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arXiv:2606.01037v1 Announce Type: new Abstract: Let $n\geq 0$ be an integer and $q$ a prime power. The polynomial $g_{n,q}$ was introduced in [10] with the purpose of finding new classes of permutation polynomials over finite fields. We investigate the permutation behaviour of the polynomial $g_{n,q}(X)$ over finite fields of even characteristic. We introduce the multivariate case of the polynomial $g_{n,q}$, and study the permutation poly..
arXiv:2606.01040v1 Announce Type: new Abstract: Fix $1 \leq n < m, k = m-n.$ The Grassmannian $Gr(n,m)$ is a compact $kn$-dimensional manifold with a unique rotation invariant probability measure $\sigma_n.$ For $W \in Gr(n,m)$, $P_W : \mathbb R^m \mapsto W$ is orthogonal projection. A lattice subset $L \subset \mathbb Z^m \subset \mathbb R^m$ is called $k$-dense if it intersects $C(O) := \bigcup_{V \in O} V\backslash \{0\}$ for every none..
arXiv:2606.01055v1 Announce Type: new Abstract: Bilevel optimization is a fundamental framework for hierarchical decision-making, but its solution is challenging due to the implicit and typically set-valued nature of the lower-level optimality condition. In this paper, we study bilevel optimization problems through an exact-penalty reformulation based on the $\ell_1$-norm of the lower-level gradient. Under suitable regularity assumptions,....
arXiv:2606.01058v1 Announce Type: new Abstract: This paper investigates the infinite-horizon classical stochastic optimal control problem with input delay under an entropy-regularized relaxed control framework. In particular, by constructing a relaxed system and introducing an entropy regularization term, we reformulate the classical optimal control problem into an entropy regularized formulation, and derive the optimal controller that fol..
arXiv:2606.01064v1 Announce Type: new Abstract: In this paper, we study some geometric constants in complete $p$-normed spaces with $0 < p \leq 1$. We introduce a new symmetric geometric constant associated with isosceles orthogonality, establish its sharp bounds, and provide an orthogonal characterization of the generalized von Neumann-Jordan constant in such spaces. We also investigate two Milman-type moduli in complete $p$-normed spaces..
arXiv:2606.01068v1 Announce Type: new Abstract: Let $X$ be a real Banach space and $\lambda \in[0,1]$. Motivated by orthogonal versions of the James constant, we introduce the weighted Birkhoff orthogonal James-type constant $$J_\lambda^{\perp}(X)=\sup \left\{\min \{\|\lambda x+(1-\lambda) y\|,\|\lambda x-(1-\lambda) y\|\}: x, y \in S_X, x \perp_B y\right\},$$ where \(\lambda\in[0,1]\) and $x \perp_B y$ stands for Birkhoff orthogonality. W..
arXiv:2606.01073v1 Announce Type: new Abstract: We study the Riemann problem for the compressible Euler equations with a stationary coupling interface across which a discontinuity in the heat flux is prescribed. This coupling gives rise to non-conservative effects and models heat addition mechanisms such as condensation-induced waves. Without imposing restrictions on sonic states, we analyze the problem in all Mach number regimes. Lax weak....
arXiv:2606.01082v1 Announce Type: new Abstract: We study \(\Gamma_{2^n}(K)\), the least positive number \(\gamma>0\) such that an \(n\)-dimensional convex body \(K\) can be covered by \(2^n\) translates of \(\gamma K\). For \(n\)-simplices \(\Delta_n\), we prove that \(\Gamma_{2^n}(\Delta_n)\), as a sequence in \(n\), tends to \(1/2\). For the cross-polytope \(B_1^n\), we show that \(\Gamma_{2^n}(B_1^n)\leq5/6\) holds for all \(n\geq2\), a..
arXiv:2606.01083v1 Announce Type: new Abstract: Let $p$ be an odd prime and let $S$ be a set of tame primes. We denote by $G_S$ the Galois group of the maximal pro-$p$ extension of $\mathbb{Q}$ unramified outside $S$. We prove that for every finite set of tame primes $S_0$ with $|S_0|\geq 2$, there exists a set $S_1$ consisting of two tame primes such that $G_{S_0\cup S_1}$ has cohomological dimension $2$. This refines a result of Labute...
arXiv:2606.01093v1 Announce Type: new Abstract: Bands and idylls are algebraic structures introduced recently by M. Baker, N. Bowler, T. Jin, and O. Lorscheid in the context of matroid theory. Bands generalize hyperrings and provide a new approach to geometry over the field with one element $\mathbb{F}_1$. In the first part of this paper, we develop the theory of modules over a band, establishing several of its fundamental properties. In ....
arXiv:2606.01096v1 Announce Type: new Abstract: For near-field communications, it is a hardware-efficient means to form an extremely large-scale array (XL-array) by concatenating multiple modular arrays (also referred to as subarrays). In this letter, we aim to investigate the effect of time synchronization errors among transmissions of different subarrays on the beam-focusing performance. To this end, we first characterize the beam patter....
arXiv:2606.01100v1 Announce Type: new Abstract: Satellite coverage analysis commonly relies on intensive numerical computations to evaluate access and revisit times, resulting in high computational costs, particularly in long-term performance assessment and large-scale constellation analysis involving numerous satellites. To address this issue, this paper presents a semi-analytic method for rapid coverage analysis for a satellite using pie....
arXiv:2606.01102v1 Announce Type: new Abstract: We propose a three-voice extension of Mazzola's algebraic model of first-species counterpoint. A three-voice sonority is represented as \(a+\varepsilon_1 .b+\varepsilon_2 .c\), where \(a\) is the lower voice and \(b,c\) are the lower--middle and lower--upper interval classes. Starting from a strong dichotomy \((X/Y)\) of \(\mathbb Z_{2k}\), we introduce a harmonic mask \(H\subseteq X\times X\..
arXiv:2606.01105v1 Announce Type: new Abstract: Let $\Lambda=\{\lambda_n\}_{n=1}^{\infty}\subset\mathbb{N}$ with $\lambda_n$ strictly increasing and such that $\sum_{n=1}^{\infty}\lambda_n^{-1}<\infty$. We show that a Hardy subspace $H^2 (\mathbb{D}, \Lambda)$ consisting of functions with sparse Fourier spectrum $\Lambda$ coincides with a M\"{u}ntz space $\overline{M^2_{\Lambda}}(\mathbb{D})$ characterized by square-summability of coeffici..
arXiv:2606.01108v1 Announce Type: new Abstract: We prove an integral type Gauss-Green formula on non-collapsed RCD spaces using the strong locality of the Laplacian and an eigenfunction approximation method. As applications, we generalize Colding's monotonicity formulas and prove an asymptotic formula linking the mean curvature of a hypersurface at a given point to the volume of small balls centered at that point.
arXiv:2606.01115v1 Announce Type: new Abstract: The existence of primes in a short interval, which asks if there are prime numbers in the interval $[x, x + x^\theta]$, is a core problem in number theory. Guth and Maynard proved the best known result for this problem with an asymptotic formula while Baker, Harman and Pintz proved the best lower bound result. In this article, we focus on Piatetski-Shapiro primes in a short interval. The stu..
MCS Spaces are CS - arxiv.org - 3 months ago - eng
arXiv:2606.01119v1 Announce Type: new Abstract: In this paper we further develop the theory of MCS spaces. Our main result shows that MCS spaces, as defined by Perelman, are CS sets with respect to their MCS stratification, and that in fact, the intrinsic stratification agrees with the MCS stratification. As a consequence, we improve on Perelman's result and answer affirmatively a question by Fujioka.
arXiv:2606.01121v1 Announce Type: new Abstract: The aim of this paper is to revisit, in Souriau's book "Structure of Dynamical Systems", the chapter devoted to the geometric quantization where the justifications of important results and formulae are not given and are difficult to prove. After recalling the coadjoint orbit method and its application to the relativistic particle with spin, we state and prove two keystone theorems that allow ..
arXiv:2606.01130v1 Announce Type: new Abstract: We study non-radial Dunkl multipliers via chamber lifting. For an arbitrary finite reflection group $G$, the chamber lifting records all reflected values of a function and conjugates a multiplier into a finite matrix-valued operator on the chamber. If the dyadic matrix entries admit off-diagonal kernels satisfying the chamber $L^2$ H\"ormander condition $\operatorname{CH}^2_{s,\eta}$ with $s>..
arXiv:2606.01140v1 Announce Type: new Abstract: Gasper gave a two-step extension of the Askey-Roy formula for a beta-integral type defined on the unit circle. This involved increasing the number of parameters and adding a balancing condition. We derive a multidimensional generalization of the final formula in Gasper's extension. By considering a two-step degeneration involving parameters our generalization becomes Tarasov-Varchenko's formu..
arXiv:2606.01153v1 Announce Type: new Abstract: Motivated by the works of Gromov and LeBrun in Riemannian geometry, we study the analogous phenomena in complex geometry. We first show that both $\int_M |S_C^-(g)|^ndV_g$ and ${\rm vol}_g(M)$ (normalized by $S_C(g)\ge -1$) are bounded below by $\frac{(n\pi)^n}{n!}\mathrm{CanVol}(M)$ for any Hermitian metric $g$ on a compact complex $n-$manifold $M$. Here $S_C$ denotes the Chern scalar curvat....
arXiv:2606.01154v1 Announce Type: new Abstract: Let $X$ be a Banach space and $f\in\mathcal{C}^1(X)$ be bounded from below. We show that if for some $m\geq 1$, the function $x\mapsto \|\nabla f(x)\|^m$ is convex, then $f$ is convex. We also establish a more general version of this result: if $f$ is continuous and bounded from below, then it is convex, provided $x\mapsto s_f(x)^m$ is convex for some $m\geq 1$, where $s_f$ denotes the (De Gi..
arXiv:2606.01156v1 Announce Type: new Abstract: We consider a semi-blind deconvolution problem arising in the decoding of blurred linear barcodes. Building on the Piecewise Constant Level Set (PCLS) framework introduced in [De\,Cezaro et al., Inv.\,Probl., 29 (2013), 015003], we propose and analyze a solution method based on augmented Lagrangians to obtain stable approximate solutions to the corresponding inverse problem with respect to no....
arXiv:2606.01163v1 Announce Type: new Abstract: We formulate a factorization hypothesis for linear orders definable by oracle polynomial-time machines. Assuming this hypothesis, we provide an approach to constructing a nonstandard model satisfying the minimization scheme for polynomial-time predicates while violating the tournament principle for graphs with polynomial-time edge relation.
arXiv:2606.01165v1 Announce Type: new Abstract: Ramesh's 2023 dissertation introduces the categorical notions of introspective theories and geminal categories, which formalize "self-internalizing" structures sharing the form of L\"ob's theorem ($\Box A \vdash A$ implies $\vdash A$). We reorganize the theory of geminal categories in a self-contained manner by introducing "code structures on fibrations," which serve as a categorical abstract..
arXiv:2606.01169v1 Announce Type: new Abstract: Spacecraft collision avoidance for low-thrust satellites often requires determining not only how to maneuver, but also how late a maneuver can begin while still ensuring safety. This paper presents a greedy time-optimal (GTO) backward-sweep method to find the latest maneuver initiation time. The method starts from the nominal time of closest approach and iteratively propagates the maneuver ba..
arXiv:2606.01180v1 Announce Type: new Abstract: We investigate several $\sigma$-ideals on the Baire space $\omega^\omega$ $(\mathbb{Z}^\omega)$, introducing and studying the ideals $\mathcal{G}$ and $\mathcal{SMZ}^+$, alongside the classical ideals of meager sets, strong measure zero sets, the eventually different ideal and infinitely equal ideal We establish structural relationships and proper inclusions among these ideals. Also we comput..
arXiv:2606.01197v1 Announce Type: new Abstract: Motivated by recent developments in full-duplex radios, cognitive radios, and data-driven signal-processing, we propose a novel class of reactive jamming adversaries wherein the adversary transmits jamming energy on the victim's frequency band while simultaneously monitoring various energy statistics in the network to detect the presence of potential countermeasures, thereby trapping the vict....
arXiv:2606.01200v1 Announce Type: new Abstract: Considered herein is a high-order regularization of the nonlinear shallow water equations within the framework of water wave theory. The regularized system is Galilean invariant and its solutions maintain an energy level that closely matches that of the nonlinear shallow water equations. However, in contrast to the classical nonlinear shallow water system, which admits discontinuous shock wav....
arXiv:2606.01206v1 Announce Type: new Abstract: Let $G$ be a split, simply connected, almost simple algebraic group over a field of characteristic zero, and let $P$ be a maximal parabolic subgroup of $G$. We study the ring of differential operators on $P^{\mathrm{der}}\backslash G$, showing that it shares several key structural properties with classical Weyl algebras. We also develop a corresponding theory of $D$-modules.
arXiv:2606.01209v1 Announce Type: new Abstract: We consider an open Jackson network with $n$ exchangeable single-server stations and weak all-to-all interaction through routing: upon service completion at station $i$, a job is routed to station $j$ with probability $p/n$, where $p\in(0,1)$, or leaves the system with probability $q=1-p$. We study a joint asymptotic regime in which the number of stations tends to infinity while the system ap....
arXiv:2606.01218v1 Announce Type: new Abstract: Collision statistics provide a finite-resolution view of information by measuring how often a fixed number of independent samples fall on the same state. These directly countable quantities form the basis of integer-order R\'enyi entropies. Here, we use low-order R\'enyi entropies to approximate Shannon entropy and mutual information, while characterizing what is necessarily lost when only fi....
arXiv:2606.01219v1 Announce Type: new Abstract: In this paper, we consider a network transport model in which agents moving along the edges can contribute to dynamics at nodes or bypass them. The model takes the form of a system of first-order partial differential equations coupled with a system of ordinary differential equations, and can describe a range of phenomena, from diseases in metapopulations to migratory systems with delays, to c..
arXiv:2606.01232v1 Announce Type: new Abstract: We study randomized stationary methods for symmetric positive definite linear systems in which component $j$ is selected with probability proportional to $|r_j|^\ell$. This power-weighted family interpolates continuously between uniform randomized Jacobi as $\ell \to 0$ and Gauss--Southwell greedy relaxation as $\ell \to \infty$. For the central case $\ell = 2$, we sharpen the standard one-st....
arXiv:2606.01245v1 Announce Type: new Abstract: Motivated by their applications in DNA-based storage systems, codes capable of correcting consecutive deletions have attracted significant attention. An important class of such codes consists of those that can correct multiple consecutive deletion errors, commonly referred to as multiple $b$-burst deletion-correcting codes. In this paper, we investigate the fundamental limits of multiple $b$-..
arXiv:2606.01257v1 Announce Type: new Abstract: Gradient-based algorithms are central to modern statistical estimation, yet their statistical analysis is often restricted to fixed-time behavior, such as convergence to a population target or fluctuations at a prescribed iteration. In many applications, however, uncertainty quantification is needed along the entire optimization path, especially when the stopping time is data-dependent or div....
arXiv:2606.01267v1 Announce Type: new Abstract: The Burrows--Wheeler transform is usually viewed as a clustering transform: it tends to group equal letters into long runs. We study the opposite extremal regime, where the BWT output is completely unclustered, that is, has as many equal-letter runs as positions. Known results imply, on the one hand, that the number of runs in the BWT of a Lyndon word can increase by at most a factor of two, ....
arXiv:2606.01268v1 Announce Type: new Abstract: We prove that Thompson's group $F$ satisfies the relative invariant subalgebra rigidity property with respect to its commutator subgroup: every von Neumann subalgebra of $L(F)$ that is invariant under conjugation by $[F,F]$ is of the form $L(N)$ for some normal subgroup $N \trianglelefteq F$. Along the way, we establish a general factoriality criterion for invariant subalgebras whose hypothes..
arXiv:2606.01278v1 Announce Type: new Abstract: We study the extremality properties of rays generated by tautological Chern classes of matroids in the polyhedral nef cones of the permutohedral variety. Our main result provides necessary and sufficient conditions a matroid has to meet for its tautological Chern classes to generate extremal rays. Our approach yields a new and large family of extremal rays that interpolates between two previo..
arXiv:2606.01284v1 Announce Type: new Abstract: Semantic communication has emerged as a promising paradigm for improving transmission efficiency by conveying task-relevant semantics rather than raw data. Although recent studies have achieved notable gains in communication efficiency and average task performance, reliability remains a fundamental bottleneck in dynamic and uncertain environments. In particular, most existing designs are stil....
arXiv:2606.01290v1 Announce Type: new Abstract: We study the behavior of Dehn functions of finitely presentable groups for presentations with finite generating sets and possibly infinite sets of defining relators. For the free abelian group $\mathbb Z^2$ of rank two on generators $a,b$, we prove that the infinite presentation $\langle a,b \mid [a^{2^k},b],\ k=0,1,2,\ldots\rangle$ has Dehn function of order $n\log n$. We also prove that, fo....
arXiv:2606.01299v1 Announce Type: new Abstract: We study the interaction between the group law on an abelian variety and the additive structure induced on its image under a morphism to a projective space. Let $A/F$ be an abelian variety, $f:A \rightarrow \mathbb{P}^n$ be a morphism which is finite onto its image, and $\Gamma \subseteq A(F)$ be a finite-rank subgroup. We show that for any affine chart $\mathbb{A}^n \subseteq \mathbb{P}^n$ a....
arXiv:2606.01303v1 Announce Type: new Abstract: We develop a multicontinuum Generalized Multiscale Finite Element Method (MC-GMsFEM) for constructing coarse-scale models in heterogeneous media that simultaneously provide accurate numerical approximations and physically consistent macroscopic equations. Classical multiscale methods efficiently approximate fine-scale solutions on coarse grids using localized basis functions, but they do not ....
arXiv:2606.01310v1 Announce Type: new Abstract: For an algebraic function field $F$ over a large field $K$, we show: 1) if $F|K$ has a rational place, then there is a finite purely inseparable extension $K'|K$ such that $K'$ is existentially closed in $F.K'$; 2) $F|K$ has a rational place admitting local uniformization if and only if $K$ is existentially closed in $F$.
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