0
votes
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
1answer
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
0answers
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
0answers
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
0answers
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
1answer
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
0answers
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
0answers
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
0answers
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
1answer
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
0answers
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
1answer
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
0answers
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
0answers
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
1answer
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
0answers
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
votes
0answers
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
6answers
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
0answers
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
votes
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
1answer
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
0answers
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
0answers
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
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
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
0answers
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
2answers
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
1answer
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
0answers
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
1answer
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
1answer
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
2answers
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 ...

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