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4cc8315040ce6330fceb0a499e4acc898a4046702ca7983551ade9aa0e465d7f | 2026-01-21T00:00:00-05:00 | 2-Adic Obstructions to Presburger-Definable Characterizations of Collatz Cycles | arXiv:2601.12772v1 Announce Type: new Abstract: I investigate structural limitations of Presburger-arithmetic-based approaches to the Collatz problem. I show that the Collatz cycle equation admits a unique solution in the $2$-adic integers, which I term a \emph{ghost cycle}. These ghost cycles are shown to be genuine p... | https://arxiv.org/abs/2601.12772 | Academic Papers | svg |
cd6b497c0ca71110265138d4ebfd5dd26c4cb3167b7b16ce5f43ceeacd498804 | 2026-01-21T00:00:00-05:00 | Probabilistic degenerate logarithm and heterogeneous stirling numbers | arXiv:2601.12794v1 Announce Type: new Abstract: Let Y be a random variable whose moment-generating function exists in some neighborhood of the origin. While probabilistic Stirling numbers of the first and second kind have been introduced, early definitions often failed to satisfy fundamental orthogonality and inverse r... | https://arxiv.org/abs/2601.12794 | Academic Papers | svg |
e4285ec8d046762082673d9daa1026b37456afcae29db0d7bf4ea964ea9d41ac | 2026-01-21T00:00:00-05:00 | Llarull's theorem on noncompact manifolds with boundary | arXiv:2601.12803v1 Announce Type: new Abstract: Recently, Zhang \cite{Zh20} and Li-Su-Wang-Zhang \cite{LSWZ24+} generalized Llarull's theorem to the noncompact complete spin manifold. In this paper, we further extend their results to the noncompact manifold with compact boundary. | https://arxiv.org/abs/2601.12803 | Academic Papers | svg |
8ddf5fbac075cbd414676a5f5e8133dccbee8c99b127fd136031d0833a2bccc7 | 2026-01-21T00:00:00-05:00 | Optimal bounds for the boundary control cost of one-dimensional fractional Schr\"odinger and heat equations | arXiv:2601.12810v1 Announce Type: new Abstract: We derive sharp bounds for the boundary control cost of the one-dimensional fractional Schr\"odinger and heat equations. The analysis of the lower bound is based on the study of the control cost of a related singular boundary control problem in finite time, using tools fr... | https://arxiv.org/abs/2601.12810 | Academic Papers | svg |
4582a75590bde22501d1fb731e55c9eaa2324925aa5bade8f8111bad304ece7d | 2026-01-21T00:00:00-05:00 | Perfect codes in weakly metric association schemes | arXiv:2601.12818v1 Announce Type: new Abstract: The Lloyd Theorem of (Sol\'e, 1989) is combined with the Schwartz-Zippel Lemma of theoretical computer science to derive non-existence results for perfect codes in the Lee metric, NRT metric, mixed Hamming metric, and for the sum-rank distance. The proofs are based on asy... | https://arxiv.org/abs/2601.12818 | Academic Papers | svg |
b6b44d43f7986d2d20f49b44f50cc8236748b192f9ce71e54258e0dd4960afc7 | 2026-01-21T00:00:00-05:00 | Sub-wavelength resonances in two-dimensional multi-layer elastic media | arXiv:2601.12821v1 Announce Type: new Abstract: In this paper, we focus on the sub-wavelength resonances in two-dimensional elastic media characterized by high contrasts in both Lam\'e parameters and density. Our contributions are fourfold. First, it is proved that the operator $\hat{\mathbf{S}}_{\partial D}^{\omega}$,... | https://arxiv.org/abs/2601.12821 | Academic Papers | svg |
795455902587e3509b712a4099d6b206e1d363fca94ca13c059808f76f66ad3d | 2026-01-21T00:00:00-05:00 | A converse of Berndtsson's theorem on the positivity of direct images | arXiv:2601.12825v1 Announce Type: new Abstract: Berndtsson's famous theorem asserts that, for a compact K\"ahler fibration $p:X\to Y$, the direct image bundle $p_*(K_{X/Y}\otimes L)$ of a semi-positive Hermitian holomorphic line bundle $L\to X$ is Nakano semi-positive. As a continuation of our previous work, we prove a... | https://arxiv.org/abs/2601.12825 | Academic Papers | svg |
9f5ca3d0db57fa37a3b48b37bd09de3ff16665f217f3b4dab1cddf47ae7ace8d | 2026-01-21T00:00:00-05:00 | Cofiniteness and $P(z)$-tensor product bifunctors in orbifold theories associated to abelian but not-necessarily-finite groups | arXiv:2601.12834v1 Announce Type: new Abstract: Let $V$ be a M\"{o}bius vertex algebra and $G$ an abelian group of automorphisms of $V$. We construct $P(z)$-tensor product bifunctors for the category of $C_{n}$-cofinite grading-restricted generalized $g$-twisted $V$-modules (without $g$-actions) for $g\in G$ and the ca... | https://arxiv.org/abs/2601.12834 | Academic Papers | svg |
c96b35ea5f30dfae487ac9921ff54f4242fda18a5b69273de8852243919ab452 | 2026-01-21T00:00:00-05:00 | A diagrammatic approach to the three-page index | arXiv:2601.12846v1 Announce Type: new Abstract: The three-page index $\alpha_3(L)$ is an invariant that measures the complexity of representing a link $L$ in a three-page book. It is known that $\alpha_3(L)$ admits a linear upper bound in terms of the crossing number, with equality realized by the Hopf link. In this pa... | https://arxiv.org/abs/2601.12846 | Academic Papers | svg |
cd5b5d439cce4b1d85b8aef1a3ceb27bf0439786dedf5d99881410fce569c073 | 2026-01-21T00:00:00-05:00 | Rankin-Cohen Bracket for Vector-Valued Modular Forms | arXiv:2601.12860v1 Announce Type: new Abstract: In this paper, we explore the relationship between Rankin-Cohen brackets for vector-valued modular forms and Petersson's inner products, deriving an explicit description of the adjoint map for the bracket operator. The study extends to the cases of Jacobi forms and skew-h... | https://arxiv.org/abs/2601.12860 | Academic Papers | svg |
415c489c40b1e9a0e3a0a991974a0a6c28f7d8cd66cc5c4469f5a88c6490b0e7 | 2026-01-21T00:00:00-05:00 | Traveling waves for monostable reaction-diffusion-convection equations with discontinuous density-dependent coefficients | arXiv:2601.12869v1 Announce Type: new Abstract: This paper concerns wave propagation in a class of scalar reaction-diffusion-convection equations with $p$-Laplacian-type diffusion and monostable reaction. We introduce a new concept of a non-smooth traveling wave profile, which allows us to treat discontinuous diffusion... | https://arxiv.org/abs/2601.12869 | Academic Papers | svg |
be8727085b8f42760d16d8b0f8c59f33a904ee60b6284b5fe1d443caf4fa12de | 2026-01-21T00:00:00-05:00 | Residues and Infinitesimal Torelli for Equisingular Curves | arXiv:2601.12873v1 Announce Type: new Abstract: We study infinitesimal Torelli problems and infinitesimal variations of Hodge structure for families of curves arising in singular and extrinsically constrained geometric settings. Motivated by the Green--Voisin philosophy, we develop an explicit approach based on Poincar... | https://arxiv.org/abs/2601.12873 | Academic Papers | svg |
ca7e81ab7d18e3bae8f0e6a56637e0f8f284f8042323d746dc919fac9c6fc14e | 2026-01-21T00:00:00-05:00 | Hunting The Poles in the Staircases | arXiv:2601.12881v1 Announce Type: new Abstract: Motivated by applications to the fractional quantum Hall effect and, in particular, to the Bernevig-Haldane conjectures, we investigates the behavior of Macdonald polynomials under specializations of the form q a t b = 1. Our main focus is to explain, in a simple and pure... | https://arxiv.org/abs/2601.12881 | Academic Papers | svg |
979ae89ad5348189312e97f309bec6fb4420a87a022d4c52c02a93f35c17a9b0 | 2026-01-21T00:00:00-05:00 | A formula for the local Heun solution | arXiv:2601.12888v1 Announce Type: new Abstract: The local Heun solution is the unique solution to Heun's equation which is analytic in the unit disk centered at $0\in\mathbb{C}$ and taking the value $1$ at the center of the disk. In this paper, as an application of the theory of orthogonal polynomials, we are able to e... | https://arxiv.org/abs/2601.12888 | Academic Papers | svg |
36efb05ab1d6f1d7e6358af5cd16f48d262b8c802d64c1ffac2026e09c9f8cf1 | 2026-01-21T00:00:00-05:00 | Bi-Lipschitz invariance of Newton polygons along gradient canyons | arXiv:2601.12897v1 Announce Type: new Abstract: We study bi-Lipschitz right-equivalence of holomorphic function germs $f:(\mathbb{C}^2,0)\to(\mathbb{C},0)$ via polar arcs and gradient canyons. For a polar arc $\gamma$ we consider the Newton polygon of $f_x(X+\gamma(Y),Y)$ and define its augmentation by adjoining the po... | https://arxiv.org/abs/2601.12897 | Academic Papers | svg |
3fc28bc3153d3cd75946b6c874f8781d8a09b0529fec3410674377eaa3d951d9 | 2026-01-21T00:00:00-05:00 | On the number of spanning trees of bicirculant graphs | arXiv:2601.12899v1 Announce Type: new Abstract: A bi-Cayley graph over a cyclic group $\mathbb{Z}_n$ is called a bicirculant graph. Let $\Gamma=BC(\mathbb{Z}_n; R,T,S)$ be a bicirculant graph with $R=R^{-1}\subseteq \mathbb{Z}_n\setminus \{0\}$ and $T=T^{-1}\subseteq \mathbb{Z}_n\setminus \{0\}$ and $S\subseteq \mathbb... | https://arxiv.org/abs/2601.12899 | Academic Papers | svg |
0767a0eb33e8b9d7f0dbd59c12f71b8fd16c1fd3f090b0f6efd78b27a8746a53 | 2026-01-21T00:00:00-05:00 | Gender and assessment in mathematics: a comparative study of managing assessment episodes | arXiv:2601.12908v1 Announce Type: new Abstract: The article focuses on the differences in mathematics performance between girls and boys visible from the first four months of compulsory schooling in the French education system. The influence of gender stereotypes in the evaluation practices of teachers and the threat o... | https://arxiv.org/abs/2601.12908 | Academic Papers | svg |
4774bfbc0f0378cb86a88495eed22d3417a96d119b926e3692d7d1f9ef1541aa | 2026-01-21T00:00:00-05:00 | A functional inequalities approach for the field-road diffusion model with (symmetric) nonlinear exchanges | arXiv:2601.12909v1 Announce Type: new Abstract: In this note, we consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions and coupled through (symmetric) nonlinear exchange terms. We propose a new and rather direct functional inequalit... | https://arxiv.org/abs/2601.12909 | Academic Papers | svg |
08e0c6a708bf356ed4d241c7c7ff0b65fc9b732fbb0f8c1300187a289b01afe1 | 2026-01-21T00:00:00-05:00 | Sharp lower bound for the Monge-Amp\`ere torsion on convex sets | arXiv:2601.12915v1 Announce Type: new Abstract: The \emph{Monge-Amp\`ere} torsion deficit of an open, bounded convex set $\Omega\subset\R^n$ of class $C^2$ is the normalized gap between the value of the torsion functional evaluated on $\Omega$ and its value on the ball with the same $(n-1)$-quermassintegral as $\Omega$... | https://arxiv.org/abs/2601.12915 | Academic Papers | svg |
4c372dd6103403436f0f3351dd600c9a036472c5b2278bee84acd2e903d68ea6 | 2026-01-21T00:00:00-05:00 | On Kippenhahn curves of low rank partial isometries | arXiv:2601.12923v1 Announce Type: new Abstract: Conditions are established for rank three partial isometries to have circular components contained in their Kippenhahn curves. In particular, such matrices with circular numerical ranges are described. It is also established that the Gau-Wang-Wu conjecture holds for matri... | https://arxiv.org/abs/2601.12923 | Academic Papers | svg |
f9c748cecfd78c158e33f4b3eae59a5c9971c93d35b9be36e43d0101d8e663f2 | 2026-01-21T00:00:00-05:00 | Stone Duality for Preordered Topological Spaces | arXiv:2601.12932v1 Announce Type: new Abstract: A preordered topological space is a topological space with a preordering. We exhibit a Stone-like duality for preordered topological spaces, Inspired by a similar duality for bitopological spaces, due to Jung-Moshier and Jakl, and by a duality for preordered sets due to B... | https://arxiv.org/abs/2601.12932 | Academic Papers | svg |
baa498e9a777d9463f253ebf00dc193d9470b48f635db445b14cc0df1bc2e7f6 | 2026-01-21T00:00:00-05:00 | Random tree Besov priors: Data-driven regularisation parameter selection | arXiv:2601.12957v1 Announce Type: new Abstract: We develop a data-driven algorithm for automatically selecting the regularisation parameter in Bayesian inversion under random tree Besov priors. One of the key challenges in Bayesian inversion is the construction of priors that are both expressive and computationally fea... | https://arxiv.org/abs/2601.12957 | Academic Papers | svg |
c97104cb5cae3a559428efed2962c7d65d3ede36bbbe859fb582d8999faa0e3a | 2026-01-21T00:00:00-05:00 | On cohomological dimensions of totally disconnected locally compact groups | arXiv:2601.12958v1 Announce Type: new Abstract: In this paper, we introduce Mackey functors for a t.d.l.c. group and define the cohomological dimension of this group over the Mackey category. We then compare this dimension to the rational discrete cohomological dimension defined by Castellano and Weigel, as well as to ... | https://arxiv.org/abs/2601.12958 | Academic Papers | svg |
ad702582a7de535f7bbf6094165f2a89198eb26e14169b225d743ea230d14699 | 2026-01-21T00:00:00-05:00 | Counting Irreducible polynomials with coefficients from thin subgroups | arXiv:2601.12968v1 Announce Type: new Abstract: L. Bary-Soroker and R. Shmueli (2026) have given an asymptotic formula for the number of irreducible polynomials over the finite fields $\mathbb F_q$ of $q$ elements, such that their coefficients are perfect squares in $\mathbb F_q$ and also extended this to classes of po... | https://arxiv.org/abs/2601.12968 | Academic Papers | svg |
638f7f28f25c2c15581baa8d0e956ce6979ddd218ee49edcb731916f1436e39e | 2026-01-21T00:00:00-05:00 | Bernstein type gradient estimate for system of weighted local heat equations with potential term | arXiv:2601.12992v1 Announce Type: new Abstract: In this article we provide Bernstein type gradient estimates for two system of local weighted heat type equations with potentials on a weighted Riemannian manifold. We derive all possible cases considering linear potential, exponential potential, combining with static man... | https://arxiv.org/abs/2601.12992 | Academic Papers | svg |
3936ebdbdf2af390a96ec53cb6ecf3bc186c5786b5bdabbec8b8ca272ff8359b | 2026-01-21T00:00:00-05:00 | The distribution of the ratio of products of independent zero mean normal random variables | arXiv:2601.12997v1 Announce Type: new Abstract: Let $X_1,\ldots,X_M$ and $Y_1,\ldots,Y_N$ be independent zero mean normal random variables with variances $\sigma_{X_i}^2$, $i=1,\ldots,M$, and $\sigma_{Y_j}^2$, $j=1,\ldots,N$, respectively, and let $X=X_1\cdots X_M$ and $Y=Y_1\cdots Y_N$. In this paper, we derive the ex... | https://arxiv.org/abs/2601.12997 | Academic Papers | svg |
d545c2c1e4d4b979771d63e9b09f705fd1524b62ec373e6f66c1dec10e643012 | 2026-01-21T00:00:00-05:00 | Isomorphism relations on classes of c.e. algebras | arXiv:2601.13005v1 Announce Type: new Abstract: We investigate the complexity of isomorphism relations for classes of finitely generated and n-generated computably enumerable (c.e.) algebras, presented via c.e. presentations -- that is, as quotients of term algebras over decidable sets of generators by c.e. congruences... | https://arxiv.org/abs/2601.13005 | Academic Papers | svg |
c518418cf4d8664bc9f91805f1c4a3ccd36242748db89718e8456b5983db75b2 | 2026-01-21T00:00:00-05:00 | Semi-infinite Lakshmibai--Seshadri paths and level-zero extremal weight modules over twisted quantum affine algebras | arXiv:2601.13016v1 Announce Type: new Abstract: In this paper, we study level-zero extremal weight modules over twisted quantum affine algebras. To this end, we introduce semi-infinite Lakshmibai--Seshadri paths associated with a level-zero dominant integral weight $\lambda$. We then show that the set $\tfrac{\infty}{2... | https://arxiv.org/abs/2601.13016 | Academic Papers | svg |
65227e385b0628d2c9433677a78cd51958b353106b3db9e0b53cdd6d9a61d665 | 2026-01-21T00:00:00-05:00 | Characterization of eigenfunctions of the Laplacian having exponential growth | arXiv:2601.13017v1 Announce Type: new Abstract: In 1993, Robert Strichartz proved a characterization for the bounded eigenfunctions of Laplacian $\Delta=-\sum_{j=1}^d \frac{\partial^2}{\partial x_j^2} $ on $\mathbb{R}^d$: If $\left\{f_k \right\}_{k\in \mathbb{Z}}$ be a doubly infinite sequence of functions on $\mathbb{... | https://arxiv.org/abs/2601.13017 | Academic Papers | svg |
9af6508bea74c268c3dfeede9cd1087ae852f9971a67fd83f5856c464d776728 | 2026-01-21T00:00:00-05:00 | The Reduced Phase Space of $N=1, D=4$ Supergravity in the BV-BFV formalism | arXiv:2601.13025v1 Announce Type: new Abstract: This paper describes the reduced phase space of $N=1$, $D=4$ supergravity in the fully off-shell Palatini--Cartan formalism. This is achieved through the KT construction, allowing an explicit description of first-class constraints on the boundary. The corresponding BFV de... | https://arxiv.org/abs/2601.13025 | Academic Papers | svg |
2eae668d5de97c3570718f9a24750449de1c1798c4acac2bdf8d4d025625a2d4 | 2026-01-21T00:00:00-05:00 | Multi-gear bandits, partial conservation laws, and indexability | arXiv:2601.13026v1 Announce Type: new Abstract: This paper considers what we propose to call multi-gear bandits, which are Markov decision processes modeling a generic dynamic and stochastic project fueled by a single resource and which admit multiple actions representing gears of operation naturally ordered by their i... | https://arxiv.org/abs/2601.13026 | Academic Papers | svg |
db5071468faadfb14b9159018f7432314992f5bde4cb165ab09a95702add018a | 2026-01-21T00:00:00-05:00 | Optimality Conditions for Sparse Bilinear Least Squares Problems | arXiv:2601.13027v1 Announce Type: new Abstract: The first-order optimality conditions of sparse bilinear least squares problems are studied. The so-called T-type and N-type stationary points for this problem are characterized in terms of tangent cone and normal cone in Bouligand and Clarke senses, and another stationar... | https://arxiv.org/abs/2601.13027 | Academic Papers | svg |
7a1b90ce1a3785718739f4905181c3c96e9dfea14f5e04082a42e5cc3e5ed524 | 2026-01-21T00:00:00-05:00 | Generalized MICZ-Kepler systems on three-dimensional sphere and hyperboloid | arXiv:2601.13028v1 Announce Type: new Abstract: We propose analogs of the generalized MICZ-Kepler system on the three-dimensional sphere and (two-sheet) hyperboloid. We then construct their energy spectra and normalized wave functions, concluding that the suggested systems are minimally superintegrable. | https://arxiv.org/abs/2601.13028 | Academic Papers | svg |
e897da308a98a10b5a3bf601758572198be14e7517d388e555d789707a560378 | 2026-01-21T00:00:00-05:00 | Complete orbit equivalence relation and non-universal Polish groups | arXiv:2601.13030v1 Announce Type: new Abstract: We show that a non-universal Polish group can induce a complete orbit equivalence relation, which answers a question of Sabok from \cite{OPENPROBLEMS}. | https://arxiv.org/abs/2601.13030 | Academic Papers | svg |
024299edbedda03a66e6b8b22d5f37c3db3d2c50e487870cb13e392ec4ddc6fe | 2026-01-21T00:00:00-05:00 | On the additive index of the Diffie-Hellman mapping and the discrete logarithm | arXiv:2601.13034v1 Announce Type: new Abstract: Several complexity measures such as degree, sparsity and multiplicative index for cryptographic functions including the Diffie-Hellman mapping and the discrete logarithm in a finite field have been studied in the literature. In 2022, Reis and Wang introduced another compl... | https://arxiv.org/abs/2601.13034 | Academic Papers | svg |
275c4730d95ac4f8e80e21746387cd17b07ae1b3f243c5f9c08fb28f36a244e1 | 2026-01-21T00:00:00-05:00 | Classification of quaternionic skew-Hermitian symmetric spaces | arXiv:2601.13036v1 Announce Type: new Abstract: We provide a complete classification of quaternionic skew-Hermitian symmetric spaces, namely symmetric spaces that admit a torsion-free ${\rm SO}^{*}(2n){\rm Sp}(1)$-structure for arbitrary $n>1$. Moreover, we prove that any homogeneous quaternionic skew-Hermitian manifol... | https://arxiv.org/abs/2601.13036 | Academic Papers | svg |
e4d47e65005052ac7914becfbbdabb0fb043e40e06054b5de859e4e32d13568b | 2026-01-21T00:00:00-05:00 | Markovian restless bandits and index policies: A review | arXiv:2601.13045v1 Announce Type: new Abstract: The restless multi-armed bandit problem is a paradigmatic modeling framework for optimal dynamic priority allocation in stochastic models of wide-ranging applications that has been widely investigated and applied since its inception in a seminal paper by Whittle in the la... | https://arxiv.org/abs/2601.13045 | Academic Papers | svg |
10765c5f72466b46c18f56ce6ce58e1cbcec80db54dbcfbfa9246229d9376df9 | 2026-01-21T00:00:00-05:00 | Optimal existence of weak solutions for the generalised Navier-Stokes-Voigt equations | arXiv:2601.13051v1 Announce Type: new Abstract: In this study, we investigate the incompressible generalised Navier-Stokes-Voigt equations within a bounded domain $\Omega \subset \mathbb{R}^d$, where $d \geq 2$. The governing momentum equation is expressed as: \begin{align*} \partial_t(\boldsymbol{v} - \kappa \Delta \b... | https://arxiv.org/abs/2601.13051 | Academic Papers | svg |
1b34c6df8087ce2d28f7c91d82850d6cba226eaaeae1725ea09c5afd62c10c85 | 2026-01-21T00:00:00-05:00 | Period growth and co-context-free groups | arXiv:2601.13058v1 Announce Type: new Abstract: We study period growth in co-context-free groups, giving general results and looking at specific examples such as Thompson groups $T$ and $V$ and the Houghton groups $H_m$. Along the way, we give a refined upper bound on the word metric in Thompson $V$, as well as efficie... | https://arxiv.org/abs/2601.13058 | Academic Papers | svg |
f3026924d32ef4a1e41e39e0db341b79ce6cbd5aecee7bc48f6d59c228736120 | 2026-01-21T00:00:00-05:00 | Generalized Reproducing Kernel Banach Spaces: A Functional Analytic Framework for Abstract Neural Networks | arXiv:2601.13062v1 Announce Type: new Abstract: In this paper, we introduce a generalization of Reproducing Kernel Banach Spaces (RKBS), which we term \emph{Generalized Reproducing Kernel Banach Spaces} (GRKBS). The motivation stems from recent results showing that classical fully connected neural networks can be under... | https://arxiv.org/abs/2601.13062 | Academic Papers | svg |
064fc0be8626c79d1fdd86ad1919df4685a1be15c588ba9bb3fe3a0ee0a57be4 | 2026-01-21T00:00:00-05:00 | Non-abelian Hodge correspondence over singular K\"ahler spaces | arXiv:2601.13071v1 Announce Type: new Abstract: In this paper, we establish the non-abelian Hodge correspondence over compact K\"ahler spaces with Kawamata log terminal (klt) singularities as well as over their regular loci, thereby extending the result of Greb-Kebekus-Peternell-Taji for projective klt varieties to the... | https://arxiv.org/abs/2601.13071 | Academic Papers | svg |
9072236477770046764215ade45996867fbf86b86a0e919476f7861b47a89f77 | 2026-01-21T00:00:00-05:00 | Faster 3-colouring algorithm for graphs of diameter 3 | arXiv:2601.13072v1 Announce Type: new Abstract: We show that given an $n$-vertex graph $G$ of diameter 3 we can decide if $G$ is $3$-colourable in time $2^{O(n^{2/3-\varepsilon})}$ for any $\varepsilon < 1/33$. This improves on the previous best algorithm of $2^{O((n\log n)^{2/3})}$ from D\k{e}bski, Piecyk and Rz\k{a}\... | https://arxiv.org/abs/2601.13072 | Academic Papers | svg |
7cdaacb32591203247ba56c6343fbab9deb05f71b5f8280288eccc23c8be2191 | 2026-01-21T00:00:00-05:00 | Wasserstein geometry of nonnegative measures on finite Markov chains I: Gradient flow | arXiv:2601.13073v1 Announce Type: new Abstract: We investigate a Benamou--Brenier type transportation metric for nonnegative measures on a finite reversible Markov chain, which endows the space of measures with a Riemannian structure. Using this geometric framework, we identify a generalized heat equation with source a... | https://arxiv.org/abs/2601.13073 | Academic Papers | svg |
37b8cb942dd499ba05cd82d0e620f433c79f6f242553efbb3a3b9f7ca45403bd | 2026-01-21T00:00:00-05:00 | Some results on the $\mathfrak{g}$-stability of surfaces with boundary | arXiv:2601.13077v1 Announce Type: new Abstract: In this paper, we investigate the geometric properties associated with the $\mathfrak{g}$-stability of surfaces with boundary whose null expansion satisfies $\Theta^{+} = h \geq 0$. First, we show that a $\mathfrak{g}$-stable hypersurface with free boundary admits a metri... | https://arxiv.org/abs/2601.13077 | Academic Papers | svg |
1cd9885b6f18e54dbf3da26ab7d85a4219d9ec8496c820c094482a4c3484185d | 2026-01-21T00:00:00-05:00 | Wasserstein geometry of nonnegative measures on finite Markov chains II: Geodesic and duality formulae | arXiv:2601.13080v1 Announce Type: new Abstract: In this paper, we investigate the geodesic structure and the associated Kantorovich-type duality for a Benamou-Brenier-type transportation metric defined on the space of nonnegative measures over a finite reversible Markov chain. The metric is introduced through a dynamic... | https://arxiv.org/abs/2601.13080 | Academic Papers | svg |
993848bb3d0e5bbf133334f53f86396d1aa83e3dcc3b0d489743ad130bc88ccd | 2026-01-21T00:00:00-05:00 | Further progress on Wojda's conjecture | arXiv:2601.13085v1 Announce Type: new Abstract: Two digraphs of order $n$ are said to pack if they can be found as edge-disjoint subgraphs of the complete digraph of order $n$. It is well established that if the sum of the sizes of the two digraphs is at most $2n-2$, then they pack, with this bound being sharp. However... | https://arxiv.org/abs/2601.13085 | Academic Papers | svg |
769123457e421562ed5116066e9f2219a6cd9e5d9ed738bf68c0f9542e744592 | 2026-01-21T00:00:00-05:00 | Brownian Loops and the Selberg Zeta Function | arXiv:2601.13086v1 Announce Type: new Abstract: We study the Brownian loop measure on hyperbolic surfaces for Brownian motion with a constant killing rate. We compute the mass of Brownian loops with killing in a free homotopy class and then relate the total mass of loops in all essential homotopy classes to the Selberg... | https://arxiv.org/abs/2601.13086 | Academic Papers | svg |
f7f1b3a856b0023b62655e8a08532a4a5ae1ed0b6a8aef9b9a94f8edd8530eab | 2026-01-21T00:00:00-05:00 | Dynamical boundaries of affine buildings: C*-simplicity and Poisson boundaries | arXiv:2601.13092v1 Announce Type: new Abstract: We investigate a class of groups acting on possibly exotic affine buildings $X$ and possessing good proximal properties. Such groups are termed of general type, and their dynamics is analyzed through their flag limit sets in the space of chambers at infinity of $X$. For a... | https://arxiv.org/abs/2601.13092 | Academic Papers | svg |
28e8b1e8693a86890d8d91dbeac74699e7d24fc4303c68bf433a98513aa5286e | 2026-01-21T00:00:00-05:00 | Quasi-maximal ideals and ring extensions | arXiv:2601.13093v1 Announce Type: new Abstract: Alan and al. defined and studied quasi-maximal ideals. We add a comprehensive characterization of these ideals, introducing submaximal ideals. The conductor of a finite minimal extension $R\subset S$ is quasi-maximal in $S$. This allows us to give a new characterization o... | https://arxiv.org/abs/2601.13093 | Academic Papers | svg |
93c27a25c24719f56862ac8778cff088a8011b5b07638e9f9b4c1c477dd080f6 | 2026-01-21T00:00:00-05:00 | Equiprojective polytopes in higher dimension | arXiv:2601.13095v1 Announce Type: new Abstract: A 3-dimensional polytope is called k-equiprojective if every planar projection along a direction non-parallel to any facet is a k-gon. In this article, we generalise equiprojectivity to higher dimensions and give a lower bound on the number of combinatorial types of equip... | https://arxiv.org/abs/2601.13095 | Academic Papers | svg |
a3ad0e43281dc5117b56bad0511ff09c256400e933079926cf6a31d9306357b9 | 2026-01-21T00:00:00-05:00 | Parallel mean curvature surfaces with constant contact angle along free boundaries | arXiv:2601.13101v1 Announce Type: new Abstract: We classify branched immersed disks in space forms with non-zero parallel mean curvature vector and non-orthogonal constant contact angle along the boundary in 4-dimensional space form. For higher codimensional case, we prove a codimension reduction theorem for branched i... | https://arxiv.org/abs/2601.13101 | Academic Papers | svg |
17bd9ee89d13c9ab2b0ea36eeb16b541d3d1425a1b224668bf1e1f00e4176e25 | 2026-01-21T00:00:00-05:00 | Full characterization of core for nonlinear optimization games | arXiv:2601.13124v1 Announce Type: new Abstract: We fully characterize the core of a broad class of nonlinear games by identifying a suitable relaxation for inherent nonlinearity, directly generalizing the linear frameworks in the literature. This characterization significantly expands the scope of cooperative games tha... | https://arxiv.org/abs/2601.13124 | Academic Papers | svg |
59be1d79800030befb262696ac9256c3e8ed805554de42dfdd77492b211c207a | 2026-01-21T00:00:00-05:00 | An algebro-geometric perspective on the topology of moduli spaces of differentials | arXiv:2601.13127v1 Announce Type: new Abstract: Differentials on Riemann surfaces correspond to translation surfaces with conical singularities, and affine transformations acting on them preserve the orders of these singularities. This viewpoint allows the moduli spaces of differentials to appear in various guises acro... | https://arxiv.org/abs/2601.13127 | Academic Papers | svg |
fd8e1cf576cfd07a3fa8b5a411c17d22c7533ec5eb3499b54b072b09f98a9760 | 2026-01-21T00:00:00-05:00 | On the splitting of Neumann eigenvalues in perforated domains | arXiv:2601.13129v1 Announce Type: new Abstract: We address the problem of splitting of eigenvalues of the Neumann Laplacian under singular domain perturbations. We consider a domain perturbed by the excision of a small spherical hole shrinking to an interior point. Our main result establishes that the splitting of mult... | https://arxiv.org/abs/2601.13129 | Academic Papers | svg |
6d2425344de4134604a211e98241935181bcfda097e9ac38d3d4e9a80a5ce18d | 2026-01-21T00:00:00-05:00 | Age of information cost minimization with no buffers, random arrivals and unreliable channels: A PCL-indexability analysis | arXiv:2601.13130v1 Announce Type: new Abstract: Over the last decade, the Age of Information has emerged as a key concept and metric for applications where the freshness of sensor-provided data is critical. Limited transmission capacity has motivated research on the design of tractable policies for scheduling informati... | https://arxiv.org/abs/2601.13130 | Academic Papers | svg |
71d9d50e63eea26be2f4e7f793d957f088e9b169ef1d69ecf438968352408d18 | 2026-01-21T00:00:00-05:00 | The descriptive complexity of the set of arc-connected compact subsets of the plane | arXiv:2601.13135v1 Announce Type: new Abstract: We compute the exact complexity of the set of all arc-connected compact subsets of $\boldmath R^2$, which turns out to be strictly higher than the classical $\boldmath \Sigma^1_1$ and $\boldmath \Pi^1_1$ classes of analytic and coanalytic sets, but stricly lower than the ... | https://arxiv.org/abs/2601.13135 | Academic Papers | svg |
5dedd82eaf179be2f58a6183df3b0734c381d4e1695143e883cae02551964296 | 2026-01-21T00:00:00-05:00 | Blackwell optimality in risk-sensitive stochastic control | arXiv:2601.13136v1 Announce Type: new Abstract: In this paper, we consider a discrete-time Markov Decision Process (MDP) on a finite state-action space with a long-run risk-sensitive criterion used as the objective function. We discuss the concept of Blackwell optimality and comment on intricacies which arise when the ... | https://arxiv.org/abs/2601.13136 | Academic Papers | svg |
f461dd3918b03e4ffb362761c87225e1de09cbbaff6e4b3ae6d700fb404ad5e0 | 2026-01-21T00:00:00-05:00 | Classical Optimal Designs for Stationary Diffusion with Multiple Phases | arXiv:2601.13149v1 Announce Type: new Abstract: We study optimal design problems for stationary diffusion involving one or more state equations and mixtures of an arbitrary number of anisotropic materials. Since such problems typically do not admit classical solutions, we adopt a homogenization-based relaxation framewo... | https://arxiv.org/abs/2601.13149 | Academic Papers | svg |
09a99c13e9d80e5d1d5e760d6ed0bdd7362402fd94e02e132d1f3adac46d01f5 | 2026-01-21T00:00:00-05:00 | Factoriality of normal projective varieties | arXiv:2601.13151v1 Announce Type: new Abstract: For a normal projective variety $X$, the $\bf Q$-factoriality defect $\sigma(X)$ is defined to be the rank of the quotient of the group of Weil divisors by the subgroup of Cartier ones. We prove a slight improvement of a topological formula of S.G. Park and M. Popa assert... | https://arxiv.org/abs/2601.13151 | Academic Papers | svg |
c4a803e3ce9e34c18b4462c0eebb22f00b849dfc319fbf78cfc38d8658a614f8 | 2026-01-21T00:00:00-05:00 | Character degrees in $2$-blocks of $\mathfrak{S}_n$ and $\mathfrak{A}_n$ | arXiv:2601.13152v1 Announce Type: new Abstract: Let $p$ be an odd prime. We show that for sufficiently large $n$, every $2$-block of $\mathfrak{S}_n$ and $\mathfrak{A}_n$ contains an ordinary irreducible character of degree divisible by $p$. For almost all $2$-blocks of $\mathfrak{A}_n$, we classify whether it contains... | https://arxiv.org/abs/2601.13152 | Academic Papers | svg |
40876afe9a2dcc3131255bd5f1a30f63165aa9eea6ae6e22fd3f2ee589a47918 | 2026-01-21T00:00:00-05:00 | On the characteristic function of the asymmetric Student's $t$-distribution and an integral involving the sine function | arXiv:2601.13158v1 Announce Type: new Abstract: We obtain a new closed-form formula for the characteristic function of the asymmetric Student's $t$-distribution. As part of our analysis, we derive a new closed-form formula for the integral $\int_0^\infty \sin(ax)/(b^2+x^2)^n\,\mathrm{d}x$, for $a,b>0$, $n\in\mathbb{Z}^... | https://arxiv.org/abs/2601.13158 | Academic Papers | svg |
375a0da3d16b7cbdc240c048b8bb45af6ef0bf470697b697c3804435bd76ef33 | 2026-01-21T00:00:00-05:00 | On the discrete logarithmic Minkowski problem in the plane | arXiv:2601.13159v1 Announce Type: new Abstract: The paper characterizes the convex hull of the closure of the cone-volume set $C_\cv(U)$, consisting of all cone-volume vectors of polygons with outer unit normals vectors contained in $U$, for any finite set $U \subseteq \R^2, \pos(U) = \R^2$. We prove that this convex h... | https://arxiv.org/abs/2601.13159 | Academic Papers | svg |
aceed42217ae5c7c0dec16d69a1f6b2e9f3ba1a942b978c92920dc8543e56a77 | 2026-01-21T00:00:00-05:00 | A new notion of dimension for dynamical systems and shift embeddability | arXiv:2601.13161v1 Announce Type: new Abstract: A dynamical system $(X,T)$ is \emph{shift embaddable} if $(X,T)$ embeds continuously and equivariantly in the shift over $[0,1]^d$ for some finite $d$. Refuting a major conjecture in the field, in a recent result of Dranishnikov and Levin it was shown that Gromov's mean d... | https://arxiv.org/abs/2601.13161 | Academic Papers | svg |
f9a7ac057b31c74fdcb2a3da6d43cf59f7fffa10c8efbc0710349e7d752e25cf | 2026-01-21T00:00:00-05:00 | Nash approximation of differentiable semialgebraic maps | arXiv:2601.13164v1 Announce Type: new Abstract: Let $T\subset{\mathbb R}^n$ be a semialgebraic set and let $\mu\ge0$ be a non-negative integer. We say that $T$ is a {\em Nash $\mu$-approximation target space} (or a $({\mathcal N},\mu)$-${\tt ats}$ for short) if it has the following universal approximation property: {\e... | https://arxiv.org/abs/2601.13164 | Academic Papers | svg |
7897fcc604a47af1a65c9efb3fcc50216fe00c22174135407d65b4fbd4fa4487 | 2026-01-21T00:00:00-05:00 | PDE aspects of the dynamical optimal transport in the Lorentzian setting | arXiv:2601.13167v1 Announce Type: new Abstract: One of the crucial features of optimal transport on Riemannian manifolds is the equivalence of the `static', original, formulation of the problem and of the `dynamic' one, based on the study of the continuity equation. This furnishes the key link between Wasserstein geome... | https://arxiv.org/abs/2601.13167 | Academic Papers | svg |
992818d4a4caf8345c2cbff32da37980b702d8b5e5cbf63c271c5fbefd7ae3cb | 2026-01-21T00:00:00-05:00 | Calculating The Local Ideal Class Monoid and Gekeler Ratios | arXiv:2601.13184v1 Announce Type: new Abstract: Let $A = \mathbb{F}_q[T]$, $\mathfrak{p} \subset A$ prime, $f(x) \in A[x]$ irreducible and set $R = A[x]/f(x)$. Denote its completion by $R_\mathfrak{p}$. The ideal class monoid $\text{ICM}(R_\mathfrak{p})$ is the set of fractional $R_\mathfrak{p}$ ideals modulo the princ... | https://arxiv.org/abs/2601.13184 | Academic Papers | svg |
70dd50e9614d9ac03b60fecdac6b9c448121888f7f965d11ca24726bea4a4a7e | 2026-01-21T00:00:00-05:00 | Radicals of Lie-solvable Novikov algebras | arXiv:2601.13185v1 Announce Type: new Abstract: We prove that in a Lie-solvable Novikov algebra, the Baer radical coincides with the set of all right-nilpotent elements, and the Andrunakievich radical coincides with the largest left-quasiregular ideal. We investigate the stability of some properties of commutative alge... | https://arxiv.org/abs/2601.13185 | Academic Papers | svg |
c14228e96905a53d2d839722e1ff93729141a46c9b50dcc3b3b61039d1e7403b | 2026-01-21T00:00:00-05:00 | Onsager's Mean Field Theory of Vortex Flows with Singular Sources: Blow-Up and Concentration without Quantization | arXiv:2601.13192v1 Announce Type: new Abstract: Motivated by the Onsager statistical mechanics description of turbulent Euler flows with point singularities, we make a first step in the generalization of the mean field theory in [Caglioti, Lions, Marchioro, Pulvirenti; Comm. Math. Phys. (1995)]. On one side we prove th... | https://arxiv.org/abs/2601.13192 | Academic Papers | svg |
5cd9de52116dd25204edcfd5fbb379d31ee26fd04f4ef29000feeb63c5e6d0a2 | 2026-01-21T00:00:00-05:00 | Asymptotic Stability of Rarefaction Waves for the Hyperbolized Navier-Stokes-Fourier System | arXiv:2601.13193v1 Announce Type: new Abstract: This paper investigates the asymptotic stability of rarefaction waves for a one-dimensional compressible fluid system, where the Newton's law of viscosity and Fourier's law of heat conduction are replaced by Maxwell's law and Cattaneo's law, respectively. The system, whic... | https://arxiv.org/abs/2601.13193 | Academic Papers | svg |
180355a01125456592effb0d959ac5f9a0960eedd9fbd32f014fd340115e4c11 | 2026-01-21T00:00:00-05:00 | A Lower Bound on the Expected Number of Distinct Patterns in a Random Permutation | arXiv:2601.13194v1 Announce Type: new Abstract: Let $\pi_n$ be a uniformly chosen random permutation on $[n]$. The authors of [2] showed that the expected number of distinct consecutive patterns of all lengths $k\in\{1,2,\ldots,n\}$ in $\pi_n$ was $\frac{n^2}{2}(1-o(1))$ as $n\to\infty$, exhibiting the fact that random... | https://arxiv.org/abs/2601.13194 | Academic Papers | svg |
59654c33e1aae851af16c05a4446d896e0c12ad604edb025bb41290af3fc4534 | 2026-01-21T00:00:00-05:00 | AI for Mathematics: Progress, Challenges, and Prospects | arXiv:2601.13209v1 Announce Type: new Abstract: AI for Mathematics (AI4Math) has emerged as a distinct field that leverages machine learning to navigate mathematical landscapes historically intractable for early symbolic systems. While mid-20th-century symbolic approaches successfully automated formal logic, they faced... | https://arxiv.org/abs/2601.13209 | Academic Papers | svg |
dadc97f03274d221d9f21400c911081fefbe67f417f3d758bef0cce4aa152dc4 | 2026-01-21T00:00:00-05:00 | A Harnack-type inequality for a perturbed singular Liouville Equation | arXiv:2601.13212v1 Announce Type: new Abstract: Motivated by the Onsager statistical mechanics description of turbulent Euler flows with point singularities, we obtain a Harnack-type inequality for sequences of solutions of the following perturbed Liouville equation, \begin{equation}\nonumber -\Delta v_n=\left({\epsilo... | https://arxiv.org/abs/2601.13212 | Academic Papers | svg |
678418897ecb4c3821370e383dd7f2093505e008a93919f3f01504d10572bd43 | 2026-01-21T00:00:00-05:00 | Volume polynomials | arXiv:2601.13249v1 Announce Type: new Abstract: Volume polynomials form a distinguished class of log-concave polynomials with remarkable analytic and combinatorial properties. I will survey realization problems related to them, review fundamental inequalities they satisfy, and discuss applications to the combinatorics ... | https://arxiv.org/abs/2601.13249 | Academic Papers | svg |
3fbc10cc58d293294c25a58682b3dd3e363d470946cc8b0d9cd0f7d9d9cac64a | 2026-01-21T00:00:00-05:00 | Inverting the Fisher information operator in non-linear models | arXiv:2601.13254v1 Announce Type: new Abstract: We consider non-linear regression models corrupted by generic noise when the regression functions form a non-linear subspace of L^2, relevant in non-linear PDE inverse problems and data assimilation. We show that when the score of the model is injective, the Fisher inform... | https://arxiv.org/abs/2601.13254 | Academic Papers | svg |
aa0ddca20aab7e45d725f34e0086acd30a5f3aebf97d9bcb220a09284c5b412b | 2026-01-21T00:00:00-05:00 | Entropy-Wasserstein regularization, defective local concentration and a cutoff criterion beyond non-negative curvature | arXiv:2601.13259v1 Announce Type: new Abstract: Notions of positive curvature have been shown to imply many remarkable properties for Markov processes, in terms, e.g., of regularization effects, functional inequalities, mixing time bounds and, more recently, the cutoff phenomenon. In this work, we are interested in a r... | https://arxiv.org/abs/2601.13259 | Academic Papers | svg |
155fe0d9e1e7c6257d99340c034b10a3bf46faaf9d700132d4b9502507e9a13e | 2026-01-21T00:00:00-05:00 | Covariant tomography of fields | arXiv:2601.13261v1 Announce Type: new Abstract: This paper addresses the Inverse Boundary Value Problem (IBVP) for classical fields, specifically focusing on the recovery of parallelly transformed fields within a region based on known boundary data. We introduce a local solution framework, termed "covariant tomography,... | https://arxiv.org/abs/2601.13261 | Academic Papers | svg |
e67a9e8de21faae91184161f339ccf7e2c3896551cad0671eb23290b6357cbad | 2026-01-21T00:00:00-05:00 | On surfaces with smooth projective models over $\mathbb{Z}$ | arXiv:2601.13277v1 Announce Type: new Abstract: In this expository article, we prove a birational classification of smooth projective models of surfaces with negative Kodaira dimension over $\mathbb{Z}$ and over more general rings of integers $\mathcal{O}_K$, depending on their arithmetic and cohomological invariants. ... | https://arxiv.org/abs/2601.13277 | Academic Papers | svg |
607b75626eb8a60039e7d5c26c91a6ee177657ccd8cc06ceab2e36ec0041450f | 2026-01-21T00:00:00-05:00 | On constructing topology from algebra | arXiv:2601.13279v1 Announce Type: new Abstract: In this thesis we explore natural procedures through which topological structure can be constructed from specific semigroups. We will do this in two ways: 1) we equip the semigroup object itself with a topological structure, and 2) we find a topological space for the semi... | https://arxiv.org/abs/2601.13279 | Academic Papers | svg |
3ef06b79d5e22dec6e4c94268f293131520dbbd78fdc02589c2855bfb80e5953 | 2026-01-21T00:00:00-05:00 | Total curvature of convex hypersurfaces in Cartan-Hadamard manifolds | arXiv:2601.13280v1 Announce Type: new Abstract: We show that if the curvature of a Cartan-Hadamard $n$-manifold is constant near a convex hypersurface $\Gamma$, then the total Gauss-Kronecker curvature $\mathcal{G}(\Gamma)$ is not less than that of any convex hypersurface nested inside $\Gamma$. This extends Borb\'{e}l... | https://arxiv.org/abs/2601.13280 | Academic Papers | svg |
ee3e26659cd6593c61f8bd8959c9d38cc6e2885aa54aa5aa938c219c8b4f6a2a | 2026-01-21T00:00:00-05:00 | Second order periodic boundary value problems with reflection and piecewise constant arguments | arXiv:2601.13291v1 Announce Type: new Abstract: In this paper, we analyze a second-order differential equation with a piecewise constant argument and reflection coupled to periodic boundary conditions. Our main contribution is the construction of the related Green's function and a detailed analysis of its properties. I... | https://arxiv.org/abs/2601.13291 | Academic Papers | svg |
7f0b5a70f83680c733be83ebb952d590fd15991e86c325dd577a37c0f7a2f3a6 | 2026-01-21T00:00:00-05:00 | Long-time behavior of solutions to fluid dynamic shape optimization problems via phase-field method | arXiv:2601.13293v1 Announce Type: new Abstract: We investigate the long time behavior of solutions to a shape and topology optimization problem with respect to the time-dependent Navier--Stokes equations. The sought topology is represented by a stationary phase-field that represents a smooth indicator function. The flu... | https://arxiv.org/abs/2601.13293 | Academic Papers | svg |
b3ff3ecb5b9fc0144717dc1233f750639173610cb2b274f933600e865482aefa | 2026-01-21T00:00:00-05:00 | Limit Theorems for $\theta$-expansions and the Failure of the Strong Law | arXiv:2601.13296v1 Announce Type: new Abstract: The paper presents fundamental metrical theorems for a class of continued fraction-like expansions known as $\theta$-expansions. We first prove Khinchine's Weak Law of Large Numbers for the sum of digits, followed by the Diamond-Vaaler Strong Law for the sum of digits min... | https://arxiv.org/abs/2601.13296 | Academic Papers | svg |
6ac60e91145df2ce1ffdcd7188bb0868c3faa9999be1b94f690497b0db061ea3 | 2026-01-21T00:00:00-05:00 | Locally involutive semigroups | arXiv:2601.13301v1 Announce Type: new Abstract: We introduce locally involutive semigroups and embed them into the category of ordered groupoids. This embedding restricts to a correspondence between quasi-involutive semigroups and ordered groupoids with mediator, extending the classical ESN-correspondence between inver... | https://arxiv.org/abs/2601.13301 | Academic Papers | svg |
0c30ad50684e52cadb8855f622f93d1a8fe2ecea84e0bd3df66cb70680835ac7 | 2026-01-21T00:00:00-05:00 | Structured eigenbases and pair state transfer on threshold graphs | arXiv:2601.13318v1 Announce Type: new Abstract: Recently, Macharete, Del-Vecchio, Teixeira and de Lima showed that a star and any threshold graph on the same number of vertices share the same eigenbasis relative to the Laplacian matrix. We use this fact to establish two main results in this paper. The first one is a ch... | https://arxiv.org/abs/2601.13318 | Academic Papers | svg |
56b09cc88b559c0543e7a06d22d974a4e01239922a9442670182f497c229d7af | 2026-01-21T00:00:00-05:00 | On the problem of generalized measures: an impossibility result | arXiv:2601.13321v1 Announce Type: new Abstract: This paper investigates the problem of extending measure theory to non-separable structures, from generalized descriptive set theory to a broader class of spaces beyond this framework. While various notions, such as the ideal of measure zero sets, have been generalized, t... | https://arxiv.org/abs/2601.13321 | Academic Papers | svg |
9bbed82d6f7d078a57c38edac7f399d46b0b2c58c764d4cf9729d9a9731794fb | 2026-01-21T00:00:00-05:00 | Ribbon complexes for the 0-Hecke algebra | arXiv:2601.13324v1 Announce Type: new Abstract: We construct explicit tableau-level maps between indecomposable projective modules for the type A 0-Hecke algebra that assemble into canonical split short exact sequences lifting the basic ribbon product rule in NSym via concatenation and near-concatenation. Iterating the... | https://arxiv.org/abs/2601.13324 | Academic Papers | svg |
3a45c4e1039ab2f72bdbd0ddcb42809e44b1edab0d2070d0e579f0e8776b0168 | 2026-01-21T00:00:00-05:00 | Domino tilings of black-and-white Temperleyan cylinders | arXiv:2601.13332v1 Announce Type: new Abstract: We consider the dimer model in cylindrical domains $\Omega_\delta$ on square grids of mesh size $\delta$ with two Temperleyan boundary components of different colors. Assuming that the $\Omega_\delta$ approximate a cylindrical domain $\Omega$ as $\delta\to 0$, we prove th... | https://arxiv.org/abs/2601.13332 | Academic Papers | svg |
f518a83bf3cd655a07f3bc1d90b5b4166c732faed2f7ff6f94cf42a5a75479dc | 2026-01-21T00:00:00-05:00 | $D$-affinity of Quadrics Revisited | arXiv:2601.13340v1 Announce Type: new Abstract: Let $K$ be aa algebraically closed field of characteristic $p\geq3$ and let $Q_{n}\subset\mathbb{P}^{n+1}_{K}$ be a smooth quadric hypersurface. We show that if $n=2m\geq4$ then $Q_{n}$ is not $D$-affine. In particular, we show the grassmannian ${Gr}(2,4)$ is not $D$-affi... | https://arxiv.org/abs/2601.13340 | Academic Papers | svg |
0cdffc859d9193dcb28925404e1b4118e5fcc091d0c4434ca86c661dd422a2d7 | 2026-01-21T00:00:00-05:00 | Existence and uniqueness of invariant measures for non-Feller Markov semigroups | arXiv:2601.13354v1 Announce Type: new Abstract: We study existence and uniqueness of invariant probability measures for continuous-time Markov processes on general state spaces. Existence is obtained from tightness of time averages under a weak regularity assumption inspired by quasi-Feller semigroups, allowing for dis... | https://arxiv.org/abs/2601.13354 | Academic Papers | svg |
33f48d1e09525507cf635daa0f77c247035d49b8575aed5ecf1e481e5ed37697 | 2026-01-21T00:00:00-05:00 | Center of distances of ultrametric spaces generated by labeled trees | arXiv:2601.13363v1 Announce Type: new Abstract: The center of distances of a metric space $(X,d)$ is the set $C(X) $ of all $t\in\mathbb{R}^+$ for which the equation $d(x,p)=t$ has a solution for each $p\in X$. We prove that the equalities $ C(X)=\{0\} $ or $C(X)=\{\operatorname{diam} X,0\} $ hold if $(X,d)$ is an ultr... | https://arxiv.org/abs/2601.13363 | Academic Papers | svg |
93d3b704830b9a56be5e77da3fcd8e3aec23d83247fe32b0ab1d38b8a208f5bd | 2026-01-21T00:00:00-05:00 | Linear relations on star coefficients of the chromatic symmetric function | arXiv:2601.13390v1 Announce Type: new Abstract: We prove that the coefficient of the star $\mathfrak{st}_{21^{n-2}}$ in the chromatic symmetric function $X_G$ determines whether a connected graph $G$ is $2$-connected. We also prove new linear relations on other star coefficients of chromatic symmetric functions. This a... | https://arxiv.org/abs/2601.13390 | Academic Papers | svg |
23087600c4b6b3528e94ea05ecd2a8e2d45c59da4dc6a5f6ba7e12eb6655d938 | 2026-01-21T00:00:00-05:00 | Discrete-Time Optimal Control of Species Augmentation for Predator-Prey Model | arXiv:2601.13394v1 Announce Type: new Abstract: Species augmentation is one of the methods used to promote biodiversity and prevent endangered species loss and extinction. The current work applies discrete-time optimal control theory to two models of species augmentation for predator-prey relationships. In discrete-tim... | https://arxiv.org/abs/2601.13394 | Academic Papers | svg |
4c3e48e8f8a84b5cb23fba3e7c49a40f46f4466893bd4d6d2f9685cebb708384 | 2026-01-21T00:00:00-05:00 | Generalized Adjoint Method | arXiv:2601.13395v1 Announce Type: new Abstract: The adjoint method is an efficient way to numerically compute gradients in optimization problems with constraints, but is only formulated to differentiable cost and constraint functions on real variables. With the introduction of complex variables, which occur often in ma... | https://arxiv.org/abs/2601.13395 | Academic Papers | svg |
e145ed089e767c1347e49e92734ee1e7a9b7d909cf7bcce4561575bce59c6e71 | 2026-01-21T00:00:00-05:00 | Analytic spectral perturbation theory for a high-contrast Maxwell operator | arXiv:2601.13408v1 Announce Type: new Abstract: We study analytic spectral perturbation theory for the time-harmonic Maxwell operator in a perfectly electrically conducting cavity containing a high-contrast core--shell structure. The dielectric permittivity equals $1$ in a bounded inclusion and a small complex paramete... | https://arxiv.org/abs/2601.13408 | Academic Papers | svg |
c99f74451f7b10fb3c28d790c5c2235a2cf98f80a39a322754ae60032fea9104 | 2026-01-21T00:00:00-05:00 | A uniformity principle for spatial matching | arXiv:2601.13426v1 Announce Type: new Abstract: Platforms matching spatially distributed supply to demand face a fundamental design choice: given a fixed total budget of service range, how should it be allocated across supply nodes ex ante, i.e. before supply and demand locations are realized, to maximize fulfilled dem... | https://arxiv.org/abs/2601.13426 | Academic Papers | svg |
52b4c5ef8160c54d2f6dfbd42924d2cd9a131a00dfce134c0e0d804dbe17d153 | 2026-01-21T00:00:00-05:00 | Stabilization of an incompressible fluid-elastic structure system using a vacuum bubble | arXiv:2601.13430v1 Announce Type: new Abstract: We prove a priori estimates for the system of partial differential equations modeling the interaction between an elastic body and an incompressible fluid in a 3D curved domain. The fluid is governed by the incompressible Navier-Stokes equations and contains a bubble whose... | https://arxiv.org/abs/2601.13430 | Academic Papers | svg |
4876d7c3dbce55b738b27a84cf4d7378937dcc1b1b303fbf5a3973f7802f2c4c | 2026-01-21T00:00:00-05:00 | Independence complexes of generalized Mycielskian graphs | arXiv:2601.13432v1 Announce Type: new Abstract: We show that the homotopy type of the independence complex of the generalized Mycielskian of a graph $G$ is determined by the homotopy type of the independence complex of $G$ and the homotopy type of the independence complex of the Kronecker double cover of $G$. As an app... | https://arxiv.org/abs/2601.13432 | Academic Papers | svg |
71ae18df4cb64ff7f9f9dc48cea7469cf4190c8b97ea6d1cf9c70ac6947570f0 | 2026-01-21T00:00:00-05:00 | A priori estimates and exact solvability for non-coercive stochastic control equations | arXiv:2601.13444v1 Announce Type: new Abstract: We establish, for the first time, explicit a priori and regularity estimates for solutions of the Dirichlet problem for Hamilton-Jacobi-Bellman operators from stochastic control, whose principal half-eigenvalues have opposite signs. In addition, if the negative eigenvalue... | https://arxiv.org/abs/2601.13444 | Academic Papers | svg |
6071cc5a24f7d586b781f0ff77c73c72d62e6788fe57075d6eba435152d4e274 | 2026-01-21T00:00:00-05:00 | Monge-Ampere type equations on compact Hermitian manifolds with bounded mass property | arXiv:2601.13446v1 Announce Type: new Abstract: In this paper, we study possibly non-closed big (1, 1)-forms on a compact Hermitian manifold satisfying the bounded mass property. We propose several criteria for the existence of rooftop envelopes. As applications, we establish the existence of solutions to complex Monge... | https://arxiv.org/abs/2601.13446 | Academic Papers | svg |
b58ea9a346f0537cd2826745952f9a82743d349cbf39477835cdc0c1bbc37024 | 2026-01-21T00:00:00-05:00 | From multiplicative to additive geometry: Deformation theory and 2D TQFT | arXiv:2601.13455v1 Announce Type: new Abstract: In this paper, we present a theory of Poisson deformation of Hamiltonian quasi-Poisson manifolds to Hamiltonian Poisson manifolds that include degenerate cases. More significantly, this theory extends to singular cases arising from symplectic implosion: we introduce a gen... | https://arxiv.org/abs/2601.13455 | Academic Papers | svg |
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