Second order PDE February 9    1

Kindly help me with this... $$U_{xy} + yU_{yy} + \sin(x+y)=0$$Here $A =0$, so how to calculate the characteristic equations ?as $$ {dy\over dx} = {B^2 \pm \sqrt D\over2A} $$Let $V=U_y$ ,Then $V_x+yV_y=-\sin(x+y)$Follow the method in http://en.wikiped

Nonlinear second order PDE February 9

I need to solve the following PDE (which is a maximized Hamilton-Jacobi-Bellman equation)\begin{align} rV(\theta_1,\theta_2) = \frac{(\theta_1^\rho + \theta_2^\rho)^{\frac{1}{\rho}}}{12(\gamma_1+\gamma_2)}-\frac{1}{6}(\alpha_1 \theta_1^2 + \alpha_2 \

How is this called February 9

If we have such relation that for $\forall x$ $f(x)\ne x$ , how is it called in one word? I can come up with only "graph of this function is not a straight line:)" Thank you

How does this picture called February 9

How does this picture called
Some time ago I saw this in my teacher's room. She called this picture in honor of some scientists (Lagrange,Lie or Liouville, or some other, but I don't remember). Please, name picture. Tha ...

The degree of Gauss map February 9    1

If $M$ is an $2m$-dimensional closed orientable hypersurface in $\mathbb R^{2m+1}$, then we have a Gauss map $G:M\rightarrow S^{2m}$.I have known from my differential geometry book that deg$G=\frac{1}{2}\chi(M)$ where $\chi(M)$ is the Euler character

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