arXiv preprints from January 1, 2026 through September 8, 2026 — 13:56:40 EST
We show that on a compact complex surface all Massey products of cohomology classes in degree one vanish beyond length three. Dually, the real Malcev completion of the fundamental group is homogeneously presented by quadratic and cubic relations. In the non-Kähler case, we give an explicit presentation, which is determined by the...
In this paper, we introduce the notion of modified Rota-Baxter operators of non-zero weight on $3$-Lie algebras and provide some examples. Next, we give various constructions of modified Rota-Baxter operators of non-zero weight according to constructions of $3$-Lie algebras. Furthermore, we define a cohomology of modified Rota-Baxter...
The families $\mathcal{A}$ and $\mathcal{B}$ are cross intersecting if $A\cap B\ne \emptyset$ for any $A\in \mathcal{A}$ and $B\in \mathcal{B}$. Let $t\geq 2$ and $k_1\geq k_2\geq \cdots \geq k_t$. We say that $(\mathcal{F}_1, \dots, \mathcal{F}_t)$ is an $(n, k_1, \dots, k_t)$-cross intersecting system if $\mathcal{F}_1...
This paper presents a comprehensive analysis of several aspects of the sinh-Gordon equation within a periodic setting. Our investigation proceeds in three main stages. First we establish the existence of periodic solutions for a fixed wave speed and varying periods by applying the mountain pass theorem. Subsequently, for a fixed...
Let $Γ$ be a signed graph. The number of negative eigenvalues of the adjacency matrix of $Γ$ is called the negative inertia index of $Γ$, which is denoted by $i_-(Γ)$. The length of the shortest cycle contained in $Γ$ is called the girth of $Γ$, and it is denoted by $g$. In this paper, we give some classes of connected signed graphs...
Hardy showed that $\sum_{n \ioe x}τ(n)-x(\log x +2γ-1)$ is not $o(x^{1/4})$. In this article, we prove that $\sum_{n \ioe x}τ(n)(1-\frac{x}{n})-xP(\log x)=\frac{1}{4}+O \left( \frac{\log x}{x^{1/4}} \right)$, where $P$ is a polynomial of degree 2. As a corollary, this estimate enables us to settle a conjecture surmised by Berkane,...
We develop a structure-preserving ADMM method, denoted SP-ADMM, for learning energy-stable spatial derivative stencils for Maxwell equations from noisy data. Starting from the source-free Maxwell system, we focus on a one-dimensional reduction whose energy conservation depends on the skew-adjointness of the spatial derivative...
We establish dimension-free quantum Talagrand-type inequalities with explicit constants on the quantum Boolean cube, via a unified variance-decay perspective. For individual observables, short-time variance decay along the depolarizing semigroup, with rates estimated through hypercontractivity, naturally yields Talagrand-type bounds....
In this paper, we combine Bochner formula, Saloff-Coste's Sobolev inequality and the Nash-Moser iteration method to study the local and global behaviors of solutions to the nonlinear elliptic equation $Δ_pu+Δ_qu+h(u,|\nabla u|^2)=0$ defined on a complete Riemannian manifold $\left(M,g\right)$, where $q\ge p>1$, $h\in...
We propose a new unstructured numerical subgrid method for solving the shallow water equations using a finite volume method with enhanced bathymetry resolution. The method employs an unstructured triangular mesh with support for triangulation of elements to form finer subgrids locally. The bathymetry is represented on the fine mesh,...
This article investigates time-discrete approximations of Allen-Cahn type SPDEs driven by space-time white noise near the sharp interface limit $ε\to 0$, where the small parameter $ε$ is the diffuse interface thickness. We propose an explicit and easily implementable exponential integrator with a modified nonlinearity for the...
The time-space fractional cable equation arises from extending the generalized fractional Ohm's law to model anomalous diffusion processes. In this paper, we develop and analyze a numerical approximation for stochastic nonlinear time-space fractional cable equation driven by rough noise. The model involves both two nonlocal terms in...
We study a homological epimorphism of proper dg algebras and show that if the source is a finite dimensional piecewise hereditary algebra, then the target is derived equivalent to some piecewise hereditary algebra.
This paper probes the dispersive shock waves (DSWs) theory in nonlinear optical systems through Whitham modulation theory for the high-order Chen-Lee-Liu (HOCLL) equation. We systematically derived the one-phase periodic solutions and the corresponding Whitham equations. For all feasible initial discontinuous conditions, we delineate...
We investigate the $L^p$ mapping properties of maximal functions associated with analytic hypersurfaces in $\mathbb R^d$, with a particular emphasis on the role of transversality. Around points that are not transversal, we show that the associated maximal function is bounded on $L^p(\mathbb R^d)$ for all $p>2$, regardless of the decay...
Born from years of teaching undergraduate and graduate algebra courses at Chongqing University, this text is designed to introduce Galois theory while minimizing prerequisites. It seeks to reconnect the abstract machinery of modern algeba: groups, rings, and fields with the historical problem that inspired its creation: determining...
This paper introduces a new theoretical framework for analyzing lead-lag relationships between point processes, with a special focus on applications to high-frequency financial data. In particular, we are interested in lead-lag relationships between two sequences of order arrival timestamps. The seminal work of Dobrev and Schaumburg...
We study the hydrodynamics of compressible active nematic liquid crystals in a three-dimensional and bounded domain, with a nonlinear viscosity tensor and nonhomogeneous boundary data, in a Landau-de Gennes framework. We prove the existence of dissipative solutions within a Beris-Edwards type model for active nematodynamics, which are...
Models of reaction diffusion processes usually employ discrete lattice models with particles interacting at the same site, resulting in localized reactions in the continuum limit. Here, various non-local interactions are considered, and two features reported. Firstly, it is shown that sufficiently non-local interactions will regulate...
We develop a Bochner theory and Bakry-Emery calculus for horizontal Laplacians associated with general Riemannian foliations. No bundle-like assumption on the metric, nor any total geodesicity or minimality condition on the leaves is imposed. Using a metric connection adapted to the horizontal-vertical splitting, we derive explicit...
We give closed formulas for the first few expansion coefficients of the basic modular forms for \(\mathrm{GL}(r, \mathbb{F}_{q}[T])\). Here the rank \(r\) is larger or equal to \(3\), and the forms in question include the coefficient forms \(g_{1}, \dots, g_{r}\) and the Eisenstein series \(E_{q^{i}-1}\) (\(i \in \mathbb{N}\)).
We study the asymptotic behaviour of modified weighted power variations of the Hermite process of arbitrary order. By selecting suitable "good" increments and exploiting their decomposition into dominant independent components, we establish a central limit theorem for weighted $p$-variations using tools from Stein-Malliavin calculus....
In this paper, we investigate the problem of prescribing Chern scalar curvatures on complete noncompact Hermitian manifolds with nonpositive curvatures, and establish some existence results. In particular, we obtain some sufficient conditions for the existence of a constant negative Chern scalar curvature metric in the conformal class.
We justify the global-in-time validity of Hilbert expansion for the ionic Vlasov-Poisson-Boltzmann system in $\mathbb{R}^3$, a fundamental model describing ion dynamics in dilute collisional plasmas. As the Knudsen number approaches zero, we rigorously derive the compressible Euler-Poisson system governing global smooth irrotational...
In this article, we develop the theory of stratified perverse Nori motives to prove a refinement of the geometric Satake equivalence of Mirković-Vilonen, for which we call the Nori motivic Satake equivalence, in contrast to the "Tate motivic" Satake equivalence of Richarz-Scholbach.