-1
votes
0answers
32 views

Uniform space structures of different metric on the same space

I started learning about uniform spaces and I got confused with the uniform structures and its relation to metric spaces. I am not sure when different metric structures on the same space produce ...
1
vote
0answers
44 views

Schubert Calculus for Quaternion-Kähler Manifolds

The cohomology ring of general Grassmannians have very nice presentations in terms of Young diagram and the rules of Littlewood-Richardson. This is called {\em Schubert calculus}. The Grassmannian of ...
0
votes
0answers
29 views

Is every $C^1$-domain which is homeomorphic to the unit ball in $\mathbb{R}^d$ Lipschitz equivalent to the unit ball?

Suppose we have a domain $\Omega\subset \mathbb{R}^n$ which is homeomorrphic to the unit ball $B(0,1)\subset \mathbb{R}^n$ and such that $\partial \Omega$ is of class $C^1$ (technically, this means ...
-4
votes
0answers
37 views

simple calculator. [on hold]

i have this gui code on calculator. i don't know how to appear the arithmetic operation on my text field. can some one help me.tnx import java.awt.; import java.awt.event.; import javax.swing.; ...
1
vote
1answer
95 views

Are monoids with zero and partial homomorphisms related?

Context: Let $\Sigma=\{U,C,A,G\}$ and $L\subset\Sigma^*$, i.e. $L$ is a language over the alphabet $\Sigma$. Let $\Sigma'=\{0,1\}$ and define a homomorphism $f:\Sigma^*\to\Sigma'^*$ by extending $U ...
3
votes
1answer
185 views

Earliest source for a Lie algebra construction

I am looking for the earliest reference to the fact that any associative algebra becomes a Lie algebra with bracket $AXB-BXA$, where $X$ is a fixed element of the algebra. This is observed in the ...
0
votes
0answers
159 views

I want to know if the below sentence is true and why? [on hold]

I want to know if the below sentence is true and why? Let $G$ be an insoluble finite group then there exists $π\subset π(G)$ such that if $K=O_{\pi}(G)$ and $\bar{G}=G/K$ it follows that $M\leq ...
-2
votes
0answers
20 views

Circumcenter of Tetrahedron (in 4D) [migrated]

I am trying to calculate the circumcenter of a tetrahedron in 4 dimensional space. Basically what I am looking for is the center of the smallest sphere which passes through all 4 vertices of the ...
0
votes
0answers
25 views

upper bound and a lower bound on the number of points that are uniformly distributed on a surface [migrated]

Can I calculate an upper bound and a lower bound (or max or min) on the number of points that are uniformly distributed on a surface, knowing the area of the surface ? More precisely, I have a sector ...
2
votes
0answers
53 views

Eigenvectors as continuous functions of matrix - diagonal perturbations

The general question has been treated here, and the response was negative. My question is about more particular perturbations. The counterexamples given in the previous question have variations not ...
0
votes
0answers
63 views

Lifting points of étale group scheme

Consider the following setting: let $(R,\mathfrak{m})$ be a Noetherian complete discrete valuation ring (with maximal ideal $\mathfrak{m}$) and let $K$ be its field of fractions. Now take $L$ be the ...
5
votes
2answers
71 views

Accuracy of the truncated Hausdorff moment problem

For a sequence of real numbers $s = (s_i)_{i \in n}$ let $M_s$ be the collection of functions $f:[0,1] \to [0,1]$ such that $$(\forall i \leq n) \int_0^1 x^i f(x) dx = s_i$$ In other words, $M_s$ ...
5
votes
1answer
226 views

Simply connected CW-complex with only finitely many nontrivial homotopy and homology groups

Let $X$ be a simply connected CW-complex such that all but finitely many of its homotopy groups and its homology groups (with $\mathbb Z$ coefficients) are 0. Is $X$ then necessarily contractible? I ...
0
votes
0answers
69 views

a construction on Stiefel manifolds

Are there any references concerning the following space $V(k,N,X)$ and $U(k,N,X)$? And the cohomology of these spaces? Thanks.
1
vote
1answer
49 views

Algorithm to generate a (pseudo-) random high-dimensional function

I don't mean a function that generates random numbers, but an algorithm to generate a random function. "High dimension" means the function is multi-variable, e.g. a 100-dim function has 100 different ...
7
votes
1answer
159 views

Is every proper regular relative algebraic space curve over a Dedekind domain projective?

This question is in some sense a follow up to a related question Is a normal proper relative curve over a DVR projective? Let $R$ be a Dedekind domain, let $S := \mathrm{Spec}(R)$, and let $X ...
11
votes
2answers
271 views

The most number of points that realize only $k$ distinct distances

For $k \ge 1$, let $f_d(k)$ be the largest possible number of points $p_i$ in $\mathbb{R}^d$ that determine at most $k$ distinct (Euclidean) distances, $\|p_i-p_j\|$. Example. For points in the plane ...
1
vote
0answers
91 views

Spherical cap is the only compact constant mean curvature surface bounded by a circle

I would like to see that the only compact rotationally invariant constant mean curvature surfaces with boundary a planar circle, are either a planar disk or a spherical cap. This is stated in the ...
35
votes
3answers
1k views

On sentences true in all finite groups

Let $w$ be a group word with two variables $x$ and $y$. Is the sentence $(\forall x)(\exists y)w=1$ true in every group if it is true in every finite group? The same question about the sentence ...
0
votes
0answers
31 views

Growth of average first derivative of orthogonal polynomials

Let $L_k(t)$ be the Legendre polynomials normalized so that $$\int_{-1}^1 L_k(t)^2\,\frac{1}{2}\,dt = 1.$$ With a few identities (http://en.wikipedia.org/wiki/Legendre_polynomials), one can show that ...
0
votes
0answers
33 views

Does anyone know how to describe the zero set of the Jacobian of injective harmonic maps in space?

For example consider the following question: Let $\mathbb{B}^m$ be hyperbolic space and let $f : \mathbb{B}^m \rightarrow \mathbb{B}^m$ be harmonic $K$-qc map. Whether $f$ has critical points on ...
-4
votes
0answers
78 views

Is it possible to compare Sobolev space and Polish space? [on hold]

This question was asked in math.stackexchange.com http://math.stackexchange.com/questions/1274873/is-it-possible-to-compare-sobolev-space-and-polish-space I did not get any comment or reply so I am ...
-3
votes
0answers
49 views

What do the equations of straight line graphs have in common? [on hold]

What do the equations representing straight line graphs have in common?
-2
votes
0answers
139 views

Is this set possibly compact?

Given $\epsilon\in(0,1)$, suppose we have collection $\mathscr{C}(\epsilon)$ of multilinear polynomials in $\Bbb R[x_1,\dots,x_n]$ that on $\{0,1\}^n$ is in range $[-\epsilon,\epsilon]$ on $S_0$ while ...
2
votes
0answers
54 views

What are “minimal lines” in complex geometry?

Schwarz reflection across a real analytic arc $C$ in $\mathbb{R}^2$ is usually defined analytically. Thinking of the arc as the image of an interval in $\mathbb{R}$ under an invertible holomorphic map ...
2
votes
0answers
77 views

When an envelope of a family of lines exists?

Given a family of lines $(\gamma_t): a(t)x+b(t)y+c(t)=0,\ t\in I$ (interval in $\mathbb{R}$), where $ a,b,c:I\to\mathbb{R},\ a^2(t)+b^2(t)\neq 0,\ \forall t\in I$ , what conditions should we impose ...
-4
votes
0answers
31 views

Large Matrix problem [on hold]

I have been searching the internet for a large matrix problem but didn't find any problem. I am searching for a problem like for example Kirchhoff's Rules Problems where you have I1, I2...etc ...
1
vote
0answers
91 views

Level-Lowering in Weight 2

Let $N$ and $p$ be relatively prime integers with $p$ a prime. Suppose $f$ is a weight $k=2$ (normalized, cuspidal, etc) newform of level $\Gamma_1(N) \cap \Gamma_0(p)$. I seem to recall the existence ...
0
votes
1answer
88 views

Finding Riemannian metric for this geodesic

In a $d$-dimensional manifold, given a geodesic equation $\gamma^i(t)=a^i\phi(tb^i),i\in 1\ldots d$, where $\phi:\mathbb{R}\rightarrow\mathbb{R}^+$ is an increasing function, $a^i>0,b^i$ are ...
3
votes
2answers
296 views

How to show whether a given knot and its mirror image are the same or not?

The title says it all: How can I show that a knot $K$ is distinct from its mirror image? May be I have to try different knot invariants. Not sure, I am new in this area.
-3
votes
0answers
173 views

Could RH be a consequence of some kind of central limit theorem? [on hold]

In the last issue of "Pour la Science" (French edition of Scientific American), there is an article about random geometry on the sphere where the authors invoke the central limit theorem to explain ...
-5
votes
0answers
29 views

Scientific notation help please [on hold]

2.71 × 10^8 correct scientific formation please convert I've tried looking online but nothing really i need it correct scientific notation form
-1
votes
0answers
66 views
0
votes
0answers
37 views

Solving nonlinear inequality that involves norm2 operator

I have an equation of the form $$ \newcommand{\norm}[1]{\left\lVert#1\right\rVert} \norm{\mathbf{Z} \left[ \sum_{n = 0}^{N - 1} (-1)^n \psi^n \mathbf{C}^n \right] \mathbf{q} }^2 \leq |p|^2, $$ where ...
3
votes
0answers
89 views

Is the braid group with $n$ strings $\mathcal{B}_n$ a lattice in a connected semi-simple Lie group?

Is the braid group with $n$ strings $\mathcal{B}_n$ known to be a lattice in a connected semi-simple Lie group ? (for $n$, say, bigger than $3$) Or is it known that it cannot be such a lattice ?
0
votes
1answer
59 views

Regular curve given implicitly

Let $F:D\subseteq\mathbb{R}^2\to\mathbb{R}$, $D$ open and connected set, be a $C^1 (D)$ application. What are the minimum requirements for $F$ such that the solutions of the equation $F(x,y)=0$ are ...
4
votes
2answers
177 views

Secant varieties of curves in $\mathbb{P}^4$

My question is motivated by the following simple observations. By a standard dimensions count in $\mathbb{P}^4$ there should not exist neither an hypersurface of degree $3$ with multiplicity $2$ in ...
2
votes
0answers
85 views

The most general set-up for tensors and connections

This is maybe a too vague question, so I will try to be as specific as possible. My question is: What is the most general set-up where one can define tensors and connections? For example, we know ...
3
votes
2answers
178 views

Do discrete valuation rings correspond to local rings of points in fibre?

Given projective curves $C$ and $C'$ and a surjective morphism $\varphi\colon C\to C'$, such that $Q\in C'$ is a smooth point and its fibre $\varphi^{-1}(Q)$ consists of smooth points. Then ...
-5
votes
0answers
428 views

What is the single and double derivative of following equation? [on hold]

d/dt(e^ (-0.06 pi t))(sin(2t-pi)) using product rule fine the double and single derivative.please help me to solve this?
-1
votes
1answer
202 views

A simple group that its order divide order of an alternating group

Let $G$ be a simple group such that 1) $|G|\mid|\mathrm{Alt}_{p}|$ 2) $p\mid | G|$, and $p>13$ is prime. 3) $G$ hasn't any elements of order $rp$ for every prime number $r$. My question: ...
8
votes
1answer
471 views

Pros and cons of Stacks Project as a reference compared with EGA/SGA

I would like to know pros and cons of Stacks Project compared with EGA and SGA and whether it serves as a nice alternative to them. Since I haven't read both of these texts, my attempt to compare the ...
8
votes
1answer
204 views

Non-orientable $6$-manifold with $H_4(M)=\mathbb{Z}/2$?

Does there exist a smooth, closed, non-orientable $6$-manifold $M$ such that $H_4(M;\mathbb{Z})=\mathbb{Z}/2$?
2
votes
0answers
74 views

A subgroup of corank 1 in a free group contains a primitive element?

Let $F$ be the free group on $\{x_i\}_{i=1}^\infty$, and let $H \leq F$ be a subgroup with $\langle H \cup \{x_1\} \rangle = F$. Must there be a free basis $B$ of $F$ for which $B \cap H \neq ...
3
votes
1answer
128 views

Which automorphisms on $H_{1}(M^{3})$ are induced by homotopy equivalences?

Let $M^{3}$ be a closed orientable 3-manifold, and $\phi:H_{1}(M;\mathbb{Z})\to H_{1}(M;\mathbb{Z})$ be an automorphism of abelian groups. My question is: Is there any characterization of $\phi$ ...
2
votes
0answers
12 views

Is there some kind of lower bound for estimation error of the estimation of (near) low-rank matrices in high-dimension?

I'm reading S.Negahban and M.J.Wainright's paper, ESTIMATION OF (NEAR) LOW-RANK MATRICES WITH NOISE AND HIGH-DIMENSIONAL SCALING. In the paper, they give a upper bound for estimation error of the ...
0
votes
0answers
28 views

Painleve test of a new PDE hierarchies

This PDE hierarchies is : $$u_t=\sum_{i=0}^{N}c_iu^iu_x-\frac{1}{2}\sum_{i=0}^N(c_iu^i)_{xxx}$$ so far, I have proved that this equation hierarchies has Resonaces at:$$j=2N+2,4N+2$$,according to ...
2
votes
0answers
61 views

A different Lie algebra structure on $\chi^{\infty}(\mathbb{R}^{2})$

In this question $\chi^{\infty}(\mathbb{R}^{2})$ or $\chi^{\infty}(S^{2})$ is the space of all smooth vector fields on the plane or sphere. A limit cycle for a vector field $X$ is an isolated closed ...
2
votes
1answer
80 views

Conditions for a set being closed under taking complement of a ball twice

Given a subset $S$ of a finite metric space $F$ with a distance function $d(,)$ and a number $\delta > 0$ let $N_\delta(S) = \{x \in F| d(x,S)\ge \delta\}$. Is there a characterization of ...
2
votes
1answer
140 views

A question on the Frechet derivative

Suppose the derivative of a functional is given by \begin{equation*} \int_{\Omega}(\vec{v}.\nabla u)|\nabla u|^{p-2} \phi=\int_{\Omega}\nabla.(u\vec{v})|\nabla u|^{p-2} \phi,~\phi\in ...

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