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arXiv:2604.00539v2 Announce Type: replace Abstract: Alexander polynomial was born one century ago, but explicit formulas have been found for only a few families of links. In this paper, we present an efficient method of computing Alexander polynomial for arborescent links. Applying this method, we express the Alexander polynomials of Montesinos links in terms of certain polynomials associated to rational tangles which can be computed recur..
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Impulse-to-Peak-Output Norm Optimal State-Feedback Control of Linear PDEs
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arxiv.org
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2 days ago
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eng
arXiv:2604.03399v2 Announce Type: replace Abstract: Impulse-to-peak response (I2P) analysis for state-space ordinary differential equation (ODE) systems is a well-studied classical problem. However, the techniques employed for I2P optimal control of ODEs have not been extended to partial differential equation (PDE) systems due to the lack of a universal transfer function and state-space representation. Recently, however, partial integral e....
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arXiv:2604.03567v2 Announce Type: replace Abstract: For a graph $H$ and an integer $k\ge 1$, the \emph{Token Sliding reconfiguration graph} $\mathsf{TS}_k(H)$ and the \emph{Token Jumping reconfiguration graph} $\mathsf{TJ}_k(H)$ have as vertices the $k$-cliques of $H$, with two vertices adjacent when one clique is obtained from the other by replacing one vertex with an adjacent non-member, and respectively by an arbitrary non-member. For a..
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Robust $\mathcal{H}_\infty$ Observer Design via Finsler's Lemma and IQCs
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arxiv.org
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2 days ago
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eng
arXiv:2604.03989v3 Announce Type: replace Abstract: This paper develops a Finsler-based LMI for robust $\mathcal{H}_\infty$ observer design with integral quadratic constraints (IQCs) and block-structured uncertainty. By introducing a slack variable that relaxes the coupling between the Lyapunov matrix, the observer gain, and the IQC multiplier, the formulation addresses two limitations of the standard block-diagonal approach: the LMI requi..
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Invariants of derived equivalences for admissible fractional Brauer graph algebras
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arxiv.org
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2 days ago
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eng
arXiv:2604.06557v2 Announce Type: replace Abstract: Characterizing derived equivalences between algebras via combinatorial structures has recently become a popular topic. In this paper, we study admissible fractional Brauer graph algebras, a new subclass of self-injective special biserial algebras, and provide several easily checkable combinatorial invariants for derived equivalences between them. In particular, we show that these algebras..
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Weighted averages of arithmetic functions and applications to equidistribution and ergodic theory
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arxiv.org
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2 days ago
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eng
arXiv:2604.07186v2 Announce Type: replace Abstract: For a wide range of functions $W\colon\mathbb{N}\to\mathbb{N}$, we establish a general result for estimating weighted averages of the form\[\mathbb{E}^{W}_{n \le N} f(\vartheta(n))= \frac{1}{W(N)}\sum_{n=1}^N (W(n)-W(n-1))f(\vartheta(n)),\]where $f\colon \{1,\ldots,N\}\to\mathbb{C}$ is an arbitrary function, and $\vartheta(n)$ is any arithmetic function that adheres to a certain Gaussian ....
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arXiv:2604.08684v2 Announce Type: replace Abstract: We construct a family of solutions $(u,B)$ of the incompressible magnetohydrodynamic (MHD) system, the $L^\infty$ norm of which blows up instantaneously at the critical rate. The solutions remain smooth except at the blowup time. An inverse energy cascade mechanism and a convex integration scheme along a time sequence are the main ingredients of the construction, inspired by our recent wo....
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arXiv:2604.09116v2 Announce Type: replace Abstract: We investigate infinite-level Shimura varieties within the framework of analytic stacks of Clausen-Scholze, developing their smooth, completed, locally analytic, and de Rham realizations. We formulate a Grothendieck-Messing-Hodge-Tate period map, and establish a Grothendieck-Messing theory for locally analytic infinite-level Shimura varieties. This theory, combined with a reformulation of....
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arXiv:2604.09808v2 Announce Type: replace Abstract: We present a complete formalization, in the Lean interactive theorem prover with the Mathlib library, of the Ramanujan--Nagell theorem: the only integer solutions to the Diophantine equation $x^2 + 7 = 2^n$ are $(n,x) \in \{(3,\pm1),(4,\pm3),(5,\pm5),(7,\pm11),(15,\pm181)\}$. The formalization includes all dependencies, notably the computation of the ring of integers of the quadratic fiel..
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An Adaptive Log-Laguerre Spectral Method for the Radial Dirac Equation: Resolving Asymptotic Decay and Core Singularities in Atomic Calculations
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arxiv.org
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2 days ago
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eng
arXiv:2604.11063v2 Announce Type: replace Abstract: The high-precision solution of the radial Dirac equation is fundamental to relativistic quantum chemistry, essential for reliable pseudopotential generation and all-electron electronic structure methods. Capturing both the non-polynomial singularities at the origin and the state-dependent asymptotic decay on semi-infinite domains presents a significant computational challenge. In this wor....
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arXiv:2604.11569v2 Announce Type: replace Abstract: We study the semiring $\mathbb{N}_0[\alpha]$ as an additive monoid where $\alpha$ is a positive real algebraic number. In the atomic case, the atoms of $\mathbb{N}_0[\alpha]$ are precisely the powers $\alpha^n$ up to a certain nonnegative integer $n$, and finite generation is governed by divisibility of the minimal polynomial by a negative-tail polynomial. Our first main result gives a co..
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arXiv:2604.11769v2 Announce Type: replace Abstract: We construct a family of solutions $(u,b)$ of the incompressible flow with a passive tracer for which both $\|u(t)\|_{L^\infty}$ and $\|b(t)\|_{L^\infty}$ blow up at time $T_*$. Away from $T_*$, the solutions remain smooth in both space and time. The argument adapts the inverse cascade mechanism from [CDP25] to the presence of an advected scalar, but the passive component creates a new co....
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arXiv:2604.14850v2 Announce Type: replace Abstract: We show that the very general Verra fourfold is irrational, using the Hodge atom framework of Katzarkov--Kontsevich--Pantev--Yu. Two novel points are: a refined analysis of Hodge atoms, based on the involution on the cohomology of $X$, and a derivation of the quantum multiplication matrix from the quantum differential operator. This gives the first successful application of the method of ..
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arXiv:2604.16126v3 Announce Type: replace Abstract: The two pillars of Algebraic topology - homology and homotopy theory rely on the availability of basic building blocks called cells. Cells take the form of simplexes, and have properties such as faces, sub-cells, convexity and contractibility. The first two cells, namely the line and point lead to the concept of homotopy. The collection of maps from the cells and the redundancies among th..
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arXiv:2604.16805v2 Announce Type: replace Abstract: Let \(\Lambda\) be a finite-dimensional Koszul algebra with Koszul dual \(\Lambda^!\). We establish derived Koszul dualities at the level of bounded derived categories, both in the graded setting \(\mathsf{D}^{b}(\Lambda\textup{-gmod})\) and in the ungraded setting \(\mathsf{D}^{b}(\Lambda\textup{-mod})\), without imposing finiteness conditions on \(\Lambda^!\). We first prove a graded de....
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arXiv:2604.17924v2 Announce Type: replace Abstract: In this paper we provide conditions for a Wasserstein barycenter to be absolutely continuous with respect to its Hausdorff measure away from the vertices of the graph. One assumption removed in v2, the result is now optimal.
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arXiv:2604.21240v2 Announce Type: replace Abstract: In this paper, we define real link Floer homology for strongly invertible and doubly periodic links in closed real $3$-manifolds with connected fixed sets, which generalizes real Heegaard Floer homology and real sutured Heegaard Floer homology. We give a combinatorial description of the theory in $S^3$ via real grid diagrams and use it to investigate structural properties of the theory as..
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The $S$-$E$ route to the Chebyshev bounds for the prime-counting function
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arxiv.org
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2 days ago
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eng
arXiv:2604.21946v2 Announce Type: replace Abstract: The Chebyshev bounds for the prime-counting function, i.e., $\pi(x) \asymp x/\ln x$, is established in a new way. This new approach follows the outline $\pi(x) \asymp \bigl(\sum_{p \le x} \sqrt{\ln p / p}\bigr)^{2} \asymp x/\ln x$. Here, the second $\asymp$ is derived from the classical estimate by Mertens, i.e., $\sum_{p \le x} (\ln p)/p = \ln x + O(1)$; while the first $\asymp$ is prove..
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arXiv:2604.22991v2 Announce Type: replace Abstract: We study a sequential coin-flipping game: a player starts with $n$~coins, each heads with probability~$p$, and in each round flips all remaining coins and must set aside at least one head, losing if none shows. The player wins once all coins have been set aside. The optimal winning probability~$w_{n,p}$ obeys a Bellman equation with a nonlinear suffix-maximum operator. For $p=\tfrac12$ ev....
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Relaxation Kernel, Spectral Dissipation, and Global Convergence of Blahut--Arimoto Dynamics
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arxiv.org
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2 days ago
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eng
arXiv:2604.25106v3 Announce Type: replace Abstract: We develop a spectral theory for continuous- and discrete-time Blahut--Arimoto (BA) dynamics, centered on the relaxation kernel $ \G = \E_p[K^*_X \otimes K^*_X] $. Five main results are established. (i) Along the continuous-time BA flow, the free energy satisfies the exact $ \chi^2 $-dissipation identity $ \dot F_\beta = -\D(q) $, where $ \D(q)=\chi^2(\T q \| q) $ is the Pearson $ \chi^2 ....
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arXiv:2604.25228v2 Announce Type: replace Abstract: For any Tychonoff space $X$ let $D(X)$ be either the set $C(X)$ of all continuous functions on $X$ or the set $C^*(X)$ of all bounded continuous functions on $X$. When $D(X)$ is endowed with the point convergence topology, we write $D_p(X)$. Zakrzewski \cite[Theorem 3.12]{kz} proved that if $X$ and $Y$ are $\sigma$-compact spaces and there is a continuous linear map $T:C_p(X)\to C_p(Y)$ s....
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arXiv:2604.25382v2 Announce Type: replace Abstract: We study the class of selfless C*-probability spaces introduced by Robert. It is known that a selfless tracial algebra has strict comparison and a unique trace. We prove that for separable tracial C*-algebras, selflessness is equivalent to approximate selflessness, a finitary condition: for every finite set $F$, every $N \geq 1$ and $\varepsilon > 0$ there exists a unitary $u$ with $|\tau..
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A result on the generic Picard number of surfaces in fake weighted projective 3-spaces
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arxiv.org
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2 days ago
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eng
arXiv:2604.25709v2 Announce Type: replace Abstract: We give a criterion for certain generic nondegenerate surfaces in a fake weighted projective $3$-space to have Picard number $>1$. These algebraic surfaces are of general type. We do this by considering degenerations (along an edge), keeping track of the geometric genus, and using vanishing cohomology classes to construct a rational Picard class on the surface not proportional to the cano..
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On submersions with definite folds of manifolds with boundary into Euclidean spaces
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arxiv.org
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2 days ago
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eng
arXiv:2604.26249v2 Announce Type: replace Abstract: Submersions with definite folds are submersions on manifolds with boundary whose restrictions to the boundary are definite fold maps. In this paper, we study differential-topological properties of manifolds with boundary admitting such maps into Euclidean spaces. When the target is $\mathbb{R}$, we obtain restrictions on the diffeomorphism types of the source manifolds by using results fo..
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Asymptotic profiles for the Cauchy problem of semilinear beam equation with two variable coefficients in the subcritical case
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arxiv.org
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2 days ago
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eng
arXiv:2605.00550v2 Announce Type: replace Abstract: In this article, we investigate the asymptotic profile of solutions to the Cauchy problem for a nonlinear beam equation with two variable coefficients in the subcritical nonlinear case. In contrast to our previous result [6], in which the asymptotic profile is governed by the linear heat kernel and the nonlinear effect is asymptotically negligible, the asymptotic profile in the present se..
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arXiv:2605.03097v2 Announce Type: replace Abstract: We prove a full support theorem for the relative good moduli space of the universal compactified Jacobian $\bar{\pi}\colon \overline{J}_{g,n}^{d,\phi}\to \overline{\mathcal{M}}_{g,n}$, showing that every direct summand appearing in the BBDG decomposition of $\mathrm{R}\bar{\pi}_*\mathrm{IC}(\overline{J}_{g,n}^{d,\phi})$ has full support on the base $\overline{\mathcal{M}}_{g,n}$. Moreover..
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arXiv:2605.03284v2 Announce Type: replace Abstract: A perfect code in a graph $\Gamma = (V, E)$ is a subset $C$ of $V$ such that no two vertices in $C$ are adjacent and every vertex in $V \setminus C$ is adjacent to exactly one vertex in $C$. A subgroup $H$ of a group $G$ is called a subgroup perfect code of $G$ if it is a perfect code in some Cayley graph of $G$. In this paper, we study the set $\Delta(G)$ of conjugacy classes of nontrivi....
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On existence of local and global strong solutions for the stochastic tamed Navier-Stokes equations on $\mathbb{R}^3$
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arxiv.org
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2 days ago
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eng
arXiv:2605.03734v2 Announce Type: replace Abstract: We study the existence of local and global strong solutions for the stochastic tamed Navier--Stokes equations on the whole space $\mathbb{R}^3$, driven by multiplicative Wiener noise and compensated L\'evy jump noise. For $p > 3$, we first prove the existence of a pathwise unique maximal local $L^p$-strong solution for divergence-free, $\mathcal{F}_0$-measurable initial data in $L^p(\Omeg..
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Empirical Bernstein Confidence Intervals for Kernel Smoothers: A Safe and Sharp Way to Exhaust Assumed Smoothness
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arxiv.org
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2 days ago
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eng
arXiv:2605.03781v4 Announce Type: replace Abstract: Using standard-normal critical-value calibration (SNC) to construct a kernel-smoother-based confidence interval faces a fundamental challenge: the normalization makes a small estimation bias become a non-negligible inferential bias. This paper takes a different route by replacing the SNC control with empirical Bernstein tail control. The resulting confidence intervals control stochastic v....
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Reentrant value fields as delayed coupled reaction-diffusion systems on finite graphs
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arxiv.org
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2 days ago
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eng
arXiv:2605.03940v4 Announce Type: replace Abstract: We describe a dynamical system in which a symbolic field is coupled to a geometric field via a bipartite Hilbert-Schmidt kernel. The system is fully described by a retarded functional differential equation (RFDE) on the history space, subject to Lipschitz and small gain conditions. We show that the RFDE is well-posed under constant input and that it admits a compact global attractor. The ..
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Wick Renormalized Parabolic Stochastic Quantization Equations on Rough Metric Measure Spaces
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arxiv.org
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2 days ago
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eng
arXiv:2605.05442v2 Announce Type: replace Abstract: On metric measure spaces with sub-Gaussian heat kernel behavior in small time, we obtain a sufficient condition to solve Wick renormalized stochastic quantization equations with polynomial interaction. Given the power of the nonlinearity, the local solution condition depends on the Hausdorff dimension $d_h$, the walk dimension $d_w$, and the maximal spatial H\"older regularity of the heat....
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Unitary-Invariant Decomposition of Reducible Total Least Squares Core Problems
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arxiv.org
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2 days ago
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eng
arXiv:2605.08091v2 Announce Type: replace Abstract: The analysis of a total least square problem (TLS) can be reduced to that of an associated core problem, which typically has lower dimension and improved solubility properties. Nevertheless, even a core problem may remain reducible, admitting further decomposition into irreducible component subproblems with simpler structure and better analytical properties. However, no systematic and inv....
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Rook theory, normal ordering in the $q$-deformed Ore algebra and the polynomial generalization
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arxiv.org
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2 days ago
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eng
arXiv:2605.09683v3 Announce Type: replace Abstract: For words in the variables $X$ and $Y$ satisfying the commutation relation of the $q$-deformed generalized Ore algebra, $XY-qYX= \mu I + \nu Y$, we show that the corresponding normal ordering coefficients can be given an interpretation in terms of mixed placements of rooks and files. In particular, the associated $q$-deformed Ore-Stirling and Ore-Lah numbers are treated in detail. We show....
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arXiv:2605.10282v2 Announce Type: replace Abstract: This paper addresses the problem of universal learning under model misspecification with log-loss. In this setting, the learner operates with a hypothesis class of models denoted by $\Theta$, while the true data-generating process belongs to a broader class $\Phi \supset \Theta$, and may lie outside the assumed hypothesis space. Classical approaches have characterized the minimax regret a....
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$p$-adic Congruences of Generalized Euler Numbers and Relations to Even Zeta Values
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arxiv.org
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2 days ago
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eng
arXiv:2605.10677v2 Announce Type: replace Abstract: Generalized Euler numbers have previously been studied mainly from a combinatorial viewpoint. The purpose of this paper is to explore them from $p$-adic and analytic perspectives. To this end, we introduce congruential Euler numbers, a new family extending generalized Euler numbers. We establish several $p$-adic congruences for these numbers, including an answer to a conjecture related to..
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arXiv:2605.11833v2 Announce Type: replace Abstract: Each self-similar dendrite K with a finite self-similar boundary defines a finite acyclic edge-labeled bipartite graph G, called the sprout of K. The paper shows that the sprout G determines the combinatorial properties of the dendrite K and its topological structure.
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arXiv:2605.11988v3 Announce Type: replace Abstract: This paper proposes a conjectural framework for Alperin's Main Problem of Block Theory from 1976. The character sets considered here are defined by nonvanishing at given elements, not only by degree conditions. From this point of view, McKay's conjecture is usually recovered as a first degree-level consequence. The guiding idea is that the right local objects governing character values ar..
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arXiv:2605.12880v3 Announce Type: replace Abstract: Ribbon decomposition matrices give determinantal formulas for skew Schur functions that include as special cases the classical Jacobi-Trudi, Giambelli, and Lascoux-Pragacz formulas. We prove that certain elements of Lusztig's dual canonical basis, called Temperley-Lieb immanants, are Schur-positive when evaluated on ribbon decomposition matrices. We conjecture that this positivity holds f..
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Analytic local resolution of Medvedev's Morse index conjecture for the critical hyperbolic catenoid in $\mathbb{H}^3$
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arxiv.org
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2 days ago
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eng
arXiv:2605.13562v5 Announce Type: replace Abstract: Let $\Sigma_a\subset B^3(r(a))\subset\mathbb{H}^3$ ($a>1/2$) be the critical hyperbolic catenoid of the Mori family, a free boundary minimal surface in the geodesic ball. The Medvedev conjecture [15] states ind$(\Sigma_a)=4$ for all $a>1/2$. We study its strong form: ind$(\Sigma_a)=4$ and nul$(\Sigma_a)=2$. The nullity condition nul$(\Sigma_a)=2$ combines the mode-$|k|=1$ result $\text{nu....
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Transfer of regularity by kinetic mollification along critical trajectories
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arxiv.org
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2 days ago
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eng
arXiv:2605.13582v2 Announce Type: replace Abstract: We give a trajectory-based proof of transfer-of-regularity estimates \`a la Bouchut-H\"ormander for kinetic equations at the weak scale of local diffusion. The proof is based on kinetic mollification along critical kinetic trajectories, whose endpoint map has precisely the kinetic scaling. Instead of using Fourier multipliers or the Kolmogorov fundamental solution, we work directly in phy..
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LLM-Enabled Automated Algorithm Design for Multiuser Fluid Antenna Communications
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arxiv.org
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2 days ago
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eng
arXiv:2605.14661v2 Announce Type: replace Abstract: Fluid antenna is a new reconfigurable antenna technology that can dynamically adjust the positions or ports of radiating elements and therefore provides a new degree of freedom for wireless communications. However, the associated port selection is a challenging large-scale combinatorial optimization problem and difficult to solve. Existing manually designed heuristic algorithms are not on....
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Non-combinatorial involutive braidings: the quantum algebra $\mathfrak{gl}_{k,m}$
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arxiv.org
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2 days ago
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eng
arXiv:2605.16121v2 Announce Type: replace Abstract: We investigate involutive, non-combinatorial solutions of the braid equation, viewing them as special deformations of the permutation map. Utilizing these solutions, we identify the associated quantum algebra and introduce it as the $\mathfrak{gl}_{k,m}$ Yangian. This newly derived Yangian is distinct from the known Yangian of the general linear Lie superalgebra; crucially, as a Hopf alge....
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A Parallel and Adaptive Mesh-Free Method for Discontinuous Coefficient Fields in Heterogeneous Porous Media
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arxiv.org
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2 days ago
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eng
arXiv:2605.16564v2 Announce Type: replace Abstract: Discontinuous coefficient fields arise in many computational physics problems and are often represented as cellwise constant data tied to a given spatial discretization. Such representations are inherently mesh-dependent, requiring interpolation or projection whenever they are transferred to a different discretization. In this work, we develop \emph{Parallel and Adaptive Mesh-Free Approxi....
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arXiv:2605.17122v4 Announce Type: replace Abstract: We generalize the fundamental bounds of Delsarte thesis (1973) on codes of given degree and designs of given strength in the new setting of Bannai et al. (2025). We assume the scheme is weakly metric in the sense of (Sol\'e, 1989). We give upper bounds on the size of codes of given degree, and also on the size of codes with a given number of pairwise distances. Codes meeting these bounds ....
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