arXiv preprints from January 1, 2026 through September 7, 2026 — 18:13:37 EST
We study clinically motivated capacity-constrained treatment-adherence outreach through a belief-state restless multi-armed bandit model, in which each patient is a partially observed two-state Markov decision process and interventions induce reset-type belief dynamics. For the discounted criterion, partial conservation law...
This paper addresses the minimization of a finite sum of prox-convex functions under Lipschitz continuity of each component. We propose two variants of the splitting proximal point algorithms proposed in \cite{Bacak,Bertsekas}: one deterministic with a fixed update order, and one stochastic with random sampling, and we extend them...
Let $(Ω^{n+1}, g)$ be an $(n+1)$-dimensional smooth compact connected Riemannian manifold with smooth boundary $Σ$, satisfying that ${\text{Ric}_Ω}\ge 0$ and $Σ$ is strictly convex, more precisely, its second fundamental form $h\ge cg_Σ$ for some positive constant $c$. Escobar {\cite{escobar1997geometry}} considered the first nonzero...
Let $A$ be a unital locally matrix algebra. Among the examples of such algebras are: (1) an infinite tensor product $\otimes M_{n_i}(\mathbb{F})$ of matrix algebras over a field $\mathbb{F}$, and (2) the Clifford algebra of a nondegenerate quadratic form on an infinite-dimensional vector space over an algebraically closed field of...
We discuss the design of ``wave packet systems'' that admit strong concentration properties in phase space. We make a connection between this problem and topics in signal processing related to the spectral behavior of spatial and frequency-limiting operators. The results have engineering applications in medical imaging, geophysics,...
We study the profinite genus of HNN-extensions whose associated subgroups are finite. We give precise formulas for the number of isomorphism classes of HNN(G,H,K,t,f) and of its profinite completion and compute the profinite genus of such an HNN-extension HNN(G,H,K,t,f). We also list various situations when HNN(G,H,K,t,f) is...
As a consequence of the Littlewood-Richardson (LR) commuters coincidence and the Kumar-Torres branching model via Kushwaha-Raghavan-Viswanath flagged hives, we have solved the Lecouvey- -Lenart conjecture on the bijections between the Kwon and Sundaram branching models for the pair $({GL}_{2n}(\mathbb{C}), {Sp}_{2n}(\mathbb{C})) $...
Deep level Deligne--Lusztig representations, which are natural analogues of classical Deligne--Lusztig representations, recently play an important role in geometrization of irreducible supercuspidals of $p$-adic groups. In this paper, we propose a construction of deep level Deligne--Lusztig varieties/representations in the tamely...
We describe all possible topological structures of typical one-parameter bifurcations of gradient flows on the 2-sphere with holes in the case that the number of singular point of flows is at most six. To describe structures, we separatrix diagrams of flows. The saddle-node singularity is specified by selecting a separatrix in the...
Standard projection-based model reduction for dynamical systems incurs closure error because it only accounts for instantaneous dependence on the resolved state. From the Mori-Zwanzig (MZ) perspective, projecting the full dynamics onto a low-dimensional resolved subspace induces additional noise and memory terms arising from the...
We characterise stable finiteness and pure infiniteness of the essential crossed product of a C*-algebra by an action of an inverse semigroup. Under additional assumptions, we prove a stably finite / purely infinite dichotomy. Our main technique is the development, using an induced action, of a ``dynamical Cuntz semigroup'' that is a...
We settle an open problem regarding palindromes; that is, positive integers which are the same when written forwards and backwards. In particular, we prove that for any fixed base $b\geq 2$, there exist infinitely many square-free palindromes in base $b$. We also provide an asymptotic expression for the number of such integers $\leq...
We propose an efficient hyper-reduced order model (HROM) designed for segregated finite-volume solvers in geometrically parametrized problems. The method follows a discretize-then-project strategy: the full-order operators are first assembled using finite volume or finite element discretizations and then projected onto low-dimensional...
This paper investigates an inverse boundary value problem for a semilinear strongly damped wave equation with Dirichlet boundary conditions in Sobolev spaces of functions bounded in time on $\R$, including periodic and almost periodic functions. In addition to constructing a bounded strong solution, we determine a time-dependent...
Despite the celebrated success of stochastic control approaches for uncertain systems, such approaches are limited in the ability to handle non-Gaussian uncertainties. This work presents an adaptive robust control for linear uncertain systems, whose process noise, observation noise, and system states are depicted by ellipsoid sets...
We compute explicitly the Riemannian volume, with respect to the Fubini-Study metric, of a domain bounded by a Hermitian quadric in complex projective space. The volume is a rational function of the eigenvalues of the defining quadratic form.
We consider the saddle point problem where the objective functions are abstract convex with respect to the class of quadratic functions. We propose primal-dual algorithms using the corresponding abstract proximal operator and investigate the convergence under certain restrictions. We test our algorithms by several numerical examples.
We study the two-dimensional time-harmonic scalar transmission problem for an impedance-matched penetrable right-angle wedge: the exterior medium has wavenumber k_0 and the interior sector |theta| < pi/4 has wavenumber k_1 = nu*k_0 with nu > 1, with continuity of the total field and its normal derivative across each face. A...
A set $\mathcal S\subset \mathbb N$ is said to be a subset-sum-distinct or dissociated if all of its finite subsets have different sums. Alternately, an equivalent classification is if any equality of the form $$\sum_{s\in \mathcal S} \varepsilon_s \cdot s =0$$ where $\varepsilon_s \in \{-1,0,+1\}$ implies that all the...
In this paper we are interested in the stability of the $2$-rank of the class group in the cyclotomic $\mathbb{Z}_2$-extension of real biquadratic fields. In fact, we give several families of real biquadratic fields $K$ such that $ rank(A(K)) =rank(A_\infty(K))$ and $rank(A(K))\leq 3$, where $A(K)$ and $A_\infty(K)$ are the $2$-class...
We give a complete description of the varieties of associative algebras over a field of characteristic zero which satisfy a polynomial identity of third degree.
We study differentiability conditions on a complex measure $ν$ at a point $x_0\in\mathbb{R}^d$, in relation with the boundary convergence at that point of the Poisson-type integral $P_tν=e^{-t\sqrt L}ν$, where $L=-Δ+|x|^2$ is the Hermite operator. In particular, we show that $x_0$ is a Lebesgue point for $ν$ iff a slightly stronger...
This article addresses two central problems in the theory of quandle rings. First, motivated by Conjecture 3.10 in Internat. J. Math. 34 (2023), no. 3, Paper No. 2350011: for a semi-latin quandle $X$, every nonzero idempotent in the integral quandle ring $\mathbb{Z}[X]$ necessarily corresponds to an element of $X$, we investigate...
We introduce a discrete-space analogue of the No-U-Turn sampler on the symmetric group $S_n$, yielding a locally adaptive and reversible Markov chain Monte Carlo method for $\mathrm{Mallows}(d,σ_0)$. Here $d:S_n\times S_n\to[0,\infty)$ is any fixed distance on $S_n$, $σ_0\in S_n$ is a fixed reference permutation, and the target...
We construct, for a $p$-adic field $F$, an explicit semisimple Tannakian category $\text{RigIsoc}_{F}$ whose category of fiber functors recovers Kaletha's Galois gerbe $\mathcal{E}_{\text{Kal}}$. We then classify and write down the simple objects in $\text{RigIsoc}_{F}$, all of which come from elliptic twisted Levi subgroups of...