# All Questions

**0**

votes

**2**answers

55 views

### a dcpo seen as a category: when does a dcpo map induce a functor with an adjoint?

Take two posets $A, B$ (partially ordered sets). Now consider these posets to be categories $Cat(A), Cat(B)$ respectively. Consider a map from $A$ to $B$, $f: A \rightarrow B$. This can be seen as ...

**1**

vote

**1**answer

47 views

### W^{2,∞} regularity of solutions of Poisson's equation if the right hand side is in L^{∞}

Let $u$ be solution of $-\Delta u = f$ in $\Omega$ and $\frac{\partial u}{\partial n} = 0$ on $\partial \Omega$.
Is it true that if $f \in L^{\infty}(\Omega)$ then $u \in W^{2,\infty}(\Omega)$?
...

**2**

votes

**2**answers

178 views

### Are there fragments of set theory which are axiomatized with only bounded (restricted) quantifiers used in axioms?

Bounded quantifiers in set theory are represented as $(\forall x \in S)$ or $(\exists x \in S)$. But since the modifier "bounded" brings up an association with "bounded variable", I prefer the term ...

**6**

votes

**1**answer

219 views

### Cohen-Lenstra heuristics for totally complex fields

If a number field $K$ is a Galois extension of $\mathbb{Q}$, and $G = \operatorname{Gal}(K/\mathbb{Q})$, then the class group of $K$ is a $\mathbb{Z}[G]$-module, and since $N = \sum_{g \in G} g$ acts ...

**1**

vote

**0**answers

61 views

### Symmetric spaces which are compact modulo the unipotent radical are compact

Is the following true?
Let $X = G/H$ be a symmetric space of a reductive group over a p-adic field $F$.
Let $X^0$ be an open orbit w.r.t. the action of the minimal parabolic $B$ of $G$.
Let $U$ be ...

**3**

votes

**0**answers

71 views

### Full-rank factorization of the graph Laplacian

Is there a combinatorially meaningful full-rank factorization of the Laplacian matrix of a graph?
The usual factorization $L=BB^{T}$, where $B$ is an oriented incidence matrix, is full-rank if and ...

**1**

vote

**1**answer

105 views

### Directed subposet of a poset containing the minimal elements

The following appears naturally in a certain context:
Let $P$ be a partially ordered set which is bounded below in the sense that for each $x\in P$ there is a minimal element $m$ with $m\leq x$. Let ...

**5**

votes

**1**answer

199 views

### Kernel of the character of congruence groups

Let $\Gamma$ be a congruence subgroup of $SL_2(\mathbb Z)$ and $\chi:\Gamma \to \mathbb{C}^*$ a character of $\Gamma$ with finite image. Is then $\ker(\chi)$ also a congruence group? If not, can ...

**2**

votes

**1**answer

77 views

### Does the right adjoint of the category of simplices functor is “homotopicaly inverse” to the category of simplices functor?

Short Version (the question)
Let $\text{Cat}$ be the category of (small) categories and $\text{sSet}$ the category of simplicial sets. There is a functor $\Gamma:\text{sSet}\to \text{Cat}$ that takes ...

**1**

vote

**0**answers

99 views

### A differential equation on toric Kahler manifolds

Let $M$ be a toric Kahler manifold with $\text{dim}_{\mathbb{R}} = 4$. Let $V$ be a Killing vector field associated to the action of the two-torus $\mathbb{T}^2$ on $M$. We also assume the existence ...

**0**

votes

**0**answers

56 views

### Algebraic subgroup lattices [on hold]

For which groups is the subgroup lattice algebraic?
Jiří Tůma has proved every algebraic lattice is an interval in a subgroup lattice. It seems there is close relation between algebraic lattices and ...

**2**

votes

**0**answers

55 views

### Highest weight spaces in arbitrary representations?

An isotypic (maybe reducible) representation V of GL(V) may be represented by its highest weight subspace HW(V). We have dim HW(V) equal to the multiplicity of the irreducible representation inside V ...

**9**

votes

**2**answers

223 views

### Faster formula to compute sum over partitions

Let $f$ be a function from the positive integers to the real numbers (or some ring...). Let
$$(\star) \quad F(n) = \sum_{n_1 \leq \cdots \leq n_j\atop n_1 + \cdots + n_j = n} f(n_1) \cdots f(n_j), $$
...

**5**

votes

**1**answer

122 views

### How to solve such an optimization problem

I encounter the following optimization problem, but I can't solve it.
Given $N$ variables satisfying $0 <= x_1 < x_2 < x_3 < ... < x_N <= 1$ and an integer $K$ no large than $N$, ...

**0**

votes

**0**answers

14 views

### Can Cavity method to analyze graph with loops that are short?

In statistical physics,Cavity method can be regarded as a generalization of the Bethe Peierls iterative method in tree-like graphs to the case of graph with loops that are not too short. And I want ...

**0**

votes

**0**answers

47 views

### Unique Limits in T1 Spaces [on hold]

It's intuitive to me that limits in T2 (Hausdorff) spaces are unique, but I'm not sure about what properties of T1 spaces allows limits to be non-unique. Could someone explain this to me and perhaps ...

**-2**

votes

**0**answers

21 views

### Can a very bad Coefficient of determination (R squared value) not be indicative of model performance? [migrated]

Thanks in advance for the advice.
I am trying to build a generalized linear model that has many predictors. The R squared value of the model is quite low (.21), but when I use the model to predict ...

**11**

votes

**1**answer

295 views

### Is there an arXiv for Beamer presentations of scientific work? [on hold]

When I give a "Beamer talk" I put in a lot of effort making the slides, and trying to give an efficient presentation of my work. The end product is often around 20 pages of figures, definitions, ...

**3**

votes

**0**answers

83 views

### Birkhoff Ergodic Theorem and Ergodic Decomposition Theorem for Continuous-Time Markov Processes

I have a couple of questions regarding ergodicity for Markov processes in continuous time. (In particular, the first question seems like it should be particularly basic, and yet I haven't managed to ...

**3**

votes

**1**answer

142 views

### Linear dependency of real numbers with integer coefficients adding up to zero [on hold]

Let $x = (x_1, \dots, x_n)$ be a vector of real number. I was asking myself if there was an efficient way of telling whether there exists a non-zero vector of integers $z \in \mathbb Z$ such that both
...

**4**

votes

**1**answer

146 views

### C*-bimodules: the mess with definitions

I used to participate in a seminar that taught students about foundations of non-commutative geometry. It isn’t very complicated to define a C*-module $\mathcal E$ (also known as C* Hilbert module) ...

**7**

votes

**1**answer

104 views

### Steady state expectation of dynamic system of urns & balls

We have a large number of urns $N+1$. (Large means that the relative difference between $N$ and $N+1$ is well within the error bounds that I care about. The reason for the $+1$ will be apparent ...

**0**

votes

**0**answers

38 views

### Characterization of certain analytic vector fields on $S^{2}$

Let $X$ be a real analytic vector field on $S^{2}$ which satisfies:
$X$ has a finite number of singularities on $S^{2}$
The equator is invariant under flow of $X$
3.$g_{*}X=X\; ...

**1**

vote

**2**answers

178 views

### Set of distinct real numbers such that all combination of sums are distinct

Let $\Lambda :=\{\lambda_1, \dots, \lambda_n\}$ be a set of $n$ distinct real numbers.
For a given $p \in \mathbb N$, consider further the set
$$I_p := \{ \{i_1, i_2, \dots, i_p\} : i_j \in \{1, ...

**4**

votes

**1**answer

115 views

### $ mult(R/I) = d_1 \cdots d_r \quad \Rightarrow \quad f_1,\dots,f_r \quad \text{is a $R$-regular sequence?}$

We define multiplicity of a module M of dimension $d>0$ as $$mult(M) := lc (P_M) (d-1)!$$ where $P_M$ denotes the Hilbert polynomial of M. Equivalently, we have $mult(M) = Q_M(1)$, where $HP_M (z) ...

**0**

votes

**0**answers

81 views

### Parahoric group schemes over curves

Let $X$ be a smooth projective curve over $\mathbb{C}$ and Let $G$
be a complex reductive group. By a parahoric group scheme $\mathcal{G}$
over $X$, I mean a smooth group scheme over $X$ whose ...

**0**

votes

**1**answer

38 views

### Parallel group topologies on Prüfer groups

Let $p$ be a prome number. Are there group topologies $\mathcal S$ and $\mathcal T$ on $\Bbb Z_{p^\infty}$ such that
$$\mathcal T \nsubseteq \mathcal S,~~\mathcal S \nsubseteq \mathcal T$$

**-4**

votes

**0**answers

243 views

### Making new sense of the three-body problem in the light of Maryam Mirzakhani math contributions [on hold]

I am unfamiliar with moduli spaces and ergodic theory which appear to be essential in Maryam Mirzakhani's math contributions which won her the Fields Medal. However, I am well conversant with ...

**4**

votes

**2**answers

387 views

### Why considering schemes over discrete valuation rings?

For many times, I find people working on schemes over DVRs, and prove theorems on such setting. For example, my latest experience is the "semi-stable reduction theorem" by Kempf, Knudsen, Mumford and ...

**-2**

votes

**0**answers

146 views

### Does this “modeling relationship” occur in mathematics (Galois connections, relation algebra, category theory)? [on hold]

Be $R$ a subset of the cartesian product $S \times T$ of two sets, and $f: S \to T, \ g: T \to S$ two partial functions, such that $f$ and $g^{-1}$ are disjoint as sets of ordered pairs, and $R = (f ...

**0**

votes

**0**answers

37 views

### quasilinear partial differential equation [on hold]

http://math.stackexchange.com/questions/898333/quasilinear-partial-differential-equation
Given a PDE
(f*e^2) * ∂f/∂x−(e*f^2) * ∂f/∂y+M1*f^4+M2*f^2+M3=0
Note that M1 , M2 and M3 are functions of ...

**1**

vote

**0**answers

41 views

### An optimization problem for a Markov Chain

Consider a Markov Chain $\{X_n\}$ whose transition probability depends on some parameter $\theta$ ($p_{ij}(\theta)$). Now I want to optimize the following quantity
$$\lambda(\theta) = ...

**-4**

votes

**0**answers

26 views

### The Multi-Step Differential Transform Method [on hold]

f(t)=sin(omega*t+alpha) then F(k)=\frac{omega^k}{k!} sin(pi*k/2 + alpha)

**0**

votes

**0**answers

52 views

### deformation of Lie algebra

How can we deform a given Lie algebra? In particular, in the attachment file how can we arrive at the commutation relations (20) by starting from the commutation relation (19)?
...

**1**

vote

**0**answers

47 views

### Quadrilaterals from a Unit Stick

This question could be seen as a coordinate-free variant of Sylvester's Four Point Problem (cf e.g. http://mathworld.wolfram.com/SylvestersFour-PointProblem.html):
Suppose one are given an ...

**1**

vote

**0**answers

67 views

### Points on the intersection of an affine quadric and cubic over a finite field

Are there absolute constants $N$ and $B$ such that the following is true?
Let $p>B$ be a prime. Let $q(x_0,\dotsc,x_n)$ and $c(x_0,\dotsc,x_n)$ be homogeneous of degree $2$ and $3$ with ...

**0**

votes

**0**answers

92 views

### First Description of how to Remove Radicals from Equations

Who first described the technique of removing radicals as indicated in the answers to questions Tools for Removing Radicals from Equations and Rewrite sum of radicals equation as polynomial equation ? ...

**6**

votes

**2**answers

164 views

### Asymptotic density of finite abelian and solvable groups

For every natural number n, let:
Gn be the number of distinct group structures with at most n elements;
An be the number of distinct abelian group structures wit at most n elements;
Sn be the number ...

**2**

votes

**1**answer

223 views

### FIltrations on a vector bundle on a curve

Let $X$ be a smooth connected projective curve of genus $g$ over an algebraically closed field.
Let $E$ be a vector bundle on $X$ of rank $n$.
Is it true that there exists a constand $N(g,n)$ such ...

**1**

vote

**1**answer

110 views

### Stability of convergence in distribution under randomization

Suppose you have a sequence of non-negative stochastic processes $(X^n)_{t \in \mathbb{R}}$, $n \geq 1$, with continuous paths and continuous in $t$ such that
$$\int_{-\infty}^{\infty} X^n_t \, ...

**13**

votes

**2**answers

233 views

### Classification of tangles?

Has anybody done any work on making a classification of low-complexity tangles, analogous to the work for knots and links? I expect most of the small ones to be rational, and those that aren't ...

**0**

votes

**0**answers

78 views

### adjoint representation of 2-Lie groups

Baez and Crans in their paper on Lie 2-algebras refer to adjoint representations of Lie 2-groups but don't say much, as far as I can tell, except to say that such a representation acts on a 2-Lie ...

**-3**

votes

**0**answers

45 views

### What is the final velocity and impact time of this anomalous object? [on hold]

A 1kg wood cube. This cube is affected by friction i reverse. Instead of decelerating it will accelerate at an equal rate. Placed in the middle of a concrete room where it has 0.63 coefficient ...

**4**

votes

**1**answer

107 views

### Characterizing the newforms s.t. the associated symmetric square $L$-function has a pole

I have a straightforward question. Let $f$ be a holomorphic cusp form of weight $k$, level $N$, and nebentypus $\chi$ that is new in the sense of Atkin-Lehner theory. Write its Fourier expansion at ...

**4**

votes

**0**answers

239 views

### Reference request: Book of Linear algebra from categorical point of view

Is there any book of Linear algebra in the modern language of Category theory?
I refer to the (systematic, formalist) study of the category whose objects are vector spaces and whose morphisms are ...

**1**

vote

**0**answers

125 views

### What's the ratio of inclusions of finite groups with a distributive lattice?

Definition: Two inclusions of finite groups are equivalent, $(A \subset B) \sim (C \subset D)$, if: $(A/A_B \subset B/A_B) \simeq (C/C_D \subset D/C_D)$ with $A_B$ the normal core of $A$ in $B$.
...

**7**

votes

**1**answer

382 views

### Learning roadmap to TQFT from a mathematics perspective

I had asked a question on math.stackexchange but did not receive any answers. I hope that this question is appropriate for this website as it is about an advanced subject. Hence I am posting it below.
...

**-2**

votes

**0**answers

40 views

### Basic Probability Conditional Expectation [on hold]

In my personal interests I read a introduction book to theory measure and probability with exercises. In order to understand definiton of conditional expectation I'm trying to solve those exercises ...

**3**

votes

**1**answer

290 views

### Lower bounds on the error term of the prime number theorem

Are there any lower bounds on the error term for the prime number theorem, or in other words, is there a nontrivial $f$ s.t.
$$f(x)\ll |\psi(x) - x|$$
where $\psi$ is the Chebyshev function.

**0**

votes

**1**answer

102 views

### Two questions about convex subsets of Hilbert Space

Let H be an infinite dimensional and separable Hilbert Space. Do there exist disjoint, closed and bounded subsets A,B of H which satisfy the following conditions? (1) Each of A,B is convex and has a ...