# All Questions

**6**

votes

**2**answers

664 views

### Publication in proceedings

Why and how publishing a paper in proceedings?
What are the difference with a "classical" journal?
What's the list of the main proceedings in which one can publish?
Do proceedings papers (never, ...

**1**

vote

**0**answers

143 views

### How rigid can a rigid object be in GR?

Consider a cubic lattice of space probes, with rocket motors and lasers to measure distance, and a clock to measure time. As they more from free space to the vicinity of some black hole, they try to ...

**4**

votes

**0**answers

126 views

### Infinite simple p-groups with only trivial irreps in characteristic p

Is there a prime $p$ and an infinite simple $p$-group $G$ such that for any field $K$ of characteristic $p$ the only irreducible $KG$-module, whether finite or infinite dimensional, is trivial (that ...

**1**

vote

**0**answers

104 views

### Characterization of the Riemann curvature tensor

Let $(M^n,g)$ be a Riemannian manifold, $a\in M$ be a fixed point. It it well known that there exists a coordinate system near $a$ (e.g. the normal one) such that
$$g_{ij}(x)=\delta_{ij}+O(|x|^2).$$
...

**2**

votes

**1**answer

78 views

### Relationship of clique, independence, and chromatic numbers

For any graph $G=(V,E)$ let $\bar{G}$ be the complement graph. Is $$\text{inf}\big\{\frac{\omega(G)+\omega(\bar{G})}{\chi(G)} : G \text{ is a finite graph}\big\}$$ known? If not, what lower bounds are ...

**0**

votes

**0**answers

21 views

### Probe permutationally matrix extreme properties-II

Call $S_{r}$, collection of $0/1$ matrices of rank atmost $r$ that increase rank if any $1$ is changed to $0$.
Given $M\in\{0,1\}^{n\times n}$ of rank $r$, what is probability that $M$ could be ...

**1**

vote

**0**answers

79 views

### Strichartz estimates for the wave equation

Strichartz estimates for the wave equation $\Box u=F $ with $u(0)=g_0$ and $\partial_t g(0)=g_1$ can be stated as
$$\Vert u\Vert_{L^q_tL^r_x}+\Vert u\Vert_{C^0_t\dot{H}_x^s}+\Vert\partial_t ...

**1**

vote

**1**answer

181 views

### Zeta functions versus Cramer's conjecture

A mathematics professor today asked me if Cramer's conjecture on prime gaps has anything to do with Riemann Zeta function. I did not know but my guess was somehow Cramer's conjecture captures local ...

**7**

votes

**2**answers

227 views

### Definition of internal field objects

Let $\mathcal{C}$ be a category with finite limits and a strictly initial object $\mathbf{0}$. The final object is denoted by $\mathbf{1}$. I propose the following definition of a field object ...

**3**

votes

**1**answer

168 views

### For a cross section $\sigma\colon G/N\to G$, how is $\sigma(y)^{-1}\sigma(x)^{-1}\sigma(xy)$ called?

Let $G$ be a locally compact group, let $N$ be a closed normal subgroup of $G$, and let $\sigma\colon G/N\to G$ be a cross section. Let us define $\alpha\colon G/N\times G/N \to N$ by the formula
$$
...

**3**

votes

**2**answers

95 views

### regular polyhedra (and polytopes) in hyperbolic geometry, and generalisations

While there exist regular tesselations of the hyperbolic plane with arbitrary regular polygons, there are no new regular polyhedra in hyperbolic (3D) space. This being quite trivial, it is probably ...

**1**

vote

**0**answers

39 views

### Isolated singularities of harmonic mappings

Can a homeomorphic harmonic mapping $f=(u,v,w):\Omega\to \Omega'$ have isolated singular points. Here $\Delta f =0$, and singular point is a point with zero Jacobian. This will extend Lewy theorem for ...

**2**

votes

**0**answers

143 views

### A lower-dimensional algebraic topology problem between homology group and fundamental group

Let
\begin{equation}
A\stackrel{\alpha}{\longrightarrow}B\stackrel{\beta}{\longrightarrow}C\quad\quad (1)
\end{equation}
be a short sequence of abelian groups and homomorphisms. We say that the ...

**11**

votes

**2**answers

1k views

### Do the real numbers “know” that they are countable in a larger model?

(This was first posted to math.stackexchange but had no answers there after several days):
Let ${\mathbb R}$ be the set of real numbers in whatever is your favorite model of $ZFC$. Then (by Levy ...

**0**

votes

**0**answers

13 views

### Whats the difference between math.SE and mathoverflow? [migrated]

i wanted to know that :
Whats the difference between math.SE and mathoverflow ?
Are they of SE community or different ?

**-3**

votes

**0**answers

41 views

### How to solve this using trig idenities [on hold]

(sin(x) + sin(-x))(cos(x) + cos(-x))
I am confused how you get 0 for the answer, can someone explain how my book go to that answer. Like the steps you did.
Thanks :)

**-1**

votes

**0**answers

48 views

### Zeros of a Real Analytic Function [on hold]

Let $f:[0,1] \rightarrow \mathbb{R}$ be a non-zero real analytic function. Consider $Z(f) \subseteq [0,1]$ as the set where $f$ vanishes. What can we say about $Z(f)$? This is (i) finite, (ii) ...

**0**

votes

**0**answers

29 views

### Journals on stochastic approximation/control theory [on hold]

What are some good journals on stochastic approximation/control theory?
Thanks

**2**

votes

**0**answers

61 views

### Uniqueness of solution of elliptic equation with exponential nonlinearity

Consider the following equation
$$\Delta v + p(r)e^v = 0$$ on $\mathbb{R}^n$
where $p(r)$ is a polynomial in $r = |(x_1,..., x_n)|$. I want to understand when equations like these have unique ...

**1**

vote

**1**answer

129 views

### Does the ring of invariants inherit normality?

Let $A$ be a normal ring (in the sense that its localizations at prime ideals are normal domains), and suppose that a finite group $G$ acts on $A$ by ring automorphisms. Form the subring $A^G \subset ...

**3**

votes

**2**answers

235 views

### Etale local fibrations in the Grothendieck ring of varieties

Let $k$ be a field and $K_0(Var_k)$ the Grothendieck ring of varieties over $k$. This is the ring generated by isomorphism classes of varieties over $k$ with multiplication given by
$$
[X \times_k Y] ...

**0**

votes

**0**answers

19 views

### Finding the bound of a mixture model percentile [on hold]

I could do with some help on the following issue. I'm trying to obtain $\alpha$ from:
$\beta = \int_{\alpha}^{\infty} \sum_{i=1}^{n} p_i f_i(x) dx$
I have that:
$0 \leq p_i \leq 1$, $\sum_{i=1}^{n} ...

**2**

votes

**0**answers

62 views

### degenerate points in the moduli space of flat principal $G$-bundle with respect to a linear representation on a complex

Let $(A^\bullet,\partial)$ be a complexe of $\mathbb{C}$-vector spaces. We suppose that this complex is of finite length, and all $A^\bullet$ are finite dimensional. Let $H^\bullet$ be the cohomology ...

**1**

vote

**0**answers

40 views

### Select n vectors from k vectors (in 3D) such that each component of the resultant vector >= each component of a given vector M

this was left unanswered for 1 week on MStackExchange, so I thought MOverflow would be more appropriate. Thanks :)
Let $R = (R_x, R_y, R_z)$ be the resultant vector of the n vectors and $M = (M_x, ...

**0**

votes

**1**answer

85 views

### generalization of highest weight theorem for semisimple lie algebras

Let $\mathfrak g$ be a real semisimple Lie algebra (without compact factors) with Iwasawa decomposition
$\mathfrak g=\mathfrak k\oplus \mathfrak a\oplus \mathfrak u$.
Let $\mathfrak p$ be a
...

**6**

votes

**0**answers

62 views

### Vanishing of Dolbeault cohomologies and Steinness

That Stein manifolds have all $(p,q), p \geq 0, q \geq 1$ vanishing Dolbeault cohomology groups is more or less standard. I am a little bit confused about the reverse implication: whether the ...

**1**

vote

**2**answers

83 views

### Ascending chain condition on radical ideals

There is a basic theorem in the geometry of schemes saying that the Spec of a Noetherian ring is a Noetherian topological space. It can be formulated as the ACC condition implies the ACCR condition ...

**5**

votes

**0**answers

156 views

### Is there a citeable reference for star-shaped open subsets of R^n being diffeomorphic to R^n?

A folk theorem says that star-shaped open subsets of R^n are diffeomorphic to R^n.
Is there a citeable reference for this result?
For the sake of being definite, let's say that
“citeable” means ...

**1**

vote

**1**answer

50 views

### Division methods for divergent continued fractions

I hadn't even noticed before entering the subject above the parellel with the title of an earlier question posted here titled Summation methods for divergent series. And it's just mutatis mutandis as ...

**4**

votes

**1**answer

195 views

### Frequency of a representation of SO(3)

When generalizing the basic tenets of Fourier Theory to the symmetric group $S_n$, we can define a notion of the frequency of a basis function (i.e. an irreducible representation of $S_n$). In ...

**5**

votes

**3**answers

230 views

### A balls and urns model for a hashing problem

Fix $N \in \mathbb{N}$. Suppose we throw $N$ numbered balls into $N$ numbered urns, so that for each $b \in \{1,\ldots,N\}$, ball $b$ lands in urn $j$ with equal probability $1/N$. Choose a number $c ...

**4**

votes

**0**answers

64 views

### Approximation of convex body by polytopes

In a recent survey paper, Approximation of convex sets by polytopes, Bronstein claims that under Hausdorff distance $\rho_H$, for every convex body $U$,
$$\rho_H(U,\mathcal{P}_n)\leq c(U) ...

**1**

vote

**0**answers

23 views

### Can we give efficiently the solution of a bilinear system of equations over a finite field?

Consider a finite field $F$ and suppose we have a system of equations
$$h_1(\alpha,\beta)=0,h_2(\alpha,\beta)=0,...,h_t(\alpha,\beta)=0$$
where $\alpha=(\alpha_1,...,\alpha_s)$ and ...

**4**

votes

**1**answer

182 views

### Decomposing $(\mathbb C^n)^{\otimes m}$ as a representation of $S_n\times S_m$

$V=\mathbb C^n$ is a $\mathbb CS_n$-module, where $S_n$ is the symmetric group of degree $n$, via the representation sending a permutation to the corresponding permutation matrix. The tensor power ...

**0**

votes

**1**answer

114 views

### $u_n$ bounded in $L^\infty(0,T;H) \cap L^2(0,T;V)$ implies $u_n \to u$ strongly in $L^2(0,T;H)$?

Let $V \subset H$ be a dense and compact embedding. Let $$\lVert u_n\rVert_{L^\infty(0,T;H)} + \lVert u_n \rVert_{L^2(0,T;V)} < C$$ where $C$ is independent of $n$. It follows that eg. $u_n ...

**3**

votes

**1**answer

137 views

### The Jordan Plane and Enveloping Algebras

Let $k$ denote a field of characteristic $0$ (assume algebraically closed for convenience). Define $J=k\langle x,y|[x,y]=y^{2}\rangle$. This noncommutative algebra (which can be viewed as a derivation ...

**1**

vote

**0**answers

119 views

### Density of numbers whose prime factors all come from a fixed congruence class

Let $q$ be a positive integer greater than one, and let $a$ be an integer such that $\gcd(a,q) = 1$. Define
$$D(a,q) = \{n \in \mathbb{N} : p | n \Rightarrow p \equiv a \pmod{q} \}.$$
Do we know the ...

**-4**

votes

**0**answers

58 views

### The Birthday Paradox [on hold]

I was looking at the birthday paradox, and the many solutions. One of them that came up was the Poisson Distribution. The website I was looking at detailed the process to solve ...

**0**

votes

**0**answers

36 views

### Property of summations [on hold]

Suppose to have the following identity:
$$
\sum_{i=i_0}^{i_1}\sum_{j=j_0}^{j_1} f(i,j) = \sum_{i=i_0}^{i_1}\sum_{j=j_0}^{j_1} f(i,j)g(i,j),
$$
for 'good' indexes $i,j$ and some functions $f,g$.
What ...

**1**

vote

**2**answers

142 views

### Bertini theorem for big divisors and klt pairs

Let $X$ be a smooth projective variety and let $D$ be a big $\mathbb Q$-divisor on $X$. Assume that for $m$ large $|mD|$ has no fixed components. Is there a $\mathbb Q$-divisor $D'\equiv D$ so that ...

**8**

votes

**0**answers

134 views

### History of preservation theorems in forcing theory

For my honours thesis, I am studying a general preservation theorem using a framework provided by Shelah. I am mainly concerned about revised countable support iteration of $\dot{S}$-semiproper ...

**2**

votes

**1**answer

113 views

### Coupon Collector Problem for Non-Uniform Coupons: Bound on the number of missed Coupons

Suppose $\mathcal B=\{1,2,..,b\}$ is the set of all possible coupons, with $\mathbf p = ( p_1,p_2,...,p_b)$ assigning the probability of occurrence for all coupons in $\mathcal B$.
The "traditional ...

**2**

votes

**1**answer

80 views

### Coarsely trivial Borel cross section for $G\to G/N$

Let $G$ be a locally compact group, and let $N$ be a closed, normal subgroup, and let $\pi\colon G\to G/N$ be the quotient homomorphism. It is known that there exists a Borel cross section, i.e., a ...

**0**

votes

**1**answer

67 views

### Are Zariski connected and closed semisimple subgroups of semisimple and simply connected algebraic groups again simply connected? [on hold]

Let $G$ be a semisimple and simply connected linear algebraic group over $\mathbb{C}$.
Let $H$ be a connected, Zariski closed and semisimple linear algebraic $\mathbb{Q}$-subgroup of $G$.
Is $H$ a ...

**4**

votes

**1**answer

91 views

### Infinite dimensional Cauchy-Lipschitz theorem [duplicate]

From the answers to Mathoverflow Question "Continuity in Banach space for non-linear maps", it is possible to infer that the assumption of the Cauchy-Lipschitz theorem for the autonomous equation
$$
...

**3**

votes

**1**answer

70 views

### Probe permutationally matrix extreme properties

Suppose given $M\in\{0,1\}^{n\times n}$ of rank $r$.
Assume that changing even a single $1$ to $0$ in $M$ raises rank. Does it follow that $M$ is permutationally equivalent to a block diagonal ...

**2**

votes

**1**answer

340 views

### Why are 1 and -1 eigenvalues of this matrix?

This is a subject I've been working on for a very long time now, but still did not manage to fully understand the interesting properties of this matrix $\mathbf{A}$.
First, let's define two matrices:
...

**2**

votes

**0**answers

53 views

### Potentiality classes and Borel reductions

In a 1998 paper by Hjorth, Kechris, and Louveau, there was a definition given of a "potentiality class." That is, given an invariant equivalence relation $E$ on a standard Borel space $X$, we say $E$ ...

**8**

votes

**0**answers

184 views

### Neighborly family of coins

Here is a puzzle:
Find 5 identical coins. Can you arrange them so that every coin is touching every other coin?
The solution is here. The hint is: use the third dimension.
My questions are ...

**0**

votes

**0**answers

110 views

### Moving lemma for algebraic curves

Let $X$ be a smooth irreducible projective curve contained in $\mathbb{P}^3$ and $Y$ be another reduced but not necessarily irreducible curve in $\mathbb{P}^3$. Denote by $P$ the Hilbert polynomial of ...