This tag is used if a reference is needed in a paper or textbook on a specific result.

**6**

votes

**2**answers

341 views

### Can phase significantly concentrate a function's spectrum?

Let $F$ denote the Fourier transform over some group. What is known about the following quantity?
$$\gamma:=\inf_{x\neq 0}\frac{\|Fx\|_1}{\|F|x|\|_1}$$
Here, $|x|$ denotes the pointwise absolute ...

**3**

votes

**0**answers

81 views

### Lie group cohomology with coefficients in Lie algebra

I'm looking for a reference, and basic results, about Lie algebra as modules over a Lie group (with the adjoint representation), from the point of view of cohomology. Links with the Lie algebra ...

**7**

votes

**2**answers

270 views

### When is a sequence the sum of two Beatty sequences?

In other words, given a sequence $(s_n)$, how can we tell if there exist irrationals $u>1$ and $v>1$ such that
$$s_n = \lfloor un\rfloor + \lfloor vn\rfloor$$
for every positive integer $n$?
...

**1**

vote

**0**answers

48 views

### Singularity Confinement For Differential-Difference Systems

This is a follow-up question to an old question on this site (link) which has a solution that describes the singularity confinement property for discrete systems.
Are there any papers or books that ...

**12**

votes

**0**answers

495 views

### “To operate the machine, it is not necessary to raise the bonnet.”

The quotation in the title is attributed to Frank Adams and appears in several places:
In the preface of [2002, Operads in algebra, topology and physics]: "to operate the machine, it is not ...

**1**

vote

**0**answers

151 views

### Can triangulated categories be “approximated by countable subcategories” (that are triangulated but not full!)?

For a given (finite) set of (objects and) morphisms $f_i$ in a triangulated category $C$ I am interested in a (non-full!) triangulated subcategory $C'\subset C$ of "small size" that would contain ...

**0**

votes

**0**answers

59 views

### Inverse Laplace Transforms of Exponential Form

I'm trying to find the velocity component of an MHD flow using Laplace transforms. R.B. Hetnarski's algorithm for inverting the laplace transforms of some exponential functions was recommended to me ...

**3**

votes

**2**answers

165 views

### Transitivity of discriminant for flat algebras

Sorry if the question doesn't feed this site, I'm reposting it from MSE. Nobody answered it there and I couldn't find the proof in general case(whenever it was mentioned the proof was referred to as a ...

**3**

votes

**0**answers

122 views

### When there exists some “cone” of a morphism of (ind-representable) cohomological functors?

I am interested in cohomological functors from a certain small triangulated category $C$ to abelian groups.
The question is: given a tranformation $F\to G$ of two functors of this sort, is it ...

**4**

votes

**1**answer

188 views

### continuity of the Boltzmann entropy in the Wasserstein metric

For Lebesgue-absolutely continuous probability measures $\rho\ll \mathcal{L}^d$ in the whole space $\mathbb{R}^d$ with finite second moments (i-e $\rho\in \mathcal{P}^2_{ac}(\mathbb{R}^d)$), let
$$
...

**1**

vote

**0**answers

98 views

### References for modular curves over finite fields [closed]

I'm looking for a detailed reference for modular curves over finite fields, such as $X(N)$, $X_1(N)$, and $X_0(N)$. There seems to be a lot of literature dealing with them over $\mathbb{C}$, but I'm ...

**1**

vote

**2**answers

114 views

### Are spherical harmonics uniformly bounded?

The spherical harmonics are given by
$$Y^m_l(\phi,\theta):=N^m_l e^{im\theta}P^m_l(\cos \phi) $$
where $P^m_l$ are the associated Legendre Polynomials and $N^m_l$ is the normalisation.
From ...

**0**

votes

**1**answer

134 views

### Marcel Berger's “Sur les groupes d'holonomie homogènes de variétés à connexion affine et des variétés riemanniennes.”

I would appreciate any reference that contains either a translation or proof of the main theorem in this paper. Thank you in advanced.

**4**

votes

**2**answers

290 views

### Understanding how to construct Bruhat-Tits buildings for non-split groups by Galois descent

Is there any way to get on top of the procedure for constructing Bruhat-Tits buildings for non-split groups over a non-archimedean local field $k$, by Galois descent, other than reading both the ...

**3**

votes

**1**answer

178 views

### Transcendence of $\Gamma(1/3), \Gamma(1/4)$

This is a re-post from MSE as I did not get even a single comment there.
Wikipedia mentions that the transcendence of $\Gamma(1/3), \Gamma(1/4)$ was proved by G. V. Chudnovsky. Does anyone have a ...

**4**

votes

**0**answers

99 views

### Generalization of Sprague-Grundy Theorem

In my research on Combinatorial Game Theory, I used a certain theorem that is essentially a generalization of the Sprague-Grundy theorem. Because the result hinges too much on the work of others to be ...

**0**

votes

**0**answers

102 views

### book for help on problems with noetherian rings

Can you please introduce to me a book which would help me to prove the two following problems?
In a noetherian ring, every integrally closed ideal is unmixed.
Let $R$ be a noetherian ring, $P$ a ...

**2**

votes

**1**answer

87 views

### Stationary distribution for time-inhomogeneous Markov process

I have a two state, discrete time, time-inhomogeneous Markov process with transition matrix defined by
$$T_i=\begin{pmatrix}
1-p_i\alpha & p_i\alpha \\
p_i\beta& 1-p_i\beta
\end{pmatrix}$$
...

**1**

vote

**1**answer

252 views

### Van Kampen colimits

nLab uses the following definition of van Kampen colimits --- a colimit in a category $\mathbb{C}$ is called van Kampen iff it is preserved by the internal indexing functor $\mathbb{C}/(-) \colon ...

**2**

votes

**1**answer

73 views

### Domain of fractional powers of operators

Let $A$ and $B$ be non-negative ($(A x, x) \geq 0$ for all $x \in \mathcal{D}(A)$, similarly for $B$) densely defined self-adjoint operators on a Hilbert space $H$. Then the spectral theorem defines ...

**1**

vote

**1**answer

135 views

### Unitary irreps of the Poincare group in dimension <4

It is well-known that long ago, Wigner classified the unitary irreducible representations of the Poincare group in dimension 4.
I am looking for a convenient reference describing all unitary ...

**10**

votes

**0**answers

240 views

### Reference request: a combinatoric result [closed]

When I tried to construct a counterexample in my research, I encountered the following result, which should be true.
Let $m=m(n)$ be a function that grows faster than $\sqrt n$, so $m(n) = ...

**6**

votes

**3**answers

709 views

### Ambidexterity and Quantization

Here the nlab says about Hopkins-Lurie's ambidexterity paper:
"The discussion in the article is apparently motivated as part of what it takes to make precise the discussion of quantization in ...

**1**

vote

**1**answer

160 views

### Spherical harmonics and ellipticity of the Laplacian

Let us consider the sphere $S^n$ and the Laplacian $-\Delta$ on it. Let $L^2(S^n) = \bigoplus_k V_k$, where $V_k$ represents the eigenspace of the Laplacian with eigenvalue $k(k + n - 1)$. We know ...

**1**

vote

**0**answers

37 views

### Parametric Sard-Smale theorem - when is the generic set open?

I am learning Morse/Floer Theory and in my work on my master's thesis I want to apply the parametric Sard-Smale theorem. I.e. I consider a Banach bundle $\mathcal{L} \to \mathcal{M}\times \mathcal{G}$ ...

**3**

votes

**1**answer

155 views

### Reference request: Intrinsic definition of the strong Whitney topology on $\mathcal{C}^{\infty}(M,\mathbb{R})$ without using charts or jets

Let $M$ and $N$ be smooth manifolds. There is a description of the strong Whitney topology on $\mathcal{C}^{\infty}(M,N)$ in terms of partial derivative in charts (using locally finite sets of charts ...

**0**

votes

**1**answer

180 views

### Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height [closed]

I asked this in MSE, it flashed and disappeared.
Let $V_n$ be the volume on the set of polytopes in $\mathbb R^n$, defined axiomatically, i.e. a functional, that assigns to each polytope ...

**5**

votes

**1**answer

237 views

### If a topological space has vanishing $n$th homology for every possible homology theory, does it have vanishing $n$th homotopy?

I don't have any strong preference as to whether or not the homology theories are required to be ordinary.
Also, if this does not hold in general, does it hold for some nice category of spaces, like ...

**5**

votes

**0**answers

155 views

### Does there exist a smooth version of Cohen's factorization theorem?

A famous factorization theorem of Cohen states that for any locally compact group $G$, $$L^1(G)=L^1(G)*L^1(G).$$
I want to know if analogous results exist for the class of smooth functions when $G$ is ...

**4**

votes

**1**answer

153 views

### Unicity of additive, $(-1)$-homogeneous, and shift invariant probability measures on $\mathbf N^+$

Let $\mathcal D$ be the set of all (finitely) additive probability measures $\mu^\ast: \mathcal P(\mathbf N^+) \to [0,\infty[$ such that $\mu^\ast(k \cdot X + h) = \frac{1}{k} \mu^\ast(X)$ for all $X ...

**1**

vote

**0**answers

52 views

### Does there exist $k\ge2$ s.t. $X \subseteq \mathbf N^+$ has positive upper Banach density if the counting function of $X$ is $\gg n/\log^{[k]}(n)$?

Does there exist an integer $k \ge 1$ such that ${\sf bd}^\ast(X) > 0$ whenever $X \subseteq \mathbf N^+$ and $\pi_X(n) \gg \frac{n}{\log^{[k]}(n)}$ as $n \to \infty$? Here, ${\sf bd}^\ast$ is the ...

**3**

votes

**1**answer

86 views

### Generalization of maximum principle to other norms

Consider the Laplace equation $\Delta u=0$ in $\Omega \subset \mathbb{R}^d$ with Dirichlet boundary conditions, i.e. $u=g$ on $\delta \Omega$. By the maximum principle we know that the solution $u$ ...

**1**

vote

**0**answers

59 views

### Convergence to equilibrium for time in-homogeneous diffusions

Consider the long time behavior for a time in-homogeneous diffusion such as
$$dX_t = dB_t - \nabla V(X_t)\,dt + b_t(X_t)dt,$$
where $V(x)$ is a smooth convex function and $b_t(x)$ is a time-dependent ...

**2**

votes

**0**answers

111 views

### Complex sum of squares of vector fields (hypoelliptic operators)

Consider a compact $M$ of dimension $n$. Consider real smooth vector fields $X_0, X_1, X_2,..., X_n$ on $M$ and consider the differential operator $\mathcal{L}_1 = \sum_{i = 1}^n X_i^2 + X_0.$
Now, by ...

**8**

votes

**0**answers

170 views

### Simplices and cubes

Question: What is the first appearance in the literature of one of the
following statements:
The result of intersecting a simplex with a cell of the dual
subdivision is a cube
There ...

**3**

votes

**1**answer

236 views

### Equivariant Derived Category

Can someone give me a reference for the following or an idea on why it is true? (This is taken from remark 1.5 on page 5 of http://arxiv.org/abs/0810.0794.)
Suppose we have an algebraic group $G$ ...

**0**

votes

**0**answers

63 views

### The following ODE global existence theorem reference?

There is an ODE existence theorem of the form:
Let $f:[a,b]\times \mathbb{R}^n \to \mathbb{R}^n$ be a Caratheodory function.
Suppose that there is a constant $c$ such that if $y$ is a ...

**6**

votes

**1**answer

117 views

### Monte-Carlo computation of the Smith normal form

Quite some time ago I saw an article where a Monte-Carlo algorithm for computing the Smith normal form of an integer matrix was described. In this article the following problem was posed:
Suppose $P, ...

**1**

vote

**0**answers

136 views

### Mathematical journals (maybe in the past) with regular competitions? [closed]

This question from SEM but no answer :
In Yōko Ogawa's "The Housekeeper and the Professor," there is a character who regularly takes part in contests published in a fictitious mathematical journal ...

**0**

votes

**1**answer

94 views

### Borel subsets of Polish groups

Suppose that I have a polish group $G$ and two subsets $A$ and $B$ of $G$ such that: $A$ is open in $G$ and $B$ is closed in $G,$ from this, can I conclude that $AB$ is a Borel subset of $G$? if not, ...

**1**

vote

**0**answers

41 views

### Is there a polynomial time algorithm for Poly-trees (Oriented trees) isomorphism?

In terms of graph isomorphism complexity classes Trees have a polynomial time algorithm and Directed Acyclic Graphs (DAG's) do not (so far).
What about Poly-trees (oriented trees)? These are DAG's ...

**15**

votes

**1**answer

975 views

### The list of problems for Grothendieck's thesis

Is the list of open problems which were given by Dieudonne and Schwartz to Grothendieck for his thesis published somewhere? I know a quotation of Dieudonne that the problems concerned duality theory ...

**5**

votes

**1**answer

185 views

### Proof of a soft version of Moschovakis's lemma

The following fact, which I've heard being called "soft version of Moschovakis's lemma" (see top answer here) is the following:
Under AD, if there is a surjection $\Bbb R\rightarrow\alpha$, then ...

**1**

vote

**0**answers

92 views

### Evaluation of Macdonald Polynomials at $x_1=x_2=…=x_n = h$

This question is related to my previous question (here).
Let $P_\lambda$(q,t) be the Macdonald polynomials with partition $\lambda$. Let $\Lambda$ denote the ring of symmetric functions over the ...

**3**

votes

**0**answers

85 views

### A “nice” Orthogonal Basis for Translation Invariant Symmetric Polynomials

It is going to be a rather long question, so I will first state it and then try to explain and motivate it.
Take $\Lambda_n $ as the graded ring of symmetric polynomials of a field $F$ in $n$ ...

**1**

vote

**0**answers

86 views

### derivative of the adiabatic limit of the eta invariant

To ask my question I have to write down the setup. Basically the setup is the adiabatic limit of the reduced eta invariant of Dirac operator associated to the submersion metric and connection. So if ...

**0**

votes

**0**answers

21 views

### Methods for RCPSP

I have an Resource Constrained Project Scheduling Problem (RCPSP) with and additional strict precedence graph $H$, where $(j, j') \in H$ means $j'$ should stay closely after $j$.
Can you advise any ...

**4**

votes

**1**answer

207 views

### Ref. request: Additive probability measure on $\mathcal P({\bf N})$ supplies subset of $\mathbf R$ without Baire property

ZFC proves, among the other things, the existence of a (finitely) additive probability measure $\theta: \mathcal P(\mathbf N) \to \mathbf R$ on the power set of $\mathbf N$ such that $\theta(X) = 0$ ...

**27**

votes

**4**answers

898 views

### Why there is a relation among the second-order minors of a symmetric $4\times 4$ matrix?

A $4\times 4$ symmetric matrix
$$
\left(
\begin{array}{cccc}
a_{11} & a_{12} & a_{13} & a_{14} \\
a_{12} & a_{22} & a_{23} & a_{24} \\
a_{13} & a_{23} & a_{33} & ...

**2**

votes

**1**answer

146 views

### Elliptic regularity of second order pseudos

Let $M$ be a compact manifold. Choose a point $q \in M$. Let $P$ be a second order positive self-adjoint pseudodifferential operator such that $\text{Spec}(P) \subset (0, \infty)$. Also, we know that ...