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e4dd00312eea9d09d829e25a46c89593e511b3aed749ac022358ea15513d0c82 | 2026-01-23T00:00:00-05:00 | The distinguishing number of complete bipartite and crown graphs | arXiv:2601.15913v1 Announce Type: new Abstract: The distinguishing number of a permutation group $G\leqslant\Sym(\Omega)$ is the minimum number of colours needed to colour $\Omega$ in such a way that the only colour preserving element of $G$ is the identity. The distinguishing number of a graph is the distinguishing nu... | https://arxiv.org/abs/2601.15913 | Academic Papers | svg |
47d9ee2345db260cd90200f0b465888388974bdb4ce0e7086f618e6e8b6a44da | 2026-01-23T00:00:00-05:00 | Mutation Of Matrices Over Group Rings | arXiv:2601.15920v1 Announce Type: new Abstract: We give a precise definition of mutation of skew symmetrizable matrices over group rings and relate it to folding and mutation of quivers with symmetries. These matrices can have non-zero diagonal entries and we explain a mutation rule in some of these cases as well. This... | https://arxiv.org/abs/2601.15920 | Academic Papers | svg |
7ccc32f827be2beccfd98c35d7db2077a2af2aef82bf7e98fb45ad0d5109165e | 2026-01-23T00:00:00-05:00 | A new proof of unboundedness of Riesz operator in $L^\infty$ and applications to mild ill-posedness in $W^{1,\infty}$ of the Euler type equations | arXiv:2601.15922v1 Announce Type: new Abstract: In this paper, we first present a new and simple proof of unboundedness of Riesz operator in $L^\infty$ and then establish the mild ill-posedness in $W^{1,\infty}$ of 3D rotating Euler equations and 2D Euler equations with partial damping. To the best of our knowledge, ou... | https://arxiv.org/abs/2601.15922 | Academic Papers | svg |
db26fa9460d56668b9718dcb46dbfbc51e9e7e64704e6f87b9812657462f7fdb | 2026-01-23T00:00:00-05:00 | Higher-dimensional Heegaard Floer homology and spectral networks | arXiv:2601.15923v1 Announce Type: new Abstract: Given a closed surface $C$ and a real exact Lagrangian $\Sigma \subset T^*C$ associated to a spectral curve, we construct a homomorphism $\operatorname{BSk}_\kappa(C)\to\operatorname{Mat}(N^{\kappa},\operatorname{BSk}_\kappa(\Sigma))$ from the braid skein algebra of $C$ t... | https://arxiv.org/abs/2601.15923 | Academic Papers | svg |
1814c83547cf2d0600c05f6d4753f603eb8f68a8ab84717499af22e5121b004f | 2026-01-23T00:00:00-05:00 | The representations of the Lie superalgebra p(3) in prime characteristic | arXiv:2601.15932v1 Announce Type: new Abstract: Let g be the Lie superalgebra p(3) of rank 2 over an algebraically closed field K of characteristic p > 3. We classify all irreducible modules of g, and give the character formulae for irreducible modules. | https://arxiv.org/abs/2601.15932 | Academic Papers | svg |
faa052a01f53775eb81b10ba09a459f6b52f37c09e523c887b4e3d3a220ce82f | 2026-01-23T00:00:00-05:00 | Extreme Score Distributions in Countable-Outcome Round-Robin Tournaments of Equally Strong Players | arXiv:2601.15950v1 Announce Type: new Abstract: We consider a general class of round-robin tournament models of equally strong players. In these models, each of the $n$ players competes against every other player exactly once. For each match between two players, the outcome is a value from a countable subset of the uni... | https://arxiv.org/abs/2601.15950 | Academic Papers | svg |
b5b3f5e278386afbb465289417e7b06326d86e68eeab174b1e69299d5214010c | 2026-01-23T00:00:00-05:00 | Geometry of spherical spin glasses | arXiv:2601.15966v1 Announce Type: new Abstract: Spherical spin glasses are canonical models for smooth random functions in high dimensions. In this review, we survey several interrelated lines of research on their geometric structure. We begin with results concerning critical points and their relationship to the Gibbs ... | https://arxiv.org/abs/2601.15966 | Academic Papers | svg |
84d34af1c031ad8efa018a1f9c8c15e034fdbba7f4386276cdea7d89b480f09c | 2026-01-23T00:00:00-05:00 | Iteration complexity of the Difference-of-Convex Algorithm for unconstrained optimization: a simple proof | arXiv:2601.15970v1 Announce Type: new Abstract: We propose a simple proof of the worst-case iteration complexity for the Difference of Convex functions Algorithm (DCA) for unconstrained minimization, showing that the global rate of convergence of the norm of the objective function's gradients at the iterates converge t... | https://arxiv.org/abs/2601.15970 | Academic Papers | svg |
95a9de52034de3f285323516eb2a5a5642ed9d4bffd29300b36035b3f60437d4 | 2026-01-23T00:00:00-05:00 | On maximal rank properties for symmetric polynomials in an equigenerated monomial complete intersection | arXiv:2601.15978v1 Announce Type: new Abstract: It is well known that a monomial complete intersection has the strong Lefschetz property in characteristic zero. This property is equivalent to the statement that any power of the sum of the variables is a maximal rank element on the complete intersection. In this paper, ... | https://arxiv.org/abs/2601.15978 | Academic Papers | svg |
4d0132de95e88b0f1a769326f68e0d8a73966f3ab20903821bf495a934e594e6 | 2026-01-23T00:00:00-05:00 | Primes and The Field of Values of Characters | arXiv:2601.15987v1 Announce Type: new Abstract: Let $p$ be a prime. For $p=2$, the fields of values of the complex irreducible characters of finite groups whose degrees are not divisible by $p$ have been classified; for odd primes $p$, a conjectural classification has been proposed. In this work, we extend this conject... | https://arxiv.org/abs/2601.15987 | Academic Papers | svg |
1a157b58fed7b6c7391fdf8bcc3374ca828131d8b3ce64b159cf2eb99ff421ff | 2026-01-23T00:00:00-05:00 | Rank of elliptic curves and class groups of real quadratic fields | arXiv:2601.15988v1 Announce Type: new Abstract: In this paper, we are going to prove the relation between rank of elliptic curves and the non-triviality of class groups of infinitely many real quadratic fields. | https://arxiv.org/abs/2601.15988 | Academic Papers | svg |
9fee75bf11a8636270781a68e7476e98f97909c6020956c127737bac5f432241 | 2026-01-23T00:00:00-05:00 | A sharp criterion and complete classification of global-in-time solutions and finite time blow-up of solutions to a chemotaxis system in supercritical dimensions | arXiv:2601.15990v1 Announce Type: new Abstract: We consider the chemotaxis system with indirect signal production in the whole space, \begin{equation}\label{abst:p}\tag{$\star$} \begin{cases} u_t = \Delta u - \nabla \cdot (u\nabla v),\\ 0 = \Delta v + w,\\ w_t = \Delta w + u \end{cases} \end{equation} with emphasis on ... | https://arxiv.org/abs/2601.15990 | Academic Papers | svg |
0a992f9e64d956891ab623db504f1c7a03f0954c5e4d3f877de91f89de61a453 | 2026-01-23T00:00:00-05:00 | Counting Saddle Connections on Hyperelliptic Translation Surfaces with a Slit | arXiv:2601.15993v1 Announce Type: new Abstract: We consider saddle connections on a translation surface in a hyperelliptic connected component of a stratum that do not intersect the interior of a distinguished saddle connection. For this restricted set of saddle connections, we show that it satisfies an $L (\log L)^{d-... | https://arxiv.org/abs/2601.15993 | Academic Papers | svg |
7e49abf2c8d09bd7df482cf2b76fa1bebd7c1896b1cd582eacd197c7999b03ba | 2026-01-23T00:00:00-05:00 | Minimax-optimal Halpern iterations for Lipschitz maps | arXiv:2601.15996v1 Announce Type: new Abstract: This paper investigates the minimax-optimality of Halpern fixed-point iterations for Lipschitz maps in general normed spaces. Starting from an a priori bound on the orbit of iterates, we derive non-asymptotic estimates for the fixed-point residuals. These bounds are tight... | https://arxiv.org/abs/2601.15996 | Academic Papers | svg |
b99dfa8503d16d2456c369620af2e323762845e162aa341b22fdd7075cbf316b | 2026-01-23T00:00:00-05:00 | The Recovery of Semilinear Potentials Satisfying Null Conditions From Scattering Data | arXiv:2601.15997v1 Announce Type: new Abstract: We construct oscillatory solutions of fully semilinear wave equations in Minkowski space satisfying a null condition of the form $$\square u:=(-\partial_{x_0}^2 +\sum_{j=1}^n \partial_{x_j}^2 )u= q(x,u)((\partial_{x_0}u)^2-|\nabla_{x'}u|^2),$$ $$x=(x_0,x'), \;\ x'=(x_1,\l... | https://arxiv.org/abs/2601.15997 | Academic Papers | svg |
9cf7cf5ade8719615cf7170e32f4cf317d804c51f35ea0046fdd77d29fd48e56 | 2026-01-23T00:00:00-05:00 | A brief note about p-curvature on graphs | arXiv:2601.16010v1 Announce Type: new Abstract: In this paper, we consider Wang's $CD_p(m,K)$ condition on graphs, which depends on the $p$-Laplacian $\Delta_p$ for $p>1$ and is an extension of the classical Bakry-\'Emery $CD(m,K)$ curvature dimension condition. We calculate several examples including paths, cycles and... | https://arxiv.org/abs/2601.16010 | Academic Papers | svg |
5987d58e0732b1e72455fa3fbace49b76b875a670096398d59bbcdb255319093 | 2026-01-23T00:00:00-05:00 | Infinite random graphs | arXiv:2601.16013v1 Announce Type: new Abstract: We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, we do not require that probabilities assigned to pairs of points are all equal. We give examp... | https://arxiv.org/abs/2601.16013 | Academic Papers | svg |
a5ac5064d27d250a3d5e1603a557451cc46e35e29f83e94e14e9e0a4651201d5 | 2026-01-23T00:00:00-05:00 | The T-tensor of spherically symmetric Finsler metrics | arXiv:2601.16021v1 Announce Type: new Abstract: This paper is devoted to the study of the T-tensor associated with a spherically symmetric Finsler metric $F=u\phi(r,s)$ on \(\mathbb{R}^n\). We derive a general expression for the T-tensor in terms of the scalar function \(\phi(r, s)\) and its partial derivatives. Furthe... | https://arxiv.org/abs/2601.16021 | Academic Papers | svg |
8fa08d35db02d364f3771d148cb16d471d4c0a175a2d43e6de3b3ac44932fcda | 2026-01-23T00:00:00-05:00 | A Second-Order Dynamical System for Solving Generalized Inverse Mixed Variational Inequality problems | arXiv:2601.16043v1 Announce Type: new Abstract: In this paper, we study a class of generalized inverse mixed variational inequality problems (GIMVIPs). We propose a novel projection-based second-order time-varying dynamical system for solving GIMVIPs. Under the assumptions that the underlying operators are strongly mon... | https://arxiv.org/abs/2601.16043 | Academic Papers | svg |
a8ae53476f7cd75b1e4d5e3e626d72f5045bd5de213a99a39bac044f9f2ba0e6 | 2026-01-23T00:00:00-05:00 | On the Identification of Elliptic Curves That Admit Infinitely Many Twists Satisfying the Birch-Swinnerton-Dyer Conjecture | arXiv:2601.16044v1 Announce Type: new Abstract: Recent work of Burungale-Skinner-Tian-Wan established the first infinite families of quadratic twists of non-CM elliptic curves over $\mathbb{Q}$ for which the strong Birch-Swinnerton-Dyer (BSD) conjecture holds. Building on their results, we encode the required hypothese... | https://arxiv.org/abs/2601.16044 | Academic Papers | svg |
201a1445d69e9a66b290b731facd3598a79be5e707c1ce82e90fe897bfd9c9f6 | 2026-01-23T00:00:00-05:00 | Fujita exponents on quantum Euclidean spaces | arXiv:2601.16053v1 Announce Type: new Abstract: We study the well-posedness of a non-linear heat equation with power nonlinearity with positive initial data on quantum Euclidean spaces. We prove a noncommutative analogue of the classical Fujita theorem by identifying the critical exponent separating finite-time blow-up... | https://arxiv.org/abs/2601.16053 | Academic Papers | svg |
d5fc4bac5bb8e096dcb3294c4c4cfa3e3b5c6e4ebcb0ba043402eacdc6284744 | 2026-01-23T00:00:00-05:00 | Fully Functional Weighted Testing for Abrupt and Gradual Location Changes in Functional Time Series | arXiv:2601.16058v1 Announce Type: new Abstract: Change point tests for abrupt changes in the mean of functional data, i.e., random elements in infinite-dimensional Hilbert spaces, are either based on dimension reduction techniques, e.g., based on principal components, or directly based on a functional CUSUM (cumulative... | https://arxiv.org/abs/2601.16058 | Academic Papers | svg |
ffddf38c57428641a8086050b6041ce7b75a0792a61d7565d9fdc30286e4b900 | 2026-01-23T00:00:00-05:00 | Bivariate topological complexity: a framework for coordinated motion planning | arXiv:2601.16059v1 Announce Type: new Abstract: We introduce a bivariate version of topological complexity, $\mathrm{TC}(f,g)$, associated with two continuous maps $f\colon X\to Z$ and $g\colon Y\to Z$. This invariant measures the minimal number of continuous motion planning rules required to coordinate trajectories in... | https://arxiv.org/abs/2601.16059 | Academic Papers | svg |
f80d6250a40d9132f324a5c8bc5e1571d473dc16691d353d4405b3f860b7eee2 | 2026-01-23T00:00:00-05:00 | Continuum limit of hypergraph $p$-Laplacian equations on point clouds | arXiv:2601.16063v1 Announce Type: new Abstract: This paper studies a class of $p$-Laplacian equations on point clouds that arise from hypergraph learning in a semi-supervised setting. Under the assumption that the point clouds consist of independent random samples drawn from a bounded domain $\Omega\subset\mathbb{R}^d$... | https://arxiv.org/abs/2601.16063 | Academic Papers | svg |
a460fd36126db4619584c42971784b087577f9f529f32fa147e36c7aeef00a3c | 2026-01-23T00:00:00-05:00 | On the Stable Euclidean Distance Degree of Algebraic Layers | arXiv:2601.16071v1 Announce Type: new Abstract: We study the projective geometry of algebraic neural layers, namely families of maps induced by a polynomial activation function, with particular emphasis on the generic Euclidean Distance degree ($\mathrm{gED}$). This invariant is projective in nature and measures the nu... | https://arxiv.org/abs/2601.16071 | Academic Papers | svg |
85f911d3d2ea4ff58e4691f36c989a00cef8713dd287623e719e981ea88f51cb | 2026-01-23T00:00:00-05:00 | The Hyperrigidity Conjecture for Spectrahedra | arXiv:2601.16075v1 Announce Type: new Abstract: We show that if K is a compact spectrahedron whose set of extreme points is closed, then the operator system of continuous affine functions on K is hyperrigid in the C*-algebra C(ex(K)). | https://arxiv.org/abs/2601.16075 | Academic Papers | svg |
ba8594566d2d6e4dbcdaf8ef6613e6e7f2889c35db64373af56e6579f96601f8 | 2026-01-23T00:00:00-05:00 | Rainbow spanning structures in strongly edge-colored graphs | arXiv:2601.16084v1 Announce Type: new Abstract: An edge-colored graph is a graph in which each edge is assigned a color. Such a graph is called strongly edge-colored if each color class forms an induced matching, and called rainbow if all edges receive pairwise distinct colors. In this paper, by establishing a connecti... | https://arxiv.org/abs/2601.16084 | Academic Papers | svg |
e30f7365705bf603ee9f319e78a716d990f095b7bfc5aa199cbbb2159fcb3181 | 2026-01-23T00:00:00-05:00 | Birational automorphism groups in families of hyper-K\"ahler manifolds | arXiv:2601.16090v1 Announce Type: new Abstract: We study the behavior of birational automorphism groups in families of projective hyper-K\"ahler manifolds. | https://arxiv.org/abs/2601.16090 | Academic Papers | svg |
d33f8a04836868bede8877f06407180bfe2c0425632e40761db892c5c51723aa | 2026-01-23T00:00:00-05:00 | Monoidal adjunctions and abelian envelopes | arXiv:2601.16092v1 Announce Type: new Abstract: We show how monoidal adjunctions can be used to prove the existence of monoidal abelian envelopes of pseudo-tensor categories, in particular, those admitting a combinatorial description with certain properties. We derive concrete general criteria that we demonstrate by gi... | https://arxiv.org/abs/2601.16092 | Academic Papers | svg |
276b2fb57d1623b3bd3dea8477095bd3f39fc506769e5a9a2ca8e54839872120 | 2026-01-23T00:00:00-05:00 | On Seshadri constants of adjoint divisors on surfaces and threefolds in arbitrary characteristic | arXiv:2601.16094v1 Announce Type: new Abstract: We develop a new approach towards obtaining lower bounds of the Seshadri constants of ample adjoint divisors on smooth projective varieties $X$ in arbitrary characteristic. Let $x\in X$ be a closed point and $A$ an ample divisor on $X$. If $X$ is a surface, we recover som... | https://arxiv.org/abs/2601.16094 | Academic Papers | svg |
88acc2666284c3b7d5de4a1bec827c23e5123310dcc8227a7052adb9bb7d3cf6 | 2026-01-23T00:00:00-05:00 | Intersections of Convex Hulls of Polynomial Shifts and Critical Points | arXiv:2601.16102v1 Announce Type: new Abstract: Let $p(z)$ be a complex polynomial of degree $n\ge 2$. For each $c\in\mathbb{C}$, let $K_c$ denote the convex hull of the zeros of $p(z)+c$, and let $K'$ denote the convex hull of the zeros of $p'(z)$. We prove that $$\bigcap_{c\in\mathbb{C}} K_c = K',$$ by combining a st... | https://arxiv.org/abs/2601.16102 | Academic Papers | svg |
f0c4097bd20390539fb412c982a0b348cf755ff1c88d1eb382fd91fb1721aa0a | 2026-01-23T00:00:00-05:00 | The Eisenbud-Goto conjecture for projectively normal varieties with mild singularities | arXiv:2601.16103v1 Announce Type: new Abstract: For a nondegenerate projective variety $X$, the Eisenbud-Goto conjecture asserts that $\operatorname{reg}X\leq\operatorname{deg}X-\operatorname{codim}X+1$. Despite the existence of counterexamples, identifying the classes of varieties for which the conjecture holds remain... | https://arxiv.org/abs/2601.16103 | Academic Papers | svg |
b69b92ab2f0cb420902a7ab05e486e5ed862f44e42af0242091a68227ce4fb1b | 2026-01-23T00:00:00-05:00 | A Linear Bound on the Rich Flow Number for Graphs with a Given Maximum Degree | arXiv:2601.16104v1 Announce Type: new Abstract: A rich $k$-flow is a nowhere-zero $k$-flow $\phi$ such that, for every pair of adjacent edges $e$ and $f$, $|\phi(e)| \neq |\phi(f)|$. A graph is rich flow admissible if it admits a rich $k$-flow for some integer $k$. In this paper, we prove that if $G$ is a rich flow adm... | https://arxiv.org/abs/2601.16104 | Academic Papers | svg |
7f512ed8330aca7881c91ccfc66b321bcda121b86c970352916478d569af7bc6 | 2026-01-23T00:00:00-05:00 | Stability and Decay for the 2D Anisotropic Navier-Stokes Equations with Fractional Horizontal Dissipation on $\mathbb{R}^2$ | arXiv:2601.16110v1 Announce Type: new Abstract: The stability problem for the 2D Navier-Stokes equations with dissipation in only one direction on $\mathbb R^2$ is not fully understood. This dissipation is in the intermediate regime between the fully dissipative Navier-Stokes and the inviscid Euler. Navier-Stokes solut... | https://arxiv.org/abs/2601.16110 | Academic Papers | svg |
c26d663e749a5d7127a21f2a0f69c5fd9657008c413d98ce2e9e42379b7c123c | 2026-01-23T00:00:00-05:00 | Equivariant Morse-Bott cohomology through stabilization | arXiv:2601.16119v1 Announce Type: new Abstract: For closed manifolds with compact Lie group actions, we study Austin-Braam's Morse-theoretic construction of Borel equivariant cohomology using the technique of stabilization. We show that a $C^1$-small equivariant perturbation produces stable invariant Morse-Bott functio... | https://arxiv.org/abs/2601.16119 | Academic Papers | svg |
36fbd7deeb2886797e060f988b64d8289838a6128015ad542a11a8b11d8351d7 | 2026-01-23T00:00:00-05:00 | Proximity Operator of the $\ell_1$ over $\ell_2$ Function | arXiv:2601.16128v1 Announce Type: new Abstract: We study the proximity operator of the nonconvex, scale-invariant ratio $h(\vx)=\|\vx\|_{1}/\|\vx\|_{2}$ and show it can be computed exactly in any dimension. By expressing $\vx=r\vu$ and exploiting sign and permutation invariance, we reduce the proximal step to a smooth ... | https://arxiv.org/abs/2601.16128 | Academic Papers | svg |
6f36073eb4e1711e74b5fb729335a367c7ace8e76af6bdde56da640db8113b6d | 2026-01-23T00:00:00-05:00 | A pseudo-bosonic Klein-Gordon field with finite two-points function | arXiv:2601.16131v1 Announce Type: new Abstract: We introduce a class of pseudo-bosonic Klein-Gordon fields in 1+1 dimensions and we discuss some of their properties. This work originates from non Hermitian quantum mechanics and deformed canonical commutation relations. We show that, within this class of fields, there e... | https://arxiv.org/abs/2601.16131 | Academic Papers | svg |
c985ee6fcc3b8ae0b89cc4ab07f2ae07829920e064318a0a2d529c351a7f7f1c | 2026-01-23T00:00:00-05:00 | Modular Weil representation and compatibility of cuspidals with congruences | arXiv:2601.16132v1 Announce Type: new Abstract: Let $F$ be a non-archimedean local field of characteristic different from $2$ and of residual characteristic $p$. We generalise the theory of the Weil representation over $F$ with complex coefficients to $\ell$-modular representations \textit{i.e.} when the complex coeffi... | https://arxiv.org/abs/2601.16132 | Academic Papers | svg |
8c3f9116408d95fb2f749c1c830131a14b112610980be54bb9aef5c3846cc389 | 2026-01-23T00:00:00-05:00 | Pointwise Ergodic Averages Along the Omega Function in Number Fields | arXiv:2601.16136v1 Announce Type: new Abstract: We show the failure of the pointwise convergence of averages along the Omega function in a number field. As a consequence, we show, for instance, that the averages \[ \frac{1}{N^2}\sum_{1\leq m,n \leq N} f(T^{\Omega(m^2+n^2)}x)\] do not converge pointwise in ergodic syste... | https://arxiv.org/abs/2601.16136 | Academic Papers | svg |
c356ef752d4ab2e75b4b7f7b654777c6f39609f4494f454a0dee8b8709abc287 | 2026-01-23T00:00:00-05:00 | On the rationality of the Weil Representation and the local theta correspondence | arXiv:2601.16141v1 Announce Type: new Abstract: We prove that the Weil representation over a non-archimedean local field can be realised with coefficients in a number field. We give an explicit descent argument to describe precisely which number field the Weil representation descends to. Our methods also apply over mor... | https://arxiv.org/abs/2601.16141 | Academic Papers | svg |
07396532e300a7928fcd30c71d2a65e79aedfe7545fd629d728e3ed6c64a2cd4 | 2026-01-23T00:00:00-05:00 | High-Degree Polynomial Approximations for Solving Linear Integral, Integro-Differential, and Ordinary Differential Equations | arXiv:2601.16143v1 Announce Type: new Abstract: This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for resolving ill-posed problems. Central... | https://arxiv.org/abs/2601.16143 | Academic Papers | svg |
4da1973afc58462e5cfef0fc8cba1b86105010bb1235e32bebc236a7e1a6234c | 2026-01-23T00:00:00-05:00 | On the Ginzburg-Landau approximation for quasilinear pattern forming reaction-diffusion-advection systems | arXiv:2601.16145v1 Announce Type: new Abstract: We prove that the Ginzburg-Landau equation correctly predicts the dynamics of quasilinear pattern-forming reaction-diffusion-advection systems, close to the first instability. We present a simple theorem which is easily applicable for such systems and relies on key maxima... | https://arxiv.org/abs/2601.16145 | Academic Papers | svg |
0128408acf80e9ebafc91e3623aec1f2004fa30e5dc9bba265e64ecb2e47e933 | 2026-01-23T00:00:00-05:00 | On the structural properties of Lie algebras via associated labeled directed graphs | arXiv:2601.16161v1 Announce Type: new Abstract: We present a method for associating labeled directed graphs to finite-dimensional Lie algebras, thereby enabling rapid identification of key structural algebraic features. To formalize this approach, we introduce the concept of graph-admissible Lie algebras and analyze pr... | https://arxiv.org/abs/2601.16161 | Academic Papers | svg |
f13e7e94b81a7f1dae4427ab768688dba6fb7ff886fb388ad323476774dd3c0a | 2026-01-23T00:00:00-05:00 | Maximal toroids and Cartan subgroups of algebraic groups | arXiv:2601.16162v1 Announce Type: new Abstract: We introduce a unified theory of Cartan subgroups and maximal toroids - defined as connected multiplicative type subgroups that are maximal amongst all such subgroups - which holds for all affine algebraic groups over a field, regardless of smoothness. For instance we sho... | https://arxiv.org/abs/2601.16162 | Academic Papers | svg |
bae5025882d1026f54402ec931e64ca0bc95248a8300050558d6420bdb8aff2f | 2026-01-23T00:00:00-05:00 | On the dimension drop for harmonic measure on uniformly non-flat Ahlfors-David regular boundaries | arXiv:2601.16167v1 Announce Type: new Abstract: We extend earlier results of Azzam on the dimension drop of the harmonic measure for a domain $\Omega\subset \R^{n}$ with $n\geq 3$, with dimensional Ahlfors regular boundary $\partial\Omega$ of dimension $s$ with $n-1-\delta_0 \leq s\leq n-1$, that is uniformly non flat.... | https://arxiv.org/abs/2601.16167 | Academic Papers | svg |
864fb2cf012ff3700d6a115470b40108760c29a9b24ffea7c9712f3a868bab4c | 2026-01-23T00:00:00-05:00 | Fixed-point proportion of geometric iterated Galois groups | arXiv:2601.16173v1 Announce Type: new Abstract: In 1980, Odoni initiated the study of the fixed-point proportion of iterated Galois groups of polynomials motivated by prime density problems in arithmetic dynamics. The main goal of the present paper is to completely settle the longstanding open problem of computing the ... | https://arxiv.org/abs/2601.16173 | Academic Papers | svg |
0516cb5d9184d66d7cdbbd0f0e83998ef8522aa80eacb9c4d785ae581844a32a | 2026-01-23T00:00:00-05:00 | Metric-uniform spectral inequality for the Laplacian on manifolds with bounded sectional curvature | arXiv:2601.16176v1 Announce Type: new Abstract: Given a Riemannian manifold $M$ endowed with a smooth metric $g$ satisfying upper and lower sectional curvature bounds, we show an equivalence property between the $\mathrm{L}^2$ norm on $M$ and the $\mathrm{L}^2$ norm on subsets $\omega$ satisfying a thickness condition,... | https://arxiv.org/abs/2601.16176 | Academic Papers | svg |
81b76d043e541d3b9c27b13f2db21193e88680dd96e95cb69d5fc87540135b32 | 2026-01-23T00:00:00-05:00 | Mild Solutions for Path-Dependent Parabolic PDEs with Neumann Boundary Conditions via Generalized BSDEs | arXiv:2601.16178v1 Announce Type: new Abstract: We study a system of Forward-Backward Stochastic Differential Equations (FBSDEs) with time-delayed generators. The forward process includes a reflection component expressed via a Stieltjes integral, while the backward process takes the form of a Generalized BSDE. We estab... | https://arxiv.org/abs/2601.16178 | Academic Papers | svg |
2fef10926f266295d9a1e0cc05d21a0d9a21a307553fe518ccf1518ffe97366c | 2026-01-23T00:00:00-05:00 | Gaussian maps on trigonal curves | arXiv:2601.16183v1 Announce Type: new Abstract: In this paper we study higher even Gaussian maps of the canonical bundle for cyclic trigonal curves. More precisely, we study suitable restrictions of these maps determining a lower bound for the rank, and more generally, a lower bound for the rank for the general trigona... | https://arxiv.org/abs/2601.16183 | Academic Papers | svg |
cfa9c3919aae4ec147c711a20883f4df1f9bb7f6b4f23b7464290fa7cc6478f4 | 2026-01-23T00:00:00-05:00 | The Pohozaev identity for the Spectral Fractional Laplacian | arXiv:2601.16185v1 Announce Type: new Abstract: In this paper, we prove a Pohozaev identity for the Spectral Fractional Laplacian (SFL). This identity allows us to establish non-existence results for the semilinear Dirichlet problem $(-\Delta|_{\Omega})^su = f(u)$ in star-shaped domains. The first such identity for non... | https://arxiv.org/abs/2601.16185 | Academic Papers | svg |
8f899e1d2cf8f2ecd07a0bfcabcb41df2596cf9896269d74ea641ccb4578e973 | 2026-01-23T00:00:00-05:00 | Inversion problem in algebras of integrable functions with summable Fourier transforms | arXiv:2601.16186v1 Announce Type: new Abstract: In this paper, we study the norm-controlled inversion problem in two classes of algebras of integrable functions. In contrast of the classical case of $L^{1}(G)$, we prove that this problem has a positive solution in our setting without any additional restrictions. | https://arxiv.org/abs/2601.16186 | Academic Papers | svg |
9d51c102180f2ce37aa5416ef593330335f195b2e2f53064ffa770f629aee20d | 2026-01-23T00:00:00-05:00 | Ergodic averages for commutative transformations along return times | arXiv:2601.16188v1 Announce Type: new Abstract: In this paper, we extend recent results on the convergence of ergodic averages along sequences generated by return times to shrinking targets in rapidly mixing systems, partially answering questions posed by the first author, Maass and the third author in [6]. In particul... | https://arxiv.org/abs/2601.16188 | Academic Papers | svg |
61db48fb4e44dcc49de67016038a0de3c2ab761996471b9ad38f4cf876421e68 | 2026-01-23T00:00:00-05:00 | Density-based structural frameworks for prime numbers, prime gaps, and Euler products | arXiv:2601.16193v1 Announce Type: new Abstract: We develop a unified density-based framework for primality, coprimality, and prime pairs, and introduce an intrinsic normalized model for prime gaps constrained by the Prime Number Theorem. Within this setting, a structural tension between Hardy-Littlewood, Cramer, and PN... | https://arxiv.org/abs/2601.16193 | Academic Papers | svg |
402b26da03c3a5e76199771adeb9fd3e126e1b766566f1ec80843b22bb0433e8 | 2026-01-23T00:00:00-05:00 | Generalized Bassian Modules over Non-primitive Dedekind Prime Rings | arXiv:2601.16201v1 Announce Type: new Abstract: A right $A$-module $M$ is said to be generalized bassian if the existence of an injective homomorphism $M\to M/N$ for some submodule $N$ of $M$ implies that $N$ is a direct summand of $M$. We describe singular generalized bassian modules over non-primitive Dedekind prime ... | https://arxiv.org/abs/2601.16201 | Academic Papers | svg |
2ecb58b5c79baacfdb3dcba3cfe5bb5b99a7e55ba2aaddac03ffc28b82c24afd | 2026-01-23T00:00:00-05:00 | Pairwise Beats All-at-Once: Behavioral Gains from Sequential Choice Presentation | arXiv:2601.15332v1 Announce Type: cross Abstract: This paper presents the Sequential Rationality Hypothesis, which argues that consumers are better able to make utility-maximizing decisions when products appear in sequential pairwise comparisons rather than in simultaneous multi-option displays. Although this involves ... | https://arxiv.org/abs/2601.15332 | Academic Papers | svg |
2469d3b6bd178139d82fcface8205cbfdb417914cf6ca37777a57de65fcdba48 | 2026-01-23T00:00:00-05:00 | Exactly solvable topological phase transition in a quantum dimer model | arXiv:2601.15377v1 Announce Type: cross Abstract: We introduce a family of generalized Rokhsar-Kivelson (RK) Hamiltonians, which are reverse-engineered to have an arbitrary edge-weighted superposition of dimer coverings as their exact ground state at the RK point. We then focus on a quantum dimer model on the triangula... | https://arxiv.org/abs/2601.15377 | Academic Papers | svg |
33ffefc75929e61fc1a5a95568d457fd32b953acd5923f50a3fe6e4267165de2 | 2026-01-23T00:00:00-05:00 | Quadratic tensors as a unification of Clifford, Gaussian, and free-fermion physics | arXiv:2601.15396v1 Announce Type: cross Abstract: Certain families of quantum mechanical models can be described and solved efficiently on a classical computer, including qubit or qudit Clifford circuits and stabilizer codes, free-boson or free-fermion models, and certain rotor and GKP codes. We show that all of these ... | https://arxiv.org/abs/2601.15396 | Academic Papers | svg |
d881d565eea8a9b6d8d9fb6db6124b6a415812aa328c6d401215f4a9cae9563b | 2026-01-23T00:00:00-05:00 | Dynamic Mean Field Theories for Nonlinear Noise in Recurrent Neuronal Networks | arXiv:2601.15462v1 Announce Type: cross Abstract: Strong, correlated noise in recurrent neural circuits often passes through nonlinear transfer functions, complicating dynamical mean-field analyses of complex phenomena such as transients and bifurcations. We introduce a method that replaces nonlinear functions of Ornst... | https://arxiv.org/abs/2601.15462 | Academic Papers | svg |
86255efdff01faf091d8cfcd31bc9635a4832e1379fe273d8a1f5af7bacd8da7 | 2026-01-23T00:00:00-05:00 | A Modified Center-of-Mass Conservation Law in Finite-Domain Simulations of the Zakharov--Kuznetsov Equation | arXiv:2601.15573v1 Announce Type: cross Abstract: We investigate conservation laws of the two-dimensional Zakharov-Kuznetsov (ZK) equation, a natural higher-dimensional and non-integrable extension of the Korteweg--de Vries equation. The ZK equation admits three scalar conserved quantities -- mass, momentum, and energy... | https://arxiv.org/abs/2601.15573 | Academic Papers | svg |
2659ecb296fc92aaddd9e6b655cc63785577a42997094e95f536e5b0cb9e228d | 2026-01-23T00:00:00-05:00 | A two-sample pseudo-observation-based regression approach for the relative treatment effect | arXiv:2601.15880v1 Announce Type: cross Abstract: The relative treatment effect is an effect measure for the order of two sample-specific outcome variables. It has the interpretation of a probability and also a connection to the area under the ROC curve. In the literature it has been considered for both ordinal or righ... | https://arxiv.org/abs/2601.15880 | Academic Papers | svg |
337aba6d2a24fdfc3c2be941c9774a8c7db7ca462ae119ca7e14a39d24c56070 | 2026-01-23T00:00:00-05:00 | On the spherical cardioid distribution and its goodness-of-fit | arXiv:2601.16095v1 Announce Type: cross Abstract: In this paper, we study the spherical cardioid distribution, a higher-dimensional and higher-order generalization of the circular cardioid distribution. This distribution is rotationally symmetric and generates unimodal, multimodal, axial, and girdle-like densities. We ... | https://arxiv.org/abs/2601.16095 | Academic Papers | svg |
218169404e549b70876df658c39d0e407ff10294153a5b15ec57b099361144b7 | 2026-01-23T00:00:00-05:00 | Exceptional points in Gaussian channels: diffusion gauging and drift-governed spectrum | arXiv:2601.16121v1 Announce Type: cross Abstract: McDonald and Clerk [Phys.\ Rev.\ Research 5, 033107 (2023)] showed that for linear open quantum systems the Liouvillian spectrum is independent of the noise strength. We first make this noise-independence principle precise in continuous time for multimode bosonic Gaussi... | https://arxiv.org/abs/2601.16121 | Academic Papers | svg |
927869583f65ffc05962dccb77f983018eabf9a47f75c51acfce19bb612d8688 | 2026-01-23T00:00:00-05:00 | Gauge Theory and Skein Modules | arXiv:2601.16213v1 Announce Type: cross Abstract: We study skein modules of 3-manifolds by embedding them into the Hilbert spaces of 4d ${\cal N}=4$ super-Yang-Mills theories. When the 3-manifold has reduced holonomy, we present an algorithm to determine the dimension and the list of generators of the skein module with... | https://arxiv.org/abs/2601.16213 | Academic Papers | svg |
60d5071fea2a37856e35db0f30db1fb95c7d8db0bb6d8811f8a624b492ecae3d | 2026-01-23T00:00:00-05:00 | Deterministic Structures in the Stopping Time Dynamics of the 3x+1 Problem | arXiv:1709.03385v5 Announce Type: replace Abstract: The $3x+1$ problem concerns the iteration of the map $T:\mathbb{Z}\to\mathbb{Z}$ defined by $T(x)=x/2$ for even $x$ and $T(x)=(3x+1)/2$ for odd $x$. This paper investigates the stopping time dynamics associated with $T$ within a deterministic and algebraic framework. ... | https://arxiv.org/abs/1709.03385 | Academic Papers | svg |
3dc871e473d2291df9001be7d603440d780313819621f147dc01b9150559ed47 | 2026-01-23T00:00:00-05:00 | Unbounded field operators in categorical extensions of conformal nets | arXiv:2001.03095v5 Announce Type: replace Abstract: We prove the equivalence of VOA tensor categories and conformal net tensor categories for the following examples: all WZW models; all lattice VOAs; all unitary parafermion VOAs; type $ADE$ discrete series $W$-algebras; their tensor products; their regular cosets. A ne... | https://arxiv.org/abs/2001.03095 | Academic Papers | svg |
89a110910d6a112ad9d127b799349d1f8741cce2b92f10fd10ea0dafb7c8b270 | 2026-01-23T00:00:00-05:00 | On rationality for $C_2$-cofinite vertex operator algebras | arXiv:2108.01898v3 Announce Type: replace Abstract: Let $V$ be an $\mathbb{N}$-graded, simple, self-contragredient, $C_2$-cofinite vertex operator algebra. We show that if the $S$-transformation of the character of $V$ is a linear combination of characters of $V$-modules, then the category $\mathcal{C}$ of grading-rest... | https://arxiv.org/abs/2108.01898 | Academic Papers | svg |
d55a3a590c969669e514fa127ff5f2da308103afdd85388177513e790b58ba2d | 2026-01-23T00:00:00-05:00 | Parameterising the effect of a continuous treatment using average derivative effects | arXiv:2109.13124v2 Announce Type: replace Abstract: The average treatment effect (ATE) is commonly used to quantify the main effect of a binary treatment on an outcome. Extensions to continuous treatments are usually based on the dose-response curve or shift interventions, but both require strong overlap conditions and... | https://arxiv.org/abs/2109.13124 | Academic Papers | svg |
dadcfc43c1b28e1f866dda026c6de379945dbcd83870a5449d38da3a4789a3e5 | 2026-01-23T00:00:00-05:00 | Uni-width subgroups, universal elements, and lambda number of finite groups | arXiv:2202.09818v2 Announce Type: replace Abstract: A cyclic subgroup $N$ of a finite group $G$ is called a uni-width subgroup of $G$ if $N$ is the unique cyclic subgroup of $G$ of order $|N|$. In this article, we prove that a finite group $G$ admits a unique largest uni-width subgroup denoted by $U(1;G)$. We then show... | https://arxiv.org/abs/2202.09818 | Academic Papers | svg |
4807e2a6ec07a7349492edb4d62a6d829276b757fa7e12507b65c234c3b93d8b | 2026-01-23T00:00:00-05:00 | Proper harmonic embeddings of open Riemann surfaces into $\mathbb{R}^4$ | arXiv:2206.03566v2 Announce Type: replace Abstract: We prove that every open Riemann surface admits a proper embedding into $\mathbb{R}^4$ by harmonic functions. This reduces by one the previously known embedding dimension in this framework, dating back to a theorem by Greene and Wu from 1975. | https://arxiv.org/abs/2206.03566 | Academic Papers | svg |
1eae3fb23ecce039ee422972c82edd88730e572bae0213e20758611057d76f4d | 2026-01-23T00:00:00-05:00 | On the additivity of Newton-Okounkov bodies | arXiv:2207.09229v3 Announce Type: replace Abstract: We study the additivity of Newton-Okounkov bodies. Our main result states that on two-dimensional subcones of the ample cone the Newto-Okounkov body associated to an appropriate flag acts additively. We prove this by induction relying on the slice formula for Newton-O... | https://arxiv.org/abs/2207.09229 | Academic Papers | svg |
0866786a232eecf7dfc5102ca21febb97989b4af192356d03b86bdc96a35fd9f | 2026-01-23T00:00:00-05:00 | Mixing times of a Burnside process Markov chain on set partitions | arXiv:2207.14269v3 Announce Type: replace Abstract: Let $X$ be a finite set and let $G$ be a finite group acting on $X$. The group action splits $X$ into disjoint orbits. The Burnside process is a Markov chain on $X$ which has a uniform stationary distribution when the chain is lumped to orbits. We consider the case wh... | https://arxiv.org/abs/2207.14269 | Academic Papers | svg |
d4819a338e4b1377efe9873b22b5e8fd5db0421d8c4d519cf87c8bd7560aa72c | 2026-01-23T00:00:00-05:00 | Conformal and extrinsic upper bounds for the harmonic mean of Neumann and Steklov eigenvalues | arXiv:2208.13959v5 Announce Type: replace Abstract: Let $M$ be an $m$-dimensional compact Riemannian manifold with boundary. We obtain the upper bound of the harmonic mean of the first $m$ nonzero Neumann eigenvalues and Steklov eigenvalues involving the conformal volume and relative conformal volume, respectively. We ... | https://arxiv.org/abs/2208.13959 | Academic Papers | svg |
1a49c758fc6713947825940f3b78a619fd5386932b63d2d5ff30f42121bd6c8e | 2026-01-23T00:00:00-05:00 | An analogue of Bonami's Lemma for functions on spaces of linear maps, and 2-2 Games | arXiv:2209.04243v2 Announce Type: replace Abstract: We prove an analogue of Bonami's (hypercontractive) lemma for complex-valued functions on $\mathcal{L}(V,W)$, where $V$ and $W$ are vector spaces over a finite field. This inequality is useful for functions on $\mathcal{L}(V,W)$ whose `generalised influences' are smal... | https://arxiv.org/abs/2209.04243 | Academic Papers | svg |
7c1dc9f9ceebd3b4e470be9b513a05b88514699199545f34fa02081351ac6c59 | 2026-01-23T00:00:00-05:00 | Fibrantly-transferred model structures | arXiv:2301.07801v2 Announce Type: replace Abstract: We develop new techniques for constructing model structures from a given class of cofibrations, together with a class of fibrant objects and a choice of weak equivalences between them. As a special case, we obtain a more flexible version of the classical right-transfe... | https://arxiv.org/abs/2301.07801 | Academic Papers | svg |
91307ac24559888f1a3408ac24bc69711238e8d99bf3f7bc1b6d535b26244b84 | 2026-01-23T00:00:00-05:00 | Determinantally equivalent nonzero functions | arXiv:2302.02471v4 Announce Type: replace Abstract: We study the problem raised in [Marco Stevens, Equivalent symmetric kernels of determinantal point processes, RMTA, 10(03):2150027, 2021] concerning the extension of its main result to the more general (potentially non-symmetric) setting. We construct a counterexample... | https://arxiv.org/abs/2302.02471 | Academic Papers | svg |
84274be276f825ea350d40891aa69d7affbde5b8215e5653ef3a5d83ff03ee30 | 2026-01-23T00:00:00-05:00 | Hopf 2-algebras and Braided Monoidal 2-Categories | arXiv:2304.07398v4 Announce Type: replace Abstract: Following the theory of principal $\infty$-bundles of Niklaus-Schreiber-Steveson, we develop a homotopy categorification of Hopf algebras, which model quantum groups. We study their higher-representation theory in the setting of $\mathsf{2Vect}^{hBC}$, which is a homo... | https://arxiv.org/abs/2304.07398 | Academic Papers | svg |
2cca507e186812f375bf2ed45d5fcc377ee95bf3f8f17c80000f2c2458f46102 | 2026-01-23T00:00:00-05:00 | Nijenhuis operators on 2D pre-Lie algebras and 3D associative algebras | arXiv:2308.12121v3 Announce Type: replace Abstract: In this paper, we describe all Nijenhuis operators on 2-dimensional complex pre-Lie algebras and 3-dimensional complex associative algebras. As an application, using these operators, we obtain solutions of the classical Yang-Baxter equation on the corresponding sub-ad... | https://arxiv.org/abs/2308.12121 | Academic Papers | svg |
6995d2e125a0f7b56bfba46745d5e70253fba1a09a374ab07683d41c03d99226 | 2026-01-23T00:00:00-05:00 | K\"{a}hler Solitons, Contact Structures, and Isoparametric Functions | arXiv:2310.11328v3 Announce Type: replace Abstract: All known examples of simply-connected gradient K\"{a}hler-Ricci soliton in real dimension four are toric, and the symmetry is intrinsically related to the potential function $f$ and the scalar curvature $\SS$. In this article, we consider the case that $f$ and $\SS$ ... | https://arxiv.org/abs/2310.11328 | Academic Papers | svg |
0e7a959c074b596c8d55547493d224c5e755e75d1b017383ae5345def16fab4c | 2026-01-23T00:00:00-05:00 | Sharp quantitative stability for the fractional Sobolev trace inequality | arXiv:2312.01766v3 Announce Type: replace Abstract: In this paper, we study the stability of fractional Sobolev trace inequality within both the functional and critical point settings. In the functional setting, we establish the following sharp estimate: $$C_{\mathrm{BE}}(n,m,\alpha)\inf_{v\in\mathcal{M}_{n,m,\alpha}}\... | https://arxiv.org/abs/2312.01766 | Academic Papers | svg |
5a25d7f64f86499870887ec90f37791113898190d22d52fc731ceffe49e6abbe | 2026-01-23T00:00:00-05:00 | Classification of positive solutions to the H\'enon-Sobolev critical systems | arXiv:2312.01784v2 Announce Type: replace Abstract: In this paper, we investigate positive solutions to the following H\'enon-Sobolev critical system: $$ -\mathrm{div}(|x|^{-2a}\nabla u)=|x|^{-bp}|u|^{p-2}u+\nu\alpha|x|^{-bp}|u|^{\alpha-2}|v|^{\beta}u\quad\text{in }\mathbb{R}^n,$$ $$ -\mathrm{div}(|x|^{-2a}\nabla v)=|x... | https://arxiv.org/abs/2312.01784 | Academic Papers | svg |
3ba1f8e61e33f8472ba6088968ce163bee4048253faf3ce945aab44062a84926 | 2026-01-23T00:00:00-05:00 | Differential operators on the base affine space of $SL_n$ and quantized Coulomb branches | arXiv:2312.10278v2 Announce Type: replace Abstract: We show that the algebra $D_\hbar(SL_n/U)$ of differential operators on the base affine space of $SL_n$ is the quantized Coulomb branch of a certain 3d $\mathcal{N} = 4$ quiver gauge theory. In the semiclassical limit this proves a conjecture of Dancer-Hanany-Kirwan a... | https://arxiv.org/abs/2312.10278 | Academic Papers | svg |
a32a8923e7697669d49425b0f5cd5c85f88004a80aa5df21f8aed521a547eb88 | 2026-01-23T00:00:00-05:00 | The stability on the Caffarelli-Kohn-Nirenberg and Hardy-type inequalities and beyond | arXiv:2312.15735v3 Announce Type: replace Abstract: In this paper, we establish several improved Caffarelli-Kohn-Nirenberg and Hardy-type inequalities. Our main results are divided into two parts. In the first part, we consider the following Caffarelli-Kohn-Nirenberg inequality: \begin{equation*} \left(\int_{\mathbb{R}... | https://arxiv.org/abs/2312.15735 | Academic Papers | svg |
498a896b88ebb8044899c3dd7d0f49177dd05b49158d963cc3b9de4f53ba45e2 | 2026-01-23T00:00:00-05:00 | Recursion relations and BPS-expansions in the HOMFLY-PT skein of the solid torus | arXiv:2401.10730v2 Announce Type: replace Abstract: Inspired by the skein valued open Gromov-Witten theory of Ekholm and Shende and the Gopakumar-Vafa formula, we associate to each pair of non-negative integers $(g,l)$ a formal power series with values in the HOMFLY-PT skein of a disjoint union of $l$ solid tori. The f... | https://arxiv.org/abs/2401.10730 | Academic Papers | svg |
e4dcfcc168c5a96d6d78bf707e7b3aafd2dc13b31814508a8e5ace8bea0df5b0 | 2026-01-23T00:00:00-05:00 | Operational Methods Applied to the Spherical Mean and X-Ray Transform | arXiv:2402.10272v4 Announce Type: replace Abstract: We employ the framework of operational calculus to derive the operators associated with the spherical mean and a class of related averaging means of a function in $n$-dimensional space. Beginning with the classical definition of the spherical mean, we obtain a compact... | https://arxiv.org/abs/2402.10272 | Academic Papers | svg |
ea2743ada965213e1103f5206279edef28d5cd5317ae293ff4149f8fe44625be | 2026-01-23T00:00:00-05:00 | Toughness and A{\alpha}-spectral radius in graphs | arXiv:2402.17421v2 Announce Type: replace Abstract: Let $\alpha\in[0,1)$, and let $G$ be a connected graph of order $n$ with $n\geq f(\alpha)$, where $f(\alpha)=6$ for $\alpha\in[0,\frac{2}{3}]$ and $f(\alpha)=\frac{4}{1-\alpha}$ for $\alpha\in(\frac{2}{3},1)$. A graph $G$ is said to be $t$-tough if $|S|\geq tc(G-S)$ f... | https://arxiv.org/abs/2402.17421 | Academic Papers | svg |
4bc3b48d4b22b1fcde32058475087af44aba26b10befe440cf78ce7e8d0b078e | 2026-01-23T00:00:00-05:00 | Unipotent normal subgroups of algebraic groups | arXiv:2404.12221v2 Announce Type: replace Abstract: Let $G$ be an affine algebraic group scheme over a field $k$. We show there exists a unipotent normal subgroup of $G$ which contains all other such subgroups; we call it the restricted unipotent radical $\mathrm{Rad}_u(G)$ of $G$. We investigate some properties of $\m... | https://arxiv.org/abs/2404.12221 | Academic Papers | svg |
867be02539a8e9e05683fec1f39be1b8ba8e829569ca592e8e5285854bb0a19a | 2026-01-23T00:00:00-05:00 | Fujita-Kato Solutions and Optimal Time Decay for the Vlasov-Navier-Stokes System in the Whole Space | arXiv:2405.09937v2 Announce Type: replace Abstract: We are concerned with the construction of global-in-time strong solutions for the incompressible Vlasov-Navier-Stokes system in the whole three-dimensional space. One of our goals is to establish that small initial velocities with critical Sobolev regularity and suffi... | https://arxiv.org/abs/2405.09937 | Academic Papers | svg |
7c13e044a1f13b062049183ceb31b81ecfdee2aa6396da8890275d144c08602a | 2026-01-23T00:00:00-05:00 | A combinatorial interpretation of the Bernstein degree of unitary highest weight modules | arXiv:2405.18766v2 Announce Type: replace Abstract: Consider the $(\mathfrak{g}, K)$-modules $L_{\lambda}$ for unitary highest weight representations of the real reductive group $G_{\mathbb{R}} = \operatorname{U}(p,q)$, $\operatorname{Mp}(2n, \mathbb{R})$, or $\operatorname{O}^*(2n)$, where $\operatorname{Mp}(2n,\mathb... | https://arxiv.org/abs/2405.18766 | Academic Papers | svg |
0d0a061047bdf657645b0f53c9b08ff2c3c621b14c8d52da84f128f624ec3475 | 2026-01-23T00:00:00-05:00 | Crossed product splitting of intermediate operator algebras via 2-cocycles | arXiv:2406.00304v2 Announce Type: replace Abstract: We investigate the C*-algebra inclusions $B \subset A \rtimes_{\rm r} \Gamma$ arising from inclusions $B \subset A$ of $\Gamma$-C*-algebras. The main result shows that, when $B \subset A$ is C*-irreducible in the sense of R{\o}rdam, and is centrally $\Gamma$-free in t... | https://arxiv.org/abs/2406.00304 | Academic Papers | svg |
1e9b23ed79f112b2261f7ce1ae382f229aa88432e7186b94f67d08c8ed966a1b | 2026-01-23T00:00:00-05:00 | Surface groups among cubulated hyperbolic and one-relator groups | arXiv:2406.02121v3 Announce Type: replace Abstract: Let $X$ be a non-positively curved cube complex with hyperbolic fundamental group. We prove that $\pi_1(X)$ has a non-free subgroup of infinite index unless $\pi_1(X)$ is either free or a surface group, answering questions of Gromov and Whyte (in a special case) and W... | https://arxiv.org/abs/2406.02121 | Academic Papers | svg |
67aab8bc7b5b786b0ec039c8755da705ac7060635bb164633b7fa1dbd6c395fc | 2026-01-23T00:00:00-05:00 | Exact worst-case convergence rates of gradient descent: a complete analysis for all constant stepsizes over nonconvex and convex functions | arXiv:2406.17506v2 Announce Type: replace Abstract: We consider gradient descent with constant stepsizes and derive exact worst-case convergence rates on the minimum gradient norm of the iterates. Our analysis covers all possible stepsizes and arbitrary upper/lower bounds on the curvature of the objective function, thu... | https://arxiv.org/abs/2406.17506 | Academic Papers | svg |
bba13ed0be86d12b3eec01b1d833debcb91bb09994c5b739b2c27a931a5e6173 | 2026-01-23T00:00:00-05:00 | The convergence and uniqueness of a discrete-time nonlinear Markov chain | arXiv:2407.00314v2 Announce Type: replace Abstract: In this paper, we prove the convergence and uniqueness of a general discrete-time nonlinear Markov chain with specific conditions. The results have important applications in discrete differential geometry. First, we prove the discrete-time Ollivier Ricci curvature flo... | https://arxiv.org/abs/2407.00314 | Academic Papers | svg |
12905aff395719eab222d17dd7fc595a47a9958219253b089e731eab4abdc86f | 2026-01-23T00:00:00-05:00 | Degenerate stability of critical points of the Caffarelli-Kohn-Nirenberg inequality along the Felli-Schneider curve | arXiv:2407.10849v2 Announce Type: replace Abstract: In this paper, we investigate the validity of a quantitative version of stability for the critical Hardy-H\'enon equation \begin{equation*} H(u):=\div(|x|^{-2a}\nabla u)+|x|^{-pb}|u|^{p-2}u=0,\quad u\in D_a^{1,2}(\R^n), \end{equation*} \begin{equation*} n\geq 2,\quad ... | https://arxiv.org/abs/2407.10849 | Academic Papers | svg |
57d996392544a3134e60f99c6c482a2478cd3d1a2b59671df009c061e3a4590c | 2026-01-23T00:00:00-05:00 | Polynomials Counting Group Colorings in Graphs | arXiv:2409.12404v5 Announce Type: replace Abstract: Jaeger et al. in 1992 introduced group coloring as the dual concept to group connectivity in graphs. Let $A$ be an additive Abelian group, $ f: E(G)\to A$ and $D$ an orientation of a graph $G$. A vertex coloring $c:V(G)\to A$ is an $(A, f)$-coloring if $c(v)-c(u)\ne f... | https://arxiv.org/abs/2409.12404 | Academic Papers | svg |
9df6e0be5126fa6b83b081ce346f007678db66469d0020eabcbf09ac99447bf4 | 2026-01-23T00:00:00-05:00 | The Hilbert scheme of points on a threefold: broken Gorenstein structures and linkage | arXiv:2409.17009v2 Announce Type: replace Abstract: We investigate the Hilbert scheme of points on a smooth threefold. We introduce a notion of broken Gorenstein structure for finite schemes, and show that its existence guarantees smoothness on the Hilbert scheme. Moreover, we conjecture that it is exhaustive: every sm... | https://arxiv.org/abs/2409.17009 | Academic Papers | svg |
c33ece82a4af351865836097a13a58f8833fefacf052d7349636b94c8012890e | 2026-01-23T00:00:00-05:00 | On Ulam widths of finitely presented infinite simple groups | arXiv:2410.07512v2 Announce Type: replace Abstract: A fundamental notion in group theory, which originates in an article of Ulam and von Neumann from $1947$ is uniform simplicity. A group $G$ is said to be $n$-uniformly simple for $n \in \mathbf{N}$ if for every $f,g\in G\setminus \{id\}$, there is a product of no more... | https://arxiv.org/abs/2410.07512 | Academic Papers | svg |
cb7d04200ee1e088276b707783217bfa9249d8d8c50ff482213014c08de292d6 | 2026-01-23T00:00:00-05:00 | Sobolev estimates for the Keller-Segel system and applications to the JKO scheme | arXiv:2410.15095v3 Announce Type: replace Abstract: We prove $L^{\infty}_{t}W^{1,p}_{x}$ Sobolev estimates in the Keller-Segel system with linear diffusion in any dimensionby proving a functional inequality, inspired by the Brezis-Gallou\"et-Wainger inequality. These estimates are also valid at the discrete level in th... | https://arxiv.org/abs/2410.15095 | Academic Papers | svg |
be1d61daa00b27981f7885aaa24fec7f99a5e42f486cef03d7d8a324a93020a6 | 2026-01-23T00:00:00-05:00 | The Calder\'on problem for third order nonlocal wave equations with time-dependent nonlinearities and potentials | arXiv:2411.08657v3 Announce Type: replace Abstract: In this article, we study the Calder\'on problem for nonlocal generalizations of the semilinear Moore--Gibson--Thompson (MGT) equation and the Jordan--Moore--Gibson--Thompson (JMGT) equation of Westervelt-type. These partial differential equations are third order wave... | https://arxiv.org/abs/2411.08657 | Academic Papers | svg |
e933765a38ae678f784d069207e7feec8947d73f01f4636fa097de4c338aaa7d | 2026-01-23T00:00:00-05:00 | Berkovich Motives | arXiv:2412.03382v3 Announce Type: replace Abstract: We construct a theory of (etale) Berkovich motives. This is closely related to Ayoub's theory of rigid-analytic motives, but works uniformly in the archimedean and nonarchimedean setting. We aim for a self-contained treatment, not relying on previous work on algebraic... | https://arxiv.org/abs/2412.03382 | Academic Papers | svg |
6836316dec9c30d7cd438494c4f1d02965e88f721ca6151a0fb7bb8584e8373c | 2026-01-23T00:00:00-05:00 | On a class of Nonlinear Grushin equations | arXiv:2412.08039v2 Announce Type: replace Abstract: In this paper, we study two kinds of nonlinear degenerate elliptic equations containing the Grushin operator. First, we prove radial symmetry and a decay rate at infinity of solutions to such a Grushin equation by using the moving plane method in combination with suit... | https://arxiv.org/abs/2412.08039 | Academic Papers | svg |
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