# All Questions

**7**

votes

**0**answers

48 views

### Applications of $p$-adic Hodge theory

I am trying to learn $p$-adic Hodge theory. I found some materials explaining main theorems (or aspects) of the theory. However, I could not find references which explaining how to use the theory. ...

**0**

votes

**0**answers

21 views

### Bombieri-Vinogradov in short intervals

In 1985 Perelli, Pintz & Salerno proved a short-interval form of the Bombieri-Vinogradov theorem with $\theta \in (7/12, 1]$. Have there been any improvements on this, in particular with the ...

**0**

votes

**0**answers

9 views

### Kan extension pseudo-2-functor

Consider the 2-category $[S, H] $ of 2-functors $S\to H $ (in which, obviously, $S$ and $H$ are 2-categories). And consider a (possibly fully faithful) functor $T: S\to Z $
For simplicity, let's ...

**0**

votes

**0**answers

25 views

### Space of positive matrices of a form

Let $a_i\in\Bbb R_{\geq 0}^n$ from $i=1,\dots, k\leq n$ be a list of $k$ vectors of length $n$ each. Then $\sum_{i=1}^{k}a_ia_i'$ characterizes all the matrices in $\mathsf{Sym}^+_n$ (the space of ...

**0**

votes

**0**answers

27 views

### Futaki invariant on $X=Bl_p(\mathbb CP^2)$ for different line bundles

Let $X$ be a projective variaty which blow up at a point $p$ , i.e, $X=Bl_p(\mathbb CP^2)$, then for the Line bundle $L=-K_X$, we have for Futaki invariant $Fut_L\neq 0$, I want to see what about ...

**0**

votes

**0**answers

35 views

### Maximum connected components $0-1$ matrix

Let the notion of connected matrix be as in here Connected components $0-1$ matrices
Here a matrix has one component means we can traverse from a matrix entry $(i,j)$ which is $1$ to any other one by ...

**-1**

votes

**0**answers

37 views

### Are the following interpretations elementarily equivalent? [on hold]

Are the following interpretations elementarily equivalent?
$$ < \mathbb N, \le > \text{ and }<\mathbb N + \mathbb Z, \le> $$
If so, prove it. Else make a formula that distinguishes them.
...

**2**

votes

**2**answers

108 views

### Removing subtrees

Let $T$ be a complete infinite rooted binary tree. Is it possible to remove (infinitely many) subtrees of $T$ and get a subgraph $G$ such that:
$G$ has no complete subtrees (the graph below any ...

**1**

vote

**1**answer

51 views

### Combinations Question about the construction of some special sets

Let n and k be two given numbers. The goal is to choose n subsets from {1,2,…,n} such that the union of any k of these subsets is the set {1,2,…,n} and the union of any m < k of ...

**1**

vote

**1**answer

55 views

### Deterministic finite-state automaton driven by a Markov chain

I've stumbled on some problem, and I have the feeling that this is closed to something well-studied in dynamical systems. The problem is the following. Consider a finite-state automaton with state ...

**1**

vote

**0**answers

37 views

### Measuring products of finitely generated subgroups of free groups

Let $F$ be a finitely generated free group, $H_1, \dots, H_n$ finitely generated subgroups of infinite index in $F$, and $\epsilon > 0$. Must there be an epimorphism to a finite group $\phi \colon ...

**2**

votes

**1**answer

103 views

### Is there any elementary proof of No wandering domain for polynomials

It seems that it is almost impossible to give a elementary proof of Sullivan's no wandering domain for rational map or even more general class of maps.
I think it is interesting to ask whether we ...

**7**

votes

**1**answer

143 views

### Can a positive measure subset of a free group be nowhere dense?

Let $F$ be a finitely generated free group and let $S \subseteq F$ be a subset for which there is some $\epsilon > 0$ such that for any epimorphism to a finite group $\phi \colon F \to G$ we have ...

**2**

votes

**2**answers

101 views

### Tensor product over a monoid in a monoidal category

nLab article on tensor product says:
"Given two objects in a monoidal category $(C,\otimes)$ with a right and left action, respectively, of some monoid $A$, their tensor product over $A$ is the ...

**3**

votes

**1**answer

40 views

### Extension of an involutive automorphism

Suppose that $g$ is a complex semi-simple Lie algebra and $g'$ its reductive subalgebra.
If $\tau$ is an involutive automorphism of $g'$, can $\tau$ be extended to an involutive automorphism of $g$ ...

**17**

votes

**1**answer

174 views

### Cantor's theorem for presheaves?

Some years back (before MathOverflow was born), Tom Leinster asked an interesting question at the $n$-Category Café which I don't recall ever seeing an answer for:
Does there exist a ...

**5**

votes

**1**answer

105 views

### Blow-ups of $\mathbb{P}^{n-3}$ and $(\mathbb{P}^1)^{n-3}$

Let us consider the points
$$p_1=[1:0:...:0],p_2 = [0:1:...:0],...,p_{n-2} =[0:...:0:1],\\
p_{n-1}=[1:1:...:1]\in\mathbb{P}^{n-3}$$
and the blow-up $X = Bl_{p_1,...,p_{n-1}}\mathbb{P}^{n-3}$.
...

**0**

votes

**0**answers

22 views

### Caffarelli-Silvestre extension definition of fractional Laplace-Beltrami on hypersurface

Let $\Gamma \subset \mathbb{R}^{n+1}$ be a $n$-dimensional (closed) $C^k$-hypersurface. Consider the problem
$$\nabla_\Gamma \cdot (y^{1-2s}\nabla_\Gamma u)(x,y) =0 \quad \text{for $(x,y) \in \Gamma ...

**0**

votes

**0**answers

35 views

### The hypertriangular function of $n$

I'm looking for papers or recent results on the hypertriangular function of $n$:
$$H_t(n)= \displaystyle\sum\limits_{k=1}^{n} k^k$$
This is A001923 in the OEIS.
I don't have much experience with ...

**1**

vote

**0**answers

59 views

### The definition of $SK_1$ for an arbitrary ring

Let $R$ be a unitary associative ring. If $R$ is commutative, then one defines $SK_1(R)$ as the quotient $$SK_1(R)=SL(R)/E(R)$$ (Definition 2.8 of ...

**-1**

votes

**0**answers

48 views

### $V(A)\cong {\mathbb N}\cup\{0\}$ and $$V(A_+)\cong\{(m,n)\in {\mathbb Z}^2 \mid m,n \geq 0, \hbox{ $m+n$ even}\}. $$ [on hold]

In Professor Blackadar's book "K theory for operator algebras", there is an example in Chapter 3, $K_0$-theory and order:
Let
$$ A=\{f :[0,1]\to M_2 \mid f(0)={\rm diag}(x,0), f(1)={\rm ...

**1**

vote

**0**answers

43 views

### How would you call a variety that is locally a complete intersection up to defect c?

Let $X$ be an equidimensional variety of dimension $n$ over a field that can be covered by open subvarieties of certain intersections of $N-n$ hypersurfaces in $P^N$ (for a large enough $N$; we ...

**0**

votes

**0**answers

14 views

### Maximizing a certain concave function over a non-convex set

I have been working on a problem which involves maximizing a concave function over a non convex constraint set. The problem is the following $$max. \frac{1}{2}x^TBx\\ s.t.\ x_i(1-x_i)=0,\ \ ...

**-2**

votes

**0**answers

31 views

### Finding ellips equation by focuses and tangent line [migrated]

The Ellips which has focuses in $(±3,0)$ and a tangent line $x+y-5=0$.
I need to find ellips equation.
I've founded these equations
$\frac{x_{0}}{a^2} = \frac{1}{5}, \frac{y_{0}}{b^2} = \frac{1}{5}$
...

**0**

votes

**0**answers

120 views

### Solution to a recursive equation [on hold]

Given $n$ arguments, how does one solve following recursive equation:
$$T(n)=3T(n/4)+n.ln^3.n$$

**4**

votes

**2**answers

199 views

### Do geodesics in SL2R map to geodesics in the hyperbolic plane?

I am looking for a reference/proof/disproof of the following statement.
Equip the Lie group $SL_2(\mathbb{R})$ with the left-invariant Riemannian metric, whichis given on the Lie algebra by $\langle ...

**-2**

votes

**0**answers

44 views

### Blood type frequency given probability [on hold]

I have calculated the probability that any child will have a particular blood type from both the genotype level and the phenotype level assuming the human ABO Rh system is followed.
Here are the ...

**0**

votes

**1**answer

80 views

### Connected curve

Assume we have a normal,connected quasi projective scheme $Y:=X\backslash D$ where $X$ is a quasi projective scheme over field $k$, not necessarily char zero and also $D$ is a simple divisor, not ...

**0**

votes

**0**answers

24 views

### on the existence of holomorphic coordinates under bounded curvature

Let $(X,g)$ be a complete Kahler manifold with the Riemann curvature and its derivatives bounded. Suppose also the injectivity radius of this manifold is bounded below by a constant $i_0>0$. My ...

**3**

votes

**2**answers

107 views

### Can the pre-image of the real points in the complex upper-half plane of a modular elliptic curve under the modular parametrization be identified?

Consider an elliptic curve $E/\Bbb Q$ and let $\Phi:\Gamma_0(N)\backslash\overline{\mathfrak{H}}\rightarrow E(\Bbb C)$ be the analytical description of its modular parametrization. We know that this ...

**4**

votes

**1**answer

208 views

### Open problems in compressed sensing

What are the main open problems in compressed sensing?
I am interested in theoretical as well as in numerical point of view.

**-4**

votes

**0**answers

45 views

### How can i be distinguished from -i? [migrated]

Mathematicians designate one solution to x^2 = -1 as i and the other as -i. Would anybody notice if we switched their identities? Any polynomial p(x) with a complex root will also have its conjugate ...

**3**

votes

**2**answers

180 views

### Sets of squares representing all squares up to $n^2$

Let $S_n=\{1,2,\ldots,n\}$ be natural numbers up to $n$.
Say that a subset $S \subseteq S_n$
square-represents $S_n^2$ if every
square $1^2,2^2,\ldots,n^2$ can be represented by adding or subtracting
...

**2**

votes

**1**answer

188 views

### Primes $p=x^2+27y^2$ and Ramanujan's $x_1^{1/3} + x_2^{1/3} + x_3^{1/3}$

I was trying to generalize,
...

**1**

vote

**0**answers

74 views

### Prime labelling of graphs

A prime labeling of a graph is an injective function $f: V(G) \to \{1, 2, ..., |V(G)|\}$
such that for every pair of adjacent vertices $u$ and $v$, $\text{gcd}(f(u), f(v)) = 1$ (labels of any two ...

**-3**

votes

**0**answers

24 views

### Model of function of 2 random variables [on hold]

In my model W = f(E, K). f is a complex function (several operations on E and K).
for any W, infinity pairs of (E, K) exist that satisfy f.
E and K are between [0, +oo]
I have observations for W ...

**3**

votes

**0**answers

23 views

### On a continuous extension of a linear 2nd order PDE

Consider an elliptic (hyperbolic) equation
$A(x,y) u_{xx} + 2B(x,y) u_{xy} + C(x,y) u_{yy} = 0$
in a bounded open plane set $D$, with real-valued functions $A$, $B$, and $C$. Is it true that at least ...

**1**

vote

**0**answers

36 views

### How the modular theory of von Neumann algebras, deal with generating C*-algebras?

Let $H$ be a separable infinite dimensional Hilbert space, $M \subset B(H)$ a von Neumann algebra and $A \subset M$ a separable $C^*$-algebra such that $A''=M$. Suppose the existence of a bicyclic ...

**1**

vote

**0**answers

39 views

### Uniqueness of an embedding theorem for Real differential fields

I will follow a preliminary exposition for the problem in question, which will essentially follow the format on http://www4.ncsu.edu/~singer/papers/model_diff_fields.pdf [pg. 87]:
Let $K$ be a real ...

**0**

votes

**1**answer

98 views

### Murray–von Neumann equivalence on C$^*$-algebra and von Neumann algebra

Let $H$ be a separable infinite dimensional Hilbert space, $M \subset B(H)$ a von Neumann algebra and $A \subset M$ a separable $C^*$-algebra such that $A''=M$.
Let $p,q \in M_{\infty}(A)$ be ...

**3**

votes

**1**answer

360 views

### What's so special about $1$-categories?

I have been pretty thoroughly convinced for some time now that, when thinking about mathematics, one really should be thinking 'categorically', that is, one should always be thinking of the morphisms ...

**0**

votes

**0**answers

48 views

### Arithmetic functions associated with Hurwitz Zeta function raised to arbitrary complex powers, $\zeta(s,q)^z$ for $q \in \mathbb{N}$?

If $\zeta(s)$ is the Riemann Zeta function, then $\zeta(n)^z$, with $z \in \mathbb{C}$, $\Re(s)>1$, can be represented as
$$\zeta(s)^z=\sum_{n=1}^\infty \frac{d_z(n)}{n^{-s}}$$
where $d_z(n)$ ...

**0**

votes

**0**answers

15 views

### What happens to the angles of an isosceles triangle if one vertex is at infinity? [migrated]

My son and I were trying to decide whether an isosceles triangle can ever have 90 degree base angles. I would argue that if the two equal length sides are both infinitely long, they must have 90 ...

**2**

votes

**0**answers

49 views

### variants of ramification groups - need terminology and sources

I've asked this question in several more elementary forums, and haven't get any answer. So I presume this is not so an elementary question.
Let $L/K$ be a Galois extension, and $w$ be a valuation of ...

**1**

vote

**1**answer

106 views

### Bounded dg algebra vs unbounded dg algebras

1)Let $Cd_{\geq 0}ga$ be the category of non negatively commutative cochain dg algebra over a field $\Bbbk$ of charachteristic zero. Let $w\: : \: Cd_{\geq 0}ga\to dg_{\geq 0}Mod$ be the forgethfull ...

**7**

votes

**0**answers

198 views

### Application of the Riemann hypothesis and the ABC conjecture to independence results

In Old Home Page of Andreas Weiermann Andreas Weiermann has stated the following:
Quite recently I submitted a preprint about an application of the Riemann hypothesis and the ABC conjecture to ...

**1**

vote

**1**answer

102 views

### Cardinality of the prime divisor set of a k-power sum

Let $a_{1},\dots,a_{n}$ be positive natural numbers ($n>2$) such that $a_{i}\neq a_{j}$ if $i\neq j$. I want to prove that
$$ \left\lvert \left\{ p \text{ prime} \; : \; p \mid \sum_{i=1}^n ...

**0**

votes

**0**answers

74 views

### this sequence $A_{n}$ have recursive relations?

Let $$A_{n}=\sum_{i=0}^{n-3}(-1)^{n+i-2}\dfrac{13n^2-31n-10ni+9i+i^2+16}{(3n-i-3)(3n-i-4)(2n-i-3)!\cdot i!}$$
I want find the $A_{n}$ recursive relations,such as following form
...

**0**

votes

**1**answer

137 views

### How to solve this differential equation with an infinite sum?

I would like to find solutions of the following differential equation:
$ \sum_{1}^{\infty} a_n f(nx) + f''(x)+ x^2 f(x)=\lambda f(x)$
For example in space of function from $\mathbb R^*$ to $\mathbb ...

**0**

votes

**2**answers

564 views

### Where do Set Theory and Number Theory meet together?

As all know, by absoluteness theorems in Set Theory, most of theorems in number theory are $ZFC$-provable if and only if they are consistent with $ZFC$, it's because of absoluteness of essence of ...