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Stability results for regularized least-squares problems via generalized Hessian expressions and monotone generalized equations
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arxiv.org
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2 days ago
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eng
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 ....
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Perturbation-resilient inertial Krasnosel'skii-type hybrid retractions for generalized nonexpansive mappings
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arxiv.org
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2 days ago
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eng
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 ....
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The number of cut-edges and conflict-free connection number in planar graphs
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arxiv.org
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2 days ago
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eng
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.
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Analytical Solutions of 3D Maxwell's Equations via Infinite-Order Curl-Operator Expansions
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arxiv.org
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2 days ago
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eng
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 ....
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Classification of blow-ups for the Alt--Phillips problem in three dimensions
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arxiv.org
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2 days ago
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eng
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 $3$.
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On a Local Radial Rigidity Phenomenon of Elliptic Systems on Riemannian Manifolds
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arxiv.org
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2 days ago
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eng
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..
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A hybrid method for countable equilibrium, variational inequality and maximal monotone inclusion problems with fixed point constraints
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arxiv.org
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2 days ago
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eng
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....
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Stein's Method for Convergence Rates of Invariant Measures in the Nonlocal-to-Local Limit
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arxiv.org
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2 days ago
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eng
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..
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Quasisimple groups with a proper subgroup having the same vector orbits in characteristic $2$
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arxiv.org
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2 days ago
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eng
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.
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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..
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Convolution-type Identity for Characteristic Polynomials of Geometric Semilattices
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arxiv.org
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2 days ago
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eng
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..
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Large time intrinsic growth and asymptotic behavior for the classical Timoshenko system
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arxiv.org
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2 days ago
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eng
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....
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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.
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Traveling waves for combustion reaction-diffusion-convection equations: the full range of wave speeds
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arxiv.org
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2 days ago
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eng
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
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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....
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A Refinement of the Fixed--Pixed Points Equidistribution on restricted Permutations
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arxiv.org
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2 days ago
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eng
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..
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Asymptotic estimates for multiple point ranges of transient random walks on graphs
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arxiv.org
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2 days ago
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eng
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..
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Eigenfunction correlators under power-law SULE and localization for lattice operators
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arxiv.org
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2 days ago
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eng
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....
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Combinatorial interpretations of Tutte polynomials at the point $(2,-1)$
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arxiv.org
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2 days ago
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eng
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,..
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Tensor gradient flow with quasi-entropy for smectic liquid crystals and discretizations keeping coupled physical constraints
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arxiv.org
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2 days ago
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eng
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 ....
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Hybrid Bit and Semantic Communications for UAV-Enabled Wireless Power Transfer Networks: A Decision-Assisted Deep Reinforcement Learning Approach
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arxiv.org
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2 days ago
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eng
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....
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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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arXiv:2606.00687v1 Announce Type: new Abstract: From a generating function for a Legendrian in a $1$-jet bundle, we may extract the following topological information: (1) a trivialization of the stable Gauss map, (2) the sheaf of sub-level-set stable cohomotopies, and (3) an identification of the microlocalization of the latter with the J-homomorphism image of the former. Here we show that in fact (1), (2), (3) completely classify generati..
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Sharp $A_\alpha$-Spectral Conditions for Odd $[1,b]$-Factors When $\alpha>1/2$
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arxiv.org
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2 days ago
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eng
arXiv:2606.00691v1 Announce Type: new Abstract: We solve, for all sufficiently large even orders, the problem proposed by Chen et al. on sharp $A_\alpha$-spectral conditions for the existence of odd $[1,b]$-factors when $\alpha>1/2$. Chen et al. showed that every connected graph of even order $n$ with no odd $[1,b]$-factor has $A_\alpha$-spectral radius at most $\max_{1\le s\le k}\rho_\alpha(G_s)$, where $G_s=K_s\nabla\left(K_{n-(b+1)s-1}\....
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arXiv:2606.00693v1 Announce Type: new Abstract: We define a bi-invariant word metric on a group using keis. We discuss whether such a word metric is trivial or non-trivial in various examples coming from group theory, dynamical systems, as well as complex and symplectic geometry.
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Information-Theoretic Lower Bounds for Bit-Constrained Stochastic Optimization via a Reduction to Compressed Gaussian Mean Estimation
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arxiv.org
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2 days ago
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eng
arXiv:2606.00703v1 Announce Type: new Abstract: Low-precision pretraining (FP8, MXFP4, NVFP4) is now standard for frontier language models, yet the literature is almost entirely achievability -- algorithms and empirical scaling laws -- with no matching characterization of what is information-theoretically possible. We study a B-bit quantized stochastic first-order oracle: an optimizer interacts for T rounds and receives, each round, a B-bi....
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Small-Scale Magnitude Below One for Cyclic Two-Chunk Finite Metric Spaces
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arxiv.org
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2 days ago
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eng
arXiv:2606.00707v1 Announce Type: new Abstract: Motivated by the small-scale viewpoint of Roff and Yoshinaga, we study finite metric spaces whose scaled copies collapse to a single point while their magnitude remembers how the collapse takes place. The limit metric space is geometrically indistinguishable from a point, but the magnitude function can detect differences in the path of collapse. We introduce a four-parameter family of cyclic ..
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Structural Causal Discovery and Predictive Sufficiency in High-Dimensional Dynamical Systems
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arxiv.org
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2 days ago
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eng
arXiv:2606.00710v1 Announce Type: new Abstract: High-dimensional environmental systems often contain variables that are strongly predictive, structurally informative, and physically coupled, but these roles are not equivalent. In precipitation dynamics, this distinction is particularly important because rainfall emerges from multiscale thermodynamic, kinematic, microphysical, and land--atmosphere interactions, while observations are sparse....
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Liouville Type Theorem for the Steady Fractional Compressible MHD Equations in $\mathbb{R}^{3}$
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arxiv.org
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2 days ago
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eng
arXiv:2606.00713v1 Announce Type: new Abstract: This paper is concerned with the Liouville-type problem for the stationary fractional compressible magnetohydrodynamics (MHD) equations. The main difficulty comes from the nonlocal fractional Laplace operator $(-\Delta)^s$. To overcome it, we combine the Caffarelli-Silvestre extension technique with truncation arguments. Under suitable regularity and decay conditions, we prove that the only s..
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arXiv:2606.00719v1 Announce Type: new Abstract: Let $\kappa^{\prime}(G)$ be the edge-connectivity of the graph $G$. The \textit{strength} of $G$, denoted by $\overline{\kappa}^{\prime}(G)$, is the maximum edge-connectivity of its subgraphs. A simple graph $G$ is called $k$-\textit{edge-maximal} if $\overline{\kappa}^{\prime}(G) \leq k$ but for any edge $e$ not in $G$, $\overline{\kappa}^{\prime}(G+e) \geq k+1$. In this paper, we propose th..
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arXiv:2606.00731v1 Announce Type: new Abstract: In this paper, we introduce and study the notion of Q-filters in bounded lattices.
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arXiv:2606.00736v1 Announce Type: new Abstract: We prove that, over any ring $R$, the supremum of the projective dimensions of the flat left $R$-modules coincides with the supremum of the Gorenstein projective dimensions of the Gorenstein flat left $R$-modules. As a consequence, we obtain new characterizations of left $n$-perfect rings in terms of Gorenstein projective, Ding projective, and projectively coresolved Gorenstein flat dimension..
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Realization, interpolation, extension on the pentablock and applications to $\mathbb D^2$, $\mathbb G_2$
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arxiv.org
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2 days ago
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eng
arXiv:2606.00760v1 Announce Type: new Abstract: We introduce Schur-Agler class for the pentablock $\mathbb P$ and establish a realization theorem for functions in this class. Then we prove an interpolation theorem for the pentablock with interpolating functions belonging to the corresponding Schur-Agler class. Also, we obtain an extension theorem for $\mathbb P$. Applying these results, we add a few new characterizations in the existing re..
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The Gaussian Gabor system at the critical density is a weighted lower semi frame
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arxiv.org
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2 days ago
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eng
arXiv:2606.00764v1 Announce Type: new Abstract: We show that the Gaussian Gabor system at the critical density is a weighted lower semi frame, thus resolving an open question. This complements recent results showing that the system is neither a weighted frame nor admits a reproducing partner. In fact, after removing any atom from the system, suitable weights produce a complete Riesz Fischer sequence and lower semi frame.
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arXiv:2606.00772v1 Announce Type: new Abstract: Let $\lambda = (\lambda_1, \ldots, \lambda_n)$ be a partition with $\lambda_1 = m$. Denote by $J_\lambda$ the cover ideal in the polynomial ring \( S = k[x_1, \ldots, x_n, y_1, \ldots, y_m] \) associated to the Ferrers graph corresponding to $\lambda$. Let $d(\lambda)$ denote the number of distinct parts of $\lambda$. We prove that \[ \operatorname{pd}(S/J_\lambda^t) = \min\{t,\; d(\lambda)\}..
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A path-following framework on fiber bundle for variational inequalities
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arxiv.org
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2 days ago
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eng
arXiv:2606.00778v1 Announce Type: new Abstract: Variational inequality (VI) is a fundamental mathematical framework for many classical problems. We present a path-following framework for finite-dimensional VIs with arbitrary continuous functions and compact convex domains. The approach first approximately reduces a general VI to a smooth VI on simplex. Its key innovation is to formulate the smooth VI on simplex on a fiber bundle called the....
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arXiv:2606.00781v1 Announce Type: new Abstract: We introduce a continuous-time mutation model with two types determined by a finite measure $\Lambda$ on the unit interval. The model satisfies a certain consistency property known from mathematical population genetics and includes so called harmonic models being of interest in mathematical statistical physics. We mainly focus on the situation when the number of particles is equal to some con..
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Coupled Routing and Charge Schedule Optimization of Electrified Delivery Truck Fleets: Feasibility Analyses
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arxiv.org
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2 days ago
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eng
arXiv:2606.00792v1 Announce Type: new Abstract: Electrifying truck fleets has the potential to improve energy efficiency and reduce carbon emissions from the freight transportation sector. However, the range limitations and substantial capital costs with current battery technologies imposes constraints that challenge the overall cost feasibility of electrifying fleets for logistics companies. In this paper, we investigate the coupled routi....
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arXiv:2606.00799v1 Announce Type: new Abstract: A classic theorem of Weyl (1921) states that a Weyl metric -- a natural generalisation of a pseudo-Riemannian metric -- is uniquely determined by its conformal and projective structures (i.e. by its conformal structure and its set of unparametrised geodesics). An equivalent formulation of Weyl's result is that a torsion-free linear connection compatible with a pseudo-Riemannian conformal stru..
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arXiv:2606.00802v1 Announce Type: new Abstract: Given a graph $G$, a set $F$ of edges is an edge dominating set of $G$ if every edge in $G$ is either in $F$ or adjacent to an edge in $F$. A graph $G$ is said to be well-edge-dominated if every minimal edge dominating set has the same cardinality. This definition is the edge version of domination in that a set $D\subseteq V(G)$ is a dominating set if every vertex in $G$ is in $D$ or adjacent..
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arXiv:2606.00812v1 Announce Type: new Abstract: We define a new Ehrenfeucht-Fra\"iss\'e game for dependence logic. The previously known rendition of such a game was based on moves that are teams. Since teams can be massive, making team moves may be quite complicated. To remedy this, our new Ehrenfeucht-Fra\"iss\'e game for dependence logic has only moves that consist of single elements, as in the classical Ehrenfeucht-Fra\"iss\'e game of f..
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arXiv:2606.00833v1 Announce Type: new Abstract: We prove the Nielsen--Schreier property for the variety of algebras defined by the identity $x(x^2)^2=(x^2)^2x$: every subalgebra of every free algebra in this variety is itself free. We also show that this variety of algebras does not have the Poincar\'e--Birkhoff--Witt property for universal multiplicative enveloping algebras. Our strategy of proof actually leads to infinitely many new vari..
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arXiv:2606.00836v1 Announce Type: new Abstract: Graphs defined over finite rings are well studied in the literature. The study of these graphs benefits from rich connections between several areas of mathematics, including number theory, algebra, combinatorics, and graph theory, and these connections often lead to interesting interactions between algebraic and combinatorial structures. In this article, we investigate gcd-graphs defined over..
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