This tag is used if a reference is needed in a paper or textbook on a specific result.
0
votes
1answer
21 views
Consistency of Analysis (second order arithmetic)
Is there a proof of the consistency of Analysis (second order arithmetic), which is similar to Gentzen's proof of the consistency of arithmetic?
1
vote
0answers
33 views
unique types and decidability
Suppose $\mathcal{M}$ is an infinite structure which has the property that every type that is realised is realised uniquely. Also assume that every element of $\mathcal{M}$ is definable but there is ...
0
votes
0answers
64 views
Confusion on Manifold
I am studying some basic conceptions on manifold, differential manifold, and Riemannian manifold. For comprehension, I read the information in ...
2
votes
0answers
60 views
Colorful model theory
There are a number of concepts in model theory - often situated around Hrushovski's amalgamation method (see for instance http://math.univ-lyon1.fr/~wagner/nijmegen.pdf) - which are colorfully named:
...
2
votes
0answers
27 views
What do we know about the generlized eigenvalue problem involving a projector?
Consider a matrix $A\in\mathbb{R}^{n\times n}$ and a projector $P\in\mathbb{R}^{n\times n}$.
Are there results regarding the generalized eigenpairs $(v,\lambda)$ of the generalized eigenproblem
...
4
votes
1answer
130 views
Perfect set property implies $\omega_1$ is a limit cardinal in $L$
Specker proved in 1957 that if in $V$ every set of real numbers has the perfect set property, than in $L$, $\omega_1^V$ is actually a limit cardinal.
The original proof is in German, and I've been ...
0
votes
2answers
79 views
Poincaré bundle and Weil pairing for Abelian schemes
In which situations is there a Poincaré bundle for Abelian schemes? In [Mumford, Abelian varieties] only the case of Abelian varieties is treated.
The same question for the Weil pairing ...
0
votes
0answers
14 views
Equivalence of Lp harmonic functions on the ball and a representation by harmonic homogeneous polynomials
In Harmonic function theory there is a theorem which say if $u$ is a harmonic function on $B\left(a,r\right)$, then there exist homogeneous harmonic polynomials $p_{m}$ in $\mathbb{R}^{n}$ such that ...
3
votes
1answer
208 views
Does there exist a function such that $\int_{\mathbb{R}_+^{\star} } t^nf(t)dt=0$? [on hold]
Let $f\in C([a,b],\mathbb{R})$ such that $\displaystyle\int_{a}^{b} t^nf(t)dt=0$ for all integer n.
We know that $f\equiv 0$. It's call Hausdorff theorem.
This theorem is wrong on $\mathbb{R^+}$, a ...
0
votes
0answers
21 views
A solution of the heat equation with Robin boundary condition on a closed interval [migrated]
Suppose $I$ is an interval $[a, b]$. $u(t,x)$ satisfies the following heat equation:
$$ \frac{\partial}{\partial t} u(t,x) =\frac{\partial^{2}}{\partial x^{2}} u(t,x) $$
with boundary condition
$ ...
1
vote
0answers
35 views
Trivial Legendrian deformations defined by infinitesimal Sasakiautomorphisms
I'm reading the paper
Y. Ohnita: On deformation of 3-dimensional certain minimal Legendrian submanifolds, Proceedings of The Thirteenth International Workshop on Differential Geometry and Related ...
4
votes
0answers
44 views
Reference for statement that almost every $n$-element partial order has trivial automorphism group
I'm looking for a reference for the statement that almost every partial order on $n$ elements has trivial automorphism group. I've been told that this is a folklore result. Does anyone know of a ...
7
votes
2answers
179 views
Cokernel of the stable J-homomorphism at odd primes
Where can one learn about odd-primary components of the cokernel of the stable J-homomorphism?
According to wonderful Wikipedia article on Homotopy groups of spheres, the "hard" part of the stable ...
5
votes
0answers
50 views
K-Theory and completion [duplicate]
I vaguely remember the existence of a statement that relates the $K$-theory (in the sense of Quillen) of a noetherian local ring $A$ with maximal ideal $\mathfrak{m}$ with the $K$-theory of the ...
5
votes
0answers
60 views
Classifying two-faces of four-polytopes
Motivation: This question is related to my study of hyperbolic Coxeter polytopes. In general, if one put some restrictions on the type of their dihedral angles (say, all dihedral angles are equal to ...
1
vote
0answers
80 views
Euler class and self-intersection number of a surface in a 4-manifold [duplicate]
In the first two paragraphs of Circle bundles over $CP^1$ and self-intersection number of $CP^1$ embeddings, it is claimed that
For a compact oriented surface $X$ in a 4-dimensional oriented ...
6
votes
1answer
151 views
Renewal systems: Intrinsic ergodicity and a question related to the Adler's conjecture
Consider the alphabet $\mathcal{A} = \{0,1\}$ and consider a finite set of words $W = \{\omega_1, \ldots , \omega_n\}$ over $\mathcal{A}$. Then the renewal system $\Sigma_{W}$ generated by $W$ is ...
5
votes
1answer
85 views
Properties of singularities that are preserved by categorical quotients
Let $G$ be a reductive group acting on an affine singular
variety $X$, and let $X/G$ be the categorical quotient. I know that if
$X$ has rational singularities, then so does $X/G$ ...
4
votes
1answer
131 views
Which hyperbolic tilings are Cayley graphs?
I realise the question is easy but after asking to a few people (and never getting a clear answer), I thought it could be instructive to ask it here:
Given a regular tiling of the hyperbolic plane is ...
3
votes
1answer
205 views
Flow of an integer
I've stumbled across this family of flow networks, and posted the sequence of maximal flows to OEIS. It doesn't appear at this time. I can't find any reference to it either. Has anyone seen it?
...
1
vote
1answer
46 views
reference request: Riesz/Newton potential and HLS inequality in L1.logL1
Let's consider in dimension $d\geq 3$ the Newton/riesz potential $f=I_2[g]$
$$
f(x)=\int_{R^d}\frac{1}{|x-y|^{d-2}}g(y)dy,
$$
which solves $-\Delta f=g$ (up to positive normalizing constants, which I ...
10
votes
0answers
126 views
Entropy in elimination theory, or a brief remark by Gelfand-Kapranov-Zelevinsky
In the introduction to their book "Discriminants, resultants and multidimensional determinant", the authors state a very intriguing observation concerning the coefficients of monomials appearing in ...
2
votes
1answer
83 views
Pullback of $L^p$ functions via exponential map
Let $M$ be a complete Riemannian manifold, endowed with its exponential map $\exp: TM \longrightarrow M$. For any $C^k$- function $u$, we get the Pullback
$$ \exp^* u = u \circ \exp$$
which is in ...
13
votes
3answers
1k views
Silly me & Van der Waerden conjecture
So I walked into this very innocent-looking combinatorics problem,
and quite soon I ended up with the problem to prove that any doubly stochastic $n \times n$ matrix has a non-zero permanent.
Now ...
3
votes
2answers
394 views
An identity in an arbitrary commutative ring
This fact might be either trivial, wrong, or well known.
Let $R$ be a commutative ring. Let $u_1,\dots,u_{s-1},u_s\in R$ and $m,M\in R$. Let us assume that $m,M$ satisfy
$$(m-u_1) \dots ...
2
votes
1answer
179 views
Forcing Notions with Unknown Real/Cardinal Preserving Situations
Question. Is there any set forcing notion $\mathbb{P}$ in one of the following categories?
(a) $\mathbb{P}$ preserves cardinals but it is still open whether $\mathbb{P}$ adds reals or not.
(b) ...
2
votes
1answer
59 views
Extendability of $L^{p}$ harmonic functions
Let $u$ be a harmonic function on some open set $\Omega\subset\mathbb{R}^{n}$ and $u\in L^{p}\left(\Omega\right)$. Is there any reference on extending $u$ to harmonic function on a larger open set ...
4
votes
1answer
172 views
Is Van der Waerden's function elementary
Van der Waerden's function was proved to have elementary upper bound on growth rate.
Is the Van der Waerden's function itself elementary in the sense of Kalmar?
3
votes
1answer
148 views
Higher dimensional analogue of Thue's equation
The classical Thue equation is
$$\displaystyle F(x,y) = h,$$
for a binary form $F(x,y) \in \mathbb{Z}[x,y]$. Recall that a binary form is a polynomial in two variables which is homogeneous, and $h$ ...
3
votes
1answer
88 views
The spectral radius of a modified graph
Let $H$ be a graph and let $G=H \vee K_{1}$ be obtained by creating a new vertex and joining it to every vertex in $H$.
This situation has many different names: $G$ is called the cone or the ...
5
votes
3answers
186 views
A weak-mixing, zero entropy measure on the 2-shift which gives equal weight to both symbols
I am currently sketching a paper in the general area of symbolic dynamics in which I would like to be able to use the following fact:
Proposition (proposed): there exists a shift-invariant ...
3
votes
1answer
101 views
Reference to definition of matrix log with domain SO(3) which is Borel measurable
I was trying to set up an inverse to matrix exponential $\exp:\mathrm{Skew}(3\times 3)\to SO(3)$ that "covers" the biggest possible domain and is Borel measurable. I was wondering if there is a ...
8
votes
0answers
126 views
Obtaining a lightface pointclass from a boldface one
Define a pointclass to be:
boldface inductive-like if it is $\mathbb{R}$-parameterized, has the scale property, and is closed under $\wedge$, $\vee$, $\forall^\mathbb{R}$, $\exists^\mathbb{R}$, and ...
5
votes
1answer
161 views
1-Wasserstein distance between two multivariate normal
The $p$-Wasserstein between two measures $\nu_1$ and $\nu_2$ on $X$ is given by
...
1
vote
0answers
55 views
Is there any study on limit sets arising from “outside” of the hyperbolic geometry?
In the projective model, hyperbolic spaces are modeled by the interior of the light cone of Lorentz spaces. Kleinian groups are isometries of the hyperbolic space, and they centainly also act on the ...
1
vote
1answer
70 views
L logL space and compactness
I think that if a sequence of L^1 functions have the integral
$$
\int f_n \log (f_n)dx
$$
uniformly bounded, then there is a subsequence that converges strongly in $L^1$.
The questions are:
1) Is ...
3
votes
0answers
63 views
Question about a length inequality in algebraic dynamics
Let $X$ be a Noetherian scheme. Let $f\colon X\rightarrow X$ be an integral self-morphism. If $x\in X$ is a closed point, I will write $\mathcal{F}_{1}^x$ for the coherent sheaf of ...
5
votes
1answer
264 views
Integer numbers of the form $m = x^n + y^n$
First of all, I am no number theorist, so this question may be a little dummy.
The two squares theorem imply that $m = x^2 + y^2$ for some (possible zero) integer numbers $x,y$ iff $m$ factors as $m ...
3
votes
3answers
297 views
Estimating a sum involving binomial coefficients [refined]
Having some work done, here is a refined version of my initial question.
For integer $m>0$ and $0\le q\le m$, consider the sum
$$ S(m,q) = \sum_{i=0}^{m-q} \binom{m}{i} \binom{m-i}{q}^2. $$
I ...
3
votes
1answer
167 views
Tor dimension in polynomial rings over Artin rings
I found this tricky problem in trying to understand some properties of local rings at non-smooth points of embedded curves. But this would be a very long story. So I make it short and I try to go ...
-1
votes
0answers
152 views
What happens if mathematics is inconsistent? [duplicate]
It is possible to prove $\neg Con(ZFC)$ within ZFC.
I am searching for references about the mathematical and non-mathematical consequences of this possible theorem. Particularly papers or lectures ...
9
votes
2answers
328 views
Historical quotation search: Equations/formulae in (Latin?) prose, before modern symbolic notation
I have been trying, without success, to find a vaguely-remembered quotation: the quadratic equation (or perhaps the quadratic formula), given in (Latin?) prose, along lines like “Consider that ...
5
votes
1answer
84 views
Reference request: embedding the hyperbolic triangulation in $\mathbb{R}^3$
Let $T_d$ be the infinite valence $d$ triangulation of the hyperbolic plane, where each triangle is equilateral and $d \ge 7$. Question: Is there an isometric embedding from $T_d \to \mathbb{R}^3$? ...
2
votes
1answer
74 views
Reproducing kernels and equivalent inner products
Suppose $H$ is a reproducing kernel Hilbert space and $K_{1}\left(x,\cdot\right)$ and $K_{2}\left(x,\cdot\right)$ two reproducing kernels with respect to two equivalent inner products on this space. ...
1
vote
2answers
166 views
Double Density Theorem?
A colleague asks me the following: "I wonder if you can give me a reference - or a guidance where to look – from a fact I recall from graduate school. I’m sure it can be generalized quite a bit but ...
1
vote
1answer
56 views
Reference to complete derivation of Kossakowski–Lindblad equation and its steady solutions
Are there recommended textbook or good intro-reference to explain with complete stretch of Kossakowski–Lindblad equation especially how is the idea to derive it from ground?
...
0
votes
0answers
12 views
References for Bayesian change point magnitude estimation [migrated]
This paper by Adams and MacKay provides a computationally efficient algorithm for the online estimation of change points in a data sequence. I am looking for similar material that estimates not only ...
7
votes
0answers
211 views
Reference for invariance of essential spectrum under relatively compact perturbations
I'm looking for a proof of the following statement:
Let $X$ be a Banach space and $T$ be a closed map on $X$. For any relatively compact map $A$ the essential spectrum of $T$ and $T+A$ are the same.
...
-3
votes
1answer
233 views
Algebraic Geometry: Question on terminology [closed]
What is a quadric surface of balanced bi-degree? Do you know of a good reference on this topic?
Thanks in advance for your replies.
4
votes
1answer
160 views
Boundaries of relatively hyperbolic groups
When the interior of an n-manifold $M$ has a pinched negative curvature metric of finite volume, then its fundamental group $\Gamma=\pi_1M$ is relatively hyperbolic relative to the parabolic groups ...
