**0**

votes

**0**answers

73 views

### Poincare inequality for connected Lie groups

Let $G$ be a compactly generated second countable locally compact group, and let $\mu$ be a probability measure which is:
symmetric,
adapted (in the sense that there is no proper subgroup $H$ such ...

**5**

votes

**2**answers

165 views

### If $f : [-a,a] \rightarrow \mathbb{IR}$ is Scott continuous, why are $f^-$ and $f^+$ measurable?

In "A domain theoretic account of Picard's theorem" (http://www.doc.ic.ac.uk/~dirk/Publications/icalp2004.pdf), the authors assert the following.
Let $\mathbb{IR}$ be the interval domain $\lbrace ...

**0**

votes

**1**answer

58 views

### Some references for f-ring

A commutative ring $R$ is said to be an $f-ring$ if every pure ideal is generated by idempotents. (Recall that the ideal $I$ is said to be pure if for each $a\in I$ there
is a $b\in I$ such that $ab = ...

**1**

vote

**0**answers

83 views

### One-sided local $L^p$ spaces

Consider the vector space $L^p_{\text{left-loc}}$ of measurable functions $f:[0,1]\to\mathbb R$ so that for all $x\in(0,1]$ there exists $\delta>0$ so that $f|_{[x-\delta,x]}\in L^p$.
Does this ...

**0**

votes

**2**answers

212 views

### Linear Algebra classic books [closed]

I'm learning linear algebra at the moment, so I'm looking for some great old classic books. Something like Fermat's or Gauss books of some great mathematians.
I don't really like the nowadays books ...

**1**

vote

**0**answers

170 views

### system with solutions $\{x-a:0\leqslant a\leqslant z-1\}$ [on hold]

What must be $F$ there where $0=F(1,x,0)=F(x-0,x,z)=F(x-1,x,z)=F(x-2,x,z)=F(x-3,x,z)=$ $\dots$ $=f(x-z-1,x,z)=0$?
Define $F$ in the domain where a continuous function exists that behaves so for ...

**0**

votes

**0**answers

51 views

### interpreting the difference between curves [closed]

Is there any sophisticated mathematical method to interpret the difference between shape of two curves? (for example two log-logistic curves with different scale and shape)
to be specific, I have two ...

**-2**

votes

**1**answer

59 views

### Ricci Tensor and Directional Derivatives confirmation [closed]

I did a computation which, I feel, requires confirmation. Consider the metric on $\mathbb{R}^2$ given by $$g_{ij} = \dfrac{\delta _{ij}}{1 + x^2 + y^2} .$$ This yields the coefficients for the Ricci ...

**1**

vote

**0**answers

45 views

### “Friedrichs extension Laplacian” vs “Weak Laplacian” and fractional powers

Take $\Omega$ to be a bounded domain and consider Neumann BCs.
In some works, I see that a Laplacian $(-\Delta_D)^{\frac 12}$ is defined as an operator with domain $H^1(\Omega)$, and in other works, ...

**3**

votes

**1**answer

49 views

### Contracting join-incomplete lattice endomorphisms

Let $L$ be an complete lattice. A lattice homomorphism $f: L\to L$ is said to be join-incomplete if there is an infinite set $S \subseteq L$ such that $f(\bigvee_L S) \neq \bigvee_L f(S).$
If $f:L\to ...

**3**

votes

**0**answers

44 views

### Increasing integral sequence of intermediate growth which is periodic modulo almost all primes

Many integral sequences are periodic modulo (almost) all primes.
However all examples I know are either evaluations of suitable polynomials on consecutive integers (trivial examples) or grow at least ...

**0**

votes

**0**answers

97 views

### Question about Castelnuovo-Mumford regularity

let $R$ be a Noetherian ring an $I$ an ideal of $R$.
If $n,m\in N$ and $reg(G(I))=n$, then what can we say about $reg(G(I^m))$?
Here $G(I)$ is the associated graded ring.

**2**

votes

**1**answer

94 views

### Classification of commutative ring ideal closure operators?

First, some setup:
So: given a commutative ring $R$, let $Ideals(R)$ be set of ideals of $R$ and let $IdealClosure(R)$ be the set of closure operations $cl: \mathcal{P}(R) \rightarrow Ideals(R)$. In ...

**0**

votes

**0**answers

22 views

### Inscribed polytopal approximation to a convex body

This question is on the continuation of the post
Approximation of convex body by polytopes
The central problem I am interested is an explicit construction of inscribed polytope with at most $n$ ...

**7**

votes

**0**answers

229 views

### Residue class sufficiency sets for the Collatz conjecture

I have recently managed to show a sequence of sufficiency sets for the Collatz conjecture whose natural density approaches 0 (the set theoretic limit approaches the set $\{1\}$). It is an extension of ...

**0**

votes

**0**answers

22 views

### Is 6 the smallest index for an irreducible subfactor to have a principal graph with a multiplicity >1 edge?

The irreducible subfactor $(R^{S_3} \subset R)$, of index $6$, admits a principal with a multiplicity $2$ edge because the group $S_3$ admits an irreducible complex representation of dimension $2$.
...

**0**

votes

**1**answer

57 views

### The hypoellipticity of a heat-like operator

I am aware that the heat operator (on a smooth manifold) is hypoelliptic. I am also aware that there are manifolds on which the Schrödinger's operator (with a $\Bbb i = \sqrt {-1}$ multiplying $\frac ...

**7**

votes

**1**answer

179 views

### Can view the connected component of the Picard scheme $\text{Pic}^0(X)$ as a “kernel” of the first Chern class?

So on a curve, $\text{Pic}^0(X)$ is just the Jacobian variety, and just correspond to degree $0$ divisors. One way to extend the notion of divisors corresponding to a vector bundle is taking the first ...

**-6**

votes

**0**answers

68 views

### I need to know all geometry source to study geometry [closed]

I'm not specialist in geometry and I try to start learn all ph.d student need to know for their works. could you please introduce me which book should I start and please mention all book which is ...

**1**

vote

**1**answer

342 views

### Three questions about modular forms frequently asked to me

I have three questions related to the theory of modular forms and it was frequently asked to me by my collegues and even my invited teacher in our seminars of the number theory at the faculty of ...

**2**

votes

**2**answers

143 views

### When is the adjoint to a monoidal functor monoidal?

Let $\mathcal C,\mathcal D$ be monoidal categories. Recall that a functor $F : \mathcal C \to \mathcal D$ is lax monoidal if it is equipped with maps $1_{\mathcal D} \to F(1_{\mathcal C})$ and $F(X) ...

**2**

votes

**1**answer

97 views

### Inducing representations from the stabilizer of a partition

For each positive integer $i$, let $A_i$ be a fixed representation of the symmetric group $S_i$. I won't tell you exactly what $A_i$ is, but let's say that I have a very explicit description of its ...

**1**

vote

**1**answer

172 views

### pull back of an ample line bundle under a blow up

Suppose $\mu:X\rightarrow Y$ is a blow up of a smooth irreducible subvariety $Z$ of $Y$. Let $L$ be an ample line bundle on $Y$. Let $E$ be the exceptional divisor of $f$. Is it true that there ...

**5**

votes

**1**answer

194 views

### Is $\liminf \frac{\sigma_{k}(n)}{n}$ finite for every $k$?

Can someone show me how to prove that $$\liminf_{n \to \infty} \frac{\sigma_{k}(n)}{n} < \infty$$ for every natural number $k$? Or is this problem open?
Here, ...

**6**

votes

**0**answers

307 views

### “Forthcoming paper” of Goldston-Graham-Pintz-Yıldırım

The above-named authors of [1] and its (significantly different) published version [2] write:
In a forthcoming paper, we will show how the methods here can be extended to prove corresponding ...

**-7**

votes

**0**answers

25 views

### Find the function f(x)=Ca^x going through points (-1, 2) and (-3, 32) [closed]

I've solved a few of these but this ones giving me trouble.
2 = Ca^-1
2/(a^-1) = C
32 = [2/(a^-1)] * a^-3
2a^-3/a^-1 simplifies to 2a^-2
32 = 2a^-2
32/2 = a^-2
16 = a^-2
16 = 1/a^2
16a^2=1
a = ...

**1**

vote

**0**answers

50 views

### Fractional Sobolev space as a Cameron-Martin space

In their paper "On Fractional Brownian Processes" (link here to the working paper), Feyel and Pradelle (1997) write in the introduction: "we give very simple proofs of the existence of different ...

**-5**

votes

**0**answers

30 views

### Algorithm for 10 point rating system [closed]

How would i approach making a rating system with the following rules:
An items rating is within 1 to 10,0 points
Users rate items from 1 to 10 points.
1 review can not give 10 points.
I figure ...

**2**

votes

**1**answer

84 views

### Partial differential equation from Kirchhoff system

I was seeking for the solution of following partial differential equation for two unknowns $\vec{u}(s,t), \vec{w}(s,t)$
$$\partial_t \vec{u} = \partial_s \vec{w} - [\vec{w} \times \vec{u}].$$
Using ...

**3**

votes

**0**answers

53 views

### Is the family of probabilities generated by a random walk on a finitely generated amenable group asymptotically invariant?

Is the family of probabilities $\mu^n$ (convolution) generated by a random walk $\mu$ on a finitely generated amenable group $G$ asymptotically invariant ($\|g\mu^n-\mu\|_{L^1}\to 0$ for any $g\in ...

**-4**

votes

**0**answers

51 views

### This is a quadratic equating question [closed]

If p,q,r,s are the roots of (x^2+x+4)^2 + 3x(x^2+x+4)+2x^2 = 0, then |p|+|q|+|r|+|s| is equal to :

**8**

votes

**1**answer

162 views

### Automorphisms of del Pezzo surfaces

Let $S$ be a del Pezzo surface of degree six over $\mathbb{C}$. Then $S$ is the blow-up of $\mathbb{P}^2$ in three general points $p_1,p_2,p_3$.
Is it true that its automorphism group is ...

**0**

votes

**0**answers

39 views

### Is there a way to approximate a logarithmic function with a Gaussian at a point? [closed]

One way of Gaussian approximation to a function g(x) at a point x_0 is the Laplace approximation, but that requires an exp log g(x) transform, which would result in a log log f(x) expression if g(x) = ...

**1**

vote

**0**answers

63 views

### Lipschitz-like behaviour of quartic polynomials [migrated]

I have observed the following phenomenon:
Let the biquadratic $q(x)=x^4-Ax^2+B$ have four real roots and perturb it by a linear factor $p(x)=q(x)+mx$, so that $m$ not too large with respect to ...

**2**

votes

**0**answers

86 views

### Modular property of indefinite degenerate theta series

Is there anything known about the (mock)modular properties, if any, of the following theta series,
$\sum_{n\in {\mathbb Z}^r_+} e^{2\pi i \langle b, n\rangle} q^{\frac12 \langle n,n\rangle}$,
where ...

**2**

votes

**0**answers

45 views

### Are all locally compact anisotropic groupoids etale up to equivalence?

By groupoid I mean "open topological groupoid",i.e. topological groupoids whose source and target maps are open surjections, and the notion of equivalence I'm considering is the isomorphism in the ...

**-3**

votes

**0**answers

114 views

### Mathjax vs Katex [closed]

Whats the difference between KaTex and Mathjax. I think KaTex has a better Font while math rendered by MathJax looks so bulky and ugly. Are the MathJax people working on improving their program in ...

**0**

votes

**0**answers

31 views

### Deducing probability density functions from model equations [closed]

I need to code stochastic models:
$x_{n+1} = f(x_{n},\theta)$
where $x_n$ is the state of my system at time $n$ and $\theta$ is a set of parameters for this model, constant through time, and ...

**0**

votes

**1**answer

27 views

### Optimal covering and CSPNG

Consider a function $f: \{0,1\}^n \to \{0,1\}^{cn}$, where $c>1$.
A random $f$ with high probability generates optimal covering of $\{0,1\}^{cn}$,
i. e.:
$\forall x \in \{0,1\}^{cn}$ $\exists y ...

**2**

votes

**2**answers

124 views

### “Nice” and “nasty” partitions in graphs

Let $G=(V,E)$ be a simple, undirected graph, that is $V$ is a set and $E \subseteq [V]^2 = \{\{v,w\}: v,w \in V \land v\neq w\}$.
For $v\in V$ and $S\subseteq V$ we set $$N(v,S) = \{w\in S: \{v,w\} ...

**6**

votes

**2**answers

150 views

### Generalized Characteristic Polynomial with Unimodular Roots

Let us define a diagonal matrix $\mathbf{D}(z) = diag(z^{m_1}, \dots, z^{m_N})$ with $z\in\mathbb{C}$ and positive integers $m_1, \dots, m_N$.
The generalized characteristic polynomial of a matrix ...

**1**

vote

**0**answers

30 views

### How to analyse the stability of hyperbolic balance laws with diffusion?

Assume we have the following system of balance laws:
$$ U_t+\partial_x F(U,x)=S(U,x)+\partial_x(D(U,x)U_x). $$
Is there any method to analyse the stability of its solution (assume that the solution ...

**1**

vote

**0**answers

114 views

### Symplectic spectrum

I have a question about a step in the proof of the following theorem from symplectic geometry.
The theorem is: Given any ellipsoid $E:=\{ w \in \mathbb{R}^{2n}; \sum_{i,j =1}^{2n} a_{ij}w_iw_j \le ...

**2**

votes

**0**answers

58 views

### Ultraproducts and subobjects of projectives

Usually the question whether the class of projective algebras in a given variety is closed under taking subalgebras seems to be quite hard. In varieties with well understood dual geometry (e. g. ...

**4**

votes

**1**answer

40 views

### Self-concordant function for dual cone

I wonder if there is any existing result for self-concordant function in the literature about the following question.
Suppose $f$ is a self-concordant barrier function of a proper cone $K$ (pointed, ...

**2**

votes

**3**answers

323 views

### Integral points on a particular family of curves

This is a follow-up to this question (and comments thereon). Namely, it follows from Felipe Voloch's comment that for any $n>2$ there is a finite set of integral $(x, y),$ such that
$$
...

**8**

votes

**2**answers

143 views

### Symmetries of module categories over the category of representations of quantum $sl(2)$

The category $\mathcal{C}_l$ of tilting modules of the quantum group $U_q(sl_2)$ quotiented out by the modules of zero quantum dimension has a natural structure as a semisimple monoidal category when ...

**8**

votes

**2**answers

280 views

### Are there congruence subgroups other than $SL_2(\mathbb Z)$ with exactly 1 cusp?

Are there any congruence subgroups other than $SL_2(\mathbb Z)$ which have exactly 1 cusp? By congruence subgroup, I mean a subgroup of $SL_2(\mathbb Z)$ containing $\Gamma(N)$ for some $N$.
This ...

**0**

votes

**0**answers

47 views

### Jackson's theorem to optimize mean queue length of a traffic model

The following question I posted in mathematics stack exchange one month ago[http://math.stackexchange.com/questions/1307077/jacksons-theorem-to-optimize-mean-queue-length-of-a-traffic-model] but ...

**6**

votes

**1**answer

268 views

### Connected CW complex, isomorphism?

Let $\pi$ be a group and let $K(\pi, 1)$ be a connected CW complex such that $\pi_1(K(\pi, 1)) = \pi$ and $\pi_q(K(\pi, 1)) = 0$ for $q \neq 1$. My question is, are $H_*(K(\pi, 1);A)$ and ...