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# LaTeX2HTML 95.1 (Fri Jan 20 1995)# Associate image original text (scrambled) with physical files.$key = q/{_inline}$psirightarroww${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img228.gif">'; $key = q/{_inline}$hatS_18:(1.,0.5,1.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img453.gif">'; $key = q/{figure}[htbp]centerframeboxinputt_fig2p3d.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img833.gif">'; $key = q/{_inline}$omega_i=1over2${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img889.gif">'; $key = q/{_inline}$u_r=overlineu_r${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img169.gif">'; $key = q/{_inline}$epsilon_i3=0.${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img137.gif">'; $key = q/{_inline}$hatS_13:(0.,0.,1.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img488.gif">'; $key = q/{_inline}$H^1_0,Gamma_1(Omega)={v,vinH^1(Omega),v_|Gamma_1=0}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img742.gif">'; $key = q/{_inline}$g=0.5(1+sqrt3over5)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img473.gif">'; $key = q/{_inline}$(u,lambda)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img758.gif">'; $key = q/{_inline}$displaystyle[E]=left(arraycE_11....sym.arrayarraycE_12E_22....arrayarraycE_13E_23E_33...arrayarraycE_14E_24E_34E_44..arrayarraycE_15E_25E_35E_45E_55.arrayarraycE_16E_26E_36E_46E_56E_66arrayright)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img118.gif">'; $key = q/{_inline}$e_1${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img652.gif">'; $key = q/{_inline}$displaystyleDu_T=left(arraycdisplaystyleu_rdisplaystylepartialu_roverpartialrdisplaystylepartialu_roverpartialzdisplaystylepartialu_zoverpartialrdisplaystylepartialu_zoverpartialzarrayright)=[calDcalP]{u_T}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img187.gif">'; $key = q/{_inline}$(psi,psi,_1,psi,_2)rightarrow(w,w,_1,w,_2)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img240.gif">'; $key = q/{_inline}$e_ij${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img1027.gif">'; $key = q/{_inline}$10^9${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img1024.gif">'; $key = q/{_inline}$rho,PT_x,PT_y,PT_z,I_y,I_z,S${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img632.gif">'; $key = q/{_inline}$beta${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img339.gif">'; $key = q/{_inline}$u_z=overlineu_z${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img170.gif">'; $key = q/{_inline}$f^Omega(i,k)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img505.gif">'; $key = q/{_inline}$w_h${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img217.gif">'; $key = q/{_inline}$Q^prime2${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img360.gif">'; $key = q/{_inline}$calIm(E_22)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img689.gif">'; $key = q/{_inline}$displaystylefracpartialsigma_ijpartialx_i${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img50.gif">'; $key = q/{figure}[htbp]centerframeboxinpute_figq25c.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img615.gif">'; $key = q/{_inline}$AB+lambda.AC${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img634.gif">'; $key = q/{_inline}$-varepsilon^S_13${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img1023.gif">'; $key = q/{_inline}${calIm(f^Omega)(i,2j,k)(i=1,NDSM;j=1,3;k=1,npiv${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img708.gif">'; $key = q/{_inline}$displaystyleleft.arrayllla(tildeu,tildev);SPM_amp;=;SPM_amp;displaystyleDint_Omega[u_11v_11+2(1-nu)u_12v_12+u_22v_22+nu(u_11v_22+u_22v_11)]dbxb(tildeu,phi);SPM_amp;=;SPM_amp;displaystyleint_Gamma[-M_n(tildev)partialphioverpartialn+M_ntau(tildev)partialphioverpartialtau+Q_n(tildev)phi]dsl_V(tildev);SPM_amp;=;SPM_amp;displaystyle-a(tildef,tildev)mboxo鵷ildefmboxestsolutiondeAtildef=f^OmegamboxdansT,forallTincalT_hl_X(phi);SPM_amp;=;SPM_amp;displaystyle-b(tildef,phi)arrayright.${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img238.gif">'; $key = q/{_inline}$u_1${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img299.gif">'; $key = q/{_inline}$psiinP3${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img510.gif">'; $key = q/{_inline}$hatS_9:(0.,1.,0.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img484.gif">'; $key = q/{_inline}$f^Gamma${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img713.gif">'; $key = q/{_inline}$displaystyle{u_|T}=[P]{u_T}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img808.gif">'; $key = q/{_inline}$displaystyle[calP]=left(arraycP00arrayarrayc0P0arrayarrayc00Parrayright)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img101.gif">'; $key = q/{_inline}$E_i=-Phi_,i${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img956.gif">'; $key = q/{_inline}$C^E_26${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img996.gif">'; $key = q/{figure}[htbp]centerframeboxinputt_fig2q2d.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img835.gif">'; $key = q/{_inline}$hatS_10:(0.,0.,1.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img485.gif">'; $key = q/{_inline}$w=partialwoverpartialn=0mboxsurGamma${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img202.gif">'; $key = q/{_inline}$f^Gamma(1,y,S_12)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img297.gif">'; $key = q/{_inline}$displaystyleDP=DP(bx)=left(arraycdisplaystylepartialp_1overpartialxdisplaystylepartialp_1overpartialydisplaystylepartialp_1overpartialzarrayarraycdisplaystylepartialp_2overpartialxdisplaystylepartialp_2overpartialydisplaystylepartialp_2overpartialzarrayarrayc.........arrayarraycdisplaystylepartialp_noverpartialxdisplaystylepartialp_noverpartialydisplaystylepartialp_noverpartialzarrayright)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img105.gif">'; $key = q/{_inline}$displaystylebarX=prod_TinT_hH(div;T)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img766.gif">'; $key = q/{_inline}$displaystyleZ={lambdainP_0(l)foralllmboxar阾edecalT_h,forallTincalT_h}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img231.gif">'; $key = q/{_inline}$displaystyleP=P(bx)=[p_1(bx),p_2(bx),...,p_N_T(bx)]=[p_1,p_2,...,p_N_T]${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img100.gif">'; $key = q/{_inline}$psi=0${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img501.gif">'; $key = q/{figure}[htbp]centerframeboxinpute_figcltr.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img566.gif">'; $key = q/{_inline}$lambda^prime=2lambdamuover(lambda+2mu)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img143.gif">'; $key = q/{_inline}$calIm(u_1)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img673.gif">'; $key = q/{_inline}$delta_ij${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img67.gif">'; $key = q/{_inline}$E_33,E_14${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img385.gif">'; $key = q/{_inline}$P_T=P_2${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img22.gif">'; $key = q/{_inline}$-varepsilon^S_22${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img1021.gif">'; $key = q/{_inline}$psi=partialpsioverpartialx=partialpsioverpartialy=0${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img563.gif">'; $key = q/{_inline}$displaystyleDu_T=left(arraycdisplaystylepartialuoverpartialxdisplaystylepartialuoverpartialyarrayright)=[DP]{u_T}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img795.gif">'; $key = q/{_inline}$E_1,I_1,S_1${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img629.gif">'; $key = q/{_inline}$C^E_14${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img989.gif">'; $key = q/{_inline}$displaystyle{u_|T}=left(arraycu_1(bx)u_2(bx)arrayright)_|T=left(arraycP0arrayarrayc0Parrayright)left(arraycu_1Tu_2Tarrayright)=[calP]{u_T(t)}${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img147.gif">'; $key = q/{_inline}$b_k${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img333.gif">'; $key = q/{_inline}$C^E_35${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img998.gif">'; $key = q/{_inline}$omega_k=1over2${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img590.gif">'; $key = q/{_inline}$displaystylerhopartialuoverpartialt${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img727.gif">'; $key = q/{_inline}$C^E_56${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img1003.gif">'; $key = q/{_inline}$beta=0.0508449063702055${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img545.gif">'; $key = q/{_inline}$M^f^Gamma${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img756.gif">'; $key = q/{_inline}$Gamma_1${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img44.gif">'; $key = q/{_inline}$Phi(t,x,y,z)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img947.gif">'; $key = q/{_inline}$10^6${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img723.gif">'; $key = q/{_inline}$hatS_5:(0.5,0.,0.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img413.gif">'; $key = q/{_inline}$omega=1${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img880.gif">'; $key = q/{_inline}$hatS_3:(1.,1.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img357.gif">'; $key = q/{_inline}${calRe(f^Gamma),calIm(f^Gamma)}(i)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img937.gif">'; $key = q/{_inline}$displaystyle%left.arrayldisplaystylea(u_h,v_h)quad=quadint_Omegaquadsigma_ij(u_h)epsilon_kh(v_h)dbxdisplaystylecalL(v_h)quad=quadint_Omegaquadf^Omegav_hquaddbxquad+quadint_Gamma_1quadf^Gammav_hdGammaarrayright.${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img85.gif">'; $key = q/{_inline}$[calDP]${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img186.gif">'; $key = q/{_inline}$calIm(E)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img681.gif">'; $key = q/{_inline}$calRe(E_11)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img684.gif">'; $key = q/{_inline}$[K]^-1${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img744.gif">'; $key = q/{_inline}$epsilon_33${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img139.gif">'; $key = q/{_inline}${calRe(f^Omega),calIm(f^Omega)}(i.k)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img936.gif">'; $key = q/{_inline}$hatS_3:(0.,1.,0.)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img381.gif">'; $key = q/{_inline}$P_T${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img7.gif">'; $key = q/{_inline}$f^Omega(i)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img860.gif">'; $key = q/{_inline}$X_h,V_h${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img223.gif">'; $key = q/{_inline}$X_ih${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img176.gif">'; $key = q/{_inline}$e_15${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img984.gif">'; $key = q/{_inline}$C^E_23${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img993.gif">'; $key = q/{_inline}$p_2(r,z)${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img179.gif">'; $key = q/{_inline}$kappa${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img911.gif">'; $key = q/{_inline}$e_36${_inline}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img1018.gif">'; $key = q/{figure}[htbp]centerframeboxinputt_fig3q1d.texcenter{figure}/;$cached_env_img{$key} ='<IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img844.gif">'; $key = q/{_inline}$C^E_44${_inline}/;
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