All Questions

0
votes
0answers
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 ...
0
votes
0answers
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 ...
1
vote
0answers
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 ...
2
votes
0answers
21 views

Is the Amitsur-Levitzki identity essentially unique?

Let us consider the matrix algebra. $Mat_n(\mathbb{C})$. The Amitsur-Levitzki identity states that for any matrices $X_1, X_2, ..., X_{2n} \in Mat_n(\mathbb{C})$ the sum $\Sigma_{\sigma \in S_{2n}} ...
-1
votes
0answers
10 views

Double Summation and factors in bracket multiplycation [on hold]

(http://i.imgur.com/3ODbg6n.jpg) Can you please solve this. I don't know how to best describe this. I hope I put it into the best words as possible. Thank you.
-3
votes
0answers
25 views

Find a prime when some primitive roots are given [on hold]

p is a prime. some primitive roots modulo p are 2, 3, 5, 7, 11. How can I find p?
1
vote
2answers
75 views

Notion of manifold curvature?

Consider a particular embedding of a $C^2$ manifold $\mathcal{M}\subseteq\mathbb{R}^m$. Given $p\in\mathcal{M}$, suppose $\epsilon>0$ is small enough that the portion $U$ of $\mathcal{M}$ which is ...
1
vote
2answers
21 views

Continuity in banach space for non-linear maps

I want to find an example of a Banach space $X$ and a continuous map $f:X\rightarrow X$ such that $f$ is not bounded on the unit ball. I do not doubt that such an example exists, but I cannot make it ...
-1
votes
0answers
23 views

how to reduce 3-colorable graph to this?

suppose we have a finite set X and a set S of subsets of X and we want to determine is there a subset S' of S such that all members of X belong to exactly one set in S' I think the best problem to ...
1
vote
1answer
23 views

Norm of swapped power series in the unit disk

Suppose $f(z)=a_0+a_1z+\cdots+a_nz^n+\cdots$ is defined in the unit disk and $\|f\|_{\infty}\leq 1.$ Lets form another series $g$ by interchanging $a_1$ and $a_k$ i.e. ...
0
votes
0answers
55 views

Testing the faithfulness of group homomorphisms by testing on the level of induced Lie Algebras

Let $G$ be a group and let $\Gamma_G(k)$ be the $k$th term of the lower central series of $G$. For each $k\geq 1$, set $\mathrm{gr}_k(G)=\Gamma_G(k)/\Gamma_G(k+1)$ and ...
0
votes
0answers
10 views

matching Robinson-Foulds distance and way to compute RF dist in Phylip

In Comparison of Phylogenetic Trees, Robinson D.F. and Foulds L.R., didn't show how to compute the RF distance between trees, counting the different partition generated by the removing of an internal ...
3
votes
0answers
33 views

Trying to understand straightening functor associated to a right fibration of simplicial sets

Let $p:X \to S$ be a right fibration of simplicial sets; one can roughly think of it as some sort of "functor" $S^{op} \to Set_\Delta$ (where $Set_\Delta$ denotes simplicial sets) sending $s \in S$ ...
1
vote
0answers
45 views

E- and A-algorithms for finite arithmetic prime progressions and other sets

There is certain Eratosthenes spirit to my problem. First of all I'd like to stress the mathematical aspect of my question. Also, my question does not amount to the divide and conquer (despite a ...
1
vote
1answer
29 views

Calculating the “Belvedere Hull” of a Simple Planar Polygon

As an informal motivation the problem, imagine a tower with polygonal footprint, that is located in a beautiful landscape, the "Belvedere Hull" is then related to the directions, in which one would ...
2
votes
0answers
47 views

Donsker's Theorem for triangular arrays

I should mention that I already posed this question on Math Stack Exchange, but didn't receive much feedback. Assume we have a sequence of smooth i.i.d. random variables $(X_i)_{i=1}^{\infty}$. Given ...
-4
votes
0answers
27 views

Help to write the generating function [on hold]

How do I write the generating function and the closed for form the generating function The sequence is 0 0 0 1 1 1 1 1 1 Is this correct? A(x) = 0+0x+0x^2+1x^3+1x^4+1x^5+1x^6+1x^7+1x^8 This is ...
1
vote
0answers
14 views

Restricted spectrum of random matrix

Let $X \in \mathbb{R}^{p\times p}$ be a large square matrix, consisting of i.i.d. Gaussian entries. Then it is known that the spectrum of $X$ follows the Marchenko-Pastur law. Now let's introduce an ...
0
votes
0answers
53 views

Finding an overgroup or a subgroup in PGL

Let k be a nonperfect field of characteristic $2$. Let $a\in k\backslash k^2$. Let $G=PGL_4(k)$. Let $H=\{ \small\left[\begin{array}{cccc} x & ...
3
votes
0answers
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 ...
0
votes
0answers
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 ...
3
votes
0answers
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, ...
-1
votes
0answers
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 ...
-1
votes
0answers
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) ...
2
votes
0answers
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 ...
0
votes
1answer
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 $\mathbb Q$?
4
votes
1answer
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 ...
0
votes
0answers
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 $λ \in \mathbb{Q}$", ...
-1
votes
0answers
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 ...
-2
votes
0answers
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 ...
1
vote
0answers
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 ...
2
votes
0answers
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 ...
0
votes
0answers
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?
3
votes
2answers
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 ...
0
votes
0answers
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 ...
18
votes
1answer
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 ...
9
votes
0answers
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 ...
2
votes
1answer
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 $\Delta$ ...
-4
votes
0answers
53 views

Changing a unipotent matrix into upper triangular form [on hold]

Let $k$ be a nonperfect field of characteristic $2$. Let $a\in k\backslash k^2$. Let $h= \left[\begin{array}{cc} 0 & a \\ ...
2
votes
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 ...
0
votes
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 ...
13
votes
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 ...
-2
votes
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
0
votes
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 ...
4
votes
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) ...
0
votes
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 ...
2
votes
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 ...
4
votes
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}} ...
3
votes
0answers
49 views

What's the geometric statement of this fibrewise integration on a symplectic manifold with Lagrangian fibration?

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 ...
0
votes
0answers
144 views

Hartshorne Proposition III 8.1

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 ...

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