arXiv preprints from January 1, 2026 through July 20, 2026 — 07:22:40 EST
This letter presents a data-driven framework for the design of stabilizing controllers from input-output data in the continuous-time, linear, and time-invariant domain. Rather than relying on measurements or reliable estimates of input and output time derivatives, the proposed approach uses filters to derive a parameterization of the...
The fact that moisture propagates in soils at a finite speed is confirmed by natural everyday experience as well as by controlled laboratory tests. In this text, we rigorously derive analytical upper bounds for the speed of moisture front propagation under gravity for the solution to the Richards equation with compactly supported...
We investigate dimensional constraints arising from representation theory when abstract graph edges possess internal degrees of freedom but lack geometric properties. We prove that such internal degrees of freedom can only encode directional information, necessitating quantum states in $\mathbb{C}^2$ (qubits) as the minimal...
This paper introduces a boundary integral equation for time-harmonic electromagnetic scattering by composite dielectric objects. The formulation extends the classical Müller equation to composite structures through the global multitrace method. The key ingredient enabling this extension is the use of the Stratton-Chu representation in...
We consider reachable sets of switching systems, which are families of linear ODE $\dot x(t) \, = \, \, A(t) \, x(t)$ with a function $A(\cdot)$ taking values on a given compact set of $d\times d$ matrices. An eigenset is a compact set $M \ne \{0\}$ that possesses the following property: the closure of the set of points reachable by...
In this expository paper, we review the history and the recent breakthroughs in the spectral theory of large volume hyperbolic surfaces. More precisely, we focus mostly on the investigation of the first non-trivial eigenvalue $λ_1$ and its possible behaviour in the large volume regime.
Residues appear naturally in various questions in complex and algebraic geometry: interpolation, duality, representation problems, and obstructions. The first global vanishing result in the projective plane, known as the Euler-Jacobi theorem, was established by Jacobi in 1835. In the toric case, the input is a system of n Laurent...
The dispersive estimate plays a pivotal role in establishing the long-term behavior of solutions to the nonlinear equation, thereby being crucial for investigating the well-posedness of the equation.In this work we prove that the solutions to Klein-Gordon equation on 1-d lattices follow the dispersive estimate provided that potential...
Correlation analysis is a fundamental problem in statistics. In this paper, we consider the correlation detection problem between a pair of Erdos-Renyi graphs. Specifically, the problem is formulated as a hypothesis testing problem: under the null hypothesis, the two graphs are independent; under the alternative hypothesis, the two...
In this paper we develop a Bregman regularized proximal point algorithm for solving monotone equilibrium problems on Hadamard manifolds. It has been shown that the regularization term induced by a Bregman function is, in general, nonconvex on Hadamard manifolds unless the curvature is zero. Nevertheless, we prove that the proposed...
This study examines generalized cross-validation for the tuning parameter selection for ridge regression in high-dimensional misspecified linear models. The set of candidates for the tuning parameter includes not only positive values but also zero and negative values. We demonstrate that if the second moment of the specification error...
We develop some tools, of an algebraic and combinatorial nature, which enable us to obtain a detailed description of certain quadratic subgroups of the (outer) reduced Weyl group of the Cuntz algebra ${\mathcal O}_n$. In particular, for $n=4$ our findings give a self-contained theoretical interpretation of the groups tabulated in...
In this article, we have introduced the notion of a near-isometric covariant representation of a $C^*$-correspondence. The other objective is to provide a unified approach to several known results for a large class of left-invertible covariant representations of a product system and prove Wold-type decomposition for the case of doubly...
We establish topological necessary and sufficient conditions under which a pair of statistical hypotheses can be consistently distinguished when i.i.d. observations are recorded only to finite precision. To accommodate finite-precision data, we introduce finite-precision tests: tests whose decision regions are open in the sample-space...
Given a nonempty graph $G$, a collection of nonempty graphs $\cal{H}$, and a positive integer $k$, the Gallai-Ramsey number $\mathrm{gr}_k(G:\mathcal{H})$ is defined to be the minimum positive integer $n$ such that every exact $k$-edge-coloring of a complete graph $K_n$ contains either a rainbow copy of $G$ or a monochromatic copy of...
In 2021, Henk, Schymura and Xue introduced packing minima, associated with a convex body and a lattice, as packing counterparts to the covering minima of Kannan and Lovász. Motivated by conjectures on the volume inequalities for the successive minima, we generalized the definition of the packing minima to the class of all convex...
We evaluate the misclustering probability of a spectral clustering algorithm under a Gaussian mixture model with a general covariance structure. The algorithm partitions the data into two groups based on the sign of the first principal component score. As a corollary of the main result, the clustering procedure is shown to be...
In this paper, we suggest a sufficient condition on the properadic envelope of a quadratic dioperad to be Koszul in terms of twisted associative algebras. As a particular new example, we show that the properad of quadratic Poisson structures is Koszul.
Let $(X,x)$ be a pointed geometrically connected smooth projective variety over a sub-$p$-adic field $K$. For any given rank $n$, we prove that there are only finitely many isomorphism classes of representations $π_{1}^{EF}(X,x)\rightarrow \mathrm{GL}_{n}$, where $π_{1}^{EF}(X,x)$ is Nori's fundamental group of essentially finite...
We prove some Liouville theorems for the stationary Navier-Stokes system for incompressible fluids. We provide some sufficient conditions on the low frequency part of the solution, using some properties of classical singular integrals with respect to Wiener algebras.
We study multivariate monomial Vandermonde matrices $V_N(Z)$ with arbitrary distinct nodes $Z=\{z_1,\dots,z_s\}\subset B_2^n$ in the high-degree regime $N\ge s-1$. Introducing a projection-based geometric statistic -- the \emph{max-min projection separation} $ρ(Z,j)$ and its minimum $κ(Z)=\min_jρ(Z,j)$ -- we construct Lagrange...
Barn-type houses have become one of the most popular single-family housing typologies in Poland and across Europe due to their simplicity, functionality, and potential for energy efficiency. Despite their widespread use, systematic methods for optimizing their geometry in terms of envelope area and energy performance remain limited....
Improved local numerical solution for the ADER-DG numerical method with a local DG predictor for solving the initial value problem for a first-order ODE system is proposed. The improved local numerical solution demonstrates convergence orders of one higher than the convergence order of the local numerical solution of the original...
An ordered $r$-uniform matching of size $n$ is a collection of $n$ pairwise disjoint $r$-subsets of a linearly ordered set of $rn$ vertices. For $n=2$, such a matching is called an $r$-pattern, as it represents one of $\tfrac12\binom{2r}r$ ways two disjoint edges may intertwine. Given a set $\mathcal{P}$ of $r$-patterns, a...
We study LU-type factorizations of the infinitesimal generator of a birth--death process on $\mathbb{N}_0$. Our goal is to characterize those factorizations whose Darboux transformations (that is, inverting the order of the factors) yield new infinitesimal generators of birth--death processes. Two types are considered: lower--upper...