0
votes
0answers
4 views

EFIE - Efficiency Web Platform

I'm Alessandro Torriani. Swiss. Live in Kenya. My parents and I own and run our hotel, The Funzi Keys (www.thefunzikeys.com). Apart from this, I am very interested in apps and web platforms. Spent ...
0
votes
0answers
8 views

Jones polynomial of tangles using Temperley-Lieb algbra?

The definition of the Jones polynomial of tangles (a la Reshetikhin and Turaev) uses the space of invariants for $U_q sl_2$ and R-matrices. It seems to me the same thing cane be done in terms of the ...
0
votes
0answers
3 views

about the weak comparison principle for p - Laplace equation

Let $\Omega$ an open bounded domain in $R^n$ with smooth boundary. Let $\varphi \in W^{1,p}(\Omega) \cap L^{\infty}(\Omega)$ and $u \in W^{1,p}(\Omega) $ with $\Delta_p u = 0$ in $\Omega$ and $u - ...
-5
votes
0answers
31 views

A New set for The Riemann Hypothesis with $\zeta(2)$

Does the following is acceptable? Let $s=2$ then for any function $f(n)$ with $n>1$ we have ...
0
votes
0answers
22 views

Analogues of the Lagrange inversion theorem. [on hold]

Does anyone know if there exists other theorems similar to the Lagrange Inversion Theorem. I'm interested in collecting methods for determining the asymptotic behaviour of implicitly defined ...
2
votes
2answers
61 views

Is it consistent that $\frak{d} < 2^{\aleph_0}$?

Let $\omega^\omega$ denote the set of all functions $f:\omega\to\omega$. We write $f <^* g$ if there is $N\in\omega$ such that $f(n) < g(n)$ for all $n>N$. A set $D\subseteq \omega^\omega$ is ...
-4
votes
0answers
21 views

Probably some naive question on conditional probability [on hold]

As known, three variables x_1, x_2 and y, if x_1 and x_2 are conditional independent given y, we have p(x_1, x_2|y) = p(x_1|y)p(x_2|y). I was wondering about p(y|x_1, x_2), is that possible to get ...
0
votes
1answer
25 views

Powers in compact coset spaces

Let $G$ be a topological group, let $K$ be a closed cocompact subgroup (i.e. the coset space $G/K$ is compact in the quotient topology) and let $g \in G$. Is there a sequence of positive powers ...
0
votes
0answers
41 views

Two (strictly related) proofs by induction of inequalities

This is a question I originally asked on MSE, receiving no answer, even with a bounty (which expired) on it. Therefore I am crosslinking in order to prevent duplication of effort: see here for the ...
-3
votes
0answers
39 views

Proving integration techniques [on hold]

I've recently competed my A levels and now that I'm in the university I finally found the time to understand calculus on a intuitive level. So I've been reading up on books such as "Calculus with ...
1
vote
0answers
35 views

Inequivalent definitions of Cartan subalgebra

As far as I can tell, there exists no acknowledgment on the internet of the fact (or maybe it's not a fact) that inequivalent definitions of "Cartan subalgebra" of a real Lie algebra exist in the ...
2
votes
1answer
179 views

Anti-compactness

Let $(X,\tau)$ be a topological space such that $\tau$ is a proper superset of $\{\emptyset, X\}$. We call an open cover $\mathcal{U}$ of $(X,\tau)$ proper if $X\notin \mathcal{U}$. Moreover we say ...
5
votes
4answers
220 views

Sierpinski's construction of a non-measurable set

In the early 20th century there was a lot of fuss over the axiom of choice implying that there are Lebesgue non-measurable sets of reals. In his book about The Axiom of Choice, Gregory Moore points to ...
-4
votes
0answers
60 views

Two problems in functional analysis [on hold]

Let $f$ be linear functional on Banach space $B$ and $ker f$ is closed subspace of $B$, prove that $f$ is a bounded linear functional. Let $\{e_n\}$ be an orthonormal basis of Hilbert space H. T is ...
5
votes
1answer
183 views

Is there a “good” reason that the universal central extension of $SL(2,\mathbb Z)$ is $Br_3$?

Let $$ Br_3 := \langle \tau_1,\tau_2\ :\ \tau_1 \tau_2 \tau_1 = \tau_2 \tau_1 \tau_2 \rangle $$ be the braid group on three strands, and consider the surjection $$\phi : Br_3 \twoheadrightarrow ...
9
votes
0answers
147 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. ...
1
vote
1answer
95 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
0answers
23 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
0answers
50 views

Space of positive matrices of a form [on hold]

$\mathsf{Sym}^+_n$ be the space of symmetric matrices with entries in $\Bbb R_+\cup\{0\}$. $\sum_{i=1}^{k}a_ia_i'$ where $a_i\in\Bbb R_{\geq 0}^n$ from $i=1,\dots, k\leq n$ characterizes all the ...
0
votes
0answers
71 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 ...
-1
votes
0answers
75 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 ...
-2
votes
0answers
54 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
2answers
143 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
1answer
70 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
1answer
64 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 ...
2
votes
1answer
62 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
1answer
114 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 ...
8
votes
2answers
201 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
2answers
129 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
1answer
53 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 $g$ ...
22
votes
1answer
346 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 ...
6
votes
1answer
166 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
0answers
28 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
0answers
41 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
0answers
72 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
0answers
49 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
0answers
61 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
0answers
18 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
0answers
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 $\frac{x_{0}}{a^2} = \frac{1}{5}, \frac{y_{0}}{b^2} = \frac{1}{5}$ ...
4
votes
3answers
277 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
0answers
45 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
1answer
87 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
0answers
26 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
2answers
112 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
1answer
217 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
0answers
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
2answers
187 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 ...
3
votes
1answer
109 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
0answers
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 ...

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