arXiv preprints from January 1, 2026 through July 20, 2026 — 21:06:44 EST
In this paper, we establish a Struwe type global compactness result for a class of nonlinear critical Hardy-Sobolev exponent problems driven by the fractional $p$-Laplace Hardy-Sobolev operator.
Let $H$ be a $k$-graph (i.e. a $k$-uniform hypergraph). Its minimum codegree $δ_{k-1}(H)$ is the largest integer $t$ such that every $(k-1)$-subset of $V(H)$ is contained in at least $t$ edges of~$H$. The \emph{codegree Turán density} $γ(\mathcal{F})$ of a family $\mathcal{F}$ of $k$-graphs is the infimum of $γ> 0$ such that every...
In this paper we solve an open question formulated in the original paper of twisted skew group codes regarding when a twisted skew group code is checkable. Also, we prove that all ideals of dimension 3 over a twisted group algebra are abelian group codes, generalising another previous result over group algebras. Finally, we prove a...
We rigorously establish a formula for the correlation energy of a two-dimensional Fermi gas in the mean-field regime for potentials whose Fourier transform $\hat{V}$ satisfies $\hat{V}(\cdot) | \cdot | \in \ell^1$. Further, we establish the analogous upper bound for $\hat{V}(\cdot)^2 | \cdot |^{1 + \varepsilon} \in \ell^1$, which...
For a given variety of groups $\X$, we develop a systematic theory of $\CSX$-groups and $\XT$-groups, extending ideas proposed in \cite{Shah}. We analyze the interplay between these classes, describe their structural properties, and examine their connections with equational domains and residually $A$-free groups. Furthermore, we prove...
For a Tychonoff space $X$, $B_1(X)$ denotes the space of all Baire-one functions on $X$ endowed with the pointwise topology. We prove that the following assertions are equivalent: (1) $B_1(X)$ is a (semi-)Montel space, (2) $B_1(X)$ is a (semi-)reflexive space, (3) $B_1(X)$ is a (quasi-)complete space, (4) $B_1(X)=\mathbb{R}^X$, (5)...
Urban transportation networks face significant challenges due to traffic congestion, leading to adverse environmental and socioeconomic impacts. Vehicular admission control (VAC) strategies have emerged as a promising solution to alleviate congestion. By leveraging information and communication technologies, VAC strategies regulate...
This paper presents a comprehensive overview of several multidimensional reduction methods focusing on Multidimensional Principal Component Analysis (MPCA), Multilinear Orthogonal Neighborhood Preserving Projection (MONPP), Multidimensional Locally Linear Embedding (MLLE), and Multidimensional Laplacian Eigenmaps (MLE). These...
This article proves that there are no self-intersections in the dragon curve when the unfolding angle is greater than 98.195°. This is shown by constructing a hull for the dragon curve that is mapped onto itself by the generating mappings for the dragon curve. The treatment is purely geometric. The proof is supplemented by a...
This paper focuses on symbolic integration of differential forms, with a particular emphasis on historical and modern developments, from Abel's addition theorems for Abelian integrals to Zeilberger's creative telescoping for parameterized integrals. It explores closed rational $p$-forms and provides algorithmic approaches for their...
In this article, we will first establish some density results for a locally $C^*$-algebra $\mathcal A$ and then identify a property, called Kaplansky density property (KDP). We then give a induced faithful continuous $*$-representation $\varphi$ of $\mathcal A^{**}$ (equipped with unique Arens product) on the space $B_{loc}(\mathcal...
The first goal of this paper is to give a precise and simple definition for off-shell Bethe vectors in a generic $g$-invariant integrable model for $g=gl_n$, $o_{2n+1}$, $sp_{2n}$ and $o_{2n}$. We prove from our definition that the off-shell Bethe vectors indeed become on-shell when the Bethe equations are obeyed. Then, we show that...
In this paper, two formulations for the computation of the dyadic Green's functions of Maxwell's equations in layered media are presented in details. The first formulation derived using TE/TM decomposition is well-known and intensively used in engineering community while the second formulation derived using vector potential and a...
We present a general regularization procedure for piecewise smooth vector fields whose discontinuity locus is a variety of normal crossings type. We show that such regularization can be smoothed through a finite sequence of blowings-up, thereby reducing the problem to study of the dynamics of a smooth vector field in a manifold with...
In this paper, we obtain results on exponential stability of second order delay differential equations, which are based on a version of the Floquet theory for delay differential equations of the second order we proposed. Our version allows researchers to preserve the order of equation and to obtain analogues of the classical results...
We prove the Hernandez conjecture on the simple $(q,t)$-characters (an analog of the Kazhdan--Lusztig conjecture) for untwisted quantum loop algebras of classical type. This result is new in type $\mathrm{C}$. We also prove that the folding homomorphism, introduced by Hernandez, gives a dimension-preserving bijective correspondence...
We give a presentation of the $\mathrm{GL}_n(\mathbb{C})$-equivariant cohomology ring with $\mathbb{Z}$-coefficients of the variety $\mathrm{Hom}(\mathbb{Z}^2,\mathrm{GL}_n(\mathbb{C})) \subseteq \mathrm{GL}_n(\mathbb{C})^2$ for any $n$. It is torsion free and minimally generated as a $H^\ast B\mathrm{GL}_n(\mathbb{C})$-algebra by...
Let $F$ be a non-Archimedean local field. For an irreducible smooth representation $π$ of $\mathrm{GL}_n(F)$ and a multisegment $\mathfrak m$, one associates a simple quotient $D_{\mathfrak m}(π)$ of a Bernstein-Zelevinsky derivative of $π$. In the preceding article, we showed that \[ \mathcal S(π, τ) :=\left\{ \mathfrak m :...
In this paper, we study the finite element operator network (FEONet), an operator-learning method for parametric problems, originally introduced in J. Y. Lee, S. Ko, and Y. Hong, Finite Element Operator Network for Solving Elliptic-Type Parametric PDEs, SIAM J. Sci. Comput., 47(2), C501-C528, 2025. FEONet realizes the...
For univariate polynomials over arbitrary field the degree gives an upper bound on the number of roots (factor theorem) and as a related result for any finite point-set one can construct a polynomial of degree equal to the cardinality having all the points as roots (interpolation theorem). Tao noted in [48] that the theory of...
This paper presents a method for reducing a three-dimensional gradient damage model to a one-dimensional model for slender rods (with a small radius-to-length ratio, $δ= R/L \to 0$). The 3D model minimizes an energy functional that includes elastic strain energy, a damage-dependent degradation function $a_η(α)$, a damage energy term...
The aim of this paper is to generalize the link between Heyting algebras and Nelson algebras, established independently by Fidel and Vakarelov at the end of the 1970s, in the framework of bounded distributive hemi-implicative lattices. For this purpose, we introduce the variety of hemi-Nelson algebras. Moreover, we characterize the...
Transfer learning aims to improve performance on a target task by leveraging information from related source tasks. We propose a nonparametric regression transfer learning framework that explicitly models heterogeneity in the source-target relationship. Our approach relies on a local transfer assumption: the covariate space is...
This article introduces a simple weak Galerkin (WG) finite element method for solving convection-diffusion-reaction equation. The proposed method offers significant flexibility by supporting discontinuous approximating functions on general nonconvex polytopal meshes. We establish rigorous error estimates within a suitable norm....
We present new proofs of two identities arising in the work of Mourad Ismail using partition theoretic generating function interpretations.