id
stringlengths
64
64
published
stringlengths
19
25
title
stringlengths
7
262
description
stringlengths
6
54.4k
link
stringlengths
31
227
category
stringclasses
6 values
image
stringlengths
3
247
bb78ac3bdc4c17d8b6656d05bc4a07e1f9da5370215b967f225594b7f0911f75
2026-01-01T00:00:00-05:00
On quadratic Lie algebras containing the Heisenberg Lie algebra
arXiv:2512.24333v1 Announce Type: new Abstract: In this work we study quadratic Lie algebras that contain the Heisenberg Lie algebra $\h_m$ as an ideal. We give a procedure for constructing these kind of quadratic Lie algebras and prove that any quadratic Lie algebra $\g$ that contains the Heisenberg Lie algebra as an ...
https://arxiv.org/abs/2512.24333
Academic Papers
svg
3daf15ce65a0cb06f76f6cea45e096b384889ce055c2dfeb0c729551aa107e36
2026-01-01T00:00:00-05:00
Backpropagation from KL Projections: Differential and Exact I-Projection Correspondences
arXiv:2512.24335v1 Announce Type: new Abstract: We establish two exact correspondences between reverse-mode automatic differentiation (backpropagation evaluated at a fixed forward pass) and compositions of projection maps in Kullback--Leibler (KL) geometry. In both settings, message passing defined by alternating KL pr...
https://arxiv.org/abs/2512.24335
Academic Papers
svg
61ee031697c3d0161822abd4c6cde5651ecdf517aae3f5f32b99ffd3c04c9afd
2026-01-01T00:00:00-05:00
Charge functions for all dimensional partitions
arXiv:2512.24343v1 Announce Type: new Abstract: The charge functions for n-dimensional partitions are known for n=2,3,4 in the literature. We give the expression for arbitrary odd dimension in a recent work, and now further conjecture a formula for all even dimensional cases. This conjecture is proved rigorously for 6D...
https://arxiv.org/abs/2512.24343
Academic Papers
svg
0eae0b89b094b42364378f1ba3de662286b31121487f48005b794a1e013ae7b0
2026-01-01T00:00:00-05:00
The $k$-Plancherel measure and a Finite Markov Chain
arXiv:2512.24346v1 Announce Type: new Abstract: Let $\mathcal{P}_k(n)$ denote the set of partitions of $n$ whose largest part is bounded by $k,$ which are in well-known bijection with $(k+1)$-cores $\mathcal{C}_k$. We study a growth process on $\mathcal{C}_k$, whose stationary distribution is the $k$-Plancherel measure...
https://arxiv.org/abs/2512.24346
Academic Papers
svg
6b612c2a7e497c08bd2452796332e461bc7c658860d1e2f9d4efdf1f1cfcec1e
2026-01-01T00:00:00-05:00
The period map from commutative to noncommutative deformations
arXiv:2512.24347v1 Announce Type: new Abstract: We study the period map from infinitesimal deformations of a scheme $X$ over a perfect field $k$ to those of the associated $k$-linear $\infty$-category $\mathrm{QC}(X)$. For quasicompact, smooth, and separated $X$, we identify the corresponding map on tangent fibres with...
https://arxiv.org/abs/2512.24347
Academic Papers
svg
4773eecf3c554a94636dff4ee153aeba974b46ef5b8f31bdceb630c7618fa78c
2026-01-01T00:00:00-05:00
An explicit construction of heat kernels and Green's functions in measure spaces
arXiv:2512.24348v1 Announce Type: new Abstract: We explicitly construct a heat kernel as a Neumann series for certain function spaces, such as $L^{1}$, $L^{2}$, and Hilbert spaces, associated to a locally compact Hausdorff space $\mathfrak{X}$ with Borel $\sigma$-algebra $\mathcal{B}$, and endowed with additional measu...
https://arxiv.org/abs/2512.24348
Academic Papers
svg
f16a1d68224bc225a7d0daccf22fad45cf52053407a5ae974b8f6c7e00daaf61
2026-01-01T00:00:00-05:00
The story of geometry told by coins
arXiv:2512.24349v1 Announce Type: new Abstract: In three articles published in CNJ in 2012 and 2016 , we discussed some links between mathematical sciences, coin minting and numismatics. This article is a continuation of this cycle. It tells the story of selected important developments in the history of geometry using ...
https://arxiv.org/abs/2512.24349
Academic Papers
svg
d62c7e1be3765f19b85e79528a1abc387209651e988b73ce939154fb8510103b
2026-01-01T00:00:00-05:00
Heavy-tailed distributions; extreme value theory; large deviations; ruin probabilities; solvency risk
arXiv:2512.24352v1 Announce Type: new Abstract: We establish sharp large deviation asymptotics for the maximum order statistic of independent and identically distributed heavy-tailed random variables, valid for all Borel subsets of the right tail. This result yields exact decay rates for exceedance probabilities at thr...
https://arxiv.org/abs/2512.24352
Academic Papers
svg
0543a8030a88742af49fc1ca195b35957ac535094e75b7ea46767f68308d94f6
2026-01-01T00:00:00-05:00
Functional models for $\Gamma_n$-contractions
arXiv:2512.24353v1 Announce Type: new Abstract: This article develops several functional models for a given $\Gamma_n$-contraction. The first model is motivated by the Douglas functional model for a contraction. We then establish factorization results that clarify the relationship between a minimal isometric dilation a...
https://arxiv.org/abs/2512.24353
Academic Papers
svg
73b37ebf4c31a0776980fe96c419b30a847ddb770888cdf32673685fcb8ba607
2026-01-01T00:00:00-05:00
On $R$-equivalence of Automorphism Groups of Associative Algebras
arXiv:2512.24357v1 Announce Type: new Abstract: Let $A$ be a finite-dimensional associative $k$-algebra with identity. The primary aim of this paper is to study the rationality properties of the group of all $k$-algebra automorphisms of $A$, as an affine algebraic group over an arbitrary field $k$. We investigate mainl...
https://arxiv.org/abs/2512.24357
Academic Papers
svg
4052daa9d81359129bec9fac01aefc449829d79484ba2490dcbd38ad6e83a27e
2026-01-01T00:00:00-05:00
Permutations with only reduced co-BPDs
arXiv:2512.24361v1 Announce Type: new Abstract: Bumpless pipe dreams (BPDs) are combinatorial objects used in the study of Schubert and Grothendieck polynomials. Weigandt recently introduced a co-BPD object associated to each BPD and used them to give an analogue to the change of bases formulas of Lenart and Lascoux be...
https://arxiv.org/abs/2512.24361
Academic Papers
svg
343d5a41deb0746367f661175ae6e54176726e0eb514479043f7a4a50a6233b7
2026-01-01T00:00:00-05:00
On Solvability of Automorphism Groups of Commutative Algebras
arXiv:2512.24364v1 Announce Type: new Abstract: Let $A$ be a finite-dimensional commutative associative algebra with unity over an algebraically closed field $\mathbb{K}$. The purpose of the paper is to study the solvability of $G_A$, where $G_A$ is the identity component of $\text{Aut}_\mathbb{K}(A)$. Inspired by Poll...
https://arxiv.org/abs/2512.24364
Academic Papers
svg
32b474126cd190110251d43206feea7f8e9cb546a5a746d82476fa106d22c2e3
2026-01-01T00:00:00-05:00
Limit theorems for the distance of random points in $l_p^n$-balls
arXiv:2512.24367v1 Announce Type: new Abstract: In this paper, we prove that the Euclidean distance between two independent random vectors uniformly distributed on $l_p^n$-balls $(1 \leq p \leq \infty)$ or on its boundary satisfies a central limit theorem as $n$ tends to $\infty$. Also, we give a compact proof of the c...
https://arxiv.org/abs/2512.24367
Academic Papers
svg
f79e37fd59bda755f3d0bec7b1174135e94f3e29b8734795093ac65ed57fe4bf
2026-01-01T00:00:00-05:00
On a Bruhat decomposition related to the Shalika subgroup of $GL(2n)$
arXiv:2512.24368v1 Announce Type: new Abstract: Let $F$ be a non-archimedean local field or a finite field. In this article, we obtain an explicit and complete set of double coset representatives for $S\backslash GL_{2n}(F)/Q$ where $S$ is the Shalika subgroup and $Q$ a maximal parabolic subgroup of the group $GL_{2n}(...
https://arxiv.org/abs/2512.24368
Academic Papers
svg
389dd6a85def7aede05f208c427d5d9cce15526c88729670555b395ce13e2f44
2026-01-01T00:00:00-05:00
Incremental Certificate Learning for Hybrid Neural Network Verification . A Solver Architecture for Piecewise-Linear Safety Queries
arXiv:2512.24379v1 Announce Type: new Abstract: Formal verification of deep neural networks is increasingly required in safety-critical domains, yet exact reasoning over piecewise-linear (PWL) activations such as ReLU suffers from a combinatorial explosion of activation patterns. This paper develops a solver-grade meth...
https://arxiv.org/abs/2512.24379
Academic Papers
svg
00ee9a96efeca33c49c7b3dea108319ce68afae7a0ca9b23d9926986cf9364a8
2026-01-01T00:00:00-05:00
Equivariant Partially Wrapped Fukaya Categories on Liouville Sectors
arXiv:2512.24382v1 Announce Type: new Abstract: We develop an equivariant Lagrangian Floer theory for Liouville sectors that have symmetry of a Lie group $G$. Moreover, for Liouville manifolds with $G$-symmetry, we develop a correspondence theory to relate the equivariant Lagrangian Floer cohomology upstairs and Lagran...
https://arxiv.org/abs/2512.24382
Academic Papers
svg
134e25cb4ad4f712867a9df8d1df2daca532da1a3cd3458196d996df2c5c7a09
2026-01-01T00:00:00-05:00
Mean-Field Limits of Deterministic and Stochastic Flocking Models with Nonlinear Velocity Alignment
arXiv:2512.24383v1 Announce Type: new Abstract: We study the mean-field limit for a class of agent-based models describing flocking with nonlinear velocity alignment. Each agent interacts through a communication protocol $\phi$ and a non-linear coupling of velocities given by the power law $A(\bv) = |\bv|^{p-2}\bv$, $p...
https://arxiv.org/abs/2512.24383
Academic Papers
svg
469c4ed3f94f8ad33829a74b8cef83d3d47253921bc5658a7a5cf9a3af54820c
2026-01-01T00:00:00-05:00
Stability of the reconstruction of the heat reflection coefficient in the phonon transport equation
arXiv:2512.24394v1 Announce Type: new Abstract: The reflection coefficient is an important thermal property of materials, especially at the nanoscale, and determining this property requires solving an inverse problem based on macroscopic temperature measurements. In this manuscript, we investigate the stability of this...
https://arxiv.org/abs/2512.24394
Academic Papers
svg
a2e7c710e43201c12a0b5214a124fd9e212c47551d6762e5d2a08f3c0feb4c84
2026-01-01T00:00:00-05:00
Variation of Physical Measures in Nontrivial Mixed Partially Hyperbolic Systems
arXiv:2512.24409v1 Announce Type: new Abstract: We construct a smooth nontrivial mixed partially hyperbolic system and explicitly identify its skeleton. This example shares characteristics with the classical examples. Moreover, the support of each physical measure contains three fixed points with mutually distinct unst...
https://arxiv.org/abs/2512.24409
Academic Papers
svg
3eefe1e301431f3adf1a90e871a80f898dd6c327be2fbeac019513380027b105
2026-01-01T00:00:00-05:00
A causal Markov category with Kolmogorov products
arXiv:2512.24417v1 Announce Type: new Abstract: In Fritz & Rischel, Infinite products and zero-one laws in categorical probability, the problem was posed of finding an interesting Markov category which is causal and has all (small) Kolmogorov products (there Problem 6.7). Here we give an example where the deterministic...
https://arxiv.org/abs/2512.24417
Academic Papers
svg
0afce61c8b8a55188c3bed415bf4c90c076528e1edf38ef4ed5ac918d7396026
2026-01-01T00:00:00-05:00
The non-backtracking transition probability matrix and its usage for node clustering
arXiv:2512.24434v1 Announce Type: new Abstract: Relation between the real eigenvalues of the non-backtracking matrix and those of the non-backtracking Laplacian is considered with respect to node clustering. For this purpose we use the real eigenvalues of the transition probability matrix (when the random walk goes thr...
https://arxiv.org/abs/2512.24434
Academic Papers
svg
1bdd737d11d4849f0282cc41e121a91fb66400a0f26545071278590db7a7fb4f
2026-01-01T00:00:00-05:00
Uniform Continuity in Distribution for Borel Transformations of Random Fields
arXiv:2512.24441v1 Announce Type: new Abstract: Simple sufficient conditions are given that ensure the uniform continuity in distribution for Borel transformations of random fields.
https://arxiv.org/abs/2512.24441
Academic Papers
svg
9de396f6054e2c728a87c909926a794cfd619e42318d91b182c7087925472fb6
2026-01-01T00:00:00-05:00
On the work of Zhiren Wang on rigidity in dynamics
arXiv:2512.24444v1 Announce Type: new Abstract: In honor of Zhiren Wang on the occasion of being awarded the Brin Prize, we report on his exciting and deep work on rigidity of higher rank abelian groups and lattices in higher rank semisimple groups.
https://arxiv.org/abs/2512.24444
Academic Papers
svg
8b73e4fd0ad64457b6bff5b55d5ded33ea7cf483a61b34a840c38b74edec2d44
2026-01-01T00:00:00-05:00
Skein relations on punctured surfaces
arXiv:2512.24447v1 Announce Type: new Abstract: This thesis studies skein relations in cluster algebras arising from punctured surfaces. We introduce skein-type identities expressing cluster variables associated with incompatible curves on a surface in terms of cluster variables corresponding to compatible arcs. Incomp...
https://arxiv.org/abs/2512.24447
Academic Papers
svg
cb690673b3400da83368cc97e22ec87576e94a7912c9b092353f89b44a5fe0d2
2026-01-01T00:00:00-05:00
Topology, Hyperbolicity, and the Shafarevich Conjecture for Complex Algebraic Varieties
arXiv:2512.24458v1 Announce Type: new Abstract: This survey presents recent developments concerning the Shafarevich conjecture, non-abelian Hodge theories, hyperbolicity, and the topology of complex algebraic varieties, as well as the interplay among these areas. More precisely, we present the main ideas and techniques...
https://arxiv.org/abs/2512.24458
Academic Papers
svg
35d25cd9ecfc70ba2fed9d0f1e08b24203ca0913078072528bbbb5409067c54a
2026-01-01T00:00:00-05:00
Solvability conditions for some non-Fredholm operators with shifted arguments
arXiv:2512.24476v1 Announce Type: new Abstract: In the first part of the article we establish the existence in the sense of sequences of solutions in $H^{2}(R)$ for some nonhomogeneous linear differential equation in which one of the terms has the argument translated by a constant. It is shown that under the reasonable...
https://arxiv.org/abs/2512.24476
Academic Papers
svg
6cd513b2edbe66ce10810bceb836ad174be198abb9e757880ef250b464f8da0b
2026-01-01T00:00:00-05:00
Decentralized Optimization over Time-Varying Row-Stochastic Digraphs
arXiv:2512.24483v1 Announce Type: new Abstract: Decentralized optimization over directed graphs is essential for applications such as robotic swarms, sensor networks, and distributed learning. In many practical scenarios, the underlying network is a Time-Varying Broadcast Network (TVBN), where only row-stochastic mixin...
https://arxiv.org/abs/2512.24483
Academic Papers
svg
028a3d22c3b0dd1b946a31c33add041f1bd86a37767986ca557d5b72d75c36b2
2026-01-01T00:00:00-05:00
Minimal Solutions to the Skorokhod Reflection Problem Driven by Jump Processes and an Application to Reinsurance
arXiv:2512.24491v1 Announce Type: new Abstract: We consider a reflected process in the positive orthant driven by an exogenous jump process. For a given input process, we show that there exists a unique minimal strong solution to the given particle system up until a certain maximal stopping time, which is stated explic...
https://arxiv.org/abs/2512.24491
Academic Papers
svg
d6fc627bf0f1904403d62aa28b6b9d05c8a3476c0456d4dab15fafa6f3bcdae9
2026-01-01T00:00:00-05:00
From Yang-Mills to Yang-Baxter: In Memory of Rodney Baxter and Chen--Ning Yang
arXiv:2512.24494v1 Announce Type: new Abstract: The year 2025 marked the passing of two towering figures of twentieth-century mathematical physics, Rodney Baxter and Chen-Ning Yang. Yang reshaped modern physics through the introduction of non-abelian gauge theory and, independently, through the consistency conditions u...
https://arxiv.org/abs/2512.24494
Academic Papers
svg
8327bec1fb54591fc2fbcf8610bbf39c99dd802db00ebf4dc7c50f7f4ead4fa5
2026-01-01T00:00:00-05:00
Steady Self-Propelled Motion of a Rigid Body in a Viscous Fluid with Navier-Slip Boundary Conditions
arXiv:2512.24510v1 Announce Type: new Abstract: We investigate the steady self-propelled motion of a rigid body immersed in a three-dimensional incompressible viscous fluid governed by the Navier-Stokes equations. The analysis is performed in a body-fixed reference frame, so that the fluid occupies an exterior domain a...
https://arxiv.org/abs/2512.24510
Academic Papers
svg
43ed450785f7b945abcc3b4c3e8bd4c45637e42b43c9c6e266ea8e98a6d527c0
2026-01-01T00:00:00-05:00
Classification of ancient cylindrical mean curvature flows and the Mean Convex Neighborhood Conjecture
arXiv:2512.24524v1 Announce Type: new Abstract: We resolve the Mean Convex Neighborhood Conjecture for mean curvature flows in all dimensions and for all types of cylindrical singularities. Specifically, we show that if the tangent flow at a singular point is a multiplicity-one cylinder, then in a neighborhood of that ...
https://arxiv.org/abs/2512.24524
Academic Papers
svg
53cfa445441b7cd095e4c019b0ddff5c2cdcc5519145fb961c11c263924de079
2026-01-01T00:00:00-05:00
Dimension-free estimators of gradients of functions with(out) non-independent variables
arXiv:2512.24527v1 Announce Type: new Abstract: This study proposes a unified stochastic framework for approximating and computing the gradient of every smooth function evaluated at non-independent variables, using $\ell_p$-spherical distributions on $\R^d$ with $d, p\geq 1$. The upper-bounds of the bias of the gradien...
https://arxiv.org/abs/2512.24527
Academic Papers
svg
3b9c094f8419d71238bd6df4d5e8d28796ce0e8fb78376b9fd996d3b0cd2a2ca
2026-01-01T00:00:00-05:00
On semisimplicity criteria and non-semisimple representation theory for the Kadar-Yu algebras
arXiv:2512.24535v1 Announce Type: new Abstract: The Kadar--Yu algebras are a physically motivated sequence of towers of algebras interpolating between the Brauer algebras and Temperley--Lieb algebras. The complex representation theory of the Brauer and Temperley--Lieb algebras is now fairly well understood, with each c...
https://arxiv.org/abs/2512.24535
Academic Papers
svg
d878508f6d10036ec79869318b02bf0d212169433da82fd4453d8e1b85a5230d
2026-01-01T00:00:00-05:00
The square of a subcubic planar graph without a 5-cycle is 7-choosable
arXiv:2512.24536v1 Announce Type: new Abstract: The square of a graph $G$, denoted $G^2$, has the same vertex set as $G$ and has an edge between two vertices if the distance between them in $G$ is at most $2$. Thomassen [12] showed that $\chi(G^2) \leq 7$ if $G$ is a subcubic planar graph. A natural question is whether...
https://arxiv.org/abs/2512.24536
Academic Papers
svg
a8564afe99c4a0633f7bf56c00b061e929fcd508d2f90bf0bcc7ceb071f17dca
2026-01-01T00:00:00-05:00
The Diagrammatic Spherical Category
arXiv:2512.24541v1 Announce Type: new Abstract: We construct a diagrammatic categorification of the spherical module over the Hecke algebra. We establish a basis for the morphism spaces of this category, and prove that it is equivalent to an existing algebraic spherical category.
https://arxiv.org/abs/2512.24541
Academic Papers
svg
e0042e3fd855f71ec6f2f3827ca58fe8b61e2989af31afe1306d1847504be457
2026-01-01T00:00:00-05:00
Non-isomorphic metacyclic $p$-groups of split type with the same group zeta function
arXiv:2512.24546v1 Announce Type: new Abstract: For a finite group $G$, let $a_n(G)$ be the number of subgroups of order $n$ and define $\zeta_G(s)=\sum_{n\ge 1} a_n(G)n^{-s}$. Examples are known of non-isomorphic finite groups with the same group zeta function. However, no general criterion is known for when two finit...
https://arxiv.org/abs/2512.24546
Academic Papers
svg
a8d8cf0dda6054c4b97d3d1914761e2e2c316408b2d3baae840b37b0064be9fa
2026-01-01T00:00:00-05:00
Poincar\'e duality for singular tropical hypersurfaces
arXiv:2512.24548v1 Announce Type: new Abstract: We find a partial extension of Poincar\'e duality theorem of Jell-Rau-Shaw to hypersurfaces obtained by non-primitive Viro's combinatorial patchworking. We define a classification of the triangulations of a lattice polytope by a level of primitivity and we find a partial ...
https://arxiv.org/abs/2512.24548
Academic Papers
svg
f703c3ce2d29dfbcdc14d2c009ac6abfc1a3583d748bce30dcf7d112e0630a87
2026-01-01T00:00:00-05:00
Anomalous Dissipation at Onsager-Critical Regularity
arXiv:2512.24568v1 Announce Type: new Abstract: We construct solutions to the three-dimensional Euler equations exhibiting anomalous dissipation in finite time through a vanishing viscosity limit. Inspired by \cite{BDL23} and \cite{cheskidov2023dissipation}, we extend the \(2\frac{1}{2}\)-dimensional constructions and ...
https://arxiv.org/abs/2512.24568
Academic Papers
svg
05dbc0f92b5ec26e11cb66942dbaccab1bd44ea39623e46897282c126b59ea62
2026-01-01T00:00:00-05:00
Isomorphisms between Covering-Induced Lattices and Classical Geometric Lattices
arXiv:2512.24569v1 Announce Type: new Abstract: Lattices induced by coverings arise naturally in matroid theory and combinatorial optimization, providing a structured framework for analyzing relationships between independent sets and closures. In this paper, we explore the structural properties of such lattices, with a...
https://arxiv.org/abs/2512.24569
Academic Papers
svg
3314d48e82177fa399323b4f2bc78bca60307a95052017027490157e15a37479
2026-01-01T00:00:00-05:00
Functional Calculi, Positivity, and Convolution of Matrices
arXiv:2512.24575v1 Announce Type: new Abstract: Convolution admits a natural formulation as a functional operation on matrices. Motivated by the functional and entrywise calculi, this leads to a framework in which convolution defines a matrix transform that preserves positivity. Within this setting, we establish result...
https://arxiv.org/abs/2512.24575
Academic Papers
svg
e148805bb4db70d43c32c16645a3fa7645e45ff23932431d63dff0f389b19d49
2026-01-01T00:00:00-05:00
The Dual Majorizing Measure Theorem for Canonical Processes
arXiv:2512.24576v1 Announce Type: new Abstract: We completely characterize the boundedness of the log-concave-tailed canonical processes. The corresponding new majorizing measure theorem for log-concave-tailed canonical processes is proved using the new tree structure. Moreover, we introduce the new growth condition. C...
https://arxiv.org/abs/2512.24576
Academic Papers
svg
94b6d6e6a4e5db2ccff4c4b7279984db644a08f7bb4b6aff4ce0eea4e8ac05c0
2026-01-01T00:00:00-05:00
Propagation of space-time singularities for perturbed harmonic oscillators
arXiv:2512.24582v1 Announce Type: new Abstract: We discuss propagation of space-time singularities for the quantum harmonic oscillator with time-dependent metric and potential perturbations. Reformulating the quasi-homogeneous wave front set according to Lascar (1977) in a semiclassical manner, we obtain a characteriza...
https://arxiv.org/abs/2512.24582
Academic Papers
svg
f6084e52566e4e842d59bd923082536408a9ee7d17a61adf244e4fe0ce130591
2026-01-01T00:00:00-05:00
Two-Distance Sets over Finite Fields
arXiv:2512.24590v1 Announce Type: new Abstract: We show that Blokhuis' quadratic upper bound for two-distance sets is sharp over finite fields in almost all dimensions. Our construction complements Lison\v{e}k's higher-dimensional maximal constructions that were carried out in Lorentz spaces.
https://arxiv.org/abs/2512.24590
Academic Papers
svg
85d19445574c56a41c92c7d438c5365a0d3c0dab1777c5deb6f41986e74fa0b5
2026-01-01T00:00:00-05:00
On the number of pairwise touching cylinders in $\mathbb{R}^d$
arXiv:2512.24595v1 Announce Type: new Abstract: John E. Littlewood posted the question {\em ``Is it possible in 3-space for seven infinite circular cylinders of unit radius each to touch all the others? Seven is the number suggested by counting constants.''} Boz\'oki, Lee, and R\'onyai constructed a configuration of 7 ...
https://arxiv.org/abs/2512.24595
Academic Papers
svg
85c148498e3893962e50d40c26cb286bc2496bdb25c22f178766f2bd4dbfcea9
2026-01-01T00:00:00-05:00
A categorical proof of the nonexistence of (120, 35, 10)-difference sets
arXiv:2512.24597v1 Announce Type: new Abstract: A difference set with parameters $(v, k, \lambda)$ is a subset $D$ of cardinality $k$ in a finite group $G$ of order $v$, such that the number $\lambda$ of occurrences of $g \in G$ as the ratio $d^{-1}d'$ in distinct pairs $(d, d')\in D\times D$ is independent of $g$. We ...
https://arxiv.org/abs/2512.24597
Academic Papers
svg
467668b2d3cc85a31111971932bc4d4f92b7a3dbe3d999395bb57e7b999a54d0
2026-01-01T00:00:00-05:00
Phase transition thresholds and chiral magnetic fields of general degree
arXiv:2512.24598v1 Announce Type: new Abstract: We study a variational problem for the Landau--Lifshitz energy with Dzyaloshinskii--Moriya interactions arising in 2D micromagnetics, focusing on the Bogomol'nyi regime. We first determine the minimal energy for arbitrary topological degree, thereby revealing two types of...
https://arxiv.org/abs/2512.24598
Academic Papers
svg
b4df7ee0e9b947327d0f57777a12d68d1889d1f50bc56d2669b2b7d0b22ecf20
2026-01-01T00:00:00-05:00
Polynomial mixing for the stochastic Schr\"odinger equation with large damping in the whole space
arXiv:2512.24599v1 Announce Type: new Abstract: We study the long-time mixing behavior of the stochastic nonlinear Schr\"odinger equation in $\mathbb{R}^d$, $d\le 3$. It is well known that, under a sufficiently strong damping force, the system admits unique ergodicity, although the rate of convergence toward equilibriu...
https://arxiv.org/abs/2512.24599
Academic Papers
svg
8f1489b93a88a9ad177944309c71cdc2def52fd920ff65bb22b12715364ba12f
2026-01-01T00:00:00-05:00
Intermediate topological entropies for subsets of nonautonomous dynamical systems
arXiv:2512.24606v1 Announce Type: new Abstract: Motivated by the notion of intermediate dimensions introduced by Falconer et al., we introduce a continuum of topological entropies that are intermediate between the (Bowen) topological entropy and the lower and upper capacity topological entropies. This is achieved by re...
https://arxiv.org/abs/2512.24606
Academic Papers
svg
98dc924376115e12e55be8c3f4a0c9d19ba1945d43debd894020305632b2c137
2026-01-01T00:00:00-05:00
Regulators on some abelian coverings of $\mathbb{P}^1$ minus $n+2$ points
arXiv:2512.24607v1 Announce Type: new Abstract: In this paper, we construct certain rational or integral elements in the motivic cohomology of superelliptic curves which are quotient curves of abelian coverings of $\mathbb{P}^1$ minus $n+2$ points, and prove that these elements are non-trivial by expressing their regul...
https://arxiv.org/abs/2512.24607
Academic Papers
svg
f1113c3264e499a91b50ed4a6731d3e183dc743d9b58974ff97971bb4ade74eb
2026-01-01T00:00:00-05:00
Injective hom-complexity between groups
arXiv:2512.24608v1 Announce Type: new Abstract: We present the notion of injective hom-complexity, leading to a connection between the covering number of a group and the sectional number of a group homomorphism, and provide estimates for computing this invariant.
https://arxiv.org/abs/2512.24608
Academic Papers
svg
e3dd4079d76b36f3533d58b9cf0e4ae5b6a929d4e64dbe4741c6a79aa30f5182
2026-01-01T00:00:00-05:00
Half-space minimizing solutions of a two dimensional Allen-Cahn system
arXiv:2512.24610v1 Announce Type: new Abstract: This paper studies minimizing solutions to a two dimensional Allen-Cahn system on the upper half plane, subject to Dirichlet boundary conditions, \begin{equation*} \Delta u-\nabla_u W(u)=0, \quad u: \mathbb{R}_+^2\to \mathbb{R}^2,\ u=u_0 \text{ on } \partial \mathbb{R}_+^...
https://arxiv.org/abs/2512.24610
Academic Papers
svg
6c8742140e511936f445b3e23e6e6212a943aa8ac23cae25a3a6062f69a2ffea
2026-01-01T00:00:00-05:00
Arithmetic spectral transition for the unitary almost Mathieu operator
arXiv:2512.24616v1 Announce Type: new Abstract: We study the unitary almost Mathieu operator (UAMO), a one-dimensional quasi-periodic unitary operator arising from a two-dimensional discrete-time quantum walk on $\mathbb Z^2$ in a homogeneous magnetic field. In the positive Lyapunov exponent regime $0\le \lambda_1<\lam...
https://arxiv.org/abs/2512.24616
Academic Papers
svg
393b8d7a7019801358b9b35c9366789a5607c94e39f62456732a298b990b61d9
2026-01-01T00:00:00-05:00
A Study on the Algorithm and Implementation of SDPT3
arXiv:2512.24623v1 Announce Type: new Abstract: This technical report presents a comprehensive study of SDPT3, a widely used open-source MATLAB solver for semidefinite-quadratic-linear programming, which is based on the interior-point method. It includes a self-contained and consistent description of the algorithm, wit...
https://arxiv.org/abs/2512.24623
Academic Papers
svg
3e5956faca79c9b2e3c7da23b656c6801bd221aa8d4d03ed6a0848beb1116813
2026-01-01T00:00:00-05:00
Geometric Quantization by Paths Part II: The General Case
arXiv:2512.24627v1 Announce Type: new Abstract: In Part I, we established the construction of the Prequantum Groupoid for simply connected spaces. This second part extends the theory to arbitrary connected parasymplectic diffeological spaces $(\mathrm{X}, \omega)$. We identify the obstruction to the existence of the Pr...
https://arxiv.org/abs/2512.24627
Academic Papers
svg
ba78bbc516178040c332f73255690eeaa66d45140c36a9cf752decf2c4667199
2026-01-01T00:00:00-05:00
Average first-passage times for character sums
arXiv:2512.24631v1 Announce Type: new Abstract: Let $\varepsilon>0$ and, for an odd prime $p$, set $$ S_\ell(p):=\sum_{n\le \ell}\left(\frac{n}{p}\right). $$ Define the first-passage time $$ f_\varepsilon(p):=\min\{\ell\ge 1:\ S_\ell(p)0$ such that, as $x\to\infty$, $$ \sum_{p\le x} f_\varepsilon(p)\sim c_\varepsilon \...
https://arxiv.org/abs/2512.24631
Academic Papers
svg
47e7d029ea7a0e5508c0a34dd04f17dce7a69905e9f94123eb13cd7318547dc2
2026-01-01T00:00:00-05:00
A Differential Game with Symmetric Incomplete Information on Probabilistic Initial Condition and with Signal Revelation
arXiv:2512.24640v1 Announce Type: new Abstract: In this paper, we investigate the existence and characterization of the value for a two-player zero-sum differential game with symmetric incomplete information on a continuum of initial positions and with signal revelation. Before the game starts, the initial position is ...
https://arxiv.org/abs/2512.24640
Academic Papers
svg
41e5f499660d9c0cde31d96fd4d43e58115d5c3759db710bd56ede0b76bbb53b
2026-01-01T00:00:00-05:00
Periodic Beurling-Ahlfors Extensions and Quasisymmetric Rigidity of Carpets
arXiv:2512.24649v1 Announce Type: new Abstract: We establish periodic quasiconformal extension theorems for periodic orientation-preserving quasisymmetric self homeomorphisms of quasicircles or quasi-round carpets. As applications, we prove that, if $f$ is a periodic orientation-preserving quasisymmetric self homeomorp...
https://arxiv.org/abs/2512.24649
Academic Papers
svg
1286117ff61a7fda03e9e6c5ee77730f9be43e8c245039e363d41140a74154af
2026-01-01T00:00:00-05:00
Rational Angle Bisection Problem in Higher Dimensional Spaces and Incenters of Simplices over Fields
arXiv:2512.24660v1 Announce Type: new Abstract: In this article, we generalize the following problem, which is called the rational angle bisection problem, to the $n$-dimensional space $k^n$ over a subfield $k$ of $\mathbb R$: on the coordinate plane, for which rational numbers $a$ and $b$ are the slopes of the angle b...
https://arxiv.org/abs/2512.24660
Academic Papers
svg
39e3596698a5db26b5807e06f560f8d6826128e9c08abf7c3f49daba357727eb
2026-01-01T00:00:00-05:00
Collective behaviors of an electron gas in the mean-field regime
arXiv:2512.24666v1 Announce Type: new Abstract: In this paper, we study the momentum distribution of an electron gas in a $3$-dimensional torus. The goal is to compute the occupation number of Fourier modes for some trial state obtained through random phase approximation. We obtain the mean-field analogue of momentum d...
https://arxiv.org/abs/2512.24666
Academic Papers
svg
910bc9d1294e1d978510525f64c2880ecce17139a7660a7c7fb168ceb5f05493
2026-01-01T00:00:00-05:00
Nonparametric Bandits with Single-Index Rewards: Optimality and Adaptivity
arXiv:2512.24669v1 Announce Type: new Abstract: Contextual bandits are a central framework for sequential decision-making, with applications ranging from recommendation systems to clinical trials. While nonparametric methods can flexibly model complex reward structures, they suffer from the curse of dimensionality. We ...
https://arxiv.org/abs/2512.24669
Academic Papers
svg
4721086b87ae97c481edfca60b87024d871127c1483c884b3de59e3f0cbc9a4a
2026-01-01T00:00:00-05:00
Some inequalities related to Heinz mean constant with Birkhoff orthogonality
arXiv:2512.24675v1 Announce Type: new Abstract: Motivated by the work of Baronti et al. [J. Math. Anal. Appl. 252(2000) 124-146], where they defined the supremum of an arithmetic mean of the side lengths of a triangle, summing antipodal points on the unit sphere, we introduce a new geometric constant for Banach spaces,...
https://arxiv.org/abs/2512.24675
Academic Papers
svg
a957cbf1cd459382c37b22bef19b29a591992403b72ac93bb964faf57ca7def5
2026-01-01T00:00:00-05:00
Small 3-fold blocking sets in $\mathrm{PG}(2,p^n)$
arXiv:2512.24689v1 Announce Type: new Abstract: A $t$-fold blocking set of the finite Desarguesian plane $\mathrm{PG}(2,p^n)$, $p$ prime, is a set of points meeting each line of the plane in at least $t$ points. The minimum size of such sets is of interest for numerous reasons; however, even the minimum size of nontriv...
https://arxiv.org/abs/2512.24689
Academic Papers
svg
1e55fb5731d8963985b3cf4bc31832be86a1c0fb22f340204489123d7f141a5b
2026-01-01T00:00:00-05:00
Counting Lattices with Local Hecke Series
arXiv:2512.24690v1 Announce Type: new Abstract: We count the maximal lattices over $p$-adic fields and the rational number field. For this, we use the theory of Hecke series for a reductive group over nonarchimedean local fields, which was developed by Andrianov and Hina-Sugano. By treating the Euler factors of the cou...
https://arxiv.org/abs/2512.24690
Academic Papers
svg
e3c9893fcc9c3452ab2bf429fa971a56f941a1eb987d8630c29827bb76dcd602
2026-01-01T00:00:00-05:00
Strict germs on normal surface singularities
arXiv:2512.24699v1 Announce Type: new Abstract: We show that any holomorphic germ $f \colon (X,x_0) \to (Y,y_0)$ of topological degree $1$ between normal surface singularities can be written as $f=\pi \circ \sigma$, where $\pi \colon Y' \to (Y,y_0)$ is a modification and $\sigma \colon (X,x_0) \to (Y',y_1)$ is a local ...
https://arxiv.org/abs/2512.24699
Academic Papers
svg
7956a406235a486da5f22ea4df0565690c89a142c252335e566433db75937d93
2026-01-01T00:00:00-05:00
Reformulating Confidence as Extended Likelihood
arXiv:2512.24701v1 Announce Type: new Abstract: Fisher's fiducial probability has recently received renewed attention under the name confidence. In this paper, we reformulate it within an extended-likelihood framework, a representation that helps to resolve many long-standing controversies. The proposed formulation acc...
https://arxiv.org/abs/2512.24701
Academic Papers
svg
3d8659ec37920152809589ad8a6e3356f77f34038eabbaf623cc399020d7f55a
2026-01-01T00:00:00-05:00
$L_p$-estimates for nonlocal equations with general L\'evy measures
arXiv:2512.24704v1 Announce Type: new Abstract: We consider nonlocal operators of the form \begin{equation*} L_t u(x) = \int_{\mathbb{R}^d} \left( u(x+y)-u(x)-\nabla u(x)\cdot y^{(\sigma)} \right) \nu_t(dy), \end{equation*} where $\nu_t$ is a general L\'evy measure of order $\sigma \in(0,2)$. We allow this class of L\'...
https://arxiv.org/abs/2512.24704
Academic Papers
svg
d988d508e76540ec32cd527c981797f8e0cb3f056829dbe347672b656585089c
2026-01-01T00:00:00-05:00
On $\mathscr{M}$-arrangements of conics and lines with ordinary singularities
arXiv:2512.24707v1 Announce Type: new Abstract: In this paper, we study combinatorial aspects of reduced plane curves known as $\mathscr{M}$-curves. This notation is a natural generalization of maximizing plane curves which are well-known in the theory of algebraic surfaces. We focus here on $\mathscr{M}$-arrangements ...
https://arxiv.org/abs/2512.24707
Academic Papers
svg
c56564b336786abde941c0dc0ff3b67caea4ddb69a5c35fa08ac2af466b011fe
2026-01-01T00:00:00-05:00
Absolutely Summing Toeplitz operators on Bergman spaces in the unit ball of $\mathbb{C}^n$
arXiv:2512.24710v1 Announce Type: new Abstract: In this paper, for $p> 1 $ and $r \ge 1$ we provide a complete characterization of the positive Borel measures $\mu$ on the unit ball $\B_n$ of $\mathbb {C}^n$ for which the induced Toeplitz operator $T_\mu$ is $r$-summing on the Bergman space $A^{p}$. We prove that the $...
https://arxiv.org/abs/2512.24710
Academic Papers
svg
478b657acb2c79cb90df2dbc64f3615eacf022c3a117f1ddd17e61b5a5c2c020
2026-01-01T00:00:00-05:00
A proximal subgradient algorithm for constrained multiobjective DC-type optimization
arXiv:2512.24717v1 Announce Type: new Abstract: In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous gradient, then subtracting a we...
https://arxiv.org/abs/2512.24717
Academic Papers
svg
e0f3da7d80485d25d65e7c11d080ef080c5608e0bd9bc9eae798023b6e83f940
2026-01-01T00:00:00-05:00
Products of random Hermitian matrices and brickwork Hurwitz numbers. Products of normal matrices
arXiv:2512.24720v1 Announce Type: new Abstract: We consider products of $n$ random Hermitian matrices which generalize the one-matrix model and show its relation to Hurwitz numbers which count ramified coverings of certain type. Namely, these Hurwitz numbers count $2k$-fold ramified coverings of the Riemann sphere with...
https://arxiv.org/abs/2512.24720
Academic Papers
svg
e59fbf081cd8c1552604c4d7c6bb4d23b5c40f1ad20a66a0e71464a39c3deb48
2026-01-01T00:00:00-05:00
Isocapacitary constants for the $p$-Laplacian on compact manifolds
arXiv:2512.24725v1 Announce Type: new Abstract: In this paper, we introduce Steklov and Neumann isocapacitary constants for the $p$-Laplacian on compact manifolds. These constants yield two-sided bounds for the $(p,\alpha)$-Sobolev constants, which degenerate to upper and lower bounds for the first nontrivial Steklov a...
https://arxiv.org/abs/2512.24725
Academic Papers
svg
a8dde0be27af04202e00d28d9d187604e055c27703225efad9b51cc29b2e8bdd
2026-01-01T00:00:00-05:00
Isomorphism between Hopf algebras for multiple zeta values
arXiv:2512.24732v1 Announce Type: new Abstract: The classical quasi-shuffle algebra for multiple zeta values have a well-known Hopf algebra structure. Recently, the shuffle algebra for multiple zeta values are also equipped with a Hopf algebra structure. This paper shows that these two Hopf algebras are isomorphic.
https://arxiv.org/abs/2512.24732
Academic Papers
svg
6d3e0e6e2e854ef24edb411b10540fbc3386193a87211fa371da1a64ff6d360f
2026-01-01T00:00:00-05:00
From boundary random walks to Feller's Brownian Motions
arXiv:2512.24734v1 Announce Type: new Abstract: We establish an invariance principle connecting boundary random walks on $\mathbb N$ with Feller's Brownian motions on $[0,\infty)$. A Feller's Brownian motion is a Feller process on $[0,\infty)$ whose excursions away from the boundary $0$ coincide with those of a killed ...
https://arxiv.org/abs/2512.24734
Academic Papers
svg
cc0d4a33baf7d7b0890d53d3b3bd2adc2e5dd96e8791ae325a12e722bcc04b9e
2026-01-01T00:00:00-05:00
Some Studies on Stochastic Optimization based Quantitative Risk Management
arXiv:2512.24736v1 Announce Type: new Abstract: Risk management often plays an important role in decision making under uncertainty. In quantitative risk management, assessing and optimizing risk metrics requires efficient computing techniques and reliable theoretical guarantees. In this paper, we introduce several topi...
https://arxiv.org/abs/2512.24736
Academic Papers
svg
2f1ec5b51ca43dc6dde8d1c0a1eabe0cf70902a8fc47aa5ce61364b832f7f5eb
2026-01-01T00:00:00-05:00
Structure of twisted Jacquet modules of principal series representations of $GL_{2n}(F)$
arXiv:2512.24737v1 Announce Type: new Abstract: Let $F$ be a non-archimedean local field or a finite field. Let $\pi$ be a principal series representation of $GL_{2n}(F)$ induced from any of its maximal standard parabolic subgroups. Let $N$ be the unipotent radical of the maximal parabolic subgroup $P$ of $GL_{2n}(F)$ ...
https://arxiv.org/abs/2512.24737
Academic Papers
svg
2ba9ede121287927986301f6a06df61d045d96e49bd5dee5300f4f4be8d22ff4
2026-01-01T00:00:00-05:00
The Radon--Nikodym topography of acyclic measured graphs
arXiv:2512.24741v1 Announce Type: new Abstract: We study locally countable acyclic measure-class-preserving (mcp) Borel graphs by analyzing their "topography" -- the interaction between the geometry and the associated Radon--Nikodym cocycle. We identify three notions of topographic significance for ends in such graphs ...
https://arxiv.org/abs/2512.24741
Academic Papers
svg
7d295ed4b40366d91e3ee584a7205ca4cec2a7086a30612e366d8e9e628050cb
2026-01-01T00:00:00-05:00
The function-operator convolution algebra over the Bergman space of the ball and its Gelfand theory
arXiv:2512.24746v1 Announce Type: new Abstract: We investigate the structure of the commutative Banach algebra formed as the direct sum of integrable radial functions on the disc and the radial operators on the Bergman space, endowed with the convolution from quantum harmonic analysis as the product. In particular, we ...
https://arxiv.org/abs/2512.24746
Academic Papers
svg
6d055944b01979afbf70c01b95a112c7309eacd48339a81349a5a0e4a4b77cb0
2026-01-01T00:00:00-05:00
Non-Commutative Maximal Inequalities for State-Preserving Actions of amenable groups
arXiv:2512.24751v1 Announce Type: new Abstract: In this article, we establish maximal inequalities and deduce ergodic theorems for state-preserving actions of amenable, locally compact, second-countable groups on tracial non-commutative $L^1$-spaces. As a further consequence, in combination with the Neveu decomposition...
https://arxiv.org/abs/2512.24751
Academic Papers
svg
b5761944e9291418a771231482fe3bed4ee403f2922b3444c7739874a027bfdb
2026-01-01T00:00:00-05:00
Phase Reduction of Limit Cycle Oscillators: A Tutorial Review with New Perspectives on Isochrons and an Outlook to Higher-Order Reductions
arXiv:2512.24775v1 Announce Type: new Abstract: The phase reduction technique is essential for studying rhythmic phenomena across various scientific fields. It allows the complex dynamics of high-dimensional oscillatory systems to be expressed by a single phase variable. This paper provides a detailed review and synthe...
https://arxiv.org/abs/2512.24775
Academic Papers
svg
b31b92f1b2031f3e38b953c104289e8ed92b427989341b1ac3b61b13db797c16
2026-01-01T00:00:00-05:00
The tournament ratchet's clicktime process, and metastability in a Moran model
arXiv:2512.24779v1 Announce Type: new Abstract: Muller's ratchet, in its prototype version, models a haploid, asexual population whose size~$N$ is constant over the generations. Slightly deleterious mutations are acquired along the lineages at a constant rate, and individuals carrying less mutations have a selective ad...
https://arxiv.org/abs/2512.24779
Academic Papers
svg
20671ab39d87f08757f1ca88a91c5c6bc2ec26fbc33325ab89eecd67de95a804
2026-01-01T00:00:00-05:00
On rational orbits in some prehomogeneous vector spaces
arXiv:2512.24783v1 Announce Type: new Abstract: Let $k$ be a field with characteristic different from $2$. In this paper, we describe the $k$-rational orbit spaces in some irreducible prehomogeneous vector spaces $(G,V)$ over $k$, where $G$ is a connected reductive algebraic group defined over $k$ and $V$ is an irreduc...
https://arxiv.org/abs/2512.24783
Academic Papers
svg
6cb7c08aa7c267d3ed3d1c60e6b73b452b8e54e5dabea02ddcbc37c32c580e30
2026-01-01T00:00:00-05:00
Coarse geometry of extended admissible groups
arXiv:2512.24784v1 Announce Type: new Abstract: Extended admissible groups belong to a particular class of graphs of groups that admit a decomposition generalizing those of non-geometric 3-manifold groups and Croke-Kleiner admissible groups. In this paper, we study several coarse-geometric aspects of extended admissibl...
https://arxiv.org/abs/2512.24784
Academic Papers
svg
e1f9d8aa2195b4781fabd47a49257a78a743d908687711c59b6ff590493f8dd2
2026-01-01T00:00:00-05:00
A first approximation algorithm for the Bin Packing Problem with Setups
arXiv:2512.24785v1 Announce Type: new Abstract: We study constant-factor approximation algorithms for the Bin Packing Problem with Setups (BPPS). First, we show that adaptations of classical BPP heuristics can have arbitrarily poor worst-case performance on BPPS instances. Then, we propose a two-phase heuristic for the...
https://arxiv.org/abs/2512.24785
Academic Papers
svg
23c39bc3eb5a8dade2d51e8ed2dbf5dbe6d954e8d7592a3fc5181990035e7206
2026-01-01T00:00:00-05:00
Rational orbits in some prehomogeneous vector spaces associated to $Sp_{6}$ revisited
arXiv:2512.24789v1 Announce Type: new Abstract: Let $k$ be a field with $\text{char}(k)\neq 2$. We prove that all maximal flags of composition algebras over $k$, appear as the $k$-rational $Sp_{6}$-orbits in a Zariski-dense $Sp_{6}$-invariant subset $V^{ss}\subset V=\wedge^{3}V_{6}$, where $V_{6}$ is the standard $6$-d...
https://arxiv.org/abs/2512.24789
Academic Papers
svg
074e5641dd065e4057248a57c6688b479f638b5266c5410f73ed6849e49f0230
2026-01-01T00:00:00-05:00
Curvature of left-invariant complex Finsler metric on Lie groups
arXiv:2512.24791v1 Announce Type: new Abstract: Let $ G $ be a connected Lie group with real Lie algebra $ \mathfrak{g}$. Suppose $G$ is also a complex manifold. We obtain explicit holomorphic sectional and bisectional curvature formulas of left-invariant strongly pseudoconvex complex Finsler metrics $F$ on $G$ in term...
https://arxiv.org/abs/2512.24791
Academic Papers
svg
9b86b47ea07ca9e9f60864809e243091c70a29c09fd6160b33501e3c3c1ebd4f
2026-01-01T00:00:00-05:00
Geometric approaches to Lie bialgebras, their classification, and applications
arXiv:2512.24795v1 Announce Type: new Abstract: This PhD Thesis consists of two parts. The first part focuses on novel algebraic and geometric approaches to the classification problem of coboundary Lie bialgebras up to Lie algebra automorphisms. More specifically, Grassmann, graded algebra and algebraic invariant techn...
https://arxiv.org/abs/2512.24795
Academic Papers
svg
b335e710a7c1009391ac5b9bdbbf2ff80d0aa76e82107407571b56e0b86584e5
2026-01-01T00:00:00-05:00
Global spherically symmetric classical solutions for arbitrary large initial data of the multi-dimensional non-isentropic compressible Navier-Stokes equations
arXiv:2512.24799v1 Announce Type: new Abstract: In 1871, Saint-Venant introduced the shallow water equations. Since then, the global classical solutions for arbitrary large initial data of the multi-dimensional viscous Saint-Venant system have remained a well-known open problem. It was only recently that [Huang-Meng-Zh...
https://arxiv.org/abs/2512.24799
Academic Papers
svg
8cf5f9bf46572dc895e9acce6f4bcca47a977dbfec3e31b1a3d9997c6de79926
2026-01-01T00:00:00-05:00
A Study of S-primary Ideals in Commutative Semirings
arXiv:2512.24800v1 Announce Type: new Abstract: In this article, we define the concept of an $S$-$k$-irreducible ideal and $S$-$k$-maximal ideal in a commutative semiring. We also establish several results concerning $S$-$k$-primary ideals and prove the existence theorem and the $S$-version of the uniqueness theorem us...
https://arxiv.org/abs/2512.24800
Academic Papers
svg
95921f27dece6d1b48693e1f25437c5e68b6ea4bfae94f81b20784f5f421bd9b
2026-01-01T00:00:00-05:00
Heat kernel estimates for Markov processes with jump kernels blowing-up at the boundary
arXiv:2512.24807v1 Announce Type: new Abstract: In this paper, we study purely discontinuous symmetric Markov processes on closed subsets of ${\mathbb R}^d$, $d\ge 1$, with jump kernels of the form $J(x,y)=|x-y|^{-d-\alpha}{\mathcal B}(x,y)$, $\alpha\in (0,2)$, where the function ${\mathcal B}(x,y)$ may blow up at the ...
https://arxiv.org/abs/2512.24807
Academic Papers
svg
67cddd994853e429ec11656708cc3c489a79a9e89555ec82d41bb528ff4601b5
2026-01-01T00:00:00-05:00
H\"older continuity of weak solutions to the thin-film equation in $d=2$
arXiv:2512.24809v1 Announce Type: new Abstract: The thin-film equation $\partial_t u = -\nabla \cdot (u^n \nabla \Delta u)$ describes the evolution of the height $u=u(x,t)\geq 0$ of a viscous thin liquid film spreading on a flat solid surface. We prove H\"older continuity of energy-dissipating weak solutions to the thi...
https://arxiv.org/abs/2512.24809
Academic Papers
svg
22b06ee4649f508a6dc95671c7c5b19d7486889138cb24c2eb121240ce8b7e13
2026-01-01T00:00:00-05:00
Four collapsing one-dimensional particles: a dynamical system approach of the spherical billiard reduction
arXiv:2512.24812v1 Announce Type: new Abstract: We consider a system of four one-dimensional inelastic hard spheres evolving on the real line $\mathbb{R}$, and colliding according to a scattering law characterized by a fixed restitution coefficient $r$. We study the possible orders of collisions when the inelastic coll...
https://arxiv.org/abs/2512.24812
Academic Papers
svg
a29c786dd79fb74cd07a53b1ed25a2ee4c1ca21dd73d311362f1c02f30284ca6
2026-01-01T00:00:00-05:00
Number of $K$-rational points with given $j$-invariant on modular curves
arXiv:2512.24817v1 Announce Type: new Abstract: In this article, we study how to compute the number of $K$-rational points with a given $j$-invariant on an arbitrary modular curve. As an application, for each positive integer $n$, we determine the list of possible numbers of cyclic $n$-isogenies an elliptic curve over ...
https://arxiv.org/abs/2512.24817
Academic Papers
svg
2f899b98bfe644b97009086926661acd54cd8deb3eb5b98ceeba4f105d8bc5f4
2026-01-01T00:00:00-05:00
A ccc indestructible construction with CH
arXiv:2512.24821v1 Announce Type: new Abstract: We introduce a variant of the Kurepa family. We then use one such family to construct a ccc indestructible property associated with a complete coherent Suslin tree $S$. Moreover, in every ccc forcing extension that preserves Suslin of $S$, forcing with $S$ induces a stron...
https://arxiv.org/abs/2512.24821
Academic Papers
svg
99e4cf4e82ed149f690a8d87b5e7aea4048c4536398ccb9d350f0adac2c6d02f
2026-01-01T00:00:00-05:00
Bol's type inequality for singular metrics and its application to prescribing $Q$-curvature problems
arXiv:2512.24828v1 Announce Type: new Abstract: In this article, we study higher-order Bol's inequality for radial normal solutions to a singular Liouville equation. By applying these inequalities along with compactness arguments, we derive necessary and sufficient conditions for the existence of radial normal solution...
https://arxiv.org/abs/2512.24828
Academic Papers
svg
8b9bd212cb4bda3fc8ee76b912f725e44505465fa9fc27e9b706016a2a6cbcf9
2026-01-01T00:00:00-05:00
Penny graphs in the hyperbolic plane
arXiv:2512.24832v1 Announce Type: new Abstract: We consider the problem of finding the maximum number $e_d(n)$ of pairs of touching circles in a packing of $n$ congruent circles of diameter $d$ in the hyperbolic plane of curvature $-1$. In the Euclidean plane, the maximum comes from a spiral construction of the tiling ...
https://arxiv.org/abs/2512.24832
Academic Papers
svg
4a3ae2dfb9b2233d87c52d380203f913c40c04c7d4e6d5c399d3f9b7cd8b3093
2026-01-01T00:00:00-05:00
A Comparison Principle for Bifurcation of Periodic Solutions of Hamiltonian Systems
arXiv:2512.24835v1 Announce Type: new Abstract: We obtain novel criteria for the existence of local bifurcation for periodic solutions of Hamiltonian systems by a comparison principle of the spectral flow. Our method allows to find the appearance of new solutions by a simple inspection of the coefficients of the system...
https://arxiv.org/abs/2512.24835
Academic Papers
svg
e7619c8d1e65cc32e72cf603f4aaac6876e0c3f946219948fe39a7dc270f2224
2026-01-01T00:00:00-05:00
Boundedness of Fourier Integral Operators with complex phases on Fourier Lebesgue spaces
arXiv:2512.24854v1 Announce Type: new Abstract: In this paper, we develop boundedness estimates for Fourier integral operators on Fourier Lebesgue spaces when the associated canonical relation is parametrised by a complex phase function. Our result constitutes the complex analogue of those obtained for real canonical r...
https://arxiv.org/abs/2512.24854
Academic Papers
svg
918e71ba40eec151c27369c571c528e64d6e02c99d44d276c8e7e69d77e900c6
2026-01-01T00:00:00-05:00
On a conjecture of Almgren II: area-minimizing submanifolds with fractal singular sets on almost any manifold
arXiv:2512.24859v1 Announce Type: new Abstract: This paper is the second in a two-part solution to Almgren's conjecture on the existence of area-minimizing submanifolds with fractal singular sets. In part one, we construct area-minimizing submanifolds with fractal singular sets on certain special manifolds. Here we con...
https://arxiv.org/abs/2512.24859
Academic Papers
svg
ac88ba503ec8678068543a608de52ff01aa20497ad4a8f8746a57a1527c8e006
2026-01-01T00:00:00-05:00
Configuration Spaces of Finite Representation Type Algebras
arXiv:2512.24870v1 Announce Type: new Abstract: To every finite-dimensional $\mathbb C$-algebra $\Lambda$ of finite representation type we associate an affine variety. These varieties are a large generalization of the varieties defined by "$u$ variables" satisfying "$u$-equations", first introduced in the context of op...
https://arxiv.org/abs/2512.24870
Academic Papers
svg
5f0b1e21519d277c5966244651cff718fb57118e31f0f7d2bb22f909237e87fa
2026-01-01T00:00:00-05:00
Tensor Based Proximal Alternating Minimization Method for A Kind of Inhomogeneous Quartic Optimization Problem
arXiv:2512.24872v1 Announce Type: new Abstract: In this paper, we propose an efficient numerical approach for solving a specific type of quartic inhomogeneous polynomial optimization problem inspired by practical applications. The primary contribution of this work lies in establishing an inherent equivalence between th...
https://arxiv.org/abs/2512.24872
Academic Papers
svg