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arXiv:2606.00945v1 Announce Type: new Abstract: In this survey, we extend conclusions on the hexagonal lattice to 3-12 lattice: the connective constant for the 3-12 lattice can be derived from the connective constant for the hexagonal lattice; the conformal invariance of the Ising model and of the percolation on the 3-12 lattice can be derived from their conformal invariance on the hexagonal lattice.
arXiv:2606.00952v1 Announce Type: new Abstract: This is the second of a pair of papers where we construct and investigate a closed monoidal structure on the category of generalized algebraic theories (in the sense of Cartmell). Having presented the tensor product of theories in a syntactic way, we now study the same structure from the perspective of contextual categories. We define the exponential $\mathcal A^\mathcal B$ between two conte....
arXiv:2606.00958v1 Announce Type: new Abstract: The square-and-multiply algorithm, also known as binary exponentiation or repeated squaring, is a technique for fast exponentiation commonly used in modern cryptography and computational number theory. Despite its prominence, the historical origins of the algorithm are not known with certainty. This paper critically examines the origins and formalization of the algorithm through primary sourc....
arXiv:2606.00961v1 Announce Type: new Abstract: We show that the conflated expression graph for an arbitrary permutation has a unique minimal element and a unique maximal element, and every reduced expression sits on a maximal chain from the source to the sink. This generalizes the work of Manin-Schechtman regarding higher Bruhat orders, and gives an independent and self-contained proof of certain results in Hothem. In addition, we give ex..
arXiv:2606.00964v1 Announce Type: new Abstract: We construct a mean curvature flow with surgery starting with any compact mean convex hypersurface in $\mathbb{R}^{n+1}$, extending previous results of Huisken-Sinestrari, Brendle-Huisken, and Haslhofer-Kleiner for 2-convex flows. In contrast with previous constructions of mean curvature flow with surgery, the topological surgeries are performed by the flow itself through nondegenerate cylind..
arXiv:2606.00969v1 Announce Type: new Abstract: In this paper, we introduce a higher-order averaging theory and method for a wide range of nonsmooth systems that are generally characterized by the classical averaging canonical form. Utilizing tools from generalized derivatives theory, we provide a nonsmooth near-identity transformation analogous to the one in smooth averaging theory. Additionally, we exploit sharp calculus rules from lexic....
arXiv:2606.00976v1 Announce Type: new Abstract: An edge-colored graph is called rainbow if all its edges have distinct colors. For a fixed graph $H$, the rainbow Tur\'an number $\exstar(n, H)$ is the maximum number of edges in a properly edge-colored graph with $n$ vertices that does not contain a rainbow subgraph isomorphic to $H$. A $t$-fan $\Ft$ ($t \geq 2$) is a graph formed by $t$ triangles sharing a common vertex. A wheel graph $\Wn$....
arXiv:2606.00978v1 Announce Type: new Abstract: This paper studies two problems that are motivated by combining two novel approaches, namely DNA composite and rank modulation. The recent approach of composite DNA takes advantage of the DNA synthesis property which generates a huge number of copies for every synthesized strand. Under this paradigm, every composite symbols does not store a single nucleotide but a mixture of the four DNA nucl..
arXiv:2606.00983v1 Announce Type: new Abstract: We formulate a program to prove the categorical local Langlands conjecture (CLLC) of Fargues-Scholze, for all quasisplit $p$-adic groups where the Fargues-Scholze $L$-parameters agree with the semisimplification of a known "automorphic" local Langlands parametrization. A key working hypothesis - which we expect to prove elsewhere jointly with Hamann - is the compatibility of the enhanced Whit....
arXiv:2606.00993v1 Announce Type: new Abstract: In this paper we study the Stokes phenomenon of the quantum confluent hypergeometric supersystem, certain meromorphic linear system of ordinary differential equation with a second order pole, associated to the Lie superalgebra $\mathfrak{gl}_{m|n}$. We prove that its Stokes supermatrices satisfy the Yang-Baxter equation, and thus give rise to the quantum supergroup $U_q(\mathfrak{gl}(m|n))$.
arXiv:2606.01001v1 Announce Type: new Abstract: We show that axisymmetric Willmore surfaces admit a first-order formulation obtained by combining two independent first integrals. If $\rho$ denotes the distance from the axis of revolution and $\Psi=\sin\psi$, where $\psi$ is the tangent angle of the generating curve, then the profile satisfies \begin{equation*} \frac{\left[\Psi(\rho\Psi'-\Psi)^2+2(\rho\Psi'-\Psi)+2C_1\rho\right]^2}{1-\Psi^2..
arXiv:2606.01011v1 Announce Type: new Abstract: This paper studies conditional independence testing under the Gaussian additive noise model (GANM), where two variables are modeled as nonlinear functions of covariates with independent bivariate Gaussian regression errors. Under this framework, conditional independence can be characterized by the correlation coefficient of the regression errors, which motivates a test based on the Pearson co....
arXiv:2606.01017v1 Announce Type: new Abstract: Thurston constructed codimension one foliations on $S^3$ thereby proved that the homomorphism $gv: \pi_3(B\overline{\Gamma}^\infty_1)\rightarrow \mathbb{R}$ induced by the Godbillon-Vey invariant is surjective. By another real analytic construction, he proved that the homomorphism $gv: H_3(B\overline{\Gamma}^\omega_1)\rightarrow \mathbb{R}$ is also surjective where $B\overline{\Gamma}^\omega_....
arXiv:2606.01035v1 Announce Type: new Abstract: We utilize multi-virtual knot theory where there are a multiplicity of virtual crossings to study strict virtual linkoids. In strict virtual linkoid theory, local moves define all virtual moves and Reidemeister moves. In the strict equivalence, no moves, classical or virtual, can transfer an arc across a linkoid endpoint. By taking closures of strict virtual linkoids that are multi-virtual kn..
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 - 1 month 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.
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