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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 |
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