arXiv preprints from January 1, 2026 through September 8, 2026 — 09:54:00 EST
Given an (affine) integral arrangement $\mathcal{A}$ in $\mathbb{R}^n$, the reduction of $\mathcal{A}$ modulo an arbitrary positive integer $q$ naturally yields an arrangement $\mathcal{A}_q$ in $\mathbb{Z}_q^n$. Our primary objective is to study the combinatorial aspects of the restriction $\mathcal{A}^{(B,\bm b)}$ to the solution...
Diamond open access journals charge neither readers nor authors. Despite long-standing support for this ideal within mathematics, relatively few such journals exist. This article documents the Association for Mathematical Research's experience building and operating diamond open access journals, focusing on the infrastructure, cost,...
We study nonlinear elliptic equations that arise as stationary states of inhomogeneous nonlinear Schrödinger equations with competing singular nonlinearities. The model involves the Laplacian combined with weighted power-type terms and naturally leads to a variational formulation in a weighted Sobolev space obtained from the...
We study the 2-systole on compact Kähler surfaces of positive scalar curvature. For any such surface $(X,ω)$, we prove the sharp estimate $\min_X S(ω)\cdot\operatorname{sys}_2(ω)\le 12π$, with equality if and only if $X=\mathbb{P}^2$ and $ω$ is the Fubini-Study metric. Using the classification of positive scalar curvature Kähler...
We propose a single-loop variance-reduced acceleration framework, which relates checkpoint update probabilities to momentum parameters, for solving the composite general convex problem where the smooth part has the finite-sum structure. Under the proposed framework, the growth rate of the momentum parameter is further altered,...
Dwyer-Kan localization at pairs of quasi-isomorphisms of the category of dg Lie-Rinehart pairs $(A,M)$, where $A$ is a semi-free cdga over a field $k$ of characteristic zero and $M$ a cell complex in $A$-modules, is shown to be equivalent to that of strong homotopy Lie-Rinehart (SH LR) pairs satisfying the same cofibrancy condition....
We study fractional evolution equations driven by rational-kernel time operators with non-singular memory, including the Atangana-Baleanu-Caputo operator and a generalized W-operator. These operators are characterized by Laplace symbols that do not necessarily belong to the classical Bernstein class. The analysis is carried out in the...
A constructive method is given for obtaining cospectral vertices in undirected graphs, along with an operation that preserves this construction. We prove that the construction yields cospectral vertices, as well as strongly cospectral vertices under additional conditions. Furthermore, we generalize cospectral vertices to the case of...
We introduce a new two-parameter fractional time operator with Volterra structure, denoted by ${}^{W}D_{t}^{α,β}$, defined through the Laplace symbol \[ Φ_{α,β}(s) = \frac{s^α}{\bigl(1+(1-α)s^{α-1}\bigr)^β}, \qquad 0<α<1, \ β\ge0. \] The operator preserves the Caputo-type high-frequency behavior while allowing a controlled...
We exhibit new biorthogonal sequences generated by index integrals of the squares of the modified Bessel functions and gamma functions. The composition orthogonality, involving differential operators is employed. Generalized Wilson polynomials are introduced. Some properties are investigated.
We investigate the Cauchy-Dirichlet problem for linear parabolic equations in divergence form. Under mild assumptions on the source term and the domain, we prove the existence of globally Hölder continuous solutions. Notably, our results accommodate data exhibiting singularities nearly as critical as the inverse square of the distance...
We prove an upper bound for the Morse index of min-max stationary integral varifolds realizing the $d$-dimensional $p$-width of a closed Riemannian manifold.
For a given second order elliptic operation $\mathcal{L}$ in a domain $Ω\subset{\mathbb{R}}^\mathbf{N}$, $\mathbf{N}\ $, and a compact set $\mathbf{K}\subsetΩ$, order $\mathbf{N}$-$2$-Ahlfors-David regular, we define the space $\mathcal{H}^{\mathbf{r}+ω}_{\mathcal{L}}(\mathbf{K})$ of continuous functions $f(x),\, x\in\mathbf{K}$,...
Using a modified curve shortening flow, we construct $λ$-Angenent curve, which was first constructed by the shooting method.
We study traces of Hecke operators on spaces of elliptic cusp forms and Drinfeld cusp forms and show that, modulo any prime power, these traces are periodic in the weight.
We consider the policy gradient adaptive control (PGAC) framework, which adaptively updates a control policy in real time, by performing data-based gradient descent steps on the linear quadratic regulator cost. This method has empirically shown to react to changing circumstances, such as model parameters, efficiently. To formalize...
Recent studies have shown that fractional calculus is an effective alternative mathematical tool in various scientific fields. However, some investigations indicate that results established in differential and integral calculus do not necessarily hold true in fractional calculus. In this work we will compare various methods presented...
Registration methods in bounded domains have received significant attention in the model reduction literature, as a valuable tool for nonlinear approximation. The aim of this work is to provide a concise yet complete overview of relevant results for registration methods in $n$-dimensional domains, from the perspective of parametric...
We study binary optimization problems of the form \( \min_{x\in\{-1,1\}^n} f(Ax-b) \) with possibly nonsmooth loss \(f\). Following the lifted rank-one semidefinite programming (SDP) approach\cite{qian2023matrix}, we develop a majorization-minimization algorithm by using the difference-of-convexity (DC) reformuation for the rank-one...
In this paper, we study backward stochastic differential equations driven by G-Brownian motion where the generator has time-varying monotonicity with respect to y and Lipsitz property with respect to z. Through the Yosida approximation, we have proved the existence and uniqueness of the solutions to these equations.
A non-trivial topological group is called \emph{$d$-independent} if for every subgroup of cardinality less than the continuum there exists a countable dense subgroup intersecting it trivially. This notion was introduced by Márquez and Tkachenko and has been intensively studied in the metrizable setting. In particular, they proved that...
Bojańczyk, Pilipczuk, and Grohe [LICS '18] proved that for graphs of bounded linear clique-width, clique-decompositions of bounded width can be produced by a CMSO transduction. We show that in the case of tournaments, a first-order transduction suffices. This implies that the logics CMSO and existential MSO are equivalent over bounded...
Lawler and Trujillo Ferreras constructed a well-known coupling between the Brownian loop soups on $\mathbb{R}^2$ and the (discrete-time) random walk loop soups on $\mathbb{Z}^2$ (one rescales the random walk loops by $1/N$, their time parametrizations by $1/(2N^2)$, and lets $N\to \infty$), which led to numerous applications. It...
For every flat surface, almost every flat surface in its $\mathsf{SL}(2,\mathbb{R})$ orbit has the following property: the sequence of its saddle connection lengths in non-decreasing order is uniformly distributed in the unit interval.
To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional constant-coefficient elliptic equations with both divergence and non-divergence forms and all types of...