# All Questions

**-4**

votes

**0**answers

19 views

### k to 12 curriculum philippines [on hold]

what will happen to students who didn't undergo the senior high school in k to 12, students who graduated in the old curriculum in ched the not k to 12 curriculum, what will happen to them in college ...

**-2**

votes

**0**answers

26 views

### k to 12 philippines [on hold]

i just want to ask this question, hope you will answer..what will happen to students who didn't undergo the senior high school in k to 12, students who graduated in the old curriculum in ched the not ...

**0**

votes

**1**answer

20 views

### NonLinear Maps and homogeneity

An example of a function $\phi : R^2 \to R$ such that $\phi(av) = a \phi(v)$ but $\phi$ is not linear.
So I know that I need to find a function that has linear homogeneity but doesn't have the ...

**1**

vote

**0**answers

14 views

### $G$-invariant part of products of determinants of minors

Let $G = SL_n$; then for any tuple $\lambda$ such that $\sum \lambda_i = n$, define $f_\lambda(g)$ as the product of the determinants of successive minors of lengths $\lambda_i$ of $g$ (e.g. for ...

**4**

votes

**0**answers

39 views

### Factors of the polynomial $X^n-a$

I am interested in the polynomial $X^n-a$ in $\mathbb{Q}[X]$, for some $a\in \mathbb{Q}^*$, and would like to know the irreducible factors of it. Is there something in the literature which gives a ...

**-1**

votes

**0**answers

40 views

### Is there a group-theoretic proof of the Riemann rearrangement theorem? [on hold]

The analytic proofs are easy to understand but they don't explain why commutativity breaks down when you go from finite sums to infinite sums of real numbers. I suspect that this involves the action ...

**0**

votes

**0**answers

10 views

### Generators for lattice polytopes

Let $V$ be a finite set of integral vectors in $\mathbb{R}_n$. Consider the real (positive) convex cone $\mathbb{R}^+V$ spanned by $V$. We can assume that all vectors in $V$ are extremal in ...

**5**

votes

**2**answers

83 views

### Not-lonely runners

The lonely runner conjecture
has several formulations.
They all involve a number $n$ runners running on a circular track,
each with a different speeds, and the conjecture is that each runner is ...

**1**

vote

**0**answers

11 views

### Compact imbedding - reference request

I am looking for reference to the following imbedding theorem
Theorem
For any $s>1/2$ fractional Sobolev space $W^{s}_2(0,1)$ imbeds compactly into $C([0,1])$.
I know how to prove it but I need ...

**-1**

votes

**0**answers

40 views

### How subset is a set is proved in ZF system? [on hold]

I guess that all subset is a set is guaranteed by the axiom of separation in ZF system. Otherwise the notion of power-set will not make sense.
But I wander how it's proved. I guess that the prove ...

**1**

vote

**0**answers

18 views

### Number of faces of a polytopal subdivision

Let $\mathcal{P}$ be a (bounded) polytope in $\mathbb{R}^d$ and let $\mathcal{C}$ be a polytopal subdivision of $\mathcal{P}$ [1].
Is there a known tight upper bound in the number of polytopes in ...

**5**

votes

**1**answer

356 views

### Removing an article from arxiv

I put up my paper on arxiv before sending it for submission. But now the journal I wish to submit it to is not accepting it since its already been published (or because its publicly available). Is ...

**2**

votes

**0**answers

62 views

### The embeddings $S^{6} \to S^{7}$ and $S^{7}\to S^{8}$

Is the standard smooth structure of $S^{7}$ the only structure for which each of the following canonical embedding is an smooth embedding?:
1)$S^{6}\to S^{7}$
2)$S^{7}\to S^{8}$

**1**

vote

**0**answers

53 views

### Universal cover of elliptic curve without a point

This is something that I perhaps would be expected to know, but don't. Let $E_\tau$ be the elliptic curve ${\mathbb C}/({\mathbb Z +\mathbb Z} \tau)$. Consider the complement of a point in $E_\tau$,
...

**2**

votes

**0**answers

38 views

### Degree of join of two varieties

Let $X\subset\mathbb{P}^n$ be an irreducible variety of degree $d$ and dimension $n-4$. Let $L\subset X$ be a line of mulitplicity $m$ in $X$. Assume that $m+1\leq d$ so that the general line spanned ...

**4**

votes

**1**answer

178 views

### Serious introduction to the Langlands program for nonspecialist

I recently became interested in the Langlands program and hope to learn more.
For context, I am an analytic number theorist but have some light background in algebraic number theory and modular ...

**0**

votes

**0**answers

23 views

### Any software that can symmetrize input sets?

Is there any software that contains symmetrization techniques ex. polarization, Steiner Symmetrization etc. I suppose not.
Which software would you suggest for rigid transformations?
Thank you

**0**

votes

**0**answers

26 views

### Calculating the the ratio of two Dirac delta functions as the limit of the ratio of nasent delta functions?

I am in a situation where I find myself with the ratio of Dirac delta functions. Specifically, I find myself with the ratio of the nascent deltas:
$\frac{\lim_{\varepsilon \rightarrow ...

**5**

votes

**0**answers

72 views

### Hecke-module structure implicit in definition of automorphic forms in Borel-Jacquet's Corvallis article

Let $G$ be a connected reductive group over a number field $F$, $G_\infty=\prod_{v\mid\infty} G(F_v)$, $\mathbf{A}$ the adèles of $F$, $\mathbf{A}_f$ the finite adèles of $F$. Fix a maximal compact ...

**-2**

votes

**1**answer

56 views

### What does “group size” mean in the -G option of directg in nauty?

To be sure I understand the definitions used in the nauty user manual: An automorphism group size (for a digraph) is the number of re-labelings (including the trivial original digraph) of the ...

**10**

votes

**0**answers

119 views

### function field analogy and global/absolute geometry

The "function field analogy" seems to be a topic that is considerably bigger than any one existing writeup conveys. There are several old question on MO and and MathSE that ask for details. One of the ...

**2**

votes

**0**answers

32 views

### Symplectic sum and Symplectic cut

The symplectic sum of Gompf and the symplectic cut of Lerman are known to be inverse of each other, in the sense that if you apply one of these first and the other one afterward, you obtain the ...

**0**

votes

**0**answers

17 views

### mixed semi definite and second order programming complexity order

Consider the following mixed semi definite and second order programming:
$\begin{array}{l}
\mathop {{\rm{min}}}\limits_{\bf{X}} \,{\rm{Tr}}\left( {{\bf{XA}}} \right)\\
{\rm{s}}{\rm{.t:}}\, & ...

**0**

votes

**1**answer

153 views

### Computing the Chern class of $S^6$

I am trying to calculate the Chern class of the tangent bundle of the sphere $S^6$. I am told that this is an interesting case, since $S^6$ is not a complex manifold, but it has an almost complex ...

**-4**

votes

**0**answers

34 views

### Integer solutions for multiple variable equations [on hold]

Obviously it will take some brute-force.
But how do I minimize the brute-force needed (optimize)?
I know one can solve Diophantine equations and quadratic Diophantine equations. But what if I have ...

**0**

votes

**0**answers

45 views

### Examples of manifolds whose second Stiefel-Whitney satisfies a nontriviality condition

I'm looking for examples of pairs $(M,L)$ where $M$ is a symplectic manifold, $L$ a (closed, connected) Lagrangian submanifold, such that the second Stiefel-Whitney of $L$, $w_2(TL)$, evaluates ...

**5**

votes

**1**answer

135 views

### Detection of stable homotopy by K-theory spectra

This is primarily a reference request. Does anyone know of any writing about algebraic K-theory spectra picking up elements in the stable homotopy groups of spheres in their Hurewicz image coming from ...

**-1**

votes

**0**answers

32 views

### Closed sets on the product space and operators [on hold]

$H$ is an hilbert space and $C$ is a closed subset of $H\times H$ with the product topology. If $P$ is the projection $P: (x,y) \in F\times F \to y \in F$ do we have that
the set $$P(C)= \{ P((x,y)), ...

**1**

vote

**1**answer

74 views

### Identity involving shifted Legendre coefficients

For small values of $n$ ($2\leqslant n\leqslant 5$), the coefficients $a_k = (-1)^k{n\choose k}{n+k\choose k}$ of the shifted Legendre polynomial $\tilde{P}_n(x)$ satisfy the identity ...

**-2**

votes

**1**answer

87 views

### AI / Machine Learning related to high/modern/front mathematics [on hold]

I major math and cs. and i'm interested in ai/machine learning/data mining.
so i want to know what math subjects are used in frontier of these technology.
especially, high mathematical tool, like ...

**3**

votes

**1**answer

49 views

### Boolean completion (of a forcing notion) isomorphic to each of its cones

Suppose $ \mathbb{P} := (P, {\leq_P}, 1_P) $ is a separative partial order. Let $ \mathbb{B} := \operatorname{RO}(\mathbb{P}) $ denote the Boolean completion.
Fix some dense embedding $ i \colon P ...

**0**

votes

**0**answers

47 views

### Collection of pointset topological spaces which form the terminal Grothendeick infinity topos

In Lurie's "Higher Topos Theory", he mentions two models of the terminal (Grothendieck) $(\infty,1)$-topos of "spaces". Firstly, the collection of Kan complexes and simplicial maps. Secondly, the ...

**0**

votes

**1**answer

43 views

### Invariance of mutual information

Let $I(X,Y):=H(X)+H(Y)-H(X,Y)$ be the mutual information of the joint probability distribution $p_{XY}$ (here $H(\cdot)$ is the Shannon entropy of its argument). I know that the mutual information is ...

**1**

vote

**1**answer

38 views

### Uniqueness of solution of a nonconvex optimization problem

What conditions need to be hold for a nonconvex optimization problem to have a unique solution?
Specifically, I have the following minimization problem that I'd like to know whether it has a unique ...

**0**

votes

**0**answers

37 views

### Can we deduce that all the real zeros of those $k^{th}$ derivatives are also simple?

Let $$L(C,s)=\sum_{n=1}^\infty \frac{a_n}{n^s}$$ be the Dirichlet series of the Hasse--Weil L-function of an elliptic curve $C$ over $ℚ$. The modularity theorem implies that $L(C,s)$ is the ...

**-1**

votes

**0**answers

42 views

### Approximation of bounded continuous functions by Lispschitz bounded functions

Let $H$ be an Hilbert space and $f : H \rightarrow \mathbb{R}$ a continuous and bounded by $M>0$ function. Is it possible to construct a sequence of functions $f_n$ Lipschitz uniformly bounded by ...

**2**

votes

**0**answers

25 views

### Approximating a superharmonic function, by smooth superharmonic functions

Let $\Omega\subset\mathbb{R}^N$ be a bounded smooth domain. Assume that $u\in W_0^{1,2}(\Omega)$, $u\ge 0$ and $-\Delta u\ge 0$ in the sense of distributions ($u$ is superharmonic).
The standard ...

**-4**

votes

**0**answers

36 views

### non-degenerated vector spaces and Lie algebras [on hold]

A symplectic space is a finite dimensional vector space V over GF(2) equiped with an alternating bilinear form and if the form is non-degenerated then V is called a non-degenerated symplectic space.
...

**-1**

votes

**1**answer

152 views

### How to prove this equality in $\ell_1$ [on hold]

Let $w$ be any element in $\ell_1$, and $(w_n)$, $(z_n)$ two bounded sequence in $\ell_1$ that converge to 0 pointwise. Then we have ...

**2**

votes

**0**answers

30 views

### König-Wittstock norm on Banach space

Let $(E,\Vert.\Vert)$ be a real Banach space and $\ell\ne 0$
an non-continuous linear form on $E$.
Let $a\in E$ be such that $\ell(a)=1$.
König-Wittstock [Non-equivalent complete norms
and would-be ...

**2**

votes

**2**answers

114 views

### Is the hypersurface satisfying $\langle x-x_0,\nu\rangle>0$ diffeomorphic to sphere?

Let $p:M\to \mathbb{R}^{n+1}$ be the immersed hypersurface. Is the following thing right? If there exists a point $x_0$ in $\mathbb{R}^{n+1}$ such that $\langle x(p)-x_0,\nu(p)\rangle>0$ for all ...

**-2**

votes

**0**answers

61 views

### Any other operators that may convert agebraic function into transcendental ones [on hold]

As we know,integral may convert or map a rational function or algebraic function into transcendental one,are there any other operators that may convert a rational function or algebraic function into ...

**1**

vote

**0**answers

32 views

### d-refining covering of normal space

If $X$ is normal, it is well known that for any open-covering $(U_i)$ of $X$, there exist closed subspaces $F_i$ and $G_i$ and an open subspaces $O_i$ such that $$F_i\subset O_i\subset G_i\subset ...

**1**

vote

**0**answers

51 views

### How to test whether a distribution follows a power law? [on hold]

I have the data of how many users post how many questions.
For example,
[UserCount, QuestionCount]
[2, 100]
[9, 10]
[3, 80]
... ...
it means each of the 2 users posts 100 questions, each of the 9 ...

**2**

votes

**0**answers

60 views

### Lagrangian submanifolds in $T^\ast S^n$

Let $L\subset T^\ast S^n$ be a properly embedded Lagrangian submanifold homeomorphic to $\mathbb{R}^n$ with respect to the canonical symplectic structure on $T^\ast S^n$, and suppose $L$ intersects ...

**2**

votes

**2**answers

90 views

### Product of Lebesgue and counting measures

Let $\mathbb R$ be endowed with the standard Euclidean topology and let $\widetilde {\mathbb R}$ denote the line endowed with the discrete topology. Let $\mu$ and $\nu$ denote the Lebesgue and ...

**3**

votes

**2**answers

54 views

### Is this generating family of a measurable space of point measures a pi-system?

I'm learning some probability and measure theory and working my way through the first few paragraphs of [1]. My question is perhaps too basic for Math Overflow, but I hope it is welcome here.
Point ...

**0**

votes

**0**answers

53 views

### Symplectic isotopies between small balls?

Let $(X,\omega)$ be a connected symplectic manifold, possibly with boundary. Let $g_1, g_2: B(1) \to X$ be two balls in $X$. Is it true that if $\delta$ is sufficiently small, then there is an ...

**-4**

votes

**0**answers

41 views

### let A be an n*n matrix with real entries which of the following is coorect? [on hold]

let A be an n*n matrix with real entries which of the following is coorect?
(a) if A^2 =0 then A diagonalisable over complex numbers
(b) if A^2= I then A diagonalisable over real numbers
(c) if A^2 ...

**-4**

votes

**0**answers

42 views

### Which of the following conversion is wrong in the number system? [on hold]

Here is a diagram.
which of the 2 boxes' conversion is wrong and please provide me a reason for it. I am doing the same conversion in 2 different procedure. where am i making the mistake.Please help ...