**-1**

votes

**0**answers

42 views

### Multisets and set cardinality [on hold]

Consider $0<\lambda<1$, and let $A$ be a multiset of positive integers. Let $A_n=\{a\in A: a\leq n\}$. Assume that for every $n\in\mathbb{N}$, the set $A_n$ contains at most $n\lambda$ numbers. ...

**0**

votes

**1**answer

131 views

### about the horizontal lift in a principal bundle [on hold]

I'm currently studying Fibre Bundle by Nakahara's book, and I'm a bit confused about the following:
Imagine we have a Principal Bundle $P(M,G)$ with open chart {$U_i$} and a local section ...

**0**

votes

**0**answers

67 views

### Proving a functional inequality [on hold]

Consider two monotonically decreasing functions $f_0(x)$ and $f_1(x)$ for which the following holds:
\begin{equation}
1-t\leq f_0(t)\leq f_1(t)\leq1.
\end{equation}
Let $n,m\in\mathbb{N}$ and $m\leq ...

**3**

votes

**1**answer

133 views

### When can you canonically extend an ultrafilter after forcing?

Suppose that $V$ is a model of $\sf ZFC$, and fix some regular $\kappa$, say $\omega_1$ for practical purposes.
Let $\cal U$ be an ultrafilter on $\omega_1$ in $V$ which is non-principal and even ...

**3**

votes

**0**answers

84 views

### Obtaining the metric from the mixed Ricci tensor $R^i{}_j$

In chapter 5 of the book "Einstein Manifolds", Arthur Besse discusses the possibility to find the metric $g$ when knowing the Ricci curvature tensor $Ric(g)$ ($=R_{ij}$).
But what do we know about ...

**1**

vote

**1**answer

101 views

### Linear forms that avoid numbers with lot of factors

Is following true?
For every given $c>0$ there is an $n_c>0$ such that for every $n>n_c$ there are integers $n<a,b<2n$ such that there are two positive integers $\frac{n}{2(\log ...

**1**

vote

**0**answers

68 views

### Has every Lusin vector space a stronger Polish vector space topology?

Let $X$ be a topological vector space or even a locally convex space such that its (vector space) topology is Lusin, i.e. there is some stronger Polish topology. Does there also exist a stronger ...

**-2**

votes

**0**answers

76 views

### exponential tail bound for conditional probability [on hold]

I am aware of exponential tail probabilities for unconditional probability (for ex: Normal). Are there any similar results available for conditional probability (w.r.t to a sigma field) in literature ...

**0**

votes

**0**answers

132 views

### Time Hierarchy Theorem and P vs NP

One obvious strategy for proving P not equal to NP would be to show that there is some problem in NP which is hard for a time class strictly containing P (the origin of this question is the recent ...

**-7**

votes

**0**answers

81 views

### Show that $G$ a group? [on hold]

Suppose that $G$ is a semigroup , and for every $a$ in $G$ there is unique $a^*$ in $G$ that
$aa^*a=a$
Prove that $G$ is a group.

**-4**

votes

**0**answers

28 views

### Curve with Matlab [on hold]

I have posted this question:
http://math.stackexchange.com/questions/1547373/curve-with-matlab
but I have not answers. Can you help me?

**0**

votes

**1**answer

69 views

### Simple question about notation: formulas starting with a quantification [on hold]

Let $C\subset\mathbb{R}$ and suppose that $f:C\to2^C$ is a point to set map. Suppose that $f(x)$ is a set containing only negative real numbers for every $x\in C$. Are there any problems with the ...

**3**

votes

**0**answers

37 views

### Traces of fractional Sobolev spaces $W^{s,p}$ with $0<s<1/p$

I've stumbled upon a problem involving the trace of a function in a fractional Sobolev space of the form $W^{s,2}(H)$, where $H$ is a half-plane in $\mathbb{R}^2$. Would it be possible to define a ...

**1**

vote

**0**answers

219 views

### Hypothesis test beyond simple hypotheses (mathematical statistics)

In mathematical statistics, the following problem (simple hypothesis test) is considered: given a data sample, test the hypothesis $H_0$ stating that all sampled values are values of a random variable ...

**3**

votes

**0**answers

92 views

### Wreath product of an abelian group with a nilpotent group

By work of Coulbois, the wreath product of two finitely generated free abelian group is $LERF$; i.e, every finitely generated group of this wreath product is closed in the profinite topology.
Is there ...

**7**

votes

**1**answer

119 views

### Equalizing Geometric means of Graph Cycles

Consider a strongly connected directed graph $G$. I have been stuck on the following question: can you assign real numbers in $[0,1]$ to each edge of $G$ so that the geometric mean of all cycles are ...

**6**

votes

**1**answer

274 views

### P.G.Goerss, J.F.Jardine, “Simplicial Homotopy Theory” prerequisites

I know that such questions may be better suited for math.stackexchange, but I believe that that the topic of simplicial homotopy theory is advanced enough for mathoverflow.
Besides, I know that there ...

**7**

votes

**2**answers

585 views

### A new result on the Diophantine equation $x^3 + y^3 +z^3 = 3$ [on hold]

The above Diophantine equation is unknown to have any further integer solutions other than $(x, y, z) = (1, 1, 1)$ and $(4, 4, -5)$.
I am a prospective undergraduate mathematics student in Zimbabwe ...

**2**

votes

**0**answers

126 views

### Was “arithmetical translation” (coding in the Goedel sense) ever a part of Hilbert's Program?

Was "arithmetical translation" (that is, coding in the Goedel sense) ever a part of Hilbert's Program? I ask this question for several reasons:
i) it gives the numerals |, ||, |||,.... an ersatz ...

**-1**

votes

**1**answer

35 views

### Convex Optimization in an Ellipsoid

Suppose we want to minimize a linear objective inside an ellipsoid that is,
$\min _x l^Tx$
such that $(x - \mu)^TA(x - \mu) \leq \beta ^2$.
Here, A is PSD and $\mu$ is a fixed vector. Can this be ...

**0**

votes

**0**answers

46 views

### Solution of the system of differential equations [on hold]

Consider that we are working in the polynomial ring $\mathbb{C}[x]$.
Suppose we have the following system of linear differential equations:
$$\left\{\begin{matrix}
L_1(y)=f_1\\
L_2(y)=f_2
...

**1**

vote

**0**answers

24 views

### How does a permutation $P$ affect the singular value $\sigma_{\text{max}}(Q^\top P^\top Q)$ for orthogonal $Q$?

Let $q_i$ for $i=1,\ldots,m$ be the columns of the matrix $Q\in\mathbb{R}^{n\times m}$, $n>m$, which are pairwise orthonormal ( i.e.
$q_i^\top q_j = \begin{cases} 1 & \text{if}\quad i=j \\ 0 ...

**7**

votes

**2**answers

166 views

### What characterizations of relative information are known?

Given two probability distributions $p,q$ on a finite set $X$, the quantity variously known as relative information, relative entropy, information gain or Kullback–Leibler divergence is defined ...

**11**

votes

**0**answers

289 views

### If $k$ is an algebraically closed field of any characteristic, then the fundamental group of $A$ is abelian

This is a followup to my earlier question, see here. I reproduce it as follows.
Let $A$ be an abelian variety over a field $k$ of characteristic $0$. How do I prove, without using transcendental ...

**14**

votes

**1**answer

316 views

### Okounkov-Vershik approach to representation theory of $S_n$

This is a rather soft question. I was wondering if someone could explain on a fundamental and intuitive level, what the Okounkov-Vershik approach to representation theory of $S_n$ is all about. It's ...

**0**

votes

**1**answer

46 views

### Maximal chromatic number with a fixed number of edges

Given a graph $G$ with $m$ edges, what is the maximum chromatic number $\chi(G)$ that the graph can have?
My guess is that $\chi(G) \leq r(m)$ where $r(m) := \max\{k\in \mathbb{N}:
\frac{k(k-1)}{2} ...

**3**

votes

**0**answers

109 views

### Definition of a normed ring

A normed ring "should" be a monoid object in the monoidal category of normed abelian groups. There are (at least) two choices of morphisms of normed groups, namely bounded or short homomorphisms, ...

**0**

votes

**0**answers

59 views

### Advanced use of commutation matrices [on hold]

I am aware of matrix operators vec and kronecker product, commutation matrices and various related identities like stated in ...

**0**

votes

**0**answers

29 views

### Compact factors of Lie groups; possibly varying definitions [migrated]

Let $G$ be a real connected semisimple Lie group. Are the following equivalent?:
(1) $G$ has no proper cocompact Normal subgroups.
(2) $G$ has no proper cocompact connected Normal subgroups.
In ...

**-4**

votes

**1**answer

165 views

### The difference between Hilbert Scheme and Chow Scheme

I am confused by Hilbert Scheme and Chow Scheme. Whenever you have a point in hilbert scheme, take its fiber in the universal family and take its fumdamental class, we get a point in Chow Scheme; and ...

**5**

votes

**1**answer

124 views

### Strongly real elements of odd order in sporadic finite simple groups

Recall that an element of a finite group is said to be real if it is conjugate to its inverse, and strongly real if the conjugating element can be chosen to be an involution.
Question: Is it true ...

**1**

vote

**1**answer

150 views

### Jensen formula in $\mathbb{C}^n$?

Let $f:\mathbb{C}\to\mathbb{C}$ be an entire function with zero set $X\subset \mathbb{C}$. Jensen's formula reads
$$
\log(|f(0)|)+\int_0^R\frac{|X\cap B_t(0)|}{t}dt = ...

**1**

vote

**1**answer

82 views

### Tight binomial left tail bound

Let $X \sim \text{Bin}(n,p)$. Wikipedia claims
$$\mathbf P[X \leq (p-\epsilon)n ] \leq e^{ - 2 \epsilon^2 n}.$$
This follows from Hoeffding's inequality ...

**-1**

votes

**0**answers

33 views

### conformal deformation with fixed boundaries

For a flat plane with certain boundary, e.g., a rectangular patch, is it possible to conformally displace or deform such patch to a curved bump with exact same boundary? In this thesis, Dr. Keenan ...

**2**

votes

**1**answer

72 views

### F-points of product of closed subgroups vs. product of F-points, F a local field, reference?

Let $F$ be a finite extension of $\mathbb Q_p$, where p is an odd prime. Let $G$ be a connected reductive group defined over $F$. Let $M, H$ be closed $F$-subgroups of $G$ (in particular, I'm ...

**63**

votes

**28**answers

9k views

### What are some very important papers published in non-top journals?

There has already been a question about important papers that were initially rejected. Many of the answers were very interesting. The question is here.
My concern in this question is slightly ...

**6**

votes

**0**answers

249 views

+100

### “The” natural double complex associated to a principal $G$-bundle?

Let $\pi: P \to M$ be a principal $G$-bundle. We have the associated adjoint bundle $ad(P)= P \times_{ad} \mathfrak g$ whose sections correspond to infinitesimal guage trasformations.
Consider the ...

**5**

votes

**0**answers

162 views

### all subsets borel

Assume Martin's axiom plus $\neg CH$. It is well known, via almost disjoint forcing, that every set of reals of size less than continuum is an example of a metric space whose subsets are all ...

**1**

vote

**0**answers

84 views

### Algebraic independence criterion

Is there any criterion for checking algebraic independence of a set of polynomials in $n$ variables in terms of the leading monomials with respect to some monomial order ? The Jacobian criterion is ...

**3**

votes

**0**answers

116 views

### Integrations of Ricci curvature of the Weil-Petersson metric on the moduli space of varieties of general type is a rational numbers?

It is known that the integrations of Ricci curvature of the Weil-Petersson metric on the moduli space of Calabi-Yau varieties is a rational numbers
My question is on moduli space of varieties of ...

**0**

votes

**0**answers

104 views

### Is the positive existential theory undecidable?

Could you tell if the positive existential theory of $\mathbb{C}[e^{\mu x} \mid \mu \in \mathbb{C}]$ is undecidable in the language $\{+, \cdot , \frac{d}{dx} , 0, 1, e^x\}$ ?
How can we prove the ...

**1**

vote

**0**answers

51 views

### Shape-related vector fields

Assume that $M$ is a surface in $\mathbb{R}^{3}$. We denote its shape operator by $S$. A vector field $X$ is shape related to $Y$ if $S(X)=Y$.
(of course it is not an equivalent relation).
...

**3**

votes

**1**answer

256 views

### K theory long exact sequence

(1) Suppose that $Z\subset X$ is a closed embedding, $U = X\setminus Z$ is the complement. If relevant, suppose that both $X, Z$ are smooth and even (if relevant) that the normal bundle of $Z\subset ...

**17**

votes

**3**answers

806 views

### Is there any pattern to the continued fraction of $\sqrt[3]{2}$?

Is there any pattern to the continued fraction of $\sqrt[3]{2}$ ? Wolfram Alpha returns for cube root of 2:
$\sqrt[3]{2}=$ [1; 3, 1, 5, 1, 1, 4, 1, 1, 8, 1, 14, 1, 10, 2, 1, 4, 12, 2, 3, 2, 1, 3, ...

**7**

votes

**2**answers

192 views

### $p$-torsion of an abelian variety of $p$-rank $0$

Let $k$ be an algebraically closed field of characteristic $p > 0$ and let $A$ be an abelian variety over $k$ such that $A[p](k) = 0$, i.e., such that $A$ has $p$-rank $0$. If I am not mistaken, ...

**10**

votes

**0**answers

449 views

### Quaternions: ellipse effect

I would be interested in an explanation of the "six ellipse effect" produced by the pseudocode below (I also wonder how close are these to being actual ellipses). Note the code is somewhat similar to ...

**1**

vote

**1**answer

77 views

### Uniqueness of $\partial_t u -u\Delta u=0$ with $u(0,\cdot)=1$

Is there anything known about uniqueness of classical solutions to
$$
\partial_t u -u\Delta u=0\quad u(0,\cdot)=1
$$
on smooth domains $[0,T]\times D$ without boundary conditions? I know that ...

**2**

votes

**1**answer

61 views

### Complexity of Deciding Feasibility of a system of linear inequalities over restricted variables

I am working out an interesting problem and would like some help with this particular sub problem:
Suppose we have a matrix $ M =\left\lbrace a_{ij}\right\rbrace $ of size $n\times m$ where $ ...

**6**

votes

**0**answers

99 views

### Improving Baumgartner's result?

Q1: Is it consistent with the failure of CH to have an $\aleph_1$-dense subset $A \subseteq \mathbb{R}$ such that for every $X \subseteq \mathbb{R}$ of size $\aleph_1$, there is a $C^{\infty}$ map $F: ...

**-1**

votes

**0**answers

38 views

### Alternative Geometries [migrated]

In our world, the distance between two points (in 2d) is defined as $\sqrt{(\Delta x)^2 + (\Delta y)^2}$. Suppose that in an alternative geometry, it was defined as $\sqrt[p]{|\Delta x|^p + |\Delta ...