 5.52002 0.959961 Td (\))Tj /R72 9.96264 Tf 3.6001 3.96021 Td (;)Tj /R22 9.96264 Tf 12.7195 0 Td (0)Tj /R72 9.96264 Tf 5.03101 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (5)Tj /R75 9.96264 Tf 5.03101 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R78 6.97385 Tf 5.7793 4.7998 Td (j)Tj 7.55981 TL (i)' /R22 9.96264 Tf 6.36011 2.76001 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td (u)Tj /R78 6.97385 Tf 5.76929 4.7998 Td (j)Tj /R94 6.97385 Tf 3.5957 0 Td ( )Tj /R69 6.97385 Tf 6.23462 0 Td (2)Tj /R78 6.97385 Tf -9.83032 -7.55981 Td (i)Tj /R75 9.96264 Tf 14.28 2.76001 Td (j)Tj 5.51929 0 Td ()Tj 10.5505 0 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R78 6.97385 Tf 5.06079 -3 Td (C)Tj /R69 6.97385 Tf 6.2334 0 Td (\()Tj ET Q 374 356 6.83984 0.359863 re f q 1 0 0 1 0 0 cm BT /R78 6.97385 Tf 373.91 350.48 Td (D)Tj /R84 4.98132 Tf 6.4895 -0.960205 Td (T)Tj /R69 6.97385 Tf 5.52002 0.960205 Td (\))Tj /R72 9.96264 Tf 3.59985 3 Td (;)Tj /R22 9.96264 Tf -262.8 -16.5601 Td (w)Tj 6.95288 0 Td (e)Tj 7.67334 0 Td (ha)Tj 10.3103 0 Td (v)Tj 5.03003 0 Td (e)Tj /R75 9.96264 Tf 28.2334 -12.72 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td ( )Tj /R69 6.97385 Tf 6.48047 -1.43994 Td (3)Tj /R22 9.96264 Tf 4.56006 1.43994 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj /R75 9.96264 Tf 3.83545 0 Td (j)Tj 5.51929 0 Td ()Tj 10.4307 0 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R78 6.97385 Tf 5.07153 -3 Td (C)Tj /R69 6.97385 Tf 6.2334 0 Td (\()Tj ET Q 253 327 6.83984 0.359863 re f q 1 0 0 1 0 0 cm BT /R78 6.97385 Tf 253.311 321.2 Td (D)Tj /R84 4.98132 Tf 6.60938 -0.959961 Td (T)Tj /R69 6.97385 Tf 5.52002 0.959961 Td (\))Tj /R81 9.96264 Tf 3.59985 11.04 Td ( )Tj /R75 9.96264 Tf 4.56006 -8.04004 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td ( )Tj /R69 6.97385 Tf 6.48047 -1.43994 Td (1)Tj /R22 9.96264 Tf 4.43994 1.43994 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj /R75 9.96264 Tf 3.83545 0 Td (j)Tj 4.43945 0 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R78 6.97385 Tf 5.06201 -3 Td (C)Tj /R69 6.97385 Tf 6.2334 0 Td (\()Tj ET Q 330 327 6.83984 0.359863 re f q 1 0 0 1 0 0 cm BT /R78 6.97385 Tf 330.35 321.2 Td (D)Tj /R84 4.98132 Tf 6.4895 -0.959961 Td (T)Tj /R69 6.97385 Tf 5.52002 0.959961 Td (\))Tj /R22 9.96264 Tf 5.88013 3 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td ( )Tj /R69 6.97385 Tf 6.48926 -1.43994 Td (2)Tj /R22 9.96264 Tf 4.43994 1.43994 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R69 6.97385 Tf 5.76465 4.07983 Td (2)Tj /R22 9.96264 Tf 4.43994 -4.07983 Td (\))Tj /R81 9.96264 Tf 3.83984 8.04004 Td ()Tj /R72 9.96264 Tf 4.68018 -8.04004 Td (:)Tj /R22 9.96264 Tf -264.96 -16.2 Td (Therefore)Tj 45.0725 0 Td (from)Tj 23.5039 0 Td (\(4.3\))Tj 23.8528 0 Td (it)Tj 9.95508 0 Td (follo)Tj 18.3403 0 Td (ws)Tj /R75 9.96264 Tf -95.4048 -22.2002 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td ( )Tj /R69 6.97385 Tf 6.48047 -1.43994 Td (3)Tj /R22 9.96264 Tf 4.56006 1.43994 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj /R75 9.96264 Tf 3.83545 0 Td (j)Tj 5.51929 0 Td ()Tj /R72 9.96264 Tf 15.4915 6.84009 Td (h)Tj ET Q 197 288 13.3198 0.47998 re f q 1 0 0 1 0 0 cm BT /R75 9.96264 Tf 196.56 286.16 Td (p)Tj ET Q 205 286 5.03979 0.47998 re f q 1 0 0 1 0 0 cm BT /R22 9.96264 Tf 204.839 277.88 Td (2)Tj /R75 9.96264 Tf 7.80127 7.91968 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R78 6.97385 Tf 5.05078 -3 Td (C)Tj /R69 6.97385 Tf 6.2334 0 Td (\()Tj ET Q 238 289 6.83984 0.359863 re f q 1 0 0 1 0 0 cm BT /R78 6.97385 Tf 237.831 282.8 Td (D)Tj /R84 4.98132 Tf 6.48926 -0.959961 Td (T)Tj /R69 6.97385 Tf 5.52002 0.959961 Td (\))Tj /R81 9.96264 Tf 3.6001 14.1602 Td ()Tj /R75 9.96264 Tf 6 -11.1602 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R78 6.97385 Tf 5.05054 -3 Td (C)Tj /R69 6.97385 Tf 6.2334 0 Td (\()Tj ET Q 285 289 6.83984 0.359863 re f q 1 0 0 1 0 0 cm BT /R78 6.97385 Tf 284.63 282.8 Td (D)Tj /R84 4.98132 Tf 6.4895 -0.959961 Td (T)Tj /R69 6.97385 Tf 5.52002 0.959961 Td (\))Tj /R75 9.96264 Tf 3.6001 3 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R78 6.97385 Tf 2.76196 -2.15991 Td (W)Tj /R87 4.98132 Tf 8.52002 2.3999 Td (2)Tj -1.07983 -4.55981 Td (2)Tj /R69 6.97385 Tf 5.03979 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (e)Tj /R84 4.98132 Tf 3.7229 -0.959961 Td (ij)Tj /R69 6.97385 Tf 6.36011 0.959961 Td (\))Tj /R22 9.96264 Tf 5.87988 2.15991 Td (+)Tj /R75 9.96264 Tf 9.95068 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R69 6.97385 Tf 5.76978 4.2002 Td (2)Tj /R75 9.96264 Tf 4.43994 -4.2002 Td (j)Tj /R78 6.97385 Tf 2.76001 -2.15991 Td (W)Tj /R87 4.98132 Tf 8.52002 2.3999 Td (2)Tj -1.07983 -4.55981 Td (2)Tj /R69 6.97385 Tf 4.91992 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (e)Tj /R84 4.98132 Tf 3.7229 -0.959961 Td (ij)Tj /R69 6.97385 Tf 6.47998 0.959961 Td (\))Tj /R81 9.96264 Tf 3.59985 13.3201 Td ()Tj /R72 9.96264 Tf 6 -11.1602 Td (:)Tj /R22 9.96264 Tf 28.0793 0 Td (\(4)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (6\))Tj -305.146 -22.2 Td (It)Tj 10.792 0 Td (can)Tj 18.2236 0 Td (b)Tj 5.75928 0 Td (e)Tj 7.79321 0 Td (sho)Tj 14.2654 0 Td (wn)Tj 15.9521 0 Td (that)Tj /R81 9.96264 Tf -14.5857 -8.3999 Td ()Tj 6 TL ()' /R72 9.96264 Tf 3.23999 -2.52002 Td (l)Tj /R22 9.96264 Tf 3.23853 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R69 6.97385 Tf 5.76611 4.08008 Td (3)Tj /R22 9.96264 Tf 4.43994 -4.08008 Td (\))Tj /R75 9.96264 Tf 6.11523 0 Td ( )Tj /R72 9.96264 Tf 9.95068 0 Td (l)Tj /R22 9.96264 Tf 3.23853 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj /R72 9.96264 Tf 3.83545 0 Td (l)Tj /R22 9.96264 Tf 3.23853 0 Td (\()Tj /R72 9.96264 Tf 3.83545 0 Td (u)Tj /R69 6.97385 Tf 5.79248 4.08008 Td (2)Tj /R22 9.96264 Tf 4.32007 -4.08008 Td (\))Tj /R81 9.96264 Tf 3.83984 8.52002 Td ()Tj ()' /R75 9.96264 Tf 6.12012 -2.52002 Td ()Tj /R22 9.96264 Tf 10.4307 0 Td (4)Tj /R72 9.96264 Tf 5.03101 0 Td (h)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R69 6.97385 Tf 2.78223 4.08008 Td (2)Tj /R78 6.97385 Tf 7.2002 TL (W)' /R87 4.98132 Tf 8.52002 2.40015 Td (1)Tj -1.08008 -4.56006 Td (4)Tj /R69 6.97385 Tf 4.91992 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (e)Tj /R84 4.98132 Tf 3.7229 -0.959961 Td (ij)Tj /R69 6.97385 Tf 6.47998 0.959961 Td (\))Tj /R75 9.96264 Tf 3.59985 3.12012 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R78 6.97385 Tf 5.05078 -3 Td (C)Tj /R69 6.97385 Tf 6.2334 0 Td (\()Tj ET Q 364 249 6.83984 0.359863 re f q 1 0 0 1 0 0 cm BT /R78 6.97385 Tf 364.19 243.68 Td (D)Tj /R84 4.98132 Tf 6.4895 -0.959961 Td (T)Tj /R69 6.97385 Tf 5.52002 0.959961 Td (\))Tj /R72 9.96264 Tf 3.59985 3 Td (:)Tj /R22 9.96264 Tf 52.3193 0 Td (\(4)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (7\))Tj -305.146 -18.72 Td (According)Tj 47.3545 0 Td (to)Tj 12.1067 0 Td (the)Tj 17.1479 0 Td (estimates)Tj 43.8777 0 Td (\(4.5\),)Tj 26.4927 0 Td (\(4.6\),)Tj 26.4927 0 Td (\(4.7\))Tj 23.8528 0 Td (from)Tj 23.5039 0 Td (\(4.4\),)Tj 26.4927 0 Td (w)Tj 6.95288 0 Td (e)Tj 7.79321 0 Td (obtain)Tj /R75 9.96264 Tf -222.588 -20.04 Td (j)Tj /R22 9.96264 Tf 2.75952 0 Td (\()Tj /R75 9.96264 Tf 3.83545 0 Td (L)Tj /R72 9.96264 Tf 6.83423 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj /R78 6.97385 Tf 3.85254 4.80005 Td (j)Tj 7.56006 TL (i)' /R75 9.96264 Tf 4.32007 2.76001 Td (j)Tj 5.51929 0 Td ()Tj /R72 9.96264 Tf 10.5505 0 Td (c)Tj /R69 6.97385 Tf 4.33008 -1.43994 Td (2)Tj /R72 9.96264 Tf 4.43994 1.43994 Td (h)Tj /R81 9.96264 Tf 5.76001 11.1599 Td ()Tj /R75 9.96264 Tf 5.88013 -11.1599 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R78 6.97385 Tf 2.76221 -2.15991 Td (W)Tj /R87 4.98132 Tf 8.52002 2.3999 Td (2)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 5.04004 2.16016 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (e)Tj /R84 4.98132 Tf 3.72266 -0.960205 Td (ij)Tj /R69 6.97385 Tf 6.36011 0.960205 Td (\))Tj /R22 9.96264 Tf 5.87988 2.15991 Td (+)Tj /R75 9.96264 Tf 9.95068 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R69 6.97385 Tf 2.77148 4.19995 Td (2)Tj /R78 6.97385 Tf 7.19995 TL (W)' /R87 4.98132 Tf 8.52002 2.3999 Td (1)Tj -1.07983 -4.55981 Td (4)Tj /R69 6.97385 Tf 4.91992 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (e)Tj /R84 4.98132 Tf 3.7229 -0.959961 Td (ij)Tj /R69 6.97385 Tf 6.47998 0.959961 Td (\))Tj /R22 9.96264 Tf 5.76001 3 Td (+)Tj /R75 9.96264 Tf 9.95068 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R69 6.97385 Tf 5.76978 4.19995 Td (2)Tj /R75 9.96264 Tf 4.43994 -4.19995 Td (j)Tj /R78 6.97385 Tf 2.76001 -2.15991 Td (W)Tj /R87 4.98132 Tf 8.52002 2.3999 Td (2)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 5.04004 2.16016 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (e)Tj /R84 4.98132 Tf 3.7229 -0.960205 Td (ij)Tj /R69 6.97385 Tf 6.47998 0.960205 Td (\))Tj /R81 9.96264 Tf 3.59985 13.3198 Td ()Tj /R72 9.96264 Tf 5.88013 -11.1599 Td (;)Tj /R22 9.96264 Tf -271.68 -20.52 Td (where)Tj /R72 9.96264 Tf 28.7742 0 Td (c)Tj /R69 6.97385 Tf 4.3457 -1.43994 Td (2)Tj /R22 9.96264 Tf 7.19995 1.43994 Td (:=)Tj /R72 9.96264 Tf 13.3101 0 Td (m)Tj /R69 6.97385 Tf 8.77002 3.6001 Td (2)Tj /R22 9.96264 Tf 6.6001 -3.6001 Td (+)Tj /R72 9.96264 Tf 9.95068 0 Td ()Tj /R69 6.97385 Tf 10.5693 3.6001 Td (2)Tj /R22 9.96264 Tf 6.71997 -3.6001 Td (+)Tj 9.95068 0 Td (4)Tj /R72 9.96264 Tf 5.03101 0 Td ()Tj /R22 9.96264 Tf 13.9116 0 Td (and)Tj /R72 9.96264 Tf 19.3096 0 Td ()Tj /R22 9.96264 Tf 8.15332 0 Td (is)Tj 10.0745 0 Td (dened)Tj 34.3037 0 Td (in)Tj 11.6387 0 Td (Lemma)Tj 35.4988 0 Td (3.4.)Tj ET Q Q Q endstream endobj 121 0 obj 26445 endobj 124 0 obj <> stream q 1 0 0 1 0 0 cm q q 1 0 0 1 0 0 cm BT /R63 6.97385 Tf 126.72 739.88 Td (Klein{Gor)Tj 37.1663 0 Td (don)Tj 15.95 0 Td (Equation)Tj /R69 6.97385 Tf 260.85 0 Td (131)Tj /R22 9.96264 Tf -302.086 -23.8799 Td (Therefore)Tj /R75 9.96264 Tf 0.840088 -18.4802 Td (kL)Tj /R72 9.96264 Tf 11.8655 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R69 6.97385 Tf 5.05615 4.08008 Td (2)Tj /R78 6.97385 Tf 6.59985 TL (Q)' /R84 4.98132 Tf 6.23999 -0.960205 Td (s)Tj /R22 9.96264 Tf 6.95996 3.47998 Td (=)Tj /R72 9.96264 Tf 10.5505 0 Td (h)Tj /R69 6.97385 Tf 5.76953 4.08008 Td (2)Tj /R81 9.96264 Tf 6.11987 5.40015 Td (X)Tj /R78 6.97385 Tf 2.04004 -21.3601 Td (Q)Tj /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R22 9.96264 Tf 6 12.8398 Td (\()Tj /R75 9.96264 Tf 3.83545 0 Td (L)Tj /R72 9.96264 Tf 6.83423 0 Td (u)Tj /R22 9.96264 Tf 5.7583 0 Td (\))Tj /R69 6.97385 Tf 3.85205 4.08008 Td (2)Tj /R75 9.96264 Tf 7.32007 -4.08008 Td ()Tj /R22 9.96264 Tf 10.5505 0 Td (3)Tj /R72 9.96264 Tf 5.03101 0 Td (c)Tj /R69 6.97385 Tf 4.33838 4.08008 Td (2)Tj (2)' /R72 9.96264 Tf 4.32007 2.51978 Td (h)Tj /R69 6.97385 Tf 5.76001 4.08008 Td (4)Tj /R81 9.96264 Tf 4.43994 6.95996 Td ()Tj /R75 9.96264 Tf 6 -11.04 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R69 6.97385 Tf 2.76221 4.08008 Td (4)Tj /R78 6.97385 Tf 7.19995 TL (W)' /R87 4.98132 Tf 8.52002 2.3999 Td (1)Tj -1.08008 -4.55981 Td (4)Tj /R69 6.97385 Tf 4.92017 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (D)Tj /R84 4.98132 Tf 6.48267 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.95996 0.959961 Td (\))Tj /R22 9.96264 Tf 5.76001 3.11987 Td (+)Tj /R75 9.96264 Tf 9.95068 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R69 6.97385 Tf 2.77148 4.08008 Td (2)Tj /R78 6.97385 Tf (W)' /R87 4.98132 Tf 8.52002 2.3999 Td (2)Tj -1.07983 -4.55981 Td (2)Tj /R69 6.97385 Tf 5.03979 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (D)Tj /R84 4.98132 Tf 6.48291 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.84009 0.959961 Td (\))Tj /R22 9.96264 Tf 5.76001 3.11987 Td (+)Tj /R75 9.96264 Tf 9.95068 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R69 6.97385 Tf 5.76978 4.08008 Td (2)Tj /R75 9.96264 Tf 4.43994 -4.08008 Td (j)Tj /R69 6.97385 Tf 2.76001 4.08008 Td (2)Tj /R78 6.97385 Tf (W)' /R87 4.98132 Tf 8.52002 2.3999 Td (2)Tj -1.08008 -4.55981 Td (2)Tj /R69 6.97385 Tf 5.04004 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (D)Tj /R84 4.98132 Tf 6.48291 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.83984 0.959961 Td (\))Tj /R81 9.96264 Tf 3.6001 14.1599 Td ()Tj /R72 9.96264 Tf 6 -11.04 Td (;)Tj /R22 9.96264 Tf -310.44 -28.2 Td (i.e.,)Tj 18.7119 0 Td (as)Tj 12.2261 0 Td (w)Tj 6.95288 0 Td (e)Tj 7.79321 0 Td (note)Tj 22.0593 0 Td (that)Tj /R75 9.96264 Tf 3.77661 -20.3999 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R69 6.97385 Tf 5.76025 4.08008 Td (2)Tj /R75 9.96264 Tf 4.44019 -4.08008 Td (j)Tj /R69 6.97385 Tf 2.76001 4.08008 Td (2)Tj /R78 6.97385 Tf (W)' /R87 4.98132 Tf 8.52002 2.40015 Td (2)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 5.04004 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (D)Tj /R84 4.98132 Tf 6.48267 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.84009 0.959961 Td (\))Tj /R75 9.96264 Tf 6.36011 3.12012 Td ()Tj /R22 9.96264 Tf 10.5505 0 Td (8)Tj /R81 9.96264 Tf 5.04932 11.04 Td ()Tj /R72 9.96264 Tf 5.88013 -11.04 Td ()Tj /R69 6.97385 Tf 4.7998 4.08008 Td (2)Tj /R75 9.96264 Tf 6.12012 -4.08008 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R69 6.97385 Tf 2.76221 4.08008 Td (2)Tj /R78 6.97385 Tf (W)' /R87 4.98132 Tf 8.52002 2.40015 Td (2)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 4.91992 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (D)Tj /R84 4.98132 Tf 6.48291 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.95996 0.959961 Td (\))Tj /R22 9.96264 Tf 5.76001 3.12012 Td (+)Tj /R75 9.96264 Tf 9.95068 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R69 6.97385 Tf 2.77148 4.08008 Td (4)Tj /R78 6.97385 Tf (W)' /R87 4.98132 Tf 8.52002 2.40015 Td (1)Tj -1.08008 -4.56006 Td (4)Tj /R69 6.97385 Tf 5.04004 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (D)Tj /R84 4.98132 Tf 6.48291 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.83984 0.959961 Td (\))Tj /R81 9.96264 Tf 3.6001 14.1602 Td ()Tj /R72 9.96264 Tf 6 -11.04 Td (;)Tj /R22 9.96264 Tf -251.64 -20.52 Td (w)Tj 6.95288 0 Td (e)Tj 7.67334 0 Td (ha)Tj 10.3103 0 Td (v)Tj 5.03003 0 Td (e)Tj /R75 9.96264 Tf 21.5134 -18.48 Td (kL)Tj /R72 9.96264 Tf 11.8655 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (k)Tj /R69 6.97385 Tf 5.05615 4.19995 Td (2)Tj /R78 6.97385 Tf 6.6001 TL (Q)' /R84 4.98132 Tf 6.23999 -0.959961 Td (s)Tj /R75 9.96264 Tf 6.95996 3.36011 Td ()Tj /R22 9.96264 Tf 10.5505 0 Td (3)Tj /R72 9.96264 Tf 5.03101 0 Td (c)Tj /R69 6.97385 Tf 4.33838 4.19995 Td (2)Tj (2)' /R72 9.96264 Tf 4.44019 2.40015 Td (h)Tj /R69 6.97385 Tf 5.76001 4.19995 Td (4)Tj /R81 9.96264 Tf 4.43994 6.84009 Td ()Tj /R22 9.96264 Tf 5.87988 -11.04 Td (9)Tj /R75 9.96264 Tf 5.03101 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R69 6.97385 Tf 2.77124 4.19995 Td (4)Tj /R78 6.97385 Tf 7.32007 TL (W)' /R87 4.98132 Tf 8.52002 2.40015 Td (1)Tj -1.08008 -4.56006 Td (4)Tj /R69 6.97385 Tf 4.92017 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (D)Tj /R84 4.98132 Tf 6.48267 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.84009 0.959961 Td (\))Tj /R22 9.96264 Tf 5.87988 3.12012 Td (+)Tj 9.95068 0 Td (\(1)Tj 11.0266 0 Td (+)Tj 9.95068 0 Td (8)Tj /R72 9.96264 Tf 5.03101 0 Td ()Tj /R69 6.97385 Tf 4.84106 4.19995 Td (2)Tj /R22 9.96264 Tf 4.43994 -4.19995 Td (\))Tj /R75 9.96264 Tf 3.83545 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (u)Tj /R75 9.96264 Tf 5.7583 0 Td (j)Tj /R69 6.97385 Tf 2.76685 4.19995 Td (2)Tj /R78 6.97385 Tf (W)' /R87 4.98132 Tf 8.52002 2.40015 Td (2)Tj -1.08008 -4.56006 Td (2)Tj /R69 6.97385 Tf 5.04004 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (D)Tj /R84 4.98132 Tf 6.48291 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.83984 0.959961 Td (\))Tj /R81 9.96264 Tf 3.6001 14.1602 Td ()Tj /R72 9.96264 Tf 6 -11.04 Td (:)Tj /R22 9.96264 Tf 33.7195 0 Td (\(4)Tj /R72 9.96264 Tf 8.8667 0 Td (:)Tj /R22 9.96264 Tf 2.75952 0 Td (8\))Tj -317.026 -21.6001 Td (Since)Tj /R72 9.96264 Tf 26.5046 0 Td (W)Tj /R69 6.97385 Tf 10.8152 3.6001 Td (2)Tj -1.43994 -6.12012 Td (2)Tj /R75 9.96264 Tf 9.71997 2.52002 Td ()Tj /R72 9.96264 Tf 11.5107 0 Td (W)Tj /R69 6.97385 Tf 10.8093 3.6001 Td (1)Tj -1.43994 -6.12012 Td (4)Tj /R22 9.96264 Tf 5.87988 2.52002 Td (,)Tj 6.83936 0 Td (then)Tj 23.2673 0 Td (from)Tj 24.2239 0 Td (\(4.8\))Tj 24.3328 0 Td (follo)Tj 18.3403 0 Td (ws)Tj 14.988 0 Td (the)Tj 17.748 0 Td (v)Tj 4.67017 0 Td (alidit)Tj 22.4248 0 Td (y)Tj 9.10986 0 Td (of)Tj 11.9897 0 Td (the)Tj 17.748 0 Td (rst)Tj 21.105 0 Td (estimate)Tj -289.147 -12 Td (in)Tj 11.3987 0 Td (\(2.7\).)Tj 27.5725 0 Td (The)Tj 20.2654 0 Td (v)Tj 4.67017 0 Td (alidit)Tj 22.4248 0 Td (y)Tj 8.38989 0 Td (of)Tj 11.1497 0 Td (the)Tj 16.908 0 Td (second)Tj 31.8914 0 Td (estimate)Tj 39.6826 0 Td (in)Tj 11.5188 0 Td (\(2.7\))Tj 23.4927 0 Td (can)Tj 18.1035 0 Td (b)Tj 5.75928 0 Td (e)Tj 7.55322 0 Td (easily)Tj 27.2087 0 Td (obtained)Tj -287.989 -11.8799 Td (using)Tj /R75 9.96264 Tf 26.0244 0 Td (k)Tj /R72 9.96264 Tf 5.03101 0 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (k)Tj /R69 6.97385 Tf 5.07031 3.59985 Td (2)Tj /R78 6.97385 Tf 6.83984 TL (C)' /R69 6.97385 Tf 6.2334 0 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R84 4.98132 Tf 4.20947 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.59985 0.959961 Td (\))Tj /R75 9.96264 Tf 6.36011 3.23999 Td ()Tj /R22 9.96264 Tf 10.5505 0 Td (2)Tj /R72 9.96264 Tf 5.03101 0 Td (sh)Tj /R75 9.96264 Tf 10.4307 0 Td (j)Tj /R72 9.96264 Tf 2.75952 0 Td (Z)Tj /R75 9.96264 Tf 7.5542 0 Td (j)Tj /R69 6.97385 Tf 2.79395 3.59985 Td (2)Tj /R78 6.97385 Tf 7.19995 TL (W)' /R87 4.98132 Tf 8.52002 2.40015 Td (1)Tj -1.07983 -4.56006 Td (2)Tj /R69 6.97385 Tf 4.91992 2.15991 Td (\()Tj /R78 6.97385 Tf 3.11719 0 Td (\r)Tj /R84 4.98132 Tf 4.20288 -0.959961 Td (s)Tj /R69 6.97385 Tf 3.71997 0.959961 Td (\))Tj /R22 9.96264 Tf 3.59985 3.6001 Td (,)Tj /R72 9.96264 Tf 6.11938 0 Td (s)Tj /R22 9.96264 Tf 7.43213 0 Td (=)Tj 10.5505 0 Td (3)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj /R22 9.96264 Tf 4.43945 0 Td (4)Tj /R72 9.96264 Tf 5.03101 0 Td (;)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj 4.43945 0 Td (:)Tj /R22 9.96264 Tf 4.19946 0 Td (.)Tj /R117 9.96264 Tf 128.759 0 Td ()Tj /R12 9.96264 Tf -199.641 -27.24 Td (A)Tj 7.91919 0 Td (ckno)Tj 24.4673 0 Td (wledgment)Tj /R22 9.96264 Tf -139.066 -17.8801 Td (This)Tj 23.627 0 Td (pap)Tj 16.3096 0 Td (er)Tj 12.4683 0 Td (has)Tj 18.5852 0 Td (b)Tj 5.75928 0 Td (een)Tj 18.4658 0 Td (supp)Tj 20.7529 0 Td (orted)Tj 26.9744 0 Td (b)Tj 5.2793 0 Td (y)Tj 9.34985 0 Td (GNSF)Tj 31.4177 0 Td (of)Tj 12.2297 0 Td (Georgia)Tj 37.8721 0 Td (\(pro)Tj 18.9409 0 Td (ject)Tj 19.7808 0 Td (ST06/3-)Tj -289.693 -12 Td (005\).)Tj /R12 9.96264 Tf 133.92 -34.6799 Td (References)Tj /R128 7.97011 Tf -129.72 -15.8401 Td (1.)Tj /R131 7.97011 Tf 10.791 0 Td (M.)Tj 13.1926 0 Td (Reed)Tj 23.0283 0 Td (and)Tj 17.5122 0 Td (B.)Tj 11.3914 0 Td (Simon)Tj /R128 7.97011 Tf 23.2646 0 Td (,)Tj 4.9187 0 Td (Metho)Tj 23.8552 0 Td (ds)Tj 10.7935 0 Td (of)Tj 9.3501 0 Td (mo)Tj 11.5095 0 Td (dern)Tj 19.0662 0 Td (mathematical)Tj 52.8677 0 Td (ph)Tj 9.1167 0 Td (ysics.)Tj 22.1819 0 Td (I)Tj 3.23657 0 Td (I.)Tj 8.03564 0 Td (F)Tj 4.79517 0 Td (ourier)Tj 24.2144 0 Td (anal-)Tj -292.321 -9.95996 Td (ysis,)Tj 18.4678 0 Td (self-adjoin)Tj 37.5222 0 Td (tness.)Tj /R134 7.97011 Tf 23.2578 0 Td (A)Tj 5.87207 0 Td (c)Tj 3.47314 0 Td (ademic)Tj 29.1416 0 Td (Pr)Tj 8.8689 0 Td (ess)Tj /R128 7.97011 Tf 13.783 0 Td ([)Tj /R134 7.97011 Tf 2.39893 0 Td (Har)Tj 13.7864 0 Td (c)Tj 3.47314 0 Td (ourt)Tj 18.3501 0 Td (Br)Tj 9.10791 0 Td (ac)Tj 7.79297 0 Td (e)Tj 6.83301 0 Td (Jovanovich,)Tj 46.772 0 Td (Publishers)Tj /R128 7.97011 Tf 37.8818 0 Td (])Tj /R134 7.97011 Tf 2.39893 0 Td (,)Tj 5.51782 0 Td (New)Tj -294.699 -10.0801 Td (Y)Tj 5.7522 0 Td (ork-L)Tj 19.8994 0 Td (ondon)Tj /R128 7.97011 Tf 22.5552 0 Td (,)Tj 5.27881 0 Td (1975.)Tj -64.2856 -9.95996 Td (2.)Tj /R131 7.97011 Tf 10.791 0 Td (A.)Tj 13.0779 0 Td (R.)Tj 12.8306 0 Td (Bishop,)Tj 33.3389 0 Td (J.)Tj 11.0374 0 Td (A.)Tj 13.0779 0 Td (Kr)Tj 11.3967 0 Td (umhansl,)Tj 39.9292 0 Td (and)Tj 18.7124 0 Td (S.)Tj 11.396 0 Td (E.)Tj 12.4722 0 Td (Tr)Tj 10.9106 0 Td (ullinger)Tj /R128 7.97011 Tf 34.7734 0 Td (,)Tj 6.23877 0 Td (Solitons)Tj 33.0906 0 Td (in)Tj 10.7974 0 Td (condensed)Tj -273.071 -9.95996 Td (matter:)Tj 31.0498 0 Td (a)Tj 7.07202 0 Td (paradigm.)Tj /R134 7.97011 Tf 39.9243 0 Td (Phys.)Tj 23.4993 0 Td (D)Tj /R137 7.97011 Tf 9.95947 0 Td (1)Tj /R128 7.97011 Tf 7.79736 0 Td (\(1980\),)Tj 28.6394 0 Td (No.)Tj 15.7031 0 Td (1,)Tj 9.35083 0 Td (1{44.)Tj -183.796 -9.95996 Td (3.)Tj /R131 7.97011 Tf 10.791 0 Td (M.)Tj 13.7927 0 Td (Fla)Tj 14.145 0 Td (to,)Tj 15.7139 0 Td (J.)Tj 10.3174 0 Td (C.)Tj 12.1108 0 Td (H.)Tj 12.478 0 Td (Simon,)Tj 29.0232 0 Td (and)Tj 18.1123 0 Td (E.)Tj 11.7522 0 Td (T)Tj 5.51245 0 Td (aflin)Tj /R128 7.97011 Tf 20.6265 0 Td (,)Tj 5.63892 0 Td (Asymptotic)Tj 45.9199 0 Td (completeness,)Tj 53.5874 0 Td (global)Tj 25.2932 0 Td (exis-)Tj -294.015 -9.95996 Td (tence)Tj 21.6963 0 Td (and)Tj 16.189 0 Td (the)Tj 14.1479 0 Td (infrared)Tj 31.4109 0 Td (problem)Tj 32.6147 0 Td (for)Tj 12.5857 0 Td (the)Tj 14.1479 0 Td (Maxw)Tj 22.2993 0 Td (ell-Dirac)Tj 33.9294 0 Td (equations.)Tj /R134 7.97011 Tf 39.804 0 Td (Mem.)Tj 23.9841 0 Td (A)Tj 6.11206 0 Td (mer.)Tj 19.9033 0 Td (Math.)Tj -288.825 -9.95996 Td (So)Tj 8.6377 0 Td (c.)Tj /R137 7.97011 Tf 9.47095 0 Td (127)Tj /R128 7.97011 Tf 17.5122 0 Td (\(1997\),)Tj 28.6394 0 Td (No.)Tj 15.7031 0 Td (606.)Tj -90.7634 -9.95996 Td (4.)Tj /R131 7.97011 Tf 10.791 0 Td (F.)Tj 11.2732 0 Td (J.)Tj 10.0771 0 Td (Alexander)Tj 47.019 0 Td (and)Tj 17.7522 0 Td (S.)Tj 10.4358 0 Td (Habib)Tj /R128 7.97011 Tf 23.1531 0 Td (,)Tj 5.03882 0 Td (Statistical)Tj 40.0369 0 Td (mec)Tj 14.2654 0 Td (hanics)Tj 26.0173 0 Td (of)Tj 9.71021 0 Td (kincs)Tj 21.4661 0 Td (in)Tj 9.95728 0 Td (1)Tj 6.11206 0 Td (+)Tj 8.39893 0 Td (1)Tj 7.19189 0 Td (dimensions.)Tj /R134 7.97011 Tf -267.896 -9.96021 Td (Phys.)Tj 23.4993 0 Td (R)Tj 5.75244 0 Td (ev.)Tj 13.5442 0 Td (L)Tj 4.91577 0 Td (ett.)Tj /R137 7.97011 Tf 15.1055 0 Td (71)Tj /R128 7.97011 Tf 12.5947 0 Td (\(1993\),)Tj 28.6394 0 Td (955{958.)Tj -114.851 -9.95996 Td (5.)Tj /R131 7.97011 Tf 10.791 0 Td (A.)Tj 12.1179 0 Td (Inoue)Tj /R128 7.97011 Tf 22.5474 0 Td (,)Tj 5.27881 0 Td (Sur)Tj /R140 7.97011 Tf 15.7119 0 Td ()Tj /R143 7.97011 Tf 6.59912 0 Td (u)Tj /R128 7.97011 Tf 6.8374 0 Td (+)Tj /R143 7.97011 Tf 8.51904 0 Td (u)Tj /R146 5.97758 Tf 4.95728 2.88013 Td (3)Tj /R128 7.97011 Tf 6.71997 -2.88013 Td (=)Tj /R143 7.97011 Tf 9.1189 0 Td (f)Tj /R128 7.97011 Tf 7.91235 0 Td (dans)Tj 19.9043 0 Td (un)Tj 12.3564 0 Td (domaine)Tj 33.9316 0 Td (noncylindrique.)Tj /R134 7.97011 Tf 59.8425 0 Td (J.)Tj 10.3174 0 Td (Math.)Tj 24.95 0 Td (A)Tj 6.11206 0 Td (nal.)Tj 17.1558 0 Td (Appl.)Tj /R137 7.97011 Tf -290.881 -9.95996 Td (46)Tj /R128 7.97011 Tf 12.5947 0 Td (\(1974\),)Tj 28.6394 0 Td (777{819.)Tj -52.0342 -10.3201 Td (6.)Tj /R131 7.97011 Tf 10.791 0 Td (K.)Tj 12.3572 0 Td (J)Tj 4.93164 0.719971 Td ()Tj -0.359863 -0.719971 Td (or)Tj 9.71509 0 Td (gens)Tj /R128 7.97011 Tf 18.1079 0 Td (,)Tj 6.25708 2.04004 Td ()Tj -1.08008 -2.04004 Td (Ub)Tj 11.2705 0 Td (er)Tj 10.0691 0 Td (die)Tj 13.6714 0 Td (nic)Tj 10.5515 0 Td (h)Tj 4.43823 0 Td (tlinearen)Tj 35.4863 0 Td (W)Tj 7.91943 0 Td (ellengleic)Tj 33.083 0 Td (h)Tj 4.43823 0 Td (ungen)Tj 25.0615 0 Td (der)Tj 14.7476 0 Td (mathematisc)Tj 46.6321 0 Td (hen)Tj 16.1907 0 Td (Ph)Tj 10.1929 0 Td (ysik.)Tj /R134 7.97011 Tf -293.672 -9.95996 Td (Math.)Tj 24.95 0 Td (A)Tj 6.11206 0 Td (nn.)Tj /R137 7.97011 Tf 14.9937 0 Td (138)Tj /R128 7.97011 Tf 17.5122 0 Td (\(1959\),)Tj 28.6394 0 Td (179{202.)Tj -103.007 -9.95996 Td (7.)Tj /R131 7.97011 Tf 10.791 0 Td (H.)Tj 11.9978 0 Td (Lindblad)Tj 39.2158 0 Td (and)Tj 17.7522 0 Td (A.)Tj 11.9978 0 Td (Soffer)Tj /R128 7.97011 Tf 27.8315 0 Td (,)Tj 5.03882 0 Td (A)Tj 9.11182 0 Td (remark)Tj 28.8936 0 Td (on)Tj 11.7505 0 Td (asymptotic)Tj 43.5198 0 Td (completeness)Tj 50.8284 0 Td (for)Tj 12.8257 0 Td (the)Tj 14.5081 0 Td (critical)Tj -285.263 -9.95996 Td (nonlinear)Tj 37.1672 0 Td (Klein-Gordon)Tj 53.1228 0 Td (equation.)Tj /R134 7.97011 Tf 36.9285 0 Td (L)Tj 4.91577 0 Td (ett.)Tj 15.3455 0 Td (Math.)Tj 24.8298 0 Td (Phys.)Tj /R137 7.97011 Tf 23.2593 0 Td (73)Tj /R128 7.97011 Tf 12.5947 0 Td (\(2005\),)Tj 28.6394 0 Td (No.)Tj 15.8232 0 Td (3,)Tj 9.35083 0 Td (249{258.)Tj -272.777 -9.95996 Td (8.)Tj /R131 7.97011 Tf 10.791 0 Td (J.)Tj 10.1973 0 Td (Sa)Tj 9.35498 0 Td (ther)Tj /R128 7.97011 Tf 18.8333 0 Td (,)Tj 5.27881 0 Td (The)Tj 17.6252 0 Td (existence)Tj 36.0842 0 Td (of)Tj 9.83008 0 Td (a)Tj 7.19189 0 Td (global)Tj 25.1731 0 Td (classical)Tj 32.6003 0 Td (solution)Tj 32.2505 0 Td (of)Tj 9.83008 0 Td (the)Tj 14.6279 0 Td (initial-b)Tj 29.498 0 Td (oundary)Tj 33.2144 0 Td (v)Tj 3.95923 0 Td (alue)Tj -295.54 -9.95996 Td (problem)Tj 32.9749 0 Td (for)Tj /R140 7.97011 Tf 12.8257 0 Td ()Tj /R143 7.97011 Tf 6.59912 0 Td (u)Tj /R128 7.97011 Tf 6.8374 0 Td (+)Tj /R143 7.97011 Tf 8.39893 0 Td (u)Tj /R146 5.97758 Tf 4.96387 2.76001 Td (3)Tj /R128 7.97011 Tf 6.47998 -2.76001 Td (=)Tj /R143 7.97011 Tf 8.99902 0 Td (f)Tj /R128 7.97011 Tf 4.91235 0 Td (.)Tj /R134 7.97011 Tf 5.15869 0 Td (A)Tj 6.11206 0 Td (r)Tj 3.1145 0 Td (ch.)Tj 14.0308 0 Td (R)Tj 5.75244 0 Td (ational)Tj 28.6726 0 Td (Me)Tj 11.1482 0 Td (ch.)Tj 14.0308 0 Td (A)Tj 6.11206 0 Td (nal.)Tj /R137 7.97011 Tf 16.7957 0 Td (22)Tj /R128 7.97011 Tf 12.5947 0 Td (\(1966\),)Tj 28.6394 0 Td (292{307.)Tj -255.953 -9.96021 Td (9.)Tj /R131 7.97011 Tf 10.791 0 Td (C.)Tj 11.6309 0 Td (W.)Tj 14.0374 0 Td (W)Tj 7.79907 0 Td (a)Tj 4.4375 0 Td (yne)Tj /R128 7.97011 Tf 14.2744 0 Td (,)Tj 4.9187 0 Td (P)Tj 5.5144 0 Td (erio)Tj 13.9006 0 Td (dic)Tj 13.4314 0 Td (and)Tj 16.189 0 Td (quasi-p)Tj 26.8601 0 Td (erio)Tj 13.9006 0 Td (dic)Tj 13.3113 0 Td (solutions)Tj 35.126 0 Td (of)Tj 9.3501 0 Td (nonlinear)Tj 36.9272 0 Td (w)Tj 5.87305 0 Td (a)Tj 3.95215 0 Td (v)Tj 4.19922 0 Td (e)Tj 6.35376 0 Td (equations)Tj 37.6448 0 Td (via)Tj -299.623 -9.95996 Td (KAM)Tj 23.5059 0 Td (theory)Tj 22.8953 0 Td (.)Tj /R134 7.97011 Tf 5.27881 0 Td (Comm.)Tj 30.2266 0 Td (Math.)Tj 24.8298 0 Td (Phys.)Tj /R137 7.97011 Tf 23.2593 0 Td (127)Tj /R128 7.97011 Tf 17.5122 0 Td (\(1990\),)Tj 28.6394 0 Td (No.)Tj 15.7031 0 Td (3,)Tj 9.47095 0 Td (479{528.)Tj -216.321 -9.95996 Td (10.)Tj /R131 7.97011 Tf 14.9834 0 Td (T.)Tj 12.1108 0 Td (Cazena)Tj 28.6577 0 Td (ve,)Tj 15.3552 0 Td (A.)Tj 12.3579 0 Td (Hara)Tj 20.9929 0 Td (ux,)Tj 15.5935 0 Td (L.)Tj 11.2742 0 Td (V)Tj 5.51953 0 Td (azquez,)Tj 33.2163 0 Td (and)Tj 18.1123 0 Td (F.)Tj 11.5132 0 Td (B.)Tj 12.1116 0 Td (Weissler)Tj /R128 7.97011 Tf 36.0964 0 Td (,)Tj 5.63892 0 Td (Nonlinear)Tj 39.2009 0 Td (eects)Tj 25.8909 0 Td (in)Tj -303.626 -9.95996 Td (the)Tj 14.6279 0 Td (w)Tj 5.87305 0 Td (a)Tj 3.95215 0 Td (v)Tj 4.19922 0 Td (e)Tj 6.59375 0 Td (equation)Tj 34.5293 0 Td (with)Tj 19.3062 0 Td (a)Tj 7.07202 0 Td (cubic)Tj 22.0637 0 Td (restoring)Tj 35.3579 0 Td (force.)Tj /R134 7.97011 Tf 22.7727 0 Td (Comput.)Tj 34.9045 0 Td (Me)Tj 11.1482 0 Td (ch.)Tj /R137 7.97011 Tf 13.7908 0 Td (5)Tj /R128 7.97011 Tf 7.67725 0 Td (\(1989\),)Tj 28.6394 0 Td (49{72.)Tj -287.508 -9.95996 Td (11.)Tj /R131 7.97011 Tf 14.9834 0 Td (B.)Tj 12.3516 0 Td (N.)Tj 12.5979 0 Td (Lu)Tj 13.9131 0 Td (and)Tj 18.3523 0 Td (S.)Tj 11.0359 0 Td (M.)Tj 14.0327 0 Td (F)Tj 4.6748 0 Td (ang)Tj /R128 7.97011 Tf 14.9917 0 Td (,)Tj 5.87891 0 Td (Con)Tj 14.7437 0 Td (v)Tj 4.19922 0 Td (ergence)Tj 30.8022 0 Td (on)Tj 12.3506 0 Td (nite)Tj 22.3057 0 Td (dierence)Tj 38.365 0 Td (solution)Tj 32.7305 0 Td (of)Tj 10.1902 0 Td (semilinear)Tj -273.499 -9.95996 Td (w)Tj 5.87305 0 Td (a)Tj 3.95215 0 Td (v)Tj 4.19922 0 Td (e)Tj 6.71362 0 Td (equation)Tj 34.5293 0 Td (in)Tj 9.83716 0 Td (one)Tj 15.4646 0 Td (space)Tj 22.6538 0 Td (v)Tj 3.95923 0 Td (ariable.)Tj /R134 7.97011 Tf 30.0891 0 Td (Chin.)Tj 23.627 0 Td (Q.)Tj 12.2371 0 Td (J.)Tj 10.1973 0 Td (Math.)Tj /R137 7.97011 Tf 24.71 0 Td (12)Tj /R128 7.97011 Tf 12.5947 0 Td (\(1997\),)Tj 28.6394 0 Td (35{40.)Tj -264.277 -9.96021 Td (12.)Tj /R131 7.97011 Tf 14.9834 0 Td (J.)Tj 9.71729 0 Td (K.)Tj 11.8772 0 Td (Perring)Tj 35.0222 0 Td (and)Tj 17.3923 0 Td (T.)Tj 11.5107 0 Td (H.)Tj 11.6379 0 Td (R.)Tj 11.5105 0 Td (Skyrme)Tj /R128 7.97011 Tf 30.103 0 Td (,)Tj 4.79883 0 Td (A)Tj 8.87183 0 Td (mo)Tj 11.5095 0 Td (del)Tj 13.1914 0 Td (unied)Tj 27.4666 0 Td (eld)Tj 17.9897 0 Td (equation.)Tj /R134 7.97011 Tf 36.4485 0 Td (Nucle)Tj 20.4973 0 Td (ar)Tj 10.7942 0 Td (Phys.)Tj /R137 7.97011 Tf -290.323 -9.95996 Td (31)Tj /R128 7.97011 Tf 12.5947 0 Td (\(1962\),)Tj 28.6394 0 Td (550{555.)Tj -56.2341 -9.95996 Td (13.)Tj /R131 7.97011 Tf 14.9834 0 Td (Y.)Tj 13.7979 0 Td (L.)Tj 12.5942 0 Td (Zhou)Tj /R128 7.97011 Tf 20.1484 0 Td (,)Tj 7.43872 0 Td (Applications)Tj 50.8342 0 Td (of)Tj 11.3901 0 Td (discrete)Tj 32.7261 0 Td (functional)Tj 41.4858 0 Td (analysis)Tj 33.5708 0 Td (to)Tj 11.9878 0 Td (the)Tj 16.3081 0 Td (nite)Tj 23.3857 0 Td (dierence)Tj -275.651 -9.95996 Td (metho)Tj 23.1379 0 Td (d.)Tj /R134 7.97011 Tf 9.95728 0 Td (International)Tj 51.9292 0 Td (A)Tj 5.87207 0 Td (c)Tj 3.47314 0 Td (ademic)Tj 29.3818 0 Td (Publishers,)Tj 43.6399 0 Td (Beijing)Tj /R128 7.97011 Tf 26.6121 0 Td (,)Tj 5.15869 0 Td (1991.)Tj ET Q Q Q endstream endobj 125 0 obj 19453 endobj 149 0 obj <> stream q 1 0 0 1 0 0 cm q q 1 0 0 1 0 0 cm BT /R69 6.97385 Tf 126.72 739.88 Td (132)Tj /R63 6.97385 Tf 68.1421 0 Td (G.)Tj 11.7505 0 Td (Berikelashvili,)Tj 53.8267 0 Td (O.)Tj 11.7517 0 Td (Jokhadze,)Tj 37.6526 0 Td (S.)Tj 10.071 0 Td (Kharib)Tj 24.1042 0 Td (e)Tj 3.47559 0 Td (gashvili,)Tj 32.1294 0 Td (and)Tj 16.0701 0 Td (B.)Tj 11.2705 0 Td (Mido)Tj 17.8696 0 Td (dashvili)Tj /R128 7.97011 Tf -298.114 -23.8799 Td (14.)Tj /R131 7.97011 Tf 14.9834 0 Td (O.)Tj 11.9971 0 Td (G.)Tj 12.1165 0 Td (Goman)Tj /R128 7.97011 Tf 27.7041 0 Td (,)Tj 4.9187 0 Td (The)Tj 17.1453 0 Td (equation)Tj 34.2893 0 Td (of)Tj 9.3501 0 Td (a)Tj 6.83203 0 Td (re\rected)Tj 33.5642 0 Td (w)Tj 5.87305 0 Td (a)Tj 3.95215 0 Td (v)Tj 4.19922 0 Td (e.)Tj 8.75293 0 Td (\(Russian\))Tj /R134 7.97011 Tf 38.123 0 Td (V)Tj 5.7522 0 Td (estn.)Tj 20.3813 0 Td (Mosk.)Tj 24.9409 0 Td (Univ.,)Tj 25.7773 0 Td (Ser.)Tj -295.653 -9.96021 Td (I)Tj /R137 7.97011 Tf 6.11572 0 Td (23)Tj /R128 7.97011 Tf 12.5947 0 Td (\(1968\),)Tj 28.6394 0 Td (84{87.)Tj -62.3499 -9.95996 Td (15.)Tj /R131 7.97011 Tf 14.9834 0 Td (S.)Tj 9.83594 0 Td (D.)Tj 11.5176 0 Td (Tr)Tj 10.9106 0 Td (oitska)Tj 25.1836 0 Td (y)Tj 4.4375 0 Td (a)Tj /R128 7.97011 Tf 4.91748 0 Td (,)Tj 4.67871 0 Td (On)Tj 13.4375 0 Td (a)Tj 6.47192 0 Td (b)Tj 4.91821 0 Td (oundary)Tj 32.6145 0 Td (v)Tj 3.95923 0 Td (alue)Tj 17.2634 0 Td (problem)Tj 32.3748 0 Td (for)Tj 12.3457 0 Td (h)Tj 4.43823 0 Td (yp)Tj 9.35767 0 Td (erb)Tj 11.9878 0 Td (olic)Tj 14.9841 0 Td (equations.)Tj 39.564 0 Td (\(Russian\))Tj /R134 7.97011 Tf -275.182 -9.95996 Td (Izv.)Tj 17.1418 0 Td (R)Tj 5.75244 0 Td (oss.)Tj 17.8677 0 Td (A)Tj 6.11206 0 Td (kad.)Tj 19.0706 0 Td (Nauk)Tj 23.0237 0 Td (Ser.)Tj 18.8235 0 Td (Mat.)Tj /R137 7.97011 Tf 21.1101 0 Td (62)Tj /R128 7.97011 Tf 13.4348 0 Td (\(1998\),)Tj 29.7195 0 Td (No.)Tj 16.5432 0 Td (2,)Tj 10.4309 0 Td (193{224;)Tj 35.9448 0 Td (English)Tj 31.0569 0 Td (transl.:)Tj /R134 7.97011 Tf 31.2942 0 Td (Izv.)Tj -297.326 -9.95996 Td (Math.)Tj /R137 7.97011 Tf 24.71 0 Td (62)Tj /R128 7.97011 Tf 12.5947 0 Td (\(1998\),)Tj 28.6394 0 Td (No.)Tj 15.7031 0 Td (2,)Tj 9.47095 0 Td (399{428.)Tj -106.118 -9.95996 Td (16.)Tj /R131 7.97011 Tf 14.9834 0 Td (G.)Tj 11.9966 0 Td (K.)Tj 11.9971 0 Td (Berikelashvili,)Tj 63.9148 0 Td (O.)Tj 11.8772 0 Td (M.)Tj 13.1926 0 Td (Jokhadze,)Tj 43.0566 0 Td (S.)Tj 10.0759 0 Td (S.)Tj 10.1958 0 Td (Kharibegashvili,)Tj 70.2815 0 Td (and)Tj 17.5122 0 Td (B.)Tj 11.2715 0 Td (G.)Tj 12.1165 0 Td (Mido-)Tj -287.472 -9.95996 Td (d)Tj 4.79761 0 Td (ashvili)Tj /R128 7.97011 Tf 27.2178 0 Td (,)Tj 5.03882 0 Td (On)Tj 14.0374 0 Td (the)Tj 14.5081 0 Td (existence)Tj 35.8442 0 Td (and)Tj 16.429 0 Td (nonexistence)Tj 49.5132 0 Td (of)Tj 9.59009 0 Td (global)Tj 24.813 0 Td (solutions)Tj 35.2458 0 Td (of)Tj 9.47021 0 Td (the)Tj 14.5081 0 Td (rst)Tj 17.3848 0 Td (Darb)Tj 18.9458 0 Td (oux)Tj -297.344 -9.96021 Td (problem)Tj 33.8149 0 Td (for)Tj 13.6658 0 Td (nonlinear)Tj 38.0073 0 Td (w)Tj 5.87305 0 Td (a)Tj 3.95215 0 Td (v)Tj 4.19922 0 Td (e)Tj 7.55371 0 Td (equations.)Tj 41.0042 0 Td (\(Russian\))Tj /R134 7.97011 Tf 39.0833 0 Td (Dier.)Tj 28.2996 0 Td (Ur)Tj 9.46655 0 Td (avn.)Tj /R137 7.97011 Tf 19.429 0 Td (44)Tj /R128 7.97011 Tf 13.4348 0 Td (\(2008\),)Tj 29.7195 0 Td (No.)Tj 16.5432 0 Td (3,)Tj -304.046 -9.95996 Td (359{372.)Tj /R22 9.96264 Tf 100.56 -37.6799 Td (\(Receiv)Tj 32.238 0 Td (ed)Tj 13.1926 0 Td (15.09.2008\))Tj -149.111 -23.8801 Td (Authors')Tj 41.3672 0 Td (addresses:)Tj -41.3672 -17.6399 Td (G.)Tj 13.9102 0 Td (Berik)Tj 23.2517 0 Td (elash)Tj 21.4585 0 Td (vili,)Tj 19.4287 0 Td (O.)Tj 13.7903 0 Td (Jokhadze,)Tj 46.2681 0 Td (S.)Tj 11.6387 0 Td (Kharib)Tj 30.8152 0 Td (egash)Tj 23.73 0 Td (vili)Tj -204.291 -11.8799 Td (A.)Tj 13.5515 0 Td (Razmadze)Tj 47.7131 0 Td (Mathematical)Tj 63.3047 0 Td (Institute)Tj -124.569 -12 Td (1,)Tj 11.0308 0 Td (M.)Tj 15.2351 0 Td (Aleksidze)Tj 44.356 0 Td (St.,)Tj 18.2339 0 Td (Tbilisi)Tj 31.0659 0 Td (0193)Tj -119.922 -12 Td (Georgia)Tj 11.8801 TL (E-mail:)' 36.1006 0 Td (b)Tj 5.75928 0 Td (ergi@rmi.acnet.ge)Tj -4.53979 -12 Td (o)Tj 5.63086 0 Td (jokhadze@y)Tj 51.0576 0 Td (aho)Tj 15.8215 0 Td (o.com)Tj -72.51 -12 Td (kharib@rmi.acnet.ge)Tj -37.3201 -17.52 Td (B.)Tj 13.1929 0 Td (Mido)Tj 22.6658 0 Td (dash)Tj 19.7849 0 Td (vili)Tj -55.6436 -12 Td (Gori)Tj 22.7766 0 Td (Univ)Tj 20.7412 0 Td (ersit)Tj 18.699 0 Td (y)Tj -62.2168 -12 Td (53,)Tj 16.0618 0 Td (Cha)Tj 17.5034 0 Td (v)Tj 5.03003 0 Td (c)Tj 4.19336 0 Td (ha)Tj 10.3103 0 Td (v)Tj 4.67017 0 Td (adze)Tj 22.4167 0 Td (St.,)Tj 18.2339 0 Td (Gori)Tj 22.7766 0 Td (1400)Tj -121.196 -11.8799 Td (Georgia)Tj ET Q Q Q endstream endobj 150 0 obj 4617 endobj 7 0 obj <> /Contents 8 0 R >> endobj 17 0 obj <> /Contents 18 0 R >> endobj 64 0 obj <> /Contents 65 0 R >> endobj 89 0 obj <> /Contents 90 0 R >> endobj 101 0 obj <> /Contents 102 0 R >> endobj 108 0 obj <> /Contents 109 0 R >> endobj 112 0 obj <> /Contents 113 0 R >> endobj 119 0 obj <> /Contents 120 0 R >> endobj 123 0 obj <> /Contents 124 0 R >> endobj 148 0 obj <> /Contents 149 0 R >> endobj 3 0 obj << /Type /Pages /Kids [ 7 0 R 17 0 R 64 0 R 89 0 R 101 0 R 108 0 R 112 0 R 119 0 R 123 0 R 148 0 R ] /Count 10 >> endobj 1 0 obj <> endobj 16 0 obj <> endobj 25 0 obj <>stream 0 0 0 0 7 6 d1 7 0 0 6 0 0 cm BI /IM true /W 7 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID 1QT]< EI endstream endobj 26 0 obj <>stream 0 0 0 3 4 9 d1 4 0 0 6 0 3 cm BI /IM true /W 4 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID ㇌ @ EI endstream endobj 27 0 obj <>stream 0 0 0 0 6 6 d1 6 0 0 6 0 0 cm BI /IM true /W 6 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID &Ep EI endstream endobj 28 0 obj <>stream 0 0 0 3 5 6 d1 5 0 0 3 0 3 cm BI /IM true /W 5 /H 3 /BPC 1 /D[1 0] /F/CCF /DP<> ID @ EI endstream endobj 29 0 obj <>stream 0 0 0 3 6 9 d1 6 0 0 6 0 3 cm BI /IM true /W 6 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID &~8 EI endstream endobj 30 0 obj <>stream 0 0 0 0 4 6 d1 4 0 0 6 0 0 cm BI /IM true /W 4 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID և @ EI endstream endobj 31 0 obj <>stream 0 0 0 4 3 6 d1 3 0 0 2 0 4 cm BI /IM true /W 3 /H 2 /BPC 1 /D[1 0] /F/CCF /DP<> ID P EI endstream endobj 32 0 obj <>stream 0 0 0 3 4 9 d1 4 0 0 6 0 3 cm BI /IM true /W 4 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID Vޠ EI endstream endobj 33 0 obj <>stream 0 0 0 3 5 9 d1 5 0 0 6 0 3 cm BI /IM true /W 5 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID &% EI endstream endobj 34 0 obj <>stream 0 0 0 0 4 6 d1 4 0 0 6 0 0 cm BI /IM true /W 4 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID V2kb EI endstream endobj 35 0 obj <>stream 0 0 0 0 7 6 d1 7 0 0 6 0 0 cm BI /IM true /W 7 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID /*+Rja` @ EI endstream endobj 36 0 obj <>stream 0 0 0 3 4 6 d1 4 0 0 3 0 3 cm BI /IM true /W 4 /H 3 /BPC 1 /D[1 0] /F/CCF /DP<> ID V0 EI endstream endobj 37 0 obj <>stream 0 0 0 3 4 6 d1 4 0 0 3 0 3 cm BI /IM true /W 4 /H 3 /BPC 1 /D[1 0] /F/CCF /DP<> ID V @ EI endstream endobj 38 0 obj <>stream 0 0 0 0 5 9 d1 5 0 0 9 0 0 cm BI /IM true /W 5 /H 9 /BPC 1 /D[1 0] /F/CCF /DP<> ID &]E J# EI endstream endobj 39 0 obj <>stream 0 0 0 3 6 9 d1 6 0 0 6 0 3 cm BI /IM true /W 6 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID &^QJ# EI endstream endobj 40 0 obj <>stream 0 0 0 3 4 9 d1 4 0 0 6 0 3 cm BI /IM true /W 4 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID VJ# EI endstream endobj 41 0 obj <>stream 0 0 0 3 7 6 d1 7 0 0 3 0 3 cm BI /IM true /W 7 /H 3 /BPC 1 /D[1 0] /F/CCF /DP<> ID /*+P EI endstream endobj 42 0 obj <>stream 0 0 0 0 4 6 d1 4 0 0 6 0 0 cm BI /IM true /W 4 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID &%=u @ EI endstream endobj 43 0 obj <>stream 0 0 0 0 4 6 d1 4 0 0 6 0 0 cm BI /IM true /W 4 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID 2kC EI endstream endobj 44 0 obj <>stream 0 0 0 0 4 9 d1 4 0 0 9 0 0 cm BI /IM true /W 4 /H 9 /BPC 1 /D[1 0] /F/CCF /DP<> ID UAb2k}@ @ EI endstream endobj 45 0 obj <>stream 0 0 0 0 4 6 d1 4 0 0 6 0 0 cm BI /IM true /W 4 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID 0\ EI endstream endobj 46 0 obj <>stream 0 0 0 3 4 9 d1 4 0 0 6 0 3 cm BI /IM true /W 4 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID UAb0 EI endstream endobj 47 0 obj <>stream 0 0 0 3 7 9 d1 7 0 0 6 0 3 cm BI /IM true /W 7 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID &js#P @ EI endstream endobj 48 0 obj <>stream 0 0 0 4 5 5 d1 5 0 0 1 0 4 cm BI /IM true /W 5 /H 1 /BPC 1 /D[1 0] /F/CCF /DP<> ID EI endstream endobj 49 0 obj <>stream 0 0 0 3 5 9 d1 5 0 0 6 0 3 cm BI /IM true /W 5 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID ;PZ EI endstream endobj 50 0 obj <>stream 0 0 0 3 7 9 d1 7 0 0 6 0 3 cm BI /IM true /W 7 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID &a(8ET @ EI endstream endobj 51 0 obj <>stream 0 0 0 1 7 9 d1 7 0 0 8 0 1 cm BI /IM true /W 7 /H 8 /BPC 1 /D[1 0] /F/CCF /DP<> ID &QOWp @ EI endstream endobj 52 0 obj <>stream 0 0 0 3 7 6 d1 7 0 0 3 0 3 cm BI /IM true /W 7 /H 3 /BPC 1 /D[1 0] /F/CCF /DP<> ID b* EI endstream endobj 53 0 obj <>stream 0 0 0 4 3 5 d1 3 0 0 1 0 4 cm BI /IM true /W 3 /H 1 /BPC 1 /D[1 0] /F/CCF /DP<> ID EI endstream endobj 54 0 obj <>stream 0 0 0 0 4 6 d1 4 0 0 6 0 0 cm BI /IM true /W 4 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID &%=u @ EI endstream endobj 55 0 obj <>stream 0 0 0 0 4 6 d1 4 0 0 6 0 0 cm BI /IM true /W 4 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID V EI endstream endobj 56 0 obj <>stream 0 0 0 3 6 9 d1 6 0 0 6 0 3 cm BI /IM true /W 6 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID &QN B EI endstream endobj 57 0 obj <>stream 0 0 0 0 5 6 d1 5 0 0 6 0 0 cm BI /IM true /W 5 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID &Kt EI endstream endobj 58 0 obj <>stream 0 0 0 5 2 6 d1 2 0 0 1 0 5 cm BI /IM true /W 2 /H 1 /BPC 1 /D[1 0] /F/CCF /DP<> ID @ @ EI endstream endobj 59 0 obj <>stream 0 0 0 0 5 6 d1 5 0 0 6 0 0 cm BI /IM true /W 5 /H 6 /BPC 1 /D[1 0] /F/CCF /DP<> ID & EI endstream endobj 60 0 obj <> endobj 88 0 obj <> endobj 95 0 obj <>stream Adobe d C $, !$4.763.22:ASF:=N>22HbINVX]^]8EfmeZlS[]Y C**Y;2;YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY " } !1AQa"q2#BR$3br %&'()*456789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz w !1AQaq"2B #3Rbr $4%&'()*56789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz ? c*BRinX`MH=_9RŚ\'U=G iy;HE*xdMRK[x"51*Кζ.|c<