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What would you do with a new model of linear logic?

I have been working for some time with collaborators developing some models of linear logic which we are confident are new. However, none of us is deep enough in the field to answer the sceptic's ...
Morgan Rogers's user avatar
-3 votes
0 answers
61 views

$a \cos(x) + ib \sin(x)$ reduced to $\cos(x+iy) $form [closed]

As the titled suggests, is there is formula remotely near this expression? $a \cos(x) + ib \sin(x)$ reduced to $\cos(x+iy)$. Contextual basis, I'm required to convert a Laurent polynomial to a trig ...
dereuodeum's user avatar
0 votes
0 answers
53 views

Optimality condition for strongly convex function under sparsity constraint

Let $f: \mathbb{R}^p \to \mathbb{R}$ be a $2s$-sparse strongly smooth, $2s$-sparse strongly convex and twice differentiable function. In other words, there exists positive constants $\alpha, L >0$ ...
De vinci's user avatar
  • 329
0 votes
0 answers
54 views

asymptotic expansions for $C^{1+\epsilon}$operators

I want to understand the asymptotic expansion for $C^{1+\epsilon}$ operators. More precisely, if a complex operator $T(z)=\sum_{n \ge 1}T_n z^n$ is defined on a closed unit disk, and it is $C^{1+\...
user avatar
4 votes
1 answer
188 views

Height of a conductor ideal

We say an extension of Noetherian rings $R\subset S$ is elementary subintegral if $S=R[b]$ for some $b\in S$ with $b^2,b^3\in R$. The conductor ideal is defined to be $\operatorname{Ann}_R(S/R)$. What ...
Varadharajan R's user avatar
7 votes
1 answer
236 views

Some fusion rings/categories I don't recognize

Recently (what I believe are) all multiplicity-free fusion categories up to rank 7 have been posted on the AnyonWiki. Most of the fusion rings belonging to these categories belong to one of the ...
Gert's user avatar
  • 253
9 votes
1 answer
156 views

Matrix ring isomorphisms of different sizes

Do there exist (unital, associative, noncommutative) rings $R$ and $S$, where $\mathbb{M}_2(R)\cong \mathbb{M}_3(S)$, but these matrix rings are not isomorphic to $\mathbb{M}_6(T)$ for any ring $T$?
Pace Nielsen's user avatar
5 votes
0 answers
167 views

Reference request: Automorphisms of $\mathbb C\{x,y\}$ which preserve the equation of the cusp, $x^3 - y^2$

In my research I encountered automorphisms of the ring of convergent power series $$\varphi: \mathbb C\{x,y\} \to \mathbb C\{x,y\},$$ which preserve $f = x^3 - y^2$, i.e. $\varphi(f) = f$. I'm ...
red_trumpet's user avatar
  • 1,061
2 votes
1 answer
83 views

Does a polynomial $P(X,Y)$ that specializes to a polynomial $P(x_0,Y)$ with distinct roots in $\overline{k}$ have distincts roots in $\overline{k(X)}$

Let $k$ be a field, $P\in k[X][Y]$ be a monic polynomial of degree $n$ in $Y$. I am looking for a simple proof of the following fact. "If there exists $x_0\in k$ such that $P(x_0,Y) \in k[Y]$ has ...
Oblomov's user avatar
  • 2,491
2 votes
1 answer
79 views

Is this form of replacement suitable for ZF - Powerset + well-ordering principle?

The following scheme can be understood as a form of replacement. Axiomatizing $\sf ZF$ with it instead of the usual replacement schema renders it immune to removal of extensionality; see here. In an ...
Zuhair Al-Johar's user avatar
2 votes
0 answers
118 views

Question about pro-representable Automorphism functor in Sernesi's "Deformations of algebraic schemes" with trivial relative Tangent space

Let $k$ be an algebraically closed field of arbitrary characteristic, $R$ a complete local noetherian, but non Artinian (see #Edit below for justification) $k$-algebra with residue field $k$ and $S$ a ...
user267839's user avatar
  • 5,786
3 votes
0 answers
183 views

A problem about the series $\sin(n^p)$

Prove that when $p>0,$ the series $$\sum_{n=1}^\infty \sin(n^p)$$ is divergent
adobereader's user avatar
0 votes
0 answers
21 views

Building hypercubes from the bottom up

let $H^k$ denote a $k$-dimensional hypercube in a complete symmetric graph $G(V,E)$ without self-loops and parallel edges; let $|V|=2^n$ be the number of vertices. setting $\mathbb{H}^0 := V$, i.e. ...
Manfred Weis's user avatar
  • 12.6k
1 vote
1 answer
65 views

Convexity property of an equivalent norm on $\ell_2$

Let us consider the space $\ell_2$ with an equivalent norm defined by $$ \Vert x \Vert = \max \{ \Vert x^{'} \Vert_2, \Vert x^{''} \Vert_2 \}, $$ where $x^{'}=(0, x_2, x_3, \cdots)$, $x^{''} = (x_1, 0,...
PPB's user avatar
  • 73
1 vote
0 answers
58 views

Representing geodesic compactifications of $S^1\times \Bbb R$ as analytic sections over base (analytic) foliations

Given a smooth nested set of "partial" foliations $\mathcal F_{\alpha}=\big\lbrace e^{\frac{\alpha}{\log x}}: \alpha \in (1/k,k), x\in(0,1),k\in [1,\infty) \big\rbrace$ of $X^2=(0,1)^2$ with ...
53Demonslayer's user avatar
1 vote
1 answer
94 views

Problem in understanding maximum principle for subharmonic functions

I am reading subharmonic functions and their properties from the book From Holomorphic Functions to Complex Manifolds by Grauert and Fritzsche. Let me first define what a subharmonic function is. ...
Anacardium's user avatar
0 votes
0 answers
73 views

Classification of principally polarized abelian surfaces - reference request

I found in Encyclopedia of math https://encyclopediaofmath.org/wiki/Abelian_surface there is a claim that: "A principally polarized Abelian surface $(A,λ)$ is either the Jacobi variety $J(H)$ of ...
finiteness's user avatar
0 votes
1 answer
27 views

Regular maps on hyperbolic plane for large number of vertices

I want to generate large regular maps of a tiling on hyperbolic space. How I can start doing that?
Zahid Malik's user avatar
0 votes
0 answers
112 views

Noether's formula for real algebraic surfaces

Is there a version of Noether's formula for the Euler characteristic of a surface for Real algebraic surfaces? Specifically, given $X$ a real algebraic compact smooth surface, what is the relationship ...
Serge the Toaster's user avatar
3 votes
0 answers
158 views

What should be unipotent de Rham homotopy group?

What exactly should unipotent $\pi_1^\text{dR}$ be conceptually? What formal properties should it satisfy? This seems to be answered by Chen's theorem, which is stated in Corollary 3.269 of Multiple ...
W. Zhan's user avatar
  • 343
3 votes
0 answers
75 views

Composition of Frobenius $n$-homomorphisms, characteristic-free?

This question is, as so often, a crossbreed of curiosity and laziness. The former has led me to an interesting, but somewhat unsatisfactory paper by Khudaverdian and Voronov (arXiv:2002.02395v2) and, ...
darij grinberg's user avatar
2 votes
0 answers
49 views

Reference request: Fréchet embedding

Given a separable metric space $(X,d)$, we have an isometric embedding $X\to\ell^\infty$ given by taking $x_n$ the countable dense subset and sending $x\mapsto\lvert(x,x_n)-d(x,x_0)\rvert$. This ...
Gesh's user avatar
  • 83
1 vote
0 answers
43 views

Reverse mathematics on lightface $\Pi^1_1$-uniformization for unary relation

It is known that the following form of $\Pi^1_1$-uniformization is equivalent to $\Pi^1_1$-Comprehension over $\mathsf{ATR}_0$ (cf. VI.2.6 of Simpson's book) : (Kondo's uniformization theorem) For ...
Hanul Jeon's user avatar
  • 2,754
2 votes
1 answer
149 views

Estimating ${\left(\sum_{i=j}^k {x_i}\right)^2} \times \left\lvert\sum_{i=j}^k {a_i}\right\rvert$

Given two sets; $X = \{x_i : x_i \geq 0; i \in [\sqrt{n}]\}$ and $A = \{a_i : |a_i| \leq 1; i \in [\sqrt{n}]\}$ of size $n^{\frac{1}{2}}$ each, with the following properties \begin{equation}\label{...
Krish's user avatar
  • 23
2 votes
0 answers
41 views

Perron-Frobenius theory for operators on matrices

Let $A$ be a Hermitian linear operator on the space of $n\times n$ complex matrices. Let's suppose $A$ is "non-negative" in the sense that it preserves the cone of non-negative definite (...
AdamNie's user avatar
  • 53
2 votes
1 answer
74 views

Simple curves on hyperbolic tori

In the paper "Simple curves on hyperbolic tori" by McShane and Rivin, they show that if $T$ is a hyperbolic once punctured torus, one can define a norm on the homology $H_1(T,\mathbb{Z})$ by ...
stupid_question_bot's user avatar
-2 votes
0 answers
96 views

Extending a map between $A$ and $B$ to a map between $L(A)$ and $L(B)$

Are any known results about extending a map $\phi:A\to B$ to a map $\overline{\phi}:L(A)\to L(B)$ or $\phi':HOD(A)\to HOD(B)$? This seems like something that would have been investigated already, and ...
blark's user avatar
  • 97
1 vote
0 answers
66 views

Unique polarization on a very general curve with Mumford-Tate

I try to understand why a very general curve (smooth, projective over $\mathbb{C}$) has an unique polarization up to scalar on the $H^1(X,\mathbb{Q})$. I was advised to look at the maximality of the ...
Christopher Nicol's user avatar
7 votes
0 answers
120 views

Are there any interesting classes of limits containing finite limits?

Let $\Phi$ be a class of limit diagrams that contains all finite diagrams. Some examples include the classes $\Phi_{\kappa}$ of all diagrams of size bounded by a cardinal $\kappa$... but are there any ...
Morgan Rogers's user avatar
-4 votes
0 answers
46 views

Calculate the rotational volume that arises when the area enclosed by the curve 𝑦 = 𝑒^−𝑥^2 and the x-axis can rotate around the y-axis? [closed]

so my question for thiscalculus homework is : Calculate the rotational volume that arises when the area enclosed by the curve 𝑦 = 𝑒^−𝑥^2 and the x-axis can rotate around the y-axis? now am i ...
janedoe's user avatar
1 vote
0 answers
21 views

Multivariate delta method gradient calculation with mixed moments

Here's a slightly simplified version of my problem (using fewer dimensions than what I'm actually solving). Take $X \in \mathbb{R}^2$. We already know that $\sqrt{n}(X - \mu) \overset{d}{\to} N_2(0,\...
James Ilken's user avatar
0 votes
0 answers
20 views

How to control the angles of Kuramoto model by controlling its order parameter?

Consider Homogenous Kuramoto model in this paper. In theorem 3.1, the author derive condition on $A$ such that all second-order critical points of $E(\theta)$ are in two opposite quadrants, by saying ...
happyle's user avatar
  • 29
2 votes
1 answer
331 views

The Fourier transform of the Liouville function?

The Liouville function in number theory is defined as: $$\lambda(n) := (-1)^{\Omega(n)} \text{ where } \Omega(n) := \sum_{p|n} v_p(n)$$ Taking the discrete time Fourier transform and then taking the ...
mathoverflowUser's user avatar
2 votes
1 answer
63 views

Generating sets for a module and scalar extension

Let $k$ be an algebraically closed field and $K/k$ a (transcendental) field extension. Let $A$ be a finite dimensional $k$-algebra, and $M$ an $A$-module. Suppose that the $K \otimes_k A$-module $K \...
bm3253's user avatar
  • 23
1 vote
1 answer
70 views

Mittag-Leffler expansions converging to bounded function

Is it true that $$\lim_{N\to\infty}\left\langle\sum_{n=-N^2}^{N^2}\frac1{(Nx-n)^2}\right\rangle_N=\pi^2$$ for some suitable definition of "minima smoothing" such as $\langle f(x)\rangle_N\...
Adam's user avatar
  • 113
6 votes
2 answers
223 views

If a Banach / Fréchet manifold $M$ happens to be a topological vector space, is $M$ just a Banach / Fréchet space?

In finite dimensions, if $M$ is a smooth manifold that happens to be a vector space, then it is indeed just the Euclidean space. I wonder if the same result holds valid in infinite dimensions. More ...
Isaac's user avatar
  • 2,625
0 votes
0 answers
69 views

Hyperbolicity in sense of Koszul

Question : I have a question about the notion of hyperbolicity in the sense of Koszul. Koszul asserts that locally flat compact hyperbolic manifolds do not contain a parallel vector field. Do you have ...
Emmanuel Gnandi's user avatar
14 votes
2 answers
2k views

Is Freyd's thesis available online anywhere?

Peter Freyd is a great category theorist. His PhD dissertation, Functor Theory, dates from Princeton in 1960. It's cited as [14] in Mitchell's book Theory of categories. In fact, Google scholar says ...
David White's user avatar
  • 27.8k
4 votes
1 answer
136 views

Is the asymptotic rank of a tensor bounded by (naive) border rank?

Write $R(T)$ for the rank of an order-$3$ tensor $T \in \mathbb C^{m \times n \times p}$ over the complex numbers. If $T' \in \mathbb {C}^{m' \times n' \times p'}$ is another such tensor then let $T \...
Sean Eberhard's user avatar
2 votes
0 answers
44 views

Degeneracy maps of Drinfeld modular curves

Over number fields, we have two natural degeneracy maps $$X_0(N)\leftarrow X_0(pN) \rightarrow X_0(N)$$ between the (compactified) moduli space of elliptic curves with level $pN$ and $N$ respectively (...
curious math guy's user avatar
3 votes
2 answers
119 views

Are there outer models $V \subset W$ of $L$ such that $V$ is "far" from $L$ but $W$ is "not too far" from $V$?

In the following, whenever I say "$V_1$ is an outer model of $V_2$", I mean $V_1, V_2$ are transitive models of $\mathsf{ZFC}$, $V_2 \subset V_1$,and $ORD^{V_1} = ORD^{V_2}$. I am curious ...
Zoorado's user avatar
  • 1,193
1 vote
0 answers
39 views

Defining properties of categories out of an indicial category

$\newcommand{\Hom}{\operatorname{Hom}}$Suppose we want to define the category of arrows of $S$. Below are two forms of doing it. Definition 1: If $D$ is of the following type: $\bullet \to \bullet$, ...
user234212323's user avatar
4 votes
0 answers
117 views

Permutation generation problem using swaps

This is motivated by Aaronson's post, Probability of generating a desired permutation by random swaps. I am interested in a related problem where the swaps are given in the input. We're given as input ...
Mohammad Al-Turkistany's user avatar
16 votes
3 answers
2k views

What's the earliest result (outside of logic) that cannot be proven constructively?

Although mathematicians usually do not work in constructive mathematics per se, their results often are constructively valid (even if the original proof isn't). An obvious counter-example is the law ...
Christopher King's user avatar
0 votes
0 answers
33 views

complexity of membership problem in finite general linear group

Suppose $G$ is a subgroup of $GL(n,q)$ given by a list of generators. What is known about the complexity of the corresponding "membership problem", that is, the problem of deciding whether a ...
Pierre's user avatar
  • 2,145
1 vote
0 answers
21 views

How to extract 'top k' multiple solutions from a quadratic optimization problem?

Imagine we are interested in the following problem: $$ \min_{w} \left( w^T V w + \lambda \|w\| \right) \\ \text{s.t. } w^T R \geq c $$ Where 𝑤 is an $N \times 1$ vector, $V$ is an $N \times N$ ...
Azmy Rajab's user avatar
1 vote
1 answer
208 views

A possible ${\sf (ZF)}$-theorem in the spirit of the $3$-set-lemma

The number $3$ plays an interesting role in the following statement: $\newcommand{\S}{\sf(S_3)}\S$ Let $X$ be a non-empty set and let $f:X \to X$ be fixpoint-free (that is $f(x) \neq x$ for all $x\in ...
Dominic van der Zypen's user avatar
2 votes
0 answers
32 views

Geometric explanation of Fueter-Sce-Qian Theorem and similar situations

In Clifford analysis there is a fundamental theorem due to Fueter and extended by Sce and Qian that says (in modern terminology) that the given a slice regular function $f:\mathbb{R}^{m+1}\to\mathbb{R}...
Giulio Binosi's user avatar
0 votes
0 answers
68 views

Upper-bound of the tail of a weighted sum of iid random variables

I have a question related to this one. $X_i$ are n iid random variables with CDF $1_{[0,+\infty[}(x) \Phi(x)$, i.e. it is a mixture between a folded Gaussian and a delta in $0$, both with weight $1/2$....
odile's user avatar
  • 55
1 vote
0 answers
51 views

Is the adjoint action of $\mathrm{SU}(2)$ on the Schwartz space proper and free?

$\DeclareMathOperator\SU{SU}$Let $t_1, t_2, t_3$ be generators of the Lie algebra $\mathfrak{su}(2)$. Let us consider a Schwartz space $\mathcal{S}$ defined as \begin{equation} \mathcal{S}:= \Bigl\{ \...
Isaac's user avatar
  • 2,625

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