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b9856d8baea09787b49b9f69244a26492de101c0fae7ce5cbbf57df5a9473931 | 2026-01-01T00:00:00-05:00 | Enhanced premelting at the ice-rubber interface using all-atom molecular dynamics simulation | arXiv:2508.20448v2 Announce Type: replace-cross Abstract: The ice-rubber interface is critical in applications such as tires and shoe outsoles, yet its molecular tribology remains unclear. Using all-atom molecular dynamics simulations, we studied premelting layers at the basal face of ice in contact with styrene-butadi... | https://arxiv.org/abs/2508.20448 | Academic Papers | svg |
a80922ac2fd2e44f4faef128c77cbfe66173cbdd4b1b4728bafdb9897b7dbc9e | 2026-01-01T00:00:00-05:00 | Setting limits on blazar-boosted dark matter with xenon-based detectors | arXiv:2509.07265v2 Announce Type: replace-cross Abstract: Dual-phase xenon time-projection chambers achieve optimal sensitivity to dark matter in the mass range from about 10 to 1000~GeV/$c^{2}$. However, sub-GeV dark-matter particles do not produce nuclear recoils above detection thresholds in these detectors. Blazar-... | https://arxiv.org/abs/2509.07265 | Academic Papers | svg |
cce9bd41d1b27114a017c8c59959624d3c690c8f362af36cc066ceca17cce4f9 | 2026-01-01T00:00:00-05:00 | Constraints on inelastic dark matter from the CDEX-1B experiment | arXiv:2510.07800v2 Announce Type: replace-cross Abstract: We present limits on spin-independent inelastic weakly interacting massive particles (WIMP)-nucleus scattering using the 737.1 kg$\cdot$day dataset from the CDEX-1B experiment. Expected nuclear recoil spectra for various inelastic WIMP masses $m_\chi$ and mass s... | https://arxiv.org/abs/2510.07800 | Academic Papers | svg |
12cf59885d43ba134e16a14ded9569eece88959dc77436a8275efb670e45fc5d | 2026-01-01T00:00:00-05:00 | GoodRegressor: A General-Purpose Symbolic Regression Framework for Physically Interpretable Materials Modeling | arXiv:2510.18325v4 Announce Type: replace-cross Abstract: Symbolic regression offers a promising route toward interpretable machine learning, yet existing methods suffer from poor predictability and computational intractability when exploring large expression spaces. I introduce GoodRegressor, a general-purpose C++-bas... | https://arxiv.org/abs/2510.18325 | Academic Papers | svg |
671962be6fd2d0dec8164eb9811890733b808f9a424193ea08359ed74c0d28e4 | 2026-01-01T00:00:00-05:00 | A mini-review on combinatorial solutions to the Marcus-Lushnikov irreversible aggregation | arXiv:2512.11459v3 Announce Type: replace-cross Abstract: Over the past decade, a combinatorial framework for discrete, finite, and irreversibly aggregating systems has emerged. This work reviews its progress, practical applications, and limitations. We outline the approach's assumptions and foundations, based on direc... | https://arxiv.org/abs/2512.11459 | Academic Papers | svg |
280c619e123e510c3f02c5d8e36d5e35f7aa562ee196599e672d7a0547432fbe | 2026-01-01T00:00:00-05:00 | Measuring the time-scale-dependent information flow between maternal and fetal heartbeats during the third trimester | arXiv:2512.22270v2 Announce Type: replace-cross Abstract: Prenatal maternal stress alters maternal-fetal heart rate coupling, as demonstrated by the Fetal Stress Index derived from bivariate phase-rectified signal averaging. Here, we extend this framework using information-theoretical measures to elucidate underlying m... | https://arxiv.org/abs/2512.22270 | Academic Papers | svg |
44ebdab467d44f6d15d10c0aeb464f30f08609d542c639ec00bbb2abe53305c3 | 2026-01-01T00:00:00-05:00 | Pair Space in Classical Mechanics III. Some Four-Body Central Configurations | arXiv:2512.23730v1 Announce Type: new Abstract: We study central configurations in the four body problem, i.e., configurations in which the forces on all the bodies point to a fixed, single point in space. The newly formulated pair-space formalism yields a set of vectorial equations that fully characterize such configu... | https://arxiv.org/abs/2512.23730 | Academic Papers | svg |
930078b4fafdfb172cc61df0a19b380872abe23822adf07adf8db33588ae523c | 2026-01-01T00:00:00-05:00 | Solvability of the B\'ezout Equation for Banach Algebra-Valued $H^\infty$ Functions on the Polydisk | arXiv:2512.23733v1 Announce Type: new Abstract: In connection with the still unsolved multidimensional corona problem for algebras of bounded holomorphic functions on convex domains, we study the solvability of the B\'ezout equation for the algebra of bounded holomorphic functions on the polydisk with values in a compl... | https://arxiv.org/abs/2512.23733 | Academic Papers | svg |
ad8a5f418e7c43c8391a149e0fb4b31e35acce428f025342e1c582d55fd5c039 | 2026-01-01T00:00:00-05:00 | Linear Preservers of Real Matrix Classes Admitting a Real Logarithm | arXiv:2512.23735v1 Announce Type: new Abstract: In real Lie theory, matrices that admit a real logarithm reside in the identity component $\mathrm{GL}_n(\mathbb{R})_+$ of the general linear group $\mathrm{GL}_n(\mathbb{R})$, with logarithms in the Lie algebra $\mathfrak{gl}_n(\mathbb{R})$. The exponential map \[ \exp :... | https://arxiv.org/abs/2512.23735 | Academic Papers | svg |
9d021e96cef4d363e55a95fe94275acda0d9b0a8ed62e84d865e6d86e78ebeae | 2026-01-01T00:00:00-05:00 | A Discrete Logarithm Construction for Orthogonal Double Covers of the Complete Graph by Hamiltonian Paths | arXiv:2512.23802v1 Announce Type: new Abstract: During their investigation of power-sequence terraces, Anderson and Preece briefly mention a construction of a terrace for the cyclic group $\mathbb{Z}_n$ when $n$ is odd and $2n+1$ is prime; it is built using the discrete logarithm modulo $2n+1$. In this short note we se... | https://arxiv.org/abs/2512.23802 | Academic Papers | svg |
38002830fad0b2160f880ed5eb8a16ff95cc89e31fef173c43e221fa30fd4241 | 2026-01-01T00:00:00-05:00 | A new kind of automorphic form and a proof of the essential transformation laws | arXiv:2512.23823v1 Announce Type: new Abstract: We utilize the structure of quasiautomorphic forms over an arbitrary Hecke triangle group to define a new vector analogue of an automorphic form. We supply a proof of the functional equations that hold for these functions modulo the group generators. | https://arxiv.org/abs/2512.23823 | Academic Papers | svg |
70c10e07957a75b331aa655a4b9986946af5d04bd98a2506799f0410fd0a4d9e | 2026-01-01T00:00:00-05:00 | Gradings on the Hecke category, and categorification with unequal parameters | arXiv:2512.23827v1 Announce Type: new Abstract: We classify gradings on the Hecke category that refine the standard integer grading. We also classify object-preserving autoequivalences of the Hecke category. We obtain a natural bigrading on the Hecke category which is related to the Frobenius automorphism. We also obta... | https://arxiv.org/abs/2512.23827 | Academic Papers | svg |
cc1d76caaf755ff3a3193e4fc356213922fa114c9419ec4d2344c60d4e13f7b9 | 2026-01-01T00:00:00-05:00 | Hoffman-London graphs: When paths minimize $H$-colorings among trees | arXiv:2512.23828v1 Announce Type: new Abstract: Given a graph $G$ and a target graph $H$, an $H$-coloring of $G$ is an adjacency-preserving vertex map from $G$ to $H$. The number of $H$-colorings of $G$, $\hom(G,H)$, has been studied for many classes of $G$ and $H$. In particular, extremal questions of maximizing and m... | https://arxiv.org/abs/2512.23828 | Academic Papers | svg |
c108a21b53efc03a30dfa1bd4afa0e3d0e486b2cde2d5a7733aa35baa947aca9 | 2026-01-01T00:00:00-05:00 | Fractal Mehler kernels and nonlinear geometric flows | arXiv:2512.23830v1 Announce Type: new Abstract: In this paper we introduce a two-parameter family of Mehler kernels and connect them to a class of Baouendi-Grushin flows in fractal dimension. We also highlight a link with a geometric fully nonlinear equation and formulate two questions. | https://arxiv.org/abs/2512.23830 | Academic Papers | svg |
55e4d6b84b06bdb38bb1d8372a3d1e2b514f8aee0a88f2489a05bbfdaf42322b | 2026-01-01T00:00:00-05:00 | Absolutely partially hyperbolic surface endomorphisms are dynamically coherent | arXiv:2512.23831v1 Announce Type: new Abstract: We show that if an endomorphism $f:\mathbb{T}^2 \to \mathbb{T}^2$ is absolutely partially hyperbolic, then it has a center foliation. Moreover, the center foliation is leaf conjugate to that of its linearization. | https://arxiv.org/abs/2512.23831 | Academic Papers | svg |
7f9413cab2366124a11f6add197252d531ca9c61654b1df721fde26f764dfbca | 2026-01-01T00:00:00-05:00 | Prime ideals in the Boolean polynomial semiring | arXiv:2512.23839v1 Announce Type: new Abstract: In this article, we disprove a conjecture of F. Alarc\'on and D. Anderson and give a complete classification of the prime ideals in the one variable polynomial semiring with coefficients in Boolean semifield. We group the prime ideals of $\mathbb{B}[x]$ into three classes... | https://arxiv.org/abs/2512.23839 | Academic Papers | svg |
d108f5aa90e340bc5a2954e30e2b03e6be79069c3bb0aeb4de08f314b3d2a3be | 2026-01-01T00:00:00-05:00 | Multigraphs and Time Ordered Isserlis-Wick formulae | arXiv:2512.23845v1 Announce Type: new Abstract: Given a m-dimensional Gaussian process and polynomial m variables with real coefficients, we calculate the induced path odered exponenial in two different ways: one is purely algebraic in spirit and the other one is diagrammatic in spirit and uses multigraph labelings (an... | https://arxiv.org/abs/2512.23845 | Academic Papers | svg |
b4d632242d82ad80547918fe7d5f1abf3743cb5ceb1d22d9942ece0f2c3803ab | 2026-01-01T00:00:00-05:00 | A positive eigenvalue result for semilinear differential equations in Banach spaces with functional initial conditions | arXiv:2512.23876v1 Announce Type: new Abstract: We study the existence of positive eigenvalues with associated nonnegative mild eigenfunctions for a class of abstract initial value problems in Banach spaces with functional, possibly nonlocal, initial conditions. The framework includes periodic, multipoint, and integral... | https://arxiv.org/abs/2512.23876 | Academic Papers | svg |
d3570d7c8bf9eac3c809918b0832df6c7d33654ab4890c2cffb1d340be3cb679 | 2026-01-01T00:00:00-05:00 | Powers of Hamiltonian cycles in randomly augmented P\'osa-Seymour graphs | arXiv:2512.23886v1 Announce Type: new Abstract: We study the question of the least number of random edges that need to be added to a P\'osa-Seymour graph, that is, a graph with minimum degree exceeding $\frac k{k+1}n$, to secure the existence of the $m$-th power of a Hamiltonian cycle, $m>k$. It turns out that, dependi... | https://arxiv.org/abs/2512.23886 | Academic Papers | svg |
a8b1f9825ab6d230351270998648a1dc69c6b75b0210f566f971ed1e6585e1e8 | 2026-01-01T00:00:00-05:00 | Tree-independence number VII. Excluding a star | arXiv:2512.23887v1 Announce Type: new Abstract: We prove that for every fixed integer $s$ and every planar graph $H$, the class of $H$-induced-minor-free and $K_{1,s}$-induced-subgraph-free graphs has polylogarithmic tree-independence number. This is a weakening of a conjecture of Dallard, Krnc, Kwon, Milani\v{c}, Muna... | https://arxiv.org/abs/2512.23887 | Academic Papers | svg |
73e078df47d1d5cf56367019418c1dcee873bd1f18bd0741945e0688872df4e6 | 2026-01-01T00:00:00-05:00 | Algorithms for numerical semigroups with fixed maximum primitive | arXiv:2512.23891v1 Announce Type: new Abstract: We present an algorithm to explore various properties of the numerical semigroups with a given maximum primitive. In particular, we count the number of such numerical semigroups and verify that there is no counterexample to Wilf's conjecture among the numerical semigroups... | https://arxiv.org/abs/2512.23891 | Academic Papers | svg |
66cfb96dc7f63a8ef0cb95f84c2a65e7cd438a26065082ef88d56d3b645c3399 | 2026-01-01T00:00:00-05:00 | On $GL(1|1)$ Higgs bundles | arXiv:2512.23909v1 Announce Type: new Abstract: We investigate the moduli space of holomorphic $GL(1|1)$ Higgs bundles over a compact Riemann surface. The supergroup $GL(1|1)$, the simplest non-trivial example beyond abelian cases, provides an ideal setting for developing supergeometric analogues of classical results i... | https://arxiv.org/abs/2512.23909 | Academic Papers | svg |
1082e21e456b62793118b3ff8a7c30a009110c45a30ad5f8aecdf06b882d7b6f | 2026-01-01T00:00:00-05:00 | From Stable Rank One to Real Rank Zero: A Note on Tracial Approximate Oscillation Zero | arXiv:2512.23911v1 Announce Type: new Abstract: We present a relation between stable rank one and real rank zero via the method of tracial oscillation. Let $A$ be a simple separable $C^*$-algebra of stable rank one. We show that $A$ has tracial approximate oscillation zero and, as a consequence, the tracial sequence al... | https://arxiv.org/abs/2512.23911 | Academic Papers | svg |
a829950c5dbeea42a1962d5011190a1d364181c625324a4a2dca2acb751d30f4 | 2026-01-01T00:00:00-05:00 | $p$-Adic $\lambda$ Functions for Cyclic Mumford Curve | arXiv:2512.23913v1 Announce Type: new Abstract: We express the branch points cross ratio of cyclic Mumford curves as quotients of $p$-adic theta functions evaluated at the p-adic period matrix | https://arxiv.org/abs/2512.23913 | Academic Papers | svg |
c4b396fba7947c943cf1b008115568b304a7944c0b4375bf79d2bd0c7912b96f | 2026-01-01T00:00:00-05:00 | The probability of isomorphic group structures of isogenous elliptic curves over finite fields | arXiv:2512.23921v1 Announce Type: new Abstract: Let l be a prime number and let E and E' be l-isogenous elliptic curves defined over Q. In this paper we determine the proportion of primes p for which E(F_p) is isomorphic to E'(F_p). Our techniques are based on those developed in \cite{ck} and \cite{rnt}. | https://arxiv.org/abs/2512.23921 | Academic Papers | svg |
268e98d01279af5f6c30099e5c582583ef8773133290b2bed168e5b6ed49db4a | 2026-01-01T00:00:00-05:00 | Stable envelopes for critical loci | arXiv:2512.23929v1 Announce Type: new Abstract: This is the first in a sequence of papers devoted to stable envelopes in critical cohomology and critical $K$-theory for symmetric GIT quotients with potentials and related geometries, and their applications to geometric representation theory and enumerative geometry. In ... | https://arxiv.org/abs/2512.23929 | Academic Papers | svg |
6240769cfee07aeb70ad686de8b70190b0ec6257dfa9af3bc386101307659530 | 2026-01-01T00:00:00-05:00 | On strongly multiplicative sets | arXiv:2512.23935v1 Announce Type: new Abstract: A multiplicative subset S of a ring R is called strongly multiplicative if (\cap_{i \in \Delta} s_i R) \cap S is non-empty for each family (s_i)_{i \in \Delta} of S. In this paper, we study how these sets help stabilize localization and ideal operations. We show that loca... | https://arxiv.org/abs/2512.23935 | Academic Papers | svg |
c190a4758ea01baa63afd23861683307acf433eaa7d0ea28b67272f6963b33f0 | 2026-01-01T00:00:00-05:00 | Positive specializations of K-theoretic Schur P- and Q-functions | arXiv:2512.23944v1 Announce Type: new Abstract: Yeliussizov has classified the positive specializations of symmetric Grothendieck functions, defined in several different ways, providing a K-theoretic lift of the classical Edrei-Thoma theorem. This note studies the analogous classification problem for Ikeda and Naruse's... | https://arxiv.org/abs/2512.23944 | Academic Papers | svg |
2122f122e5154f7b78482ebf09ee7baf7470707a436ae7a01eb7d0da145c0e90 | 2026-01-01T00:00:00-05:00 | A nonlinear instability result to the Navier-Stokes equations with Navier slip boundary conditions | arXiv:2512.23946v1 Announce Type: new Abstract: In this paper, we investigate the instability of the trivial steady states to the incompressible viscous fluid with Navier-slip boundary conditions. For the linear instability, the existence of infinitely many normal mode solutions to the linearized equations is shown via... | https://arxiv.org/abs/2512.23946 | Academic Papers | svg |
854bc5763193fd46a3d9fcf80f11a69e40ffc9134463374ffce0ea86469b5347 | 2026-01-01T00:00:00-05:00 | Comonotone approximation and interpolation by entire functions II | arXiv:2512.23949v1 Announce Type: new Abstract: A theorem of Hoischen states that given a positive continuous function $\varepsilon:\mathbb{R}\to\mathbb{R}$, an integer $n\geq 0$, and a closed discrete set $E\subseteq\mathbb{R}$, any $C^n$ function $f:\mathbb{R}\to\mathbb{R}$ can be approximated by an entire function $... | https://arxiv.org/abs/2512.23949 | Academic Papers | svg |
2120bbe557065e0437bc59d1f249bd6adaa59880676f9bc3eec7c9792329e0e6 | 2026-01-01T00:00:00-05:00 | Concentration and fluctuations of sine-Gordon measure around topological multi-soliton manifold | arXiv:2512.23957v1 Announce Type: new Abstract: We study the sine-Gordon measure defined on each homotopy class. The energy space decomposes into infinitely many such classes indexed by the topological degree $Q \in \mathbb{Z}$. Even though the sine-Gordon action admits no minimizer in homotopy classes with $|Q| \ge 2$... | https://arxiv.org/abs/2512.23957 | Academic Papers | svg |
0e8b582992da3801d10a19cc2963d15fd7a6773d09f7549361ca088f1bd193b9 | 2026-01-01T00:00:00-05:00 | Adjoint L-Infinity Actions and Conserved Charges in GR | arXiv:2512.23970v1 Announce Type: new Abstract: In this work we compute the conserved currents and charges associated to the action of an infinitesimal isometry (Killing field) in Einstein--Cartan--Palatini gravity. We offer a new approach to these quantities through the formalism of $L_\infty$-algebras and the work of... | https://arxiv.org/abs/2512.23970 | Academic Papers | svg |
8885da2551a73cf7879f123099763eca80fe5cae9762ed62a200c43d47b122cc | 2026-01-01T00:00:00-05:00 | Sub-structure in module category of Virasoro vertex operator algebras $L(c_{p,q}, 0)$ | arXiv:2512.23980v1 Announce Type: new Abstract: We determine all premodular subcategories and modular tensor subcategories in the module categories of Virasoro vertex operator algebras $L(c_{p,q},0)$ and the module categories of the simple current extensions of $L(c_{p,p+1},0)$. | https://arxiv.org/abs/2512.23980 | Academic Papers | svg |
f643c84fc9038b4f5da94ac3ac1d3a65b3a8bcc6ed44adaa7cb3b6945b3eca5d | 2026-01-01T00:00:00-05:00 | A Short Proof that Every Claw-Free Cubic Graph is (1,1,2,2)-Packing Colorable | arXiv:2512.24001v1 Announce Type: new Abstract: It was recently proved that every claw-free cubic graph admits a (1, 1, 2, 2)-packing coloring--that is, its vertex set can be partitioned into two 1-packings and two 2-packings. This result was established by Bre\v{s}ar, Kuenzel, and Rall [Discrete Mathematics 348 (8) (2... | https://arxiv.org/abs/2512.24001 | Academic Papers | svg |
3d778db66eaeb6bec402e38dfba78cc583cfaea01d4db8542d10645015470609 | 2026-01-01T00:00:00-05:00 | Integrality of a trigonometric determinant arising from a conjecture of Sun | arXiv:2512.24012v1 Announce Type: new Abstract: In this paper we resolve a conjecture of Zhi-Wei Sun concerning the integrality and arithmetic structure of certain trigonometric determinants. Our approach builds on techniques developed in our previous work, where trigonometric determinants were studied via special valu... | https://arxiv.org/abs/2512.24012 | Academic Papers | svg |
c4fdee2f1c5dacb56e431b42eb0a839d6193bdc5b6e53c2992d097bf83750467 | 2026-01-01T00:00:00-05:00 | Moduli of surfaces fibered in (log) Calabi-Yau pairs II: elliptic surfaces | arXiv:2512.24017v1 Announce Type: new Abstract: This paper continues the study initiated in [ISZ25] on the moduli of surfaces admitting lc-trivial fibrations. Using the techniques developed in [ISZ25], we (1) provide a classification of the surfaces appearing on the boundary of the KSBA-moduli space of elliptic surface... | https://arxiv.org/abs/2512.24017 | Academic Papers | svg |
f1aab343a47bd6d8dd36ca40564f184214e105f2b4cbf740dcc6418ee31b9d72 | 2026-01-01T00:00:00-05:00 | A regularity theory for second-order parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces | arXiv:2512.24020v1 Announce Type: new Abstract: We develop an optimal regularity theory for parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces. The results extend the classical Schauder estimates to coefficients that are merely measurable in time and to the critical case of integer-o... | https://arxiv.org/abs/2512.24020 | Academic Papers | svg |
630750dd4f40f3ed7fc557c76c7ade468532f9b65352a04dd8e639679cc4f30c | 2026-01-01T00:00:00-05:00 | Filtered cospans and interlevel persistence with boundary conditions | arXiv:2512.24025v1 Announce Type: new Abstract: We develop the notion of a "filtered cospan" as an algebraic object that stands in the same relation to interlevel persistence modules as filtered chain complexes stand with respect to sublevel persistence modules. This relation is expressed via a functor from a category ... | https://arxiv.org/abs/2512.24025 | Academic Papers | svg |
ce8d882506f2db366f5af7993820403b019ab79625d5da9ae3594583c886e259 | 2026-01-01T00:00:00-05:00 | On the finiteness of the group associated with weighted walks in multidimensional orthants | arXiv:2512.24027v1 Announce Type: new Abstract: In the study of walks with small steps confined to multidimensional orthants, a certain group of transformations plays a central role. In particular, several techniques to potentially compute the generating function, including the orbit sum method, can only be applied whe... | https://arxiv.org/abs/2512.24027 | Academic Papers | svg |
f0fce38a6b77a4af3c615fcd0759765bb41e0019a48caabe0cd45d0f79c1944c | 2026-01-01T00:00:00-05:00 | Secondary Term for the Mean Value of Maass Special $L$-values | arXiv:2512.24028v1 Announce Type: new Abstract: In this paper, we discover a secondary term in the asymptotic formula for the mean value of Hecke--Maass special $L$-values $ L (1/2+it_f, f) $ with the average over $f (z)$ in an orthonormal basis of (even or odd) Hecke--Maass cusp forms of Laplace eigenvalue $1/4 + t_f^... | https://arxiv.org/abs/2512.24028 | Academic Papers | svg |
0189bae7aef5359e6c7e749acc3af71d7dea79f61d6981c63fe8dc7e9b881e87 | 2026-01-01T00:00:00-05:00 | Whittaker modules and representations of finite $W$-algebras of queer Lie superalgebras | arXiv:2512.24030v1 Announce Type: new Abstract: We study various categories of Whittaker modules over the queer Lie superalgebras $\mathfrak q(n)$. We formulate standard Whittaker modules and reduce the problem of composition factors of these standard Whittaker modules to that of Verma modules in the BGG categories $\m... | https://arxiv.org/abs/2512.24030 | Academic Papers | svg |
710eefbaa12c2c7449487a6c635ef6966af58c27a6b81bcd4fdec74c0c94730e | 2026-01-01T00:00:00-05:00 | An anti-classification theorem for minimal homeomorphisms on the torus | arXiv:2512.24031v1 Announce Type: new Abstract: We show that it is impossible to classify topological conjugacy relation of minimal homeomorphisms on the torus by countable structures. | https://arxiv.org/abs/2512.24031 | Academic Papers | svg |
890491b6898abcf31e5ada600a2928eb55c2c306c5c6d93ab05c6d020ccb544b | 2026-01-01T00:00:00-05:00 | Jordan Nilpotent Group Rings of index $4$ | arXiv:2512.24033v1 Announce Type: new Abstract: Let $RG$ be the group ring of an arbitrary group $G$ over an associative non-commutative ring $R$ with identity. In this paper, we have obtained the necessary and sufficient conditions under which $RG$ is Jordan nilpotent of index $4$. | https://arxiv.org/abs/2512.24033 | Academic Papers | svg |
33c59c31ddbcc3419903c53dc6e3a021977c1b525d7efa699bae88133f19f8e1 | 2026-01-01T00:00:00-05:00 | Push-forward of smooth measures and strong Thom stratifications | arXiv:2512.24034v1 Announce Type: new Abstract: We study the collection of measures obtained via push-forward along a map between smooth varieties over p-adic fields. We investigate when the stalks of this collection are finite-dimensional. We provide an algebro-geometric criterion ensuring this property. This criterio... | https://arxiv.org/abs/2512.24034 | Academic Papers | svg |
5dcdcb8db678a58b6353371648c14d6069aec347350c4a89ac9adb162a83a2a3 | 2026-01-01T00:00:00-05:00 | Local Asymptotic Normality for Mixed Fractional Brownian Motion with $0<H<3/4$ | arXiv:2512.24042v1 Announce Type: new Abstract: This paper establishes the Local Asymptotic Normality (LAN) property for the mixed fractional Brownian motion under high-frequency observations with Hurst index $H \in (0, 3/4)$. The simultaneous estimation of the volatility and the Hurst index encounters a degeneracy pro... | https://arxiv.org/abs/2512.24042 | Academic Papers | svg |
5890cf06b39ef13fe8a84c0d67b52f1f72bc2de27b56c340fb4b7411f037ada6 | 2026-01-01T00:00:00-05:00 | On spectral equations for an evolution operator of a $q$-oscillator lattice | arXiv:2512.24043v1 Announce Type: new Abstract: We propose a set of algebraic equations describing eigenvalues and eigenstates of a relativistic evolution operator for a two-dimensional $q$-oscillator Kagom\'e lattice. Evolution operator is constructed with the help of $q$-oscillator solution of the Tetrahedron Equatio... | https://arxiv.org/abs/2512.24043 | Academic Papers | svg |
5eeb7ed451d61f09ab60d0787a8cd8cc794bcffb54aa6e94ac76f390f21876a1 | 2026-01-01T00:00:00-05:00 | Quantum two-dimensional superintegrable systems in flat space: exact-solvability, hidden algebra, polynomial algebra of integrals | arXiv:2512.24045v1 Announce Type: new Abstract: In this short review paper the detailed analysis of six two-dimensional quantum {\it superintegrable} systems in flat space is presented. It includes the Smorodinsky-Winternitz potentials I-II (the Holt potential), the Fokas-Lagerstrom model, the 3-body Calogero and Wolfe... | https://arxiv.org/abs/2512.24045 | Academic Papers | svg |
934d149c26640ac758e47785968b075d0f6c83c7d21298c249c75d485ebc059b | 2026-01-01T00:00:00-05:00 | Yaglom theorem for critical branching random walk on $\mathbb{Z}^d$ | arXiv:2512.24047v1 Announce Type: new Abstract: We study the critical branching random walk on $\mathbb{Z}^d$ started from a distant point $x$ and conditioned to hit some compact set $K$ in $\mathbb{Z}^d$. We are interested in the occupation time in $K$ and present its asymptotic behaviors in different dimensions. It i... | https://arxiv.org/abs/2512.24047 | Academic Papers | svg |
b5917a60f438bf9dea84173802672999074531b25dc85b30a0e7fd4003bb865a | 2026-01-01T00:00:00-05:00 | Polynomial functors over free nilpotent groups | arXiv:2512.24048v1 Announce Type: new Abstract: Let $k$ be a unital commutative ring. In this paper, we study polynomial functors from the category of finitely generated free nilpotent groups to the category of $k$-modules, focusing on comparisons across different nilpotency classes and polynomial degrees. As a consequ... | https://arxiv.org/abs/2512.24048 | Academic Papers | svg |
3a8ec4dcd341114035ef2ea446e0abd291f26a21473e83968c96421a77a386dd | 2026-01-01T00:00:00-05:00 | Complexity and convergence analysis of a single-loop SDCAM for Lipschitz composite optimization and beyond | arXiv:2512.24059v1 Announce Type: new Abstract: We develop and analyze a single-loop algorithm for minimizing the sum of a Lipschitz differentiable function $f$, a prox-friendly proper closed function $g$ (with a closed domain on which $g$ is continuous) and the composition of another prox-friendly proper closed functi... | https://arxiv.org/abs/2512.24059 | Academic Papers | svg |
343b6c12758d007bca0ed337503dfeb6a7abdef4e2504b3f85f8e3e8ca33739b | 2026-01-01T00:00:00-05:00 | Propagation of chaos for the homogeneous Boltzmann equation with moderately soft potentials | arXiv:2512.24065v1 Announce Type: new Abstract: We show that the Kac particle system converges, as the number of particles tends to infinity, to the solution of the homogeneous Boltzmann equation, in the regime of moderately soft potentials, $\gamma \in (-2,0)$ with the common notation. This proves the propagation of c... | https://arxiv.org/abs/2512.24065 | Academic Papers | svg |
6b749839c259ebaac0143cdeaf79ffe2a0ad5d64a9f3c99a7e9fa29a79c65d7e | 2026-01-01T00:00:00-05:00 | Short sums of trace functions over function fields and their applications | arXiv:2512.24080v1 Announce Type: new Abstract: For large enough (but fixed) prime powers $q$, and trace functions to squarefree moduli in $\mathbb{F}_q[u]$ with slopes at most $1$ at infinity, and no Artin--Schreier factors in their geometric global monodromy, we come close to square-root cancellation in short sums. A... | https://arxiv.org/abs/2512.24080 | Academic Papers | svg |
ecf06ad8860c0b6631bcb04521926fc228b3fa51fcf6051c6bdd1a978ad75f1f | 2026-01-01T00:00:00-05:00 | On generalized metric structures | arXiv:2512.24082v1 Announce Type: new Abstract: Let $M$ be a smooth manifold, let $TM$ be its tangent bundle and $T^{*}M$ its cotangent bundle. This paper investigates integrability conditions for generalized metrics, generalized almost para-complex structures, and generalized Hermitian structures on the generalized ta... | https://arxiv.org/abs/2512.24082 | Academic Papers | svg |
ebe9d2aa2b145a63fdde12cf58412616b31eca4c665ae680c0454e7e113b9355 | 2026-01-01T00:00:00-05:00 | Rank three representations of Painlev\'e systems: II. de Rham structure, Fourier--Laplace transformation | arXiv:2512.24083v1 Announce Type: new Abstract: We use formal microlocalization to describe the Fourier--Laplace transformation between rank 3 and rank 2 D-module representations of Painleve systems. We conclude the existence of biregular morphism between the corresponding de Rham complex structures. | https://arxiv.org/abs/2512.24083 | Academic Papers | svg |
b1ac6dfd06042710443d87332b11c1abe18b5272e289c8740c5f94c4f712e47c | 2026-01-01T00:00:00-05:00 | Dirac solitons in one-dimensional nonlinear Schr\"odinger equations | arXiv:2512.24089v1 Announce Type: new Abstract: In this paper we study a family of one-dimensional stationary cubic nonlinear Schr\"odinger (NLS) equations with periodic potentials and linear part displaying Dirac points in the dispersion relation. By introducing a suitable periodic perturbation, one can open a spectra... | https://arxiv.org/abs/2512.24089 | Academic Papers | svg |
c8b7d231abf81b18c91d65f8bd92415e4432cb5af3afabc815b2d7334ff587e7 | 2026-01-01T00:00:00-05:00 | Herman Rings: Structure, Dynamics, and Open Problems | arXiv:2512.24118v1 Announce Type: new Abstract: The existence of the Herman ring of a function adds interest and complexity to the dynamics of the function. We present a detailed and understandable summary of the core discoveries and recent developments on the Herman ring of rational and transcendental meromorphic func... | https://arxiv.org/abs/2512.24118 | Academic Papers | svg |
456f55002d3a6247ea25b25f72090b7b10211649ec52de70df3b4bb853d4d0b1 | 2026-01-01T00:00:00-05:00 | A goodness-of-fit test for the Zeta distribution with unknown parameter | arXiv:2512.24128v1 Announce Type: new Abstract: We introduce a new goodness-of-fit test for count data on $\mathbb{N}$ for the Zeta distribution with unknown parameter. The test is built on a Stein-type characterization that uses, as Stein operator, the infinitesimal generator of a birth-death process whose stationary ... | https://arxiv.org/abs/2512.24128 | Academic Papers | svg |
06824a16a95c580559eecb195c690efc0e255e212d585d4efaaff961c9462e94 | 2026-01-01T00:00:00-05:00 | Bicombing the mapping class group and Teichm\"uller space via stable cubical intervals | arXiv:2512.24136v1 Announce Type: new Abstract: In this mostly expository article, we provide a new account of our proof with Minsky and Sisto that mapping class groups and Teichm\"uller spaces admit bicombings. More generally, we explain how the hierarchical hull of a pair of points in any colorable hierarchically hyp... | https://arxiv.org/abs/2512.24136 | Academic Papers | svg |
caf6f023bd3a5a3d1e0d72ea7d1182904863fd6152704749c031fbd777a28b53 | 2026-01-01T00:00:00-05:00 | Large values of quadratic character sums revisited | arXiv:2512.24147v1 Announce Type: new Abstract: We study large values of quadratic character sums with summation lengths exceeding the square root of the modulus. Assuming the Generalized Riemann Hypothesis, we obtain a new Omega result. | https://arxiv.org/abs/2512.24147 | Academic Papers | svg |
e0a4e607be16c479f758560674ff90077c10660ef7a186189e329e66cee05db7 | 2026-01-01T00:00:00-05:00 | Some Congruences Involving Fourth Powers of Generalized Central Trinomial Coefficients | arXiv:2512.24148v1 Announce Type: new Abstract: Let $ p \ge 5 $ be a prime and let $ b, c \in \mathbb{Z} $. Denote by $ T_k(b,c) $ the generalized central trinomial coefficient, i.e., the coefficient of $ x^k $ in $ (x^2 + bx + c)^k $. In this paper, we establish congruences modulo $ p^3 $ and $ p^4 $ for sums of the f... | https://arxiv.org/abs/2512.24148 | Academic Papers | svg |
7faf3d21ccac1c572af7fa99ff7cf86392bb32137340e5a71a98e437dc324cf3 | 2026-01-01T00:00:00-05:00 | Transitive partially hyperbolic diffeomorphisms in dimension three | arXiv:2512.24151v1 Announce Type: new Abstract: We prove that any $C^{1+\alpha}$ transitive conservative partially hyperbolic diffeomorphism of a closed 3-manifold with virtually solvable fundamental group is ergodic. Consequently, in light of \cite{FP-classify}, this establishes the equivalence between transitivity an... | https://arxiv.org/abs/2512.24151 | Academic Papers | svg |
f5cbc38fbb6cd52c71b1113fd7b6c007632f78a7857ae95c0d4e987bd10e6221 | 2026-01-01T00:00:00-05:00 | Minimal Polynomials in Spin Representations of Symmetric and Alternating Groups | arXiv:2512.24158v1 Announce Type: new Abstract: We determine the minimal polynomial of each element of the double cover $G$ of the symmetric or alternating group in every irreducible spin representation of $G$. | https://arxiv.org/abs/2512.24158 | Academic Papers | svg |
372374ad91da06827e594555a15ca11a8dc27eda90a8f0c7fd8ea5dcc9fc2666 | 2026-01-01T00:00:00-05:00 | Admissible HYM metrics on klt KE varieties and the MY equality for big anticanonical K-stable varieties | arXiv:2512.24161v1 Announce Type: new Abstract: This short note includes three results: $(1)$ If a reflexive sheaf $\mathcal{E}$ on a log terminal K\"{a}hler-Einstein variety $(X,\omega)$ is slope stable with respect to a singular K\"{a}hler-Einstein metric $\omega$, then $\mathcal{E}$ admits an $\omega$-admissible Her... | https://arxiv.org/abs/2512.24161 | Academic Papers | svg |
7d138c812b95c1c3a57ac972ef2fe7adb63b29b7d2bb24e2588563e051a7aab8 | 2026-01-01T00:00:00-05:00 | Cheeger Bounds for Stable Phase Retrieval in Reproducing Kernel Hilbert Spaces | arXiv:2512.24169v1 Announce Type: new Abstract: Phase retrieval seeks to reconstruct a signal from phaseless intensity measurements and, in applications where measurements contain errors, demands stable reconstruction. We study local stability of phase retrieval in reproducing kernel Hilbert spaces. Motivated by Grohs-... | https://arxiv.org/abs/2512.24169 | Academic Papers | svg |
d12cff853313789b92ea19fef6c91692c8d687c418232994a37600bf9295a019 | 2026-01-01T00:00:00-05:00 | On the MLC Conjecture and the Renormalization Theory in Complex Dynamics | arXiv:2512.24171v1 Announce Type: new Abstract: In this Note, we present recent developments in the Renormalization Theory of quadratic polynomials and discuss their applications, with an emphasis on the MLC conjecture, the problem of local connectivity of the Mandelbrot set, and on its geometric counterparts. | https://arxiv.org/abs/2512.24171 | Academic Papers | svg |
26ff587310f0145d674167cba27dfc369aba6c766207731816925ecc3b274418 | 2026-01-01T00:00:00-05:00 | Tensor-Network Analysis of Root Patterns in the XXX Model with Open Boundaries | arXiv:2512.24182v1 Announce Type: new Abstract: The string hypothesis for Bethe roots represents a cornerstone in the study of quantum integrable systems, providing access to physical quantities such as the ground-state energy and the finite-temperature free energy. While the $t-W$ scheme and the inhomogeneous $T-Q$ re... | https://arxiv.org/abs/2512.24182 | Academic Papers | svg |
dbc00364c7907090ba914f363aa97033ff280c6c8785170e02bf032e83b23cf6 | 2026-01-01T00:00:00-05:00 | On the 1-leg Donaldson-Thomas $\mathbb{Z}_2\times\mathbb{Z}_2$-vertex | arXiv:2512.24196v1 Announce Type: new Abstract: We introduce a notion of restricted pyramid configurations for computing the 1-leg Donaldson-Thomas $\mathbb{Z}_2\times\mathbb{Z}_2$-vertex. We study a special type of restricted pyramid configurations with the prescribed 1-leg partitions, and find one unique class of the... | https://arxiv.org/abs/2512.24196 | Academic Papers | svg |
dfae03aa3ba7ef4d6fa4ce315fa1cca8a11df12abdd941353a00ec56322738da | 2026-01-01T00:00:00-05:00 | Gaussian free fields on Hamming graphs and lattice spin systems | arXiv:2512.24199v1 Announce Type: new Abstract: We discuss a class of discrete Gaussian free fields on Hamming graphs, where interactions are determined solely by the Hamming distance between vertices. The purpose of examining this class is that it differs significantly from the commonly discussed spin system on the in... | https://arxiv.org/abs/2512.24199 | Academic Papers | svg |
5bc18005ec82fe890f4061776222954a30b5a9c5e5afa6d0b9a12aab3068e976 | 2026-01-01T00:00:00-05:00 | Instanton 2-torsion and fibered knots | arXiv:2512.24206v1 Announce Type: new Abstract: We prove that the unreduced singular instanton homology $I^\sharp(Y,K;\mathbb{Z})$ has $2$-torsion for any null-homologous fibered knot $K$ of genus $g>0$ in a closed $3$-manifold $Y$ except for $\#^{2g}S^1\times S^2$. The main technical result is a formula of $I^\sharp(Y... | https://arxiv.org/abs/2512.24206 | Academic Papers | svg |
3b43bb1ecff4f29a66d8efd254b204a7a34c368db80f58805282d09d452f574f | 2026-01-01T00:00:00-05:00 | Notes on the LVP and the CVP in $p$-adic Fields | arXiv:2512.24207v1 Announce Type: new Abstract: This paper explores computational methods for solving the Longest Vector Problem (LVP) and Closest Vector Problem (CVP) in $p$-adic fields. Leveraging the non-Archimedean property of $p$-adic norms, we propose a polynomial time algorithm to compute orthogonal bases for $p... | https://arxiv.org/abs/2512.24207 | Academic Papers | svg |
b443321ea0b8a14e1f73e3d66208df99110518fbec7af7f41b7c9209ed130d0d | 2026-01-01T00:00:00-05:00 | An Equivalence Result on the Order of Differentiability in Frobenius' Theorem | arXiv:2512.24218v1 Announce Type: new Abstract: This paper examines the simplest case of total differential equations that appears in the theory of foliation structures, without imposing the smoothness assumptions. This leads to a peculiar asymmetry in the differentiability of solutions. To resolve this asymmetry, this... | https://arxiv.org/abs/2512.24218 | Academic Papers | svg |
9facd6690d53c31b03092c12744abe8e02fabc38b257cfaff5d1b2309e201994 | 2026-01-01T00:00:00-05:00 | Node-Kayles on Trees | arXiv:2512.24221v1 Announce Type: new Abstract: Node-Kayles is a well-known impartial combinatorial game played on graphs, where players alternately select a vertex and remove it along with its neighbors. By the Sprague-Grundy theorem, every position of an impartial game corresponds to a non-negative integer called its... | https://arxiv.org/abs/2512.24221 | Academic Papers | svg |
c1ce1476ef33e7182e9aa219b02f8230afb31173a9753d2a89a32b40d9ba28b1 | 2026-01-01T00:00:00-05:00 | Explicit bounds for the graphicality of the prime gap sequence | arXiv:2512.24230v1 Announce Type: new Abstract: We establish explicit unconditional results on the graphic properties of the prime gap sequence. Let \( p_n \) denote the \( n \)-th prime number (with $p_0=1$) and \( \mathrm{PD}_n = (p_\ell - p_{\ell-1})_{\ell=1}^n \) be the sequence of the first \( n \) prime gaps. Bui... | https://arxiv.org/abs/2512.24230 | Academic Papers | svg |
126794e93a3a7346b982fb8de56437dbd5655f21f59bd1b3ca52c55b2aa5df17 | 2026-01-01T00:00:00-05:00 | Multi-bump solutions for sublinear elliptic equations with nonsymmetric coefficients | arXiv:2512.24234v1 Announce Type: new Abstract: We investigate the existence of nonnegative bump solutions to the sublinear elliptic equation \[ \begin{cases} -\Delta v - K(x)v + |v|^{q-2}v = 0 & \text{in } \mathbb{R}^N, \\ v(x) \to 0 & \text{as } |x| \to \infty, \end{cases} \] where $q \in (1,2)$, $ N \geq 2$, and the... | https://arxiv.org/abs/2512.24234 | Academic Papers | svg |
9fdfc38621583ffd7b44eee02e86363b30bdc231fdcc0f6bed27bff28b3a51c5 | 2026-01-01T00:00:00-05:00 | Semiclassical Limits of Strongly Parabolic Higgs Bundles and Hyperpolygon Spaces | arXiv:2512.24236v1 Announce Type: new Abstract: We investigate the Hitchin hyperk\"ahler metric on the moduli space of strongly parabolic $\mathfrak{sl}(2,\C)$-Higgs bundles on the $n$-punctured Riemann sphere and its degeneration obtained by scaling the parabolic weights $t\alpha$ as $t\to0$. Using the parabolic Delig... | https://arxiv.org/abs/2512.24236 | Academic Papers | svg |
72e77fd5ee0474ebc2400e386ea52737d899f8dd6266a859daa36fc38635a8d3 | 2026-01-01T00:00:00-05:00 | Geometric Eisenstein series in non-abelian Hodge theory and hyperholomorphic branes from supersymmetry | arXiv:2512.24239v1 Announce Type: new Abstract: Using geometric Eisenstein series, foundational work of Arinkin and Gaitsgory constructs cuspidal-Eisenstein decompositions for ind-coherent nilpotent sheaves on the de Rham moduli of local systems. This article extends these constructions to coherent (not ind-coherent) n... | https://arxiv.org/abs/2512.24239 | Academic Papers | svg |
3bf1bb57e9ee010da697550d0d2e3a2b0401dcecb374d81ee441eb185ba2b5f7 | 2026-01-01T00:00:00-05:00 | Spanning Components and Surfaces Under Minimum Vertex Degree | arXiv:2512.24242v1 Announce Type: new Abstract: We study minimum vertex-degree conditions in 3-uniform hypergraphs for (tight) spanning components and (combinatorial) surfaces. Our main results show that a 3-uniform hypergraph $G$ on $n$ vertices contains a spanning component if $\delta_1(G) \gtrsim \tfrac{1}{2} \binom... | https://arxiv.org/abs/2512.24242 | Academic Papers | svg |
4c60cc56cd8b942bb841f8ade16f379f3bb5976a6816f65d88f5cc4e233d2515 | 2026-01-01T00:00:00-05:00 | On the Schwarz Lemma for Bergman metrics of bounded domains | arXiv:2512.24244v1 Announce Type: new Abstract: We present a new Schwarz Lemma for bounded domains with Bergman metrics. The key ingredient of our proof is the Cauchy-Schwarz inequality from probability theory. | https://arxiv.org/abs/2512.24244 | Academic Papers | svg |
ea95d2f5fc29a1f705f5d1647486250ef9354991c4e161fc2c3e696f45e811d0 | 2026-01-01T00:00:00-05:00 | On the Consistency of Combinatorially Symmetric Sign Patterns and the Class of 2-Consistent Sign Patterns | arXiv:2512.24248v1 Announce Type: new Abstract: A sign pattern is a matrix that has entries from the set $\{+,-,0\}$. An $n\times n$ sign pattern $\mathcal{P}$ is called consistent if every real matrix in its qualitative class has exactly $k$ real eigenvalues and $n-k$ nonreal eigenvalues for some integer $k$, with $1\... | https://arxiv.org/abs/2512.24248 | Academic Papers | svg |
30039cb9463454c87ccb1d4e162fd2f329f9e6b26f238c796c5db654f9019303 | 2026-01-01T00:00:00-05:00 | Simple factor graphs associated with split graphs | arXiv:2512.24252v1 Announce Type: new Abstract: We introduce and study a loopless multigraph associated with a split graph $S$: the factor graph of $S$, denoted by $\Phi(S)$, which encodes the combinatorial information about 2-switch transformations over $S$. This construction provides a cleaner, compact and non-redund... | https://arxiv.org/abs/2512.24252 | Academic Papers | svg |
17a5802d975997f99d60374e69714763f6ce7503d3d323802d7f33506f0756a2 | 2026-01-01T00:00:00-05:00 | Complete lift of control system | arXiv:2512.24262v1 Announce Type: new Abstract: We study affine control systems on smooth manifolds and their complete lifts to the tangent bundle, providing an explicit geometric description of the solutions of the lifted system. We show that, although controllability of the complete lift implies controllability of th... | https://arxiv.org/abs/2512.24262 | Academic Papers | svg |
7097fa20e356e900fe0611599e08e3194f21ff223374bb3100754009580989ce | 2026-01-01T00:00:00-05:00 | Construction of sign k-potent sign patterns and conditions for such sign patterns to allow k-potence | arXiv:2512.24264v1 Announce Type: new Abstract: A sign pattern is a matrix whose entries are from the set $\{+,-, 0\}$. A square sign pattern $A$ is called sign $k$-potent if $k$ is the smallest positive integer for which $A^{k+1}=A$, and for $k=1$, $A$ is called sign idempotent. In 1993, Eschenbach \cite{01} gave an a... | https://arxiv.org/abs/2512.24264 | Academic Papers | svg |
dff5adf5579f33e5d8d5232915d059aa03997610ba9b3033395132a5e21cc0da | 2026-01-01T00:00:00-05:00 | On the word problem for just infinite groups | arXiv:2512.24266v1 Announce Type: new Abstract: In this note we establish that the word problem is algorithmically decidable for finitely generated just infinite groups given by a recursively enumerable set of relations. The proof does not use the Wilson--Grigorchuk theorem on the classification of just infinite groups... | https://arxiv.org/abs/2512.24266 | Academic Papers | svg |
98801ea4e049dfbc9d510cdcd6ceac2aec491b39d748ad67b4e4c402a3156cd3 | 2026-01-01T00:00:00-05:00 | Proper moduli spaces of orthosymplectic complexes | arXiv:2512.24275v1 Announce Type: new Abstract: We apply the formalism of Alper-Halpern-Leistner-Heinloth to construct proper good moduli spaces for moduli stacks of Bridgeland semistable orthosymplectic complexes on a complex smooth projective variety, which we propose as a candidate for compactifying moduli spaces of... | https://arxiv.org/abs/2512.24275 | Academic Papers | svg |
404d5073c0c9f8d200e11c2e1be78a5decd8bd45fe01ed87c1ff261266a93fd0 | 2026-01-01T00:00:00-05:00 | Tropical methods for building real space sextics with totally real tritangent planes | arXiv:2512.24277v1 Announce Type: new Abstract: This paper proposes the use of combinatorial techniques from tropical geometry to build the 120 tritangent planes to a given smooth algebraic space sextic. Although the tropical count is infinite, tropical tritangents come in 15 equivalence classes, each containing the tr... | https://arxiv.org/abs/2512.24277 | Academic Papers | svg |
927ee310bc5a275e5ff496d5942bd90247c29746a83acd3b03b21d6dc3953361 | 2026-01-01T00:00:00-05:00 | On $\mathrm{Ext}^{\bullet}$ between locally analytic generalized Steinberg with applications | arXiv:2512.24279v1 Announce Type: new Abstract: Let $n\geq 2$ be an integer, $p$ be a prime number and $K$ be a finite extension of $\mathbb{Q}_p$. Motivated by Schraen's thesis and Gehrmann's definition of automorphic simple $\mathscr{L}$-invariants, we study the first non-vanishing extension groups between a pair of ... | https://arxiv.org/abs/2512.24279 | Academic Papers | svg |
f32aa1ad31dddc7eba18fa43ddad8b7665f43877d9a1e9e9c97c314cd89ae762 | 2026-01-01T00:00:00-05:00 | On the Picard-Lindel\"of Argument and the Banach-Caccioppoli Contraction Mapping Principle | arXiv:2512.24283v1 Announce Type: new Abstract: The aim of this note is to present the simple observation that a slight refinement of the Contraction Mapping Principle allows one to recover the precise convergence rate in the Picard-Lindel\"of Theorem. | https://arxiv.org/abs/2512.24283 | Academic Papers | svg |
68879815cba4e01e5d967806c0ca620aacc80d97285fe0ba57a99f62435e687b | 2026-01-01T00:00:00-05:00 | On Characterizations of W-weighted DMP and MPD Inverses | arXiv:2512.24285v1 Announce Type: new Abstract: Recently, the weak Drazin inverse and its characterization have been crucial studies for matrices of index k. In this article, we have revisited W-weighted DMP and MPD inverses and constructed a general class of unique solutions to certain matrix equations. Moreover, we h... | https://arxiv.org/abs/2512.24285 | Academic Papers | svg |
a4aaf7b97e6f9d390ce5deebc64d3667df0166516574584007aa2c8acc086518 | 2026-01-01T00:00:00-05:00 | Adaptive Algorithms for Nonconvex Bilevel Optimization under P{\L} Conditions | arXiv:2512.24291v1 Announce Type: new Abstract: Existing methods for nonconvex bilevel optimization (NBO) require prior knowledge of first- and second-order problem-specific parameters (e.g., Lipschitz constants and the Polyak-{\L}ojasiewicz (P{\L}) parameters) to set step sizes, a requirement that poses practical limi... | https://arxiv.org/abs/2512.24291 | Academic Papers | svg |
2a0d1f2b419584a31738ccd9d999267bf8dc88c88087ae3f9f3e938df9dea159 | 2026-01-01T00:00:00-05:00 | Quasi Neighborhood Balanced Coloring of Graphs | arXiv:2512.24293v1 Announce Type: new Abstract: For a simple graph G = (V, E), a coloring of vertices of G using two colors, say red and blue, is called a quasi neighborhood balanced coloring if, for every vertex of the graph, the number of red neighbors and the number of blue neighbors differ by at most one. In additi... | https://arxiv.org/abs/2512.24293 | Academic Papers | svg |
f2e646238e6a7a3338f9828e941fb488ac746dfe0a506e8876c6b388dac54d79 | 2026-01-01T00:00:00-05:00 | Optimization over Trained Neural Networks: Going Large with Gradient-Based Algorithms | arXiv:2512.24295v1 Announce Type: new Abstract: When optimizing a nonlinear objective, one can employ a neural network as a surrogate for the nonlinear function. However, the resulting optimization model can be time-consuming to solve globally with exact methods. As a result, local search that exploits the neural-netwo... | https://arxiv.org/abs/2512.24295 | Academic Papers | svg |
499e8815b2e8eb8b442932f6c48d8466e194630df1ed85bbd740b5d9d89a11ac | 2026-01-01T00:00:00-05:00 | On Trivial Cyclically Covering Subspaces of $\mathbb{F}_q^n$ in Non-Coprime Characteristic | arXiv:2512.24301v1 Announce Type: new Abstract: A subspace $U$ of $\mathbb{F}_q^n$ is called \textit{cyclically covering} if the whole space $\mathbb{F}_q^n$ is the union of the cyclic shifts of $U$. The case $\mathbb{F}_q^n$ itself is the only covering subspace, is of particular interest. Recently, Huang solved this p... | https://arxiv.org/abs/2512.24301 | Academic Papers | svg |
6521ca0ad51c55229d986f6a2f8562fee238db9096a6982147cfad362b2e4fc5 | 2026-01-01T00:00:00-05:00 | Approximation algorithms for integer programming with resource augmentation | arXiv:2512.24302v1 Announce Type: new Abstract: The classic algorithm [Papadimitriou, J.ACM '81] for IPs has a running time $n^{O(m)}(m\cdot\max\{\Delta,\|\textbf{b}\|_{\infty}\})^{O(m^2)}$, where $m$ is the number of constraints, $n$ is the number of variables, and $\Delta$ and $\|\textbf{b}\|_{\infty}$ are, respectiv... | https://arxiv.org/abs/2512.24302 | Academic Papers | svg |
a412d2decea8b05ab4a6da16fd599f8673e499b78c3c1a6e0ec570a38319e40c | 2026-01-01T00:00:00-05:00 | Universality of cutoff for independent random walks on the circle conditioned not to intersect | arXiv:2512.24307v1 Announce Type: new Abstract: In the present paper, we consider a class of Markov processes on the discrete circle which has been introduced by K\"onig, O'Connell and Roch. These processes describe movements of exchangeable interacting particles and are discrete analogues of the unitary Dyson Brownian... | https://arxiv.org/abs/2512.24307 | Academic Papers | svg |
e5226a391aac42b8ccf26335a12efaf0c628cb30759f497a95db4578cea128b4 | 2026-01-01T00:00:00-05:00 | 1-Lefschetz contact solvmanifolds | arXiv:2512.24311v1 Announce Type: new Abstract: We study the contact Lefschetz condition on compact contact solvmanifolds, as introduced by B.\ Cappelletti-Montano, A.\ De Nicola and I.\ Yudin. We seek to fill the gap in the literature concerning Benson-Gordon type results, characterizing $1$-Lefschetz contact solvmani... | https://arxiv.org/abs/2512.24311 | Academic Papers | svg |
078471bf209041cf006a38e35b02a036e0c41b79bd5bcc9444aa42626863ba07 | 2026-01-01T00:00:00-05:00 | Discrete-Time Mean Field Type Games: Probabilistic Setup | arXiv:2512.24313v1 Announce Type: new Abstract: We introduce a general probabilistic framework for discrete-time, infinite-horizon discounted Mean Field Type Games (MFTGs) with both global common noise and team-specific common noises. In our model, agents are allowed to use randomized actions, both at the individual le... | https://arxiv.org/abs/2512.24313 | Academic Papers | svg |
cb8303901b7fed4ba6992428f6eb67b9c8a6e33dc10e8f6b3becfe92b02f10ae | 2026-01-01T00:00:00-05:00 | On the $\tau$-tilting finiteness and silting-discreteness of graded (skew-) gentle algebras | arXiv:2512.24316v1 Announce Type: new Abstract: This paper investigates finiteness conditions for gentle and skew-gentle algebras. First, we prove that a skew-gentle algebra is $\tau$-tilting finite if and only if it is representation-finite, which extends the result for gentle algebras by Plamondon (2019). Second, usi... | https://arxiv.org/abs/2512.24316 | Academic Papers | svg |
ba00fe0e5474ff668d0dab2f24a93207f101d4409157252f1a9b438e14e06edc | 2026-01-01T00:00:00-05:00 | Fractal behavior of tensor powers of tilting modules of $\text{SL}_2$ | arXiv:2512.24317v1 Announce Type: new Abstract: Given a group $G$ and $V$ a representation of $G$, denote the number of indecomposable summands of $V^{\otimes k}$ by $b_k^{G, V}$. Given a tilting representation $T$ of $\text{SL}_2(K)$ where $K=\overline{K}$ and of characteristic $p>2$, we show that $Ck^{-\alpha_p}(\tex... | https://arxiv.org/abs/2512.24317 | Academic Papers | svg |
1318112dc85b5842492ad21545ed2857cc4b9e66942468aa58e309fefbac9602 | 2026-01-01T00:00:00-05:00 | Isomorphism types of definable (maximal) cofinitary groups | arXiv:2512.24318v1 Announce Type: new Abstract: Kastermans proved that consistently $\bigoplus_{\aleph_1} \mathbb{Z}_2$ has a cofinitary representation. We present a short proof that $\bigoplus_{\mathfrak{c}} \mathbb{Z}_2$ always has an arithmetic cofinitary representation. Further, for every finite group $F$ we constr... | https://arxiv.org/abs/2512.24318 | Academic Papers | svg |
d1cd36e547fa1b9cee1d0af714e46e7400684c82df698cf3618e8041beae9aa0 | 2026-01-01T00:00:00-05:00 | Arithmetic in the Boij S\"oderberg Cone | arXiv:2512.24320v1 Announce Type: new Abstract: We study two long-standing conjectures concerning lower bounds for the Betti numbers of a graded module over a polynomial ring. We prove new cases of these conjectures in codimensions five and six by reframing the conjectures as arithmetic problems in the Boij-S\"oderberg... | https://arxiv.org/abs/2512.24320 | Academic Papers | svg |
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