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1 answer
193 views

Analysis of Sobolev spaces [closed]

I just wanted to know wthether the following is OK or not. Let $X$ be $H_0^1(\Omega)\bigcap L^{\infty}(\Omega)$, thought of as a subspace of $H^1_0(\Omega)$ and endowed solely with the usual $H^1$ ...
Alexander's user avatar
  • 157
-2 votes
1 answer
202 views

Natural constructions (not depending on parameters) [closed]

Consider graph clusterings as a prototypical example of (logical) constructions. Let a clustering of a graph $(V,E)$ be any covering of $V$, i.e. a set $C$ with $\bigcup C = V$. I am looking for a ...
Hans-Peter Stricker's user avatar
-2 votes
1 answer
295 views

When does the adjoint operator map closed convex subsets to closed convex subset?

Let $T:X\rightarrow Y$ be a linear continuous map between Banach spaces $X$ and $Y$ and denote by $T':Y'\rightarrow X'$ the norm adjoint of $T$. Let $M\subseteq U'$ be a subset of the unit sphere $U'$ ...
Andy Teich's user avatar
-2 votes
3 answers
700 views

Good books on fields and Galois theory [closed]

What are some good books on field and Galois theory?
-2 votes
1 answer
151 views

Averaged measure in integrations

Consider \begin{align} & F(n,x)\equiv \int_0^x \cdots g (x_5)\int_0^{x_5} ~\int_0^{x_4} g (x_3)~~\int_0^{x_3} ~\int_0^{x_2} g (x_1)~~A(x_1)\,dx_1\cdots dx_n \end{align} where $g(x)$ is a measure. ...
Math2024's user avatar
  • 141
-3 votes
1 answer
630 views

Can mathematics help in defining free-will? [closed]

In the celebrated Free Will Theorem of Conway and Kochen it is made use of "free will" without giving a "mathematical definition" of it. The definition of the experimenter is the &...
mathoverflowUser's user avatar
-3 votes
1 answer
315 views

Are the injective functions dense in $C([0,1]^n,\mathbb R^n) $?

Let $n\geq 2$. Are injective functions dense in $C([0,1]^n,\mathbb R^n) $ with the uniform norm?
Dattier's user avatar
  • 4,074
-3 votes
1 answer
251 views

Is the imaginary part of $\displaystyle\ \zeta(s)\zeta(1-s)=0$ for $\operatorname{Re}(s)=\frac{1}{2}$ [closed]

Some of my computations here showed to me that the imaginary part of $\displaystyle\ \zeta(s)\zeta(1-s)=0$ for $\operatorname{Re}(s)=\frac{1}{2}$, really i w'd like to know if there is any paper ...
zeraoulia rafik's user avatar
-3 votes
1 answer
154 views

Proving that $P($$\{\text{$a$ and $b$ are co-prime}$ }$)=0$ for $a,b$ following the Uniform distribution over $[n, 2n]$ as $n \rightarrow \infty$

I have been working on a problem concerning the "line of sight" from a fixed integer co-ordinate — let's say $(0,0)$ — to a variable co-ordinate $(a,b)$. Having a line of sight means that ...
FD_bfa's user avatar
  • 147
-3 votes
1 answer
232 views

Function satisfying $f(x)^{f^{-1}(x)}=x^2$ with $ f^{-1}$ is a compositional inverse of $f$ and $f:\mathbb{R+}\to \mathbb{R+}$?

Let $f$ be a function such that :$f:\mathbb{R+}\to \mathbb{R+}$ and $f^{-1}$ is a compositional inverse of $f$ , I have tried to find solution of the following functional $f(x)^{f^{-1}(x)}=x^2$, I ...
zeraoulia rafik's user avatar
-3 votes
1 answer
215 views

Topology of the moduli space of a 2-dim closed surface

Consider the moduli space $\cal{M}_{\Sigma_g}$ of a 2-dim closed surface $\Sigma_g$ of genus $g$. What is the topology of such a moduli space $\cal{M}_{\Sigma_g}$? For example, what is $\pi_n ( \cal{M}...
Xiao-Gang Wen's user avatar
-3 votes
1 answer
361 views

Basis for space of continuous, surjective monotone functions on $\mathbb{R}$ [closed]

$\DeclareMathOperator\CM{CM}$ I recently came across Okhezin - Study of families of monotone continuous functions on Tychonoff spaces describing monotone functions on general topological spaces and I ...
ABIM's user avatar
  • 5,405
-3 votes
1 answer
579 views

How does deletion-contraction affect chromatic number? Can it increase chromatic number? [closed]

Question: In graph theory, contracting an edge or deleting an edge are basic operations in many topics such as graph minors or Wagner's theorem on planar graphs. And I'm interested in how these ...
user19906's user avatar
  • 419
-3 votes
2 answers
768 views

Question on Linear Operators

Let $V$ be a normed infinite dimensional vector space. Let $L: V \longrightarrow V$ be a bounded linear operator. Moreover assume that $L$ is 'locally nilpotent' that is: $$ \forall v \in V \quad \...
Najdorf's user avatar
  • 741
-3 votes
1 answer
380 views

References of research papers which lead to starting of Sieve Theory

Question - I am thinking to present one or two papers on Sieve Theory in my masters thesis. I will also present 3 other papers on Riemann Zeta Function which I have studied earlier . But I have no ...
Arnold's user avatar
  • 793
-3 votes
1 answer
634 views

compactly supported harmonic functions [closed]

Do a significant class of compactly supported smooth functions u on Ω⊂Rn such that Δu≥0 exist? Thanks!
hardy's user avatar
  • 25
-3 votes
1 answer
194 views

Bounding a number-theoretic integral

Find a good upper bound on $$\int_1^T\frac{\zeta'(s)}{\zeta(s)\zeta(1-s)}X^sdt,$$ where $s=c+it$ for a constant $c>1$ and $X>0$ is a parameter. If needed, we can assume RH. My attempt here is ...
charlie_beck's user avatar
-3 votes
1 answer
392 views

A generalization of Chebyshev's sum inequality

From some my previous questions here and here and well-known rearrangement inequality. I pose an inequality as follows and I am looking for the proof or a reference. Inequality: Let $y=f(x,y)$ is ...
Đào Thanh Oai's user avatar
-3 votes
1 answer
76 views

Minimal norm problem with linear combination of translation operator to be estimated

Follow up question from this one Suppose $X = L^2(G)$, where $G$ is some locally compact group. Let $x, y \in G$ I for fixed $n$ I am seeking for an operator $H \in B(X)$ of the form $$ H = H(\alpha_1,...
user8469759's user avatar
-3 votes
1 answer
222 views

What is the basis for the quantifier notation? [closed]

The symbols $\forall, \exists$ are the ones officially used to denote universal and existential quantifiers respectively. I understand that the choice of $\exists$ was made by Peano, while of $\forall$...
Zuhair Al-Johar's user avatar
-3 votes
1 answer
63 views

How to show $\lambda_i \in \sigma_A(x)$?

Let $\sigma_A(x)$ be the spectrum of $x$ in $A$, and linear functional $\phi$ satisfying $\phi(x)\in \sigma_A(x)$ for every $x \in A$, consider $p(\lambda)=\phi((\lambda e-x)^n)$, and denote its roots ...
nanshan's user avatar
  • 33
-3 votes
1 answer
166 views

Decidable theorem or result that is not weaker than Tarski's theorem

I am wondering what other decidable theorem or results that is not weaker or stronger than Tarski's theorem. Could any one give reference or a simple introduction about such result known in their ...
XL _At_Here_There's user avatar
-3 votes
1 answer
330 views

Is there a precise definition of "mathematical formula"? [closed]

In the Wikipedia article for Formula (which has no references), it is claimed that: "The informal use of the term formula in science refers to the general construct of a relationship between given ...
Brian Rushton's user avatar
-3 votes
0 answers
67 views

Exercise generalizing (related to) Hölder's inequality

I came across this exercise and feel absolutely stuck: Let $p, q, r \in (1, \infty]$ be such that $1/p + 1/q = 1 + 1/r$. Suppose that $F : \mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R}$ satisfies ...
HZA's user avatar
  • 1
-3 votes
1 answer
451 views

Exponential decay of kernel

Let $A: \ell^2 \rightarrow \ell^2$ be a bounded operator given by \begin{equation} (Au)(\alpha) = \sum_{\beta}A(\alpha,\beta)u(\beta) \end{equation} where $\left|A(\alpha,\beta) \right|\le Ce^{-|\...
Marcel's user avatar
  • 11
-4 votes
3 answers
670 views

Remarkable articles about the distribution of prime numbers that were written by contemporary physicists [closed]

I would like to ask about if you know papers containing remarkable achievements that were written by contemporary physicists concerning the distribution of prime numbers (or closely related, maybe the ...
-4 votes
2 answers
6k views

Factorizing polynomials of several variables (in a different perespective)

I am looking for factorization of polynomials of several variables in the way outlined below. Consider a second degree polynomial of two variables over the complex numbers. "P(x,y) = Ax^2 + Bxy + Cy^...
-4 votes
3 answers
524 views

Relation between elliptic curve and Fermat's last thereom

I am looking for a elaborate explanation how the elliptic curve $E (a, b) := y^2=x(x-a)(x-b)$ is associated with the solution of $a^n+b^n=c^n$. In 1969 Hellegouarch performed the elliptic curves $E (a,...
Consider Non-Trivial Cases's user avatar
-4 votes
2 answers
272 views

Has nontrivial solution in positive integers of a diophantine equation: $x_1^2+x_2^2+x_3^2+x_4^2=y_1^2+y_2^2+y_3^2+y_4^2$ [closed]

Has nontrivial solution in positive integers of a diophantine equation as follows ? $$x_1^2+x_2^2+x_3^2+x_4^2=y_1^2+y_2^2+y_3^2+y_4^2$$ Where trivial solutions are $x_i=y_j$. Can you send me any ...
Cố Gắng Lên's user avatar
-4 votes
1 answer
582 views

What's the minimum amount of knowledge to start doing research? [closed]

There are cases in which you have too much knowledge of something to do anything interesting ,and cases in which a lack of experience with a problem (and the prejudices about it) helps someone solve ...
-4 votes
2 answers
530 views

Inverse square-law as a positive definite kernel?

Newtons law for gravity states that: $$F_{12} = \frac{G m_1 m_2} {|x_1-x_2|^2}$$ The function : $$k(x,y):=\exp(-| x-y|^2)$$ is known to be a positive definite function, called the RBF-kernel. It ...
mathoverflowUser's user avatar
-4 votes
1 answer
600 views

Is SOC known to imply the Grand Riemann Hypothesis? [closed]

I'm currently working on a conditional proof of the Grand Riemann Hypothesis, which is based on the assumption that every field automorphism of $\mathbb{C}$ that commutes with an element of the ...
Sylvain JULIEN's user avatar
-4 votes
2 answers
286 views

Does the Laplacian commutes with the indicator function [closed]

We define the laplacian operator $\Delta$ with the Neumann boundary conditions on the space $H^2(\Omega)$, where $\Omega$ is an open set of $\mathbb{R}^n$ with a smooth boundary $\partial\Omega$, and ...
driss-alamilouati's user avatar
-4 votes
1 answer
200 views

How I can choose $(t_1,t_2,...,t_{r}) \in (0,1)^{r}$ such that $f^{(k)}\left(1-2\prod_{j=1}^{k}t_{j}\right)=0$?

Let $f:\mathbb{R} \to \mathbb{R}$ be a real analytic function. Assume that $f$ has simple trivial zeros at each nonpositive integer. Then, all the $k$-th derivatives $f^{(k)}$ of $f$ have necessarily ...
Safwane's user avatar
  • 1,197
-4 votes
1 answer
370 views

Is delta function symmetric against real axis? [closed]

Is $\delta\left(a+bi\right)=\delta\left(a-bi\right)$? I wonder whether Dirac Delta (as defined via Fourier transform) is symmetric against the real axis. We can write Delta function as $$\delta(z) = \...
Anixx's user avatar
  • 10.1k
-4 votes
1 answer
303 views

Reference request in optimal stopping [closed]

I am given the following task. Distributed over a trading day, I am supposed to buy a certain quantity of a good. The price of this good changes during the day. The goal is to buy the required ...
Bettina Kraus's user avatar
-4 votes
1 answer
144 views

Coordinate free computation of the second derivative of a functional [closed]

Let $F(g(f))$ be a functional that sends functions of a vector variable (from $n$-dimensional vector space) to $\mathbb R$. $g$ is some function of scalar valued functions $f$. I'm interested in a ...
Gauge's user avatar
  • 1
-5 votes
1 answer
244 views

Is smooth stack separated?

Let $X$ be a smooth algebraic stack. Is it true that $X$ is separated? I was searching on google but could not find the answer. Please provide a reference.
user avatar
-6 votes
2 answers
2k views

Is there a transformation or a proof for these integrals?

Here are certain weighted Gaussian integrals I have encountered for which numerical computation reassures equality. Question. Is this true? If so, is there an underlying transformation or just a ...
T. Amdeberhan's user avatar
-6 votes
1 answer
180 views

An analog of Anderson's result in C* algebra setting [closed]

Let $\mathcal{A}$ be a unital $C^{*}$-algebra and $S(\mathcal{A})$ denote the states space of $\mathcal{A}$. For $a\in \mathcal{A}$ , define $W(a) =\{\phi(a):\phi\in S(\mathcal{A})\}$ It's known that $...
SoG's user avatar
  • 307
-6 votes
1 answer
488 views

Automorphisms of partitions [closed]

I would like to know whether the notion of automorphism of the set of partitions of a positive integer $n$ has been considered so far or not. To make things clearer, I say that a partition of $n$ in $...
Sylvain JULIEN's user avatar
-8 votes
2 answers
859 views

Homotopy theory and algebraic topology last 10 years. Is it a dying field? [closed]

I'm under the impression that algebraic topology is a dying field in mathematics. That was my impression but I think I'm wrong. As every person I do need some evidence that my impression is not ...

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