Unanswered Questions
49,209 questions with no upvoted or accepted answers
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votes
1
answer
267
views
To what equal constant in the Gibbs lemma
The Gibbs lemma is broadly used in games theory and in mathematical economics (optimal distributions of resourses, Cournot competition e.t.c.). Here it is:
Lemma (Gibbs). $f_1,f_2,\ldots,f_n$ be ...
- 1,329
-1
votes
1
answer
130
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How to recover the ideal from grobner basis of kernel of ann(x)
M -> ann(x)
i can find the grobner basis of kernel of ann(x) and need the final step to recover this basis to ideal
as i know, eliminate is not for all cases, what is the general practice to treat ...
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-1
votes
2
answers
155
views
What is the likehood function in the noise free observation case
In the nonlinear Bayesian Tracking problem, if we consider the noise exists only in the state equation : x[k] = f(x[k-1],v[k-1]) where vk-1 here is an iid process noise sequence
And we suppose that ...
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-1
votes
1
answer
676
views
does equi-integrability implies uniform convergence?
A collection $\{f_n\}$ of real valued functions is said to be HK-equi-integrable on $I=[a,b]$, if there exists a gauge $\delta$ on $I$ such that for every $\epsilon>0$, there exists a $\delta$-fine ...
-1
votes
1
answer
421
views
linear versus non-linear integral equations
I'm having trouble solving an integral equation. It appears to me to be a homogenous fredholm equation of the second kind. However, I'm being told that this can't be a fredholm equation, because it ...
- 111
-1
votes
1
answer
191
views
Floquet tranform of the derivative of a function $f(r)$
The derivative of the Floquet transform equals the Floquet tranform of the derivative.
But can the Floquet tranform of the derivative of a function $f(r)$ can be expressed in terms of the Floquet ...
- 1
-1
votes
1
answer
694
views
Isometric embedding of 1-manifold
Suppose the unit circle $\gamma$ in $R^2$ is not endowed with the canonical
inner product of $R^2$. Let the riemannian metric defined be
$g:=[2, 1;1, 1]$. So the length is measured with this metric ...
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-1
votes
1
answer
333
views
Quantum cohomology of isomorphic Poisson varieties
This question is related with my previous one Quantum cohomology rings as invariants, but now, I want to ask a more concrete thing. If $X$ and $Y$ are Poisson varieties which are isomorphic (as a ...
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-1
votes
1
answer
537
views
Relative flatness
Can someone me say if this (perhaps obvious!) claim is true:
let $f:X\rightarrow S$ be an open, surjective morphism of complex spaces reduced or without embedded components and with $n$-pure ...
- 435
-1
votes
1
answer
265
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About sufficient condition for smoothness
Dear Brian.
The dimension 1 case is very special. We assume $X$ no compact (Stein if we want), normal and of dimension >1...
In fact, i want to prove the following:
Let $f:X\rightarrow S$ be an ...
- 435
-1
votes
1
answer
243
views
Inversion shift of a Galois radius
Say a non negative $r$ is a Galois radius of $n$ of type $(a,b)$ if $n-r=p^a$ and $n+r=q^b$ with $p$ and $q$ prime and positive $a$ and $b$. If $a\neq b$, say $r$ is "unbalanced" and say $s$ ...
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-1
votes
1
answer
383
views
On the permanent dominance conjecture for symmetric group
The Lieb's permanent dominance conjecture states that the expression $$\frac{d_{\chi}^HA}{\chi(e)}\le per(A)$$ holds for all positive semidefinite matrices $A$, where $d_{\chi}^HA=\sum_\limits{\sigma\...
- 2,089
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votes
1
answer
143
views
Help with notations from 2D to 3D FFT representations as 1D FFT
I have this question on mathematics forum too, Notations, I thought of posting here, which ever place I get an answer, I will try to close it in the other.
I need some help and clarifications for my ...
- 105
-1
votes
1
answer
446
views
What is wrong with the argument that zero permanent is polynomial?
This Lecture summarizes some well known facts about $\#P$ completeness of permanent.
Given a CNF formula $\phi$ on $n$ variables, they construct
matrix $A$ such that:
$$perm(A)=4^{3m} \#SAT(\phi)$$
...
- 25.4k
-1
votes
1
answer
474
views
How to prove completness of my axioms for Wumpus world game
I have an implementation of Wumpus world game with some specific rules. Basically, you are an agent which does not see adjacent tiles. There are pits and exactly one wumpus. Moving into pit or tile ...
- 1
-1
votes
1
answer
259
views
Pure Quotient and pure sub-object
Let $\mathcal{C}$ be the category of modules over a ring.
Let also $\mathcal{F}$ be a class of objects in $\mathcal C$ closed under pure subobject (pure quotient) and direct limit. Is $\mathcal{F}$ ...
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-1
votes
1
answer
129
views
How to compute the expectation of $\frac{Y^L}{Y^L + (N-Y)^L}$ where Y is Binomial(n,p)
How to compute the expectation of $\frac{Y^L}{Y^L + (N-Y)^L}$ where $Y$ is Binomial(n,p)? If it is not exactly computable, then are their ways to approximate this qty?
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votes
0
answers
27
views
Convergence of $ \vec{x_{n+1}} = A^{-1} f(\vec{x_{n}},\vec{y_{n}}), \:\:\: \vec{y_{n+1}} = A^{-1} g(\vec{x_{n}},\vec{y_{n}}) $
I have two systems
$$ A \vec{x} = f(\vec{x}, \vec{y}), \:\:\: A \vec{y} = g(\vec{x}, \vec{y}) $$
Both have the same constant, square, invertible matrix $A$. I implemented an iterative algorithm with ...
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votes
0
answers
54
views
Density of squared bessel process
I was trying to find a transition density function for a squared Bessel process. In the book "Continuous martingale and Brownian motion" by Revuz and Yor, I find a Corollary on page 441 that ...
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votes
0
answers
64
views
A Problem using Limits of Sequences of Functions
Suppose $\{f_n\}$ is a sequence of nonnegative extended real-valued functions on $X$ and $\lim_{n\to\infty}f_n=f$. Take a simple function $0\leq\varphi\leq f$. If $X_{\infty}=\{x\in X: \varphi(x)=a>...
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-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. ...
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-2
votes
1
answer
183
views
Property of positive semi-definite
Let $A$ is a positive semi-definite matrix like this:
$$ A = \begin{bmatrix}
1 & \alpha_{1,2} & \alpha_{1,3} & \alpha_{1,4}\\
\alpha_{1,2} & 1 & \alpha_{2,3} & \alpha_{2,4}\\
\...
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-2
votes
1
answer
159
views
Can having no more than countably many classes, be inferred from, having every class being countable?
In a theory having proper classes it won't be that easy to phrase how many classes we have in comparison to the number of elements of some class. Here, I'll adopt the following method:
We'd say that: ...
- 11.3k
-2
votes
1
answer
118
views
In which cases $E(e^{t S_n S_m})$ converges to $E(e^{t X Y})$
Suppose that $S_n$ and $S_m$ are two random binomial variables, which are independent and with the same distribution parameter $p$. I am wondering, in which cases $E(e^{t S_n S_m})$ converges to $E(e^...
-2
votes
1
answer
138
views
Problem arising from martingale solutions to SPDE: $Law(u)=Law(v)$ on $C([0,T]; X)$, can $Law(u)=Law(v)$ on $C([0,t]; X)$ for $t<T$?
I ask this question because I found in some papers of martingale solutions to SPDE, to prove the approximate solutions $u_n$ is a convergent sequence, one can use "stochastic compact" method to find ...
-2
votes
1
answer
174
views
What is known about iterated matching as a TSP heuristic
A fairly wellknown heuristic for TSP that is based on matching is described in the 2003 paper Match twice and stitch: a new TSP tour construction heuristic by Andrew B. Kahng and Sherief Reda.
Its ...
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-2
votes
1
answer
209
views
Strong estimates for the zeta function on natural numbers
Let $$\zeta(s) = \sum_{n = 1}^\infty \frac{1}{n^s}$$
be the Riemann zeta function (here we just consider real $s$).
We do have a description given by
$$\zeta(s) = \frac{s}{s-1}-s\int_{1}^\infty \frac{...
- 749
-2
votes
1
answer
187
views
behavior of multiplicity in exact sequences
Bruns-Herzog define multiplicity When the ring and module are not necessarily graded as $e(M)=e(gr_m(M))$, see B-H 4.6. I have two questions:
Question1. Many concepts in commutative algebra have ...
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votes
1
answer
871
views
Rank of a random matrix
Let $x$ a random Gaussian vector of size $n$ with i.i.d coefficients $N(0,1)$. Let $J$ a random matrix with i.i.d coefficients $N(0,\sigma^2/n)$ where $\sigma \in [0,1]$. For any integer T>n, define:
$...
- 840
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votes
1
answer
332
views
A kind of economic objective function in assignment
I recently thought about a concept that seems like it should come up in economics, but I don't know if there's a name for it and where people would have encountered it elsewhere: Suppose we have a ...
-2
votes
1
answer
205
views
Are there infinitely many karmic numbers, i.e numbers whose primality radii equal one or a prime power?
For $n$ a large enough positive composite integer, say $r$ is a primality radius of $n$ if both $n-r$ and $n+r$ are prime. Say $n$ is a karmic number if the following holds: $r$ is a primality radius ...
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votes
1
answer
185
views
What do you call continous transformations that preserve the finite group structure?
A number of years ago I studied a preon model (Journal of Mathematical Physics 38:3414-3426, 1997) in which the preons interacted like group elements. I thought it curious that you could sometimes ...
-2
votes
1
answer
210
views
class structure constants relation
Let $C_{j,k}^l$ ,usually called class structure constants, eg Jansen and Boon and/or JQ Chen, be the number of times the class $l$ is generated from the product of classes $j,k$ and $c_j=c_{-j}$ (a ...
-2
votes
1
answer
151
views
Quadratic extension and prime ideals
Let $B/A$ be a quadratic Galois extension between local domains. Define ${\mathrm{Gal}}(B/A) = \{e,\sigma\}$.
Choose two prime ideals ${\frak P}_1, {\frak P}_2$ of $B$ such that ${\frak P}_2 = {\...
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votes
0
answers
28
views
Convergence of measures in the Lévy–Prokhorov metric and weak convergence of measures
How to prove that over R the convergence of measures in the Levi-Prokhorov metric is equivalent to the weak convergence of measures
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-3
votes
0
answers
75
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 ...
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votes
0
answers
157
views
A presentation for the group $GL(n,\mathbb{Z}_p)$
Let $n\ge 2$. Let $p$ be a prime and $\mathbb{Z}_p$ denote the finite field with $p$ elements.
I want to know about the presentation for the group $GL(n,\mathbb{Z}_p)$ consisting of its generators and ...
- 103
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votes
0
answers
73
views
Is the upper bound on $H_{1}$ a decreasing function of the proportion of critical zeros of Zeta?
This question stems from https://arxiv.org/abs/2411.19762 and the numerical observation that the best unconditional upper bound for $H_{1}:=\lim\inf_{n\to\infty}p_{n+1}-p_{n}$, namely $H_{1}^{\flat}=...
- 6,984
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votes
0
answers
143
views
Divisors of n and n + 1
Suppose $a$ is a proper divisor of $n$ (where $n$ is a positive integer), and $b$ a proper divisor of $n + 1$.
Is there a general criterion (or general property of $n$) which enables one to conclude ...
- 4,547
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votes
0
answers
137
views
Approximation on Dirichlet's arithmetic progression by means of central limit theorem
In this video lecture on
Number theory over function fields taught by Will Sawin
is presented a 'conceptional' reason for error estimation
$\#\{p \in \Bbb P: p =a \ \text{mod} \ N, p <x \}
=\frac{1}...
- 619
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votes
1
answer
162
views
Amenable non-Hausdorff groupoids
Is there any clear definition of amenable non Hausdorff groupoids? It should be possibly non-separable nuclear C*-algebras? Please let me know if there is any existing literature talking about this.
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votes
1
answer
130
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Equation $p\cdot q\cdot r=a^3-1+43\cdot (b^2-1)$
$p\cdot q\cdot r=a^3-1+43\cdot (b^2-1)$
p, q, r are primes.
a, b integers>0.
Is this equation a Mordell equation?
Has this equation infinitely many solutions?
-3
votes
1
answer
141
views
Approximate martingales by truncation
Let $(X,Y)$ be a $\mathbb R-$valued martingale. For any $\varepsilon>0$, is it possible to find another martingale $(X',Y')$ s.t. $X'$ and $Y'$ are supported on a compact set, and
$$
\mathbb E\big[\...
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votes
1
answer
270
views
Relationship of eigenvalue/eigenvector of hermitian matrix R and QRQ (Q is diagonal)
For a hermitian matrix R and a diagonal one Q, is there any relationship between eigenvalues/eigenvectors of R and QRQ?
To be specific, assuming the eigenvalue decomposition of R is R=VDV*, then can ...
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votes
0
answers
62
views
Is the real and imaginary part of the Dirichlet eta function closest to its partial sums when trigonometric function changes signs?
To grasp the question we are concerned with three Theorems 1,2, and 3 in bold font below. First let us consider the Dirichlet eta function $\eta: \mathbb{C}\rightarrow \mathbb{R}$
$$
\eta(s) = \sum_{n=...
-4
votes
0
answers
135
views
Which arithmetic\set theory is synonymous with this theory?
$\textbf{Logic:}$ Mono-sorted first order logic with equality.
$\textbf{Extralogical Primitives: } <, \in$
Define: $x > y \iff y < x$
Define: $x \leq y \iff x < y \lor x=y$
$ \textbf{...
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votes
0
answers
189
views
Can ZFC be interpreted in this infinitary logic theory?
Working in language $\mathcal L_{\Omega^+,\Omega^+}$ where $\Omega$ is the first strongly inaccessible cardinal. If we add a primitive partial $\Omega$-ary function $F$ and a primitive constant $\...
- 11.3k
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votes
0
answers
52
views
In surreal numbers, why log-atomic numbers are not EL-numbers?
In surreal numbers, the log-atomic numbers are those numbers that can be obtained from $\omega$ and its powers via iterated logarithm or exponential function.
At the same time, Timothy Chow's EL-...
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votes
1
answer
302
views
A Question in Fourier Analysis proposing a conjecture
Let $f$ be a $2\pi$ periodic BV function whose derivative is also BV.Let the amount of jump at a point $x$ is denoted as $\lfloor f \rfloor (x) = f(x+0)-f(x-0)$ Define function $J:\mathbb{R} \to\...
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votes
1
answer
175
views
Charpit's method and a nonlinear PDE
I have the nonlinear PDE
$$p^2 + 2q = x$$
with the initial condition $u(0, y) = -y^2$, and $y > 0$.
Here's what I have done so far:
I defined the function $F$ to be equal
$$F(x, y, p, q, u) = p^2 + ...
