# All Questions

**0**

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24 views

### Weierstrass model for Calabi-Yau fourfolds

The local Weierstrass model for a Calabi-Yau threefold looks like:
$$ y^2 = x^3 + f\left(z_i\right)x + g\left(z_i\right) \subset \mathbb{P}^2_{\left[x,y\right]} $$
With $f\left(z_i\right) \in ...

**0**

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18 views

### The Cauchy Problem in General Relativity: Existence of a Hausdorff Development

This is related to a problem that I posed about a year ago. I was given several references by a number of experts who were kind enough to entertain my rather arcane question. Those references were ...

**0**

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21 views

### Zariski open set of linear forms

Let $I$ be a graded homogeneous ideal over $k[x_1, ... ,x_n]$ and $h$ a linear form, let $H$ be the corresponding hyperplane and $I_H$ the restriction of $I$ to $H$.
I am looking for a Zariski open ...

**0**

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7 views

### How to characterize elements in the Bruhat open cell? [migrated]

This might be an elementary question. For simplicity, let's assume $G=GL(n,F)$, where $F$ is a local field. Let $U$ be the subgroup of upper triangular unipotents, $A$ the subgroup of diagonal ...

**-2**

votes

**0**answers

19 views

### Alternating series sum [on hold]

How to find such alternating series sum?
\begin{equation}
\sum_{n = 0}^\infty \frac {(-1)^{n-1}}{3^{n-1}}
\end{equation}

**1**

vote

**0**answers

27 views

### Open covering of the Hilbert functor of points

Let $R \to A$ be a homomorphism of commutative rings. Define the functor $$\mathrm{Hilb}^n_{A/R} : \mathsf{CAlg}(R) \to \mathsf{Set}$$ as follows: If $B$ is a commutative $R$-algebra, then ...

**-1**

votes

**0**answers

30 views

### Is der a relation between the product of 2 numbers and their sum? [on hold]

a * b = x
a + b = y
Is there a way to obtain y from x without using a,b ?
PS: a,b are prime-numbers. so there is only one possible y.

**-2**

votes

**0**answers

24 views

### Possible Regularity of “non- Platonic solid” Polygons [on hold]

I present the question Most Regularity of a Polygon. Some readers have discussion about its informality. A formal version of this question is presented here:
Let P be a polygon with the following ...

**0**

votes

**0**answers

76 views

### Is Independent University of Moscow recognized?

What graduate schools recognize the degree from Independent University of Moscow? It is not a university strictly speaking and their degree doesn't have any official status in Russia, but they claim ...

**1**

vote

**0**answers

47 views

### Can this graph polynomial be efficiently computed?

I am a physicist, so apologies in advance for any confusing notation or terminology; I'll happily clarify. To provide a minimal amount of context, the following graph polynomial came up in my research ...

**2**

votes

**0**answers

32 views

### Software tools for medium-scale systems of polynomial equations

I am attempting to find all real solutions of a system of 12 polynomial equations in 12 unknowns. The equations each have total degree 6 and contain up to 1700 terms. I am only interested in real ...

**-3**

votes

**0**answers

39 views

### Symmetric group representation from alternating groups [on hold]

Is the symmetric group $S_n$ isomorphic to a direct sum or tensor product of alternating groups $A_m$? Can any combination of alternating groups ($(A_m \otimes A_m)\oplus A_m$ .. etc) yield a valid ...

**0**

votes

**0**answers

105 views

### Non-Abelian Fourier Analysis

I'm currently thinking to generalize a known result on abelian groups to non-abelian groups. This is the problem. Fix an abelian group $G$. We know that:
$\mathbb{E}_{\chi\in ...

**1**

vote

**1**answer

56 views

### An inequality concerning convexity and expectation

Assume $f$ and $g$ are nonnegative with
$$\int_0^\infty f(x)dx=1=\int_0^\infty g(x)dx
$$
and
$$\int_0^\infty xf(x)dx<\infty > \int_0^\infty xg(x)dx
$$
Is it true for nonnegative numbers $p$, $q$ ...

**0**

votes

**0**answers

34 views

### Geometry of the triangle: from the centroid to the orthocenter and beyond [on hold]

Let A', B', C' be points on the perpendicular bisectors of the sides of a triangle ABC so that the angles A'BC, B'CA and C'AB are equal. The lines AA', BB' and CC' concur.
Which is the locus? Do you ...

**2**

votes

**2**answers

66 views

### Pairwise dependent random walk recurrent

Let $\{D_i\}_{i=0,1,2,\dots }$ be independent $\exp(1)$ random variables. We use the collection $\{D_i\}$ to define a random walk on $\mathbb Z$ by $S_0 = 0$ and $S_n = \sum_1^n X_i$ with $X_i \in ...

**-1**

votes

**0**answers

16 views

### Asymptotic expansion on 3 nonlinear ordinary differential equations

The 3 nonlinear differential equations are as follows
\begin{equation}
\epsilon \frac{dc}{dt}=\alpha I + \ c (-K_F - K_D-K_N s-K_P(1-q)), \nonumber
\end{equation}
\begin{equation}
\frac{ds}{dt}= ...

**6**

votes

**1**answer

150 views

### Compute an arbitrary decimal place of $\pi$

Is there a method to find the value of the $n$-th decimal place of $\pi$ which is more efficient than having to compute all decimal places before as well?

**0**

votes

**1**answer

38 views

### How do I show that a separable isogeny is central?

I've been trying to prove this (probably very simple) result that is stated in a paper that I'm reading:
Let $G$ and $H$ be connected semisimple algebraic groups defined over a field $F$, and let $f: ...

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votes

**0**answers

23 views

### Finite differencing scheme for Hamilton's equation with planar linkages

I am trying to simulate the movement of a planar linkage in the plane whose position and momentum obey Hamilton's equations, which is to say that $${{dq}\over{dt}} = {{dH}\over{dp}}$$ and ...

**6**

votes

**0**answers

117 views

### Representation of finite groups in a compact Lie group

Let $H$ be a finite $p$-group, and let $G$ be a compact connected Lie group. Then
it is well-known that $[BH,BG]\cong Rep(H,G)$, where $BH$ and $BG$ are classifying spaces and $Rep(H,G)$ is the set ...

**1**

vote

**0**answers

61 views

### Reference for analyticity of $K$-theory

This is a follow-up to my last question, Homotopy excision for structured ring spectra -- reference?. The immediate reason why I care about Blakers-Massey theorems for ring spectra is to prove that ...

**4**

votes

**1**answer

96 views

### Most Regularity of a Polygon

Conseider $n$ electrons in an empty sphere. What structure do they make?
This question have two cases: (i) if electrons should be sit on the boundry of sphere (one can suppose that the boundry of ...

**2**

votes

**1**answer

88 views

### Carlsson's spectrum BG^-V

In the appendix to Carlsson's "Equivariant stable homotopy and Segal's Burnside ring conjecture," he introduces a spectrum BG^-V associated to a G-representation V. It is like a Thom spectrum of the ...

**0**

votes

**0**answers

50 views

### Albanese map on a universal jacobian associated to a curve on an abelian surface

Given an abelian surface $A$ and a curve $C$ on it, consider the component $\{C\}$ of the Hilbert scheme of curves with the same cohomology class of $C$.
I would say that it has a fibration structure ...

**1**

vote

**0**answers

80 views

### Error in trace of operator

Imagine you have a Schroedinger operator $H:=-\frac{d^2}{dx^2}+V$ with $V \in C[a,b]$ on some compact interval $[a,b]$. The boundary conditions are supposed to be taken in such a way that this ...

**-4**

votes

**0**answers

38 views

### What do rank-2 tensor entries represent? What's their geometrical meaning? [on hold]

given a vector (with, say, 3 dimensions), if I multiply that with a second-rank tensor, I can make it change in both direction and magnitude (for that 2nd rank tensors are involved in vector-vector ...

**0**

votes

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96 views

### Cohomology group vs sheaf of cohomology group

Suppose $F$ is a coherent sheaf on a smooth (algebraic or complex) variety $X$. Then we can consider the cohomology groups $$H^p(X,F)$$ for all $i$. Now, let we consider the sheaf ...

**1**

vote

**0**answers

57 views

### Singularities of secant varieties of rational normal curves

Let $C\subset\mathbb{P}^n$ be a rational normal curve of degree $n$, and let $Sec_k(C)\subset\mathbb{P}^n$ be its $k$-th secant variety. By Theorem 1.1 in this paper:
...

**1**

vote

**1**answer

109 views

### Linear map with two “incompatible” representations

Let $K$ be a field and let $V$ be the set of sequences $\{v_1,v_2,\dots\}$ of elements of $K$. If $A=\{a_1,a_2,\dots\}$ is also a sequence of elements of $K$, then it defines an endomorphism of $V$ ...

**3**

votes

**1**answer

94 views

### What is a degenerate Legendre Transformation?

I am studying the Lagrangian and Hamiltonian description of some dynamical systems. The problem with this description of the particular kind of systems I am studying, is that the Legendre ...

**0**

votes

**1**answer

63 views

### Is there some lattice not rigid

I heard that in complex hyperbolic space setting for example CH2, there is some deformation of lattice nontrivial. What confused me is it seems contradicting Mostow Rigidity. Could someone explain ...

**0**

votes

**0**answers

24 views

### Representation of piecewise functions using variational inequalities

I need some help about how to represent piecewise smooth functions defined over N subintervals by using variational inequalities. From a paper I'm analyzing I get:
"If we can find a function ...

**6**

votes

**1**answer

124 views

### Homotopy excision for structured ring spectra — reference?

I'm looking for a reference for analogues of the Blakers-Massey triad connectivity theorem (and its higher-order generalization) for ring spectra. That is:
Suppose that $A\to A_1$ is a ...

**0**

votes

**0**answers

44 views

### quasiprimitive non-solvable groups

I'm looking for the reference about quasiprimitive unsoluble groups. Actually we can find a lot of useful things about quasiprimitive solvable groups in "Representations of solvable groups by Manz and ...

**2**

votes

**0**answers

52 views

### Which valuations of a field yield codimension $1$ subschemes of their 'models'

For a field $F$ (for example, a one generated by a finite number of its elements) there is a directed set of its 'models' (in this case those are 'arithmetic' schemes whose fraction field is $F$). It ...

**0**

votes

**1**answer

56 views

### On two notions of 'generators' for a 'large' triangulated category

Let $C$ be a triangulated category that is closed with respect to arbitrary small coproducts; let $D$ be some class of objects of $C$. Then it would be natural to say that $D$ generates $C$ either if
...

**1**

vote

**0**answers

47 views

### Interior gradient estimate for uniformly elliptic equations

I am struggling with a problem like this: In dimension $n\geq 3$,
For the following uniformly elliptic equation, do we have interior gradient estimates?
$$a^{ij}(x)u_{ij}(x)+u_{nn}=0.$$, where ...

**6**

votes

**1**answer

228 views

### The (un)decidability of Robinson-Arithmetic-without-Multiplication?

I asked this over at math.stackexchange, and though a number of people were interested enough to vote up the question, I didn't get an answer -- which makes me wonder whether it isn't quite so ...

**2**

votes

**1**answer

72 views

### Vanishing patterns of minors of matrix

Let $M$ be a $m\times n$ matrix with entries in, say $\mathbb{C}$; assume $n\leq m$. Denote by $I\subseteq\{1,2,\ldots, n\}$ a subset of the columns of M. I am interested in positive results to the ...

**8**

votes

**1**answer

172 views

### A strengthening of base 2 Fermat pseudoprime

If $n$ is a prime then for all $k$ with $1 \le k \le [n/2]$,
$k$ divides ${n-1 \choose 2k-1}$ because of the identity
${n-1 \choose 2k-1} \frac{n}{k}=2{n \choose 2k}$. My question is whether
an ...

**0**

votes

**1**answer

31 views

### Fitting a quadratic using regression when the y-intercept needs to be 0 [on hold]

I'm trying to fit a quadratic $a_0 + a_1x + a_2x^2$ by Polynomial Regression:
$$
\begin{pmatrix}
n & \Sigma x_i & \Sigma x_i\\
\Sigma x_i & \Sigma x_i^2 & \Sigma x_i^3\\
\Sigma ...

**0**

votes

**0**answers

74 views

### A linear/Lie algebra problem

Let $\mathfrak{g}$ be a complex linear Lie algebra of dimension $n$. If there exists a basis $\{e_1,\dots,e_n\}$ of $\mathfrak{g}$ such that ...

**16**

votes

**2**answers

730 views

### Why do Lie algebras pop up, from a categorical point of view?

Groups pop up as automorphism groups in any category.
Rings pop up as endomorphism rings in any additive category.
Is there a similar way to attach a Lie algebra to an object in a category of a ...

**1**

vote

**0**answers

46 views

### If a compact real submanifold of $\mathbb{CP}^n$ is approximable by complex algebraic curves, is it algebraic?

To make this into a separate question:
If the supports of a sequence of complex algebraic curves in $\mathbb{CP}^n$ (images of non-constant holomorphic maps from compact Riemann surfaces) converge to ...

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votes

**0**answers

75 views

### a question on sum of Gaussian binomial coefficients

I was trying to calculate something and at some point I get the following sum:
\begin{equation}
\sum_{t=0,t \text{ even}}^{s}{s+3n \brack s-t}\sum_{i = 0}^{t/2}q^{2i^2}{t/2+2n-i \brack t/2-i}{n ...

**2**

votes

**2**answers

227 views

### $K$-homology of $BG$

Let $G$ be a finite group. Atiyah proved that the $K$-cohomology of $BG$ vanishes in odd degrees and in even degrees is the completion of the representation ring of $G$ at the augmentation ideal.
...

**1**

vote

**0**answers

18 views

### Degenerations and spanning monomials

Let $R = \mathbb{C}[x_1,…,x_n]$, let $J\subset R$ be a graded ideal, and consider the initial monomial ideal $\operatorname{in}(J)$ with respect to some term order. Suppose that we are given a linear ...

**-4**

votes

**0**answers

58 views

### Video Lecture for topolgy [on hold]

want to study general topology.
i find video lecture at nptel, but instructor's pronunciation is hard to understand.
so other course to study general topology?
thankyou!

**0**

votes

**0**answers

19 views

### Mutual information staying constant under composition of channels

Consider the following scenario: one has 2 communication channels $C_1$ and $C_2$. Denote by $p(x)$ the input probability distribution.
The mutual information between the input and the output of ...