arXiv preprints from January 1, 2026 through September 6, 2026 — 17:51:23 EST
Projection-based model reduction enables efficient simulation of complex dynamical systems by constructing low-dimensional surrogate models from high-dimensional data. The Operator Inference (OpInf) approach learns such reduced surrogate models through a two-step process: constructing a low-dimensional basis via Singular Value...
We study congruences relating Fourier coefficients of meromorphic modular forms and Frobenius eigenvalues of elliptic curves corresponding to their poles. We develop a $p$-adic cohomological framework that interprets these congruences via the interaction between the rigid cohomology of modular curves and the crystalline structure of...
Let $K\langle X_d\rangle$ denote the free associative algebra of rank $d \geq 2$ over a field $K$. By results of Lane (1976) and Kharchenko (1978), the algebra of invariants $K\langle X_d\rangle ^G$ is free for any subgroup $G \leq \GL_d(K)$ and any field $K$. Koryukin (1984) introduced an additional action of the symmetric group...
We study a semilinear equation involving the fractional Laplacian on the hyperbolic space $\mathbb{H}^n$. Unlike in conformally compact Einstein manifolds, the fractional Laplacian on $\mathbb{H}^n$ does not enjoy conformal covariance. By employing Helgason-Fourier analysis, we explicitly derive the Green's function of the fractional...
This paper investigates the recent Connes-Consani-Moscovici $D_{\log}^{(λ, N)}$ operators, whose spectra are currently hypothesized to approach the zeros of $ζ\left(\frac{1}{2} +is\right)$ as $λ, N \rightarrow \infty$. It turns out that when considering different standard notions of error, the dissonance between the spectra and...
We study the stationary flow of incompressible micropolar fluid in a thin three-dimensional domain under Navier slip boundary condition for the velocity and no-spin condition for microrotation. After rescaling the governing equations, we perform a rigorous asymptotic analysis as the film thickness tends to zero, considering a friction...
We show that the Hausdorff dimension of $\boldsymbol w$-weighted $τ$-exactly approximable vectors in $\mathbb R^d$ coincides with the Hausdorff dimension of $\boldsymbol w$-weighted $τ$-approximable vectors, generalizing a result of the first named author and De Saxcé.
Offline policy learning aims to use historical data to learn an optimal personalized decision rule. In the standard estimate-then-optimize framework, reweighting-based methods (e.g., inverse propensity weighting or doubly robust estimators) are widely used to produce unbiased estimates of policy values. However, when the propensity...
We prove that any Kato manifold satisfies the Hodge decomposition, in the sense that $b_k=\sum_{p+q=k}h^{p, q}$, by relating its cohomology to the corresponding cohomology of its modification data. We give, therefore, more evidence supporting a conjecture of Ornea--Verbitsky stating that compact locally conformally Kähler manifolds...
We study one-variable equations over the lamplighter group $\MZ_2 \wr \MZ$. While the decidability of arbitrary equations over $L_2$ remains open, we prove that the Diophantine problem for single equations in one variable is decidable. Our approach reduces the problem to a divisibility question for families of parametric Laurent...
Let $χ=χ_q$ be a primitive character mod $q$ and fix $Δ>0$. In 1989 Graham and Ringrose gave strong bounds on character sums $\sum_{M<n\leq M+N} χ(n)$ in intervals of length $N=q^Δ$ whenever $q$ is squarefree and is sufficiently smooth. Here we show that the smoothness parameter can be taken to be $N^{1-ε}$. We also discuss various...
It is well known that the spectrum of the Dirichlet Laplacian for a compact perturbation of a three-dimensional, periodically twisted tube is unstable with respect to domain deformations. This means that if the periodically twisted tube is unperturbed, then the spectrum of the Dirichlet Laplacian is purely essential. On the other...
State-dependent parameter identification, where unknown model parameters depend on one or more state variables in partial differential equations (PDEs) or coupled PDE systems, is fundamental to a wide range of problems in physics, engineering, and materials science. This review surveys PDE-constrained optimization approaches for such...
A dual pre-Poisson algebra is an algebraic structure that integrates a permutative algebra and a Leibniz algebra under certain compatibility conditions. As the Koszul dual notion of the pre-Poisson algebra, this structure serves as a natural generalization of the Poisson algebra. In this paper, we commence a study on dual pre-Poisson...
In services such as retail audits and urban infrastructure monitoring, a platform dispatches rewarded, location-based micro-tasks to mobile workers traveling along personal origin-destination (OD) trips under hard time budgets. As requests with time constraints arrive online over a finite horizon, the platform must decide which...
Matthew de Brecht raised the question of whether countable frames are continuous lattices. We prove that the continuity of a countable frame implies the quasicontinuity of its corresponding spectrum in the dual specialization order. We further show that this question admits a positive answer if the frame's spectrum is a $T_1$ space or...
We isolate the limit-stage filter construction needed for countable-support symmetric iterations built from standard successor-step symmetric systems. At successor stages we take the $ω_1$-completion of the usual successor-stage symmetry filter. At limit stages of uncountable cofinality, countable supports are bounded and the...
Physics-informed extreme learning machines (PIELMs) typically impose boundary and initial conditions through penalty terms, yielding only approximate satisfaction that is sensitive to user-specified weights and can propagate errors into the interior solution. This work introduces Null-Space Projected PIELM (NP-PIELM), achieving exact...
The main purpose of this short note, on the one hand, to is rigorize some part of the proof of Theorem 1.3 in [11] in a simple way, and on the other hand, to give an alternative argument from local inequalities to global ones.
This paper investigates an optimal control problem where the system is described by a stochastic differential equation with extended mixed delays that contain point delay, extended distributed delay, and extended noisy memory. The model is general in that the extended mixed delays of the state variable and control variable are...
In this paper, we propose a model order reduction based adaptive parareal method for time-dependent partial differential equations. By using the data obtained by the fine propagator in each iteration of the plain parareal method together with some model order reduction technique, we construct the coarse propagator adaptively in each...
We propose a novel non-compact, positivity-preserving scheme for linear non-divergence form parabolic equations. Based on the Feynman-Kac formula, the solution is expressed as a conditional expectation of an associated diffusion process. Instead of using compact Markov chain approximations, we employ a wide stencil scheme to...
A map is a cellular decomposition of a closed surface. In the framework of classifying all regular maps by their supporting surface, it is an open problem to find all closed surfaces that support no regular maps. Classification of regular maps on surfaces with Euler characteristic $-p, -p^2, -p^3, -2p,$ and $-3p$ has already been done...
Dengue, which affects millions of people each year, is one of the most common diseases transmitted by infected \textit{Aedes aegypti} mosquitoes. In the Philippines, the annual economic cost of dengue infections is estimated at around PHP 17 billion. Previous studies have shown that controlling the population of mosquitoes capable of...
We present exact analytical solutions for the radial Dunkl-Schrödinger equation (DSE) confined by the Deng-Fan molecular potential. By employing the Pekeris approximation to resolve the centrifugal singularity and applying the parametric Nikiforov-Uvarov method, we derive closed-form expressions for the energy eigenspectrum and the...