Chevalley's Theorem: $(A,m)$ : a complete local ring. ${a_n}$ : a descending sequence of ideals with $\bigcap a_n=(0)$ Then for each $k$, there is an $n(k)$ s …

We know Laplace equation (elliptic equations) $ Δ u = 0$ Heat equation (parabolic equations) $u_t − Δu = 0$ Wave equation (hyperbolic equations) $u_{tt} − Δu = 0$ we have - H …

Disclaimer - I don't have much experience in topology/complex geometry, so I apologize if what I'm asking is too elementary for this site. Let $S$ be some orientable surface obtai …

As you may know, if a system can be written in the form: $$\dot{\mathbf{x}}= -\bigtriangledown V$$ for some continuously differentiable, single-valued scalar function $V(x)$. suc …

For probably twenty years, category theorists have known of some objects in the Platonic universe called "(weak) $\infty$-categories", in which there are $k$-morphisms for all $k\i …

Prove that (a or b) -> c = ( a -> c ) or ( b -> c ) using natural deductoon for sentences. Can anyone help?

Can someone recommend a resource to help my wife learn more complicated mathematics? She had a really terrible maths education, and while she essentially OK with every day maths sh …

Prove that (a or b) -> c = ( a -> c ) or ( b -> c ) using natural deductoon for sentences. Can anyone help?

When do the notions of totally disconnected space and zero-dimensional space coincide? From what I gather, there are at least three common notions of topological dimension: coverin …

Assume we have a smooth Riemannian metric $g$ on a small one-sided neighborhood $U$ of $0$ on the plane, say $U_\epsilon=\lbrace(x, y): x^2+y^2<\epsilon, y\geq 0\rbrace$. When …

I am planing to study Kirillov's orbit method. I have seen Kirillov's method in several branch of mathematics, for instance, functional analysis, geometry, .... Why is this theory …

I hesitate to ask a question like this, but I really have tried finding answers to this question on my own and seemed to come up short. I readily admit this is due to my ignorance …

I have a problem understanding the meaning of a distributional solution. Let me tell you the context the problem appeared: I read thorugh some papers by DiPerna and Lions concernin …

Let $T>0$, $\Omega$ is $C^1$, $u(x,t)$ is $C^2$ is $x$ and $C^1$ in $t$. Suppose $u$ solves $$u_t-\triangle u=0,\mbox{ in }\Omega\times (0,T),$$ $$u(\cdot,T)=0,\mbox{in }\Omega,$$ …

Given an ellipses, enlarge it along normal direction a fixed length say 1cm. Do we get another ellipses? If so, how to prove ?