# All Questions

**0**

votes

**0**answers

32 views

### Single element extensions of subspace arrangement over finite field

Matroids have single element extensions found by Crapo[2] to create ground set size $n+1$ matroids from ground set size $n$ matroids. Do subspace arrangements over a finite field $\mathbb{F}_q$ have ...

**-1**

votes

**1**answer

100 views

### notable inductive proofs relating to fractals

what are notable/ prominent inductive proofs relating to fractals?
the motivation for this question is:
fractals are very difficult mathematical objects to work with, and many ...

**5**

votes

**1**answer

192 views

### Can eta invariant be written in terms of topological data?

The eta invariant was introduced by Atiyah, Patodi, and Singer. It roughly measures the asymmetry of the spectrum of a self-adjoint elliptic operator with respect to the origin. In ...

**0**

votes

**0**answers

16 views

### norm is invariant under scaling for subspace of wiener space

Consider the subspace H_1 of $C_0(0,\infty)$, where $\phi=\int_0^t\dot{\phi}(s)ds$ and $\int_0^{\infty}{\dot{\phi}}^2ds<\infty$. The transformation is $(T\phi)(t)=t\phi(\frac{1}{t})$. How to show ...

**0**

votes

**0**answers

72 views

### Eigenvalue of (0-1) matrix [on hold]

Assume I have 2 matrices, each of size nxn with only 1 and 0 as entries in both. (n>10)
The first matrix (call it A) has each row summing up to 2 (ie: on each row, it has two "1" and n-2 "0"). It is ...

**1**

vote

**1**answer

95 views

### On the geometry of roots of a sum of complex linear fractions

I was wondering if there is anything known about the geometry (position) of the roots of a rational map of the form
$$R(z):= \sum_{j=1}^{n} \frac{a_j}{z-p_j},$$
where the $a_j$'s are nonzero complex ...

**-1**

votes

**0**answers

17 views

### Gradient Estimation Using Bicubic Interpolation and Finite Differences [closed]

Suppose we know the values f(x,y) takes on in a 4x4 grid defined by all pairwise combinations of x={0,1,2,3} and y={0,1,2,3}. Bicubic interpolation using centered differences provides a way of ...

**-3**

votes

**0**answers

34 views

### complexe integration around a branch point [closed]

I have this complex integral to which I don't know if it's possible to assign a value:
The integral is on a small circle around the origin. The function is 1/((z-1)*sqrt(z)).
The fact is that z=0 is ...

**4**

votes

**1**answer

149 views

### Section of the homology functor on spectra

Consider the (reduced) homology functor $H_*$ from the category of spectra to the category of graded Abelian groups. I wanted to know whether there is a "section" of this functor, i.e., a functor $F$ ...

**2**

votes

**1**answer

179 views

### What is “tilting” in the context of large deviations?

I have seen references to the "tilting method" in the theory of large deviations. Is there a simple explanation of what this is, exactly?

**2**

votes

**2**answers

87 views

### Bounds for the fat tail after trimming the mean?

I am interested in the quantity $$f(X,t) = \int_t^\infty\negthinspace x\ p(x)\ dx,$$ where $p$ is a probability distribution for a positive variable $X$.
1) Does this quantity $f(X,t)$ have a name? ...

**-1**

votes

**1**answer

96 views

### Suppose I know $\int h(t) dt = H(t)$, is there a way to find $\int h(t)^N dt$?

I am trying to find the -1 moments of sum of N geometric random variable, i.e. $E[\frac{1}{\sum_{i=1}^N X_i}]$
Suppose the probability mass function is $f_X(x) = (1 - p)^{x - 1} p$
The moment ...

**1**

vote

**1**answer

105 views

### Follow up: Is continuity preserved when taking comma object?

Here, I asked wether taking lax pullback preserves continuity, but got no precise answer.
However, I have found this recent article by Riehl and Verity which proves something very similar, but I ...

**1**

vote

**1**answer

127 views

### Question on an arithmetic function with the sieve of Eratosthenes

I want to ask some question related with the sieve of Eratosthenes.
The sieve of Eratosthenes: write it as $E_1(x) (=\pi(x)-\pi(\sqrt x)+1)$.
Then we have an obvious result
$$E_1(x)/x\ln^{-1}x = ...

**1**

vote

**1**answer

72 views

### Equivalence of star products on two differents Poisson algebras?

Let $A$, $B$ be two commutative and associative $\mathbb k$-algebras and let $A_\hbar:=A[[\hbar]]$, $B_\hbar:=B[[\hbar]]$ be the corresponding ring of formal series. Of sense [Deformation theory and ...

**0**

votes

**0**answers

48 views

### plotting parametrized algebraic curves near singularities

I have a parametrized algebraic curve:
x(t)=A(t)/D(t);
y(t)=B(t)/D(t);
with A(t) and B(t) being polynomials in t. The curve is solution of a linear system in two unknowns x and y with Cramer's ...

**1**

vote

**1**answer

92 views

### what's the cohomological dimension of a Stein space?

I want to know the "cohomological dimension" of a Stein manifold.
I know that:
for $X$ differential manifold and for every sheaf $F$ of abelian
groups, I have $H_c^j(X,F)=H^j(X,F)=0$ for ...

**3**

votes

**2**answers

144 views

### Structure of an intersection of $L^p$-spaces

In what follows, $L^p$ denotes the space of functions from $\mathbb{R}$ to $\mathbb{R}$ such that $\int_{\mathbb{R}} |f(x)|^p\mathrm{d}x < \infty$.
I am interested to understand the structure we ...

**3**

votes

**1**answer

172 views

### What is the group cohomology of the mapping class group of a surface

Let $MCG_g$ be the mapping class group of genus $g$ closed surface.
(Say $MCG_1=SL(2,Z)$).
I would like to know what is the group cohomology of $MCG_g$ with coefficients in Z, such as ...

**2**

votes

**2**answers

285 views

### Beautiful constructions in algebraic topology that facilitate one's understanding of homotopy theory [closed]

There is an army of interesting constructions in AT, and Understanding them are usually very helpful for appreciate the theory underneath. So I would like to invite you to share those examples that ...

**1**

vote

**0**answers

61 views

### Reference Request: Algebraic Serre's Duality Theorem for Curves

Serre's Duality Theorem is well known and well studied and, as far as I know, there is a "big" algebraic proof for the general case, which is now kind of standard, and can be found in Hartshorne ...

**12**

votes

**1**answer

366 views

### Normality of $\pi$ in base 16

It seems that in spite of the Bailey–Borwein–Plouffe formula it is still unknown whether $\pi$ is normal in base 16. What are the difficulties in using it for this purpose?
In a comment to his answer ...

**1**

vote

**0**answers

64 views

### Local system over $\mathcal A_{g,[n]}$ with unipotent monodromy

Let $\mathcal A_{g,[n]}$ denote the moduli space of principal polarized abelian varieties with level-[n] structure and
$\bar {\mathcal A}_{g,[n]}\supset \mathcal A_{g,[n]}$ a smooth Toroida ...

**2**

votes

**1**answer

37 views

### Centre manifold theory for a curve of equilibrium points

I am looking for advice concerning a specific situation related to centre manifold theory (compare Perko 2001).
The part which is known
Let's consider a differential equation in higher-dimensional ...

**1**

vote

**0**answers

138 views

### Integer solutions of $ z^3 y^2 = x(x-1)(x+1)$

According to a conjecture there are no three
consecutive powerful numbers.
Necessary condition for this is integer solution of
$$ z^3 y^2 = x(x-1)(x+1) \qquad (1) $$
What are integer solutions ...

**1**

vote

**2**answers

84 views

### Invariant measure of Euler-Maruyama Discretisation of an Ito diffusion

Let $(X_t)_{t \geq 0}$ be a diffusion process with dynamics governed by the stochastic differential equation
\begin{equation}
dX_t = b(X_t)dt + \sigma(X_t)dW_t, ~~ X_0 = x_0,
\end{equation}
where ...

**0**

votes

**0**answers

82 views

### Degree and quasi projective family

Let $V$ be a quasi-projective variety in $\mathbb{P}^{n}\times\mathbb{P}^m$. If $p\in \mathbb{P}^m$, we define the degree of $V_p$ as the degree of its closure in $\mathbb{P}^n$.
Question : $\exists ...

**-4**

votes

**0**answers

76 views

### Where to include contact details in math paper? [closed]

I recently submitted a paper to a math journal on a prime number patter using latex formatting, but they sent an email back saying that the contact details for the corresponding author should be in ...

**2**

votes

**0**answers

62 views

### $f, \hat{f} \in L^{p}\cap L^{\infty} \implies f\in B(\mathbb R)$ (algebra of Fourier- Stieltjes transforms )?

For a bounded complex Borel measure $\mu$ on $\mathbb R$, we define, its Fourier-Stieltjes transform, $\hat{\mu}(y)= \int_{\mathbb R} e^{-2\pi ix\cdot y} d\mu(x); (y\in \mathbb R).$
Let $1\leq p \leq ...

**1**

vote

**2**answers

166 views

### Can $T$ act trivial in a repn of SL$_2(\mathbb{Z}_N)$?

I am confronted with the following problem:
If $\rho : \text{SL}_2(\mathbb{Z}) \to \text{GL}_{\mathbb{C}}(V)$ is a finite dimensional representation such that $\text{ker}(\rho)$ contains the ...

**0**

votes

**0**answers

54 views

### On the schur Multiplier of a group [closed]

Let $G$ be a finite simple group and its Schur multiplier is 2.
Is it true that if ${M\over K}\cong G$ and $|K|=2$, then $M\cong {\Bbb Z}_2\times G$ or $M\cong 2.G$, according to the symbols in the ...

**1**

vote

**1**answer

142 views

### lattice in number field already a fractional ideal?

Let $K=\mathbb{Q}[\alpha]$ where $\alpha$ is integral over $\mathbb{Z}$ such that the Galois hull of $K$ can be embedded in $\mathbb{R}$. Let $S=\mathbb{Z}[\alpha]$. Let $x_1, \ldots , x_n$ be a ...

**10**

votes

**2**answers

209 views

### Algorithms in hyperbolic groups

I'm stuck in some algorithms in hyperbolic groups, which may be rather simple.
Let $G$ be a hyperbolic group given by a finite presentation. It is known that the hyperbolicity constant $\delta$ can ...

**2**

votes

**0**answers

46 views

### QR-Decomposition of matrix valued function

Suppose I have a matrix valued function
$$
F:\mathbb{R}\rightarrow\mathbb{R}^{m\times n},\qquad F(x)=\tilde Q\tilde R+xu_1v_1^T+xu_2v_2^T
$$
where $\tilde Q\in\mathbb{R}^{m\times m}$ is orthogonal, ...

**2**

votes

**1**answer

108 views

### Estimate infinity norm with Lp and W1p norm

Let $p \in [1,\infty)$. Does there exist $C>0$ such that for every $f \in W^{1,p}([0,1],\mathbb{R})$ we have
$$\|f\|_{L^\infty}\leq C\|f\|_{L^p}^{1-\frac{1}{p}}\|f\|_{W^{1,p}}^{\frac{1}{p}}?$$
My ...

**4**

votes

**0**answers

56 views

### Can an acyclic continuum be metrically homogenous? (I'd say: no way! :-)

I asked recently on MO about algebraic structures admitted by topologically homogenous continua like the Hilbert cube $\ I^{\mathbb N}\ $ or the Knaster pseudo-arc. There is a relation between the ...

**2**

votes

**0**answers

90 views

### Inn characteristic in Aut [migrated]

If $G$ is a centerless group then is $\mathrm{Inn}(G)$ necessarily characteristic in $\mathrm{Aut}(G)$?
The condition of being centerless is necessary as $D_8$ provides a counterexample otherwise.

**1**

vote

**0**answers

23 views

### Trace of Inverse matrix from Cholesky

This question was somewhat answered here: Fast trace of inverse of a square matrix. However, I feel like there was no complete answer wrt the Cholesky case.
I have the matrix $\Sigma=LL^T$. Is there ...

**-1**

votes

**1**answer

74 views

### Variety of commutative semi group [closed]

V is a variety of commutative semi group satisfying the identity $x^2 = x^3$.
I need to prove that:
$|F_V(\{x_1\dots,x_n\})|$ = $3^n -1$.
Any hints on this ?
$F_V$ is V-free algebra.

**6**

votes

**2**answers

189 views

### How to define the square root of $1-\Delta $?

If $M$ is a Riemannian manifold with $\Delta $ its Laplacian, how can we define $(1-\Delta)^{1/2}$?
The book I am reading says that $(1-\Delta)^{1/2}$ is an invertible first-order pseudo-differential ...

**-3**

votes

**1**answer

88 views

### SHPS and SPHS inequality using monounary algebra

Let $A_n = \{(1,\ldots,n) , f \}$ where $f(i) = (i+1)$ if $i \neq n $ otherwise $f(n) = 1$.
This describes a mono unary algebra.
The proof for $HPS \neq SPHS$ I know uses metabelian groups and was ...

**3**

votes

**1**answer

110 views

### Is every sufficiently dense well mixed set an additive basis?

Let $B \subset \mathbb{N}$ be a set of natural numbers such that $|B \cap [1,N]| \sim N^\gamma$, for some $\gamma > 0$ with the following property:
For any pair of positive integers $k,n$ we ...

**13**

votes

**0**answers

183 views

### A question about small sets of reals

In ZFC, does there exist an uncountable set of reals $A$ such that for every closed measure zero set of reals $B$, $ A + B = \{a+b : a \in A, b \in B\} \neq \mathbb{R}$?
This question is motivated ...

**3**

votes

**0**answers

102 views

### “Almost” prime k-tuples in intervals

In this paper, Heath-Brown proves that there are $ \gg x(\log{x})^{-k}$ integers $n \leq x$ such that $$ \prod_{i=1}^{k} (a_{i}x + b_{i}) $$ is squarefree and that each term has a "small" number of ...

**4**

votes

**2**answers

521 views

### Why Cech cohomology does not compute sheaf cohomology on an open annulus

Let $A=\{z\in\mathbf{C}:1/2<|z|<1\}$ be an open annulus. Let us cover $A$ by 3 open sets:
$U_0,U_1$ and $U_2$ which we assume to be all homeomorphic to a 2 dimensional open disc. Moreover, we ...

**1**

vote

**1**answer

77 views

### Normal coordinates near the boundary

Let $M$ be an Riemannian manifold with boundary $\partial M$ and $e_n$ be a unit normal vector on $\partial M$. With respect to $e_n$, around a point $p$ on boundary, we have the usual normal ...

**0**

votes

**1**answer

60 views

### Equivalent of Stirling-like numbers

let $b_{n,k}$ be the numbers defined formally by $$X^n=\sum_{k=0}^n b_{n,k}\binom{X}{k}$$ where $\binom{X}{n}=\frac{1}{n!}\prod_{k=0}^{n-1}(X-k)$.
I am looking for an equivalent of $b_{n,k}$ when $k$ ...

**-1**

votes

**0**answers

45 views

### Is an even-dimensional real projective space (RP^2 or RP^4) a spin(or spin^C) manifold or not? [closed]

I have a dumb question.
Let us consider an even-dimensional real projective space (for instance, RP^2 or RP^4). I wonder if those spaces allow spin structure. In other words, is the real projective ...

**1**

vote

**0**answers

33 views

### Pseudofunctors of 2-variables and Gray tensor product of bicategories

Let $\mathcal{A}, \mathcal{B}, \mathcal{C}$ be bicategories. We say a 'pseudofunctors of 2-variables' consists of two families of pseufunctors
Fix $A\in obj\mathcal{A}$, we have a pseudofunctor ...

**1**

vote

**1**answer

83 views

### M/M/1 Queue with probability of new customer leaving [on hold]

I'm looking at a M/M/1 queue system and trying to show that $\{M_t\}_{t\geq}0$, the number of clients in the system, is a birth-death process. In the simplest of cases this is true if $\lambda_i = ...