# All Questions

3 views

### Sigma-Algebra MATLAB code

By Definition of Sigma-Algebra, I want to use MATLAB to computing any Sigma-Algebra. Actually I want to know is there any program to compute the smallest sigma-algebra of 2 sets or more? I think ...
8 views

### Measurability of solution of diffusion equation in sub sigma algebra

I want to solve the following problem: Get $\omega \in \Omega \subset \mathbb{R}$, $x \in D \subset \mathbb{R}^2$ and $0<a_i\leq a(.,.)\leq a_x<\infty$. Let $a( x;. )$ and $f(x;.)$ be ...
36 views

### Log schemes, differentials, Beilinson

Let $K$ be a $p$-adic field and $K'$ be a finite extension of $K$. Let $\Omega_{(K',\mathcal{O}_{K'})}$ be the sheaf of relative log differentials of the pair $(K',\mathcal{O}_{K'})$ over ...
21 views

49 views

### Partitions with each part dividing the original number

I have a question on partitions that I have not seen being discussed. It deals with those related to divisors. My definition of partitions I am working with is as follow: a sequence of weakly ...
24 views

### Minimal surface dividing a simply connected region into two regions of equal volume

let $\Omega \subset R^3$ (not necessarily convex) be simply connected. The the surface $\Gamma$ with minimal area that divides $\Omega$ into two regions of equal volume has constant mean curvature and ...
94 views

### Unitary representations of Tarski Monsters and other beasts

Did people study the unitary representations of Tarsky Monsters, for example the ones constructed by Ol'shanskii? Are there any exotic representations, ie. except the ones related to the left regular, ...
33 views

### when a given graph is 3-colorable? [on hold]

I want to use graph 3-colorability to prove a problem is NP-complete But I'm not sure when a given graph is 3-colorable. I think if it doesn't have any node to be connected to all 3 vertices of a ...
18 views

### Calculate point P(x,y) in a circle given a radius and angle degree [on hold]

I'm doing a program in Java to draw a PieChart based on given value as link below. data for piechart Given that the diameter, radius, angle degree, center point (150,150) and First Point A (150,0) ...
35 views

### Is this a generic $L$-parameter?

I am wondering if some local $L$-parameter of the unitary group is generic or non-generic parameter. Let me introduce my $L$-parameter I have. Let $E/F$ be a quadratic extension of number fields and ...
85 views

### Computing the nonsingular projective model of a plane curve

Is there an implemented algorithm available in standard software systems (Sage, Magma, Macaulay, etc.) that will compute the nonsingular projective model of a plane curve over $\mathbb Q$?
91 views

### When does $\mathbf{Top}/X$ embedd fully faithfully into $\mathbf{Top}$?

Under what conditions on the topological space $X$ is the overcategory $\mathbf{Top}/X$ of topological spaces over $X$ equivalent to a full subcategory of $\mathbf{Top}$? Surely if $X$ terminal i.e. a ...
79 views

### Rational multiple of a line bundle

In the paper http://arxiv.org/pdf/1207.5011.pdf of Chi Li and Song Sun, they say that "$D$ is a smooth divisor which is $\mathbb{Q}$-linearly equivalent to $−\lambda K_X$ for some $λ \in \mathbb{Q}$", ...
22 views

### How can i simplify the sum of modified partial bell polynomials

I am trying to prove my conjecture that uses partial bell polynomials as well as modified partial bell polynomials. Putting these bell polynomials into a workable form is a huge problem for me. The ...
34 views

### About diagonal entries of the graph Laplacian

[..in the following you can assume its a regular graph if necessary..] Is anything special known about them? Are they characterized in any other way? Is the largest diagonal entry in any power of ...
30 views

### Reducible reductive Lie subalgebras of so(p,q)

Is it true that $S(O(p) \times O(q))$ is the only proper subgroup of $SO(p,q)$ with full rank acting on the natural representation $\mathbb{R}^{p+q}$ of $SO(p,q)$ stabilizes a $p$-dimensional positive ...
56 views

### Limits in Span(Vec)

Let Vec be the category of real vector spaces and linear maps. Let Span(Vec) be the bicategory of correspondences between real vector spaces. I am trying to understand lax limits in Span(Vec). What ...
30 views

### Discrete subgroup of complex orthogonal group

Is there any reference for the discrete subgroup of complex orthogonal group SO(n,C)? Any classification or examples?
109 views

### Stability of minimal surfaces

Let $\Gamma$ be a prescribed $n-2$ dimensional set and assume $S \subset R^n$ is a minimal hyper-surface with respect to some smooth metric $g$ on $R^n$, and $\partial S= \Gamma$. Is $S$ is stable ...
42 views

### Reduction argument from a general vertex set V(G) to a prime power in Prof. Keevash's proof on the Existence of Designs

The proof flow of the paper "On the Existence of Designs" by Prof. Keevash as I understand it is the following: -- Reduction from the general case to $V = \mathbb{F}_{p^a}$ (Lemma 6.3) -- Covering ...
685 views

### The view from inside of a mirrored tetrahedron

Suppose you were standing inside a regular tetrahedron $T$ whose internal face surfaces were perfect mirrors. Let's assume $T$'s height is $3{\times}$ yours, so that your eye is roughly at the ...
111 views

### Can all $L^2$ holomorphic functions on a domain vanish at a particular point?

Let $\Omega \subset \mathbb{C}^n$. Is it possible that there is a point $p \in \Omega$ such that every $f \in A^2(\Omega) = L^2(\Omega) \cap \mathcal{O}(\Omega)$ has a zero at $p$? The space ...
59 views

### Relationship between Laplacian and Hessian on compact Lie groups

If $f: \mathbb{R}^n \rightarrow \mathbb{R}$ is smooth and compactly supported, one has $$\int |\Delta f(\mathbf{x})|^2\,d\mathbf{x} = \int \| Hf(\mathbf{x}) \|_F^2\,d\mathbf{x}\,,$$ where $\Delta$ ...
53 views

Let $k$ be a nonperfect field of characteristic $2$. Let $a\in k\backslash k^2$. Let $h= \left[\begin{array}{cc} 0 & a \\ ... 1answer 69 views ### (Alternative) Presentation for the pure braid group of the sphere First I need some notation (it's all standard I think). For a manifold$M$, let$F_nM = F_{0,n}M$be the space of$n$-tuples of distinct points on$M$; let$B_nM = B_{0,n}M = F_nM / \Sigma_n$. When ... 0answers 63 views ### Von Dyck Theorem Let$G= \langle X\mid R\rangle$,$X$and$R$the set of generators and relations, respectively. Now we define$H = \langle X \mid R \cup \{x\}\rangle $for some$x \in X$. Indeed in group$H$, we ... 0answers 138 views ### Is there a cotangent bundle of a stable$\infty$-category? Let$C$be a stable$\infty$-category. Is there any categorical construction$C \mapsto T^* C$, where$T^* C$is another stable$\infty$-category, that specializes to the following? When$C$is the ... 0answers 75 views ### X^2e + X^e + 1 is irreducible for e which is a power of 3? [on hold] I am looking for a proof or reference to the fact that the trinomials of the form X^2e + x^e + 1 Are irreducible in GF(2) for e which is a power of 3. Please help! Lear 0answers 20 views ### Constructing parallel group topologies on Prüfer groups By this post, there exist infinitely many parallel group topologies on a Prüfer group. But is there a way to construct such group topologies? For example, a Prüfer group can be embedded uniquely in ... 0answers 44 views ### Eichler-Shimura congruence I'm trying to understand the Eichler-Shimura congruence which relates the Hecke operator$T_p$to Frobenius at$p$in characteristic$p$. Two possible ways to compute$T_p$mod$p$seem to be: A) ... 0answers 105 views ### Regular point of a map in algebraic geometry What is the correct definition of a regular point of a map in algebraic geometry? More specifically, let$f:X\to Y$be a map of varieties with$f(p) = q$, and let$Z=f^{-1}(q)$. Let$\hat{X}$be the ... 0answers 99 views ### bound on degree of certain polynomials Consider$m$polynomials$f_i$for$i=\{1,\dots,m\}$in$\Bbb R[x_1,\dots,x_n]$of degree$d_i$such that $$Z(f_i)\bigcap Z((p))\neq \emptyset$$ for the sphere$p$passing through$\{0,1\}^n$. What is ... 1answer 47 views ###$L^p$stability of the Beltrami equation Let's assume that$f$is a quasiconformal homeomorphism of$\mathbb{C}$with Beltrami coefficient$\mu = \frac{\bar{\partial} f}{\partial f}$. Notice that by definition$\Vert \mu \Vert _{L^{\infty}} ...
I understand this statement from the physics side. Consider an $n-$dimensional manifold $\cal M$ ("configuration space") and its cotangent bundle ${\cal P} = T^*\cal M$ ("phase space"), a symplectic ...
In the proposition mentioned in the title, Hartshorne states that for each $i\geq 0$ the higher direct image sheaf $R^if_*\mathcal F$ is exactly the sheafification of the presheaf given by \$V \mapsto ...