**0**

votes

**0**answers

4 views

### About irreducible representation of symmetric group [migrated]

Consider the tensor space
$$\mathbb{C}^m\otimes \mathbb{C}^n\otimes\mathbb{C}^n\otimes\cdots\otimes\mathbb{C}^n$$ with $k$ factors.
The symmetric group $S_k$ on $k$ letters acts on this space (on ...

**-3**

votes

**0**answers

39 views

### Arun Bhandari,Master of philosophy in applied mathematicsm, Kathmandu University ,Nepal [on hold]

Greetings from Arun Bhandari, I am doing research in Numerical methods for nonlinear differential equations. Currently, I am working on He's Variational Iteration Method for this I need following ...

**-1**

votes

**0**answers

24 views

### What would be the impact - to the foundation of First Order Logic - of a sentence whose truth value is impossible to verify or know?

Suppose there's a sentence F written in L(PA) that is undecidable in PA, and whose truth value is impossible to verify (know), then face value it seems both the formal systems T1 = PA + {F} and T2 = ...

**0**

votes

**0**answers

6 views

### Avoiding the range of a bivariate function or Diophantine function

I have a bivariate integer function where x,y are positive integers in the function $f(x,y)=5+23x+7y+30xy$. The lattice points of this function, or its range, contain a large number of values. I'm ...

**0**

votes

**0**answers

15 views

### Gauss Curvature Equation for hypersurface in Semi-Riemannian manifold

We have the Gauss curvature equation:
$$\langle R(V,W)X,Y\rangle = \langle R'(V,W)X,Y\rangle - \langle II(V,X),II(W,Y)\rangle + \langle II(V,Y),II(W,X)\rangle$$
Here $M$ is an immersion in $N$. ...

**0**

votes

**1**answer

40 views

### Is the locus of points which have irreducible fibers constructible?

Suppose $X \rightarrow Y$ is a map of projective schemes over a field $k$. Is $\{y \in Y: \pi^{-1}(y) \text{ is irreducible}\}$ a constructible subset of $Y$?
Note: One cannot hope to do "better" ...

**0**

votes

**0**answers

22 views

### Thomsen Blaschke condition

I am reading a paper (Paper 1: https://ideas.repec.org/p/cwl/cwldpp/76.html, that cites another paper ( Paper 2) for its proof.
Paper 1, page 1, line 10 says : Consider the topological image G of a ...

**0**

votes

**0**answers

18 views

### Brownian bridge on a Lie group as a stochastic differential equation

Brownian motion $g_t$ on a compact Lie group satisfies the stochastic differential equation
$$dg_t = dB_t \circ g_t$$
where $B_t$ is Brownian motion on the Lie algebra and $\circ$ denotes ...

**0**

votes

**1**answer

48 views

### Solving Shroedinger Equation for the electronic energies of the Molecular Ion Hydrogen H2+ in the Elliptic coordinate system

Electronic Energies of Molecular Ion Hydrogen $H_2^{+}$
$r_1$ is the distance between the proton $1$ and the electron.
$r_2$ is the distance between the proton $2$ and the electron.
$R$ is the ...

**3**

votes

**0**answers

45 views

### Adjacency matrix, quivers

Let $Q$ be a quiver with finitely many edges and such that the underlying graph is connected. Let $I = \{1, \dots, n\}$ be the vertex set of $Q$, so we have $\mathbb{R}\{I\} \cong \mathbb{R}^n$.
For ...

**0**

votes

**0**answers

20 views

### Problem regarding sum of a recursive sequence

Problem of the recursive sum is as follows.
Find the sum
$$\sum_{r=1}^n U_r$$
where
$$U_r = \frac{U_{r-1}M_r}{M_{r-1}(a+b M_r)}$$
and
$$U_1 = \frac{M_1}{a+b M_1} , \ \ \sum_{r=1}^{n} M_r = 1.$$
Here ...

**0**

votes

**0**answers

13 views

### A Statement from Brauer and Nohel's book on stability of time-depending linear systems

On page 158 (The qualitative theory of differential equations; an introduction) the authors cite a 2x2 couterexample by Vinograd to the system y'=A(t)y where A(t)= \begin{matrix} -1 -9 cos^2 6t + 12 ...

**1**

vote

**1**answer

123 views

### Covering space theory, category theory

Requiring covering spaces of a well-behaved connected topological space $X$ to be connected, let $\mathcal{Cov}(X)$ be the category of covering spaces of $X$ and maps over $X$ and maps over $X$. Can ...

**1**

vote

**0**answers

27 views

### Jordan-Hölder-like statements for modules with $\Delta$-filtrations over a quasihereditary algebra

Definitions
Let $A$ be an Artin algebra (for instance, take $A$ to be a finite dimensional algebra over some field) and label the isomorphism classes of simple $A$-modules by the elements of a ...

**1**

vote

**1**answer

87 views

### Complete regularity in C*-algebras

It is clear that commutative C*-algebras correspond to locally compact Hausdorff spaces. And locally compact Hausdorff spaces are completely regular. Now, does the complete regularity statement have ...

**-2**

votes

**0**answers

19 views

### How to compute the direction of flattest ascent for a convex function

Consider an infinitely differentiable convex function $f:\mathbb{R}^n\rightarrow\mathbb{R}$ at the point $x_0$. So long as $x_0$ is not the minimum, it is well known that we can compute a unit vector ...

**0**

votes

**0**answers

19 views

### graph reconstruction via canonical labeling [on hold]

Graph edge deleted reconstruction: Given an edge deleted deck find the canonical lexicographically ordered largest representation for each card. Find the card with largest canonical label this is the ...

**0**

votes

**1**answer

43 views

### Probability of having no cycles of fixed length in $d$-regular graphs

According to this paper, the probability that a random $d$-regular graph of order $n$ has no cycles of length $c_1,c_2,\ldots,c_t$ is $$P=\exp\left(-\sum_{i=1}^t\mu_i+o(1)\right)$$ as ...

**0**

votes

**1**answer

58 views

### Why does optimization of a sum of two terms result in “neat” answers? [on hold]

This is a somewhat vague and philosophical question.
Consider the following three problems:
Problem 1:
Minimize over all real-valued $x,$ the function $f(x) = bx-ax^2$ where $a,b>0.$
...

**2**

votes

**0**answers

23 views

### How much larger than the relaxation time can the mixing time be?

The notation is mostly taken from the book "Markov chains and mixing times" by Levin, Peres, and Wilmer.
Consider an irreducible, aperiodic, time-reversible, discrete-time Markov chain on a finite ...

**0**

votes

**0**answers

253 views

### Some counter examples in group theory

In this question, which we flag it as a community wiki question, we search for a big list of groups $G$ which can not be isomorphic to a structure mentioned in $i.$ for some $i \in ...

**2**

votes

**0**answers

72 views

### A conjecture like Cayley–Bacharach theorem

Let five conics and 12 points on a plane, one conic through six points,
and one point lie on two conics. Then every cubic that passes through any
eleven of the points also passes through the 12th ...

**3**

votes

**0**answers

71 views

### Do very general hypersurfaces contain smooth surfaces with $c_1^2>2c_2?$

Let $X$ be a very general hypersurface of degree $d$ in $\mathbb{P}^n.$ Does $X$ contain a smooth surface $S$ with $c_1(T_S)^2>2c_2(T_S)$?
For $d<<\sqrt{n}$ the answer is yes, as $X$ will ...

**4**

votes

**0**answers

147 views

### Is a determinant 2x2 positive and increasing?

Let $X_1,X_2,X_3$ be a three discrete (integer and non-negative valued) random variables with local probabilities $a_k:=\mathbb{P}(X_1=k)$, $b_k:=\mathbb{P}(X_2=k)$, $c_k:=\mathbb{P}(X_3=k)$ and ...

**0**

votes

**0**answers

16 views

### Estimate $\int_0^1 g_k(x) d\mu(x)$, where $\{g_k(x)\}_{k=0}^\infty$ is a generic Parseval frame for $L^2(\mu)$

I came across the following integral in some applied problem:
$$\int_0^1 g_k(x) d\mu(x)$$
where $\mu$ is a Borel probability measure on $[0, 1)$, and $\{g_k(x)\}_{k=0}^\infty$ is a generic Parseval ...

**5**

votes

**2**answers

301 views

### The sum of a series, continued

In this question the OP asks whether the sum
$$
f(q, \alpha) = \sum _{k=1}^{\infty } \frac{q^k \left(q^k-1\right)^\alpha}{(q;q)_k}
$$
is ever zero. An experiment with Mathematica indicates, to any ...

**0**

votes

**1**answer

57 views

### Intersection of compact sets in the compact-open topology

Let $(X,\tau)$ be a topological space. We topologize $\tau$ itself in the following way. For $K\subseteq X$ compact, we set $${\cal V}_K=\{U\in \tau: U \supseteq K\}.$$ The compact-open topology on ...

**7**

votes

**1**answer

108 views

### Physical interpretation of the mellin transform variable?

I shall keep this to the point: Given a time domain signal say microphone recording of a conversation:
Laplace tranfrom of x is some function X(s) say defined in the complex plane. I like to think ...

**2**

votes

**0**answers

51 views

### The converse of von Neumann's mean ergodic theorem

Recall that the Hilbert space version of von Neumann's mean ergodic theorem says the following.
Let $\{F_n\}_{n=1}^\infty$ be a right Følner sequence of a countable discrete amenable group $\Gamma$ ...

**3**

votes

**0**answers

45 views

### Wavelet-like Schauder basis for standard spaces of test functions?

The Schwartz space of test functions $\mathcal{S}(\mathbb{R})$ is isomorphic to $\mathfrak{s}$ the space of sequences of real numbers with faster than power-like decay. Likewise, the space ...

**2**

votes

**0**answers

63 views

### Modules over an Azumaya algebra and modules over the associated Brauer-Severi variety

Assume $\mathcal{A}$ is an Azumaya algebra of rank $r^2$ on a smooth projective scheme $Y$ over $\mathbb{C}$. Let $f: X\rightarrow Y$ be the Brauer-Severi variety associated to $\mathcal{A}$.
I read ...

**2**

votes

**2**answers

38 views

### Algorithm to determine isomorphism of 2 maximal planar graphs

I read on wikipedia that there are efficient algorithms to answer the question whether 2 (maximal) planar graphs F and G are isomorphic. However, after some (IMHO) substantial searching I don't seem ...

**10**

votes

**0**answers

134 views

### Del Pezzo surfaces and homotopy groups of spheres

A (complex) del Pezzo surface is a smooth projective complex surface with ample anticanonical line bundle. Such surface has a degree defined as the self intersection of the canonical divisor. It is ...

**-1**

votes

**0**answers

39 views

### Geometry of a submanifold of $\Bbb S^n$ [on hold]

Let assume that $S$ is a subspace of $\Bbb R^{n+1}$ and $M:=S\cap {\Bbb S^n}$, we know that $M$ is a submanifold of $\Bbb S^n$. I need to know the tangent space of $M$ at every $x\in M$ as well as the ...

**1**

vote

**1**answer

60 views

### Does totally proper forcing imply countable distributivity?

For a suitable model $M$ for $Q$ and a condition $q \in Q$ we say that $q$ is $(M,Q)$-generic if whenever $r \leqslant q$, $D \in M$ dense, $D \subset Q$, $r$ is compatible with an element of $D \cap ...

**0**

votes

**0**answers

47 views

### A question regarding the relation between Freiling's Axiom of Symmetry and real-valued measurable cardnals

A major argument against Freiling's Axiom of Symmetry is the following (this from the wikipedia article of the same name):
"The naive probabalistic notion used by Freiling tacitly assumes that there ...

**0**

votes

**0**answers

26 views

### Homogeneous regular manifolds

In order to solve the well-known Plateau-Problem on a general (non-compact) Riemannian 3-manifold, Morrey first introduced the condition of homogeneous regularity and defined it in the following way:
...

**-1**

votes

**1**answer

43 views

### Parseval frame, convergence of $\sum_{k=0}^\infty \left\|g_k\right\|$

Let $\mu$ be a Borel probability measure on $[0, 1)$, and $\{g_k\}_{k=0}^\infty$ be a Parseval frame for $L^2(\mu)$. Does
$$\sum_{k=0}^\infty \left\|g_k\right\|$$
converges?

**0**

votes

**1**answer

40 views

### When is the identity Hilbert-Schmidt between weighted Sobolev spaces?

Set $w(x) = (1 + |x|^2)^{1/2}$ with $|\cdot|$ the Euclidian norm on $\mathbb{R}^n$. For $s,\mu \in \mathbb{R}$, we define the Sobolev space
$$H_2^{s}(\mathbb{R}^n) = \left\{f : \lVert f \rVert_{s} := ...

**0**

votes

**1**answer

39 views

### Numerical methods for solving a hyperbolic nonlinear PDE

What type of numercial methods are there to solve PDE of the sorts of:
$$f(x,t,u(x,t))u_{xx} - g(x,t,u(x,t))u_{tt} = F(x,t,u(x,t))$$
$$u(x,0)=G_1(x) , \frac{\partial u(x,0)}{\partial t}=H_1(x) ...

**3**

votes

**1**answer

67 views

### Dynamics of the distribution of prime factorization types in increasing intervals

I've tagged this as reference request as surely this question must be very well investigated, I just don't know how to look for it. Most likely the perfect answer will be in form of a keyword for ...

**-2**

votes

**0**answers

80 views

### almost complex embedding of $S^2$ and $S^6$ into $\mathbb{C}^N$ [migrated]

In Which Spheres are Complex Manifolds? , I find that $S^2=\mathbb{C}P^1$ is a complex manifold and $S^6$ is an almost complex manifold.
Are there references about:
What is the smallest integer $N$ ...

**-1**

votes

**0**answers

18 views

### norm of a matrix that have integral operator as its entries [on hold]

what is the norm of a matrix that have integral operator as its entries?
for example
$$\bordermatrix{\text{corner}&c_1&c_2&\ldots &c_n\cr
& A_{11} & A_{12}\cr
...

**3**

votes

**0**answers

27 views

### Current upper bound on length of addition chain

An addition chain for $n$ is a finite sequence of integers starting at 1 and ending at $n$, such that each element is a sum of two previous elements. A short addition chain for $n$ can be used, for ...

**-4**

votes

**0**answers

23 views

### constant rate of change [on hold]

When downloading a large file, Travis noticed that the estimated time remaining to complete the download decreased by 35 seconds for each additional megabyte downloaded. When he started the download ...

**3**

votes

**1**answer

130 views

### characteristic classes of tangent bundle of 2-nd unordered configuration space

Given a (real or almost complex) manifold $M$, Let the 2-nd unordered configuration space be the quotient space
$$
B(M,2)=(M\times M\setminus\ \Delta)/\ \mathbb{Z}_2
$$
where
$$
\Delta=\{(m,m)\mid ...

**0**

votes

**1**answer

93 views

### Is the map $\exp_x(\nabla_x \sum_{i=1}^m d^2(x_i,x))$ Lipschitz?

The last question is too general, this is a modification.
Let $M$ be an $n$ dimensional Riemannian manifold. Fix $m$ points $x_1,...,x_m$. Suppose $y$ is not in the cut locus of $x_i$ for $1 ...

**4**

votes

**0**answers

44 views

### Cutting a piece of cake that $n$ people value as exactly $w$

Stromquist and Woodall (1985) study the problem of Sets on which several measures agree. There are $n$ non-atomic value measures on the unit circle, and a parameter $w\in(0,1)$. The goal is to find a ...

**0**

votes

**0**answers

26 views

### Help with notations from 2D to 3D FFT representations as 1D FFT

I have this question on mathematics forum too, Notations, I thought of posting here, which ever place I get an answer, I will try to close it in the other.
I need some help and clarifications for my ...

**3**

votes

**0**answers

58 views

### How can I include irreducibility in a Groebner basis calculation?

I'm trying to prove impossibility of certain systems of differential/polynomial equations using Groebner basis techniques.
For example, consider the equation $qn = mf$, where each of the variables ...