# All Questions

**-4**

votes

**0**answers

20 views

### Show that the mapping A linear. Lays down rules for adjoint transformation A * [on hold]

Let V n-expansive real vector space with scalar product, a and b given linearly independent vectors from the space V. mapping A: V -> V is given by Regulations Ax = (x, a), * b
Assign eigen values ...

**0**

votes

**1**answer

85 views

### The kernel of the natural map $\pi_k(BU(r)) \to \pi_k (BU)$

Is this group known outside of the stable range? If so, what is it? If not, what is known about it?

**2**

votes

**0**answers

52 views

### Condition number after preconditioning

Suppose $A$ and $P$ are symmetric, positive definite matrices and that we factor $P^{-1}=EE^\top.$ Is it true that the condition number of $PA$ is upper-bounded by the condition number of ...

**0**

votes

**0**answers

24 views

### Picard sequence for sujective morphisms

Given $\phi:X\rightarrow Y$ a surjective morphism of $k$-algebraic varieties ($k$ separably closed), I wanted to find how the write an exact sequence involving Pic(X) and Pic(Y). We can use the long ...

**-4**

votes

**0**answers

18 views

### How many are there orthogonal transformations? [on hold]

which transform the line x = y / 2 = z line -x / 2 = y = z and the line x = -y = with the line x = y = z? Find the matrix of any of them in a standard basis
I have tried to equal equations.

**-2**

votes

**0**answers

40 views

### embedding dimension of normal surface singularity [on hold]

the following is a part of the proof of Lemma 4.23 in this book.
Let $0\in X$ be a (germ of) normal surface singularity.
Let $C_1, C_2$ be hypersurface sections of $0\in X$ and $(C_1 \cdot ...

**1**

vote

**0**answers

21 views

### Extract a “fraction” bipartite subgraph from a given graph

Question:
Do there exist real constants $k,c$ such that: for every graph $G$ of large minimum degree, there exists a spanning subgraph $H$ of $G$ such that $H$ is bipartite and
...

**1**

vote

**1**answer

40 views

### Problem about the existence of a continuous surjective map

Let $F$ be a closed set in $\Bbb R^2$, $F\neq \varnothing,\Bbb R^2$, and $F^\circ\neq \varnothing$,
does there exist a continuous surjective map from $\Bbb R\times \Bbb Z$ to $F^{\circ-}-F^\circ$？

**1**

vote

**0**answers

55 views

### How can I calculate the adjoint of the wave operator $\square_{g}$ in $H^{k}$?

I have a three part question, which I could only received an answer for the first part here.
The Laplace-Beltrami operator is an operator which is the typical example of a self-adjoint operator in ...

**2**

votes

**0**answers

72 views

### Rational curves in projective spaces

Let $X\subset(\mathbb{P}^{N})^n$ be the variety defined as follows: $(p_1,...,p_n)\in (\mathbb{P}^{N})^n$ such that there exists a rational curve $C$ of degree $d$ with $p_1,...,p_n\in C$.
Is there a ...

**0**

votes

**0**answers

10 views

### VC-dimension for conjunctions with negations [migrated]

I need any hint in the following problem.
Let $\mathcal{F}_k$ be a set of all possible conjunctions of binary variables $x_1, \dots, x_k$ and their negations. How could I prove that ...

**6**

votes

**2**answers

188 views

### Lower bound on the first eigenvalue of the Laplace-Beltrami on a closed Riemannian manifold

It has been proved by Li-Yau and Zhong-Yang that if $M$ is a closed Riemannian manifold of dimension $n$ with nonnegative Ricci curvature, then the first nonzero eigenvalue $\lambda_1(M)$ of the ...

**0**

votes

**0**answers

28 views

### Probability distribution [on hold]

I have 2 groups of elements, say A={a} (only 1 element) and B = {b1, b2,..., bn}.
Now the take the probability of picking "a" is 0.3 and the probability of picking an element in B is 0.7. An element ...

**16**

votes

**1**answer

404 views

### The sum of squared logarithms conjecture

I am searching for the first proof of (or counterexample to) the following conjecture.
(The sum of squared logarithms conjecture)
For all natural numbers $n$ and positive numbers $x_1,x_2, \ldots , ...

**6**

votes

**1**answer

151 views

### When does the free loop space fibration split?

This question is a repost from stack.exchange. It didn't get a lot of attention there. Perhaps it is badly written (or silly?). If so, I'd be happy to get comments/suggestions about that.
Let $X$ be ...

**3**

votes

**0**answers

46 views

### Concentration and Correlation for Magnitudes of Gaussian Vectors

Suppose we have a large collection of standard normal random variables $a_i\in\mathbb{R}^n$. We know by standard concentration results that if we take $m \geq C\left(t/\epsilon\right)^2n$ samples, ...

**2**

votes

**0**answers

54 views

### Generalized Hurwitz Spaces

In this question all the varieties are over $\mathbb{C}$. Classic Hurwitz spaces $\mathcal{H}_{g,r}$ are moduli spaces of simple branched coverings $f \colon X \to \mathbb{P}^1$ of degree $d$, where ...

**5**

votes

**1**answer

93 views

### Does the property of being a local homeomorphism descend through split surjections?

Let $f : X \to Y$ and $g : Y \to Z$ be continuous maps (between topological spaces). Assume these hypotheses:
$f : X \to Y$ is a split surjection, i.e. has a section.
$g \circ f : X \to Z$ is a ...

**-4**

votes

**0**answers

27 views

### system of linear equations [on hold]

These are the two known equations
(I2+I3)-(I1+I4)/(I1+I2+I3+I4) = 2x/L
(I2+I4)-(I1+I3)/(I1+I2+I3+I4) = 2y/L
where I know x,y,L values. How can I find the values of I1,I2,I3,I4?

**0**

votes

**1**answer

48 views

### Hadamard Product and Eigendecomposition

I just found this related question in here Q1.
Given a positive definite matrix $\mathbf{A}$, consider its eigendecomposition $(\mathbf{A}\mathbf{V} = \mathbf{V}\mathbf{D})$. Consider an arbitrary ...

**1**

vote

**0**answers

18 views

### Oscillating Markovprocess Transition Probabilities

Suppose we have an irreducible positive-recurrent Markov process $\{X(t), t\geq0\}$ with generator $G$. Let $P(t)$ be its transition probability matrix and $\pi$ its stationary distribution. Then we ...

**0**

votes

**0**answers

33 views

### Pseudo-braided fusion categories

A few definitions first, please replace with the standard terminology (and correct me if I confuse all the by-names of fusion categories :-)
I call a complex number $z$ pseudo-cyclotomic if $|z|=1$.
I ...

**11**

votes

**1**answer

175 views

### How many Fréchet manifolds are there?

Clearly the title needs clarifying. Allow me to let "how many" to mean a set larger than a skeleton of the category of Fréchet manifolds and smooth maps, if this category is indeed essentially small.
...

**1**

vote

**0**answers

78 views

### Two questions about Whittaker functions

I am watching the video: Modeling p-adic Whittaker functions, Part I. I have two questions about Whittaker functions in the video.
From 33:00 to 37:00, it is said that after changing of variables, ...

**2**

votes

**0**answers

58 views

### Analytic continuation of intertwining operator

I was trying to understand the paper "Form of GL(2) from analaytic point of view", by Gelbart and Jacquet.
On Page 226 in Remark (4.13) they mention that the kernel of the local intertwining operator ...

**1**

vote

**1**answer

82 views

### canonical divisors of a resolution of a normal surface singularity

Let $(0\in X)$ be the germ of a normal surface singularity and let $f: Y \to X$ be the minimal resolution.
Questions>
(1) How can I define a map $f_*\mathcal{O}_Y(K_Y)\hookrightarrow ...

**11**

votes

**1**answer

271 views

### Are symplectic methods used in (classical) Economics?

The tl;dr question is this: are economists using coordinate-free formulations in studying theory?
Borrowing from classical mechanics, the framework I have in mind for classical economics--involving ...

**2**

votes

**3**answers

127 views

### If $X$ is compact, is $[X]^2$ compact, too?

Let $(X,\tau)$ be a Hausdorff space. Let $[X]^2 = \big\{\{x,y\}: x,y\in X \land x\neq y\big\}$. For $U,V\in \tau$ with $U\cap V = \emptyset$ we set $[U,V] = \big\{\{x,y\} \in [X]^2: x\in U\land y\in ...

**4**

votes

**1**answer

153 views

### Are genus zero Gromov Witten Invariants on Del-Pezzo surfaces enumerative?

Let $X_k$ be $\mathbb{P}^2$ blown up at $k$ points (where $k$ is $0$ to
$8$). Let $\beta \in H_2(X_k, \mathbb{Z})$ be the homology class given by
$$ \beta := n L + m_1 E_1 + \ldots + m_k E_k $$
...

**-4**

votes

**0**answers

23 views

### log in calculating depreciation rate [on hold]

I can't understand
log160=log2000+10log(1-r);
2.2041=3.3010+10log(1-r);
10log(1-r)=2.2041-3.3010;
10log(1-r)=-1.10969;
...

**3**

votes

**0**answers

122 views

### Where can I find a proof of this result on optimal tessellation of a unit square?

Here is an excerpt from the paper "The Hexagon Theorem" by Donald J.Newman
Does anyone know where I can find a proof of the underlined statement?
Newman states it without a proof, and I could get ...

**5**

votes

**1**answer

156 views

### Map between homotopy groups of O, related to J-homomorphism and K-theory of Z

Let $s \geq 0$ be fixed. The $J$-homomorphism includes $\pi_{8s+1}(SO) = \mathbb Z/2$ in $\pi_{8s+1}^s$, the $(8s+1)$-th stable homotopy group of spheres.
Now regard $\pi_{8s+1}^s = \pi_{8s+1} ...

**1**

vote

**0**answers

37 views

### Examples of non-extremal subfactors

Every subfactor $(N \subset M)$ in this post are supposed to be finite index inclusion of ${\rm II}_1$ factors.
Definition (here p64): Such a subfactor is called extremal if $tr_{N'} = tr_M$ on ...

**1**

vote

**1**answer

91 views

### finite generation of a certain type of subring

Let $k$ be a field, and let $R$ be a finitely generated $k$-algebra. (If it helps, you may assume $R$ is an integral domain.) Let $I$ be an ideal of finite colength. Note that $A:=k+I$ is a subring ...

**0**

votes

**0**answers

23 views

### Which properties determine the uniqueness of the local Artin map?

Any abelian extension of local fields can be realized as the completion of a global abelian extension. So let $L/K$ be abelian, $w/v$ an extension of places. From the global Artin map on ideles we ...

**29**

votes

**1**answer

511 views

### What can topological modular forms do for number theory?

Topological modular forms ($TMF$) have in the recent years made an impact in algebraic topology. Roughly, the spectrum $tmf$ is the (derived) global sections of the sheaf of $E_\infty$ ring spectra ...

**1**

vote

**1**answer

87 views

### Suggestions for dealing with the “timed” balls-into-bins model

Definitions: Let $T$ (for "time") be a random variable $T \sim \text{Exp}(\lambda)$ and $\Delta t$ is a realization (or called an observed value) of $T$. Let $D$ (for "delay") be a random variable $D ...

**-7**

votes

**1**answer

141 views

### IMPA (Brazil) vs Iowa State University (USA) [on hold]

I was recently offered admission to Iowa State for a math PhD.
I thought they were to deny me admission since they had not answer me until now (I spected an answer in March). Since I had not had a ...

**-1**

votes

**0**answers

29 views

### associated prime of a module under a ring homomorphism [on hold]

Let $f: A\rightarrow B$ be a homomorphism of Noetherian rings, and $M$ a $B$-module(not necessarily finitely generated).
Question: Is $^af(Ass_B(M))=Ass_A(M)$?

**0**

votes

**0**answers

28 views

### Prove the isomorphism of categories $Fun(\mathcal{A}\times\mathcal{B},\mathcal{C})\cong Fun(\mathcal{A},Fun(\mathcal{B},\mathcal{C})),$ [migrated]

I'm a computational engineer starting with a course of Introduction to Category Theory, and perhaps is extremely basic what I'm asking but I'm trying to learn how to make proofs in category theory ...

**3**

votes

**2**answers

209 views

### Acyclic complexes for extraordinary cohomology theories

Let $X$ be a CW complex such that for all extraordinary homology theories, if you plug $X$ into them you get the same value as plugging in a point. Must $X$ be contractible?

**0**

votes

**1**answer

77 views

### When can two Cauchy transforms intersect?

Given two polynomials $p$ and $q$ over reals and being guaranteed that both have all roots real I want to know if there is any characterization of the solutions of the equation $\frac{p'}{p} = ...

**3**

votes

**0**answers

88 views

### Hyperplane sections of principal homogeneous spaces

Let $P_i$ denote the $i-th$ vertex in the Dynkin diagramm of an algebraic group. It symbolizes a parabolic subgroup of $G$ corresponding to the other vertices, meaning $G/P_i$ is a smooth, projective, ...

**1**

vote

**1**answer

180 views

### How does the solenoid structure of $\mathbb{A}/\mathbb{Q}$ lift to $PGL(2, \mathbb{A})/ PGL(2, \mathbb{Q})$?

Some papers I am reading talk about an "adelic" object $PGL(2, \mathbb{Q}) \backslash PGL(2, \mathbb{A})$ . This has sparked a lot of confusion since I don't know what such a quotient could mean.
A ...

**5**

votes

**1**answer

73 views

### Penrose tiling substitution is bijective

Let $\mathcal{P}$ a Penrose tiling built by a substitution $\omega$ with two triangles.
It is claimed, for instance, in the article of Anderson and Putnam "Topological invariants for substitution ...

**0**

votes

**0**answers

123 views

### Soft Question: Relationships Between Moduli Space and Objects They Parametrize

Apologies in advance if this question is not suitable for MO. My friend and I were wondering recently what, if any, are the relationships between the geometric properties of a moduli space and the ...

**2**

votes

**0**answers

26 views

### Dual cone of 'positive' Bochner integrable functions

If we consider the space of integrable functions $L^1([0,1];\mathbb{R})$, it can be ordered by the convex cone of positive integrable functions $L^1([0,1];\mathbb{R}_+)$. It is known that the ...

**1**

vote

**0**answers

48 views

### Quantum dimension in SU(N) level k Kac-Moody algebra

The CFT of the SU(N) level k Kac-Moody current algebra has many Kac-Moody primary fields. I wonder if any one has calculated the quantum dimensions of those Kac-Moody primary fields.
I know that, ...

**0**

votes

**0**answers

35 views

### Singularities of the product of a $(\mathbb{C}^*)$-surface with $\mathbb{C}$

Recall that any normal $\mathbb{C}^*$-surface is Cohen-Macaulay
and there exists normal $\mathbb{C}^*$-surfaces whose
singularities are not rational.
Does anyone know an example of a normal ...

**1**

vote

**1**answer

157 views

### Ask the name of a combinatorial theorem

It is a classical theorem. For given integer $n \ge 1$, among ${n\choose{n/2}} = 2^{(1-o(1)n)}$ strings in the cube $\{0, 1\}^n$ with weights $n/2$, i.e., $n/2$ indices are 1, there are at least ...