# All Questions

**4**

votes

**2**answers

209 views

### $A \wedge A \wedge A$ in Chern-Simons

I am confused with the wedging operations of Lie algebra valued differential forms. Especially, for instance, I have some problems with the Chern-Simons 3-form
$$A \wedge dA + \frac{2}{3}A \wedge A ...

**0**

votes

**1**answer

39 views

### Graph classes which are not perfect but the stability number = clique cover numer?

I have a result for graphs whose stability number=clique cover number, which naturally includes the perfect graphs, but I'm curious about if there are other known and well-definable graph classes ...

**0**

votes

**0**answers

22 views

### is the minimum envelope of two inrersecting convex functions convex? [on hold]

let C1 and C2 two convex curves representing a cost function and intersecting each other once (say). how to prove that there exists at least one point for which C2 > C1?

**6**

votes

**0**answers

88 views

### The possibility of a symmetric difference in a torsion-free group

Is there a torsion-free group containing two elements $x$ and $y$ and a finite non-empty subset $B$ such that $B=xB \triangle yB$, where $\triangle$ denotes the symmetric difference of two sets and ...

**5**

votes

**1**answer

104 views

### Example of a $G$-sphere that is not a $G$-representation sphere

Let $G$ be a finite group with the discrete topology. To set terminology:
a $G$-sphere is a sphere equipped with a continuous $G$-action
a $G$-representation sphere is a $G$-sphere obtained from an ...

**3**

votes

**0**answers

88 views

### Reference for Grothendieck's duality and Cousin, Dualizing and Residual complexes

I am a graduate student currently reading Hartshorne's Residues and Duality. In order to reach the construction of the right adjoint $f^!$ of $Rf_*$ for some special types of maps of locally ...

**4**

votes

**1**answer

108 views

### Why the term “geometric” rough path?

A "geometric" rough path is a rough path such that $Sym(\mathbb{X}_{s,t})=\frac{1}{2}X_{s,t}\otimes X_{s,t}$. For example the Ito rough path is not geometric because ...

**4**

votes

**1**answer

89 views

### Loss of derivative of subelliptic operator

Consider the differential operator $P$ on $\mathbb{R}^2$, given by $P = \frac{\partial^2}{\partial x^2} + x^2\frac{\partial^2}{\partial y^2}$. Clearly it is elliptic everywhere except on the $y$-axis. ...

**-5**

votes

**0**answers

49 views

### Genus formula for a curve in a $2$-dimensional complex torus? [migrated]

For a curve $C$ in a $2$-dimensional complex torus $T$, is there any formula to compute the genus of $C$? Say, in terms of self-intersection number?
For a curve in $\mathbb{P}^2$ or a K3 surface, ...

**5**

votes

**0**answers

67 views

### O-Minimal sentences in $L_{\omega_1,\omega}$?

Is there any meaningful sense in which we can talk about o-minimal sentences of $L_{\omega_1,\omega}$? I can give a first attempt, easily; given a countable fragment $F$ and a sentence $\Phi$ in that ...

**0**

votes

**0**answers

58 views

### Find all possible rational pairs of a parametric sextic and all cases where it is reducible for either parameter

Find all possible rational solutions pairs $(z,a)$ of the equation
$a^6 + a^4 (-18368 + 9184 z - 2912 z^2) + a^2 (61702144 - 61702144 z + 36814848 z^2 - 10694656 z^3 + 1748992 z^4) - z^2 ...

**2**

votes

**0**answers

34 views

### Sequences of transition probability measures

Suppose that $X$ and $Y$ are compact metric spaces. A Borel probability measure $\mu$ on $X\times Y$ satisfies
$$
\mu(A\times B)=\int_A\mu(B|x)\mu_X(dx),
$$
for $A$ and $B$ Borel sets in $X$ and $Y$ ...

**0**

votes

**0**answers

16 views

### Non-uniform matroids as the matroid sum of uniform matroids

Can all non-uniform matroids be written as the direct sum / matroid sum of uniform matroids? If so,
What happens to the matrices representing the uniform matroids? If the non-uniform matroid is ...

**6**

votes

**3**answers

634 views

### Catalan numbers as sums of squares of numbers in the rows of the Catalan triangle - is there a combinatorial explanation?

This question arose from an answer to my recent question How many traces are there on Temperley-Lieb, Fuss-Catalan, Iwahori-Hecke, Birman-Wenzl-Murakami-Kauffman, ... algebras?
What I need from that ...

**-2**

votes

**0**answers

20 views

### For which $x$ the inequality $ax+be^{x/2}>c$, where $a,b,c,x>0$ and $c>2b$ holds [on hold]

For which $x$ the inequality $ax+be^{x/2}>c$, where $a,b,c,x>0$ and $c>2b$ holds. Can someone help me for this. Thank you.

**0**

votes

**0**answers

5 views

### The minimum perimeter and maximum height of a triangle under constraints [migrated]

I do not get the following formulas :
...

**0**

votes

**0**answers

12 views

### Is there a field in which every rational polynomial has a root (other than the obvious fields)? [migrated]

Let $\mathbb{A} \subset \mathbb{C}$ denote the field of numbers algebraic over $\mathbb{Q}$. Is there a proper subfield $F$ of $\mathbb{A}$ such that every nonconstant polynomial $p(x) \in ...

**1**

vote

**1**answer

82 views

### Condition to obtain a not compact embedding

I have the two spaces $W_0^{1,p}$ with the norme $$||u||^p=||u||^p_{L^p}+||\nabla u||^p_{L^p}$$ and $$L^{p^*}_{\alpha}=\{ u~\text{measurable}, \int_{\Omega} (|x|^{\alpha} u(x)|)^{p^*} dx<\infty\}$$ ...

**5**

votes

**0**answers

106 views

### Rankin-Selberg for Maass form GL(3)xGL(2)

Let $F$ be a Maass cusp form for $\mathrm{SL}(3,\mathbb{Z})$ (level 1 trivial character).
Let $g$ be a Maass cusp form for $\Gamma_0(N)$ with character $\chi$ mod $N$. For convenience, you may assume ...

**1**

vote

**0**answers

40 views

### Epsilon-net of operator norm ball around Identity

Suppose I look at the set of matrices which are invertible and satisfy
$$
\left\|A-Id\right\|_{op}<r
$$
for some $r<1$, where $Id$ is the $n\times n$ identity matrix. An $\epsilon$-net of such ...

**-1**

votes

**0**answers

39 views

### Martingale definition [on hold]

To prove that one process is Martingale, generally we prove 3 things :
1)
X is adapted.
2)$$ \mathbf{E} ( \vert X_n \vert )< \infty $$
3) $$\mathbf{E} (X_{n+1}\mid X_1,\ldots,X_n)=X_n $$
I ...

**3**

votes

**6**answers

359 views

### classification of $p$-groups

I have two questions regarding to $p$-groups.
A $p$-group $G$ is said to be extraspecial of $G'=Z(G)$ has order $p$. Hence extraspecial groups are examples of $p$-groups with cyclic center. Of ...

**2**

votes

**0**answers

159 views

### On Abelian Galois Covering

Consider a complete quadrangle $\Delta$ in $\mathbb{CP}^2$ (i.e. the union of the six
lines through points $P_1$, $P_2$, $P_3$ and $P_4$ in general position). Let $f: Y := \hat{\mathbb{CP}^2}(P_1, ...

**1**

vote

**1**answer

67 views

### Arc Sine law for Random Walk conditioned to non-absorption or not?

Let $S_n$ be simple symmetric Random walk on the integers in $[-N,N]$ with states $N$ and $-N$ absorbing. Let $\tau$ be the time to absorption when $S_0 = 0$.
Is the $E(S^{2}_{n}| \tau \geq n)$ ...

**7**

votes

**1**answer

112 views

### Decompose dependent random variables into function of dependent and independent parts

Let $X$ and $Z$ be two (possibly dependent) random variables. Is it necessarily the case that there exists a Borel function f and a random variable $Y$ that is independent of $X$ such that $Z = f(X, ...

**3**

votes

**1**answer

185 views

### What are the indecomposable classes on a del-Pezzo surface?

Let $X_k$ be $\mathbb{P}^2$ blown up at $k$ points (where $k$ is $0$ to $8$).
Let $\beta \in H_2(X_k, \mathbb{Z}) $ be a homology class given by
$$ \beta := n L + m_1 E_1 + \ldots + m_k E_k $$
...

**0**

votes

**0**answers

14 views

### Number of Nodes in energy eigenstates [migrated]

I have a question from the very basics of Quantum Mechanics.Given this theorem:
For the discrete bound-state spectrum of a one-dimensional potential let the allowed energies be $E_1<E_2< ...

**22**

votes

**1**answer

672 views

### How hard is it to destroy a diamond? (with a real)

If we start with $V\models\lozenge$, it is not hard to force the failure of diamond. You can blow up the continuum, or destroy all the Suslin trees. You can blow up the continuum of $\aleph_1$, and ...

**3**

votes

**0**answers

98 views

### Does there exist a continuous surjection? [on hold]

Let $C$ be an irreducible projective cubic in $\mathbb{P}_2$ with a singular point $p$. So consider $f: \mathbb{P}_1 \to C$ defined as follows. Identify $\mathbb{P}_1$ with the set of lines in ...

**0**

votes

**0**answers

86 views

### Four kinds of generalized hypergeometric formulas for $\pi$

Given,
$$\begin{array}{|c|c|c|c|}
\hline
n&a_n&b_n&c_n\\
\hline
1 & 6541681608 & 163096908 & -640320^3\\
\hline
2 & 85840 & 4492 & -14112^2\\
\hline
3 & 28302 ...

**-1**

votes

**0**answers

43 views

### Characterize polytopes resulting from cutting a convex polytope by a hyperplane [on hold]

We have a convex polytope $P$ for which we know its set of vertices. Using this set we characterize the H-representation of $P$ as: $\mathbf{A}\mathbf{x} < \mathbf{b}$.
If a hyperplane defined by ...

**-4**

votes

**0**answers

13 views

### How to find the matrix of adjoint transformation R* according to the usual scalar product [on hold]

transformation R3 -> R3 is a" circle" around the line x / z = -y = z / 2

**0**

votes

**0**answers

16 views

### Intersection of an irreducible curve with an exceptional divisor

Suppose $A$ is an irreducible curve on the blowup of $\mathbb{P}^2$. Then if $A$ is not equal to $E$ (where $E$ is the exceptional divisor) it has to intersect it positively. However, $A.E = c_1 ...

**3**

votes

**0**answers

147 views

### Why the composition of planar tangles is well-defined?

In the planar algebra theory (see here or there section 2), a planar tangle is an isotopy class; then to define the composition of two tangles, we need to choose a representative in each classes. See ...

**4**

votes

**0**answers

105 views

### What is the probability that a Gaussian random variable is the largest of three Gaussian random variables?

Consider three independent, normally distributed RVs: $YA \sim N(a,\sigma ^{2}),$ $%
YB\sim N(b,\sigma ^{2})$ and $YC\sim N(c,\sigma ^{2})$.
What is the probability that $YA$ is the maximum?: $$\Pr ...

**2**

votes

**2**answers

234 views

### Is Eilenberg-Maclane $\wedge$ Moore space the spectrum of the cohomology theory $H^*(\ ,G)$?

In the web page http://www.encyclopediaofmath.org/index.php/Moore_space it can be found the following statement:
If $K(\mathbb Z,n)$ is the Eilenberg–MacLane space of the group of integers ...

**4**

votes

**2**answers

607 views

### Polish by compact is Polish?

Let $X,Y$ be separable and metrizable, with $Y$ Polish, and suppose there is a topological quotient map $f:X\to Y$ with compact fibers. Is $X$ Polish?
I have a specific space in mind, so if the ...

**1**

vote

**1**answer

39 views

### Intersection of complements of connected components (2)

Let $(X,d)$ be a non-compact, complete metric space and $K\subseteq X$ compact. Pick $x^* \in X\setminus K$.
Let $E$ be the connected component of $X\setminus K$ that contains $x^*$. Let ${\cal C}$ ...

**7**

votes

**2**answers

118 views

### Isomorphism problem on the class of induced subgraphs of a hypercube

A problem that I am currently studying translates to the problem of deciding whether two induced subgraphs of the hypercube $Q_k$ are isomorphic.
Now it feels to me that this class of graphs is "too ...

**4**

votes

**1**answer

99 views

### application of factorization theorem

Young's inequlity tells us that $L^{1}(\mathbb R)\ast L^{p}(\mathbb R) \subset L^{p}(\mathbb R)$ with norm inequality
$$\|f\ast g\|_{L^{p}} \leq \|f\|_{L^1}\|g\|_{L^p};$$
and of course this ...

**0**

votes

**0**answers

39 views

### Existence of Solution steady navier stokes with do nothing outflow condition

We consider the stationary navier stokes equation with mixed boundary conditions
$$
\begin{align}
-\nu\Delta u +(u\cdot\nabla) u + \nabla p &= 0\ \textrm{in}\ \Omega \\
div\ u&=0\ \textrm{in}\ ...

**4**

votes

**0**answers

97 views

### finite approximation equation on free group

An equation in a free group $F$ is an identity of the form $W(x_1,..,x_n,a_1,...a_n)$ where $x_1,...,x_n$ are variables, $a_1,...,a_n$ free generators of $F$ and $W$ a word in the free group on ...

**0**

votes

**0**answers

101 views

### Does the equality of product of integers modulo prime p holds in a given interval?

For any given prime $p$, does there exist $a_1,a_2,\dots,a_k,$ (not necessarily distinct) $b_1,b_2,\dots,b_m$ (not necessarily distinct) and $y_1$, $y_2$ such that
...

**-1**

votes

**0**answers

43 views

### Finite groups whose non-trivial elements have no fixed points [migrated]

I am interested in finite groups $G$ acting on a finite set $X$ with the following property:
(*) fix(g)=$\emptyset$ for all $g\in G\setminus\{1\}$,
where
fix(g):=$\{x\in X|gx=x\}$
denotes the set ...

**1**

vote

**1**answer

48 views

### Limiting absorption principle

I would like to know if there is a book (or a paper) which can give me an introduction to LAP. I tried to read some papers by myself, but I don't feel comfortable. I think that I need the basic ideas ...

**0**

votes

**0**answers

56 views

### Sheaves whose restriction maps are monomorphisms?

When the restriction maps of a sheaf of $\mathcal O_X$-modules are epimorphisms,
the sheaf is flasque and we have a whole theory of that. Is there a detailed study of the opposite phenomenon, i.e., ...

**-2**

votes

**0**answers

51 views

### Subgroups of the group $G_2 \times G_2$ [migrated]

Does the group $G_2 \times G_2$ have the group $SO(7)$ (or its double cover $Spin(7)$) as its subgroup? Here, $G_2$ is the compact exceptional group $G_2$.

**3**

votes

**1**answer

21 views

### Intersection of complements of connected components

Let $(X,\tau)$ be a topological space, $S\subseteq X$ such that there is $x^*\in X\setminus S$.
Let $E$ be the connected component of $X\setminus S$ that contains $x^*$. Let ${\cal C}$ be the ...

**3**

votes

**1**answer

45 views

### Normal Hopf ideals and Hopf subalgebras, quotient group schemes

There is a following theorem:
$H$ is a commutative Hopf algebra over a field $k$. Then there exists a bijective correspondence between
$$\{ \textrm{Hopf subalgebras }K\subset H \} \quad ...

**-4**

votes

**0**answers

22 views

### Compute eigenvalues and lash1e vectors (2n + 1) X (2n + 1) matrix: [on hold]

middle row: 1 ... 1 0 1 ... 1
middle column: 1 ... 1 0 1 ... 1
In the unmarked places are zero. Calculate at least in the case, when n=2
I have really no idea how to start.