# All Questions

**-1**

votes

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**2**answers

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

**1**answer

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

**0**answers

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

**1**answer

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

**1**answer

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

**2**answers

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

**0**answers

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

**3**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**2**answers

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

**0**answers

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

**0**answers

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

**0**answers

66 views

### how many pythagorean triplets can be formed with N given so that addition of all three sides is equal to N? [on hold]

Example:- N = 120
TRIPLETS = (30 ,40 ,50) , (20 ,48 ,52) , (24,45,51)

**0**

votes

**0**answers

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

**0**answers

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

**1**answer

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

**2**answers

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

**0**answers

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

**2**answers

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

**0**answers

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

**1**answer

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

**1**answer

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

**1**answer

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

**0**answers

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

**1**answer

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

**0**answers

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

**0**answers

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

**0**answers

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

**1**answer

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

**1**answer

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 ...