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$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img119.gif">'; $key = q/{_inline}$sigma_ijnu_jmboxsigne(face)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img517.gif">'; $key = q/{_inline}$f^Gamma(2,x,S_1)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img286.gif">'; $key = q/{_inline}$epsilon_22${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img141.gif">'; $key = q/{_inline}$1leqileqN_T${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img11.gif">'; $key = q/{_inline}$omega_i=1${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img666.gif">'; $key = q/{_inline}$calRe(E_12)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img686.gif">'; $key = q/{_inline}$w_2=8over18${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img367.gif">'; $key = q/{_inline}$hatS_6:(0.,1.,1.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img459.gif">'; $key = q/{_inline}$calV_M_T${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img280.gif">'; $key = q/{_inline}$hatN_3:(0.5,1.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img882.gif">'; $key = q/{_inline}$forallpinP_1${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img19.gif">'; $key = q/{_inline}$(xi_1,xi_1)=(pm1oversqrt3,pm1oversqrt3)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img667.gif">'; $key = q/{_inline}$C^E_12${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img979.gif">'; $key = q/{_inline}$rho${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img53.gif">'; $key = q/{_inline}$b_i${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img428.gif">'; $key = q/{_inline}$e_25${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img1013.gif">'; $key = q/{_inline}$C^E_33${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img981.gif">'; $key = q/{_inline}$SUBROUTINEquadCARTFI(X,Y,PHI,INDEP)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img574.gif">'; $key = q/{_inline}$epsilon=.02723031417443490${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img573.gif">'; $key = q/{_inline}$[calDcalP]${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img151.gif">'; $key = q/{figure}[htbp]centerframeboxinputt_fig2q1d.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img834.gif">'; $key = q/{figure}[htbp]centerframeboxinpute_fig3qad.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img665.gif">'; $key = q/{_inline}$hatS_9:(0.5,0.,0.5)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img417.gif">'; $key = q/{_inline}$displaystyleprod_TinT_hL^2(partialT)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img773.gif">'; $key = q/{_inline}$sigma${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img47.gif">'; $key = q/{_inline}$calRe(k_11),calIm(k_11)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img933.gif">'; $key = q/{_inline}$gamma=5over567${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img400.gif">'; $key = q/{_inline}$f^Omega_i${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img949.gif">'; $key = q/{_inline}$displaystylewidetildecalL(tildev_h)=int_Omegaf^Omega_iv_hidunderlinermx+int_Gamma_0f^Gamma_iv_hidGamma+int_Gamma^e_0qphi_hdGamma${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img966.gif">'; $key = q/{_inline}$omega_k,[P],[DP],b_k${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img411.gif">'; $key = q/{_inline}$rho,e${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img636.gif">'; $key = q/{_inline}${calRe(f^Gamma)(i,2j-1,k)(i=1,NDSM;j=1,3;k=1,npis${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img709.gif">'; $key = q/{_inline}$calDu_T${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img185.gif">'; $key = q/{_inline}$H(div;Omega)={qin(L^2(Omega))^m,divqinL^2(Omega)}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img738.gif">'; $key = q/{_inline}$sigma_11,sigma_12,sigma_22,sigma_xx${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img531.gif">'; $key = q/{_inline}$displaystyle{epsilon}=left(arrayc100000arrayarrayc000100arrayarrayc000001arrayarrayc000100arrayarrayc010000arrayarrayc000010arrayarrayc000001arrayarrayc000010arrayarrayc001000arrayright)left(arraycdisplaystylepartialu_1overpartialxdisplaystylepartialu_1overpartialydisplaystylepartialu_1overpartialz...............displaystylepartialu_3overpartialzarrayright)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img114.gif">'; $key = q/{_inline}$displaystyleM^baru={mu,muinprod_TinT_hH^-12(partialT),existsvinH^1(Omega),v_|Gamma_1=baru,mu=v_|partialTforallTinT_h}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img762.gif">'; $key = q/{_inline}$displaystyleX_h=left{tildev_hi,tildev_hiinC^0(Omega);tildev_himid_TinP_T,forallTincalT_hright}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img963.gif">'; $key = q/{_inline}${tildeu}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img787.gif">'; $key = q/{_inline}$b=6+sqrt15over21=0.47014206${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img405.gif">'; $key = q/{_inline}$displaystylewidetildeV^0_h=left{tildev_h=(v_h1,v_h2,v_h3,phi_h),tildev_hinX^4_hrm~~tel~que~v_himid_Gamma_1=0rm~et~phi_hmid_Gamma^e_1=0right}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img962.gif">'; $key = q/{_inline}$hatN_5:(1.,a,a)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img908.gif">'; $key = q/{_inline}$calIm(E_44)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img697.gif">'; $key = q/{_inline}$hatN_4:(a,a,a)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img857.gif">'; $key = q/{_inline}$left[sigma_Tright]${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img273.gif">'; $key = q/{_inline}$hatS_8:(1.,0.,0.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img483.gif">'; $key = q/{_inline}$e_13${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img1006.gif">'; $key = q/{_inline}$displaystyle{epsilon}=left(arraycepsilon_11epsilon_22epsilon_332epsilon_122epsilon_232epsilon_31arrayright)mboxetquad{sigma}=left(arraycsigma_11sigma_22sigma_33sigma_12sigma_23sigma_31arrayright)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img112.gif">'; $key = q/{_inline}$Omega${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img40.gif">'; $key = q/{_inline}$e_34${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img1016.gif">'; $key = q/{figure}[htbp]centerframeboxinputt_fig2q2c.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img836.gif">'; $key = q/{figure}[htbp]centerframeboxinputt_fig3p1d.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img841.gif">'; $key = q/{_inline}$delta=.1032173705347184${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img572.gif">'; $key = q/{_inline}$hatS_6:(0.,0.5)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img558.gif">'; $key = q/{_inline}$hatS_3:(1.,-1.,0.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img648.gif">'; $key = q/{_inline}$Gamma^-${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img916.gif">'; $key = q/{_inline}$wm_k${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img847.gif">'; $key = q/{_inline}$u_x,u_y,rotx,roty,psi${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img602.gif">'; $key = q/{_inline}$displaystylevecphi:(xi_1,xi_2)inoverlineOmegasubsetR^2rightarrowvecphi(xi)inR^3${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img246.gif">'; $key = q/{_inline}$K_h${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img554.gif">'; $key = q/{_inline}${calRe(f^Gamma_1),calIm(f^Gamma_1),calRe(f^Gamma_2),calIm(f^Gamma_2)}(i)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img712.gif">'; $key = q/{_inline}$lambda_4${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img389.gif">'; $key = q/{_inline}$u=u_0${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img29.gif">'; $key = q/{figure}[htbp]centerframeboxinpute_fig411.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img156.gif">'; $key = q/{_inline}$u_4,u_5${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img588.gif">'; $key = q/{figure}[htbp]centerframeboxinpute_fig3q2d.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img439.gif">'; $key = q/{_inline}$calRe(u_3)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img676.gif">'; $key = q/{_inline}$Q_1${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img903.gif">'; $key = q/{_inline}$displaystyle[DP]=[DP(r,z)]=left(arraycdisplaystylepartialp_1overpartialrdisplaystylepartialp_1overpartialzarrayarraycdisplaystylepartialp_2overpartialrdisplaystylepartialp_2overpartialzarrayarrayc......arrayarraycdisplaystylepartialp_noverpartialrdisplaystylepartialp_noverpartialzarrayright)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img809.gif">'; $key = q/{_inline}$displaystyle[epsilon]=left(arrayc001overr0arrayarrayc0100arrayarrayc0001arrayarrayc0001arrayarrayc1000arrayright)left(arraycdisplaystyleu_rdisplaystylepartialu_roverpartialrdisplaystylepartialu_roverpartialzdisplaystylepartialu_zoverpartialrdisplaystylepartialu_zoverpartialzarrayright)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img194.gif">'; $key = q/{_inline}$e,partialeoverpartialx,partialeoverpartialy${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img585.gif">'; $key = q/{_inline}$b=9+2sqrt15over21${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img469.gif">'; $key = q/{_inline}$beta=155+sqrt15over2400=0.066197075${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img403.gif">'; $key = q/{_inline}$e_22${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img1010.gif">'; $key = q/{_inline}$p_n(bx)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img776.gif">'; $key = q/{_inline}$u_ij+f_ijrightarroww,_ij${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img239.gif">'; $key = q/{_inline}$omega${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img532.gif">'; $key = q/{_inline}$displaystyleX^f^Omega={q,qinbarX,divq+f^Omega_|T=0forallTinT_h}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img767.gif">'; $key = q/{figure}[htbp]centerframeboxinputt_fig3p2c.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img843.gif">'; $key = q/{_inline}$Du_T${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img150.gif">'; $key = q/{_inline}$Gamma=Gamma_0cupGamma_1${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img45.gif">'; $key = q/{_inline}$lambda=0${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img502.gif">'; $key = q/{figure}[htbp]centerframeboxinpute_fig3rac.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img645.gif">'; $key = q/{_inline}$b_3${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img373.gif">'; $key = q/{_inline}$f_i^Omega${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img55.gif">'; $key = q/{_inline}$calRe(k_12),calIm(k_12)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img934.gif">'; $key = q/{_inline}$left[B_Tright]${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img274.gif">'; $key = q/{_inline}$displaystylea(vecu,vecv)=(f,vecv),quadforallvecvinvecV${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img270.gif">'; $key = q/{_inline}$tildeu_ijrightarroww,_ij${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img227.gif">'; $key = q/{_inline}$sigma_ij,i${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img49.gif">'; $key = q/{_inline}$tau=(tau_1,tau_2)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img212.gif">'; $key = q/{_inline}$displaystyledisp

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