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\begin{document}
\title{On the Representability of Line Graphs}
\begin{abstract}
A graph $G=(V,E)$ is representable if there exists a word $W$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $W$ if and only if $(x,y)$ is in $E$ for each $x$ not equal to $y$. The motivation to study representable gra... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the minimum value of \( n \) such that the line graph \( L(W_n) \) of the wheel graph \( W_n \) is guaranteed to be non-representable? Additionally, provide an example of a graph \( G \) for which \( L^k(G) \) is non-representable for \( k \geq 4 \). | 91,196 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{On second-order differentiability with respect to parameters for differential equations with state-dependent delays\thanks{This research was partially supported by the Hungarian National Foundation for Scientific Research Grant No. K73274.}} \author{Ferenc Hartung\\ Department of Mathematics\\... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a class of differential equations with state-dependent delays of the form
\[
\dot{x}(t) = f(t, x_t, x(t - \tau(t, x_t, \xi)), \theta), \quad t \in [0, T],
\]
where \( f \) is Lipschitz continuous in its arguments, and let \(\tau\) be a piecewise strictly monotone delay function, determine the necessary and su... | 59,364 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{\bf Quantum speed limit time for a two-qubit system interacting with independent and common reservoirs } \author{ N. Behzadi $^{a}$ \thanks{E-mail:n.behzadi@tabrizu.ac.ir} , A. Ektesabi $^{b}$ , B. Ahansaz $^{b}$, E. Faizi $^{b}$ \\ $^a${\small Research Institute for Fundamental Sciences, Uni... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the relationship between the quantum speed limit time \( \tau_{QSL} \) and the coupling strength \( \gamma_{0} \) for a two-qubit system initially prepared in extended Werner-like states when interacting with a common reservoir compared to independent reservoirs, specifically in the context of entering the non-... | 58,699 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Producing delocalized frequency-time Schr\"odinger cat-like states with HOM interferometry} \author{N. Fabre\footnote{nicolas.fabre@univ-paris-diderot.fr} } \affiliation{Laboratoire Mat\'eriaux et Ph\'enom\`enes Quantiques, Sorbonne Paris Cit\'e, Universit\'e de Paris, CNRS UMR 7162, 75013 Pari... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the maximum number of oscillations observed in the coincidence probability in a Hong-Ou-Mandel experiment when using frequency filters with a separation of \(0.6 \, \text{nm}\) and a spectral width of \(50 \, \text{pm}\)? Provide the relationship between the number of oscillations and the parameters of the filt... | 27,739 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{On the slope of fourgonal semistable fibrations}
\markboth{Beorchia and Zucconi}{fourgonal fibrations}
\begin{abstract} We bound the slope of sweeping curves $B$ in the $4$-gonal locus $\mfour$. Our results follow from some Bogomolov-type inequalities for nef rank two vector bundles on ruled ... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a semistable fibration \( f: S \to B \), where the general fiber is a smooth fourgonal curve of genus \( g \geq 10 \), and the slope \( s(f) \) is defined in terms of the relative canonical divisor \( K_f \) and the Euler characteristic of the sheaf associated with the fibration, what is the minimum bound for the... | 74,186 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title[]{Generalized Bernstein operators on the classical polynomial spaces}
\author{J. M. Aldaz and H. Render} \address{Instituto de Ciencias Matem\'aticas (CSIC-UAM-UC3M-UCM) and Departamento de
Matem\'aticas,
Universidad Aut\'onoma de Madrid, Cantoblanco 28049, Madrid, Spain.} \email{jesus.mun... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Let \( f_1(x) \) be a polynomial of degree \( m \geq 1 \) that is strictly increasing on the interval \([a, b]\), with \( f_1' > 0 \) for all \( x \in (a, b) \).
1. Given the generalized Bernstein operator \( B_n^{f_1} \) defined for \( n \geq m \), how can the nodes \( t_{n,k} \) be characterized in terms of \( a + ... | 3,035 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{On 4-reflective complex analytic planar billiards} \begin{abstract} The famous conjecture of V.Ya.Ivrii \cite{Ivrii} says that {\it in every billiard with infinitely-smooth boundary in a Euclidean space the set of periodic orbits has measure zero}. In the present paper we study its complex ... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What are the necessary and sufficient conditions for a collection of four holomorphic curves in the projective plane to be a 4-reflective complex analytic billiard, and how does this classification extend to real planar billiards with piecewise \(C^4\)-smooth boundaries? | 14,594 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\begin{abstract} Place one active particle at the root of a graph and a Poisson-distributed number of dormant particles at the other vertices. Active particles perform simple random walk. Once the number of visits to a site reaches a random threshold, any dormant particles there become active. For thi... | arXiv | arXiv/math_arXiv_v0.2.jsonl | In the context of the threshold frog model on an infinite complete $d$-ary tree, if the number of initially active frogs at the root follows a Poisson distribution with mean $\mu$, what is the quantity $\mu_c(\tau,d)$, defined as the infimum of $\mu$ such that the model is recurrent almost surely, for a given threshold... | 74,756 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Deletion-Contraction and the Surface Tutte Polynomial}
\begin{abstract} In this paper we unify two families of topological Tutte polynomials. The first family is that coming from the surface Tutte polynomial, a polynomial that arises in the theory of local flows and tensions. The second famil... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Let \( G \) be a connected, orientable ribbon graph with \( v \) vertices, \( e \) edges, and \( f \) boundary components. Given the definitions of the surface Tutte polynomial \( \mathcal{T}(G; x, y) \) and its relation to local flows and tensions, derive explicit recursive formulas for the number of nowhere-zero loca... | 89,786 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\author{K\k{e}stutis \v{C}esnavi\v{c}ius} \title{\resizebox{\textwidth}{!}{\mbox{The $\ell$-parity conjecture over the constant quadratic extension}}} \date{\today} \subjclass[2010]{Primary 11G10; Secondary 11G40, 11R58} \keywords{Parity conjecture, root number, arithmetic duality} \address{Department... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the relationship between the $\ell$-parity conjecture and the root numbers of abelian varieties over global fields, specifically in terms of their analytic ranks modulo 2, and how can it be proved under certain conditions on the character of the field and the degree of polarization? | 48,636 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\begin{frontmatter}
\title{Comment on: ``Threading dislocation densities in semiconductor crystals: A geometric approach''. Phys. Lett. A 376 (2012) 2838-2841} \author{Francisco M. Fern\'{a}ndez \thanksref{FMF}}
\address{INIFTA, DQT, Sucursal 4, C.C 16, \\ 1900 La Plata, Argentina}
\thanks[FMF]{e--... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given the parameters \( b = \sqrt{6} \) and \( \gamma_1 = 1 \), calculate the three lowest eigenvalues \( W_{0,1,1} \), \( W_{1,1,1} \), and \( W_{2,1,1} \) as provided by the variational method and validate if the eigenvalue \( W_{1,1,1} = 6 \) is indeed one of the energies derived from the prescribed model. What nume... | 82,430 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Unsupervised low-rank representations for speech emotion recognition}
\begin{abstract} We examine the use of linear and non-linear dimensionality reduction algorithms for extracting low-rank feature representations for speech emotion recognition. Two feature sets are used, one based on low-lev... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the minimum number of dimensions achieved through dimensionality reduction via PCA using the IS10 feature set, originally consisting of 1582 dimensions, that maintains competitive classification accuracy for speech emotion recognition as indicated in the results? | 89,292 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Entropic bounds between two thermal equilibrium states} \author{Julio A. \surname{L\'opez-Sald\'ivar}} \email{Corresponding author: \, julio.lopez@nucleares.unam.mx} \affiliation{Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de Mexico, Apdo. Postal 70-543, 04510, CDMX, Mexico} ... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What are the upper and lower bounds for the difference in entropy \( S(\hat{H}_2, T_2) - S(\hat{H}_1, T_1) \) between two thermal equilibrium states described by Hamiltonians \( \hat{H}_1 \) and \( \hat{H}_2 \) at temperatures \( T_1 \) and \( T_2 \) respectively, in terms of observable quantities like the mean values ... | 19,476 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{RIEMANNIAN METRIC BUNDLE} \author{Shouvik Datta Choudhury\thanks{shouvikdc8645@gmail.com, shouvik@capsulelabs.in}\\
\small Gapcrud Private Limited (Capsule Labs)\\
\small HA 130, Saltlake, Sector III, Bidhannagar,\\
\small Kolkata - 700097, India} \date{\today} \maketitle \begin{abstract}... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Let \( M \) be a smooth manifold of dimension \( n \). Define \( G(M) \) as the Riemannian metric bundle over \( M \), where each fiber \( G_x(M) \) at a point \( x \in M \) consists of symmetric, positive-definite bilinear forms on the tangent space \( T_xM \). If \( m \) is the number of distinct Riemannian metrics d... | 26,059 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Graph Attention Recurrent Neural Networks for Correlated Time Series Forecasting---Full Version}
\author{ \IEEEauthorblockN{Razvan-Gabriel Cirstea} \IEEEauthorblockA{\textit{Department of Computer Science} \\ \textit{Aalborg University}\\ Aalborg, Denmark \\ razvan@cs.aau.dk} \and
\IEEEauthor... | arXiv | arXiv/math_arXiv_v0.2.jsonl | In a cyber-physical system with 207 entities (e.g., speed sensors) that produce correlated time series data, if each entity generates a time series sampled every 5 minutes over a period of 121 days, how many total data points are collected for all entities combined during this time period? | 60,708 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Sudden Change of Quantum Discord under Single Qubit Noise } \author{Li-Xing Jia,$^{1,2}$ Bo Li$^2$, R.-H. Yue,$^1$ Heng Fan$^2$\footnote{hfan@iphy.ac.cn}} \affiliation{ $^1$Faculty of Science, Ningbo University, Ningbo 315211, China\\ $^2$Beijing National Laboratory for Condensed Matter Physic... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Consider a two-qubit X-shaped state described by the following density matrix:
\[
\rho = \frac{1}{4}\left(I \otimes I + r \sigma_3 \otimes I + I \otimes s \sigma_3 + \sum_{i=1}^3 c_i \sigma_i \otimes \sigma_i \right)
\]
where \(I\) is the identity operator, \(r\) and \(s\) are real numbers associated with the noise a... | 90,293 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\allowdisplaybreaks
\newcommand{2203.05852}{2203.05852}
\renewcommand{\arabic{footnote}}{}
\renewcommand{067}{067}
\FirstPageHeading
\ShortArticleName{De Finetti Theorems for the Unitary Dual Group}
\ArticleName{De Finetti Theorems for the Unitary Dual Group\footnote{This paper is a~contribution... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Let \( (x_i)_{i=1}^\infty \) be an infinite sequence of random variables in a tracial \( W^* \)-probability space \( (M, \varphi) \). If the joint distribution of \( (x_i)_{i=1}^\infty \) is invariant under the dual action of the unitary dual group, what can you conclude about the existence and distribution of the limi... | 51,419 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Group distance magic Cartesian product of two cycles}
\author{Sylwia Cichacz$^{1}$\footnote{This work was partially supported by the Faculty of Applied Mathematics AGH UST statutory tasks within subsidy of Ministry of Science and Higher Education.}, Pawe{\l} Dyrlaga$^1$, Dalibor Froncek$^2$\\ ... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What are the necessary and sufficient conditions for the Cartesian product of two cycles \( C_m \square C_n \) to be a \(\Gamma\)-distance magic graph for any Abelian group \(\Gamma\) of order \( mn \)? Specifically, can you determine if \( C_m \square C_n \) has a \(\mathbb{Z}_{\alpha}\times \mathcal{A}\)-magic labeli... | 45,564 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\begin{frontmatter}
\title{Limiting case Hardy inequalities on the sphere}
\author{Ahmed A. Abdelhakim} \address{Mathematics Department, Faculty of Science, Assiut University, Assiut 71516 - Egypt\\ Email: ahmed.abdelhakim@aun.edu.eg} \begin{abstract} We give sharp limiting case Hardy inequalities o... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the value of the sharp constant \( c_n \) for the limiting case Hardy inequality on the sphere \( \mathbb{S}^2 \) as derived from the inequality
\[
\int_{\mathbb{S}^{2}} |\nabla_{\mathbb{S}^{2}} f|^{2} d\sigma + \bar{c}_n \int_{\mathbb{S}^{2}} f^{2} d\sigma \geq c_n^2 \int_{\mathbb{S}^{2}} \left(\frac{f^{2}}{... | 90,763 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\pagestyle{plain} \pagenumbering{arabic} \date{}
\title{\textbf{\small{On The Matlis Duals of Local Cohomology Modules}}} \author{\small{Gennady Lyubeznik and Tu\u{g}ba Y\i{ı}ld\i{ı}r\i{ı}m}\thanks{The first author gratefully acknowledges NSF support through grant DMS-1500264. The second author ... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a Noetherian regular local ring \( (R, \mathfrak{m}) \) containing a field of characteristic \( p > 0 \), and a non-zero ideal \( I \) of \( R \), if the local cohomology module \( \operatorname{H}^i_I(R) \) is non-zero, what can be concluded about the support of the Matlis dual \( D(\operatorname{H}^i_I(R)) \)? ... | 75,281 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Transformation of intermediate
times in the decays of moving unstable quantum systems via the exponential modes
}
\def\bbm[#1]{\mbox{\boldmath$#1$}}
PACS: 03.65.-w, 03.30.+p
\begin{abstract} The transformation of canonical decay laws of moving unstable quantum systems is studied by approxi... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a moving unstable quantum system with mass \(M\) and decay widths \(\Gamma_1, \ldots, \Gamma_N\), if the survival probability at rest \(\mathcal{P}_0(t)\) exhibits a superposition of exponential modes described by
\[
\mathcal{P}_0(t) = \sum_{j=1}^N w_j \exp\left(-\frac{\Gamma_j}{2} t\right),
\]
where \(w_j\) ar... | 17,432 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\def{\clubsuit}{{\clubsuit}} \def{\mathbb Z}{{\mathbb Z}} \def{\mathbb G}{{\mathbb G}} \def{\mathbb C}{{\mathbb C}} \def{\mathbb Q}{{\mathbb Q}} \def{\mathbb R}{{\mathbb R}} \def{\mathbb N}{{\mathbb N}} \def\mathrm{Gal}{\mathrm{Gal}} \def\,\vrule\,{\,\vrule\,} \def{f}{{f}} \def\mathfrak{f}{\mathfrak{f... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the value of the integral
\[
\int_{{\mathbb Z}_p} b^{k-1} d \hat{\zeta}_{p,a,m}(\sigma)(b)
\]
for integers \(a\) and \(m\) with \(m > 1\), given that \( p \) does not divide \(m\), and \(k \) is a positive integer? | 48,743 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title {
{\Large Run Compressed Rank/Select for Large
Alphabets}\thanks{This work is supported by the Academy of Finland via grant
1294143 and by the EU grant H2020-MSCA-RISE-2015 BIRDS690 No.\ 690941. The first author received funding from Fondecyt grant 3170534 and Basal Funds FB0001, Conicy... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a string of length \( n \) composed of \( r \) runs from the alphabet \( \{0, 1, \ldots, \sigma - 1\} \) with \( 2 \leq \sigma \leq r \), what is the maximum number of bits required to store the string if it is represented using a succinct data structure that supports select and access queries in \( O(\log\frac{\... | 58,774 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title[]{Dynamics of isolated left orders}
\author{Shigenori Matsumoto}
\address{Department of Mathematics, College of Science and Technology, Nihon University, 1-8-14 Kanda-Surugadai, Chiyoda-ku, Tokyo, 101-8308 Japan} \email{matsumo@math.cst.nihon-u.ac.jp}
\thanks{2010 {\em Mathematics Subject Cl... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a countable group \( G \) and an isolated left order \( \lambda \) on \( G \), define the maximal convex subgroup associated with \( \lambda \). If \( G \cong B_3 \) (the braid group on three strings), how many isolated left orders can be constructed on \( G \) that are not automorphic images of each other? Speci... | 24,234 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Revisit Similarity of Neural Network Representations From Graph Perspective}
\maketitle
\begin{abstract} Understanding the black-box representations in Deep Neural Networks (DNN) is an essential problem in deep learning. In this work, we first revisit the state-of-the-art similarity index Cen... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given two representation graphs \(\mathcal{G}_1\) and \(\mathcal{G}_2\) constructed from embeddings of \(N\) input samples in a Deep Neural Network, where each edge weight is determined by the cosine similarity of their corresponding feature vectors, how can you calculate the overall similarity \(s\) between these two ... | 22,669 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Data Science Transfer Pathways from Associate's to Bachelor's
Programs}
\begin{abstract} A substantial fraction of students who complete their college education at a public university in the United States begin their journey at one of the 935 public two-year colleges. While the number of four-... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given that there are 935 public two-year colleges in the United States enrolling over 4.7 million students, if 22% of graduates from these two-year colleges successfully transfer to bachelor's programs in data science, how many students transfer to these programs? Additionally, if the average bachelor's program in data... | 30,143 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title[The Parabolic Anderson model on the hypercube]{The Parabolic Anderson model on the hypercube}
\author{Luca Avena} \address{Luca Avena\\Universiteit Leiden\\ Niels Bohrweg 1
\\ 2333 CA Leiden\\Netherlands} \email{l.avena@math.leidenuniv.nl}
\author{Onur G\"un} \address{Onur G\"un\\ Weierstras... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given the parabolic Anderson model defined on the n-dimensional hypercube $\{-1, +1\}^n$, let $\xi_n(x)$ represent a random potential at vertex $x$ and let the time scale be parametrized by a volume $c_n = \frac{1}{2} n \log n$. Consider the locations of the largest potential and the k-th largest potential, denoted as ... | 43,180 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Persistence of solutions to higher order nonlinear Schr\"odinger equation}
\author{Xavier Carvajal$^1$, Wladimir Neves$^1$}
\date{}
\maketitle
\footnotetext[1]{ Instituto de Matem\'atica, Universidade Federal do Rio de Janeiro, C.P. 68530, Cidade Universit\'aria 21945-970, Rio de Janeiro, B... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Consider the initial value problem for the higher-order nonlinear Schrödinger equation given by
\[
\begin{cases}
\partial_t u + i a \partial_x^2 u + b \partial_x^3 u + i c |u|^2 u + d |u|^2 \partial_x u + e u^2 \partial_x \bar{u} = 0, \quad (t,x) \in \mathbb{R}^2, \\
u(x,0) = u_0(x),
\end{cases}
\]
where \( u_0 \) is... | 99,503 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Witnessing criticality in non-Hermitian systems via entropic uncertainty relation} \author{You-neng Guo} \email{guoxuyan2007@163.com} \affiliation{Department of Electronic and Communication Engineering, Changsha University, Changsha, Hunan 410022, People's Republic of China} \author{Guo-you W... | arXiv | arXiv/math_arXiv_v0.2.jsonl | In a two-level non-Hermitian system characterized by the Hamiltonian
\[
\mathcal{H}_{NH} = \begin{pmatrix}
r e^{i\phi} & \sigma \\
s & r e^{-i\phi}
\end{pmatrix},
\]
determine the conditions on the parameters \( r \), \( \sigma \), and \( s \) under which the system undergoes a phase transition from the unbroken pha... | 16,895 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title[Do $n$-Lie algebras have universal enveloping algebras?]{Do $n$-Lie algebras have\\ universal enveloping algebras?} \author{X. García-Martínez} \address{[X. García-Martínez] Department of Algebra, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain.} \email{xabier.garcia@u... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the maximum dimension of a simple $n$-Lie algebra over an algebraically closed field, given that every simple $n$-Lie algebra is isomorphic to the algebra $V_n$, where $V_n$ is the $(n+1)$-dimensional $\mathbb{K}$-vector space with a specific skew-symmetric $n$-ary multiplication? | 70,956 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\thispagestyle{empty}
\vskip 20pt \begin{center} {\bf NEW LOWER BOUND FORMULAS FOR MULTICOLORED RAMSEY NUMBERS} \vskip 15pt {\bf Aaron Robertson}\\ {\it Department of Mathematics,} {\it Colgate University, Hamilton, NY 13346}\\ {\tt aaron@math.colgate.edu} \end{center} \vskip 30pt \begin{abstract}{\... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the value of \( R(3,3,3,11) \) according to Theorem 2, and how does this value compare to the previous lower bound? | 56,086 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Finite groups with five relative commutativity degrees} \author{M. Farrokhi D. G.} \date{} \keywords{Relative commutativity degree, chain of subgroups} \subjclass[2000]{Primary 20P05; Secondary 20D30, 20F16, 20F18.} \address{Department of Mathematics, Institute for Advanced Studies in Basic Sci... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What are the necessary and sufficient conditions for a finite group \( G \) to have exactly five relative commutativity degrees? Specifically, can you provide a classification of such groups based on their structure and properties? | 92,625 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{A unified recovery bound estimation for noise-aware $\ell_{q}$ optimization model in compressed sensing \author{Zhi-Long Dong, Xiao-Qi Yang, Yu-Hong Dai} \thanks{This work was supported in part by the ******************************, Grant **********, the *********************, Grant ***********... | arXiv | arXiv/math_arXiv_v0.2.jsonl | In a compressed sensing framework, consider the non-convex optimization problem defined as
\[
(P_{q,\sigma}): \min_{x} \|x\|_{q} \quad \text{s.t.} \quad \|y - Ax\|_2 \leq \sigma,
\]
where \( \|x\|_q = \left( \sum |x_i|^q \right)^{1/q} \) for \( 0 < q < 1 \). If the error between the ideal sparse solution \( x_0 \) a... | 76,129 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\begin{frontmatter}
\title{Diffusion Processes Homogenization for Scale-Free Metric Networks } \tnotetext[mytitlenote]{This material is based upon work supported by project HERMES 27798 from Universidad Nacional de Colombia, Sede Medell\'in.}
\author{Fernando A Morales \sep $\&$ \sep Daniel E Restre... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the behavior of the solutions to the diffusion equation on scale-free networks when modeled using a homogenization process, particularly for various types of diffusion coefficients and forcing terms, and how does this relate to observable convergence patterns? | 87,967 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Blow up and scattering criteria above the threshold for the focusing inhomogeneous nonlinear Schrödinger equation} \begin{abstract}\noindent We consider the inhomogeneous nonlinear Schrödinger equation (INLS) in $\mathbb{R}^N$
$$i \partial_t u + \Delta u + |x|^{-b} |u|^{p-1}u = 0,$$
with finit... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given the inhomogeneous nonlinear Schrödinger equation
\[
i \partial_t u + \Delta u + |x|^{-b} |u|^{p-1}u = 0,
\]
where \( N \geq 1 \), \( 1 < p < p^*_b \), and \( V(0) < \infty \), determine the conditions under which the solution \( u(t) \) blows up in finite time. Specifically, under what assumptions about the ma... | 34,356 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\begin{frontmatter}
\title{Multi-view Hierarchical Clustering}
\author[mymainaddress]{Qinghai Zheng}
\author[mymainaddress]{Jihua Zhu} \cortext[mycorrespondingauthor]{Corresponding author} \ead{zhujh@xjtu.edu.cn}
\author[mymainaddress]{Shuangxun Ma}
\address[mymainaddress]{School of Software Engi... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the computational complexity of the proposed Multi-view Hierarchical Clustering (MHC) method, and how does it compare to the computational complexities of multi-view spectral clustering and multi-view subspace clustering methods? | 12,809 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{The competition-common enemy graphs of digraphs satisfying Conditions $C(p)$ and $C'(p)$}
\author{\begin{tabular}{c} {\sc Yoshio SANO} \thanks{This work was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Educa... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the minimum number \( k \) such that the competition-common enemy graph \( G \) of a digraph satisfying Conditions \( C(p) \) and \( C'(p) \) can be represented as \( G \) with \( k \) new isolated vertices and become the competition-common enemy graph of an acyclic digraph? | 77,696 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{New refinable spaces and local approximation estimates for hierarchical splines}
\author[1]{Annalisa Buffa} \author[1,2,3]{Eduardo M. Garau \thanks{Corresponding author: egarau@santafe-conicet.gov.ar}} \affil[1]{\footnotesize Istituto di Matematica Applicata e Tecnologie Informatiche `E. Mage... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a hierarchical B-spline basis defined by the recursive relations involving support and truncation properties, consider the basis functions \( b_i \) generated in the space \( \Span \HH \). If we further refine the hierarchy by introducing a new level \( n+1 \) of subdomains, how would the number of new functions ... | 5,519 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Visualizing quantum mechanics in an interactive simulation -- Virtual Lab by Quantum Flytrap}
\begin{abstract} \emph{Virtual Lab by Quantum Flytrap} explores novel ways to represent quantum phenomena in an interactive and intuitive way. It is a no-code online laboratory with a real-time simul... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the minimum number of complex numbers required to represent the state of a system with three indistinguishable photons, assuming each photon has 4 degrees of freedom (position along two axes, direction, and polarization)? | 91,302 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{ Experimental demonstration of robust entanglement distribution over reciprocal noisy channels assisted by a counter-propagating classical reference light } \author{Rikizo Ikuta} \affiliation{Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan} \author{Sho... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the success probability of the entanglement distribution protocol described in the paper when the transmittance \( T \) of each quantum channel is \( 1/2 \)? Assume that the independent lossy channels are modeled as \( M_f = T U_f^u \) and \( N_f = T U_f^l \), where \( U_f^u \) and \( U_f^l \) are random unitar... | 86,150 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\maketitle
\centerline{\scshape Tran Ngoc Thang${}^1\footnotetext[1]{Corresponding author: thang.tranngoc@hust.edu.vn}$ and Dao Tuan Anh}
{\footnotesize
\centerline{ School of Applied Mathematics and Informatics}
\centerline{Hanoi University of Science and Technology}
\centerline{No. 1 Dai C... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a strictly quasiconvex multiobjective programming problem defined as
\[
\text{Vmin } f(x) \quad \text{subject to } x \in \mathcal{S}
\]
where \( f: \mathbb{R}^{n} \rightarrow \mathbb{R}^{p} \) is a strictly quasiconvex function and \( \mathcal{S} \) is a nonempty, convex, compact set, can you determine the upp... | 38,136 | mlfoundations-dev/gair_mathpile | |
\begin{document} \author{
Carsten Collon{\thanks{Younicos AG, 12489 Berlin, Germany}}\ ~and Joachim Rudolph\thanks{Department of Mechatronics, Chair of Systems Theory and Control Engineering, Saarland University,\newline 66123 Saarbr\"{u}cken, Germany}}
\title{Invariant feedback control for the kinematic car on t... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Consider a kinematic car modeled as a rigid body moving on the surface of a sphere of radius \( \rho \). The car's motion is governed by the parameters: the velocity \( v \) and the steering angle \( \varphi \). Given that the curvature of the path the car takes on the sphere is \( \kappa_g = \frac{\tan \varphi}{\ell} ... | 86,570 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Effects of mismatched transmissions on two-mode squeezing and EPR correlations with a slow light medium}
\author{Sulakshana Thanvanthri} \email{su1@umbc.edu} \affiliation{Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland, 21250} \author{Jianming Wen} \affilia... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given that loss of squeezing occurs when the mismatch in the transmission of two modes of light exceeds 40%, calculate the maximum allowable ratio of the transmission coefficients \( T_1 \) and \( T_2 \) for two modes in order to preserve two-mode squeezing. What is the range of values for \( T_1 \) and \( T_2 \) if on... | 760 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title[Ambarzumyan-type theorem]
{Ambarzumyan-type theorem for the Sturm-Liouville operator on the lasso graph}
\author[F.~Wang]{Feng Wang}
\address{School of Mathematics and Statistics, Nanjing University of
Science and Technology, Nanjing, 210094, Jiangsu, China}
\email{\mailto{wangfen... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Suppose \( L(q) \) is a Sturm-Liouville operator on a lasso graph consisting of a boundary edge of length \( l_1 \) and a loop of length \( l_2 \). Given that the eigenvalues of \( L(q) \) coincide with those of the zero potential operator \( L(0) \), what can be concluded about the potentials \( q_1 \) and \( q_2 \) o... | 774 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{{Higher integrability and the number of singular points for the Navier-Stokes equations with a scale-invariant bound }}
\author[T. Barker]{Tobias Barker} \address[T. Barker]{Department of Mathematical Sciences, University of Bath, Bath BA2 7AY. UK} \email{tobiasbarker5@gmail.com}
\keywords{} ... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a weak Leray-Hopf solution \( v \) to the Navier-Stokes equations in three dimensions, assume the pressure \( p \) satisfies the bound \( \|p\|_{L^{\infty}((0,T^*); L^{\frac{3}{2},\infty}(\mathbb{R}^3))} \leq M^2 \) and that \( v \) first blows up at a time \( T^* \) under the Type I condition \( \|v\|_{L^{\infty... | 22,228 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{ extbf{Coherent configurations over copies of association schemes of prime order}
\begin{abstract} Let $G$ be a group acting faithfully and transitively on $\Omega_i$ for $i=1,2$. A famous theorem by Burnside implies the following fact:
If $|\Omega_1|=|\Omega_2|$ is a prime and the rank of one... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Let \( G \) be a group acting transitively on two sets \( \Omega_1 \) and \( \Omega_2 \) of the same prime size \( p \). What can be said about the cardinality of the orbit of \( G \) acting on the product set \( \Omega_1 \times \Omega_2 \) if the rank of the action of \( G \) on one of the sets is greater than two? | 37,572 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Cluster structures from 2-Calabi-Yau categories with loops}
\begin{abstract} We generalise the notion of \emph{cluster structures} from the work of Buan-Iyama-Reiten-Scott to include situations where the endomorphism rings of the clusters may have loops. We show that in a Hom-finite 2-Calabi-Y... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the necessary condition for the set of maximal rigid objects in a Hom-finite 2-Calabi-Yau triangulated category to satisfy a cluster structure, and how does this relate to the presence of 2-cycles in the quivers of their endomorphism rings? | 10,014 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{\textbf{\ Secure Domination in Digraphs} } \author{ {\bf \sc Mart\'{\i}n Manrique$^{1},$ Karam Ebadi$^1$ and Morteza Ebrahimi$^{2}$ }\\{\footnotesize $^1$National Centre for Advanced Research in Discrete Mathematics ($n$-CARDMATH)} \\{\footnotesize Kalasalingam University}\\{\footnotesize A... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a directed graph \( D \) with \( n \) vertices, the maximum out-degree \( \Delta^+ \), and minimum in-degree \( \delta^- \) of \( D \), determine the exact value of \( \gamma_{so}(D) \) in terms of \( n \) and \( \Delta^+ \), and prove that \( \gamma_{so}(D) = n \) if and only if every vertex in \( D \) has eithe... | 41,201 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{\textsc{ Finding best approximation pairs for two intersections of closed convex sets }}
\author{ Heinz H.\ Bauschke\thanks{ Mathematics, University of British Columbia, Kelowna, B.C.\ V1V~1V7, Canada. E-mail: \texttt{heinz.bauschke@ubc.ca}.},~ Shambhavi Singh\thanks{ Mathematics, University ... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Consider two closed convex sets \( A \) and \( B \) in a finite-dimensional real Hilbert space \( Y \), represented as finite intersections of halfspaces. Let \( A \) have \( m \) halfspace constraints and \( B \) have \( n \) halfspace constraints.
1. If each halfspace can be defined by a linear inequality, express ... | 51,320 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Minimum-volume hyperbolic 3-manifolds} \author{Peter Milley}\thanks{Partially supported by NSF grant DMS-0554624 and by ARC Discovery grant DP0663399.}\address{Department of Mathematics and Statistics\\University of Melbourne\\Melbourne, Australia}\email{P.Milley@ms.unimelb.edu.au}
\maketitle
... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the maximum volume of a closed orientable hyperbolic 3-manifold, and to which specific manifold is it homeomorphic? | 35,866 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Structure-preserving $H^2$ optimal model reduction\\ based on Riemannian trust-region method}
\author{Kazuhiro Sato and Hiroyuki Sato \thanks{K. Sato is with the School of Regional Innovation and Social Design Engineering,
Kitami Institute of Technology,
Hokkaido 090-8507, Japan, email: ksat... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the minimum value of the objective function \( J(A_r, B_r, C_r) \) for the stability and symmetry preserving \( H^2 \) optimal model reduction problem, given that the system matrices satisfy certain conditions and the dimensionality of the reduced system is fixed at \( r < n \)? | 36,469 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\setcounter{page}{221} \publyear{22} \papernumber{2109} \volume{185} \issue{3}
\finalVersionForARXIV
\title{Coxeter Invariants for Non-negative Unit Forms of Dynkin Type $\mathbb{A}_{r}$}
\author{Jes\'us Arturo~Jim\'enez Gonz\'alez\thanks{Address of correspondence: Instituto de Matem\'aticas, ... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a connected non-negative unit form of Dynkin type \(\mathbb{A}_r\) represented by its Coxeter polynomial \(\varphi_q(\lambda)\), which satisfies the equation
\[
\varphi_q(\lambda) = (\lambda - 1)^{c - 1} \cdot \mathrm{char}_{\mathbf{ct}(q)}(\lambda),
\]
where \(\mathbf{ct}(q)\) denotes the cycle type of the fo... | 50,039 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\begin{titlepage}
\thispagestyle{empty}
\title{Online Makespan Minimization: The Power of Restart ootnote{A preliminary version of the paper to appear in APPROX 2018.}
\begin{abstract}
We consider the online makespan minimization problem on identical machines. Chen and Vestjens (ORL 1997) show ... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given the online makespan minimization problem on two identical machines, where jobs arrive over time with distinct processing times, what competitive ratio can be achieved by an algorithm that allows job replacement based on specific criteria, and how does this compare to the known lower bound of $(5 - \sqrt{5})/2 \ap... | 40,720 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{\LARGE \bf
\ifthenelse{\boolean{isconference} \thispagestyle{empty} \pagestyle{empty}
\begin{abstract} We consider the problem of bearing-based visual homing: Given a mobile robot which can measure bearing directions with respect to known landmarks, the goal is to guide the robot toward a de... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a mobile robot utilizing bearing-only measurements from known landmarks to navigate back to a predefined "home" location, suppose the robot can observe \(N\) landmarks positioned in a two-dimensional plane. If the robot successfully estimates the bearings to these landmarks and applies a control law based on a co... | 80,879 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\begin{abstract}
It is shown that for a given infinite graph $G$ on countably many vertices, and a compact, infinite set of real numbers $\Lambda$ there is a real symmetric matrix $A$ whose graph is $G$ and its spectrum is $\Lambda$. Moreover, the set of limit points of $\Lambda$ equals the essential... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the relationship between the isolated points of a compact set of real numbers $\Lambda$ and the eigenvalues of a self-adjoint operator $T$ constructed such that the standard matrix of $T$ has an infinite graph $G$ on countably many vertices, and its spectrum equals $\Lambda$? | 56,311 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Exponents and the Cohomology of Finite Groups} \author{Jonathan Pakianathan} \maketitle \centerline{Dept. of Mathematics} \centerline{University of Wisconsin} \centerline{Madison, WI 53705.}
\begin{abstract} We will provide an example of a $p$-group G which has elements of order $p^3$ in some ... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a prime \( p \) and a finite \( p \)-group \( G \) such that \( e(G) = p^3 \) and the intersection of all subgroups of index \( p^2 \) in \( G \) is trivial, what can we conclude about the relationship between \( e_{\infty}(G) \) and \( e(G) \)? What are the possible values of \( e_{\infty}(G) \) in this context? | 23,928 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Relative equilibria in continuous stellar dynamics} \titlerunning{Multiple components configurations in continuous stellar dynamics} \date{\today}
\author{Juan Campos, Manuel del Pino, and Jean Dolbeault} \institute{\textsf{M. del Pino:} Departamento de Ingenier\'{\i}a Matem\'atica and CMM, Un... | arXiv | arXiv/math_arXiv_v0.2.jsonl | In the context of stellar dynamics, consider a system consisting of \( N \) gravitating point masses \( m_1, m_2, \ldots, m_N \) located at the vertices of a regular polygon in the plane. Define the total energy of this system as
\[
\mathcal{E} = -\sum_{i < j} \frac{m_i m_j}{|\zeta_i - \zeta_j|} + \frac{1}{2}\sum_{i=... | 84,310 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Cycle up-down permutations} \begin{abstract} A permutation is defined to be {\em cycle-up-down} if it is a product of cycles that, when written starting with their smallest element, have an up-down pattern. We prove bijectively and analytically that these permutations are enumerated by the Eule... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the number of cycle-up-down permutations of length \( n \), and how is this number enumerated by the Euler numbers? Specifically, can you demonstrate the relationship between cycle-up-down permutations and the Euler numbers, including any relevant generating functions? | 74,746 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{A Brief History of the Positivity Conjecture in Tensor Category Theory} \author{Geoffrey Mason} \address{Department of Mathematics, UC Santa Cruz, CA 95064} \email{gem@ucsc.edu} \thanks{The author thanks the Simon Foundation, grant $\#427007$, for its support.}
\begin{abstract} We show the exi... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the order of the finite group \( G \) that has an irreducible character \( \chi \) with Frobenius-Schur indicator \( \nu_2(\chi) = +1 \) and such that \( \chi^2 \) has an irreducible constituent \( \varphi \) with \( \nu_2(\varphi) = -1 \)? | 30,762 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{On the rigidity of lagrangian products}
\abstract{Motivated by work of the first author, this paper studies symplectic
embedding problems of lagrangian products that are sufficiently
symmetric. In general, lagrangian products arise naturally in the study of
billiards. The main result of ... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Let \( A \) be a balanced region in \( \mathbb{R}^n \). Show that the dimension of the toric domain \( X_{4|A|} \), associated with \( 4|A| \), is equal to \( 2n \) if \( A \) is non-empty and bounded. Specifically, given the construction of symplectic embeddings such as \( B_\infty^n \times_L A \) into \( B_\infty^n \... | 76,661 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\maketitle
\section{Introduction}\label{sec:intro}
The cubic nonlinear Schr\"{o}dinger (NLS) equation \begin{equation}\label{nls} i \partial_t u(t,x) =- \Delta u(t,x) + \mu \vert u(t,x) \vert^{2}u(t,x),\qquad (t,x) \in \mathbb{R} \times \mathbb{T}^d,\quad \mu \in \mathbb{R}, \end{equation} has be... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Consider the cubic nonlinear Schrödinger equation given by
\[
i \partial_t u(t,x) = -\Delta u(t,x) + \mu |u(t,x)|^2 u(t,x), \quad (t,x) \in \mathbb{R} \times \mathbb{T}^d, \quad \mu \in \mathbb{R}.
\]
Let $H^r(\mathbb{T}^d)$ denote the Sobolev space of functions defined on the $d$-dimensional torus, and let $C_T$ be... | 13,417 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title[M/M/$\infty$ queues in semi-Markovian RE]{M/M/$\infty$ queues in semi-Markovian random environment} \author{B. D'Auria} \address{Universidad Carlos III de Madrid, Dpto. de Estadistica, Avda. de la Universidad 30, 28911 Leganés (Madrid), Spain} \email{bernardo.dauria@uc3m.es}
\thanks{Part o... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given an M/M/$\infty$ queue in a semi-Markovian random environment with parameters dependent on the state of the environment, let the arrival rate in state \( k \) be \( \lambda_k \), and assume that the sojourn times \( T_k \) are independent and have known Laplace transforms \( \tau_k(s) \). If the queue experiences ... | 42,834 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\newtheorem{theorem}{\indent Theorem}[section] \newtheorem{proposition}[theorem]{\indent Proposition} \newtheorem{definition}[theorem]{\indent Definition} \newtheorem{lemma}[theorem]{\indent Lemma} \newtheorem{remark}[theorem]{\indent Remark} \newtheorem{corollary}[theorem]{\indent Corollary}
\begin{... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Consider the fractional nonlinear Schrödinger equation given by
\[
i\partial_t u - (-\Delta)^s u + \lambda_1 |u|^{2p_1} u + \lambda_2 |u|^{2p_2} u = 0,
\]
with initial condition \( u(0,x) = u_0(x) \), where \( 0 < p_1 < p_2 < \frac{2s}{N-2s} \) and \( N \geq 2 \).
Suppose it is known that the existence of blow-up s... | 80,627 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\baselineskip=17pt
\title{Weighted generalization of the Ramadanov theorem and further considerations.}
\author{by \sc Zbigniew Pasternak-Winiarski \rm (Warsaw) \\ and \sc Pawe{\l} M. W\'ojcicki \rm (Warsaw) }
\date{} \maketitle \renewcommand{\arabic{footnote}}{} \footnote{2010 \emph{Mathematics Su... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Let \( D_n \) be a sequence of bounded domains in \( \mathbb{C}^N \) such that \( D_1 \subset D_2 \subset D_3 \subset \ldots \) and \( D = \bigcup_{n=1}^{\infty} D_n \). If the weight function \( \mu_n \) satisfies the condition \( \mu_n(z) \leq \mu_{n+1}(z) \) for all \( z \in D_n \), and \( \mu_n \to \mu \) pointwise... | 49,176 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\allowdisplaybreaks \def\mathbb R} \def\ff{\frac} \def\ss{\sqrt{\mathbb R} \def\ff{\frac} \def\ss{\sqrt} \def\B{\mathbf B} \def\mathbb W{\mathbb W} \def\mathbb N} \def\kk{\kappa} \def\m{{\bf m}{\mathbb N} \def\kk{\kappa} \def\m{{\bf m}} \def\varepsilon}\def\ddd{D^*{\varepsilon}\def\ddd{D^*} \def\del... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Let \( \mu_t \) be a probability measure on \( \mathbb{R} \) that has a finite \( p \)-th moment for some \( p > 0 \). Consider a McKean-Vlasov stochastic differential equation (SDE) defined by the equation
\[
\text{d}X_t = b(X_t, \mu_t) \text{d}t + \sigma(X_t) \text{d}W_t,
\]
where \( b: \mathbb{R} \times \mathscr{P... | 65,441 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\begin{center} {\large A hodgepodge of sets of reals } \end{center}
\begin{flushright} Arnold W. Miller\footnote{ Thanks to the conference organizers: Cosimo Guido, Ljubisa Ko\v{c}inac, Boaz Tsaban, Liljana Babinkostova, and Marion Scheepers for their generosity in inviting me to speak at the Worksho... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the minimum cardinality of a nonmeager set of reals in the context of the Souslin number, and how does it relate to the existence of a Q-set? | 50,347 | mlfoundations-dev/gair_mathpile | |
\begin{document}
~\\[-7mm]
\begin{abstract} The purpose of this note is to show that the regular locus of a complex variety is locally parabolic at the singular set. This yields that the regular locus of a compact complex variety, e.g., of a projective variety, is parabolic. We give also an application to the $L^2$-... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a Hermitian complex space \(X\) of dimension \(n\) with a singular set \(\Sing X\) of real codimension two, if a compact reduced complex variety \(X\) is defined to be parabolic, what is the necessary condition for subharmonic functions on the regular locus \(X \setminus \Sing X\) that are bounded from above? Spe... | 87,917 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Tuning Mixed Input Hyperparameters on the Fly for Efficient Population Based AutoRL}
\begin{abstract} Despite a series of recent successes in reinforcement learning (RL), many RL algorithms remain sensitive to hyperparameters. As such, there has recently been interest in the field of AutoRL, w... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the maximum expected regret bound for the PB2-Mult algorithm over a population of agents when optimizing both continuous and categorical hyperparameters, and how does it relate to the number of iterations and change points in the reward function? | 17,231 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\begin{abstract} The probability that $m$ randomly chosen elements of a finite power associative loop $C$ have prescribed orders and generate $C$ is calculated in terms of certain constants $\Gamma$ related to the action of $\aut{C}$ on the subloop lattice of $C$. As an illustration, all meaningful pr... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given the nonassociative simple Moufang loop \( C = \paige{2} \), calculate the probability that three randomly chosen elements generate the entire loop, and specifically find the probabilities for the following types of orders:
1. \( (2, 2, 2) \)
2. \( (2, 2, 3) \)
3. \( (2, 3, 3) \)
4. \( (3, 3, 3) \)
Then, com... | 75,885 | mlfoundations-dev/gair_mathpile | |
\begin{document}
Tsemo Aristide
University of Toronto
St. George Street
Toronto, Ontario Canada
M5S 3G3
tsemo58@yahoo.ca
\centerline{\bf The structure of CR manifolds.}
\centerline{Abstract.}
{\it In this paper we study the topology of CR pseudoconvex manifolds whose Reeb flow preserve the Levi metric.}
... | arXiv | arXiv/math_arXiv_v0.2.jsonl | In a compact pseudo-convex CR manifold \( N \), where the Reeb flow \( X \) preserves the Levi metric, if the closure of the orbits of \( X \) are tori, what can you conclude about the dimension of the closure of these orbits relative to the manifold \( N \)? Specifically, express the relationship between the dimension... | 44,087 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Proximal point algorithm, Douglas--Rachford algorithm and alternating projections: a case study}
\author{ Heinz H.\ Bauschke\thanks{ Mathematics, University of British Columbia, Kelowna, B.C.\ V1V~1V7, Canada. E-mail: \texttt{heinz.bauschke@ubc.ca}.},~ Minh N.\ Dao\thanks{ Department of Mathe... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Let \( f: \mathbb{R} \to \left]-\infty, +\infty\right] \) be defined by \( f(x) = \frac{1}{p}|x|^p \) for \( 1 < p < \infty \). Consider the convergence of the sequences generated by the Douglas-Rachford algorithm (DRA) and the Method of Alternating Projections (MAP) starting from \( x_0 = 1 \). How does the rate of co... | 47,976 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Automorphisms of (Affine) \texorpdfstring{$\SL(2,q)$-Unitals}
\begin{abstract}
\noindent $\SL(2,q)$-unitals are unitals of order $q$ admitting a regular action of $\SL(2,q)$ on the
complement of some block. They can be obtained from affine $\SL(2,q)$-unitals via parallelisms. We compute a s... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given an affine $\SL(2,q)$-unital of order \( q \) (where \( q \) is a prime power greater than or equal to \( 3 \)), what is the number of distinct automorphisms of this affine unital, particularly in light of the condition that the automorphism group must stabilize a block if \( \mathbb{U}_{S,\mathcal{D}} \) is a uni... | 47,878 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\twocolumn[ \icmltitle{Label Inference Attacks from Log-loss Scores} \begin{icmlauthorlist} \icmlauthor{Abhinav Aggarwal}{to} \icmlauthor{Shiva Prasad Kasiviswanathan}{to} \icmlauthor{Zekun Xu}{to} \icmlauthor{Oluwaseyi Feyisetan}{to} \icmlauthor{Nathanael Teissier}{to} \end{icmlauthorlist}
\icmlaffi... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a dataset of \(N\) datapoints classified into \(K\) label classes, and a carefully constructed prediction vector that uses distinct primes for each datapoint, how many log-loss queries does it take for an adversary to perfectly infer the true labels of all \(N\) datapoints if the adversary uses arbitrary precisio... | 42,269 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title[]{On a general implementation of $h$- and $p$-adaptive curl-conforming finite elements}
\author[M. Olm]{Marc Olm$^\dag$}
\author[S. Badia]{Santiago Badia$^{\dag,\ddag}$}
\author[A. F. Mart\'in]{Alberto F. Mart\'in$^{\dag,\ddag}$}
\thanks{$\dag$ Centre Internacional de M\`etodes Num\`erics e... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the minimum number of degrees of freedom (dof) required for a first-order edge finite element method (FEM) on a tetrahedral mesh to ensure that the tangential components of the magnetic field are continuous across element faces? Please derive your answer based on the number of edges and the properties of edge f... | 2,805 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\twocolumn[ \icmltitle{Consistent Polyhedral Surrogates for Top-$k$ Classification and Variants} \icmlsetsymbol{equal}{*}
\begin{icmlauthorlist} \icmlauthor{Jessie Finocchiaro}{cu} \icmlauthor{Rafael Frongillo}{cu} \icmlauthor{Emma Goodwill}{cu} \icmlauthor{Anish Thilagar}{cu} \end{icmlauthorlist}
\... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given that the paper presents the first consistent polyhedral surrogate for top-$k$ classification, what are the conditions on the conditional label distributions under which this new surrogate loss function becomes consistent? Formulate the constraints mathematically and explain how they relate to the properties of th... | 25,507 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Subword complexes via triangulations of root polytopes}
\begin{abstract}
Subword complexes are simplicial complexes introduced by Knutson and Miller to illustrate the combinatorics of Schubert polynomials and determinantal ideals. They proved that any subword complex is homeomorphic to a b... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a dominant permutation $\pi=1\pi'$ in $S_n$, where $\pi'$ can be represented by a partition of integers, how many reduced pipe dreams exist for the permutation $\pi$? Express this quantity in terms of its corresponding $\beta$-Grothendieck polynomial $\mathfrak{G}^{\beta=0}_{\pi}(\mathbf{1})$. | 87,064 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\begin{titlepage} \title{Reversal potential and reversal permanent charge with unequal diffusion coefficients via classical Poisson-Nernst-Planck models} \author{Hamid Mofidi\footnote{Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd., Room 405, Lawrence, Kansas 66045, USA ({\... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a quasi-one-dimensional Poisson-Nernst-Planck (PNP) model with two ion species and unequal diffusion coefficients, derive the conditions under which the reversal potential \( V_{rev} \) exists as a function of the permanent charge \( Q_0 \) and the diffusion coefficients \( D_1 \) and \( D_2 \). Specifically, det... | 81,635 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title[The extension of cochain complexes of meromorphic functions]
{The extension of cochain complexes of meromorphic functions to multiplications}
\author{Daniel Levin${}^\&$}
\address{ ${}^\&$ Mathematical Institute \\ Uiversity of Oxford \\ Andrew Wiles Building \\
Radcliffe Ob... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Consider the multiplication operation defined on the spaces of meromorphic functions $\mathcal{M}^k_m(\mathfrak g, G)$ and $\mathcal{M}^n_{m'}(\mathfrak g, G)$ that yields an element in the space $\mathcal{M}^{k+n}_{m+m'}(\mathfrak g, G)$. If the function $\mathcal{G}(g_1, x_1; \ldots; g_k, x_k) \in \mathcal{M}^k_m$ is... | 32,882 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\baselineskip=0.23in \begin{center}{\Large \bf Matching extension and matching exclusion via the size or the spectral radius of graphs\footnote{Financially supported by the National Natural Science Foundation of China (Grant Nos. 12171190, 11671164)}}
{\large Shujing Miao$^1$,\ \ Shuchao Li$^1$,\ \ ... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given an even integer \( n \geq 6 \), what is the minimum number of edges \( |E(G)| \) that a connected graph \( G \) with \( n \) vertices must have in order for \( G \) to guarantee the existence of a perfect matching? Provide the condition, as well as any examples of extremal graphs that meet this requirement. | 59,244 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{
A graph-theoretic condition for delay stability of reaction systems
}
\begin{abstract}
Delay mass-action systems provide a model of chemical kinetics when past states influence the current dynamics. In this work, we provide a graph-theoretic condition for \emph{delay stability}, i.e.,... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a reaction network with no one-step catalysis and a modified network's directed species-reaction (DSR) graph that satisfies the following conditions:
1. All cycles are s-cycles.
2. There is no S-to-R intersection.
If every reaction involves at most two different reactant species and every species has a generali... | 13,655 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{{\bf\large Rational Maps and Maximum Likelihood Decodings}
\begin{abstract} This paper studies maximum likelihood(ML) decoding in error-correcting codes as rational maps and proposes an approximate ML decoding rule by using a Taylor expansion. The point for the Taylor expansion, which will be ... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Consider an error-correcting code defined by a generator matrix \( G \) over the binary field \( \mathbb{F}_2 \). Let \( d \) be the minimum distance of the dual code \( \mathcal{C}^* \) of this code. If a code has a Taylor expansion at the fixed point \( p=(1/2,\cdots,1/2) \) that consists of only even order non-reson... | 50,355 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\author{David Gonz\'alez-\'Alvaro} \address{ Department of Mathematics, Universidad Aut\'onoma de Madrid, and ICMAT CSIC-UAM-UCM-UC3M} \curraddr{} \email{dav.gonzalez@uam.es}
\thanks{The author was supported by the following research grants: MTM2011-22612 from the Ministerio de Ciencia e Innovaci\'o... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Let \( n \) be a positive integer. What is the least integer \( k_0 \) such that the Whitney sum of any real vector bundle \( E \) over the sphere \( \mathbb{S}^n \) with a trivial bundle of rank \( k_0 \) admits a metric with nonnegative sectional curvature? Provide specific bounds for \( k_0 \) based on the congruenc... | 92,912 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Exotic smoothings via large $\mathbb{R}
\begin{abstract} We study the relationship between exotic $\mathbb{R}^4$'s and Stein surfaces as it applies to smoothing theory on more general open $4$-manifolds. In particular, we construct the first known examples of large exotic $\mathbb{R}^4$'s that... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What are the properties of the exotic $\mathbb{R}^4$'s constructed in the paper, particularly in relation to smooth embeddings into Stein surfaces and their Taylor invariants? Specifically, can you provide an example of how these exotic $\mathbb{R}^4$'s can be distinguished by their Taylor invariants and compact equiva... | 45,242 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Excited-State Adiabatic Quantum Computation Started with Vacuum States}
\author{Hayato Goto and Taro Kanao} \affiliation{ Frontier Research Laboratory, Corporate Research \& Development Center, Toshiba Corporation, 1, Komukai Toshiba-cho, Saiwai-ku, Kawasaki-shi, 212-8582, Japan}
\date{\to... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What improvement in success probability and residual energy did the excited-state adiabatic quantum computation (AQC) show compared to the standard ground-state AQC when tested on a hard instance of the four-spin Ising problem, as detailed in the study? Please specify the numerical values for both success probability a... | 87,160 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\maketitle
\begin{abstract}
In this note we use the Calabi ansatz, in the context of metrics with conical singularities along a divisor, to produce regular Calabi-Yau cones and K\"ahler-Einstein metrics of negative Ricci with a cuspidal point. As an application, we describe singularities and cuspida... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Consider a compact complex manifold \(X\) with a smooth hypersurface divisor \(D\). Assume that \( \omega_{KE} \) is a K\"ahler-Einstein metric on \(X\) with cone angle \(2\pi\beta\) along \(D\), for \(0 < \beta < 1\). Define the \(k\)-th Chern class \(c_k(X, D)\) as given in the context of the BMY inequality involving... | 24,567 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title {Linearity conditions leading to complete positivity}
\author {Iman Sargolzahi} \email{sargolzahi@neyshabur.ac.ir; sargolzahi@gmail.com} \affiliation {Department of Physics, University of Neyshabur, Neyshabur, Iran}
\begin{abstract} The reduced dynamics of an open quantum system $S$, interact... | arXiv | arXiv/math_arXiv_v0.2.jsonl | In the context of open quantum systems, consider a finite-dimensional quantum system \( S \) interacting with its environment \( E \). If the reduced dynamics of the system, described by a linear map \( \Psi_S \), satisfies the following two conditions:
1. The reduced dynamics remains linear for any arbitrary initial ... | 14,998 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\pretolerance=3000
\newcommand{\cat}[1]{\mathscr{#1}} \newcommand{\textrm{Ob}}{\textrm{Ob}} \newcommand{\textrm{Mor}}{\textrm{Mor}} \newcommand{\mathbf 1}{\mathbf 1}
\newcommand{\mathbf{sSet}}{\mathbf{sSet}} \newcommand{\mathbf{Alg}}{\mathbf{Alg}} \newcommand{\mathbf{sPr}}{\mathbf{sPr}} \newcom... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the necessary condition for the model category of differential graded categories \(\mathbf{dgCat}_{k}\) to be left proper, and how does it relate to the flat dimension of the ring \(k\)? | 81,034 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Linear precision for toric surface patches}
\author[H-C. Graf v. Bothmer]{Hans-Christian Graf von Bothmer} \address{Mathematisches Institut, Georg-August-Universiti\"at G\"ttingen,
Bunsenstr. 3-5, D-37073 G\"ottingen Germany} \email{bothmer@uni-math.gwdg.de} \urladdr{http://www.crcg.de/wik... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Classify the homogeneous polynomials \( F(x, y, z) \) in three variables that define a toric polar Cremona transformation, including their properties. How many distinct forms can such polynomials take, and what are their general characteristics based on the classification provided? | 97,685 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Realizability and exceptionality of candidate surface branched covers: methods and results}
\author{Ekaterina~{\textsc Pervova}\thanks{Supported by the Marie Curie fellowship MIF1-CT-2006-038734} \and\addtocounter{footnote}{5} Carlo~{\textsc Petronio}}
\maketitle
\begin{abstract} \noindent L... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given the candidate surface branched cover \( S^2 \argdotstoter{4:1}{(2,2),(2,2),(3,1)} S^2 \), can you demonstrate that it is exceptional and thus non-realizable? Additionally, explain the methods used to analyze its realizability, referencing techniques or theorems from the literature. | 11,126 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Experimental Test of Nonlocal Causality}
\author{M. Ringbauer$^{1,2}$, C. Giarmatzi$^{1,2}$, R. Chaves$^{3,4}$, F. Costa$^{1}$, A. G. White$^{1,2}$ \& A. Fedrizzi$^{1,2,5}$} \affiliation{$^{1}$Centre for Engineered Quantum Systems, $^{2}$Centre for Quantum Computer and Communication Technology... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the maximum value of the CHSH inequality \( S_2 \) that can be achieved in a Bell test scenario with two parties, and how does this relate to the average causal effect \( \mathrm{ACE}_{A \rightarrow B} \) in terms of the violation of local causality? Specifically, provide a quantitative relationship that links ... | 81,180 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\begin{abstract} A \emph{Hilbert basis} is a set of vectors $X \subseteq \mathbb{R}^d$ such that the integer cone
(semigroup) generated by $X$ is the intersection of the lattice generated by $X$ with the cone generated by $X$. Let $\mathscr{H}$ be the class of graphs whose set of cuts is a Hilbert... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the largest number of edges in a graph belonging to the class \(\mathscr{H}\), given that all \(K_5^{\perp}\)-minor-free graphs are in \(\mathscr{H}\) and considering the constraints mentioned in the paper regarding the structure and properties of graphs in this class? | 11,899 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{ extsc{Homogenization of Enhancing Thin Layers}
\setcounter{page}{1} \begin{abstract}
This paper derives an explicit formula for the effective diffusion tensor by using the solutions to some effective cell problems after homogenizing Road effective boundary conditions (EBCs). The concept of... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a regular pattern \(\mathcal{G}\) in the plane composed of \(C^2\) curves, define the effective diffusion tensor \(\Sigma_0\) as follows:
\[
(\Sigma_0)_{kl} = \delta_{kl} + a \int_{\Gamma_1} (\bar{w}_k)_s (x_l)_s \, ds
\]
where \( \bar{w}_k \) satisfies the corresponding corrector equations. If all arcs in \(\... | 69,023 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\thispagestyle{empty}
\title{Restrictions of continuous functions}
\section*{Introduction} Given a continuous real-valued function on $[0,1]$, and a closed subset $E\subset [0,1]$ we denote by $f\restr E$ the restriction of $f$ to $E$, that is, the function defined only on $E$ that takes the sam... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given a continuous real-valued function \( f \) on the interval \([0,1]\), what is the Hausdorff dimension of a closed subset \( E \subset [0,1] \) such that the restriction \( f \restr E \) has bounded variation, and is this dimension optimal? Specifically, can you provide a set \( E \) where \( \dim_H(E) \ge \frac{1}... | 81,796 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\newtheorem{theorem}{Theorem}[section] \newtheorem{definition}[theorem]{Definition} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{remark}[theorem]{Remark} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{example}[theorem]{Example}
\def\below#1#2{\... | arXiv | arXiv/math_arXiv_v0.2.jsonl | In a trajectory planning problem where the optimal curve \( g(t) \) lies in a Lie group \( G \) and generates a curve \( q(t) = g(t) Q_0 \) that passes near a set of prescribed target points \( q_i \) at specific times \( t_i \), what is the effect of adjusting the tolerance parameter \( \sigma \) on the optimal trajec... | 73,546 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title[H\"ormander's theorem]{H\"ormander's theorem for parabolic equations with coefficients measurable in the time variable} \author{N.V. Krylov} \thanks{The author was partially supported by
NSF Grant DMS-1160569} \email{krylov@math.umn.edu} \address{127 Vincent Hall, University of Minnesota,
M... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given the assumptions of H\"ormander's theorem concerning second-order parabolic operators \( L \) with coefficients that are infinitely differentiable with respect to spatial variables and merely measurable in time, if we impose the H\"ormander condition on the diffusion coefficients, how can we establish a quantitati... | 46,768 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\begin{center} \textbf{A generalization of Istr\u{a}\c{t}escu's fixed point theorem}
\textbf{for convex contractions}
Radu MICULESCU and Alexandru MIHAIL
\end{center}
\textbf{Abstract}. {\small In this paper we prove a generalization of Istr \u{a}\c{t}escu's theorem for convex contractions. More ... | arXiv | arXiv/math_arXiv_v0.2.jsonl | What is the unique attractor \( A \) of an iterated function system consisting of convex contractions on a complete metric space \( (X,d) \), and how is it related to the fixed points of the mappings \( f_i \) used in the system? Specifically, express \( A \) in terms of the closure of the set of limit points \( \{a_\o... | 31,921 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title[Function spaces] {On function spaces on symmetric spaces} \author{Bernhard Kr\"otz} \address{Max-Planck-Institut f\"ur Mathematik\\ Vivatsgasse 7\\ D-53111 Bonn \\email: kroetz@mpim-bonn.mpg.de}
\author{Henrik Schlichtkrull} \address{Department of Mathematics\\ University of Copenhagen\\ ... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Let \( Y = G/H \) be a semisimple symmetric space where \( G \) is a connected semisimple Lie group with finite center and \( H \) is an open subgroup of the fixed points of an involutive automorphism of \( G \). Given that the space of smooth vectors \( E_p^\infty \) for the left regular representation of \( G \) on \... | 55,698 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\parskip = 2mm \begin{center} {\bf\Large C-systems defined by universe categories: presheaves}\footnote{\em 2000 Mathematical Subject Classification: 03F50, 18C50
18D15,
}{$^,$}\footnote{For the published version of the paper see \url{http://www.tac.mta.ca/tac/volumes/32/3/32-03abs.html}}
{\la... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given two universe category functors, \({\bf \Phi} = (\Phi, \phi, \widetilde{\phi})\) from \(({\cal C}, p)\) to \(({\cal C}', p')\), how can you construct a functor morphism that ensures compatibility between their associated constructions, such that for any object \(Y\) in the categories, the following square of natur... | 66,216 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Some infinite permutation groups and
related finite linear groups}
\begin{center}
\textit{Dedicated to the memory of our late colleague
and friend \\ L.\,G.\ {\rm(}Laci\/{\rm)} Kov\'acs}
\end{center}
\begin{abstract}
This article began as a study of the structure of
infinite permu... | arXiv | arXiv/math_arXiv_v0.2.jsonl | Given an infinite group \( G \) acting on an infinite set \( \Omega \) such that every infinite normal subgroup of \( G \) is transitive, and the stabiliser \( H = G_\alpha \) (the stabiliser of a point \(\alpha \in \Omega\)) satisfies the minimal condition on normal subgroups (min-\textsc{n}), how many distinct types ... | 80,766 | mlfoundations-dev/gair_mathpile | |
\begin{document}
\title{Characterization of manifolds of constant curvature by ruled surfaces\footnote{This is a pre-print of an article published in São Paulo Journal of Mathematical Sciences (2022). The final authenticated version is available online at \url{https://doi.org/10.1007/s40863-022-00319-7}.}}
\author{L... | arXiv | arXiv/math_arXiv_v0.2.jsonl | In a connected three-dimensional Riemannian manifold \( M^3 \), suppose there exists an extrinsically flat surface tangent to every two-dimensional plane in \( T_p M^3 \) for any point \( p \in M^3 \). Under what conditions can we conclude that \( M^3 \) has constant sectional curvature? Provide a proof to support your... | 79,957 | mlfoundations-dev/gair_mathpile |
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