# All Questions

**0**

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6 views

### Radial limit does not exist almost everywhere

Problem 4 in Chapter 4 of Stein's book "Real Analysis" says
$\sum_{n\geqslant 0}z^{2^n}$
doesn't have radial limit as $z$ approaches the unit circle from inside almost everywhere. It's fairly easy ...

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10 views

### cobordism and smoth-manifold

Let M, N , N' and M' be smooth n-manifolds with nonempty boundaries , and suppose h:∂M→∂N , g:∂M'→∂N' are diffeomorphisms . Let M∪_h N be the adjunction space formed by identifying each xϵ∂M with ...

**1**

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**0**answers

11 views

### Multi-podal points

Two points $x,y \in \mathbb{R}^n$ are called antipodal if $x = -y$.
Stated differently, $x,y$ are antipodal if:
They have the same absolute value in each of their $n$ coordinates;
Each of their ...

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17 views

### Can a rigid CY threefold have infinitely many automorphisms

Let $X$ be a rigid Calabi-Yau threefold. Does $X$ have only finitely many automorphisms?
N.B. A smooth projective threefold $X$ over $\mathbb C$ is a rigid Calabi-Yau variety if $h^i(X,\mathcal O_X) ...

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9 views

### Is Wiener amalgam spaces $W^{2,1}(\mathbb R)\subset C_0(\mathbb R)$?

I have been learning Wiener amalgam spaces.
In Wiener amalgam spaces $W(X, L^2)$, I am taking $X=\mathcal{F}L^{1}=\{f\in L^{\infty}(\mathbb R):\hat{f}\in L^{1}\},$ and $m(x)=1.$
Take $f(x)= ...

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54 views

### Finite trigonometric polynomial

I noticed by numerical and some explicit calculations for a few examples that for real-valued finitely supported functions $\phi \in L^2(\mathbb{R})$ we have that
$T(x):= \sum_{n \in \mathbb{Z}} ...

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45 views

### Cohomology of Homogeneous Complex Manifolds

Let $M$ be compact $G$-homogeneous manifold, equipped with the equivariant complex structure, when $G$ is a semi-simple algebraic group. The obvious example is every flag manifold. In that case, all ...

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17 views

### Is there any topological information encoded by the zero locus of a complex Hessian?

On a Kahler manifold one can always find a function $K$ so that (up to some constant) the Kahler form $\omega$ can be written as $\omega = \partial \bar{\partial}K$ (sometimes, under conditions that I ...

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37 views

### Fiber Bundle with a perfect bilinear map

Let $\pi:X\rightarrow Y$ a double cover of Riemann surfaces, and consider a $SL_n-$bundle $E$ with a perfect $\mathcal O_Y-$bilinear pairing $$\psi:\pi_*E\times\pi_*E\rightarrow\pi_*\mathcal O_X$$
...

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22 views

### Finitely generated ordered monoids and noetherian subsets

(This question was asked a long time ago on MSE but got no answer so far...)
Let $E$ be an additively written cancellable commutative monoid with no non-trivial units. We furnish $E$ with the order ...

**7**

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104 views

### How many traces are there on Temperley-Lieb, Fuss-Catalan, Iwahori-Hecke, Birman-Wenzl-Murakami-Kauffman, … algebras?

There is a theorem (I believe by Ocneanu) that the Markov trace on the tower of Temperley-Lieb algebras is (essentially) unique.
What about just traces on separate algebras? That is, take one of ...

**4**

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**0**answers

36 views

### Analytic equivalence relations whose classes are sometimes Borel

There are analytic equivalence relations for which the statement "All classes are Borel" is independent of $ZFC$. In all the examples I know about, the classes are non Borel in $L$ or $L[z]$ for some ...

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33 views

### If $q^k n^2$ is an odd perfect number with Euler prime $q$, are the following statements known to hold in general?

Let $\sigma$ be the classical sum-of-divisors function.
A number is said to be perfect if $\sigma(N)=2N$.
If $q^k n^2$ is an odd perfect number with Euler prime $q$ (i.e., $q \equiv k \equiv 1 \pmod ...

**2**

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**0**answers

8 views

### Discrete “difference” equations that involve changes in both shift and scale

A standard use of the Z-transform ($F(z) = \sum_n (f[n] \cdot z^{-n} )$) is to understand the effect of a difference equation on a signal. For instance:
$y[n] = x[n] + y[n-1]$
$Y(z) = X(z) + Y(z) ...

**2**

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33 views

### Meager subgroups of compact groups

Suppose we have an infinite compact (Hausdorff) group $G$, and a subgroup $H\leq G$ which is meagre.
Can $H$ always be covered by a countable family of nowhere dense sets $H_n$ such that $H_n^2$ is ...

**-1**

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**1**answer

45 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 ...

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42 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 ) ...

**5**

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**1**answer

75 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 ...

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26 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?

**-4**

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16 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 ...

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85 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 ...

**3**

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**0**answers

34 views

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

Update. Based on Anthony Quas' comment below, the proof can be made sensibly shorter and the lemma can be slightly generalized by weakening the old assumption (iii).
In a joint paper that I am ...

**6**

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**0**answers

55 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**

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**0**answers

56 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 ...

**4**

votes

**1**answer

107 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 ...

**4**

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**0**answers

32 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 ...

**5**

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**1**answer

53 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 ...

**8**

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**1**answer

223 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 ...

**2**

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**0**answers

83 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**

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**0**answers

44 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 ...

**5**

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**0**answers

71 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 ...

**-4**

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**1**answer

49 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 - ...

**6**

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**0**answers

145 views

### Combinatorial formula for the number of different words

I originally posted this question here:
http://math.stackexchange.com/questions/1296199/combinatorial-formula-for-the-number-of-different-words :
I am interested in the asymptotic behaviour of the ...

**2**

votes

**0**answers

29 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 ...

**4**

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**0**answers

42 views

### Specific type of Carleman Estimate

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

**3**

votes

**1**answer

49 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 ...

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**0**answers

12 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

313 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 ...

**2**

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**0**answers

50 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, ...

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**0**answers

380 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

100 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 ...

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59 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 ...

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38 views

### Hexagonal lattice in a disk when the distance between points is $R_l$ [on hold]

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 ...

**101**

votes

**7**answers

3k views

### John Nash's Mathematical 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 ...

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28 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 = ...

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60 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 ...

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24 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 ...

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30 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 ...

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35 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 ...

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27 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 ...