arXiv preprints from January 1, 2026 through September 22, 2026 — 09:56:47 EST
Guo and Royle recently classified the connected cubic graphs without eigenvalues of their adjacency matrix in the open interval $(-1, 1)$, and raised the question of extending their classification to graphs of maximum degree at most $3$. They carried out a preliminary investigation of the subcubic case, exhibiting both infinite...
We recently characterized the separated determinantal point processes $Λ_φ$ associated with Fock spaces $\mathcal F_φ$ in the plane with doubling weight $φ$. We also showed that, as expected, a more restrictive condition is required to characterize the separated Poisson processes with the same first intensities as $Λ_φ$. To gain...
Estimating causal effects of continuous treatments is a common problem in practice, for example, in studying average dose-response functions. Classical analyses typically assume that all confounders are fully observed, whereas in real-world applications, unmeasured confounding often persists. In this article, we propose a novel...
We establish the convergence of physics-informed neural networks (PINNs) for time-dependent fractional diffusion equations posed on bounded domains. The presence of fractional Laplacian operators introduces nonlocal behavior and regularity constraints, and standard neural network approximations do not naturally enforce the associated...
The Fundamental Theorem of Algebra (FTA) asserts that every complex polynomial has as many complex roots, counted with multiplicities, as its degree. A probabilistic analogue of this theorem for real roots of real polynomials, sometimes referred to as the Kac theorem, was found between 1938 and 1943 by J. Littlewood, A. Offord, and M....
In this paper, we consider a continuous fragmentation--coagulation model in which the reacting particles can be transported in physical space through either advection or diffusion. We prove new results on the generation of $C_0$-semigroups with parameter and use them to show that the Abstract Cauchy Problem associated with a more...
We study a ruin problem for an annuity model where a fixed fraction of capital is invested in a risky asset. Under weak assumptions on jumps, the ruin probability solves a second-order integro-differential equation and decays as a power function for large initial capital.
In recent years, there has been a surge of interest in extremal problems concerning the enumeration of independent sets or cliques in graphs with specific constraints. For instance, the Kahn-Zhao theorem establishes an upper bound on the number of independent sets in a $d$-regular graph. Building on this, Cutler and Radcliffe extended...
We develop two adaptive finite difference methods for the numerical simulation of the Willmore flow, employing the kth-order backward differentiation formula (BDFk) for time discretization, together with monitor functions for dynamic mesh adaptation along evolving interfaces. The first approach is based on a weighted arc-length...
We study the finite sampling map $H \mapsto \bigl(v_{H,Λ}(x_k + iη)\bigr)_{k=1}^M$ for trace-normed canonical systems on $[0,Λ]$ with free tail $H(s)=\frac{1}{2}I$ for $s \ge Λ$, where $v_{H,Λ}$ is the Schur transform of the Weyl coefficient. At the free Hamiltonian $H_0 \equiv \frac{1}{2}I$, we obtain an explicit first-order...
Motivated by the work of Esnault-Hai, one has the notion of de Rham $K(π,1)$ schemes, defined as follows. Given a smooth proper geometrically connected scheme $X$ over a field $k$ of characteristic 0 and a base point $x \in X (k)$, one can define its differential fundamental group $π^{\mathrm{diff}}(X/k)$, which comes from the...
In this paper we consider some optimal control problems governed by elliptic partial differential equations. The solution is the state variable, while the control variable is, depending on the case, the coefficient of the PDE, the potential, the right-hand side. The cost functional is of integral type and involves both the state and...
We introduce the Equilibrated Averaging Residual Method (EARM), a unified equilibrated flux-recovery framework for elliptic interface problems that applies to a broad class of finite element discretizations. The method is applicable in both two and three dimensions and for arbitrary polynomial orders, and it enables the construction...
This series of papers is a contribution to the program of classifying $p$-blocks of finite groups up to source algebra equivalence, starting with the case of cyclic blocks. To any $p$-block $\mathbf{B}$ of a finite group with cyclic defect group $D$, Linckelmann associated an invariant $W( \mathbf{B} )$, which is an indecomposable...
We propose a MINRES-based Newton-type algorithm for solving unconstrained nonconvex optimization problems. Our approach uses the minimal residual method (MINRES), a well-known solver for indefinite symmetric linear systems, to compute descent directions that leverage second-order and non-positive curvature (NPC) information....
We consider inhomogeneous singular parabolic double phase equations of type $$ u_t-\operatorname{div}(|Du|^{p-2}Du + a(x,t)|Du|^{q-2}Du)=-\operatorname{div} (|F|^{p-2}F + a(x,t)|F|^{q-2}F) $$ in $Ω_T := Ω\times (0,T)\subset \mathbb{R}^n\times \mathbb{R}$, where $\frac{2n}{n+2}<p\leq 2$, $p<q$ and $0\leq a(\cdot)\in...
This article aims to examine the Hahn-Banach smoothness of Banach spaces and its connections to various geometrical aspects. We examine the circumstances that allow linear functionals to have unique norm-preserving extensions, with particular attention to the behavior of these properties in $L_1$-preduals and in spaces of affine...
We survey the classification of the Riemannian metrics on spheres with respect to which all equators are minimal hypersurfaces, and discuss problems related to these geometries.
The main goal of this paper is to present new bounds for certain inner products in Hilbert spaces, with applications to the numerical radius and the operator norm. The obtained results significantly improve earlier results in this direction.
Contour integral algorithms seek to compute a small number of eigenvalues located within a bounded region of the complex plane. These methods can be applied to both linear and nonlinear matrix eigenvalue problems. In the latter case, the foundation of these methods comes from the Keldysh decomposition, which breaks the nonlinear...
We study the relationship between the existence of Hall $π$-subgroups and that of irreducible characters of $π'$-degree with prescribed fields of values in finite groups. This work extends a result of Navarro and Tiep from a single odd prime to multiple odd primes.
For an $n$-vertex graph $G$, and a rooted graph $H^{(v)}$ with $v$ as the root, the rooted product graph $G\circ H^{(v)}$ is obtained from $G$ and $n$ copies of $H$ by identifying the root of the $i$th copy of $H$ with the $i$th vertex of $G$ for each $i$. As a refinement of the controllability criterion of $G\circ H^{(v)}$ obtained...
Pointwise-in-time stability notions for Ordinary Differential Equations (ODEs) provide quantitative metrics for system performance by establishing bounds on the rate of decay of the system state in terms of initial condition -- allowing stability to be quantified by e.g. the maximum provable decay rate. Such bounds may be obtained by...
We introduce Hopf images of coactions of Hopf algebras and develop their role in the geometry of quantum principal bundles. Assuming cosemisimplicity of the structure Hopf algebra, we show that every quantum principal bundle equipped with a right-covariant first-order differential calculus admits a canonical and functorial reduction...
Given a symmetric quiver with potential, we develop a geometric construction of shifted Yangians acting on the critical cohomologies of antidominantly framed quiver varieties with extended potentials, using the $R$-matrices constructed from critical stable envelopes. We relate such Reshetikhin type Yangians to Drinfeld type Yangians...