arXiv preprints from January 1, 2026 through July 21, 2026 — 18:33:51 EST
In this paper, we introduce two new forms of the dual Hartwig-Spindelb{ö}ck decomposition and employ them to derive explicit representations for several classes of dual generalized inverses. Building on these representations, we further explore and characterize the relationships and properties of these inverses, investigate the dual...
This paper investigates the regularity of Lipschitz solutions $u$ to the general two-dimensional equation $\text{div}(G(Du))=0$ with highly degenerate ellipticity. Just assuming strict monotonicity of the field $G$ and heavily relying on the differential inclusions point of view, we establish a pointwise gradient localization theorem...
Straight-line programs are a central tool in several areas of computer science, including data compression, algebraic complexity theory, and the algorithmic solution of algebraic equations. In the algebraic setting, where straight-line programs can be interpreted as circuits over algebraic structures such as semigroups or groups, they...
We study the mass-conserved reaction-diffusion system known as the wave-pinning model, which serves as a minimal framework for describing cell polarity. In this model, the interplay between reaction kinetics and slow diffusion forms a sharp interface that partitions the domain into high- and low-concentration regions. We perform a...
We prove an infinite family of linear identities for the number $A_5(n)$ of partition pairs of $n$ with $5$-cores by using certain theta function identities involving the Ramanujan's parameter $k(q)$ due to Cooper, and Lee and Park. Consequently, we deduce an infinite family of congruences for $A_5(n)$ using these linear identities.
In this paper, we provide the strong rate of convergence for the Euler--Maruyama scheme for multi-dimensional stochastic differential equations with uniformly locally (unbounded) Hölder continuous drift and multiplicative noise. Our technique is based on Itô--Tanaka trick (Zvonkin transformation) for unbounded drift. Moreover, in...
We propose an estimator of a concave cumulative distribution function under the measurement error model, where the non-negative variables of interest are perturbed by additive independent random noise. The estimator is defined as the least concave majorant on the positive half-line of the deconvolution estimator of the distribution...
We consider the fast-reaction approximation to the triangular Shigesada-Kawasaki-Teramoto model on a bounded domain in the physical dimension $d\le 3$. We provide explicit convergence rates on the whole domain in $\textnormal{L}^\infty\textnormal{L}^2\cap\textnormal{L}^2\textnormal{H}^1$ and in the interior we prove convergence with...
The aim of this paper is to give an elementary proof that Hermite expensions of a function $f$ in the modulation space $M^p(R)$ converges to $f$ in $M^p(R)$ when $1< p<+\infty$ and may diverge when $p = 1,\infty$. The result was previously established for $1< p<+\infty$ by Garling and Wojtaszczyk and for $p = 1,\infty$ by Lusky in an...
An example originally given by F.~Delon shows the existence of an algebraically maximal discretely valued field of characteristic $p>0$ which admits purely inseparable extensions of degree $p^2$ with defect $p$. These extensions are not generated by a single element. Using a trick introduced in an earlier paper of the author, we...
The existence of a finite global attractor for polynomial curve system has been known since the work of Belk et al. [5]. However, except in the hyperbolic case, the rate at which the pullback of a curve under a polynomial converges to the attractor remained unclear. In this paper, we introduce the notions of $\textit{quick returns}$...
We observe that the distribution of the eigenvalues of an $N$-by-$N$ GUE random matrix is log-concave on $\mathbb{R}^N$, and that the same is true for the law of a single gap between two consecutive eigenvalues. We use this observation to prove several concentration bounds for the semicircle-renormalised eigengaps, improving on bounds...
In this work, we present a comprehensive theoretical analysis for Virtual Element discretizations of incompressible non-Newtonian flows governed by the Carreau-Yasuda constitutive law, in the shear-thickening regime (r > 2) including both degenerate (delta = 0) and non-degenerate (delta > 0) cases. The proposed Virtual Element method...
This article proposes a method for forming invariant stochastic differential systems, namely dynamic systems with trajectories belonging to a given smooth manifold. The Itô or Stratonovich stochastic differential equations with the Wiener component describe dynamic systems, and the manifold is implicitly defined by a differentiable...
Under reasonable algebraic assumptions and under an infinite second order moment assumption, we show that the logarithm of the norm (log-norm) of a product of random i.i.d. matrices with entries in $\mathbb{R}$ or in any other local field satisfies a generalized Central Limit Theorem (GCLT) in the sense of Paul Lévi. The proof is...
In this article, we present several formulas that make it easier to compute the net single premiums when the mortality force over the fractional ages is assumed to be constant (C). More precisely, we compute the moments of the random variables $ν^{T_x}$, $T_x$, $T_xν^{T_x}$, etc., where $T_x$ denotes the future lifetime of a person...
We are concerned with the following doubly degenerate nutrient taxis system \begin{align} \begin{cases}\tag{$\star$}\label{eq-0.1} u_t=\nabla\cdot(u v\nabla u)-\nabla\cdot(u^{2} v\nabla v)+u-u^2,\\[1mm] v_t=Δv-u v, \end{cases} \end{align} posed in a bounded smooth domain $Ω\subset\mathbb{R}^2$ under homogeneous Neumann boundary...
We study Brownian loop soup clusters in $\mathbb{R}^3$ for an arbitrary intensity $α>0$. We show the existence of a phase transition for the presence of unbounded clusters and study its basic properties. In particular, we show that, when $α$ is sufficiently large, almost surely all the loops are connected into a single cluster. Such a...
This paper presents a finite element method that preserves (at the degrees of freedom) the eigenvalue range of the solution of tensor-valued time-dependent convection--diffusion equations. Starting from a high-order spatial baseline discretisation (in this case, the CIP stabilised finite element method), our approach formulates the...
Ultametrics are an important class of distances used in applications such as phylogenetics, clustering and classification theory. Ultrametrics are essentially distances that can be represented by an edge-weighted rooted tree so that all of the distances in the tree from the root to any leaf of the tree are equal. In this paper, we...
In the sufficiently sparse case, we find the probability that a uniformly random bipartite graph with given degree sequence contains no edge from a specified set of edges. This enables us to enumerate loop-free digraphs and oriented graphs with given in-degree and out-degree sequences, and obtain subgraph probabilities. Our theorems...
We investigate the following two-species chemotaxis system with two chemicals involving flux-limitation \begin{align}\tag{$\star$} \begin{cases} u_t = Δu - \nabla \cdot \left(u(1+|\nabla v|^2)^{-\frac{p}{2}}\nabla v\right), & x \in Ω, \ t > 0, \\ 0 = Δv - μ_w + w, \quad μ_{w}=f_Ω w, & x \in Ω, \ t > 0, \\ w_t = Δw - \nabla \cdot...
Let $λ$, $μ$, $λ'$, $μ'$ be partitions. The conjecture of Lam, Postnikov and Pylyavskyy states that, if $λ+μ= λ' + μ'$, and $\min(λ_i-λ_j, μ_i-μ_j) \leq λ'_i - λ'_j \leq \max(λ_i-λ_j, μ_i-μ_j)$ for all $1 \leq i<j \leq n$, then $s_{λ'} s_{μ'} - s_λ s_μ$ is Schur nonnegative. We prove this conjecture. Our proof is based on two key...
Cartoon-texture image decomposition is a critical preprocessing problem bottlenecked by the numerical intractability of classical variational or optimization models and the tedious manual tuning of global regularization parameters.We propose a Guided Variational Decomposition (GVD) model which introduces spatially adaptive quadratic...
We study the non-equilibrium stationary fluctuations of a symmetric zero-range process on the discrete interval $\{1, \ldots, N-1\}$ coupled to reservoirs at sites $1$ and $N-1$, which inject and remove particles at rates proportional to $N^{-θ}$ for any value of $θ\in\mathbb{R}$. We prove that, if the jump rate is bounded and under...