All Questions
23,892 questions
2
votes
1
answer
427
views
Logic which depends on the perspective? (Semantic space of logic / perspectivism)
I am not sure if this question is appropriate for MO, since I have only a basic understanding of Boolean logic, and am maybe not qualified to ask questions beyond that, but still I will try to write ...
CommunityBot
- 1
1
vote
1
answer
141
views
Understanding quadrature rule of a function multiplied by another $C^{\infty}$ function
Define a function $f \in C^m[-1,1],m \in \mathbb{N}$ and $g\in C^{\infty}[-1,1]$. Also define a quadrature rule $Q$ for approximating the integral $\int_{-1}^1 h(x)dx$ for some function integrable ...
- 69
11
votes
1
answer
883
views
Which paper is the "Taubes trick" from?
In symplectic geometry, the "Taubes trick" is an argument used to show that a moduli space $\mathcal{M}(J)$, depending on a parameter $J \in \mathcal{J}$, is cut out transversely for generic ...
- 188k
6
votes
2
answers
358
views
Transfer model structures, reflective subcategories and Bousfield localizations
The topic of Bousfield localizations has a lot of literature which has on most of the occasion some tameness assumption on the presentability of the model category. Recently I have been trying to ...
- 40.2k
3
votes
0
answers
101
views
Tuple rearrangement: a combinatoric problem emerging from the Hurwitz action on Coxeter groups
I am working on Artin Groups, so called Dual Artin groups and the conjecture that they are isomorphic. Tuples of $n$ group elements can be acted on by the braid group $B_n$ in a particular way called ...
- 31
10
votes
1
answer
314
views
Weakly metrizable sets in normed spaces
A similar question was asked on MSE without getting an answer.
In the proof of lemma 1.2 of Asplund operators and holomorphic maps the author (my attempt to contact him failed because the only e-mail ...
- 60.5k
4
votes
2
answers
389
views
Gaussian mixtures are dense in total variation?
Let $M_{TV}(\mathbb{R}^d)$ denote the set of probability measures on $\mathbb{R}^d$ with finite total variation norm which are absolutely continuous with respect to the Lebesgue measure.
By a Gaussian ...
- 128k
21
votes
1
answer
2k
views
Characterization of Fréchet-Urysohn spaces using sequential continuity at a point
A map $f \colon X \to Y$ is called sequentially continuous at the point $a$ if for every sequence $(x_n)$ such that $x_n\to a$, we also have $f(x_n)\to f(a)$.
$$x_n\to a \qquad \Rightarrow \qquad f(...
- 21
2
votes
0
answers
76
views
Does a matrix ring over a ring satisfy the Koethe conjecture if the coefficient ring itself satisfies the Koethe conjecture?
I just want to know whether the following statement is true or false.
If $R$ is a ring satisfying the Koethe conjecture, then the matrix ring over $R$ also satisfies the Koethe conjecture.
Or is it ...
- 12.9k
12
votes
3
answers
16k
views
Dual space of $\ell^\infty$
Why can the elements of the dual space of $\ell^\infty(\mathbb N)$ be represented as sums of elements of $\ell^1(\mathbb N)$ and Null$(c_0)$?
<hr:
EDIT: As confirmed in the comments, the OP ...
- 4,713
2
votes
1
answer
300
views
G-equivariant homotopy between G-spaces
I apologize for asking too many questions in a single post. I am not very conversant with equivariant homotopy theory. While discussing with some faculty I was told that certain fact is true. All ...
- 11.1k
1
vote
1
answer
278
views
Moduli space of complex and anti-complex tori?
$\DeclareMathOperator\GL{GL}\DeclareMathOperator\SO{SO}\DeclareMathOperator\SL{SL}$By Will Sawin's answer to Moduli Spaces of Higher Dimensional Complex Tori the moduli space of complex $d$-tori is $X ...
CommunityBot
- 1
4
votes
0
answers
128
views
Errata for "Foliations and Geometric Structures" by Aurel Bejancu and Hani Reda Farran
I'm reading "Foliations and Geometric Structures" (2006) by Aurel Bejancu and Hani Reda Farran and have been looking for an errata sheet. Unfortunately Prof. Bejancu has passed away. I ...
- 12.9k
1
vote
0
answers
104
views
Commutative Banach $\mathbb{R}$-algebras without complex structure, but with path-connected group of units
For a finite-dimensional commutative (associative, unital) $\mathbb{R}$-algebra $A$, the condition $\pi_0(A^\times) = 1$ (i.e. the group of units of $A$ being path-connected) is equivalent to $A$ ...
- 7,127
4
votes
1
answer
311
views
Conormal distributions and the wave front set
Let $X$ be a smooth closed manifold and $Y$ a regular submanifold. For all conormal distributions at $Y$ on $X$, their wave front set is contained in the conormal bundle of $Y$. Is the reciprocal true?...
CommunityBot
- 1
9
votes
1
answer
304
views
About the normal subgroups of Burnside groups
I was reading "On periodic groups of odd period $n\ge 1003$" of V. S. Atabekyan. He found that the Burnside group $B_n$ with $n\ge 1003$ has uncountably many normal subgroups. However, I was ...
- 63.9k
12
votes
2
answers
1k
views
Dihedral extensions and the Ankeny–Artin–Chowla conjecture
Jensen and Yui (Polynomials with $D_p$ as Galois group
J. Number Theory 15, 347–375 (1982)) proved that if $p = 4n+1$
is a regular prime, then there is no normal extension of the
rationals with Galois ...
- 12.9k
2
votes
1
answer
93
views
Reference needed: estimate of the second order derivatives
In $\mathbb{R}^d$ there is estimate (see 1.3, Chapter III of E.M.Stein' book Singular Integrals and Differentiability Properties of Functions)
$$\left\|\frac{\partial^2 f}{\partial x_i \partial x_j} \...
- 457
6
votes
1
answer
237
views
Resource on how the definitions of subobjects for various categories can vary
I am looking for a reference on the different possible definitions of subobjects. According to a particular friend of mine, subobjects should be at least monomorphisms (up to slice isomorphism) and at ...
- 63.1k
4
votes
1
answer
239
views
True or false? Every left or right cancellative, duo semigroup is cancellative
A semigroup $S$ is duo if $aS = Sa$ for all $a \in S$, where $aS := \{ax: x \in S\}$ and similarly for $Sa$; for instance, every commutative semigroup is duo, and so is every group. On the other hand, ...
- 10.5k
0
votes
0
answers
66
views
Taking trace of a tensor product of matrix-valued smooth functions on the thin diagonal
Let $V$ be a finite dimensional real / complex vector space and consider the space $L(V,V)$ of linear operators on $V$.
Fix $n \in \mathbb{N}$ and let $\mathcal{M}$ be the real / complex vector space ...
- 3,477
1
vote
0
answers
71
views
Integral formula of quantum dilogarithm
In the paper"Level N Teichmüller TQFT and Complex Chern-Simons Theory" arXiv:1612.06986, the authors study the quantum dilogarithm function:
\begin{equation}
\mathrm{D}_{\rm b}(x,n)=\prod_{...
- 109
3
votes
0
answers
122
views
Analytic functions and Hyperfunction as TVS
I have several related questions on Analytic functions and Hyperfunction as topological vector spaces (I am mainly interested in questions 4,6,10):
For an open set $U\subset \mathbb C^n$ we can ...
- 2,649
3
votes
0
answers
74
views
Reference for PDEs from system of SDEs
I'm working with a system of SDEs
\begin{align*}
dX_t &= b(X_t, t) + \sigma dB_t\\
dY_t &= c(X_t, Y_t, t) + \sigma dB_t.
\end{align*}
Here, the Brownian motion is the same.
I know that ...
- 869
42
votes
5
answers
14k
views
The unproved formulas of Ramanujan
Are there any formulas due to Ramanujan that have still not been proved—or disproved?
If so, what are they?
I believe this conjecture is due to Ramanujan and still open: if $x$ is a real number and $2^...
- 2,858
0
votes
0
answers
105
views
Generalizing the property of linear independent set in infinite dimensional TVS
Given a infinite dimensional Hilbert space $H$, and a countable set of vectors $\{v_{i}\}_{i=1}^{\infty}$. I want to study the following property of $\{v_{i}\}_{i=1}^{\infty}$:
There exists sequences $...
- 523
4
votes
2
answers
489
views
Mapping between Notations
$\DeclareMathOperator{\address}{address}$
As in my other question, it is assumed that the (total) function describing a given notation is denoted as $\address:p \rightarrow \Bbb{N}$ and assumed to be ...
- 6,367
2
votes
1
answer
404
views
Reference request: a cousin to the log semiring
Let $f$ be strictly increasing on $\mathbb{R}$. Then $x \oplus y := f^{-1}(f(x)+f(y))$ gives rise to a strict symmetric monoidal ($\Rightarrow$ commutative monoid) structure on $(\mathbb{R},\ge)$ with ...
CommunityBot
- 1
5
votes
0
answers
112
views
Finitely generated projective modules over Noetherian endomorphism ring
Let $\mathcal A$ be a locally Noetherian Grothendieck abelian category and $M\in \mathcal A$ be a Noetherian object. Set $B:=\text{End}_{\mathcal A}(M)$. Let $B$-mod be the category of finitely ...
- 413
5
votes
1
answer
212
views
Stability of ODEs with polynomial nonlinearity
Consider the following ODE system:
$$
x′=f(x)\iff
\begin{pmatrix}
x_1^\prime \\
\vdots\\
x_k^\prime\\
\vdots\\
x_n ^\prime
\end{pmatrix} =
\begin{pmatrix}
f_1(x) \\
\vdots\\
f_k(x)\\
\vdots\\
f_n(x)
\...
- 141
2
votes
2
answers
323
views
Reference request on computational schemes for $\inf_{x\in\Omega^n}\sup_{y\in\mathbb R^n}F(x,y)$
Let $\Omega\subset \mathbb R^d$ be compact, $\rho$ be a density function on $\Omega$ and $p_1,\ldots, p_n\in (0,1)$ be weights satisfying $\int_{\Omega}\rho(z)dz=1=\sum_{k=1}^n p_k$. We consider the ...
CommunityBot
- 1
13
votes
3
answers
3k
views
Koebe–Andreev–Thurston theorem - where can I find a proof?
Koebe–Andreev–Thurston theorem (known also as the circle packing theorem) says that any planar graph can be realized by a set of (interior-) disjoint disks corresponding to vertices, such that two ...
- 13.6k
3
votes
0
answers
267
views
Cohomology for quantum groups
I'm interested in quantum groups for two perspectives:
Compact quantum groups in the sense of Woronowicz.
Deformation of the universal enveloping algebra of a Lie algebra in the sense of Drinfeld &...
- 357
9
votes
0
answers
163
views
Moore-Penrose partial isometries and hermitian elements
Let $A$ be a unital Banach algebra. An element $a \in A$ is hermitian if $\|\mathrm{exp}(ita)\|=1$ for every $t \in \mathbb{R}$. An element $a \in A$ is Moore-Penrose invertible if there exists $b \in ...
- 3,497
11
votes
3
answers
671
views
Merging single-sorted and multi-sorted theories
The general theory of single-sorted (say, algebraic) theories is very similar to the general theory of multi-sorted (algebraic) theories. Each variable gets a sort, but apart from that nothing really ...
- 66.8k
3
votes
1
answer
370
views
Is Brascamp-Lieb inequality on the sphere applicable for these functions for some $1\leq p<2$
My question is on Brascamp-Lieb-inequality on the Euclidean sphere (which can be viewed as an analogue of Young's inequality on the sphere) obtained in [1].
(See also this question:
Brascamp-Lieb ...
- 852
1
vote
1
answer
100
views
Is Nelson-Symanzik positivity compatible with fermionic statistics?
Let $\{ S_n \}_{n =0}^\infty$ be a sequence of tempered distributions where $S_n \in \mathcal{S}'(\mathbb{R}^{nd})$ where $d \in \{2,3,4\}$ is fixed. Moreover, we put three additional conditions:
$...
0
votes
1
answer
126
views
Integral involving Bessel function and Laguerre polynomial for a Hankel transform
I'm attempting to solve the Hankel transform
\begin{align}
\int_0^\infty x^\alpha e^{-x^2/2} L_n^\nu(x^2) J_\nu(x p) \sqrt{x p} \, dx
\end{align}
or the unmodified version (redefining $\alpha$)
\begin{...
CommunityBot
- 1
8
votes
1
answer
634
views
Availability of a copy the first volume of Segre's "Forme differenziali e loro integrali"
I am precisely referring to the following, first volume of the textbook/lecture notes/monograph written by Beniamino Segre in the fifties of the twentieth century (I own a copy of the second volume)
...
- 188k
3
votes
1
answer
91
views
Conditional Expectation in Diffusion Process
Consider a $d$-dimensional diffusion process $\mathbf{X}=(\mathbf{X}_t)_{t\in [0,T]}=([X^1_t,...,X^d_t])_{t\in [0,T]}$ that is the unique strong solution of the following SDE:
$$\left\{\begin{matrix}
...
- 6,215
3
votes
1
answer
202
views
Stability of nonsmooth, Lipschitz continuous, autonomous system of differential equations
Consider the following autonomous system of differential equations:
$$\frac{\mathrm d\mathbf x}{\mathrm dt} = \mathbf v(\mathbf x)$$
where $\mathbf x, \mathbf v \in \mathbb R^n$. Assume that $\...
- 1,724
4
votes
1
answer
242
views
Regular nilpotents and minimal parabolic subalgebras in real semisimple Lie algebras
Let $\mathfrak{g}$ be a real semisimple Lie algebra. A subalgebra $\mathfrak{p}$ of $\mathfrak{g}$ is parabolic if its complexification is parabolic in $\mathfrak{g}_\mathbb{C}$, meaning it contains a ...
CommunityBot
- 1
0
votes
0
answers
33
views
Non-positive definite solution for differential Riccati equation
Consider the matrix-valued differential Riccati equation (DRE):
$$
\dot P_t +PA+A^\top P+Q-(B^\top P+S)^\top (B^\top P+S)=0, \quad t\in [0,T];\quad P(T)=G,
$$
where all coefficients are continuous.
...
- 503
0
votes
0
answers
57
views
Double-periodic functions with (possible) poles
Consider the set of double-periodic function $f:\mathbb C/(\mathbb Z+i \mathbb Z) \setminus \{z_0\} \to \mathbb C$, where $z_0$ is a fixed point inside $\mathbb C/(\mathbb Z+i \mathbb Z),$ that have a ...
1
vote
0
answers
38
views
About Carleson measures on the Hardy space on the bidisc
I have been reading the paper "Carleson Measures in Hardy and Weighted Bergman Spaces of Polydiscs" by F. Jafari and there are a few things that going on that I am not entirely convinced of.
...
2
votes
1
answer
124
views
Choice of the eigenbasis for the Dirac operator on $S^d$
This question is a simplified version of my previous one. I think that adding a gauge potential complicates the problem too much.
Let us consider the Dirac operator $D$ on the $d$-sphere $S^d$ with ...
- 34.7k
1
vote
1
answer
129
views
Is every operator range a Baire space in the relative topology?
Let $X$ be a Banach space and let $U\subseteq X$ be a (not necessarily closed) linear subspace. One says that $U$ is an operator range if there is another Banach space $E$, and a bounded linear map $...
- 16.4k
0
votes
1
answer
414
views
Sufficient conditions for an asymptotic compactness
This question relates a theory of Mosco convergence.
Let $X$ be a compact metric space, and $\mu$ a Borel measure on $X$.
A symmetric bilinear form $(\mathcal{E},\text{Dom}(\mathcal{E}))$ on $L^2(X,\...
CommunityBot
- 1
5
votes
1
answer
202
views
Independent stationary increment process but with finite propagation speed
Intuitively, standard Brownian motion has infinite propagation speed, as it has a non-zero probability of reaching any point in any arbitrarily short time. This is due to the fact that the probability ...
- 128k
1
vote
1
answer
157
views
Is finding the CDF from the Laplace transform well-posed?
In my study of Dynamic Light Scattering, I came across the following inverse problem. Let $F(s):[0,T]\rightarrow[0,T]$ be the Laplace transform of a probability distribution $f(t)$ on the real line ...
- 128k