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f524048ef83466119652723a17197084a1ac35085465c4bd11314e7808952828 | 2026-01-21T00:00:00-05:00 | One-variable equations over the lamplighter group | arXiv:2601.12112v1 Announce Type: new Abstract: We study one-variable equations over the lamplighter group $\MZ_2 \wr \MZ$. While the decidability of arbitrary equations over $L_2$ remains open, we prove that the Diophantine problem for single equations in one variable is decidable. Our approach reduces the problem to ... | https://arxiv.org/abs/2601.12112 | Academic Papers | svg |
8b9c38fd96b5468274f0461c8e48d6840370f0e58043de249b9fc90a95f9ef71 | 2026-01-21T00:00:00-05:00 | Hodge decomposition for Kato manifolds | arXiv:2601.12113v1 Announce Type: new Abstract: We prove that any Kato manifold satisfies the Hodge decomposition, in the sense that $b_k=\sum_{p+q=k}h^{p, q}$, by relating its cohomology to the corresponding cohomology of its modification data. We give, therefore, more evidence supporting a conjecture of Ornea--Verbit... | https://arxiv.org/abs/2601.12113 | Academic Papers | svg |
c72b23b6200d042b4ef3029aed87d965ab4521a0ca19a69f0ded5eccf772975d | 2026-01-21T00:00:00-05:00 | Offline Policy Learning with Weight Clipping and Heaviside Composite Optimization | arXiv:2601.12117v1 Announce Type: new Abstract: Offline policy learning aims to use historical data to learn an optimal personalized decision rule. In the standard estimate-then-optimize framework, reweighting-based methods (e.g., inverse propensity weighting or doubly robust estimators) are widely used to produce unbi... | https://arxiv.org/abs/2601.12117 | Academic Papers | svg |
07299667979cf79758659ba1ffb6979b465e2f718fa1f0fcd5a0ba2a55e696d5 | 2026-01-21T00:00:00-05:00 | On the Hausdorff Dimension of weighted exactly Approximable Vectors | arXiv:2601.12121v1 Announce Type: new Abstract: We show that the Hausdorff dimension of $\boldsymbol w$-weighted $\tau$-exactly approximable vectors in $\mathbb R^d$ coincides with the Hausdorff dimension of $\boldsymbol w$-weighted $\tau$-approximable vectors, generalizing a result of the first named author and De Sax... | https://arxiv.org/abs/2601.12121 | Academic Papers | svg |
9375bf990231fe36d68bb9ac9da5251649dc4af19a1cb7d6e04fab9bf85a5199 | 2026-01-21T00:00:00-05:00 | Navier slip effects in micropolar thin-film flow: a rigorous derivation of Reynolds-type models | arXiv:2601.12125v1 Announce Type: new Abstract: We study the stationary flow of incompressible micropolar fluid in a thin three-dimensional domain under Navier slip boundary condition for the velocity and no-spin condition for microrotation. After rescaling the governing equations, we perform a rigorous asymptotic anal... | https://arxiv.org/abs/2601.12125 | Academic Papers | svg |
5d0a0a01d0de6a1c3f3ab3deeefe97093451f6d379856e40d0ca45c940c04c7a | 2026-01-21T00:00:00-05:00 | Spectral Analysis of the $D_{\log}^{(\lambda, N)}$ Operators | arXiv:2601.12133v1 Announce Type: new Abstract: This paper investigates the recent Connes-Consani-Moscovici $D_{\log}^{(\lambda, N)}$ operators, whose spectra are currently hypothesized to approach the zeros of $\zeta\left(\frac{1}{2} +is\right)$ as $\lambda, N \rightarrow \infty$. It turns out that when considering di... | https://arxiv.org/abs/2601.12133 | Academic Papers | svg |
1f0dd737baa88cb0c71bb05c309b64b7f86cc8e69010295fd6bf76a86c43c00d | 2026-01-21T00:00:00-05:00 | Fractional Semilinear Equations on Hyperbolic Spaces | arXiv:2601.12140v1 Announce Type: new Abstract: We study a semilinear equation involving the fractional Laplacian on the hyperbolic space $\mathbb{H}^n$. Unlike in conformally compact Einstein manifolds, the fractional Laplacian on $\mathbb{H}^n$ does not enjoy conformal covariance. By employing Helgason-Fourier analys... | https://arxiv.org/abs/2601.12140 | Academic Papers | svg |
2552362a4295929676dcfd1c52a45b56cb056d364f239025f1c1d083460edbc0 | 2026-01-21T00:00:00-05:00 | On dihedral invariants of the free associative algebra of rank two | arXiv:2601.12144v1 Announce Type: new Abstract: Let $K\langle X_d\rangle$ denote the free associative algebra of rank $d \geq 2$ over a field $K$. By results of Lane (1976) and Kharchenko (1978), the algebra of invariants $K\langle X_d\rangle ^G$ is free for any subgroup $G \leq \GL_d(K)$ and any field $K$. Koryukin (1... | https://arxiv.org/abs/2601.12144 | Academic Papers | svg |
9a08a31123ec1f7e2925f9b79735776c7226d60651676a96761a8e13e1755a4a | 2026-01-21T00:00:00-05:00 | A $p$-adic cohomological approach to congruences of meromorphic modular forms | arXiv:2601.12157v1 Announce Type: new Abstract: We study congruences relating Fourier coefficients of meromorphic modular forms and Frobenius eigenvalues of elliptic curves corresponding to their poles. We develop a $p$-adic cohomological framework that interprets these congruences via the interaction between the rigid... | https://arxiv.org/abs/2601.12157 | Academic Papers | svg |
877bf27cfed03ea68b13355006a78f94e5f06ba277f8e93011c15cb27c680df6 | 2026-01-21T00:00:00-05:00 | Locating critical points attracted to p-adic attracting cycles | arXiv:2601.12163v1 Announce Type: new Abstract: In complex dynamics, a fundamental result of Fatou and Julia asserts that every attracting cycle of a rational map attracts a critical point. The analogous statement fails in non-Archimedean dynamics. For a non-Archimedean rational map, this paper establishes a sharp cond... | https://arxiv.org/abs/2601.12163 | Academic Papers | svg |
75a4b38d0afa975b685e5148918b40e754159ed34c3de8f4cb0f731005719b6b | 2026-01-21T00:00:00-05:00 | Fractional Quantum Hall States: Infinite Matrix Product Representation and its Implications | arXiv:2601.12165v1 Announce Type: new Abstract: We present a novel matrix product representation of the Laughlin and related fractional quantum Hall wavefunctions based on a rigorous version of the correlators of a chiral quantum field theory. This representation enables the quantitative control of the coefficients of ... | https://arxiv.org/abs/2601.12165 | Academic Papers | svg |
3be303117f292a0674e5483dc7625cd3f040ea96167637c6d209dfb6f9ff1f1d | 2026-01-21T00:00:00-05:00 | Balancing adaptability and predictability: K-revision multistage stochastic programming | arXiv:2601.12166v1 Announce Type: new Abstract: A standard assumption in multistage stochastic programming is that decisions are made after observing the uncertainty from the prior stage. The resulting solutions can be difficult to implement in practice, as they leave practitioners ill-prepared for future stages. To pr... | https://arxiv.org/abs/2601.12166 | Academic Papers | svg |
5e848749001382f2a36118249a8f4ea81d29426356fac12e5fbe4b9f38d5fa81 | 2026-01-21T00:00:00-05:00 | The P\'olya Web | arXiv:2601.12172v1 Announce Type: new Abstract: We introduce the P\'olya Web, a system of coalescing random walks based on the classic P\'olya urn model. This construction serves as an analogue to the web of coalescing random walks studied by T\'oth and Werner (1998), replacing simple symmetric random walks with P\'oly... | https://arxiv.org/abs/2601.12172 | Academic Papers | svg |
5f26a9305f32be833e9cff01f7f3952dcf28c75dc1fdb65cea881bb225b58b55 | 2026-01-21T00:00:00-05:00 | Kato's Ramification filtration via de Rham-Witt complex and applications | arXiv:2601.12177v1 Announce Type: new Abstract: Given an $F$-finite regular scheme $X$ of positive characteristic and a simple normal crossing divisor $E$ on $X$, we introduce a filtration on the de Rham-Witt complex $W_m\Omega^\bullet_{X\setminus E}$. When $X$ is the spectrum of a henselian discrete valuation ring $A$... | https://arxiv.org/abs/2601.12177 | Academic Papers | svg |
d5a9f3d4faef8307f324a2dbb8b0412bdeb49ad3c5c72b81f951e658ac5cda99 | 2026-01-21T00:00:00-05:00 | On a theorem of Artin and the dimension of the space spanned by the rational valued characters of a group | arXiv:2601.12185v1 Announce Type: new Abstract: In this paper, we sharpen a theorem of Artin to show that for a finite group, the dimension of the subspace of class functions spanned by the rational valued characters equals the number of conjugacy classes of cyclic subgroups. | https://arxiv.org/abs/2601.12185 | Academic Papers | svg |
5961122a48c3f59e28c389df2e0bdcc2ec790d8e8dcb5d3aa3d5f85c57497ab7 | 2026-01-21T00:00:00-05:00 | Sets of Ramsey-limit points and IP-limit points | arXiv:2601.12187v1 Announce Type: new Abstract: Let $X$ be an uncountable Polish space and let $\mathcal{H}$ be the Hindman ideal, that is, the family of all $S\subseteq \omega$ which are not $IP$-sets. For each sequence $x=(x_n)_{n \in \omega}$ taking values in $X$, let $\Lambda_{x}(FS)$ be the set of $IP$-limit point... | https://arxiv.org/abs/2601.12187 | Academic Papers | svg |
73d6f4a160a295d6eb89dcc8f55afd9e152a35297888affb70a48c31815cab92 | 2026-01-21T00:00:00-05:00 | Optimal Leveraging of Smoothness and Strong Convexity for Peaceman--Rachford Splitting | arXiv:2601.12190v1 Announce Type: new Abstract: In this paper, we introduce a simple methodology to leverage strong convexity and smoothness in order to obtain an optimal linear convergence rate for the Peaceman--Rachford splitting (PRS) scheme applied to optimization problems involving two smooth strongly convex funct... | https://arxiv.org/abs/2601.12190 | Academic Papers | svg |
6229033734c4594611361e293404c38e691bc1be155d24e478acf2324d132098 | 2026-01-21T00:00:00-05:00 | Sobolev inequalities for nonlinear Dirichlet forms | arXiv:2601.12192v1 Announce Type: new Abstract: In this short note we show an equivalence between Sobolev type inequalities and so called isocapacitary inequalities in the context of a large class of nonlinear Dirichlet forms, their associated Dirichlet spaces and their associated capacities. | https://arxiv.org/abs/2601.12192 | Academic Papers | svg |
bc218f4ccde83cee733462ae521bae989f1159a30a62d4aef2dccb1c4f660866 | 2026-01-21T00:00:00-05:00 | Bruhat Intervals in the Infinite Symmetric Group are Cohen-Macaulay | arXiv:2601.12195v1 Announce Type: new Abstract: We show that the (non-Noetherian) Stanley-Reisner ring of the order complex of certain intervals in the Bruhat order on the infinite symmetric group $S_\infty$ of all auto-bijections of $\mathbb{N}$ is Cohen-Macaulay in the sense of ideals and weak Bourbaki unmixed. This ... | https://arxiv.org/abs/2601.12195 | Academic Papers | svg |
f3cc04d9e91f1f400c4af89fbdfef0f06e1afdafc5340b0c9e2ed9ae1b8e0b05 | 2026-01-21T00:00:00-05:00 | Higher-Order Approximations of Sojourn Times in M/G/1 Queues via Stein's Method | arXiv:2601.12197v1 Announce Type: new Abstract: We study the stationary sojourn time distribution in an M/G/1 queue operating under heavy traffic. It is known that the sojourn time converges to an exponential distribution in the limit. Our focus is on obtaining pre-asymptotic, higher-order approximations that go beyond... | https://arxiv.org/abs/2601.12197 | Academic Papers | svg |
2c76d5d8bb1bddd7e5f5af3b1eef41b23ed8b830cbe80a80180bddfb14437b49 | 2026-01-21T00:00:00-05:00 | A curvature-regularized variational problem with an area constraint | arXiv:2601.12201v1 Announce Type: new Abstract: Interlocking interfaces are commonly employed to mitigate relative sliding under shear.Indeed, Their geometry is typically selected on grounds of fabrication convenience rather than analytical optimality. There is no reason to suppose that circular or polygonal profiles m... | https://arxiv.org/abs/2601.12201 | Academic Papers | svg |
9766b0af0726db37acb3c3977baa038dfb12e103fa0aa2652d3d6071b96fcf16 | 2026-01-21T00:00:00-05:00 | Characterizations of Lorentz Type Sobolev Multiplier Spaces and Their Preduals | arXiv:2601.12206v1 Announce Type: new Abstract: We provide several characterizations of Sobolev multiplier spaces of Lorentz type and their preduals. Block decomposition and K\"othe dual of such preduals are discussed. As an application, the boundedness of local Hardy-Littlewood maximal function on these spaces will be... | https://arxiv.org/abs/2601.12206 | Academic Papers | svg |
dc0fae7e68345b7bb609abb44d42464698090e10163572d5e5dbd7d12fbc4bb3 | 2026-01-21T00:00:00-05:00 | Time-asymptotic stability of composite waves of degenerate Oleinik shock and rarefaction for non-convex conservation laws with Cattaneo's law | arXiv:2601.12216v1 Announce Type: new Abstract: This paper examines the large-time behavior of solutions to a one-dimensional conservation law featuring a non-convex flux and an artificial heat flux term regulated by Cattaneo's law, forming a 2$\times$2 system of hyperbolic equations. Under the conditions of small wave... | https://arxiv.org/abs/2601.12216 | Academic Papers | svg |
a5c7cfe34dbf3706bc26c400ddc30c32550307b384073c38fd7bd0a342a25831 | 2026-01-21T00:00:00-05:00 | Interval B-Tensors and Interval Double B-Tensors | arXiv:2601.12217v1 Announce Type: new Abstract: This paper systematically investigates the properties and characterization of interval B-tensors and interval double B-tensors. We propose verifiable necessary and sufficient conditions that allow for determining whether an entire interval tensor family belongs to these c... | https://arxiv.org/abs/2601.12217 | Academic Papers | svg |
0a088b68bc4dddf4189356f3cdab3d0de8df9a06041448a2cdc567d728e33d57 | 2026-01-21T00:00:00-05:00 | Stabilization of arbitrary structures in a three-dimensional doubly degenerate nutrient taxis system | arXiv:2601.12218v1 Announce Type: new Abstract: The doubly degenerate nutrient taxis system \begin{equation}\label {0.1} \left\{ \begin{aligned} &u_{t}=\nabla \cdot (uv\nabla u)-\chi \nabla \cdot (u^{\alpha}v\nabla v)+\ell uv,&x\in \Omega,\, t>0,\\ & v_{t}=\Delta v-uv,&x\in \Omega,\, t>0,\\ \end{aligned} \r... | https://arxiv.org/abs/2601.12218 | Academic Papers | svg |
637d44f689272ffb17d419bd19326c7a3573155f0d71166e3ceaf75a8a78d5d7 | 2026-01-21T00:00:00-05:00 | Persistent Sheaf Laplacian Analysis of Protein Stability and Solubility Changes upon Mutation | arXiv:2601.12219v1 Announce Type: new Abstract: Genetic mutations frequently disrupt protein structure, stability, and solubility, acting as primary drivers for a wide spectrum of diseases. Despite the critical importance of these molecular alterations, existing computational models often lack interpretability, and fai... | https://arxiv.org/abs/2601.12219 | Academic Papers | svg |
9193c290da9ce8c9125ffb17c9adf2ead1658800ad4def38ee3bf3c74865b557 | 2026-01-21T00:00:00-05:00 | Mean-Field Games Under Model Uncertainty | arXiv:2601.12226v1 Announce Type: new Abstract: We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within an uncertainty set. Unlike in cla... | https://arxiv.org/abs/2601.12226 | Academic Papers | svg |
3f6b6cdc1cb21fcb00ef2f0d79f7043a11001dc7333ddd964e00e09f227f0503 | 2026-01-21T00:00:00-05:00 | An optimal boundary control approach to the Cherrier-Escobar problem | arXiv:2601.12232v1 Announce Type: new Abstract: We study an optimal boundary control problem associated to the boundary obstacle problem for the couple conformal Laplacian and conformal Robin operator on n-dimensional compact Riemannian manifolds with boundary and with n\geq 3. When the Cherrier-Escobar invariant of th... | https://arxiv.org/abs/2601.12232 | Academic Papers | svg |
e79978d3c6f4119f452b69d2eca2123a7d142822e85e149f009b8a66b9505308 | 2026-01-21T00:00:00-05:00 | An alternative construction of the $G_2(2)$-graph | arXiv:2601.12235v1 Announce Type: new Abstract: In this note, we give an alternative construction of the $G_2(2)$-graph from a $U_3(2)$-geometry. | https://arxiv.org/abs/2601.12235 | Academic Papers | svg |
004442f0cf8dfa61a0c63c713e056db61c3339682c96b4adee1af5dacbbb98c7 | 2026-01-21T00:00:00-05:00 | Paley-type matrices and $1$-factorizations of complete graphs | arXiv:2601.12250v1 Announce Type: new Abstract: Ball, Ortega--Moreno, and Prodromou asked whether, for every odd prime $p$, one can find a $1$-factor of the complete graph $K_{p+1}$ with some arithmetic restrictions related to quadratic residues. This problem is motivated by $1$-factorizations that are compatible with ... | https://arxiv.org/abs/2601.12250 | Academic Papers | svg |
d8f0697d79381e47a69253ca5174324cb5d349ee366eb7388bcbc36e502d9d45 | 2026-01-21T00:00:00-05:00 | The generalized Lax conjecture is true for topological reasons related to compactness, convexity and determinantal deformations of increasing products of pointwise approximating linear forms | arXiv:2601.12267v1 Announce Type: new Abstract: We develop a topological approach to prove the generalized Lax conjecture using the fact that determinants of sufficiently big symmetric linear pencils are able to express the rigidly convex sets of RZ polynomials of any degree $d$. Monicity of the representation is asses... | https://arxiv.org/abs/2601.12267 | Academic Papers | svg |
7ba65a24fad44f2a5837a2ca80d5c21a9b7bc5af8478c99637f3d4d1a60511f9 | 2026-01-21T00:00:00-05:00 | The relative GAGA Theorem and an application to the analytic mapping stacks | arXiv:2601.12299v1 Announce Type: new Abstract: We prove a relative GAGA theorem for perfect and pseudo-coherent complexes in non-archimedean analytic geometry, allowing bases given by Fredholm analytic rings, including those associated from affinoid perfectoid spaces. This answers a question raised in \cite{heuer2024p... | https://arxiv.org/abs/2601.12299 | Academic Papers | svg |
ef2ebb7dd2c1181b2193dde2f7f4318a7ab0ae74fe5673ec518e085afaa673fe | 2026-01-21T00:00:00-05:00 | Level of Faces for Exponential Sequence of Arrangements | arXiv:2601.12328v1 Announce Type: new Abstract: In this paper, we introduce the bivariate exponential generating function $F_l(x,y)$ for the number of level-$l$ faces of an exponential sequence of arrangements (ESA), and establish the formula $F_l(x,y)=\big(F_1(x,y)\big)^l$ with a combinatorial interpretation. Its spec... | https://arxiv.org/abs/2601.12328 | Academic Papers | svg |
44e0eeb4da37dc5f6ca68e8e5ded50008f21e621a683dddfcee411ec4b8b9e5f | 2026-01-21T00:00:00-05:00 | A Complete Proof of the Simon--Lukic Conjecture for Higher-Order Szeg\H{o} Theorems | arXiv:2601.12332v1 Announce Type: new Abstract: This paper provides a complete proof of Simon-Lukic conjecture for orthogonal polynomials on the unit circle. For a probability measure $d\mu = w(\theta) \frac{d\theta}{2\pi} + d\mu_s$ with Verblunsky coefficients $\alpha=\{\alpha_n\}_{n=0}^\infty$, distinct singular poin... | https://arxiv.org/abs/2601.12332 | Academic Papers | svg |
41f3492704dd969c22105a11d8e1ec49c6eb67950538fd398a245174b4c714b3 | 2026-01-21T00:00:00-05:00 | Representation theorems for nonvariational solutions of the Helmholtz equation | arXiv:2601.12335v1 Announce Type: new Abstract: We consider a possibly multiply connected bounded open subset $\Omega$ of ${\mathbb{R}}^n$ of class $C^{\max\{1,m\},\alpha}$ for some $m\in {\mathbb{N}}$, $\alpha\in]0,1[$ and we plan to solve both the Dirichlet and the Neumann problem for the Helmholtz equation in $\Omeg... | https://arxiv.org/abs/2601.12335 | Academic Papers | svg |
ee1c5f03e024932dafe547be07ffc57437fdc838f96594af1ab00accee60f398 | 2026-01-21T00:00:00-05:00 | Asymptotic Behavior of the Principal Eigenvalue Problems with Large Divergence-Free Drifts | arXiv:2601.12342v1 Announce Type: new Abstract: In this paper, we consider the following principal eigenvalue problem with a large divergence-free drift: \begin{equation}\label{0.1} -\varepsilon\Delta \phi-2\alpha\nabla m(x)\cdot\nabla \phi+V(x)\phi=\lambda_\alpha \phi\ \,\ \text{in}\, \ H_0^1(\Omega),\tag{0.1} \end{eq... | https://arxiv.org/abs/2601.12342 | Academic Papers | svg |
31380625ec73a8c3bb3607bd2903fdf1a11bd5361527ff680979172601cc3f1c | 2026-01-21T00:00:00-05:00 | Classification of the structures of stable radial solutions for semilinear elliptic equations in $\bf R^N$ | arXiv:2601.12350v1 Announce Type: new Abstract: We study the stability of radial solutions of the semilinear elliptic equation $\Delta u +f(u)=0$ in ${\bf R^N}$, where $N \geq 3$ and $f$ is a general superciritical nonlinearity. We give a classification of the solution structures with respect to the stability of radial... | https://arxiv.org/abs/2601.12350 | Academic Papers | svg |
3f09a7bdc3daa22c163560a9d330655ffbfb35e0ad2004c67ce97434551c7a28 | 2026-01-21T00:00:00-05:00 | Time-fractional nonlinear evolution equations with time-dependent constraints | arXiv:2601.12352v1 Announce Type: new Abstract: This article is devoted to presenting an abstract theory of time-fractional gradient flow equations for time-dependent convex functionals in real Hilbert spaces. The main results are concerned with the existence of strong solutions to time-fractional abstract evolution eq... | https://arxiv.org/abs/2601.12352 | Academic Papers | svg |
cdfbde0fec6814bccd68994879c260cadc3c992e37dd35bb377cdfab9e7b29c7 | 2026-01-21T00:00:00-05:00 | Skew brace extensions, second cohomology and complements | arXiv:2601.12371v1 Announce Type: new Abstract: We study extensions and second cohomology of skew left braces via the natural semi-direct products associated with the skew left braces. Let $0 \to I \to E \to H \to 0$ be a skew brace extension and $\Lambda_H$ denote the natural semi-direct products associated with the s... | https://arxiv.org/abs/2601.12371 | Academic Papers | svg |
5c52f033bb50afb359638a7a25cab5db332e6e2ef6b0f745476f383789e96028 | 2026-01-21T00:00:00-05:00 | On a Modification of the Twistor Space | arXiv:2601.12372v1 Announce Type: new Abstract: In the paper we construct a modification $S(M)$ of the twistor space of a K\"ahler scalar flat surface $M$ and study its complex-geometric and metric properties. In particular, we construct complete balanced metrics on $S(M)$ and show that $S(M)$ can not be K\"ahler when ... | https://arxiv.org/abs/2601.12372 | Academic Papers | svg |
1bd5b22ce73e0a21acc1f269e4883bff8a78aa58e22c3f736a1ebf3a7f9c0437 | 2026-01-21T00:00:00-05:00 | An efficient penalty decomposition algorithm for minimization over sparse symmetric sets | arXiv:2601.12383v1 Announce Type: new Abstract: This paper proposes an improved quasi-Newton penalty decomposition algorithm for the minimization of continuously differentiable functions, possibly nonconvex, over sparse symmetric sets. The method solves a sequence of penalty subproblems approximately via a two-block de... | https://arxiv.org/abs/2601.12383 | Academic Papers | svg |
9f5bb5ddb10b0a892044766833605e44d5a037652b1d9a2ab638669bcc6ec103 | 2026-01-21T00:00:00-05:00 | Strong Hollowness in Commutative Rings | arXiv:2601.12388v1 Announce Type: new Abstract: In this paper we study strongly hollow ideals and completely strongly hollow ideals in commutative rings without finiteness assumptions. We establish basic structural properties, including maximality phenomena and permanence under quotients and surjective homomorphisms. W... | https://arxiv.org/abs/2601.12388 | Academic Papers | svg |
226c36918ee700dbddacf75a1bf17f24e66f3da813b9a61842ec590bf7b218f9 | 2026-01-21T00:00:00-05:00 | Anderson Acceleration for Distributed Constrained Optimization over Time-varying Networks | arXiv:2601.12398v1 Announce Type: new Abstract: This paper applies the Anderson Acceleration (AA) technique to accelerate the Fenchel dual gradient method (FDGM) to solve constrained optimization problems over time-varying networks. AA is originally designed for accelerating fixed-point iterations, and its direct appli... | https://arxiv.org/abs/2601.12398 | Academic Papers | svg |
6f490ed84ea1521aed74a86f941a878c98d6b499d64003475b91909629ca5afc | 2026-01-21T00:00:00-05:00 | BiCoLoR: Communication-Efficient Optimization with Bidirectional Compression and Local Training | arXiv:2601.12400v1 Announce Type: new Abstract: Slow and costly communication is often the main bottleneck in distributed optimization, especially in federated learning where it occurs over wireless networks. We introduce BiCoLoR, a communication-efficient optimization algorithm that combines two widely used and effect... | https://arxiv.org/abs/2601.12400 | Academic Papers | svg |
4078ddb238021363632a336b6656551a3484947fc51ab7a3eabfedec0ee70f82 | 2026-01-21T00:00:00-05:00 | Weak quantum hypergroups from finite index C*-inclusions | arXiv:2601.12406v1 Announce Type: new Abstract: We study a finite index inclusion of simple unital C*-algebras and construct a canonical completely positive coproduct on the second relative commutant, thereby endowing it with a natural coalgebra structure. Motivated by this construction, we introduce the notion of a we... | https://arxiv.org/abs/2601.12406 | Academic Papers | svg |
2482ca2ce60439396ec29ce2549af91ba279f39d523fc43cc2b1fb22606c24ae | 2026-01-21T00:00:00-05:00 | Majorization between symplectic spectra of positive semidefinite matrices | arXiv:2601.12408v1 Announce Type: new Abstract: Given $2n \times 2n$ real symmetric positive semidefinite matrix $A$ with symplectic kernel, there exists a real $2n \times 2n$ \emph{symplectic matrix} $M$ such that $M^TAM= D \oplus D$, where $D$ is an $n \times n$ non-negative diagonal matrix which is unique up to perm... | https://arxiv.org/abs/2601.12408 | Academic Papers | svg |
9b8f6f0332f3e838ee2553c1c2eabd17e16f2362b665b282d2801d82aa3fe451 | 2026-01-21T00:00:00-05:00 | Dynamic resource allocation in eukaryotic Resource Balance Analysis | arXiv:2601.12411v1 Announce Type: new Abstract: Resource Balance Analysis (RBA) is a framework for predicting steady-state cellular growth under resource constraints. However, classical RBA formulations are static and do not capture the dynamic regulation of biosynthetic resources or macromolecular turnover, which is p... | https://arxiv.org/abs/2601.12411 | Academic Papers | svg |
d564fe7fa8361c37ce55b22b55e3dcdd4310163b5bd11c3ad6c4cb9329904b23 | 2026-01-21T00:00:00-05:00 | Localization and interpolation of parabolic $L^p$ Neumann problems | arXiv:2601.12429v1 Announce Type: new Abstract: We show a localization estimate for local solutions to the parabolic equation $-\partial_t u+\mbox{div} (A\nabla u)=0$ with zero Neumann data, assuming that the $L^p$ Neumann problem and $L^{p'}$ Dirichlet problem for the adjoint operator are solvable in a Lipschitz cylin... | https://arxiv.org/abs/2601.12429 | Academic Papers | svg |
ed3b6e8f9c805b49a0f4f0aff54cfc7b1db44f66a7783374ac6cd10819f27770 | 2026-01-21T00:00:00-05:00 | Periodic families in the homology of $GL_n(F_2)$ | arXiv:2601.12431v1 Announce Type: new Abstract: We construct infinite families of nonzero classes in $H_d(GL_n(F_2);F_2)$ along lines of the form $d =\frac{2}{3}n +$(constant), thereby showing that the known slope $\frac{2}{3}$-stability for these homology groups are optimal. Using the new stability Hopf algebra perspe... | https://arxiv.org/abs/2601.12431 | Academic Papers | svg |
ec434fdde61c30a0b44f84b737b617ea68e7a0ef5059feca10154726963cdb8b | 2026-01-21T00:00:00-05:00 | Disjoint non-forking amalgamation in stable AECs | arXiv:2601.12439v1 Announce Type: new Abstract: The \emph{disjoint amalgamation property} (DAP), which asserts that all spans of a class of models can be amalgamated with minimal intersection, is an important property in the context of abstract elementary classes, with connections to both Grossberg's question and Shela... | https://arxiv.org/abs/2601.12439 | Academic Papers | svg |
f32e48cc3683ad1021f53670baed61946a2f005bb31d4d8d464512b7b51d8958 | 2026-01-21T00:00:00-05:00 | Schr\"odinger Operators, Integral Curvature, and the Euler Characteristic of Riemannian Manifolds | arXiv:2601.12440v1 Announce Type: new Abstract: We establish new connections between integral curvature bounds and the Euler characteristic of closed Riemannian manifolds through the perspective of Schr\"odinger-type operators. Central to our approach is the twisted Dirac operator \(\mathcal{D}_{\theta}\), whose index ... | https://arxiv.org/abs/2601.12440 | Academic Papers | svg |
686b9bd9f29cf196e700a9007e2038d1ea72c137869abb0254af87d9f994f40c | 2026-01-21T00:00:00-05:00 | Distinct permutation dot products | arXiv:2601.12445v1 Announce Type: new Abstract: We show that for any two sets of reals numbers $A=\{a_1,\dots,a_n\}$ and $B=\{b_1,\dots,b_n\}$, the sums of the form $\sum_{i=1}^n a_i\,b_{\pi(i)}$ always take on $\Omega(n^{3})$ distinct values, as we range over all permutations $\pi \in S_n$. An important ingredient is ... | https://arxiv.org/abs/2601.12445 | Academic Papers | svg |
ec62813e71e735fe71b1686ee787e2a18342740b6e131bfb84a8e8d840440974 | 2026-01-21T00:00:00-05:00 | On spaces of embeddings of circles in surfaces | arXiv:2601.12450v1 Announce Type: new Abstract: We consider the space of embeddings of finitely many circles that bound disks in non-positively curved surfaces. We index the connected components of this space with finite rooted trees and show that the connected components are classifying spaces of the ``braided" automo... | https://arxiv.org/abs/2601.12450 | Academic Papers | svg |
62a4afbfde1d128d71d658e65cd8faf7e0d6e659bb66b66bd7a08fd82a333dd1 | 2026-01-21T00:00:00-05:00 | Even Sets and Dual Projective Geometric Codes: A Tale of Cylinders | arXiv:2601.12451v1 Announce Type: new Abstract: In this paper, we prove that the smallest even sets in ${\rm PG}(n,q)$, i.e. sets that intersect every line in an even number of points, are cylinders with a hyperoval as base. This fits into a more general study of dual projective geometric codes. Let $q$ be a prime powe... | https://arxiv.org/abs/2601.12451 | Academic Papers | svg |
c91019f20a1bcac73c149d8da898de1208d8f5eddcb6ba891d5d967f9375b1a3 | 2026-01-21T00:00:00-05:00 | Unbounded banded matrices with positive bidiagonal factorization and mixed-type multiple orthogonal polynomials | arXiv:2601.12453v1 Announce Type: new Abstract: A spectral Favard theorem is proved for semi-infinite banded matrices admitting a positive bidiagonal factorization, without assuming boundedness of the associated operator, thus covering both the bounded and unbounded settings. The result yields a matrix-valued spectral ... | https://arxiv.org/abs/2601.12453 | Academic Papers | svg |
4055eb21a16056113d71e66bdb163a10e80f6ccc7c3b40dd34b874f6ac4d1f47 | 2026-01-21T00:00:00-05:00 | Hirzebruch-Riemann-Roch for complex analytic infinity-prestacks | arXiv:2601.12454v1 Announce Type: new Abstract: We provide a cocycle-level Hirzebruch-Riemann-Roch (HRR) identity for arbitrary complex analytic infinity-prestacks. We view this work as the natural setting for Toledo and Tong's HRR philosophy and technical machinery. | https://arxiv.org/abs/2601.12454 | Academic Papers | svg |
13bb1edb914c16a4cdea0c9c31cd5ea516b450e4380229c41b1b253a43bf0d3c | 2026-01-21T00:00:00-05:00 | Structure theory of set addition with two operations | arXiv:2601.12457v1 Announce Type: new Abstract: We take the first step toward a structure theory that includes both operations of a ring $\mathcal{R}$. More precisely, we prove a series of inverse results for the structure of sets $A\subseteq \mathbf{F}_p$ such that, under certain conditions on integers $r_1, \dots, r_... | https://arxiv.org/abs/2601.12457 | Academic Papers | svg |
688af3e7aae74d743edd6d618ac7dbb8bd00ee6f50c5b4a328bf3afa766ea7c9 | 2026-01-21T00:00:00-05:00 | Symmetric preparation of systems | arXiv:2601.12458v1 Announce Type: new Abstract: In this paper we generalize the Weierstrass and Malgrange preparation theorems to the symmetric matrix valued case, proving symmetric preparation of analytic and smooth symmetric systems that vanish of first order. | https://arxiv.org/abs/2601.12458 | Academic Papers | svg |
f5b02721e73dc3ba18d9705659dca7c7e4b250c1755a3587911fd2e27895ee86 | 2026-01-21T00:00:00-05:00 | Homological $(n-2)$-systole in $n$-manifolds with positive triRic curvature | arXiv:2601.12461v1 Announce Type: new Abstract: In this paper, we prove an optimal systolic inequality and characterize the case of equality on closed Riemannian manifolds with positive triRic curvature. This extends prior work of Bray-Brendle-Neves \cite{BrayBrenleNevesrigidity} and Chu-Lee-Zhu \cite{chuleezhu_n_systo... | https://arxiv.org/abs/2601.12461 | Academic Papers | svg |
3e1e5317349a9cb6d00289fec279cf582e599b3b215ee55c49afcc43b5c114d9 | 2026-01-21T00:00:00-05:00 | Non-intersecting Squared Bessel Process: Spectral Moments and Dynamical Entanglement Entropy | arXiv:2601.12484v1 Announce Type: new Abstract: Statistical ensembles of reduced density matrices of bipartite quantum systems play a central role in entanglement estimation, but do not capture the non-stationary nature of entanglement relevant to realistic quantum information processing. To address this limitation, we... | https://arxiv.org/abs/2601.12484 | Academic Papers | svg |
27a9246dc97b3e3d97b92d69abc73aad51ba10f025ca07a10aaf3f984800f0c6 | 2026-01-21T00:00:00-05:00 | Fast Computing Formulas for some Dirichlet L-Series | arXiv:2601.12495v1 Announce Type: new Abstract: For $\chi_k$ a self$-$dual primitive Dirichlet character mod $k$ several reduced identities of Dirichlet $L-$functions $L_k(s):=L(s,\chi_k)$, expressed as linear combinations of Hurwitz $\zeta$ functions, are found for $s=2,3$ and some selected values of $k$. By using a m... | https://arxiv.org/abs/2601.12495 | Academic Papers | svg |
3ee1f2207a90aa421d98be7132745c17deff1a2324fda466c511f5d72c90abe4 | 2026-01-21T00:00:00-05:00 | The $\ell$-modular local theta correspondence in type II and partial permutations | arXiv:2601.12497v1 Announce Type: new Abstract: In this paper we compute the multiplicities appearing in the ${\overline{\mathbb{F}}_\ell}$-modular theta correspondence in type II over a non-archimedean field $\mathrm{F}$, where $\ell$ is a prime not dividing the residue cardinality of $\mathrm{F}$. Unlike for represen... | https://arxiv.org/abs/2601.12497 | Academic Papers | svg |
c6251843ca541868af7eaee560cb0da28a015f309197aa02685c477b1bb6c2d7 | 2026-01-21T00:00:00-05:00 | Heun-function analysis of the Dirac spinor spectrum in a sine-Gordon soliton background | arXiv:2601.12504v1 Announce Type: new Abstract: We study the Dirac spectrum in a sine-Gordon soliton background, where the induced position-dependent mass reduces the spectral problem to a Heun-type differential equation. Bound and scattering sectors are treated within a unified framework, with spectral data encoded in... | https://arxiv.org/abs/2601.12504 | Academic Papers | svg |
244be761145582637d5c0a2caee43fb0d1b62e2f73116325fd4a38de434e7da9 | 2026-01-21T00:00:00-05:00 | Approximability for Lagrangian submanifolds | arXiv:2601.12506v1 Announce Type: new Abstract: This paper introduces a notion of categorical approximability for metric spaces that can be viewed as a categorification of approximability for metric groups, as defined by Turing in 1938. Approximability as introduced here is a property of metric spaces that is more gene... | https://arxiv.org/abs/2601.12506 | Academic Papers | svg |
06a20021055b7e977be59ebf1d76cb669696c778f06f311c365792afd516b3d3 | 2026-01-21T00:00:00-05:00 | Extending graph total colorings to cell complexes | arXiv:2601.12514v1 Announce Type: new Abstract: Let $2\le k\in\mathbb{Z}$. A total coloring of a simple connected regular graph via color set $ \{0,1,\ldots, k\}$ is said to be {\it efficient} if each color yields an efficient dominating set, where the efficient domination condition applies to the restriction of each c... | https://arxiv.org/abs/2601.12514 | Academic Papers | svg |
26d6b6266e14a982e1d581dfbda6eda26a2b61baf839b5161c6701489dce4d71 | 2026-01-21T00:00:00-05:00 | Rigidity results in multi-bubble dynamics for non-radial energy-critical heat equation | arXiv:2601.12517v1 Announce Type: new Abstract: This paper concerns the classification of asymptotic behaviors in multi-bubble dynamics for the energy-critical nonlinear heat equations in large dimensions $N\geq7$ without symmetry. This multi-bubble dynamics appears naturally at least for a sequence of times in view of... | https://arxiv.org/abs/2601.12517 | Academic Papers | svg |
444ada904f3173c774d221c14d9025dfd0003e293f3151b5cd4d402f049fb75b | 2026-01-21T00:00:00-05:00 | Quasigeodesic languages are not context-free in some non-hyperbolic groups | arXiv:2601.12520v1 Announce Type: new Abstract: We study the full language of quasigeodesics in Cayley graphs, with fixed error constants. We show that, given a non-virtually-cyclic nilpotent group or Baumslag--Solitar group, and any finite generating set, such languages fail to be context-free for sufficiently large e... | https://arxiv.org/abs/2601.12520 | Academic Papers | svg |
cf3a00e2d18149779c5aff42b262a1a6448aebe5d7057468235f80502d983901 | 2026-01-21T00:00:00-05:00 | Derived equivalences via Tate resolutions | arXiv:2601.12531v1 Announce Type: new Abstract: For any finite sequence of elements $s_1, \ldots , s_d$ in a commutative noetherian ring $R$, we show that for $n \gg 0$, the natural map from the Koszul complex $K(s_1^n, \ldots , s_d^n)$ to the Koszul complex $K(s_1, \ldots , s_d)$ factors through the Tate resolution on... | https://arxiv.org/abs/2601.12531 | Academic Papers | svg |
05003ae61e640e6c167603ade153323d504806b462d7b153b66dcfcf2a2881ea | 2026-01-21T00:00:00-05:00 | Examples and counterexamples of injective types | arXiv:2601.12536v1 Announce Type: new Abstract: It is known that, in univalent mathematics, type universes, the type of $n$-types in a universe, reflective subuniverses, and the underlying type of any algebra of the lifting monad are all (algebraically) injective. Here, we further show that the type of ordinals, the ty... | https://arxiv.org/abs/2601.12536 | Academic Papers | svg |
b328f6af4da2004ea9f9b9a4c97eb2f1ffcef33848125bb1661a0fd11f3cd132 | 2026-01-21T00:00:00-05:00 | Connections and na\"{i}ve lifting of DG modules | arXiv:2601.12550v1 Announce Type: new Abstract: In this paper, we generalize the notion of connections, which was introduced by Alain Connes in noncommutative differential geometry, to the differential graded (DG) homological algebra setting. Then, along a DG algebra homomorphism $A \to B$, where $B$ is assumed to be p... | https://arxiv.org/abs/2601.12550 | Academic Papers | svg |
b51458a49350abd9047e37e55941ce4f4df0d66a8f7b4f4cbf92cca174865bbd | 2026-01-21T00:00:00-05:00 | Remarks on the second Chern class of a foliation | arXiv:2601.12558v1 Announce Type: new Abstract: We bound the second Chern class of the tangent sheaf of a codimension-one foliation. Equivalently, we bound the degree of the pure codimension-two part of the singular scheme. In particular, for a degree-$d$ foliation on the projective space, the codimension-two part of i... | https://arxiv.org/abs/2601.12558 | Academic Papers | svg |
d977fbe82bbd25fbef31790b3d1078c3335247c881eed0dbe86a918cc875026e | 2026-01-21T00:00:00-05:00 | Sheared displays and $p$-divisible groups | arXiv:2601.12565v1 Announce Type: new Abstract: We develop a Dieudonn\'e theory for $p$-divisible groups using sheared Witt vectors. | https://arxiv.org/abs/2601.12565 | Academic Papers | svg |
e0f1baa78aed1038eb68d93b5295d14e6f35a0c961760a71426515ff9cffcc1c | 2026-01-21T00:00:00-05:00 | Self-avoiding walk, connective constant, cubic graph, Fisher transformation, quasi-transitive graph | arXiv:2601.12571v1 Announce Type: new Abstract: We study self-avoiding walks (SAWs) on infinite quasi-transitive cubic graphs under \emph{local transformations} that replace each degree-$3$ vertex by a finite, symmetric three-port gadget. To each gadget we associate a two-port SAW generating function $g(x)$, defined by... | https://arxiv.org/abs/2601.12571 | Academic Papers | svg |
99bf850bebcb0cb8a08944419d75f4d4df55c912bc0fd63a182b5ba7a4d3950a | 2026-01-21T00:00:00-05:00 | A Functorial Approach to Multi-Space Interpolation with Function Parameters | arXiv:2601.12572v1 Announce Type: new Abstract: We introduce an extension of interpolation theory to more than two spaces by employing a functional parameter, while retaining a fully functorial and systematic framework. This approach allows for the construction of generalized intermediate spaces and ensures stability u... | https://arxiv.org/abs/2601.12572 | Academic Papers | svg |
475d28dccf99e5f9d502ff8531092143ca2a934ae266b94313934fc3be71d828 | 2026-01-21T00:00:00-05:00 | L(3,2,1)-labelings of three classes of 4-valent circulants | arXiv:2601.12574v1 Announce Type: new Abstract: An $L(3,2,1)$-labeling of a graph $G$ is an assignment $f$ of nonnegative integers to vertices such that $\vert f(x)-f(y)\vert > 3-\mbox{dist}_G(x,y)$ for every pair $x,y$ of vertices of $G$, where $\mbox{dist}_G(x,y)$ denotes the distance between $x$ and $y$ in $G$. The ... | https://arxiv.org/abs/2601.12574 | Academic Papers | svg |
d012b69b52648d4e9c82965cb31e9caebbb308a40cb069cb7b5ce040ced52bc9 | 2026-01-21T00:00:00-05:00 | A semigroup approach to iterated binomial transforms | arXiv:2601.12579v1 Announce Type: new Abstract: We study a one-parameter family of binomial-convolution operators acting on sequences. These operators form an additive semigroup with an explicit inverse, and they subsume iterated classical binomial transforms as a special case. We describe the action in terms of ordina... | https://arxiv.org/abs/2601.12579 | Academic Papers | svg |
bbf5148beb9993119d10e4fd48803f5625dd9a5b84d7d8e2c4de3f95e6bf5e9b | 2026-01-21T00:00:00-05:00 | Integrals of products of four modified Bessel functions | arXiv:2601.12590v1 Announce Type: new Abstract: We evaluate definite integrals involving the product of four modified Bessel functions of the first and second kind and a power function. We provide general formulas expressed in terms of the Meijer $G$-function and generalized hypergeometric and Lauricella $F_C$ function... | https://arxiv.org/abs/2601.12590 | Academic Papers | svg |
ac98de0762ac3c9ecca52299225ebcc6b73710eb4ec15dbac362bbf3193e2454 | 2026-01-21T00:00:00-05:00 | Ehrhart quasi-polynomials via Barnes polynomials and discrete moments of parallelepipeds | arXiv:2601.12596v1 Announce Type: new Abstract: We give novel and explicit formulas for the Ehrhart quasi-polynomials of rational simple polytopes, in terms of Barnes polynomials and discrete moments of half-open parallelepipeds. These formulas also hold for all positive dilations of a rational polytope. There is an in... | https://arxiv.org/abs/2601.12596 | Academic Papers | svg |
7d5eb2bbdc3aba95c282cd0ba3d16fa37df59cb77903571fdaa24ed21e9be943 | 2026-01-21T00:00:00-05:00 | Conjugating full cycles by adjacent transpositions: diameter and sorting time | arXiv:2601.12597v1 Announce Type: new Abstract: We establish upper and lower bounds on the maximal number of steps needed to transform a cyclic permutation to the canonical cyclic permutation using conjugation by adjacent transpositions, and on the diameter of the underlying Schreier graph. | https://arxiv.org/abs/2601.12597 | Academic Papers | svg |
ed842edb82331cda32390431d40d5eff86c99ac7220fc3fee86bf366a49d0b15 | 2026-01-21T00:00:00-05:00 | Elementary proofs of ring commutativity theorems | arXiv:2601.12599v1 Announce Type: new Abstract: Jacobson's commutativity theorem says that a ring is commutative if, for each $x$, $x^n = x$ for some $n > 1$. Herstein's generalization says that the condition can be weakened to $x^n-x$ being central. In both theorems, $n$ may depend on $x$. In this paper, in certain ca... | https://arxiv.org/abs/2601.12599 | Academic Papers | svg |
1f8567c613c9dfca95bc11203f8d0efa27fa9a7b35bfe674a096ac909db9a794 | 2026-01-21T00:00:00-05:00 | Improved Averaged Distribution of $d_3(n)$ in Prime Arithmetic Progressions | arXiv:2601.12601v1 Announce Type: new Abstract: We say that $d_3(n)$ has exponent of distribution $\theta$ if, for all $\varepsilon>0$, the expected asymptotic holds uniformly for all moduli $q \le x^{\theta-\varepsilon}$. Nguyen proved that, after averaging over reduced residue classes $a \bmod q$, the function $d_3(n... | https://arxiv.org/abs/2601.12601 | Academic Papers | svg |
044bc9d3930b42ca2b0ed514bdeb23c51c576c541575dd6862f420f302287c96 | 2026-01-21T00:00:00-05:00 | An unbounded number of canard limit cycles in linear regularizations of piecewise linear systems | arXiv:2601.12602v1 Announce Type: new Abstract: The purpose of this paper is to study the number of limit cycles of canard type in linear regularizations of piecewise linear systems with non-monotonic transition functions. Using the notion of slow divergence integral and elementary breaking mechanisms, we construct sys... | https://arxiv.org/abs/2601.12602 | Academic Papers | svg |
3805071344f55e5502a0d317bbe8b5206c96812446489251ab219cded07f37e1 | 2026-01-21T00:00:00-05:00 | On the second homology of the genus 3 hyperelliptic Torelli group | arXiv:2601.12605v1 Announce Type: new Abstract: Let $s$ be a fixed hyperelliptic involution of the closed, oriented genus $g$ surface $\Sigma_g$. The hyperelliptic Torelli group $\mathcal{SI}_g$ is the subgroup of the mapping class group $\mathrm{Mod}(\Sigma_g)$ consisting of elements that act trivially on $\mathrm{H}_... | https://arxiv.org/abs/2601.12605 | Academic Papers | svg |
af5a64ef5c66e48bcf179a7c5ab58be2748b4affc4a1709b34be6c0e6cad875a | 2026-01-21T00:00:00-05:00 | On the second Bohr radius for vector valued pluriharmonic functions | arXiv:2601.12608v1 Announce Type: new Abstract: In this paper, we introduce the notion of the second Bohr radius for vector valued pluriharmonic functions on complete Reinhardt domains in $\mathbb{C}^n$. This investigation is motivated by the work of Lev Aizenberg [Proc. Amer. Math. Soc. 128 (2000), 1147-1155], where t... | https://arxiv.org/abs/2601.12608 | Academic Papers | svg |
9fcb40439a645c38d22454978590ce7b87bf9d8322ae1027e973d56899f80a59 | 2026-01-21T00:00:00-05:00 | A class of non-cylindrical domains for parabolic equations | arXiv:2601.12609v1 Announce Type: new Abstract: We present a class of non-cylindrical domains where Dirichlet-type problems for parabolic equations, such as the heat equation, can be posed and solved. The regularity for the boundary of this class of domains is a mixed Lipschitz condition, as described in the bulk of th... | https://arxiv.org/abs/2601.12609 | Academic Papers | svg |
7928debcf53ce1550da5885fe88102d0cb650b33616e256eb6bdebf4ec006cd4 | 2026-01-21T00:00:00-05:00 | An Eventown Result for Permutations | arXiv:2601.12613v1 Announce Type: new Abstract: A family of permutations $\mathcal{F} \subseteq S_n$ is even-cycle-intersecting if $\sigma \pi^{-1}$ has an even cycle for all $\sigma,\pi \in \mathcal{F}$. We show that if $\mathcal{F} \subseteq S_n$ is an even-cycle-intersecting family of permutations, then $|\mathcal{F... | https://arxiv.org/abs/2601.12613 | Academic Papers | svg |
7ca6511145a62b7b3f48ed2fd47e2afdda4494f95655da7dec9483f44713da42 | 2026-01-21T00:00:00-05:00 | Density of growth rates of subgroups of a free group -- an alternative proof | arXiv:2601.12620v1 Announce Type: new Abstract: We give an alternative proof to the theorem recently proved by Louvaris, Wise and Yehuda, that the growth rates of finitely generated subgroups of $F_r$ are dense in $[1,2r-1]$. | https://arxiv.org/abs/2601.12620 | Academic Papers | svg |
e6d7f9319232d0f6e564b047be9b2bb93b97d9d7dd853464834f946f5e4fde2f | 2026-01-21T00:00:00-05:00 | New Trends in the Stability of Sinkhorn Semigroups | arXiv:2601.12633v1 Announce Type: new Abstract: Entropic optimal transport problems play an increasingly important role in machine learning and generative modelling. In contrast with optimal transport maps which often have limited applicability in high dimensions, Schrodinger bridges can be solved using the celebrated ... | https://arxiv.org/abs/2601.12633 | Academic Papers | svg |
0327428abd61fc43ef128495f6f32220db2a73a81b636cd4b629af16a998f6ee | 2026-01-21T00:00:00-05:00 | Torsion points of small order on cyclic covers of $\mathbb{P}^1$. III | arXiv:2601.12643v1 Announce Type: new Abstract: Let $d>1$ be an integer and $K_0$ a perfect field such that $char(K_0)$ does not divide $d$. Let $n>d$ be an integer that is prime to $d$. Let $f(x)\in K_0[x]$ be a degree $n$ monic polynomial without repeated roots, and $\mathcal{C}_{f,d}$ a smooth projective model of th... | https://arxiv.org/abs/2601.12643 | Academic Papers | svg |
d4ef9a4a06a64fa64db75d7dfe32540d8f4213d0ad2dd7eff65ec6bb2680e596 | 2026-01-21T00:00:00-05:00 | On Some Properties of Matrices with Entries Defined by Products of $k$-Fibonacci and $k$-Lucas Numbers | arXiv:2601.12644v1 Announce Type: new Abstract: In this paper, we employ combinatorial and algebraic tools to derive closed-form expressions for several classical matrix invariants, including the determinant, inverse, trace, and powers, for a family of matrices whose entries are given by products of $k$-Fibonacci and $... | https://arxiv.org/abs/2601.12644 | Academic Papers | svg |
dcf510ae475c748e91a612fca9944f0a151fb7241e9a25e23fb4380fd22829eb | 2026-01-21T00:00:00-05:00 | A Landau-de Gennes Type Theory for Cholesteric-Helical Smectic-Smectic C* Liquid Crystal Phase Transitions | arXiv:2601.12653v1 Announce Type: new Abstract: We present a rigorous mathematical analysis of a modified Landau-de Gennes (LdG) theory modeling temperature-driven phase transitions between cholesteric, helical smectic, and smectic C* phases. This model couples a tensor-valued order parameter (nematic orientational ord... | https://arxiv.org/abs/2601.12653 | Academic Papers | svg |
3446c24303a02757ee7ab6edcc56090e2f977727abb766efd4caca4990abe9b8 | 2026-01-21T00:00:00-05:00 | Stable and Fr\'echet limit theorem for subgraph functionals in the hyperbolic random geometric graph | arXiv:2601.12677v1 Announce Type: new Abstract: We study the fluctuations of subgraph counts in hyperbolic random geometric graphs on the $d$-dimensional Poincar\'e ball in the heterogeneous, heavy-tailed degree regime. In a hyperbolic random geometric graph whose vertices are given by a Poisson point process on a grow... | https://arxiv.org/abs/2601.12677 | Academic Papers | svg |
700db4310fa98cd65b8a3655f65d1b12a5cd29027fe465278772157918dc9a9e | 2026-01-21T00:00:00-05:00 | Non-parabolic Spatial Hybrid Framed Curves and Their Applications in the Spatial Hybrid Number Space | arXiv:2601.12679v1 Announce Type: new Abstract: In this paper, we define non-parabolic spatial hybrid framed curves in the spatial hybrid number space, which may have singularities, and prove the existence and uniqueness theorem for non-parabolic spatial hybrid framed curves. As appliciations, we define evolutes, invol... | https://arxiv.org/abs/2601.12679 | Academic Papers | svg |
124b6149d577265d9aea2b5c872a892f3298ae4dd458fb1d12a50f5f02ff8f17 | 2026-01-21T00:00:00-05:00 | Igusa-Todorov properties of recollements of abelian categories | arXiv:2601.12702v1 Announce Type: new Abstract: In this paper, we investigate the behavior of Igusa-Todorov properties under recollements of abelian categories. In particular, we study how the Igusa-Todorov distances of the categories involved in a recollement are related. Applications are given to Artin algebras, espe... | https://arxiv.org/abs/2601.12702 | Academic Papers | svg |
504d7c68a8c5b28ddf7d320e1e65ca3c061121e1ec34408c3e959848bb12676b | 2026-01-21T00:00:00-05:00 | On a class of logarithmic Schr\"odinger equations via perturbation method | arXiv:2601.12732v1 Announce Type: new Abstract: In this paper, we consider the following logarithmic Schr\"odinger equation \[ -\Delta u + V(x)u = u \log u^{2} \quad \text{in }\ \mathbb{R}^{N}. \] Assuming that \(V(x)\in C(\mathbb{R}^{N})\) and \(V(x)\to+\infty\) as \(|x|\to\infty\), we develop a new perturbative varia... | https://arxiv.org/abs/2601.12732 | Academic Papers | svg |
525fef17ec11c5a7b2fec6264746eeb152b9e9e22bf1efbc5b13050c974fbcff | 2026-01-21T00:00:00-05:00 | A Sharp Global Boundedness Result for Keller--Segel--(Navier--)Stokes Systems with Rapid Diffusion and Saturated Sensitivities | arXiv:2601.12733v1 Announce Type: new Abstract: We investigate the Keller--Segel--(Navier--)Stokes system posed in a smooth bounded domain \(\Omega \subset \mathbb{R}^N\) with \(N = 2,3\): \begin{equation*} \begin{cases} n_t + u \cdot \nabla n = \Delta n - \nabla \cdot \big( n S(n)\nabla c \big), \\[2mm] u \cdot \nabla... | https://arxiv.org/abs/2601.12733 | Academic Papers | svg |
af68ae7c728c1211f41424c2d0526d5e114bfc64a0b567bfd4ff7ef09c5ae355 | 2026-01-21T00:00:00-05:00 | Hausdorff dimension of sets of numbers whose continued fractions contain arbitrarily long arithmetic progressions | arXiv:2601.12737v1 Announce Type: new Abstract: Continued fractions with prescribed structures on sequences of their partial quotients have been intensively studied in the literature. As far as an integer sequence, especially a randomly generated one is concerned, an attractive question is whether it contains arbitrari... | https://arxiv.org/abs/2601.12737 | Academic Papers | svg |
5f2cbb26293dfbb94af38d2edf84ab98d3118dbdb95e9d124ae163ce2d392b2e | 2026-01-21T00:00:00-05:00 | Monotonicity of Pairs of Operators and Generalized Inertial Proximal Method | arXiv:2601.12738v1 Announce Type: new Abstract: Monotonicity of pairs of operators is an extension of monotonicity of operators, which plays an important role in solving non-monotone inclusions. One of challenging problems in this new tool is how to design the associated mappings to obtain the monotone pairs. In this p... | https://arxiv.org/abs/2601.12738 | Academic Papers | svg |
d6514fe8813a7081b1efc5a3d18e048118d756daddc28ebbd66cc18c98127d10 | 2026-01-21T00:00:00-05:00 | When all directed cycles have the same weight | arXiv:2601.12746v1 Announce Type: new Abstract: A digraph $G$ is weightable if its edges can be weighted with real numbers such that the total weight in each directed cycle equals 1. There are several equivalent conditions: that $G$ admits a 0/1-weighting with the same property, or that $G$ contains no subdivided "doub... | https://arxiv.org/abs/2601.12746 | Academic Papers | svg |
03739e989e380b812d1f79957531cdf1759f915b8517dfabaf4ed3213baf8042 | 2026-01-21T00:00:00-05:00 | Non-Wieferich property of prime ideals and a conjecture of Erd\"os | arXiv:2601.12753v1 Announce Type: new Abstract: Let $K$ be a number field with ring of integers $\mathcal{O}$ and $\alpha\in\mathcal{O}$. For any prime ideal $\mathfrak{p}$ of $\mathcal{O}$, we obtain its higher $\alpha$-Wieferich property, which implies a nonexistence theorem for higher Wieferich unramified prime idea... | https://arxiv.org/abs/2601.12753 | Academic Papers | svg |
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