# All Questions

**0**

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4 views

### stable splitting into a wedge sum

Suppose $X$ is a CW-complex such that there is a stable splitting of $X$ into wedge sum
$$
\Sigma^t X\cong \bigvee _{k=1}^\infty Y_k.
$$
(1). Does this imply
$$
X\to \Sigma^tX\to \bigvee ...

**0**

votes

**0**answers

9 views

### Hyperbolic manifold of dim 3 with finite volume.

The geometrization Theorem for 3-manifolds classifies all oriented compact (without boundary ) 3-manifolds. Is there a theorem which classifies all hyperbolic oriented 3-manifold (without boundary ) ...

**1**

vote

**0**answers

7 views

### Do non-normal states exist in the Solovay model?

Let H be an infinite dimensional Hilbert space. Then there exist non-normal states on B(H) in ZFC (i.e. states that are not represented by a density operator).
Is this also true in the Solovay model ...

**-7**

votes

**0**answers

16 views

### Is Microsoft Lumia 535 on Android and which is best online store in USA? [on hold]

Please help me to find the answer of this above question?

**0**

votes

**0**answers

11 views

### Idempotent ideal in ring of continuous functions

Is there any equivalence conditions under which an ideal $I$ in ring of continuous functions be be an idempotent ideal?

**-2**

votes

**0**answers

11 views

### How to find the odds for events (two or more) using its probability [on hold]

i am currently using the below formula
p1 odds = (p1)/(1-p1)/
(p2)(1-p2)
p1 = probability of winning of event1
p2 = probability of winning of event2
Please let me know if it is ...

**0**

votes

**0**answers

42 views

### A diophantine equation

A few days ago I saw a question about the diophantine equation $p^2+p+1=q^\alpha$ in
What is prime power of this equation of p?
and later in
A Diophantine equation with prime powers
I want the ...

**1**

vote

**0**answers

17 views

### Reference for a lemma on the asymptotic upper density of special sets with large gaps and intervals

In a joint paper that I am writing, we need (and prove) the following:
Lemma. Let $(a_n)_{n \ge 1}$ and $(b_n)_{n \ge 1}$ be sequences of positive real numbers such that:
(i) ...

**4**

votes

**0**answers

32 views

### Equation of the curve corresponding to a polarization of an abelian surface

Let $\mathbb{C}^2/\Lambda$ be a polarized abelian surface. I think it is well-known how to write down the equation of the divisor corresponding to the polarization, in terms of theta functions etc. ...

**-2**

votes

**0**answers

38 views

### Triangular Billiard Table [on hold]

I was asked an interesting question today.
Suppose that there is an arbitrary triangle, where a billiard ball is launched at a random angle.
Prove that the ball will always return to the starting ...

**1**

vote

**0**answers

44 views

### understanding of rough path

A rough path is defined as an ordered pair
$ (X, \mathbb X)$, where $X$ is a path mapping from $[0,T]$ to some Banach space $V$
and $\mathbb X:[0,T]^2 \mapsto V^2$ is another mapping for additional ...

**3**

votes

**0**answers

17 views

### Concavity of mixed volumes and mixed discriminants

For $n\times n$ symmetric matrices $A_1, \ldots, A_n$, the mixed discriminant $D(A_1, \ldots, A_n)$ can be defined as $1/n!$ times the coefficient of $t_1\ldots t_n$ in the homogeneous polynomial ...

**1**

vote

**0**answers

26 views

### Pseudodifferential operators on spaces with boundary

Consider the upper half space $\mathbb{R}^n_{+} = \{x = (x_1,..,x_n) \in \mathbb{R}^n : x_n \geq 0\}$. Consider the Laplacian on this space with either the Dirichlet boundary condition or the Neumann ...

**7**

votes

**1**answer

183 views

### On the number of consecutive divisors of an integer

Define for $n \in \mathbb{N}$ the function $$\tau_1(n):=\sum_{\substack{d|n, \\ d+1|n}}1,$$ i.e. the number of consecutive divisors of an integer. The average of $\tau_1(n)$ is $1$ since $$\sum_{n\leq ...

**1**

vote

**0**answers

62 views

### Can the epsilon induction condition be presented with successor case and limit case, similar to transfinite induction?

The epsilon induction looks like this:
$\forall x \Big(\forall y (y \in x \rightarrow P(y)) \rightarrow P(x)\Big) \rightarrow \forall x P(x)$
Here, the quantifiers "run over" any sets and not only ...

**-3**

votes

**0**answers

36 views

### Computer Science/Maths Hamming Distance [on hold]

My professor told us to try and remember the equation used for an upcoming exam, however I'm struggling to fit the equation into the question:
http://i.stack.imgur.com/RoPYG.png
(need a high ...

**3**

votes

**0**answers

53 views

### Homotopy pullback preserving functor

In the paper http://arxiv.org/pdf/math/0101162.pdf, the authors claim during the proof of Prop. 4.2 that a functor $F:A \to B$ which preserves fibrations and weak equivalences preserves homotopy ...

**-3**

votes

**1**answer

43 views

### Convergence of a complex series [on hold]

I have a complex series:
$$i - 2i + 3i - 4i + 5i - \cdots$$
And I need to know if it converges and if it does, to what.
We could make:
$$(i-2i) + (3i-4i) + \cdots$$ which gives us $$-i -i - ...

**4**

votes

**0**answers

95 views

### Combinatorial formula for the number of different words

I originally posted on
hhttp://math.stackexchange.com/questions/1296199/combinatorial-formula-for-the-number-of-different-words :
I am interested in the asymptotic behaviour of the following ...

**1**

vote

**0**answers

26 views

### Associative convolution on p-adic distribution

Let $\mathcal{D}(\mathbb{Q}_p)$ be the space of the locally constant functions with compact support and let $\mathcal{D}'$ be the space of distributions: linear functionals on $\mathcal{D}$. In the ...

**2**

votes

**0**answers

37 views

### Specific type of Carleman Estimate

Suppose that in a compact Riemannian manifold with boundary one has the following type of carleman estimate:
$$ \| e^{\tau \phi} \triangle_g e^{-\tau \phi} u\|_{L^2(M)}\ge C \tau \|u\|_{L^2(M)} $$
...

**2**

votes

**1**answer

42 views

### Spectral theorem from Jordan decomposition in infinite dimensions

The finite-dimensional spectral theorem is a simple special case of the finite-dimensional Jordan decomposition. We also have various infinite-dimensional generalizations of the spectral theorem; can ...

**1**

vote

**0**answers

11 views

### Counting variables to look for invariances/range conditions

A while back, I asked this question on m.se. I wasn't terribly happy with the answer, and when someone asked a very similar question which isn't getting any action, it got me thinking again. Let me ...

**2**

votes

**1**answer

288 views

### How I can proof this conjecture if it's not open?

Is there someone show me how I can proof this conjecture at least show me how i can doing
the first implication ?
conjecture :Assume $\alpha,\beta , \lambda \in [0,\infty) $ Then every positive ...

**1**

vote

**0**answers

38 views

### Is there a reasoned derivation of the coherence conditions for symmetric rig categories?

I know what the coherence conditions are, I can look them up in
M. Laplaza, Coherence for distributivity, Lecture Notes in Mathematics 281, Springer Verlag, Berlin, 1972, pp. 29-72.
In theory, ...

**8**

votes

**0**answers

279 views

### Algorithmic (un-)solvability of diophantine equations of given degree with given number of variables

Question: For which $d, k \in \mathbb{N}$ is there an algorithm to determine
whether a polynomial diophantine equation
$$
P(x_1, \dots, x_k) = 0, \ \ \ P \in \mathbb{Z}[x_1, \dots, x_k]
$$
...

**3**

votes

**1**answer

91 views

### Enriques classification of algebraic surfaces in characteristic zero

I am searching for a reference about the classification of algebraic surfaces over an arbitrary algebraically closed field of characteristic zero. In the 1949 book "le superficie algebriche" by ...

**0**

votes

**0**answers

56 views

### Are the elliptic curve discrete log problem and the elliptic curve Diffie-Hellman problem equivalent?

Suppose that $G=\langle g\rangle$ is a general group of order $p$. Maurer has introduced an algorithm to reduce the discrete log problem to the Diffie-Hellman problem under a conjecture about smooth ...

**0**

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**0**answers

27 views

### Hexagonal lattice in a disk when the distance between points is $R_l$

Consider a hexagonal tiling of a 2D plane where hexagons are of identical size and of radius $R_l$.
I assume we can say that the vertices together with the center of each hexagon form an integer ...

**81**

votes

**6**answers

2k views

### John Nash's Legacy

It would seem that John Nash and his wife Alicia died tragically in a car accident on 5/23/15 (reference). My condolences to his family and friends.
Maybe this is an appropriate time to ask a ...

**0**

votes

**0**answers

24 views

### Is there a better rank bound for fibered products?

Let $G$ be a profinite group of rank $d \geq 2015$, which is a fibered product of two groups of rank at most $2$. That is, there exist closed normal subgroups $N_1, N_2 \lhd_c G$ with $N_1 \cap N_2 = ...

**0**

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**0**answers

59 views

### How does one express a Lagrangian via differential forms? [duplicate]

I asked this question here on Physics.SE; and I accepted an answer, which thinking about it later I was dis-satisfied with; to save clicking on the link I'm reproducing the question below:
In ...

**0**

votes

**0**answers

18 views

### Automorphisms of a differential field and transcendence degree

Let $(\mathcal{F},+,\times,\partial)$ be a differential field, and let's define its automorphism group $Aut(\mathcal{F})$ as the group, under composition, consisting of all bijective maps ...

**-1**

votes

**0**answers

27 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

28 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

24 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

36 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.;
...

**2**

votes

**1**answer

60 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 ...

**2**

votes

**0**answers

78 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

150 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

43 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

56 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

60 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, $M_s$ ...

**4**

votes

**1**answer

183 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

60 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

43 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 ...

**5**

votes

**1**answer

139 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

246 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 ...