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arXiv:2606.02003v1 Announce Type: new Abstract: This paper introduces the $n$-th order multifractional stable motion ($n$-MFSM), a novel stochastic process that simultaneously unifies three key modelling features: heavy-tailed distributions ($\alpha$-stable with $\alpha\in(1,2]$), time-varying local regularity via a functional Hurst parameter $H(t)\in(n-1,n)$, and extended scaling behaviour of order $n\geq1$. No existing framework combines..
arXiv:2606.02023v1 Announce Type: new Abstract: We introduce two families of quandles arising from Coxeter quandles. One, which we call a double covering, is the set of roots with binary operation defined by using the negatives of reflections. The double covering is realized as a conjugation quandle in a Pin group. The other, which we call a rotational $D_n$ quandle, is the set of some right angle rotations in the Coxeter group of type $D_..
arXiv:2606.02025v1 Announce Type: new Abstract: For an internal category $\mathbb{C}$ in a cartesian category $\mathcal{C}$ we define, naturally in objects $X$ of $\mathcal{C}$, $Prin_{\mathbb{C}}(X)$. This is a category whose objects are principal $c \mathbb{C}$-bundles over $X$ and whose morphisms are principal $c(\mathbb{C}^{\uparrow})$-bundles. Here $c(\_)$ denotes taking the core groupoid of a category (same objects but only isomorphi....
arXiv:2606.02026v1 Announce Type: new Abstract: The aim of the paper is to survey results on Jordan types for pairs of nilpotent commuting matrices. We also review recent proof of the Box Conjecture on Jordan types that have equal dense orbit in the nilpotent commutator.
arXiv:2606.02030v1 Announce Type: new Abstract: Given a graph $G$, a dominating set is a subset $X\subseteq V(G)$ such that $N[X]=V(G)$. The \emph{domatic number} of $G$, denoted ${\rm dom}(G)$, is the maximum size of a partition of $V(G)$ into dominating sets. In analogy with the lower bound of the chromatic number by the clique number, the domatic number satisfies the upper bound ${\rm dom}(G)\le \delta(G)+1$ where $\delta(G)$ is the min....
arXiv:2606.02036v1 Announce Type: new Abstract: In this paper, we study self-intersection local times for a stochastic process $x(u(\cdot),t)$, where $u$ is a Gaussian process of the form $u(t)=\int^t_0k(t,s)\mathrm{d}{w(s)}$, $k$ is a deterministic kernel of the Volterra type, $w$ is a Wiener process, and $x$ is a solution to the \emph{equation with interaction}. Equations with interaction are a class of interacting particle system descri....
arXiv:2606.02040v1 Announce Type: new Abstract: A fundamental open problem in the homological theory of Banach spaces is the calculation of the injective dimension of the Banach space $c_0$. We make a contribution to the study of this problem by proving that, if the Continuum Hypothesis ($\mathsf{CH}$) holds, then the injective dimension of $c_0$ is at least 3. In the course of proving this result, we introduce the notion of an \emph{almos..
arXiv:2606.02046v1 Announce Type: new Abstract: We explicitly construct dual bimodules in a semistrict monoidal 2-category, using Frobenius algebra structure. The main result shows that a coherent dual of the underlying object can be promoted to a coherent dual of the bimodule, with zigzag 2-isomorphisms additionally require special Frobenius structures. We also prove that every special Frobenius algebra in $\mathbf{2Vect}$ is rigid, via a..
arXiv:2606.02055v1 Announce Type: new Abstract: We study exact community recovery in the two-community stochastic block model on $n$ vertices under limited and noisy access to network data. The learner may query a noisy neighborhood oracle that reveals each true neighbor of a queried vertex independently with fixed probability and never returns non-neighbors, subject to a finite query budget. We consider both oracle-only access and a combi....
arXiv:2606.02056v1 Announce Type: new Abstract: We introduce the class of \emph{Special--Dirichlet processes}, consisting of c\`adl\`ag adapted processes admitting a decomposition \[ X=M+\Gamma, \] where \(M\) is a local martingale and \(\Gamma\) is an adapted c\`adl\`ag process with vanishing continuous quadratic variation whose jumps are predictable and \(\mathcal F_{s-}\)-measurable. This class arises naturally from transformations of ....
arXiv:2606.02064v1 Announce Type: new Abstract: Overcoming the Kolmogorov barrier for constructing efficient reduced-order models (ROMs) for transport-dominated problems remains a challenge. This has impeded their use as computationally cheap surrogates for partial differential equations (PDEs) associated with optimal control problems. Since such problems require multiple computations of the full PDE, employing their reduced-order surrogat....
arXiv:2606.02070v1 Announce Type: new Abstract: In this paper, we investigate critical mass threshold for the Patlak-Keller-Segel-Navier-Stokes system on the two-dimensional whole space and obtain global existence of strong solutions if the initial mass is less than or equal to $8\pi$, regardless of the initial norm of the velocity. One new observation is that the local mass of the density function rearrangement satisfies a good inequality..
arXiv:2606.02071v1 Announce Type: new Abstract: In this article, we consider the words with cyclic indices. For given $s$, we consider the pair $(\iota,\kappa)$ of indices such that the word of length $s$ from $\iota$ is equal to the word of length $s$ from $\kappa$. We give a characterization of such pairs for a cyclic Fibonacci word, and give the number of them.
arXiv:2606.02081v1 Announce Type: new Abstract: Robust optimization offers a tractable approach to balance operating costs and reliability in power systems dominated by weather-dependent renewable uncertainty, but its performance depends critically on the uncertainty set. Standard data-driven approaches often calibrate uncertainty sets to attain predictive coverage, which can produce unnecessarily large sets and costly operating decisions.....
arXiv:2606.02086v1 Announce Type: new Abstract: We construct p-robust polynomial trace liftings on three-dimensional tetrahedral meshes. The prescribed trace is a continuous piecewise polynomial function on a boundary face patch; the tetrahedra touching this patch have one common degree, while the interior degrees may be arbitrary. The lifting is degree-preserving, supported in the corresponding boundary layer, and satisfies both an H^1 es..
arXiv:2606.02087v1 Announce Type: new Abstract: The classical Marion's theorem states that the area of the central hexagon obtained by dividing each side of a triangle into three equal parts and connecting the interior division points is exactly $1/10$ of the area of the original triangle. In this paper, the construction is extended to an arbitrary n-dimensional simplex: each edge is divided into three equal parts, and through each n-1 ver..
arXiv:2606.02088v1 Announce Type: new Abstract: We study a system of nonlinear Schrodinger equations under the mass-resonance condition and provide a complete description of the asymptotic behavior of small solutions in two space dimensions. Our analysis is based on a detailed study of an associated system of ordinary differential equations governing the asymptotic profile. We establish a phase-amplitude representation for this ODE with ar....
arXiv:2606.02110v1 Announce Type: new Abstract: Let $\mathcal{H}$ be an $r$-uniform hypergraph. For $S\in \binom{V(\mathcal{H})}{j}$, let $\mathrm{deg}(S)$ be the number of edges of $\mathcal{H}$ containing $S$, and define the $(j,p)$-norm of $\mathcal{H}$ by $\|\mathcal{H}\|_{j,p}=\left(\sum_{S\in \binom{V(\mathcal{H})}{j}}\mathrm{deg}(S)^p\right)^{1/p}$. Motivated by a problem of Chao, Dong, Shen and Yang, we determine the maximum number..
arXiv:2606.02114v1 Announce Type: new Abstract: This paper develops a switched event-triggered adaptive boundary control for a class of reaction-diffusion PDE-ODE cascade systems, where the system and input matrices in the ODE as well as the spatially-varying reaction coefficient in the PDE are uncertain. A two-step backstepping transformation is constructed to derive the continuous-time control law. Then a novel dynamic event-triggered co....
arXiv:2606.02116v1 Announce Type: new Abstract: Geodesic regression generalizes classical regression models to manifold-valued data by replacing affine models in Euclidean spaces with geodesic models on Riemannian manifolds. In this paper, we set up a framework for regression based on retractions instead of the Riemannian exponential map and its corresponding retraction-based distance. The associated optimization problem is posed on a subs..
arXiv:2606.02123v1 Announce Type: new Abstract: Maesaka, Seki and Watanabe proved a formula for multiple harmonic sums. Yamamoto generalized it to Schur-type multiple harmonic sums, and the second author proved a $q$-analogue of this generalization. In this paper, we give two applications of the $q$-analogue formula. The first is an alternative proof of the duality of a $q$-analogue of multiple zeta values. The second is a proof of an iden..
arXiv:2606.02125v1 Announce Type: new Abstract: Trace-compatible polynomial extensions are a recurring local ingredient in high-order finite element analysis on conforming hexahedral meshes. They are needed whenever prescribed edge and face traces must be preserved while a polynomial is extended into a neighboring cell or boundary patch. The main contribution of this paper is the construction of p-robust polynomial liftings on nonsingular ....
arXiv:2606.02135v1 Announce Type: new Abstract: We exhibit, in a systematic way, connections between hypergraph Tur\'an problems and extremal set theory. More specifically, we construct natural families of uniform hypergraphs for which the upper bounds on their Tur\'an densities reduce to classical problems in extremal set theory, including the Erd\H{o}s--Ko--Rado theorem, $L$-intersecting families, and the Erd\H{o}s matching problem.
arXiv:2606.02137v1 Announce Type: new Abstract: In this work, we determine the generator polynomials for the Hermitian hulls and Hermitian sums of cyclic codes defined over the composite ring $\mathbb{F}_2 \times (\mathbb{F}_2 + v\mathbb{F}_2)$, where $v^2 = v$. Based on these structures, we develop quantum error-correcting (QEC) codes by applying the Hermitian dual version of Quantum Construction~X to the obtained Hermitian hulls and sums..
arXiv:2606.02141v1 Announce Type: new Abstract: In this article, we study the existence of normalized solutions to the following mixed nonlinear Choquard equation with exponential growth \begin{align*} \left\{ \begin{aligned} \mathcal{L}u+\lambda u \; &=\; \Lambda(I_{\alpha}\ast F(u))F'(u), \quad \text{in }\mathbb{R}^{2}, \int_{\mathbb{R}^{2}}|u|^{2}\,dx \; &=\; a^{2}, \end{aligned} \right. \end{align*} where $\mathcal{L}= -\Delta....
arXiv:2606.02144v1 Announce Type: new Abstract: We investigate support thresholds for fully smeary and directionally smeary absolutely continuous probability measures on the sphere \(\mathbb{S}^m\). The motivation is inferential: smeariness is caused by degeneracy of the Hessian of the Fr\'echet function, and such degeneracy can invalidate the classical central limit theorem (CLT) for Fr\'echet means and the corresponding Wald-type \(\chi^....
arXiv:2606.02150v1 Announce Type: new Abstract: We consider the reciprocal cost function $ J(x)=\frac12(x+x^{-1})-1 $ and its $n$-dimensional extension $$J(x_1,\ldots,x_n) = \frac12(R+R^{-1})-1, \qquad R=\prod_{i=1}^n x_i^{\alpha_i}, \qquad \alpha=(\alpha_1,\ldots,\alpha_n)\in\mathbb{R}^n\setminus\{0\}.$$ In logarithmic coordinates $t_i=\log x_i$, the Hessian of $J$ has rank one at every point. The associated Hessian geometry is degenerate....
arXiv:2606.02159v1 Announce Type: new Abstract: Lambert-Cole and Meier showed that the elliptic surface $E(n)$ admits a $(12n-2,0)$-trisection, considering the property that $E(n)$ is a certain double branched cover of $S^2 \times S^2$, which is a minimal genus trisection. In this paper, we clarify a way to construct an explicit $(12n-2,0)$-trisection diagram of $E(n)$ from its handle diagram arising from its Lefschetz fibration.
arXiv:2606.02160v1 Announce Type: new Abstract: Resolving a conjecture of Espuny D\'iaz and Gir\~ao [Random Structures Algorithms, 2023], we determine the sharp minimum-degree threshold for Hamiltonicity in graphs perturbed by a uniformly random $K_r$-factor. In fact, we prove the stronger pancyclic statement. More generally, for each fixed connected graph $F$, we study the union of an arbitrary deterministic graph of linear minimum degree....
arXiv:2606.02164v1 Announce Type: new Abstract: We consider the skein algebra of an unpunctured marked surface. Thurston previously constructed its band basis topologically. We show that this band basis coincides with the common triangular basis, which is a Kazhdan-Lusztig type basis for quantum cluster algebras analogous to the dual canonical basis of quantum groups. Our result confirms a conjecture of Thurston. It also provides new cases..
arXiv:2606.02165v1 Announce Type: new Abstract: In wholesale electricity markets, electricity producers and the independent system operator (ISO) play a central role. The ISO is responsible for minimizing production costs while satisfying supply-demand balance and capacity constraints. In this paper, we study a continuous-time problem in which the ISO seeks to minimize the joint cost of operation and investment in an electricity network. T....
arXiv:2606.02176v1 Announce Type: new Abstract: This work introduces L0PathBrex, a novel method for estimating the solution path of L0-regularized problems through the use of L0 Bregman relaxations (B-rex). Recently introduced and analyzed in the literature, these relaxations provide continuous reformulations of the original objective, are applicable to possibly non-quadratic data fidelity terms, and depend on a family of functions designe....
arXiv:2606.02180v1 Announce Type: new Abstract: In this paper, we prove universality of the distribution of the cokernels of a random $p$-adic matrix with inhomogeneously balanced columns. More precisely, let $u \ge 0$ be an integer and $A(n)$ be a random $n \times (n+u)$ matrix over $\mathbb{Z}_p$ whose $i$-th column is $\alpha_n(i)$-balanced. We prove that if $\sum_{i=1}^{n+u} \exp(-\epsilon \alpha_n(i)n) \to 0$ as $n \to \infty$ for eve..
arXiv:2606.02186v1 Announce Type: new Abstract: We study $O(2)$-equivariant spectral flow for Dirac operators on a finite warped cylinder equipped with fixed admissible regularized APS boundary conditions. The twisting bundle is a real higher-rank orthogonal bundle, and reflection symmetry is implemented by a fiber involution. After complexifying the twisting bundle and diagonalizing the orthogonal twist, the Dirac equation decomposes into....
arXiv:2606.02188v1 Announce Type: new Abstract: A symmetric-tensor distributional mixed method for a fourth-order elliptic singular perturbation problem is developed in this paper. The moment variable is approximated by normal-normal continuous symmetric tensor elements, while the scalar variable is represented by an $H^1$-nonconforming virtual element space coupled with a polynomial multiplier on interior subsimplices of codimension two. ....
arXiv:2606.02193v1 Announce Type: new Abstract: Low Earth orbit (LEO) satellite links experience rapid angular variation due to high orbital velocities, which causes severe beam misalignment and array gain degradation under conventional fixed-antenna architectures. In this letter, we propose a rotatable antenna (RA)-enabled LEO communication framework, where RA arrays are deployed at both the satellite and the ground node (GN) to exploit a....
arXiv:2606.02195v1 Announce Type: new Abstract: Decarbonizing urban energy systems requires optimization approaches capable of handling the operational complexity of large-scale district heating networks. However, existing studies typically focus on a single real-world network, limiting comparability and the transferability of insights. To address this, realistic synthetic instances provide controlled, reproducible environments for testing....
arXiv:2606.02202v1 Announce Type: new Abstract: Let $\Gamma$ be an additive abelian group equipped with a commutative factor $\omega$. We describe the simple Lie colour algebras and the associated untwisted affine Lie colour algebras graded by $\Gamma$, which fulfil the Cartan-Weyl paradigm. The quantised universal enveloping algebras of these (affine) Lie colour algebras are constructed, which are colour analogues of the Drinfeld-Jimbo qu..
arXiv:2606.02203v1 Announce Type: new Abstract: A graph pair $(\Gamma, \Sigma)$ is called stable if every automorphism of the direct product $\Gamma\times\Sigma$ is induced componentwise by automorphisms of $\Gamma$ and $\Sigma$. A graph is twin-free if no two distinct vertices share the same neighbourhood in the graph. Two graphs $\Gamma$ and $\Sigma$ are coprime with respect to the direct product if there is no graph $\Delta$ of order gr....
arXiv:2606.02210v1 Announce Type: new Abstract: Balogh, Clemen, and Lidick\'{y} proved that the $\ell_{2}$-norm Tur\'{a}n problem for $K_{5}^{3}$ is asymptotically solved by the balanced bipartite construction, and they further conjectured that this construction is uniquely extremal for all sufficiently large $n$. We confirm this conjecture. We also determine exactly the maximum number of cliques in an $n$-vertex $K_{5}^{3}$-free $3$-unifo....
arXiv:2606.02225v1 Announce Type: new Abstract: We study prime endomorphisms of the free group $F_2$. The main results provide lower and upper bounds for the logarithmic density $\delta_{\mathrm{np}}$ of non-prime endomorphisms: $$ \frac34 \leq \delta_{\mathrm{np}}\leq \frac{27}{28}. $$ Equivalently, we prove corresponding lower and upper bounds for the exponential decay of the probability that a random endomorphism is non-prime, aligning ..
arXiv:2606.02227v1 Announce Type: new Abstract: This paper investigates a class of Schr\"odinger-Poisson systems in $\mathbb R^3$ featuring the (p,q)-Laplacian operator and a combination of critical and subcritical nonlinearities in the Schr\"odinger equation while the m-Laplacian and a power type nonlinearity in the Poisson's one. We consider both the attractive and repulsive cases, which correspond to different signs in front of the nonl....
arXiv:2606.02244v1 Announce Type: new Abstract: Let n be a non-zero integer not equal to 2. We consider the unit equation $\varepsilon + \delta = n$ in units $\varepsilon, \delta$ of cubic fields. We show that this equation has no solutions for 100% of cubic fields, when ordered by discriminant. This is consistent with a recent conjecture of the authors.
arXiv:2606.02249v1 Announce Type: new Abstract: We give generators and relations for the monoidal categories of crystals generated by the fundamental crystals of a simple complex Lie algebra. We also spell out several small-rank examples.
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