# All Questions

**-1**

votes

**0**answers

20 views

### generic divisibility equation for two natural numbers [on hold]

Given two natural numbers N and B, so that N > B, is there a generic equation that contains only multiplications of N and B which can tell whether N is divisible by B?
Basically, something like a ...

**1**

vote

**1**answer

43 views

### Combinatorial interpretation for coefficients of reciprocal of power series

I've seen a number of combinatorial interpretations for the coefficients of the compositional inverse (aka reversion) of a power series. Is there a known combinatorial interpretation for the ...

**-4**

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**0**answers

21 views

**2**

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**0**answers

39 views

### Confusion regarding statement of mirror symmetry for elliptic curves

I am a little bit unsure about the mirror symmetry statement for elliptic curves; specifically, how the flipping of the Kähler and complex moduli works. Perhaps I should say at the outset, the reason ...

**0**

votes

**0**answers

18 views

### Integral of Daubechies wavelets

For Daubechies wavelets according to this paper (above eq 19) this relation holds
$$
\int_{-\infty}^{-\infty} \phi(2x-i)\phi(2x-j)dx = \frac{1}{2} \int_{-\infty}^{-\infty} \phi(x-i)\phi(x-j)dx
$$
...

**0**

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**0**answers

48 views

### Number Theory Characterization Problem

Given any natural number $N = a_{n}a_{n-1}\ldots a_{1}$, let us associate to it the set $S_{N} = \bigcup_{j=1}^{n}\{(a_{j},j)\}$. We're going to define a d-self-contained number as any natural number ...

**2**

votes

**0**answers

33 views

### Homology of inverse limits over inverse systems more complicated than towers

Most textbooks discussions of homology of inverse limits of chain complexes consider only “towers,” i.e. inverse systems indexed by the natural numbers. I’d like to find a reference that explains what ...

**0**

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**0**answers

17 views

### Questions related to a summation of fraction equation

I am struggling the following problems. It is not ensured to solve completely because these problems are generated by myself. Particularly, I guess the second problem is very hard if we try to solve ...

**4**

votes

**0**answers

42 views

### Is there a name for groups of the form $Sp(1)^n$?

A (compact) torus is a Lie group isomorphic to the product of finitely many circles: $T^n = S^1 \times \cdots \times S^1$. Such groups are extremely important in Lie theory, Differential Geometry, ...

**1**

vote

**1**answer

69 views

### estimating binomial coefficients

There is a beautiful paper on the arXiv by Andrew Suk containing an asymptotic result about the Erdös-Szekeres convex polygon problem. I am struggling with one of the estimates he makes on page 4. He ...

**-3**

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**0**answers

18 views

### How many vertical or horizontal asymptotes does this equation (x^2 - 1)y = x^2 - 4 have? [on hold]

How many vertical or horizontal asymptotes does this equation (x^2 - 1)y = x^2 - 4 have?
Actual question is this(Qs11)
Answer is given as C but I think there are two horizontal asymptotes

**3**

votes

**2**answers

97 views

### Constructively, are all fibrations cloven?

A "cloven fibration" is a fibration for which we have an explicit choice of cartesian liftings; this is often phrased as, "We can pick a lifting without using the axiom of choice".
Firstly, I'm a bit ...

**0**

votes

**0**answers

14 views

### Permutation Invariant Color Class

$G$ is a $d$ regular graph, it has $n$ vertices.
$S_n$ acts on $n$ vertices of graph $G$.
Question: Does there exist a coloring algorithm for which color classes is invariant under all ...

**2**

votes

**0**answers

29 views

### Symmetries of modular categories coming from quantum groups

This is a request for references about the computation of the braided autoequivalences of fusion categories coming from a quantum group. I could not find even the description of braided ...

**5**

votes

**2**answers

134 views

### What is the intuitive meaning of the coskeleton of a simplicial set?

Consider the inclusion $i_n: \varDelta_{\leq n} \hookrightarrow \varDelta$.
This induces a truncation functor $tr_n:\mathbf{sSet}\to\mathbf{sSet}_{\leq n}$, which has a left and a right adjoint, $tr_n^...

**1**

vote

**0**answers

8 views

### The jump set of $SBV$ function for different value of parameter in image denoising problem

The classical Mumford-Shah image denoisng problem study the minimizer of the following functional, for each $\alpha>0$ where $\Omega\subset \mathbb R^2$ is open bounded with sommth boundary,
$$
u_\...

**2**

votes

**0**answers

23 views

### Negative-curvature behaviour of higher-rank symmetric spaces

Let $X$ be a symmetric space of noncompact type with $rk\ X\geq 2$ and let $G$ be the identity component of the isometry group. Pick points $p\in X$ and $\xi\in\partial_{\infty}X$, with $\xi$ regular, ...

**2**

votes

**2**answers

55 views

### A question on invariant measures

Let $(X, \mathcal{B}, T)$ be a topological dynamical system and $M(X, T)$ be the set of all invariant measures.
I do not know is there some nice functional characterization of the following set
$\{...

**1**

vote

**0**answers

32 views

### Comodules of the $B,C$ and $D$ series quantum groups

In Section 11.5 of Klimyk and Schmudgen's book on quantum groups, explicit presentations of the isomorphism classes of comodules of ${\cal O}(GL_q(N))$ are given in terms of its "quantum minors". In ...

**6**

votes

**1**answer

74 views

### Decay of Fourier coefficients for compact Lie groups

Let $G$ be a compact Lie group, $G^\natural$ the space of conjugacy classes in $G$ with the natural pushforward of $G$'s Haar measure. Let $f\in L^2(G^\natural)$. Then the Peter–Weyl Theorem tells us ...

**3**

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**0**answers

34 views

### Existence of solutions of $\Delta u = f$ such that $|u|_{L^\infty} < \infty$ if $|f|_{L^\infty} < \infty$

I am struggling with figuring out the details of Proposition 7.1. in the paper Curvature and Uniformization - R. Mazzeo and M. Taylor.
Setting is as follows.
Let $\Omega$ be a noncompact Riemann ...

**3**

votes

**3**answers

294 views

### sum of four squares with some coefficients

Is there an ordered 4-tuple of rational numbers $(a,b,c,d)$ such that $(b,d)\ne(0,0)$ and $2a^2+3b^2+30c^2+45d^2=2$?
The former (deleted) question was just about cases $(a,b,c,d)\ne(1,0,0,0)$ but it ...

**-3**

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**0**answers

63 views

### Is a surjective mapping of R2 to itself with full rank derivative everywhere injective? [on hold]

Let $f:\mathbb R^2 \rightarrow \mathbb R^2$, and $rank(\frac{df}{dx}) = 2$ everywhere. If $f$ is surjective $f$ necessarily injective?
Also, what if $f$ maps $\mathbb R^{2+}$ (i.e. $\{x_1>0, x_2&...

**3**

votes

**0**answers

81 views

### On the conjectured nonexistence of even almost perfect numbers (other than powers of two) and odd perfect numbers [on hold]

(Note: This question has been cross-posted to MSE.)
Let $\sigma(a) = \sigma_{1}(a)$ be the sum of the divisors of the positive integer $a$.
A number $M$ is called almost perfect if $\sigma(M) = 2M -...

**0**

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**0**answers

54 views

### Definition of formal adjoint of covariant derivative

I read in Einstein Manifolds, L. Besse that the covariant derivative $D: \mathcal{J}^{(r,s)}(M)\to \Omega^1(M)\otimes\mathcal{J}^{(r,s)}(M)$ admit an formal adjoint $D^*:\Omega^1(M)\otimes\mathcal{J}^{...

**7**

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**0**answers

118 views

### Collatz-like properties of finite fields

I was wondering what an equivalent of the Collatz conjecture might be for finite fields. In a Collatz sequence a number is moved down within a set $\{2^k n : k \in \mathbb{Z}^* \}$ for some odd $n$ or ...

**0**

votes

**0**answers

40 views

### Checking whether a given matrix has a non-zero determinant

For a positive integer $n$, let $c$ be the number of ordered integers tripartitions $(a_j,b_j,c_j)$ of $n$.
Now consider the $c \times c$ matrix $M$ in which the value of the $M[i,j]$ is
$M[i,j]={(...

**0**

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**0**answers

38 views

### Action is determined by a braiding

Let $H$ be a bialgebra over $\mathbb{C}$. Suppose that $V$ is a left $H$-comodule and $W$ is an $H$-module. Then we can defined map $\Psi$ by
\begin{align}
& \Psi: V \otimes W \to W \otimes V, \\
&...

**2**

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**0**answers

19 views

### Realisation of the preprojective algebras as $F(\Delta)/T$ over some quasi-hereditary algebra

Let $A$ be the Auslander algebra of $K[x]/(x^n)$ for some $n \geq 2$, which is quasi-hereditary with some characteristic tilting module $T$.
Dlab and Ringel showed in their paper "The Module ...

**2**

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**0**answers

48 views

### Generalized height of elements in abelian groups

In the book Infinite abelian groups Vol. I by L. Fuchs, on page 154, the notion of the generalized $p$-height of an element in an abelian group is defined, as follows:
Let $A$ be an abelian group ...

**2**

votes

**1**answer

55 views

### An inequality on partitions into distinct bounded parts

Let $P(n,m)$ denote the set of all positive integer partitions of $n$ into parts that are pairwise distinct and bounded by $m$. Let $p(n,m) = |P(n,m)|$.
After some numerical experiments it appears
$...

**0**

votes

**0**answers

79 views

### An ideal and its annihilator

Let $I$ be an arbitrary ideal of commutative ring $R$ with identity.
If $ann (I)=AB$, where $A$ and $B$ are comaximal, how can we fine two ideal $I_1$ and $I_2$ with $I=I_1+I_2$ such that $I_1$ ...

**2**

votes

**1**answer

53 views

### Bounds on Matrix Exponential

Suppose $A$ and $B$ are (non-commuting) hermitian $n\times n$ matrices and $k$ is a large positive number. Suppose we write the product of matrix exponentials as
$e^{kA + B} e^{-kA} = e^{C(k)}$
for ...

**5**

votes

**2**answers

509 views

### Euclid vs Eratosthenes [on hold]

Very little is known about Euclid's life--much less than about other famous ancient Greek mathematicians, which is puzzling. It is also strange to me that Euclid didn't write about the Eratosthenes ...

**2**

votes

**0**answers

59 views

### Has a continuous map from $\kappa^\omega$ to $[0,1]^\omega$ a non-scattered fiber?

Question. Let $\kappa>\mathfrak c$ be a cardinal endowed with the discrete topology and $f:\kappa^\omega\to[0,1]^\omega$ be a continuous map. Is there a point $y\in[0,1]^\omega$ whose preimage $f^{-...

**0**

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**0**answers

46 views

### Normalizing factor in Reciprocity of traces of Frobenius with solutions of equations mod p

One kind of Reciprocity tells us that we can count solutions to polynomial equations over finite fields and relate them to traces of Galois Representations with some normalization factor.
For ...

**4**

votes

**0**answers

68 views

### Meaning of the support property in the definition of Bridgeland stability condition

Let $(Z,\mathcal{P})$ be a Bridgeland stability condition on a triangulated category $\mathcal{C}$. It is said to satisfy the support property if there exists a norm on $K(\mathcal{C})\otimes_\mathbb{...

**2**

votes

**3**answers

304 views

### Krull-dimension of local domain

Let $(R,{\frak m}_R)$ be a local domain (not necessarily Noetherian). That is, $R$ is integral and ${\frak m}_R$ is the unique maximal ideal of $R$. Suppose that ${\frak m}_R$ is finitely generated.
...

**-4**

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**0**answers

44 views

### How do I figure out the next number in these series of numbers? [on hold]

I tried everything but I guess I am struggling and I am stumped what number comes next in the sequence. Hints or tips about how to go about this because I am not seeing this. I tried calculating the ...

**-1**

votes

**0**answers

92 views

### (Dynamical) mean field theory for mathematicians? [on hold]

I am looking for a readable introduction/tutorial on dynamical mean-field theory, written for someone who doesn't know anything about particle physics.
My physics background is non-existent beyond ...

**2**

votes

**0**answers

105 views

### Inverse limit of Noetherian rings

Let $R_i$ be a noetherian regular local ring of Krull dimension being finite. Suppose we are given a surjective homomorphism $\phi_{i,j} \colon R_{j} \twoheadrightarrow R_i$ for each $i,j$ with $j >...

**1**

vote

**1**answer

63 views

### Parametric solutions to a system of equations

Let $s,t$ be two independent real parameters, and let $a_2(s,t), a_1(s,t), a_0(s,t)$ be linear forms in $s, t$ with real coefficients. Put $a_4 = s, a_3 = t$ and consider the quadratic form
$$\...

**-3**

votes

**0**answers

135 views

### What is geometry? [on hold]

I wish to know what geometers and other mathematicians consider geometry.
Wikipedia defines geometry as "concerned with questions of shape, size, relative position of figures, and the properties of ...

**-4**

votes

**0**answers

83 views

### Does the group Aut(M) preserve every Dedekind Zeta function? [on hold]

Foreword:
This excerpt of a paper of mine aims at introducing the concept of automorphism of an L-function, where by L-function we mean any element of the Selberg class that is also an automorphic L-...

**0**

votes

**1**answer

48 views

### Hamiltonian potential invariant under lie group action?

Let $(M,g)$ be a riemannian manifold and $G$ a Lie group acting on $M$ by isometries.
Taking a $G$-invariant function $f\colon M \to \mathbb{R}$, we have the riemannian gradient $\operatorname{grad} ...

**1**

vote

**0**answers

35 views

### Can all Local Martingales Be Represented using Only Brownian Motion and Finite Variation Processes?

This is a cross-post of my unanswered (more than a week) question on Math.SE. Since it covers topics from my graduate-level course on stochastic processes, I thought it might be appropriate to try to ...