# All Questions

**0**

votes

**0**answers

5 views

### Exactness of pure functors

I can't prove this lemma in "Notes on motivic cohomology, Beilinson, Macpherson, Schechtman":
Lemma. A pure functor is exact.
Definitions: A mixed category $\mathcal{M}$ is a ...

**1**

vote

**0**answers

11 views

### Geodesics and Riemannian submersions

Let $X,Y$ be Riemannian manifolds, and $f\colon X\to Y$ be a Riemannian submersion.
Let $\gamma$ be a geodesic on $X$ starting at a point $x\in X$ and which is orthogonal to the fiber $f^{-1}(f(x))$.
...

**2**

votes

**0**answers

14 views

### Trigonometric polynomials on non-compact and non-abelian groups

I asked this initially in math.stackexchange, but it disappeared almost immediately, so I hope it will be proper to aks this here.
Hewitt and Ross define trigonometric polynomial on a locally compact ...

**2**

votes

**1**answer

49 views

### general formula for volume of a simplex?

I am looking for a general formula to calculate the volume of a euclidean simplex in any number of dimensions. On Wikipedia I found that a formula similar to Heron's formula can be applied to ...

**1**

vote

**0**answers

13 views

### Divisibility of the degree of an extension by the degree its residual field

Let $A$ be and integrally closed domain whose quotient field is $K$, $L$ be a finite extension of $K$, and $B$ be the integral closure of $A$ in $L$. Let $M_A$ be a maximal ideal of $A$, and $M_B$ be ...

**1**

vote

**0**answers

16 views

### Recent trends in effective analysis

The references listed at http://en.wikipedia.org/wiki/Computable_analysis have all been published 30-15 years ago. Are the approaches which they expose still relevant to the current paths of research ...

**0**

votes

**0**answers

12 views

### About the selection of reals $u_0,u_1$ such that $u_{n}$ is a positive integer

Let $r\geq 4$ and $n≥1$ be two positive integers. Let us consider the sequence $(u_{n})$ defined by:
$$u_{n}=r^{n^2}\sum_{m=1}^{n}\frac{u_1-ru_0+2(m-1)}{r^{m^2}}+u_0$$ where $u_0,u_1$ are real ...

**0**

votes

**2**answers

39 views

### On independent sets of graph

Given $G$ a regular graph on $n$ vertices, denote $\alpha(G)>1$ to be independence number.
Denote $\Gamma(G)$ to be collection of possible subset of independent vertices in $G$ of cardinality ...

**1**

vote

**0**answers

34 views

### References for general Hasse-Weil zeta function

Most research on the Hasse-Weil zeta function focuses on some particular type of algebraic variety, and general surveys usually deal mostly with the better understood elliptic curve case.
I am ...

**0**

votes

**0**answers

32 views

### Tensor product of complexes

Let $A$ be a ring and let the modules that are involved be left and right A-modules (not necessarily bimodules over A).
I'll denote as $\mathcal{E}^n_R(M, N)$ the category of n-fold extensions of M ...

**-2**

votes

**0**answers

28 views

### calculating E(Xt^2,Xt-h^2) with Xt normal(0,sigma^2) [on hold]

the problèm is
let {X_t} all normal N(0, sigma^2)
défine rho_X(h)=cov(X_t,X_t-h)/var(X) and Y_t=(X_t)^2
proove that rho_Y(h)=[rho_X(h)]^2
i know that i have to use expected value E(E(Y/X)) but i don't ...

**2**

votes

**0**answers

40 views

### Comparing the size of two sums

Let $q$ be a prime power and $\mathbb{F}_q$ be the field of $q$ elements.
Let $\mathbb{F}_q[t]$ be the polynomial ring over $\mathbb{F}_q$.
I am working on a research project, where I bounded a ...

**0**

votes

**0**answers

25 views

### 1-wasserstein distance v.s. total variation distance

Suppose that $\mu_1$ and $\mu_2$ are two distributions defined on $\mathbb{R}^n$ and $\gamma$ is a symmetric distribution (around $0$) on $\mathbb{R}^n$ with compact support. Let $\gamma_x$ denote the ...

**-1**

votes

**0**answers

37 views

### Complementary polynomials

Denote $S=\{0,1\}^n$.
$\mathsf{MLP}_{d,n}=\{p\in\Bbb R[x_1,\dots,x_n]:p\mathsf{\mbox{ is mutilinear with total degree}}(p)=d\}$.
Is there an $n\geq d^2+1$ such that there exists distinct polynomials ...

**0**

votes

**0**answers

29 views

### Analogous to a PDE but where independent variable is a function

Consider, as an example for my question, a density function $u(\boldsymbol{x},t)$ on a vector field $\boldsymbol{x}$ at some time $t$. The flow velocity vector of the density is given by ...

**0**

votes

**0**answers

36 views

### Is $\mathcal{K}(H)$ injective $\mathcal{B}(H)$-module?

Does anyone know if the right Banach $\mathcal{B}(H)$-module $\mathcal{K}(H)$ is injective?
The same question for $\ell_\infty$-module $c_0$. Both these modules are not dual, so standard arguments ...

**4**

votes

**0**answers

34 views

### Choosing a metric in which homeomorphism is Holder continuous

Let $X$ be a compact metrizable space, and let $f:X \to X$ be a homeomorphism. Is it always possible to choose a compatible metric on $X$ in which $f$ is Holder continuous? I've tried some simple ...

**5**

votes

**1**answer

118 views

### Identity for Power Series and Binomial Coefficients

This question concerns a combinatorial identity obeyed by power series coefficients. Throughout we let $[x^{M}]\{\phi(x)\}$ denote the coefficient of $x^{M}$ in a power series $\phi(x)$.
Let $k$ be ...

**-3**

votes

**0**answers

32 views

### Matrix Algebra reduction [on hold]

I am trying to reduce the following:
$x$ and $y$ column vectors
$y^t$ is the transposed column vector
$(I - \frac{1}{(1+ y^t x)} * x y^t) (I + x y^t) = I$
I am stuck at $x y^t * y^t X = x y^t (x ...

**1**

vote

**0**answers

57 views

### On the boundary of the twindragon

Let $\mathcal T$ be the famous twindragon, i.e.,
$$
\mathcal T=\left\{\sum_{n=1}^\infty a_n\left(\frac{1+i}2\right)^n : a_n\in\{0,1\}\right\}.
$$
Then, as is well known, $\mathcal T$ has a ...

**8**

votes

**2**answers

117 views

### Vanishing of certain periodic series: A question related to $L(1 , \chi) \neq 0$.

Fix $q$ to be a positive integer. Let $$f : \mathbb{N} \to \{-1 ,0, 1\}$$ be a $q$-periodic arithmetic function such that $$\sum_{n = 1}^q f(n) = 0.$$ If $f$ is not identically zero, is it true that ...

**2**

votes

**0**answers

51 views

### Asymptotic expansion for the Bell numbers

The Bell numbers $B(n)$ (that is, the numbers that count the set partitions of a set, and have exponential generating function $\exp(e^x -1)$ ) admit the asymptotic expansion
$$\frac{\log B(n)}{n} = ...

**1**

vote

**0**answers

24 views

### Measurability of eigenelements $s \mapsto (\varphi_k(s), \lambda_k(s))$ of Laplace-Beltrami on $M_s$

For each $s \in [a,b]$, let $M_s$ be a compact Riemannian manifold with no boundary.
Under what conditions on $s \mapsto M_s$ do the eigenvalues and eigenfunctions $(\varphi_k(s), \lambda_k(s))_{k ...

**-3**

votes

**0**answers

34 views

### Maximum - Minum area [on hold]

The problem is listed by this link because i couln't post images here (something about reputation).
http://math.stackexchange.com/questions/1117894/maximum-minumum-area

**0**

votes

**1**answer

79 views

### Schematic image of a relative Cartier divisor of a fiberwise dense open

Let $S$ be a scheme and $A$ an abelian $S$-scheme, i.e., $A \rightarrow S$ is a proper smooth $S$-group scheme whose fibers are $g$-dimensional abelian varieties. Suppose that one has a fiberwise ...

**0**

votes

**1**answer

39 views

### Help with notation for the state of a dynamical system defined by a PDE

Before my question let me briefly describe a simplified version of the dynamical system I'm working with. Suppose that I have a density function $m(\boldsymbol{x},t)$, that describes the abundance of ...

**5**

votes

**0**answers

73 views

### Groupoid cardinality of DM stack and point counting on coarse moduli spaces

Let $X$ be a finite type DM stack over a finite field $k$ with a coarse moduli space $X_c$. (We only assume $X_c$ is an algebraic space and $X$ might have infinite inertia stack.)
Under which ...

**0**

votes

**0**answers

55 views

### Moduli space of points - Gorenstein ideal

I've been working on algebraic covers, $\varphi\colon X\rightarrow Y$, ($\varphi_*\mathcal{O}_X$ is a locally free $\mathcal{O}_Y$-algebra of rank d).
I'm more interested in the algebraic point of ...

**2**

votes

**0**answers

53 views

### Statistical distance between discrete and continuous distributions

Are there any statistical distance functions that are capable of comparing a continuous and a discrete distribution? From reading this list
http://en.wikipedia.org/wiki/Statistical_distance
the only ...

**2**

votes

**0**answers

56 views

### Reference for cdh topology

Let $f:X\rightarrow Y$ be a proper surjective morphism over some base scheme $S$ of finite type, suppose $f$ restricts to an isomorphism over some open $U$ of $X$, we also suppose both $X$ and $Y$ are ...

**2**

votes

**1**answer

115 views

### Rankin-Selberg convolution and product of degrees

As I'm kinda obsessed with the Selberg class and because of the general converse conjecture, I'm still trying to get a rough idea of what automorphic representations and their L-functions as well as ...

**1**

vote

**0**answers

80 views

### Difference between Frobenii on Tate modules of special and generic fibre

Let $E$ be elliptic curve over $\mathbb Q$ and $p$ a prime of good reduction for $E$. Fix $\ell \neq p$.
If $E_p$ is ordinary then we have Frobenius $F_p$ on $E_p$. Assume $F_p$ lifts to ...

**1**

vote

**0**answers

84 views

### What is the technical difference between a deformation and a perturbation?

What is the technical difference between a deformation and a perturbation? Do they exist in somewhat different categories?

**2**

votes

**1**answer

102 views

### Sequence of smooth maps converging to the identity

Let $\{g_{n}:B_{1}(0) \rightarrow \mathbb{R}^{2}\}_{n\in \mathbb{N}}$ be a sequence of smooth maps where $B_{1}(0)=\{x\in \mathbb{R}^{2} \mid |x|<1\}$ is the unit ball in $\mathbb{R}^{2}$. Assume ...

**-6**

votes

**0**answers

100 views

### New algorithm discovered to find prime numbers [on hold]

I think that I have discovered a new algorithm to find prime numbers. It uses all prime numbers less than a particular number to find prime numbers within a range. I am not sure whether it generates ...

**1**

vote

**0**answers

168 views

### Can mathematics get from other sciences what it got from physics? [on hold]

Throughout history, physics has been an unparalleled source of '' inspiration'' for discovering/inventing mathematical ideas, which is due to its ability to describe the physical world. But can this ...

**3**

votes

**3**answers

208 views

### Survey papers of results (relevant to mathematics) produced during research on the relationship between mathematics and music theory

It is well-known that there is a relationship between music and mathematics, and there are many references that explore this topic (for example, Benson's book).
However, I would like to ask if there ...

**0**

votes

**0**answers

84 views

### Lower bound for constructing $n!$ with additions, subtractions, and multiplications starting from $1$

Found this on Complexity Zoo warning expired certificate
check NP Over The Complex Numbers.
[BCS+97] show the following striking result. For a positive integer $n$, let $t(n)$ denote the minimum ...

**1**

vote

**0**answers

48 views

### Relations in a space generated by indicator functions

Simple Question
I ran into the following seemingly simple question.
For an arbitrary set $M$ consider the real vector space generated by indicator functions $\chi_A$ of all subsets $A\subset M$. ...

**1**

vote

**0**answers

62 views

### Why are they called 'pernicious' numbers?

The definition of a pernicious number:
In number theory, a pernicious number is a positive integer where the Hamming weight (or digit sum) of its binary representation is prime.
The meaning of ...

**0**

votes

**1**answer

22 views

### Discrete Maximum Entropy Distribution with given mean

For a given mean $\mu$, what is the entropy maximizing probability distribution on the nonnegative integers?
Different sources indicated either the geometric or the Poisson distribution for this. As ...

**1**

vote

**2**answers

455 views

### Are hyperreal numbers isomorphic to formal power series?

I wonder whether hyperreal numbers isomorphic with formal Laurent series?
It seems that any hyperreal number can be represented in the form of Laurent series over $\omega$. For instance,
...

**7**

votes

**1**answer

119 views

### A question on the twistor space of a manifold

Let $M$ be either (a) self-dual conformal 4-manifold, or (b) hypercomplex $4n$-manifold.
In either case one can construct the twistor space $Z$ (in the case (b) $Z=\mathbb{C}\mathbb{P}^1\times M$ as a ...

**0**

votes

**1**answer

67 views

### What is a one-parameter Newton's method?

The Newton's method that I know is defined as follows:
$$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$$
However, I've recently encountered a paper that talks about a one-parameter family of Newton's method ...

**2**

votes

**0**answers

64 views

### Isomorphic subcategories of directed graphs and presets

For the purposes of this post, a digraph (directed graph) has neither loops nor multiple parallel edges, and a preset is an ordered pair consisting of a set $S$ and a preorder (viz., a reflexive and ...

**2**

votes

**1**answer

96 views

### the number of indecomposable modules of finite groups over finite fields of a fixed dimension

I am interested in determining the the number of indecomposable modules of finite groups over finite fields of a fixed dimension. Specifically, I have the following conjecture:
Conjecture. Suppose we ...

**0**

votes

**0**answers

35 views

### Isomorphic subcategories of digraphs and presets

For the purposes of this post, a digraph has neither loops nor multiple parallel edges, and a preset is an ordered pair consisting of a set $S$ and a preorder (viz., a reflexive and transitive binary ...

**0**

votes

**0**answers

50 views

### Fractional Schrödinger equation

Fractional Schrödinger equation:
$$
i\frac{\partial \psi(\mathbf{r},t)}{\partial t}
=(-\Delta )^{\alpha /2}\psi(\mathbf{r},t)
+ V(\mathbf{r},t)\psi(\mathbf{r},t).
$$
Do anybody know the physical ...

**1**

vote

**0**answers

30 views

### optimal strategies for 2-player zero-sum games of perfect information

I asked essentially this on math.SE slightly more than
3 days ago, and it hasn't received any answer there.
Do finite-state 2-player zero-sum games of perfect information with only win-draw-loss ...

**0**

votes

**0**answers

31 views

### Killing vector fields on sphere and nodal sets

Let $u$ be a smooth function on $S^2$ such that $\int_{S^2} ux_j =0$, for $j=1,2,3$. Is there a killing vector field $V$ on $S^2$ such that the nodal line of $\varphi=V(u)$ ($\{x\in S^2: ...