# All Questions

4 views

### Connection between connectivity and cohesion of a graph

Tutte [1] proved that, for every $3$-connected graph $G$ and vertices $u$ and $v$, there exists a nonseparating $uv$-path. A graph $G$ is $t$-cohesive if $G$ is connected, has at least two vertices, ...
14 views

### Contour Integration

I am trying to integrate $\frac{\sin x dx}{x(x-1)}$ over the real line except at an arbitrarily small neighborhood around 1, where the function has a singularity. My idea is to do an contour ...
46 views

39 views

### Graph Theory - k-connected graph [on hold]

I am trying to understand the concept of k-connected graphs in graph thoery. Reference books state that a graph G is k-connected if G is connected and if its vertex connectivity is greater than or ...
43 views

### Does there exist a projection (of a variety) birational onto its image and satisfying additional conditions?

Let $X \subset \mathbb P^n$ be an irreducible (projective) variety of dimension $k < n-1$. By Harris [Har, Lecture 18, page 224], the projection $\pi_p : \mathbb P^n - \{p\} \to \mathbb P^{n-1}$ ...
20 views

### Use the persistence theory to find a set of sufficient conditions for two species competitive ODE system [on hold]

Use the persistence theory to find a set of sufficient conditions for two species competitive ODE system $$\frac{du_1}{dt}=u1(b_1-a_{11}u_1-a_{12}u_2)$$ ...
65 views

### Length of quotients and relations between $\ell(\mathrm{coker}\varphi),\ell(R/\det\varphi)$

Let $R$ be domain(not necessary local) with maximal ideal $\mathfrak{p}$ and $d \in R, d \neq 0$. $(R/(d))_{\mathfrak{p}} = 0 \iff (d) \not\subset \mathfrak{p}$(?). And if $(d) \subset \mathfrak{p}$ ...
188 views

### random category theory

This question is in some sense dual to the one asked in Is there an introduction to probability theory from a structuralist/categorical perspective? since contrary to the OP who asks for references ...
47 views

### Distance Between two points [on hold]

Need help in solving my homework problem.How to find distance between 2 points when (4,5) and (12, 3) are given? I need to know the formula for finding it
62 views

### how to compute the de Rham cohomology with compact support of a mobius strip [on hold]

I am having problem computing the de Rham cohomology with compact support of an open mobius strip,it's aquestion from Bott's book, and Bott said its cohomology is identically zero which can be ...
50 views

### Schur multiplier [on hold]

Are there real world applications of Schur multiplier? I am interested in applications of topics specifically coming from Schur multiplier. for example, in biology, computer sience and other branch.
86 views

### Is there an algorithm that probably solves the Halting problem? [on hold]

Such an algorithm takes as input any program and returns a probability that it halts. In the limit of many programs, it must answer on average in the correct proportion. But im interested in other ...
38 views

### Geodesic equation and radial metric

Assume that $g(z)=f(|z|)$ is a radial metric on the unit disk in complex plane, where $f$ is a smooth real function. Is there any simple equation of geodesic lines w.r.t. metric $g$, e.g. ...
22 views

### Is C^0 fine topology is finer that metric topology? [migrated]

Let C(E,F) be a set of continious maps between metric spaces E and F. Suppose we are given $C^0$ fine topology and a metric topology on C(E,F). We now that the fine topology is finer than compat-open ...
99 views

### Descending a monomorphism of stacks

The question is about Proposition 3.8.1 in Laumon and Moret-Bailly book on algebraic stacks. Let $S$ be a scheme and let $F: \mathscr{X} \rightarrow \mathscr{Y}$ be a morphism of $S$-stacks (for the ...
I've been scanning across the web, and haven't found a good method to compute the Gauss Legendre abscisas and weights $\{ x_j, w^j \} _j$ for large N. My question is how to do it, and why should it ...