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144c05ac005cfe98e9d68941aa70c802b9b6f2c31341cda1ab6b76bcca1c9a92 | 2026-01-21T00:00:00-05:00 | Attached Submanifolds Beyond Symmetric Spaces | arXiv:2601.13461v1 Announce Type: new Abstract: We study submanifold geometry in the presence of symmetry, focusing on submanifolds of solvmanifolds with an unusual property relative to Ricci curvature. We generalize work of H. Tamaru \cite{tamaru-11} in which he explores the geometry of submanifolds of symmetric space... | https://arxiv.org/abs/2601.13461 | Academic Papers | svg |
8f3a9d08615df4c9a8d7336ce68b2e53bfead53ef09fc2d0adaf57e2a529b591 | 2026-01-21T00:00:00-05:00 | Fiber-preserving and orientation-reversing involutions of Seifert fibered 3-manifolds | arXiv:2601.13469v1 Announce Type: new Abstract: We consider fiber-preserving, orientation-reversing involutions on orientable Seifert fibered 3-manifolds and the conditions on a manifold for admissibility of such involutions. We construct a class $\Psi$ of fiber-preserving, orientation-reversing involutions that act tr... | https://arxiv.org/abs/2601.13469 | Academic Papers | svg |
6ccd871523e241999633664e8a4d84d46bbe2cbe9365c01b7004ed30c466aad9 | 2026-01-21T00:00:00-05:00 | Directional Ballistic Transport in Quantum Waveguides | arXiv:2601.13471v1 Announce Type: new Abstract: We study the transport properties of Schr\"odinger operators on $\mathbb{R}^d$ with potentials that are periodic in some directions and compactly supported in the others. Such systems are known to produce surface states that are weakly confined near the support of the pot... | https://arxiv.org/abs/2601.13471 | Academic Papers | svg |
288962e4b3918329b930eb5af1538cf1e7cfebc0cb12e3652f97c17d66617654 | 2026-01-21T00:00:00-05:00 | iCanonical basis arising from quasi-split rank one iquantum group | arXiv:2601.13482v1 Announce Type: new Abstract: We compute icanonical basis of the quasi-split rank one modified iquantum group, by obtaining explicit transition matrices among the icanonical basis, monomial basis, and standardized canonical basis; all these bases can be naturally categorified. These transition matrice... | https://arxiv.org/abs/2601.13482 | Academic Papers | svg |
b8c29e6d14ecaede0b4ad15f5b4ea62efc66e78d8e78540f09604f50bb106445 | 2026-01-21T00:00:00-05:00 | Gorenstein Special Fiber Rings of Ladder Determinantal Modules | arXiv:2601.13483v1 Announce Type: new Abstract: A ladder determinantal module is an arbitrary direct sum of ideals of maximal minors of a generic ladder matrix. In this article, we give necessary and sufficient conditions for the special fiber ring of such modules to be Gorenstein. These conditions are expressed in ter... | https://arxiv.org/abs/2601.13483 | Academic Papers | svg |
5a66efc1f0f03cb403e8d06b1f8fd91da89d84d35a98be900b7d5a04059ec5ed | 2026-01-21T00:00:00-05:00 | Self-Supervised Learning of Parametric Approximation for Security-Constrained DC-OPF | arXiv:2601.13486v1 Announce Type: new Abstract: This paper introduces a self-supervised learning framework for approximating the Security-Constrained DC Optimal Power Flow (SC-DCOPF) problem using a parametric linear model. The approach preserves the physical structure of the DC-OPF while incorporating demand-dependent... | https://arxiv.org/abs/2601.13486 | Academic Papers | svg |
62e9b7e561434580ef5298e21962b9c932d4e8b5e9b1d027ec0bc6776fe92ae3 | 2026-01-21T00:00:00-05:00 | A note on "Higher order linear differential equations for unitary matrix integrals: applications and generalisations" | arXiv:2601.13488v1 Announce Type: new Abstract: In this note, we briefly introduce the background and motivation of the collaborative work [arXiv:2508.20797], and provide an outline of the main results. The latter relates to matrix and higher order scalar differential equations satisfied by certain Hankel and Toeplitz ... | https://arxiv.org/abs/2601.13488 | Academic Papers | svg |
5406dc45713a329b619711e64889a2420711c2028823bdbf4b690fa8372cff03 | 2026-01-21T00:00:00-05:00 | Noncommutative Minkowski integral inequality and a unitary categorification criterion for fusion rings | arXiv:2601.13490v1 Announce Type: new Abstract: We prove a noncommutative analogue of Minkowski's integral inequality for commuting squares of tracial von Neumann algebras. The inequality implies a necessary condition for a quadruple of graphs to be realized as inclusion graphs of a commuting square of multi-matrix alg... | https://arxiv.org/abs/2601.13490 | Academic Papers | svg |
dc3b1b0e0fd9cb3573116d37c55d3ea98c3fb163345421311aab4ee653b31eca | 2026-01-21T00:00:00-05:00 | LQ Mean Field Games with Common Noise in Hilbert Spaces: Small and Arbitrary Finite Time Horizons | arXiv:2601.13493v1 Announce Type: new Abstract: We extend the results of (Liu and Firoozi, 2025), which develops the theory of linear-quadratic (LQ) mean field games in Hilbert spaces, by incorporating a common noise. This common noise is an infinite-dimensional Wiener process affecting the dynamics of all agents. In t... | https://arxiv.org/abs/2601.13493 | Academic Papers | svg |
fbb5e08e6404191d3058199ceb13b4086807a46ca6255fca67c14c43b09a05f9 | 2026-01-21T00:00:00-05:00 | Double Hall-Littlewood symmetric polynomials | arXiv:2601.13497v1 Announce Type: new Abstract: We establish a ring isomorphism between the derived Hall algebra of the Jordan quiver and the ring of double symmetric functions (i.e., the ring of symmetric polynomials in two sets of countably many variables, invariant under the respective actions of their symmetric gro... | https://arxiv.org/abs/2601.13497 | Academic Papers | svg |
8a300a9b2c201b33c17f75884617760abb04bb96c54dea8bee9112b49a6771a3 | 2026-01-21T00:00:00-05:00 | Hidden convexity of quadratic systems and its application to quadratic programming | arXiv:2601.13511v1 Announce Type: new Abstract: In this paper, we present sufficient conditions ensuring that the sum of the image of quadratic functions and the nonnegative orthant is convex. The hidden convexity of the trust-region problem with linear inequality constraints is established under a newly proposed assum... | https://arxiv.org/abs/2601.13511 | Academic Papers | svg |
10110d9bb8c4b2e793aadd9a8defb73f8eec3a5bfac2eb36af190010a064aa41 | 2026-01-21T00:00:00-05:00 | Categorical Entropies of Hilbert Schemes of Points on Surfaces and Hyperk\"ahler Manifolds | arXiv:2601.13526v1 Announce Type: new Abstract: This paper studies the categorical entropy of autoequivalences of derived categories of Hilbert schemes of points on surfaces and hyperk\"ahler manifolds. One of the central questions about categorical entropy is whether it satisfies a Gromov-Yomdin type formula $h_{\math... | https://arxiv.org/abs/2601.13526 | Academic Papers | svg |
0e790e832352f029a6c01172fdf31a86e6e1f9bda23f465369b96a4566f6716a | 2026-01-21T00:00:00-05:00 | A construction of smooth varieties admitting small contractions | arXiv:2601.13527v1 Announce Type: new Abstract: We construct smooth varieties admitting small contractions from arbitrary smooth projective varieties. This construction generalizes Kawamata's four-dimensional example. We also give sufficient conditions for divisors on these varieties to be nef. As an application, we ob... | https://arxiv.org/abs/2601.13527 | Academic Papers | svg |
a14d99b8b4d6d7428dce1cb9c14921eef6cc9b2793b07f3aee5207d1739cac62 | 2026-01-21T00:00:00-05:00 | Dean's conjecture and cycles modulo k | arXiv:2601.13552v1 Announce Type: new Abstract: Dean conjectured three decades ago that every graph with minimum degree at least $k\ge 3$ contains a cycle whose length is divisible by $k$. While the conjecture has been verified for $k\in \{3,4\}$, it remains open for $k\ge 5$. A weaker version, also proposed by Dean, a... | https://arxiv.org/abs/2601.13552 | Academic Papers | svg |
2d5d447d9a0fcd5017f2da0147b073664e43b62c106823137b6414305df4457e | 2026-01-21T00:00:00-05:00 | Universality of the Basilica | arXiv:2601.13553v1 Announce Type: new Abstract: We establish universality of the fat Basilica Julia set $J(z^2-\frac34)$ in conformal dynamics in the following sense: $J(z^2-\frac34)$ is quasiconformally equivalent to the fat Basilica Julia set of any polynomial as well as to the limit set of any geometrically finite c... | https://arxiv.org/abs/2601.13553 | Academic Papers | svg |
8dcd7695800e0acfbb8334944ab8dd924f920c48c934a75b58d78e2cd368a233 | 2026-01-21T00:00:00-05:00 | Mirror construction of Hecke correspondence between Nakajima quiver varieties | arXiv:2601.13555v1 Announce Type: new Abstract: Nakajima constructed geometric representations of a deformed Kac-Moody Lie algebra using Hecke correspondences between quiver varieties. In this paper, we show that Hecke correspondences, which are holomorphic Lagrangians in products of Nakajima quiver varieties, can be o... | https://arxiv.org/abs/2601.13555 | Academic Papers | svg |
b330bddd70b5f26fd2229311c1cc764f6776204c98ad2842f7f314785c2978dd | 2026-01-21T00:00:00-05:00 | On the radius of analyticity and Gevrey regularity for the Boltzmann equation | arXiv:2601.13560v1 Announce Type: new Abstract: This paper investigates the non-cutoff Boltzmann equation for hard potentials in a perturbative setting. We first establish a sharp short-time estimate on the radius of analyticity and Gevrey regularity of mild solutions. Furthermore, we obtain a global-in-time radius est... | https://arxiv.org/abs/2601.13560 | Academic Papers | svg |
bc157dbd9e48f723633f4b6db0b1a0a8a85b1d9b87acaf3b939f5c429d70e164 | 2026-01-21T00:00:00-05:00 | Logarithmic geometry and Infinitesimal Hodge Theory | arXiv:2601.13568v1 Announce Type: new Abstract: This paper develops a systematic approach to infinitesimal variations of Hodge structure for singular and equisingular families by means of logarithmic geometry and residue theory. The central idea is that logarithmic vector fields encode precisely those deformation direc... | https://arxiv.org/abs/2601.13568 | Academic Papers | svg |
4b0282c027e36a148e10f2b1621248e15ae948c77b0865353f37fe9c5654e5d6 | 2026-01-21T00:00:00-05:00 | Control policies for a two-stage queueing system with parallel and single server options | arXiv:2601.13576v1 Announce Type: new Abstract: We study a two-stage tandem service queue attended by two servers. Each job-server pair must complete both service phases together, with the server unable to begin a new job until the current one is fully processed after two stages. Immediately after the first phase of se... | https://arxiv.org/abs/2601.13576 | Academic Papers | svg |
87ced18ade73f29ed7c75e4be0b1eccd94561ce774ce146c597c4f3776b1d5d6 | 2026-01-21T00:00:00-05:00 | Balancing Independent and Collaborative Service | arXiv:2601.13586v1 Announce Type: new Abstract: We study a two-type server queueing system where flexible Type-I servers, upon their initial interaction with jobs, decide in real time whether to process them independently or in collaboration with dedicated Type-II servers. Independent processing begins immediately, as ... | https://arxiv.org/abs/2601.13586 | Academic Papers | svg |
b4b4747b8379f3d2951861da98302529b1a4aea6621a3ac2a3f4b83ef6ebc4e7 | 2026-01-21T00:00:00-05:00 | Quasi-periodic Dynamics for Multi-dimensional Quasi-linear Schr\"{o}dinger Equations via Resonant Mode Control | arXiv:2601.13611v1 Announce Type: new Abstract: This paper focuses on the problem of quasi-periodic solutions for multi-dimensional quasi-linear Schr\"odinger equation. To address the challenge of unbounded perturbations caused by quasi-linear terms in the equation, we define the resonant mode set $\mathcal{K}$ to cont... | https://arxiv.org/abs/2601.13611 | Academic Papers | svg |
a8ff3db1f05cf7c39566932bbbdb8acc3cfe56739ca88825301b7d53b65bc49e | 2026-01-21T00:00:00-05:00 | Locally analytic vectors in the completed cohomology of quaternionic Shimura curves | arXiv:2601.13625v1 Announce Type: new Abstract: We use the methods introduced by Lue Pan to study the locally analytic vectors of the completed cohomology of Shimura curves associated to an indefinite quaternion algebra $D$ which is ramified at a prime number $p$. Let $D_p^{\times}$ be the group of units of $D$ at $p$.... | https://arxiv.org/abs/2601.13625 | Academic Papers | svg |
7787c403138adf7ffcdc5b4f15137418a7f1f3303ca8c2adb01a87db129e191b | 2026-01-21T00:00:00-05:00 | Symmetric multiple Eisenstein series | arXiv:2601.13626v1 Announce Type: new Abstract: In this paper, we introduce the symmetric multiple Eisenstein series, a variant of the multiple Eisenstein series. As a fundamental result, we show that they satisfy the linear shuffle relation. As a case study, we investigate the vector space spanned by symmetric double ... | https://arxiv.org/abs/2601.13626 | Academic Papers | svg |
d7883c20d1a19a922ff006ba4ba8f05dba02b7b4514ce25c353c925107ebba4c | 2026-01-21T00:00:00-05:00 | Exact solution of the (2+1)-dimensional damping forcing coupled Burgers equation by using Darboux transformation | arXiv:2601.13634v1 Announce Type: new Abstract: In this article, we investigate the (2+1)-dimensional damping forcing coupled Burgers equation, which is obtain by adding damping and forcing terms from couple Burgers equation. The Lax pair of the (2+1)-dimensional damping forcing coupled Burgers equation is established.... | https://arxiv.org/abs/2601.13634 | Academic Papers | svg |
cf9a1c6a2fb62a78e851e8c4c71f5b6f6891af036d39c2b970ae3b2c64611836 | 2026-01-21T00:00:00-05:00 | Borcherds products approximating Gersten complex | arXiv:2601.13643v1 Announce Type: new Abstract: For an orthogonal modular variety, we construct a complex which is defined in terms of lattices and elliptic modular forms, which resembles the Gersten complex in Milnor K-theory, and which has a morphism to the Gersten complex of the modular variety by the Borcherds lift... | https://arxiv.org/abs/2601.13643 | Academic Papers | svg |
5fe7f8029faf38d6b90ce257d1d1f018cd57fd8d13704458ed35aaa2ee405f52 | 2026-01-21T00:00:00-05:00 | Gromov-Hausdorff stability of global attractors of damped wave equations under perturbations of the domain | arXiv:2601.13650v1 Announce Type: new Abstract: In this paper, we will make use of the Gromov-Hausdorff distance between compact metric spaces to establish the continuous dependence and the Gromov-Hausdorff stability of global attractors for damped wave equations under perturbations of the domain. | https://arxiv.org/abs/2601.13650 | Academic Papers | svg |
6f7c84d969c10a8721bc649ee653376dc5d9e2a2bf8dc04e1099e0ab8b2c1b1d | 2026-01-21T00:00:00-05:00 | Kenmotsu Contact Geometry Through the Lens of $\ast-\boldsymbol{\kappa}$-Ricci-Bourguignon Almost Solitons | arXiv:2601.13661v1 Announce Type: new Abstract: This paper focuses on the study of the newly introduced $\ast-\boldsymbol{\kappa}$-Ricci-Bourguignon almost soliton pertaining to Kenmotsu structure manifolds. Our analysis concerns the characteristics of this soliton and derive the scalar curvature for a Kenmotsu manifol... | https://arxiv.org/abs/2601.13661 | Academic Papers | svg |
bd3a4deccfea49bf00a3728dc47bd935fa8259de2fd4da678fd3d4fc9137fc7b | 2026-01-21T00:00:00-05:00 | The norm of the Hilbert matrix operator on Bergman spaces | arXiv:2601.13672v1 Announce Type: new Abstract: Karapetrovi\'c conjectured that the norm of the Hilbert matrix operator on the Bergman space $A^p_\alpha$ is equal to $\pi/\sin((2+\alpha)\pi/p)$ when $-1<\alpha\frac{1}{47}$ and $\alpha \not=1$. | https://arxiv.org/abs/2601.13672 | Academic Papers | svg |
2bc19e17aa919d68c614eb9d76c4bd42a4eb5042da931328aeb2fab6a6dffa9f | 2026-01-21T00:00:00-05:00 | The spectral measures of random Jacobi matrices related to beta ensembles at high temperature and Dirichlet processes | arXiv:2601.13674v1 Announce Type: new Abstract: In a high temperature regime where $\beta N \to 2c$, the empirical distribution of the eigenvalues of Gaussian beta ensembles, beta Laguerre ensembles and beta Jacobi ensembles converges to a limiting measure which is related to associated Hermite polynomials, associated ... | https://arxiv.org/abs/2601.13674 | Academic Papers | svg |
79c22b8a15dcfc4cac53705e02d1981824c6e9f5e1859d01cd1cb578912e8204 | 2026-01-21T00:00:00-05:00 | Distributed Coverage Control on Poriferous Surface via Poly-Annulus Conformal Mapping | arXiv:2601.13688v1 Announce Type: new Abstract: The inherent non-convexity of poriferous surfaces typically entraps agents in local minima and complicates workload distribution. To resolve this, we propose a distributed diffeomorphic coverage control framework for the multi-agent system (MAS) in such surfaces. First, w... | https://arxiv.org/abs/2601.13688 | Academic Papers | svg |
ac51bb746068a32595f511faa39ce5b8e9a5e1c7eb9db2aedfb0b5c5d6f30d58 | 2026-01-21T00:00:00-05:00 | On the Birkhoff Spectrum for Hyperbolic Dynamics | arXiv:2601.13720v1 Announce Type: new Abstract: In this paper, we study the structure of Birkhoff spectra for hyperbolic dynamical systems. For a H\"older observable $f$ on a basic set $\Lambda$, we prove that if the Birkhoff sums take both positive and negative values, then the Birkhoff spectrum $\mathcal{B}(f,\varphi... | https://arxiv.org/abs/2601.13720 | Academic Papers | svg |
b108d3bd667645af2dc24bd2ffd4036806b770e954e4ea5aa974453ec2cd6802 | 2026-01-21T00:00:00-05:00 | Central Limit Theorems in Multiplicative Diophantine Approximation | arXiv:2601.13726v1 Announce Type: new Abstract: We investigate the number of integer solutions to a multiplicative Diophantine approximation problem and show that the associated counting function converges in distribution to a normal law. Our approach relies on the analysis of correlations of measures on homogeneous sp... | https://arxiv.org/abs/2601.13726 | Academic Papers | svg |
e5f4e4eae808f30e17ed04d57c0423649eee671fc9d86d15ca56c33ed76029ff | 2026-01-21T00:00:00-05:00 | Some Consequences of the Grunewald-O'Halloran Conjecture for Pseudoquonic Operators | arXiv:2601.13736v1 Announce Type: new Abstract: Investigating a recent positive solution of a conjecture of Grunewald and O'Halloran for complex finite dimensional nilpotent Lie algebras, we are in the position to find results of existence and uniqueness for the construction of complex nilpotent Lie algebras of arbitra... | https://arxiv.org/abs/2601.13736 | Academic Papers | svg |
c0253bede5377bb51c8ea2e7fdcdc0002f7645fd6703cba46e01bb8bf5bdec22 | 2026-01-21T00:00:00-05:00 | Second Order Asymptotics for the Hard Wall Probability of the 2D Harmonic Crystal | arXiv:2601.13738v1 Announce Type: new Abstract: We estimate the probability that the discrete Gaussian free field on a planar domain with Dirichlet boundary conditions stays positive in the bulk. Improving upon the result by Bolthausen, Deuschel and Giacomin from 2001, we derive the order of the subleading term of this... | https://arxiv.org/abs/2601.13738 | Academic Papers | svg |
bf8cab202021974c71ca3d16bcacc8d1d4283e86a5ac6a7a2496cb3b9fa758c0 | 2026-01-21T00:00:00-05:00 | Abstract maximal hypoellipticity and applications | arXiv:2601.13741v1 Announce Type: new Abstract: We prove an abstract theorem of maximal hypoellipticy showing that in an abstract calculus under some natural assumptions, an operator is maximally hypoelliptic if and only if its principal symbol is left invertible. We then show that our theorem implies various known res... | https://arxiv.org/abs/2601.13741 | Academic Papers | svg |
caca58c05a4f2c32d3e27609928486b53dc9618e1f116446ffd95eb5a11a1622 | 2026-01-21T00:00:00-05:00 | A Note on k-NN Gating in RAG | arXiv:2601.13744v1 Announce Type: new Abstract: We develop a statistical proxy framework for retrieval-augmented generation (RAG), designed to formalize how a language model (LM) should balance its own predictions with retrieved evidence. For each query x, the system combines a frozen base model q0 ($\times$ x) with a ... | https://arxiv.org/abs/2601.13744 | Academic Papers | svg |
6aac82597939fcbfe3b4f6c4c46b087f1524dadbdd0a931b5213605362f24fa8 | 2026-01-21T00:00:00-05:00 | closed $\mathrm{G}_2$-structures with $\mathbb{T}^3$-symmetry and hypersymplectic structures | arXiv:2601.13747v1 Announce Type: new Abstract: Closed $\mathrm{G}_2$-structures $\varphi$ with an effective $\mathbb{T}^3$-symmetry on connected manifolds are roughly classified into three types according to the evaluation of $\varphi$ on the principal orbits. Type 1: if there is neither associative nor isotropic orbi... | https://arxiv.org/abs/2601.13747 | Academic Papers | svg |
85502ba1f16fe73fe094a6d0ef68bafd8cf3020ab54c249eb73350845d2da3cf | 2026-01-21T00:00:00-05:00 | Sharp Quantitative Forms of the Hardy Inequality on Cartan-Hadamard Manifolds via Sobolev-Lorentz Embeddings | arXiv:2601.13750v1 Announce Type: new Abstract: In this article, we investigate the quantitative form of the classical Hardy inequality. In our first result, we prove the following quantitative bound under the assumption that the $\mathbb{M}^N$ is a Riemannian model satisfying the centered isoperimetric inequality: We ... | https://arxiv.org/abs/2601.13750 | Academic Papers | svg |
f9e59d07d28eacba2813024ddabf8e244ad2f91dd5ee48cd9adf7a9ca6fc52ee | 2026-01-21T00:00:00-05:00 | A turnpike property in an eigenvalue optimization problem | arXiv:2601.13756v1 Announce Type: new Abstract: We consider a constrained eigenvalue optimization problem that arises in an important nonlinear dynamical model for mRNA translation in the cell. We prove that the ordered list of optimal parameters admits a turnpike property, namely, it includes three parts with the firs... | https://arxiv.org/abs/2601.13756 | Academic Papers | svg |
0c6255810ed9e7675de25e7cf9847162634da6e7d5d4c7b8fd92979afafe2216 | 2026-01-21T00:00:00-05:00 | Quantum Entanglement Geometry on Severi-Brauer Schemes: Subsystem Reductions of Azumaya Algebras | arXiv:2601.13764v1 Announce Type: new Abstract: We formulate pure-state entanglement in families as a geometric obstruction. In standard quantum information, entanglement is defined relative to a chosen tensor-product factorization of a fixed Hilbert space. In contrast, for a twisted family of pure-state spaces, which ... | https://arxiv.org/abs/2601.13764 | Academic Papers | svg |
ca475a7abbaf86cea9b8f3ea3a189d41a6c4d04ba41a2ad63c86dea8d312d563 | 2026-01-21T00:00:00-05:00 | The Harnack inequality without convexity for curve shortening flow | arXiv:2601.13767v1 Announce Type: new Abstract: In 1995, Hamilton introduced a Harnack inequality for convex solutions of the mean curvature flow. In this paper we prove an alternative Harnack inequality for curve shortening flow, i.e. one-dimensional mean curvature flow, that does not require any assumption of convexi... | https://arxiv.org/abs/2601.13767 | Academic Papers | svg |
eac5c4225ac8393e2275f59e743ffddfff7c1f286a27c4335f1b1909ef72a092 | 2026-01-21T00:00:00-05:00 | Existence and regularity of minimizers for a variational problem of species population density | arXiv:2601.13771v1 Announce Type: new Abstract: We study a variational problem motivated by models of species population density in a nonhomogeneous environment. We first analyze local minimizers and the structure of the saturated region (where the population attains its maximal density) from a free boundary perspectiv... | https://arxiv.org/abs/2601.13771 | Academic Papers | svg |
0592054e95a42e9fcd9b821b53f57e58428d0f0e2ead012157d488f564ff866f | 2026-01-21T00:00:00-05:00 | Bialgebraic structures on boolean functions | arXiv:2601.13773v1 Announce Type: new Abstract: We study several bialgebraic structures on boolean functions, that is to say maps defined on the set of subsets of a finite set $X$, taking the value $0$ on $\emptyset$. Examples of boolean functions are given by the indicator function of the hyperedges of a given hypergr... | https://arxiv.org/abs/2601.13773 | Academic Papers | svg |
91fec16573a15a2720549f7a319fd6964386c5332559d148f133ce7798f58918 | 2026-01-21T00:00:00-05:00 | Extension of the Fundamental Theorem of Algebra to Polynomial Matrix Equations over $Q$-Circulant Matrices | arXiv:2601.13775v1 Announce Type: new Abstract: In this paper, we establish an analogue of the Fundamental Theorem of Algebra for polynomial matrix equations, where both the coefficient matrices and the unknown matrix are $Q$-circulant matrices. This result generalizes Abramov's result for circulant matrices. | https://arxiv.org/abs/2601.13775 | Academic Papers | svg |
7e52940d054e0d046d72403068697542819d0ec0d54e668c0ff01e35c00a4f7c | 2026-01-21T00:00:00-05:00 | Maximum spanning trees in normed planes | arXiv:2601.13779v1 Announce Type: new Abstract: Extending some properties from the Euclidean plane to any normed plane, we show the validity of the Monma-Paterson-Suri-Yao algorithm for finding the maximum-weighted spanning tree of a set of $n$ points, where the weight of an edge is the distance between the end points ... | https://arxiv.org/abs/2601.13779 | Academic Papers | svg |
9f02c00f52b389808bf122703f0f4478bc2b4fc2af2dcf3bc587bcbf8565fb0e | 2026-01-21T00:00:00-05:00 | Moving Least Squares without Quasi-Uniformity: A Stochastic Approach | arXiv:2601.13782v1 Announce Type: new Abstract: Local Polynomial Regression (LPR) and Moving Least Squares (MLS) are closely related nonparametric estimation methods, developed independently in statistics and approximation theory. While statistical LPR analysis focuses on overcoming sampling noise under probabilistic a... | https://arxiv.org/abs/2601.13782 | Academic Papers | svg |
6d3ef3aa221336b0cc6d33f9b743c7970ab3d31f21d2974e10eb073170f11617 | 2026-01-21T00:00:00-05:00 | The Genus-Decreasing Property of Mean Curvature Flow, I | arXiv:2601.13787v1 Announce Type: new Abstract: This paper proves that, in mean curvature flow of a compact surface in a complete $3$-manifold with Ricci curvature bounded below, the genus of the regular set is a decreasing function of time as long as the only singularities are given by shrinking sphere and shrinking c... | https://arxiv.org/abs/2601.13787 | Academic Papers | svg |
e7d651d394dc395320f5a62388baf4e3770fb66e962ba7ab34cbe7cee9cedfac | 2026-01-21T00:00:00-05:00 | Characterizations of a class of Musielak--Orlicz BMO spaces via commutators of Riesz potential operators | arXiv:2601.13788v1 Announce Type: new Abstract: The fractional integral operators $I_\alpha$ can be used to characterize the Musielak--Orlicz Hardy spaces. This paper shows that for $b\in \rm BMO(\mathbb R^n)$, the commutators $[b,I_\alpha]$ generated by fractional integral operators $I_\alpha$ with $b$ are bounded fro... | https://arxiv.org/abs/2601.13788 | Academic Papers | svg |
056092ee9a6f136e4d14dcb05ad5a276f9fec9cbd4d6b652ef18e714b4973742 | 2026-01-21T00:00:00-05:00 | Nijenhuis BiHom-Lie bialgebras and differential Lie bialgebras | arXiv:2601.13791v1 Announce Type: new Abstract: In this paper, we first introduce the concept of Nijenhuis BiHom-Lie algebras. We then establish the equivalence relations between the Manin triples of Nijenhuis BiHom-Lie algebras, Nijenhuis BiHom-Lie bialgebras, and matched pairs of Nijenhuis BiHom-Lie algebras. Further... | https://arxiv.org/abs/2601.13791 | Academic Papers | svg |
098e8425681848e7bc59efe5c0fe841353809af26a70b862370bf3b63233033e | 2026-01-21T00:00:00-05:00 | Asymptotic Properties of Filtrations of Ideals | arXiv:2601.13794v1 Announce Type: new Abstract: We introduce a unified framework for studying persistence phenomena in commutative algebra via filtrations of ideals. For a filtration $\mathcal{F} = \{I_i\}_{i \in \mathbb{N}}$, we define $\mathcal{F}$-persistence and $\mathcal{F}$-strong persistence, extending the class... | https://arxiv.org/abs/2601.13794 | Academic Papers | svg |
c86066234152ab79b80f651585c92a712dd87d9d70e06bf69db7e77db113d017 | 2026-01-21T00:00:00-05:00 | On rough ideal convergence | arXiv:2601.13805v1 Announce Type: new Abstract: We continue the study of ideal convergence for sequences $(x_n)$ with values in a topological space $X$ with respect to a family $\{F_\eta:\eta\in X\}$ of subsets of $X$ with $\eta\in F_\eta$, where each $F_\eta$ measures the allowed ``roughness'' of convergence toward $\... | https://arxiv.org/abs/2601.13805 | Academic Papers | svg |
5d6c5ea248f140f9ee788e7dc42a4b42bca612b817b37a5f761f0d35afa0f286 | 2026-01-21T00:00:00-05:00 | Non-finitely generated $(\mathbb{Z}_2)^k$-equivariant bordism ring | arXiv:2601.13807v1 Announce Type: new Abstract: In 1998, Mukherjee and Sankaran posed two problems concerning the algebraic structure of the equivariant bordism ring of smooth closed $(\mathbb{Z}_2)^k$-manifolds with only isolated fixed points. One is the property of being finitely generated as a $\mathbb{Z}_2$-algebra... | https://arxiv.org/abs/2601.13807 | Academic Papers | svg |
259a00db0570ec2d1aa7899d301a941007a2b21be7aab2ee00f3dc035b8fa9eb | 2026-01-21T00:00:00-05:00 | Dimensional Constraints from SU(2) Representation Theory in Graph-Based Quantum Systems | arXiv:2601.13828v1 Announce Type: new Abstract: We investigate dimensional constraints arising from representation theory when abstract graph edges possess internal degrees of freedom but lack geometric properties. We prove that such internal degrees of freedom can only encode directional information, necessitating qua... | https://arxiv.org/abs/2601.13828 | Academic Papers | svg |
b90ae6a2401249d20a54b7c37d2b3d5705b6fff86a01231c9679a354fbf8ba11 | 2026-01-21T00:00:00-05:00 | Analytic description of the moving moisture front in soils | arXiv:2601.13833v1 Announce Type: new Abstract: The fact that moisture propagates in soils at a finite speed is confirmed by natural everyday experience as well as by controlled laboratory tests. In this text, we rigorously derive analytical upper bounds for the speed of moisture front propagation under gravity for the... | https://arxiv.org/abs/2601.13833 | Academic Papers | svg |
7d9878d0c1769a062967ecb01b168af4edeebbac7653b70d7962ca2ccec0391e | 2026-01-21T00:00:00-05:00 | Derivative free data-driven stabilization of continuous-time linear systems from input-output data | arXiv:2601.13848v1 Announce Type: new Abstract: This letter presents a data-driven framework for the design of stabilizing controllers from input-output data in the continuous-time, linear, and time-invariant domain. Rather than relying on measurements or reliable estimates of input and output time derivatives, the pro... | https://arxiv.org/abs/2601.13848 | Academic Papers | svg |
200cced42f3dbb758e07fce592575ae3d51ed29a77c7db565a83bc6f4bf1a561 | 2026-01-21T00:00:00-05:00 | Basic Albanese maps of regular Riemannian foliations | arXiv:2601.13853v1 Announce Type: new Abstract: In the paper we introduce the notion of basic Albanese map which we define for foliated Riemannian manifolds using basic 1-forms. We relate this mapping to the classical Albanese map for the ambient manifold. The study of general properties is supplemented with the descri... | https://arxiv.org/abs/2601.13853 | Academic Papers | svg |
7fc133646aa143d8a42dab61cc7716e0f3cb74d9da5d3827b3a07b8698daafe5 | 2026-01-21T00:00:00-05:00 | Jacob's ladders, point of contact of the remained in the prime-number law with the Fermat-Wiles theorem and multiplicative puzzles on some sets of integrals | arXiv:2601.13855v1 Announce Type: new Abstract: In this paper we prove, on the Riemann hypothesis, the existence of such increments of the Ingham integral (1932) that generate new functionals together with corresponding new $P\zeta$-equivalents of the Fermat-Wiles theorem. We obtain also new results in this direction. | https://arxiv.org/abs/2601.13855 | Academic Papers | svg |
997e43939bf16b5bb953f3fd9385c99f97b7e230e40c0d2e557ca7b077fbec24 | 2026-01-21T00:00:00-05:00 | Patterns and Tracks | arXiv:2601.13861v1 Announce Type: new Abstract: Patterns in triangulated $2$-spheres and $3$-spheres are investigated. A new proof of a lemma in Abigail Thompson's proof of the Recognition Algorithm for $3$-spheres is obtained. | https://arxiv.org/abs/2601.13861 | Academic Papers | svg |
81fdf58e5c97633af8f8f4c47369ea7ed37a18888286675f09d041ffaad3d2aa | 2026-01-21T00:00:00-05:00 | Optimizing the Geometry of an L-Shaped Building to Enhance Energy Efficiency and Sustainability | arXiv:2601.13884v1 Announce Type: new Abstract: The geometric form of a building strongly influences its material use, heat losses, and energy efficiency. This paper presents an analytical optimization of L-shaped residential buildings aimed at minimizing the external surface area for a prescribed volume. Both symmetri... | https://arxiv.org/abs/2601.13884 | Academic Papers | svg |
604f79a1b1596b6b99ca2726fa21056fc3f403ed4ec0537af143d1d3a357cab4 | 2026-01-21T00:00:00-05:00 | From geometry to sustainability: Optimal shapes of hip roof houses | arXiv:2601.13896v1 Announce Type: new Abstract: In this paper, we develop a rigorous mathematical framework for the optimization of hip roof house geometry, with the primary goal of minimizing the external surface of the building envelope for a given set of design constraints. Five optimization scenarios are systematic... | https://arxiv.org/abs/2601.13896 | Academic Papers | svg |
d61d5c5008829c78eae13c9967754a6efdd104c7eb5f995a8289512f7621a8e7 | 2026-01-21T00:00:00-05:00 | Homogeneous substructures in random ordered uniform matchings | arXiv:2601.13906v1 Announce Type: new Abstract: An ordered $r$-uniform matching of size $n$ is a collection of $n$ pairwise disjoint $r$-subsets of a linearly ordered set of $rn$ vertices. For $n=2$, such a matching is called an $r$-pattern, as it represents one of $\tfrac12\binom{2r}r$ ways two disjoint edges may inte... | https://arxiv.org/abs/2601.13906 | Academic Papers | svg |
c482884c03f7f9371011a4d074f8113831dbeb1bb8def93989ec3500e74546cc | 2026-01-21T00:00:00-05:00 | Designing sustainable barn-type houses: Optimal shapes for minimal envelope and energy use | arXiv:2601.13911v1 Announce Type: new Abstract: Barn-type houses have become one of the most popular single-family housing typologies in Poland and across Europe due to their simplicity, functionality, and potential for energy efficiency. Despite their widespread use, systematic methods for optimizing their geometry in... | https://arxiv.org/abs/2601.13911 | Academic Papers | svg |
72c7c6998f90637255bf233cda423ad0d4d2c61221bb2717e631dc134b020d3f | 2026-01-21T00:00:00-05:00 | Geometry-Driven Conditioning of Multivariate Vandermonde Matrices in High-Degree Regimes | arXiv:2601.13915v1 Announce Type: new Abstract: We study multivariate monomial Vandermonde matrices $V_N(Z)$ with arbitrary distinct nodes $Z=\{z_1,\dots,z_s\}\subset B_2^n$ in the high-degree regime $N\ge s-1$. Introducing a projection-based geometric statistic -- the \emph{max-min projection separation} $\rho(Z,j)$ a... | https://arxiv.org/abs/2601.13915 | Academic Papers | svg |
119d2e55a85941ae6faf0a45f4d9b3fe20e57fe50c19c0c59172f3dc422f3d9b | 2026-01-21T00:00:00-05:00 | Wiener Algebras Methods for Liouville Theorems on the Stationary Navier-Stokes System | arXiv:2601.13916v1 Announce Type: new Abstract: We prove some Liouville theorems for the stationary Navier-Stokes system for incompressible fluids. We provide some sufficient conditions on the low frequency part of the solution, using some properties of classical singular integrals with respect to Wiener algebras. | https://arxiv.org/abs/2601.13916 | Academic Papers | svg |
739a5d03b59357e081d5b1021a2d4d069ce2e9a41a318c24243e2b103a359596 | 2026-01-21T00:00:00-05:00 | A finiteness result on representations of Nori's fundamental group scheme | arXiv:2601.13917v1 Announce Type: new Abstract: Let $(X,x)$ be a pointed geometrically connected smooth projective variety over a sub-$p$-adic field $K$. For any given rank $n$, we prove that there are only finitely many isomorphism classes of representations $\pi_{1}^{EF}(X,x)\rightarrow \mathrm{GL}_{n}$, where $\pi_{... | https://arxiv.org/abs/2601.13917 | Academic Papers | svg |
715f1498a684bacb6ac54b2f7856aebdc76b2a4764d87304ed201a8092fca387 | 2026-01-21T00:00:00-05:00 | The properad of quadratic Poisson structures is Koszul | arXiv:2601.13921v1 Announce Type: new Abstract: In this paper, we suggest a sufficient condition on the properadic envelope of a quadratic dioperad to be Koszul in terms of twisted associative algebras. As a particular new example, we show that the properad of quadratic Poisson structures is Koszul. | https://arxiv.org/abs/2601.13921 | Academic Papers | svg |
dacdf84f19fa5c9a2a03fff5ac3be04d8918bd96a5336ed0bcd01e14d9ca856c | 2026-01-21T00:00:00-05:00 | On spectral clustering under non-isotropic Gaussian mixture models | arXiv:2601.13930v1 Announce Type: new Abstract: We evaluate the misclustering probability of a spectral clustering algorithm under a Gaussian mixture model with a general covariance structure. The algorithm partitions the data into two groups based on the sign of the first principal component score. As a corollary of t... | https://arxiv.org/abs/2601.13930 | Academic Papers | svg |
66e39507c09e6979b2694663b545c71fd3009dacf941f6f91e44c6105fa54cd8 | 2026-01-21T00:00:00-05:00 | Packing minima of convex bodies | arXiv:2601.13937v1 Announce Type: new Abstract: In 2021, Henk, Schymura and Xue introduced packing minima, associated with a convex body and a lattice, as packing counterparts to the covering minima of Kannan and Lov\'asz. Motivated by conjectures on the volume inequalities for the successive minima, we generalized the... | https://arxiv.org/abs/2601.13937 | Academic Papers | svg |
c6b4649ff1e4fa43886f67e6a53a12a5d36e9255a58720868362be7d5db95247 | 2026-01-21T00:00:00-05:00 | Gallai-Ramsey Numbers for $\ell$-Connected Graphs | arXiv:2601.13944v1 Announce Type: new Abstract: Given a nonempty graph $G$, a collection of nonempty graphs $\cal{H}$, and a positive integer $k$, the Gallai-Ramsey number $\mathrm{gr}_k(G:\mathcal{H})$ is defined to be the minimum positive integer $n$ such that every exact $k$-edge-coloring of a complete graph $K_n$ c... | https://arxiv.org/abs/2601.13944 | Academic Papers | svg |
a6cfe1646968e0918f6644c3108a64b0c6f2ae1228ae2a18cb5b9f8c126e6cb8 | 2026-01-21T00:00:00-05:00 | Topological Criteria for Hypothesis Testing with Finite-Precision Measurements | arXiv:2601.13946v1 Announce Type: new Abstract: We establish topological necessary and sufficient conditions under which a pair of statistical hypotheses can be consistently distinguished when i.i.d. observations are recorded only to finite precision. Requiring the test's decision regions to be open in the sample-space... | https://arxiv.org/abs/2601.13946 | Academic Papers | svg |
13fee2ec0c94b5847ff2bcd2648e111d1e1eb3d923b0f5c9cecb657056b6c841 | 2026-01-21T00:00:00-05:00 | Wold-type decomposition for doubly twisted left-invertible covariant representations | arXiv:2601.13950v1 Announce Type: new Abstract: We will introduce the notion of a near-isometric covariant representation of a $C^*$-correspondence and prove its Wold-type decomposition. Wold-type decomposition for doubly twisted left-invertible covariant representations of a product system is also obtained. | https://arxiv.org/abs/2601.13950 | Academic Papers | svg |
c2d7a0cb128ee47b955a6c0232903914c2b66edc76b34d242853e526d6509e98 | 2026-01-21T00:00:00-05:00 | Hypercube subgroups of (outer) reduced Weyl groups of the Cuntz algebras | arXiv:2601.13952v1 Announce Type: new Abstract: We develop some tools, of an algebraic and combinatorial nature, which enable us to obtain a detailed description of certain quadratic subgroups of the (outer) reduced Weyl group of the Cuntz algebra ${\mathcal O}_n$. In particular, for $n=4$ our findings give a self-cont... | https://arxiv.org/abs/2601.13952 | Academic Papers | svg |
926b18183099055b0400b4dd1a3bb51783e83430de116edd31a625a0d402aa81 | 2026-01-21T00:00:00-05:00 | Uniform Consistency of Generalized Cross-Validation for Ridge Regression in High-Dimensional Misspecified Linear Models | arXiv:2601.13955v1 Announce Type: new Abstract: This study examines generalized cross-validation for the tuning parameter selection for ridge regression in high-dimensional misspecified linear models. The set of candidates for the tuning parameter includes not only positive values but also zero and negative values. We ... | https://arxiv.org/abs/2601.13955 | Academic Papers | svg |
be8b044008fdf599696134631ab112a106169b5ecfa1c3ee2c9c156d7590c32f | 2026-01-21T00:00:00-05:00 | A Bregman Regularized Proximal Point Method for Solving Equilibrium Problems on Hadamard Manifolds | arXiv:2601.13959v1 Announce Type: new Abstract: In this paper we develop a Bregman regularized proximal point algorithm for solving monotone equilibrium problems on Hadamard manifolds. It has been shown that the regularization term induced by a Bregman function is, in general, nonconvex on Hadamard manifolds unless the... | https://arxiv.org/abs/2601.13959 | Academic Papers | svg |
1b2f522dec9a75e2b9730622eaa0b3aa5887ecc416dbcb96eb15eb0c9a43e657 | 2026-01-21T00:00:00-05:00 | Information-Theoretic and Computational Limits of Correlation Detection under Graph Sampling | arXiv:2601.13966v1 Announce Type: new Abstract: Correlation analysis is a fundamental problem in statistics. In this paper, we consider the correlation detection problem between a pair of Erdos-Renyi graphs. Specifically, the problem is formulated as a hypothesis testing problem: under the null hypothesis, the two grap... | https://arxiv.org/abs/2601.13966 | Academic Papers | svg |
71011a37190c1cdf3b2977121cea1e28a5145f727644d953063bb3652b88c7bd | 2026-01-21T00:00:00-05:00 | Dispersive estimate for quasi-periodic Klein-Gordon equation on 1-d lattices | arXiv:2601.13967v1 Announce Type: new Abstract: The dispersive estimate plays a pivotal role in establishing the long-term behavior of solutions to the nonlinear equation, thereby being crucial for investigating the well-posedness of the equation.In this work we prove that the solutions to Klein-Gordon equation on 1-d ... | https://arxiv.org/abs/2601.13967 | Academic Papers | svg |
5cc08825cf2c7f8c89b2c9e422366d65bae7e9476e49c0f6b049cca19cbd52d9 | 2026-01-21T00:00:00-05:00 | Toric Euler-Jacobi vanishing theorem and zeros at infinity | arXiv:2601.13977v1 Announce Type: new Abstract: Residues appear naturally in various questions in complex and algebraic geometry: interpolation, duality, representation problems, and obstructions. The first global vanishing result in the projective plane, known as the Euler-Jacobi theorem, was established by Jacobi in ... | https://arxiv.org/abs/2601.13977 | Academic Papers | svg |
81ba600cc9036b358d65b721ddcc5584c2edfa05234c200b8b0a3613e59a2826 | 2026-01-21T00:00:00-05:00 | Spectral Gaps on Large Hyperbolic Surfaces | arXiv:2601.13988v1 Announce Type: new Abstract: In this expository paper, we review the history and the recent breakthroughs in the spectral theory of large volume hyperbolic surfaces. More precisely, we focus mostly on the investigation of the first non-trivial eigenvalue $\lambda_1$ and its possible behaviour in the ... | https://arxiv.org/abs/2601.13988 | Academic Papers | svg |
a384f33cf5daf0e0416998f9266aa174cef661762c914c93f446fb8f8207eb81 | 2026-01-21T00:00:00-05:00 | Eigensets of switching dynamical systems | arXiv:2601.13990v1 Announce Type: new Abstract: Reachability sets of linear switching dynamical systems (systems of ODE with time-dependent matrices that take values from a given compact set) are analysed. An eigenset is a non-trivial compact set M that possesses the following property: the closure of the set of points... | https://arxiv.org/abs/2601.13990 | Academic Papers | svg |
905658f636792000a85535b398ee77cfe5c37df4b42b431b92dc74f232471213 | 2026-01-21T00:00:00-05:00 | Computing Crystalline Cohomology and p-Divisible Groups for Curves over Finite Fields | arXiv:2601.14006v1 Announce Type: new Abstract: Let $X$ be a smooth projective curve over a finite field of characteristic $p$. We describe and implement a practical algorithm for computing the $p$-divisible group $Jac(X)[p^\infty]$ via computing its Dieudonn\'{e} module, or equivalently computing the Frobenius and Ver... | https://arxiv.org/abs/2601.14006 | Academic Papers | svg |
51fc7502da9308b4b10b2a3b94db9525e688bf171bfecc7e379122a23c1f1199 | 2026-01-21T00:00:00-05:00 | Robustness for free: asymptotic size and power of max-tests in high dimensions | arXiv:2601.14013v1 Announce Type: new Abstract: Consider testing a zero restriction on the mean of a $d$-dimensional random vector based on an i.i.d. sample of size $n$. Suppose further that the coordinates are only assumed to possess $m>2$ moments. Then, max-tests based on arithmetic means and critical values derived ... | https://arxiv.org/abs/2601.14013 | Academic Papers | svg |
db0a9a5c5851497e2a8b2c0f1b03de22c8d259ef91de68d9573935f713d4adb5 | 2026-01-21T00:00:00-05:00 | Non-linear traces of Choquet type on AF algebras | arXiv:2601.14016v1 Announce Type: new Abstract: We study non-linear traces of Choquet type on AF algebras. Building on the characterization of Choquet traces on matrix algebras due to Nagisa--Watatani, we generalize the construction to arbitrary unital AF algebras. We show that there is a one-to-one correspondence betw... | https://arxiv.org/abs/2601.14016 | Academic Papers | svg |
3716ef160f4639caddf24e821b5254a2b43d9ee90ff4ea54622de7525750ab6c | 2026-01-21T00:00:00-05:00 | Principal $p-$frequency estimates on non-compact manifolds with negative Ricci curvature | arXiv:2601.14018v1 Announce Type: new Abstract: We establish a lower bound for the principal $p-$frequency $\lambda_{1,p}(\Omega)$ on a bounded domain $\Omega$ in a non-compact Riemannian manifold of dimension $n.$ Under the assumption that the Ricci curvature satisfies $\operatorname{Ric} \geq (n-1)K$ with $K \bar{\la... | https://arxiv.org/abs/2601.14018 | Academic Papers | svg |
52d98a4f285181a1d8cb91c0b895300e62d8725cf82158a08fe813d80e2e58ca | 2026-01-21T00:00:00-05:00 | Tensor Abelian geometry of VI-modules | arXiv:2601.14020v1 Announce Type: new Abstract: In this short note, we study the spectrum of prime Serre ideals of global represen tations for noetherian families. In particular, we prove that the spectrum of prime Serre ideals of finitely generated VI-modules is homeomorphic to N^{*}, the one-point compactification of... | https://arxiv.org/abs/2601.14020 | Academic Papers | svg |
1ead9fb1cae0e88567ae39a7c320564b907cf7fcdfbc7b96b5cdb11736febbe9 | 2026-01-21T00:00:00-05:00 | Some Results on Causal Modalities in General Spacetimes | arXiv:2601.14029v1 Announce Type: new Abstract: Causality is one of the fundamental structures of spacetimes, it determines the possible behaviour and propagation of physical information through different relations. Causal structure can be analysed through the various modal logics it induces. The modal logics for the s... | https://arxiv.org/abs/2601.14029 | Academic Papers | svg |
3a476c8bcbd72d57b52ab2bb6d1e19578d660cf643217031ffbdf9bca5891001 | 2026-01-21T00:00:00-05:00 | Classification of invariant tight contact structures on the 3-space, -ball and -sphere | arXiv:2601.14040v1 Announce Type: new Abstract: We prove some classification results for tight contact structure in the 3-space, -ball and -sphere that are invariant with respect to some arbitrary involution, that is conjugated to the standard rotation around the x-axis. Unlike the classical scenario, a new integral to... | https://arxiv.org/abs/2601.14040 | Academic Papers | svg |
7fe276ce07037e11aaba891a865e45a1f9f06a5f7a1a54f38579f173d65297b1 | 2026-01-21T00:00:00-05:00 | On the Diophantine Equation Involving Elementary Symmetric Polynomials and the Decomposition of Unity | arXiv:2601.14057v1 Announce Type: new Abstract: We consider the equality of the values of the $n$th and $k$th elementary symmetric polynomials of $n$ not necessarily distinct positive integers. For $k < n$, we prove that this equation always has a solution, but only finitely many solutions. Furthermore, we consider the... | https://arxiv.org/abs/2601.14057 | Academic Papers | svg |
497a902c12ad7aea907add63ba4a62c9eec13c4bbffcabd37db36d0b9d92da67 | 2026-01-21T00:00:00-05:00 | A Splitting Theorem for non-positively curved Lorentzian spaces | arXiv:2601.14058v1 Announce Type: new Abstract: We prove a splitting theorem for Lorentzian pre-length spaces with global non-positive timelike curvature. Additionally, we extend the first variation formula to spaces with any timelike curvature bound, either from above or below, and different from 0. | https://arxiv.org/abs/2601.14058 | Academic Papers | svg |
e0e091ccf67a7a7a0e826535fbb75bd1b0858de22033add94ab33d6b48076f9c | 2026-01-21T00:00:00-05:00 | Frostman dimension of Furstenberg measure for $\mathrm{SL}(2,\mathbb{R})$ random matrix products | arXiv:2601.14061v1 Announce Type: new Abstract: For compactly supported $\mu \in \mathcal{P}(\mathrm{SL}(2,\mathbb{R}))$ satisfying strong irreducibility and proximality, we obtain a formula for the Frostman dimension of the associated Furstenberg measure. We also describe the left neighbourhood of 0 for which the clas... | https://arxiv.org/abs/2601.14061 | Academic Papers | svg |
45e50313f7a56ae90b5f99a0f2e8a5f5a2218b420a5a1082ee4c8511f58d324f | 2026-01-21T00:00:00-05:00 | Time-dependent metrics and connections | arXiv:2601.14064v1 Announce Type: new Abstract: Time-dependent structures often appear in differential geometry, particularly in the study of non-autonomous differential equations on manifolds. One may study the geodesics associated with a time-dependent Riemannian metric by extremizing the corresponding energy functio... | https://arxiv.org/abs/2601.14064 | Academic Papers | svg |
138b5b0e1b471e9456b99f4a0ab45a21eb8e0306d312100450b959b4d6c9fb24 | 2026-01-21T00:00:00-05:00 | LU-type factorizations for birth--death processes and their Darboux transformations | arXiv:2601.14074v1 Announce Type: new Abstract: We study LU-type factorizations of the infinitesimal generator of a birth--death process on $\mathbb{N}_0$. Our goal is to characterize those factorizations whose Darboux transformations (that is, inverting the order of the factors) yield new infinitesimal generators of b... | https://arxiv.org/abs/2601.14074 | Academic Papers | svg |
bb98b90ce92bd38390dff20f3fe865896cd07856d38f5419c793215f1a17a002 | 2026-01-21T00:00:00-05:00 | On large periodic traveling wave solutions to the free boundary Stokes and Navier-Stokes equations | arXiv:2601.14085v1 Announce Type: new Abstract: We study the free boundary problem for a finite-depth layer of viscous incompressible fluid in arbitrary dimension, modeled by the Stokes or Navier-Stokes equations. In addition to the gravitational field acting in the bulk, the free boundary is acted upon by surface tens... | https://arxiv.org/abs/2601.14085 | Academic Papers | svg |
7b718827d19058778523dfef6a67fd2c819e164222c1ded25a4a4282302248c1 | 2026-01-21T00:00:00-05:00 | Period collapse of Markov triangles | arXiv:2601.14090v1 Announce Type: new Abstract: Cristofaro-Gardiner and Kleinman showed the complete period collapse of the Ehrhart quasipolynomial of Fibonacci triangles and their irrational limits, by studying the Fourier-Dedekind sums involved in the Ehrhart function of right-angled rational triangles. We generalize... | https://arxiv.org/abs/2601.14090 | Academic Papers | svg |
59473e952ac2b351f4b647112f291625e77950e8cd58fdd4bf9ba2026ed802c2 | 2026-01-21T00:00:00-05:00 | Basis Number and Pathwidth | arXiv:2601.14095v1 Announce Type: new Abstract: We prove two results relating the basis number of a graph $G$ to path decompositions of $G$. Our first result shows that the basis number of a graph is at most four times its pathwidth. Our second result shows that, if a graph $G$ has a path decomposition with adhesions o... | https://arxiv.org/abs/2601.14095 | Academic Papers | svg |
3b4242adbade3b6252072d18bb9fc01502cc1ec0a8e5bf71d20ff028746f4de2 | 2026-01-21T00:00:00-05:00 | Simple subquotients of crossed products by abelian groups and twisted group algebras | arXiv:2601.14097v1 Announce Type: new Abstract: Motivated by work of Poguntke we study the question under what conditions simple subquotients of crossed products $A\rtimes_{\alpha}G$ by (twisted) actions of abelian groups $G$ are isomorphic to simple twisted group algebras of abelian groups. As a consequence, we recove... | https://arxiv.org/abs/2601.14097 | Academic Papers | svg |
2ac6ddfbdab26dd08ca3360634a241fbefd7d481437f02d5ef1bec8bcb521536 | 2026-01-21T00:00:00-05:00 | Angular pair-of-pants decompositions of complex varieties | arXiv:2601.14116v1 Announce Type: new Abstract: We define the notion of torically hyperbolic varieties and we construct pair-of-pants decompositions for these in terms of angle sets of essential projective hyperplane complements. This construction generalizes the classical pair-of-pants decomposition for hyperbolic Rie... | https://arxiv.org/abs/2601.14116 | Academic Papers | svg |
35ec346b69968191a5c458b4eec5d93ba08d12ab8f75120d5a56f4a1e96ebc17 | 2026-01-21T00:00:00-05:00 | Scalar-rigid submersions are Riemannian products | arXiv:2601.14117v1 Announce Type: new Abstract: Scalar-rigid maps are Riemannian submersions by works of Llarull, Goette--Semmelmann, and the second named author. In this article we show that they are essentially Riemannian products of the base manifold with a Ricci-flat fiber. As an application we obtain a Llarull-typ... | https://arxiv.org/abs/2601.14117 | Academic Papers | svg |
94050f06d1dbebf5ab531c656b06d8ad6d72318d23e6a6b48dc7344814a8839a | 2026-01-21T00:00:00-05:00 | Universal Chord Theorem and a Topological Analysis | arXiv:2601.14120v1 Announce Type: new Abstract: We study the set of chords of a real-valued continuous function on [0,1] with f(0)=f(1)=0. We describe which chords may appear as isolated points and provide examples illustrating our characterization. Maximal Hopf sets are introduced and analyzed. | https://arxiv.org/abs/2601.14120 | Academic Papers | svg |
88ecffcd857bc51470b97912c1a3a8a85dda0c8e734e40c2e54a742c38a8881b | 2026-01-21T00:00:00-05:00 | $Q_p$-weighted zero-sum constants | arXiv:2601.14122v1 Announce Type: new Abstract: A sequence $S=(x_1,\ldots, x_k)$ in $\mathbb Z_p$ is called a $(Q_p,\mathbf 1)$-weighted zero-sum sequence if there exist $a_1,\ldots,a_k\in Q_p$ such that $a_1x_1+\cdots+a_kx_k=0$ and $a_1+\cdots+a_k=0$. The constant $E_{Q_p,\mathbf 1}$ is defined to be the smallest posi... | https://arxiv.org/abs/2601.14122 | Academic Papers | svg |
ba9ccbeae136bc79de532fe8059c8f48e2466b2cdbf6abfaf2097e3aef0d7452 | 2026-01-21T00:00:00-05:00 | Flexible curves and Hausdorff dimension | arXiv:2601.14125v1 Announce Type: new Abstract: We show that given a log-singular circle homeomorphism $h$ and given any $s\in[1,2]$, there is a flexible curve of Hausdorff dimension $s$ with welding $h$. We also see that there is another curve with welding $h$ and positive area. In particular, this implies that given ... | https://arxiv.org/abs/2601.14125 | Academic Papers | svg |
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