# All Questions

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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**

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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**

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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**

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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**

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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**

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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

**2**answers

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 ...

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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**

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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

**1**answer

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. ...

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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
...

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**0**answers

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**

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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 $s \in S$ ...

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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

**1**answer

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 ...

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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**

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**0**answers

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**

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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 ...

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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**

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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 ...

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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**

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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**

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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**

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**0**answers

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**

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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 ...

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votes

**1**answer

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

**1**answer

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 ...

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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**

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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**

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**0**answers

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**

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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**

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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 ...

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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

**2**answers

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 ...

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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

**1**answer

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

**0**answers

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

**1**answer

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

**0**answers

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

**1**answer

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 ...

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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 ...

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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

**0**answers

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**

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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

**0**answers

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

**0**answers

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**

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**0**answers

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

**1**answer

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**

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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**

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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 ...