# All Questions

**0**

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2 views

### Zeros of non-lipschitz functions (when noisy estimates are available only)

Given noisy (martingale difference) of a Lipschitz continuous function $f$ it is known how to compute zeros of it. It is the stochastic approximation approach (by Borkar, Kushner and Yin etc.). Is ...

**2**

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**0**answers

7 views

### Fixed point relation $\ Fix\ $ for pairs of manifolds

First the classical definition: a topological space $X$ has the fixed point property (fpp) $\ \Leftarrow:\Rightarrow\ $ for every continuous $\ f : X\rightarrow X\ $ there exists $\ p\in X\ $ such ...

**3**

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**0**answers

22 views

### Inverse cohomological isomorphisms

Let $\ M'\ M''\ $ be simply-connected Hausdorff compact manifolds (possibly with boundary for another variant of the question). Let $\ f:M'\rightarrow M''\ $ be a continuous function which induces an ...

**-1**

votes

**0**answers

20 views

### Infinite subset of a closed set [on hold]

This statement is true or false: If $F$ is an infinite subset of a closed set $E$, then $F$ has a limit point in $E$?
The original one is: if $E$ is an infinite subset of a compact set $K$, then $E$ ...

**0**

votes

**0**answers

9 views

### Non-finitely based varieties and pseudovarieties

The variety of semigroups defined by $B=\{xyzt=xzyt, yx^ny=xyx^{n-2}yx:n=2,3,\ldots\}$ is non-finitely based (Perkins). Is the pseudovariety defined by $B$ also non-finitely based?
More generally, if ...

**1**

vote

**0**answers

19 views

### Does projective duality preserve arithmetic-Cohen-Macaulay-ness?

Let $V$ be a vector space over $\mathbb{C}$.
Suppose $X\subset \mathbb{P} V$ is an algebraic variety, and consider its projective dual variety $X^\vee \subset \mathbb{P} V^*$. If the coordinate ring ...

**1**

vote

**0**answers

20 views

### Finitely generated groups non-embeddable into $L_1(0,1)$

I am interested in finitely generated groups which, endowed with their word metrics, do not admit bilipschitz embeddings into $L_1(0,1)$. I know two classes of such groups:
(1) Heisenberg group ...

**-1**

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**0**answers

14 views

### BNF grammar for given problem

I have a problem
(a) Give a grammar using BNF rules to construct a program in the language "witless". A witless program must follow the rules: The program must start and end with the word 'endstart' ...

**2**

votes

**0**answers

31 views

### Non-hyperelliptic families of curves with trivial Ceresa class (or Gross-Schoen class)

Suppose X/K is a curve over a field K, which we want to think of as non-algebraically closed, and let x be a point of X(K). The Ceresa cycle is defined as follows; you can embed X in Jac(X) by sending ...

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21 views

### Ostaszewski space's construction Lemma

I'm studying the Ostaszewski's article "On Countably Compact, Perfectly Normal Spaces". I'll add some context. Lemma 1.2 says the following:
Let $X$ be a locally compact, zero-dimensional and ...

**2**

votes

**1**answer

36 views

### Is there an easy way to tell if all eigenvalues of a unitary or self-adjoint matrix only have eigenvalues of multiplicity two?

I am interested in a class of $2n\times 2n$ unitary matrices with complex entries (if you prefer, we can replace "unitary" with "self-adjoint").
I know that all the eigenvalues of matrices in this ...

**2**

votes

**0**answers

13 views

### Limits and colimits in a 2-category vs. in an infinity category: the non- (2,1)-case

Suppose that $\mathscr{C}$ is a $2$-category (or more generally a bicategory) which is not a $\left(2,1\right)$-category. Is there any relation between limits and colimits in $\mathscr{C}$ (in the ...

**2**

votes

**0**answers

40 views

### Examples of unproven but likely true existential sentence (in the sense of incompleteness)

Some examples of universal statements that are unproven but likely true include the Riemann hypothesis (all non-trivial zeros of the zeta function have real part 1/2) and the Goldbach conjecture (all ...

**2**

votes

**1**answer

26 views

### Criteria for abstract polytopes to be convex polytope

Suppose I have an abstract polytope defined by a poset. Are there any methods for determining whether the abstract polytope can be geometrically realized as convex-hull on its set of vertices?

**0**

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**0**answers

19 views

### Gaussian expectation of a exponentiated outer product

Given a normal random column vector $\mathbf{x} \sim N(\mu, \Sigma)$, I need the expectation,
$$ E\left[ \exp(\mathbf{xx}^\top)\right]$$
where $\exp(\cdot)$ is element-wise exponential function (not ...

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**0**answers

46 views

### Collatz property implying infinite “fall below” trajectories, is it known?

(this was discovered analyzing Collatz empirically.)
a key aspect of resolving Collatz involves looking at the number of iterations for trajectories to "fall below" the initial value.
consider ...

**-1**

votes

**0**answers

27 views

### On a sum statistically independent of its term [on hold]

Suppose $U$ and $V$ are two non-degenerate random variables, say real-valued for simplicity. Suppose further that their sum, $U+V$, and one term, $U$, are statistically independent. This happens when ...

**12**

votes

**7**answers

414 views

### Where to find (personal) motivation [on hold]

I think it would be appropriate to make this question CW...
It is likely that this question will not survive here on MO for long, but I do hope that the community gives it a chance. I also hope to ...

**1**

vote

**1**answer

20 views

### Bi-invariant one forms on compact Lie groups

I'm hoping to learn of a criterion for the existence of a bi-invariant one form on a Lie group $G$. I'm looking for a reference that there are no such one forms son $SU(n)$ (as long as this is in fact ...

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**0**answers

7 views

### Complex parameters in the Ritz procedure

I am using the Ritz procedure to write a trial function as the superposition of other admissible functions, with the coefficients being unknown variational parameters to be determined. The variational ...

**1**

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**0**answers

56 views

### Does the canonical morphism commute with the inverse image functor?

I am trying to prove the representability of the Quotient functor.
I have the following problem.
Let $\phi \colon T \to S$ be a morphism of noetherian schemes and let $F$ be a coherent sheaf on ...

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**0**answers

46 views

### A question about subgroups [on hold]

Is there a group $G$ and a non-abelian subgroup $H$ of $G$ such that $[G:H]=2$, $|Z(H)|>1$ and $C_G(H)=2|Z(H)|$?

**1**

vote

**1**answer

21 views

### Concavity of the solution of a parametric implicit function

Suppose $F(x,y;k)=f(x,y)+kg(x,y)=0$ uniquely defines the solution $y(x;k)$ for $x\in \mathbb{D}$, a compact domain, and $0\leq k \leq 1$ is a parameter. We know that for $k=0,1$, $y(x;0)$ and $y(x,1)$ ...

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**0**answers

72 views

### Examples of etale group schemes [on hold]

What are important examples of etale group schemes over some field $F$, apart from finite group schemes?

**0**

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**1**answer

49 views

### Dimension of a similarity class

Let $K$ be an algebraically closed field with characteristic $0$. I consider the Jordan decomposition of a NILPOTENT matrix: $A=diag(J_{r_1},\cdots,J_{r_s})\in M_n(K)$ where $J_k$ is the nilpotent ...

**1**

vote

**0**answers

68 views

### What is known about the Brauer group of an arithmetic surface?

Let $X$ be an arithmetic surface over $\mathbb{Z}$, that is we have $\pi: X\rightarrow Spec(\mathbb{Z})$, $X$ is integral, two-dimensional and regular and $\pi$ is projective and flat.
What is known ...

**2**

votes

**3**answers

85 views

### Estimating the Variance of a Discrete Normal Distribution

Let $f(x; \sigma) = \frac{1}{\sigma\sqrt{2\pi}}\cdot e^{-\frac{x^2}{2\sigma^2}}$ be the probability density function of a normal distribution $\mathcal{N}(0, \sigma^2)$. We consider a discrete normal ...

**2**

votes

**1**answer

85 views

### Degree of a smooth curve in an abelian variety

Let $A$ be an abelian variety, $g$ be a positive integer and $\mathcal{L}$ be an ample line bundle on $A$.
Question : Is there a real $r>0$ such that, for all smooth curve $C$ of genus $g$ in ...

**4**

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**0**answers

74 views

### Upper bound on the number of ismorphism classes of bilinear forms on $\mathbb{Z}^n$

$\DeclareMathOperator{\Hom}{Hom}$A symmetric, positive definite bilinear form on $\mathbb{Z}^n$ is any mapping $$b : \mathbb{Z}^n \times \mathbb{Z}^n \to \mathbb{Z}$$ satisfying
$b$ is bilinear,
...

**1**

vote

**0**answers

22 views

### Stabiliser of the lamination of a free group - Invariant subgraphs

I am studying the paper "Laminations, trees, and irreducible automorphisms of free groups" of Bestvina, Feighn and Handel. But I found a note in the paper "Stabilisers of $\mathbb{R}$-trees with ...

**2**

votes

**1**answer

84 views

### Left invertible operators of $B(X,Y)$

Suppose that $X$ and $Y$ are Banach spaces. Is $\{f\in B(X,Y):f\ \text{has a left inverse}\}$ an open subset of $B(X,Y)$?

**4**

votes

**1**answer

95 views

### Arbitrarily large $n$ divides $F_n$

Is it true that there exists $n \in \mathbb{N}$ with arbitrarily many prime factors such that $n$ divides $F_n$, where $F_n$ represents the n-th Fibonacci number?

**0**

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**0**answers

38 views

### Connectedness of moduli for topologically trivial rank two bundles on $\mathbb{P}^3$

What is known about connectedness of moduli of vector bundles of rank two, with trivial Chern classes and trivial Atiyah-Rees-$\alpha$-invariant?
Ok, this is sort of a delicate question because there ...

**6**

votes

**4**answers

368 views

### Small values of a polynomial evaluated at roots of unity

The MO answer http://mathoverflow.net/a/98176/11926 notes the following: Let $\gamma$ be an algebraic number that is not a root of unity. Then Baker's theorem implies that there is a constant ...

**0**

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**0**answers

59 views

### Average distance between houses in the United States (per each of the 50 states) [on hold]

I'm trying to figure out what the average distance is between houses (per state in the U.S.). I can't seem to find it anywhere. My buddy told me about this site so here I am. I'd really appreciate ...

**1**

vote

**1**answer

92 views

### Hilbert scheme of an infinitesimal neighborhood of a subvariety

Let $X$ be a complex algebraic variety. Let $C\subset X$ be a compact (reduced) subvariety. Let $C^{(n)}$ denote the $n$th infinitesimal neighborhood of $C$ inside $X$. Let $Hilb(X)$ denote the ...

**-3**

votes

**1**answer

287 views

### Publishing problem [on hold]

First, I want appreciate your work on this platform, as I have been getting very helpful advice even though I am not a member. My problem is that I have been working on-off on a famous math problem ...

**2**

votes

**2**answers

93 views

### Automorphism group of a smooth quadric $Q\subset\mathbb{P}^4$

Let $Q$ be the smooth quadric threefold in $\mathbb{P}^4_{\mathbb{C}}$ defined by the equation
$x_0x_4+x_1x_3+x_2^2=0$.
Is it true that the automorphism group of $Q$ is $SO(Q;\mathbb{C})$ which is ...

**0**

votes

**0**answers

23 views

### Can a lower-order trigonometric polynomials fit the data generated by a higher-order one? [on hold]

Let $x$ be a discrete finite-dimension vector $x$, and write $\hat{x}(\Omega) = \mathcal{F}_{\Omega}x$ where $\mathcal{F}_{\Omega}$ is the linear mapping collecting the Fourier transform of $x$ at the ...

**7**

votes

**1**answer

134 views

### A conjecture about strongly regular graphs

Let $G \neq K_{v}$ be a $(v,k,\lambda,\mu)$ strongly regular graph. After perusing through Brouwer's tables of parameters I have formed the conjecture $$\lambda-\mu \leq \frac{k}{2}.$$
So far I have ...

**1**

vote

**1**answer

112 views

### Is any axiom system for sets categorical? [on hold]

$ZF$ define membership by conditions demanding the existence of some constructable right-side-terms $M $ ($x \in M$). Is it meaningsful to ask for a categorical axiom system here? Shouldn't it be ...

**3**

votes

**0**answers

58 views

### Clutching functions and Classifying maps

Let $E\xrightarrow{p} \Sigma X$ be a principal G-bundle over a suspension. Write $\Sigma X= C_+X\cup_X C_-X$. Then there are trivialisations of the restrictions $E|_{C_+X}\cong C_+X\times G$, ...

**4**

votes

**1**answer

55 views

### Besov Characterization of Strichartz Estimate.

On page 4 of this paper of Ibrahim, Majdoub, and Masmoudi, the authors claim in Proposition 2 that solutions to
$\left\{\begin{array}{ll}\square u=F(t,x)\\ u(0,x)=f(x), ...

**0**

votes

**0**answers

111 views

### Which are the constructs utilizing certain morphisms? [on hold]

I found my way to MathOverflow by googling questions concerning the different morphisms in the study of metric spaces: What is a metric space.
A lot of morphisms seems to be of interest: continuous ...

**0**

votes

**0**answers

17 views

### Integrating over the Intersection of Convex Regions

Is there a way to integrate over the intersection of a finite collection of convex regions, using only the definition of the regions (i.e. without actually calculating the intersections)?
The ...

**7**

votes

**1**answer

195 views

### The Diophantine equation $x^p - 4y^p = z^2$

If $p \geq 5$ is a prime, are there any integers $x, y, z > p$ such that
$(x, y) = 1$
and
$$x^{p} - 4y^{p} = z^{2}$$

**0**

votes

**1**answer

29 views

### Strongly convergent series of bounded self-adjoint operators

Let $A_n$ and $A$ be bounded self-adjoint operators in a Hilbert space, such that $A_n\to A$ strongly. Then it is well known that $(z-A_n)^{-1}\to(z-A)^{-1}$ strongly for each ...

**-1**

votes

**1**answer

116 views

### When is a local subring of a number field a valuation ring?

Do we have some good examples of local subrings of number fields which are not valuation rings?
Do we have an easy criterion for determining whether a local subring of a number field is a valuation ...

**1**

vote

**0**answers

59 views

### What is the abutment filtration of the second spectral sequence of hypercohomology?

I have been recently learning about spectral sequences, following mainly Illusie's notes and EGA, and I am about to write some expository notes, but there are still some points that I was not able to ...

**9**

votes

**0**answers

91 views

### Embeddings of finitely generated groups into uniformly convex Banach spaces

de Cornulier, Tessera, and Valette (Geom. Funct. Anal. 17 (2007), 770-792) conjectured that a finitely generated group $G$ with its word metric admits a bilipschitz embedding into a Hilbert space if ...