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$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img982.gif">'; $key = q/{_inline}$hatN_2:(beta,0.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img869.gif">'; $key = q/{_inline}$hatS_7:(0.5,1.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img561.gif">'; $key = q/{_inline}$partialPHIoverpartialx${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img576.gif">'; $key = q/{_inline}$f^Gamma(2,x,S_12)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img296.gif">'; $key = q/{_inline}$gamma=9over80=0.11250${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img401.gif">'; $key = q/{_inline}$hatS_1:(0.,0.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img302.gif">'; $key = q/{_inline}$M_n${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img208.gif">'; $key = q/{_inline}$[P]omega_k${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img355.gif">'; $key = q/{_inline}$S_j${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img375.gif">'; $key = q/{figure}[htbp]centerframeboxinpute_fig511.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img198.gif">'; $key = q/{_inline}$displaystyleV_h={v_h,v_hinX_h,mboxtelquev_h=overlineumboxsurGamma_1}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img730.gif">'; $key = q/{_inline}$displaystyledisplaystyleV={v,quadvinH^1(Omega),quadv_|Gamma_0=u_0}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img33.gif">'; $key = q/{figure}[htbp]centerframeboxinpute_fig3r2d.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img461.gif">'; $key = q/{_inline}$overlineu_i${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img57.gif">'; $key = q/{_inline}$calRe(E_14)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img702.gif">'; $key = q/{_inline}$hatS_10:(1.,0.5,0.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img445.gif">'; $key = q/{_inline}$a=9-2sqrt15over21${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img468.gif">'; $key = q/{_inline}$displaystyle{u}_|T=left(arraycu_1(bx)u_2(bx)u_3(bx)arrayright)|_T=left(arraycP00arrayarrayc0P0arrayarrayc00Parrayright)left(arraycu_1Tu_2Tu_3Tarrayright)=[calP]{u_T}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img102.gif">'; $key = q/{_inline}$displaystyleleft.arrayldisplaystylea(w_h,v_h)=int_OmegaEe^3over12(1-nu^2)[nuDeltaw_hDeltav_hdisplaystylequadquadquad+(1-nu)(w_h,_11v_h,_11+2w_h,_12v_h,_12+w_h,_22v_h,_22)]dbxdisplaystylel(v_h)=int_Omegaf^Omegav_hdbxarrayright.${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img220.gif">'; $key = q/{_inline}$beta=0.223381589678011${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img619.gif">'; $key = q/{_inline}$C^E_11${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img978.gif">'; $key = q/{_inline}$gamma=0.0828510756183929${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img546.gif">'; $key = q/{_inline}$e_24${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img1012.gif">'; $key = q/{_inline}$E_33${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img408.gif">'; $key = q/{figure}[htbp]centerframeboxinputt_fig3q2c.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img848.gif">'; $key = q/{_inline}$partial^2PHIoverpartialy^2${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img579.gif">'; $key = q/{_inline}$rho_2,I_2,S_2${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img628.gif">'; $key = q/{_inline}$overlineu(i)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img862.gif">'; $key = q/{_inline}$T,P_T,Sigma_T${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img12.gif">'; $key = q/{_inline}$hatS_2:(1.,0.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img303.gif">'; $key = q/{_inline}$b_5${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img593.gif">'; $key = q/{_inline}$Gamma^e_1${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img940.gif">'; $key = q/{_inline}$b_1=1over2-1over2sqrt3${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img567.gif">'; $key = q/{_inline}$sigma_ij,k${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img943.gif">'; $key = q/{_inline}$beta=.095091634267285${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img570.gif">'; $key = q/{_inline}$a(.,.),b(.,.),l_X,l_V${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img224.gif">'; $key = q/{_inline}$2pir${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img638.gif">'; $key = q/{_inline}$calRe(u_2)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img674.gif">'; $key = q/{_inline}$Sigma_T={p(a_i),1leqileq3}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img18.gif">'; $key = q/{_inline}$calRe(E_23)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img692.gif">'; $key = q/{_inline}$displaystyleX=prod_TinT_hH(div;T)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img760.gif">'; $key = q/{_inline}$Gamma${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img30.gif">'; $key = q/{_inline}$R^3${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img41.gif">'; $key = q/{_inline}$c=155-sqrt15over2400=0.06296959${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img343.gif">'; $key = q/{_inline}$n=(n_1,n_2)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img207.gif">'; $key = q/{_inline}$b_k=S_k${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img565.gif">'; $key = q/{_inline}$hint_Omegadiv(uT_h)div(uw_h)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img921.gif">'; $key = q/{_inline}$sigma^0(i,j,k)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img315.gif">'; $key = q/{_inline}$C^E${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img967.gif">'; $key = q/{_inline}$e_12${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img1005.gif">'; $key = q/{_inline}$phi_i${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img10.gif">'; $key = q/{_inline}$e_33${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img986.gif">'; $key = q/{_inline}$D_i${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img953.gif">'; $key = q/{_inline}$gamma.beta${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img463.gif">'; $key = q/{_inline}$[B_T]${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img124.gif">'; $key = q/{_inline}$T_hinP_1${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img919.gif">'; $key = q/{_inline}$lambda_3${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img336.gif">'; $key = q/{_inline}$displaystyleDu_T=left(arraycdisplaystylepartialuoverpartialxdisplaystylepartialuoverpartialydisplaystylepartialuoverpartialzarrayright)=[DP]{u_T}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img780.gif">'; $key = q/{_inline}$hatS_4:(0.,1.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img358.gif">'; $key = q/{_inline}$e=10-2sqrt15over40=0.0563508${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img396.gif">'; $key = q/{_inline}$displaystyle[calP]=left(arraycP0arrayarrayc0Parrayright)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img146.gif">'; $key = q/{_inline}$phi_y${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img664.gif">'; $key = q/{_inline}$nuapprox1over2${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img718.gif">'; $key = q/{_inline}$a=1over3${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img858.gif">'; $key = q/{_inline}$hatN_2:(0.,a,a)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img855.gif">'; $key = q/{_inline}$int_Tf^Omegavdbx${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img94.gif">'; $key = q/{_inline}$partialwoverpartialt${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img214.gif">'; $key = q/{_inline}$displaystyleM^f^Gamma={mu,existsqinH(div;Omega),q.n=f^GammamboxsurGamma_0,mu=q.nforallTinT_h}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img755.gif">'; $key = q/{_inline}$calIm(k)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img932.gif">'; $key = q/{figure}[htbp]centerframeboxinpute_figmorp.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img617.gif">'; $key = q/{_inline}$b_2=0.5${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img351.gif">'; $key = q/{_inline}$s_ij=1over2(u_i,j+u_j,i)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img955.gif">'; $key = q/{_inline}$gamma${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img262.gif">'; $key = q/{_inline}$Sigma_T${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img9.gif">'; $key = q/{_inline}$calIm(E_55)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img699.gif">'; $key = q/{_inline}$c=7+sqrt15over34=0.3197936${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img394.gif">'; $key = q/{_inline}$displaystyle%left.arrayldisplaystyleV_h={v_h,quadv_hinX_h^3quadmboxtelquev_hi=baru_imboxsurGamma_1}displaystyleV_h^0={v_h,quadv_hinX_h^3quadmboxtelquev_hi|Gamma_1=0}arrayright.${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img82.gif">'; $key = q/{_inline}$Re^2${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img914.gif">'; $key = q/{_inline}$e_21${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img1009.gif">'; $key = q/{_inline}$lambda=partialpsioverpartialninP2${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img507.gif">'; $key = q/{_inline}$calDu${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img191.gif">'; $key = q/{_inline}$displaystyle[calDcalP]=left(arraycDP00arrayarrayc0DP0arrayarrayc00DParrayright)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img106.gif">'; $key = q/{_inline}$hatS_2:(0.,-1.,0.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img647.gif">'; $key = q/{_inline}$displaystyle[P]=[P(r,z)]=[p_1(r,z),p_2(r,z),...,p_N_T(r,z)]${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img807.gif">'; $key = q/{_inline}$p_2(bx)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img98.gif">'; $key = q/{_inline}$nCrmm^2${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img1032.gif">'; $key = q/{_inline}$displaystyleDu_T=left(arraycdisplaystylepartialu_1overpartialxdisplaystylepartialu_1overpartialydisplaystylepartialu_1overpartialz...displaystylepartialu_3overpartialzarrayright)=[calDcalP]{u_T}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img110.gif">'; $key = q/{_inline}$f_i^Gamma${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img56.gif">'; $key = q/{_inline}$displaystyle2piint_Omega^primerhopartial^2u_hoverpartialt^2v_hrdrdzquad+quad2piint_Omega^primeE_ijkhepsilon_ij(u_h)epsilon_kh(v_h)rdrdz${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img172.gif">'; $key = q/{_inline}$b.K_v${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img553.gif">'; $key = q/{_inline}$k_11,k_12,k_22,k_13,k_23,k_33${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img842.gif">'; $key = q/{_inline}$tildeu_h=(u_h1,u_h2,u_h3,Phi_h)${_inline}/;

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