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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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