$H^k-1(\partial M;R)\rightarrow H^k(M,\partial M;R)\rightarrow H^k(M;R)\rightarrow  H^k(\partial M;R)$**strong text**$

begin{matrix} 0 & 1 \ 1 & 0 end{matrix}

begin{pmatrix} 0 & -i \ i & 0 end{pmatrix}

begin{bmatrix} 0 & -1 \ 1 & 0 end{bmatrix}

begin{Bmatrix} 1 & 0 \ 0 & -1 end{Bmatrix}

begin{vmatrix} a & b \ c & d end{vmatrix}

begin{Vmatrix} i & 0 \ 0 & -i end{Vmatrix}

begin{equation}
 left{
  begin{aligned}
  overset{.}x(t) &=A_{ci}x(t)+B_{1ci}w(t)+B_{2ci}u(t)  \
  z(t) &=C_{ci}x(t)+D_{ci}u(t) \
  end{aligned}
  right.
 end{equation}

begin{equation}
 left{
  begin{aligned}
  overset{.}x(t) &=A_{ci}x(t)+B_{1ci}w(t)+B_{2ci}u(t)  \
  z(t) &=C_{ci}x(t)+D_{ci}u(t) \
  end{aligned}
  right.
 end{equation}

begin{equation}
 left{
  begin{aligned}
  overset{.}x(t) &=A_{ci}x(t)+B_{1ci}w(t)+B_{2ci}u(t)  \
  z(t) &=C_{ci}x(t)+D_{ci}u(t) \
  end{aligned}
  right.
 end{equation}

begin{align}    text{Compare }  x^2 + y^2 &= 1               &  x^3 + y^3 &= 1               \  x         &= sqrt   {1-y^2} &  x         &= sqrt[3]{1-y^3}end{align}

begin{align}  (a + b)^3  &= (a + b) (a + b)^2        \             &= (a + b)(a^2 + 2ab + b^2) \             &= a^3 + 3a^2b + 3ab^2 + b^3end{align}begin{align}  x^2  + y^2 & = 1                       \  x          & = sqrt{1-y^2}end{align}

begin{equation}  begin{rcase}    B' &= -partialtimes E          \    E' &=  partialtimes B - 4pi j ,  end{rcase}  quad text {Maxwell's equations}end{equation}

documentclass{article} pagestyle{empty} setcounter{page}{6} setlengthtextwidth{266.0pt} usepackage{CJK} usepackage{amsmath} begin{CJK}{GBK}{song} begin{document} begin{align} (a + b)^3 &= (a + b) (a + b)^2 \ &= (a + b)(a^2 + 2ab + b^2) \ &= a^3 + 3a^2b + 3ab^2 + b^3 end{align} begin{align} x^2 + y^2 & = 1 \ x & = sqrt{1-y^2} end{align} This example has two column-pairs. begin{align} text{Compare } x^2 + y^2 &= 1 & x^3 + y^3 &= 1 \ x &= sqrt {1-y^2} & x &= sqrt[3]{1-y^3} end{align} This example has three column-pairs. begin{align} x &= y & X &= Y & a &= b+c \ x' &= y' & X' &= Y' & a' &= b \ x + x' &= y + y' & X + X' &= Y + Y' & a'b &= c'b end{align} This example has two column-pairs. begin{flalign} text{Compare } x^2 + y^2 &= 1 & x^3 + y^3 &= 1 \ x &= sqrt {1-y^2} & x &= sqrt[3]{1-y^3} end{flalign} This example has three column-pairs. begin{flalign} x &= y & X &= Y & a &= b+c \ x' &= y' & X' &= Y' & a' &= b \ x + x' &= y + y' & X + X' &= Y + Y' & a'b &= c'b end{flalign} This example has two column-pairs. renewcommandminalignsep{0pt} begin{align} text{Compare } x^2 + y^2 &= 1 & x^3 + y^3 &= 1 \ x &= sqrt {1-y^2} & x &= sqrt[3]{1-y^3} end{align} This example has three column-pairs. renewcommandminalignsep{15pt} begin{flalign} x &= y & X &= Y & a &= b+c \ x' &= y' & X' &= Y' & a' &= b \ x + x' &= y + y' & X + X' &= Y + Y' & a'b &= c'b end{flalign} renewcommandminalignsep{2em} begin{align} x &= y && text{by hypothesis} \ x' &= y' && text{by definition} \ x + x' &= y + y' && text{by Axiom 1} end{align} begin{equation} begin{aligned} x^2 + y^2 &= 1 \ x &= sqrt{1-y^2} \ text{and also }y &= sqrt{1-x^2} end{aligned} qquad begin{gathered} (a + b)^2 = a^2 + 2ab + b^2 \ (a + b) cdot (a - b) = a^2 - b^2 end{gathered} end{equation} begin{equation} begin{aligned}[b] x^2 + y^2 &= 1 \ x &= sqrt{1-y^2} \ text{and also }y &= sqrt{1-x^2} end{aligned} qquad begin{gathered}[t] (a + b)^2 = a^2 + 2ab + b^2 \ (a + b) cdot (a - b) = a^2 - b^2 end{gathered} end{equation} newenvironment{rcase} {left.begin{aligned}} {end{aligned}rightrbrace} begin{equation*} begin{rcase} B' &= -partialtimes E \ E' &= partialtimes B - 4pi j , end{rcase} quad text {Maxwell's equations} end{equation*} begin{equation} begin{aligned} V_j &= v_j & X_i &= x_i - q_i x_j & &= u_j + sum_{ine j} q_i \ V_i &= v_i - q_i v_j & X_j &= x_j & U_i &= u_i end{aligned} end{equation} begin{align} A_1 &= N_0 (lambda ; Omega') - phi ( lambda ; Omega') \ A_2 &= phi (lambda ; Omega') phi (lambda ; Omega) \ intertext{and finally} A_3 &= mathcal{N} (lambda ; omega) end{align} end{CJK} end{document}

转载本文请联系原作者获取授权，同时请注明本文来自陈跃文科学网博客。
链接地址：https://wap.sciencenet.cn/blog-1268995-921073.html


下一篇：测试公式编辑