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arXiv:2606.00378v1 Announce Type: new Abstract: Many researchers have proposed their own potential-energy functions for the study of diatomic molecules, some of which have been proved to be equivalent. In this paper we suggest the application of a few simple rules to determine the equivalence between molecular potentials. The resulting systematic procedure is illustrated by means of several examples.
arXiv:2606.00381v1 Announce Type: new Abstract: The classic Besicovitch projection theorem asserts that if a set is purely $1$-unrectifiable with finite length in $\mathbb{R}^2$, its orthogonal projection has Lebesgue measure zero in almost every direction. In the opposite direction, the two-projection theorem states that if a Borel set has zero measure under orthogonal projections onto two distinct non-antipodal directions, it must be pur..
arXiv:2606.00385v1 Announce Type: new Abstract: Let $\Bbbk$ be a field, $H$ a colour Hopf algebra and $A$ a graded $H$-comodule colour algebra. We give a sufficient condition for a colour $(A,H)$-Hopf module to be injective as a graded $H$-comodule and we deduce relative projectivity in the category of colour $(A,H)$-Hopf modules. We generalize the Fundamental Theorem of $(A,H)$-Hopf modules to the context of colour $(A,H)$-Hopf modules. U..
arXiv:2606.00388v1 Announce Type: new Abstract: High-resolution energy system capacity expansion models (CEMs) for energy transition planning often result in large-scale mixed-integer linear programming (MILP) formulations. Benders decomposition (BD) offers a scalable solution approach by iteratively solving a master problem (MP) for investment decisions and multiple subproblems (SPs) for operational decisions. However, accumulated Benders....
arXiv:2606.00389v1 Announce Type: new Abstract: We consider the periodic quintic nonlinear Schr\"odinger and prove small-mass global well-posedness in $H^s(\mathbb{T})$ for $s>0$. The proof relies on a new derivative-loss-free $L^6_{t,x}$ Strichartz estimate which is established using the high-low method, an asymmetric superlevel set estimate and a new refined broad-narrow argument. Although our $L^6_{t,x}$ Strichartz estimate is not sharp..
arXiv:2606.00396v1 Announce Type: new Abstract: We establish basic properties of the deformed mass and phase functions on the space of stability conditions. We prove that these functions are continuous and deduce that the space of stability conditions admits a homeomorphic embedding into a product space of finite measures. Subsequently, we give a proof of the triangle inequality for deformed mass functions and provide estimates for the def..
arXiv:2606.00406v1 Announce Type: new Abstract: This paper introduces a new framework for quantum simultaneous information and power transfer (QSIPT), enabling the joint use of quantum states for classical information and energy transfer in quantum communication systems. We propose a novel model in which quantum states are simultaneously used to transmit classical information through a quantum channel and transfer energy to an energy harve....
arXiv:2606.00410v1 Announce Type: new Abstract: We prove that the set of positive integers having between $1$ and $n$ prime factors, counted with multiplicity, has degree of accessibility $2^n$. In particular, the case $n=1$ answers a question of Landman and Robertson asking whether the set of prime numbers is $2$-accessible.
arXiv:2606.00420v1 Announce Type: new Abstract: Ballantine, Beck, and Merca defined the elementary symmetric partition map pre$_j$ that sends a partition $\lambda$ to a larger partition whose parts are the summands appearing in the evaluation of the $j$-th elementary symmetric polynomial on $\lambda$. They conjectured that pre$_j$ is injective on the set of partitions of $n$ with length $\ell \geq j$. The $\ell = j$ case was disproved by D..
arXiv:2606.00421v1 Announce Type: new Abstract: We construct explicit isomorphisms between three models for the $B(\infty)$ crystal in type ${\tt A}_1^{(1)}$: affine Mirkovi\'c--Vilonen polytopes, Kleshchev multipartitions, and a new model we call upper ledge diagrams. We also present some clarifying results on these crystals, giving a direct method for completing an affine MV polytope from the data of one of its boundary root partitions, ..
arXiv:2606.00466v1 Announce Type: new Abstract: We use sieving arguments to estimate the frequency of $s$-tuples of rational points $$(P_1,\dots,P_s)\in E_1(\mathbb{Q})\times\cdots\times E_s(\mathbb{Q}),$$ where $E_1,\dots,E_s$ are (not necessarily distinct) elliptic curves over $\mathbb{Q}$, for which the product of their denominators is a perfect $\ell$th power for a fixed prime $\ell$. We consider two settings: one in which the points a..
arXiv:2606.00468v1 Announce Type: new Abstract: We present a lifting-based interface reduction framework for nonlinear transmission and eigenvalue problems. The method represents the solution as a sum of a bulk component and a lifting component that carries the interface jump, thereby reducing the original problem to a nonlinear system posed on the interface. A low-dimensional approximation is obtained by restricting the interface unknown....
arXiv:2606.00469v1 Announce Type: new Abstract: We study supervised regression with neural ODEs (NODEs) from a control-theoretic perspective to derive explicit population-risk bounds. We focus on a widely used class of non-autonomous models with constant parameters and explicit time dependence, which we call semi-autonomous NODEs (SA-NODEs). We constructively prove that SA-NODEs are capable of \emph{exact} interpolation of admissible finit....
arXiv:2606.00475v1 Announce Type: new Abstract: This paper introduces interval $B_{\pi}^{R^I}$-tensors as a natural extension of $B_{\pi}^{R}$-tensors to the interval setting. We provide two practical verifiable criteria for an interval tensor to be an interval $B_{\pi}^{R^I}$-tensor, one based on endpoint inequalities and another constructing an explicit vector $\pi$. Connections with interval $P$-tensors, positive definite interval tenso..
arXiv:2606.00478v1 Announce Type: new Abstract: Online high-dimensional regression has gained increasing attention in recent years, yet existing methods typically assume that all candidate features, including important ones, are observed from the outset of data collection. This assumption is often violated in real-world scenarios, where new variables become available gradually as data accumulate. To address this gap, we introduce a novel f....
arXiv:2606.00480v1 Announce Type: new Abstract: Continuous data assimilation seeks to estimate the state of a dynamical system from partial observations. In many applications, however, the state dynamics are unknown or prohibitively expensive to simulate at the required resolution, leading to model error. Motivated by this challenge and the increasing adoption of machine learning surrogates in data assimilation, this paper develops a unifi....
arXiv:2606.00482v1 Announce Type: new Abstract: Let $k$ be a real quadratic field. Let $k_n$ be the $n$-th layer of the $\mathbb{Z}_2$-extension of $k$, and $2^{a_n}$ be the $2$-part of the class number of $k_n$. In this paper, we derive many laws concerning the sequence $(a_0,a_1,\dotsc)$, by iteratively extending the group of cyclotomic units.
arXiv:2606.00484v1 Announce Type: new Abstract: We characterize dominating sets for weighted Fock spaces $F^p_{\alpha,w}$ induced by Muckenhoupt $A_{\infty}$ weights, which leads to a sufficient condition for reverse Carleson measures for the spaces $F^p_{\alpha,w}$ with restricted $A_{\infty}$ weights. Applications to invertibility of Toeplitz operators, closed range property of Volterra operators, and atomic decomposition of $F^p_{\alpha..
arXiv:2606.00505v1 Announce Type: new Abstract: Exceptional longest-run behaviour in continued fraction expansions is studied through the interaction between fixed-symbol runs and the overall longest run. For every prescribed partial quotient value and every admissible growth scale, a full Hausdorff dimensional set of irrational numbers is constructed on which the longest run of the prescribed value has exactly the prescribed asymptotic gr..
arXiv:2606.00517v1 Announce Type: new Abstract: This paper studies the regularization of ill-posed inverse problems by deep neural networks (DNNs). We extend architecture-based regularization from shallow networks to deep models by developing a deterministic framework in which the admissible network class is enlarged adaptively and the resulting architecture complexity acts as the regularization mechanism. We propose two discrepancy-princi....
arXiv:2606.00520v1 Announce Type: new Abstract: Many stochastic gradient methods are believed not to converge when the noise in stochastic gradients has only a finite $p$-th moment for $p\in\left(1,2\right)$, a setting known as the heavy-tailed noise assumption. However, some recent studies have found that Stochastic Gradient Descent ($\textsf{SGD}$), without any modification to its update rule, can surprisingly converge in expectation for....
arXiv:2606.00525v1 Announce Type: new Abstract: We introduce a family of constants \[ C_m := \lim_{n\to\infty} \left( \sum_{k=1}^n \operatorname{Li}_m\!\left(\frac1k\right) - \log n \right), \] which may be regarded as polylogarithmic analogues of Euler's constant. We study their basic properties and derive representations in terms of iterated logarithmic integral structures associated with the gamma function. We further introduce associat..
arXiv:2606.00526v1 Announce Type: new Abstract: We study perturbation and stability properties of solution mappings associated with convex regularized least-squares problems. We first establish an implicit function theorem for generalized equations governed by maximally monotone operators and smooth perturbations, yielding conditions for local Lipschitz continuity, directional differentiability, and semismoothness of solution mappings. We ....
arXiv:2606.00528v1 Announce Type: new Abstract: Let $E$ be a uniformly smooth and uniformly convex real Banach space. We study perturbation-resilient inertial Krasnosel'skii-type hybrid retraction schemes for a countable family of generalized nonexpansive mappings satisfying the NST-condition with a family $\Gamma$. The main result shows that strong convergence is preserved when the exact $\phi$-Fej\'er decrease condition is replaced by a ....
arXiv:2606.00533v1 Announce Type: new Abstract: A \textit{cut-edge} of a connected graph is an edge whose deletion increases the number of components. In this paper, we first state some conditions for a planar graph to have a few cut-edges. After that, we use the main results to study the conditions for a colored planar graph to have a bounded conflict-free connection number.
arXiv:2606.00534v1 Announce Type: new Abstract: Solving Maxwell's equations in open-space settings with general initial conditions and source terms remains a fundamental challenge. We address this problem through an operator-based construction, developing an infinite-order curl-operator expansion that yields analytical solutions as function-to-function mappings from initial data and source terms to electromagnetic fields. The framework is ....
arXiv:2606.00538v1 Announce Type: new Abstract: We prove a flatness theorem for classical stable homogeneous solutions of the $\gamma$-Alt--Phillips free boundary problem in three dimensions in the range $0<\gamma\le 2/3$, where $\gamma$ is the exponent in the energy density $|\nabla u|^2+u^\gamma$. In particular, this implies full regularity of the free boundary for minimizers of the corresponding Alt--Phillips energy in dimension $3$.
arXiv:2606.00554v1 Announce Type: new Abstract: In this paper, we study local radial rigidity phenomena for a broad class of general-order elliptic systems on Riemannian manifolds via a reduction to singular ordinary differential equations of Euler type. These rigidity properties have natural applications to several geometric problems, including prescribed curvature problems of Yamabe and Paneitz type in conformal geometry, higher-order an..
arXiv:2606.00575v1 Announce Type: new Abstract: Let $C$ be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space $E$ with dual space $E^{*}$. We introduce a hybrid projection method for approximating a common element of four classes of constraints: the set of fixed points of a countable family of generalized nonexpansive-type maps, the solution sets of countably many equilibrium problems, the solu....
arXiv:2606.00586v1 Announce Type: new Abstract: We utilize Stein's method to establish quantitative bounds on the total variation distance between the invariant measure of a drifted nonlocal Markov operator and that of its local counterpart under minimal assumptions on the drifts. The main ingredient is a reduction via Stein's method that transforms the original problem into analyzing growth estimates for solutions to a nonlocal Poisson eq..
arXiv:2606.00589v1 Announce Type: new Abstract: Let $p$ be a prime, $G$ be a finite group, $H$ a proper subgroup of $G$ and $V$ a finite dimensional $GF(p)G$-module. The triple $(G,H,V)$ is immutable if and only if $G$ and $H$ have the same orbits on the vectors of $V$. We determine the immutable triples for $G$ a quasisimple group, $H$ a subgroup of $G$ and $V$ a $GF(2)G$-module.
arXiv:2606.00594v1 Announce Type: new Abstract: We propose an energy-based nonlocal $p$-Laplacian interface problem. Neumann interface conditions are naturally formulated via the energy, while Dirichlet conditions are enforced through a penalty term. A key feature is that the model retains a sharp interface, which facilitates extension to other interface problems; we illustrate this by developing a nonlocal approximation for the $p$-Laplac..
arXiv:2606.00599v1 Announce Type: new Abstract: We establish a convolution formula for the characteristic polynomial of a finite geometric semilattice $M$: \[ \chi(M,st)=\sum_{X\in \underline{M}} s^{r-{\rm rk}_{\underline{M}}(X)}\chi(\underline{M}^X,t)\,\chi(M_{(X)},s), \] where $\underline{M}$ denotes the centralization of $M$, and $M_{(X)}$ denotes the localization at $X$. This generalizes a nice formula of Southerland, Southern, and Zho..
arXiv:2606.00623v1 Announce Type: new Abstract: In this paper, we investigate the large time behavior of solutions to the classical Timoshenko system in the whole space $\mathbb{R}$. Although the system is conservative and its natural energy is conserved in time, the transversal displacement $\varphi$ and the rotation angle $\psi$ exhibit intrinsic polynomial growths. We establish sharp $L^p-L^q$ estimates for the solutions and show that t....
arXiv:2606.00633v1 Announce Type: new Abstract: The $P(t)$-adic Littlewood conjecture is a function field analogue of the famous $p$-adic Littlewood conjecture in Diophantine approximation. In this paper, we prove that the $P(t)$-adic Littlewood conjecture fails for any irreducible polynomial $P(t)$ over any ground field of odd characteristic.
arXiv:2606.00638v1 Announce Type: new Abstract: We consider traveling wave solutions to a reaction--diffusion--convection equation with a combustion-type reaction term. While a necessary condition for the existence of traveling waves is $c \geq H^*:=\sup_{0
arXiv:2606.00639v1 Announce Type: new Abstract: We apply ideas of geometric measure theory and Baire category theory to topological problems, namely, to topological embeddings of compact sets into Euclidean spaces. In 1947, Borsuk constructed a Cantor set in $\mathbb R^N$, $N\geqslant 3$, such that its projection onto any $(N-1)$-plane contains an $(N-1)$-dimensional ball. This can be strengthened: a desired Cantor set can be obtained fro....
arXiv:2606.00646v1 Announce Type: new Abstract: Motivated by a recent conjecture of Bsila, Cox, Hugo, Styron and Zhuang concerning fixed points and pixed points on pattern-avoiding permutations, we prove a bivariate refinement involving descent statistics. Given a set of permutations $\Pi$, let $\mathfrak{S}_n(\Pi)$ denote the set of permutations in the symmetric group $\mathfrak{S}_n$ that avoid every element of $\Pi$ in the sense of patt..
arXiv:2606.00648v1 Announce Type: new Abstract: We study multiple point ranges for random walks on graphs, extending known asymptotic results obtained for random walks on groups. A distinctive feature is that algebraic and translation-invariance assumptions are replaced by a uniform tail condition on the first return time to the starting point. Under this condition, we obtain upper and lower bounds of linear order for the expectations of t..
arXiv:2606.00650v1 Announce Type: new Abstract: We develop a deterministic framework showing that a power-law form of semi-uniform localization of eigenfunctions (SULE) imposes strong structural and dynamical constraints on lattice operators. In particular, we prove that power-law SULE yields geometric constraints on localization centers, quantitative bounds on eigenfunction correlators, and power-law localization in the sense of finite mo....
arXiv:2606.00653v1 Announce Type: new Abstract: Let $G$ be a simple connected graph, and let $T_{G}(x,y)$ be the Tutte polynomial of $G$. Motivated by the works in \cite{Ma}, we, in this paper, introduce the even-left spanning forests of $G$ and odd $G$-partitionable permutations, and show that $T_{G}(2,-1)$ is equal to both the number of even-left spanning forests of $G$ and the number of odd $G$-partitionable permutations. In particular,..
arXiv:2606.00659v1 Announce Type: new Abstract: A gradient flow for the concentration and a $2\times 2$ tensor is constructed to describe smectic liquid crystals. The free energy consists of the entropy term and interaction term involving squared second order spatial derivatives. The entropy term incorporates the concentration in the quasi-entropy originally proposed for the tensor only, which is a strictly convex and lower semicontinuous ....
arXiv:2606.00668v1 Announce Type: new Abstract: Semantic communications which can significantly reduce spectrum consumption in wireless networks, have recently become a popular research area. When combined with wireless power transfer (WPT), semantic communications can help achieve high spectral efficiency for energy-limited devices in wireless communications. In energy-constrained and link budget-limited scenarios such as UAV networks, th....
AHA! RSK - arxiv.org - 1 month ago - eng
arXiv:2606.00679v1 Announce Type: new Abstract: We give a spectral realization of the Robinson-Schensted-Knuth (RSK) correspondence in terms of the representation theory of the symmetric group $S_n$ and the degenerate affine Hecke algebra (AHA) $H_n$. We view RSK, which builds a pair of standard Young tableaux from a permutation, as a special case of rectification, also known as Jeu de Taquin, which turns skew tableaux into straight ones. ....
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