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arXiv:2606.00843v1 Announce Type: new Abstract: Let $G$ be a simple graph with degree diagonal matrix $D(G)$ and adjacency matrix $A(G)$. The signless Laplacian matrix of $G$ is defined as $Q(G)=D(G)+A(G)$. For a real number $\alpha \in [0, 1]$, Nikiforov (2017) proposed the $A_\alpha$-matrix of a graph $G$ as $A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G)$. The $A_\alpha$-spectral radius of $G$, denoted by $\rho_\alpha(G)$, is the largest eige....
arXiv:2606.00845v1 Announce Type: new Abstract: In this article we study the notion of completeness for conjunctive reducibilities. We investigate the relationship between $c$-completeness and $r$-completeness of computably enumerable (c.e.) sets with respect to various strong reducibilities $\le_r$. By using simplicity properties of sets, we prove that there exist c.e. sets that are simultaneously $Q$-complete and $bd$-complete, yet fail ..
arXiv:2606.00850v1 Announce Type: new Abstract: We state and prove a Toeplitz corona theorem for the pentablock $\mathbb{P}$, a domain in $\mathbb{C}^3$ given by \[ \mathbb{P}=\{(a_{21}, \text{tr}(A), \det(A)) \in \mathbb C^3 : A=[a_{ij}] \in M_2(\mathbb C), \|A\|<1\}. \] By two different applications of this theorem, we obtain a few new characterizations in the Toeplitz corona theorems for the bidisc and the symmetrized bidisc.
arXiv:2606.00853v1 Announce Type: new Abstract: We present and analyze Frank-Wolfe with Moreau Envelope Smoothing (FRAMES) for solving nonsmooth nonconvex constrained optimization problems, taking advantage of iterative smoothing via the Moreau envelope followed by one Frank-Wolfe step per iteration. The problem template we consider encompasses splitting problems with multiple convex constraint sets as well as problems with nonsmooth weakl....
arXiv:2606.00855v1 Announce Type: new Abstract: We propose constrained neural parameterization schemes for several classes of constraints arising in optimization problems in function spaces. This is achieved by constructing smooth neural parameterizations whose image lies entirely in the admissible set while remaining asymptotically dense. In this way, the original constrained optimization problem is transformed into a smooth unconstrained..
arXiv:2606.00861v1 Announce Type: new Abstract: Powell introduced the Axiom of Double Complement ($\mathsf{DCom}$) to give his double-negation interpretation of $\mathsf{ZF}$ into $\mathsf{IZF_{Rep}}$. However, the consistency, strength, and compatibility of $\mathsf{DCom}$ remain open problems. This article aims to survey the compatibility and consistency strength of $\mathsf{DCom}$, its consequence and opposites, which will be named $\ma..
arXiv:2606.00863v1 Announce Type: new Abstract: We study the generation problem in the Higman-Thompson groups $F_n$ via the core and closure of subgroups of $F_n$ and associated automata. We give sufficient conditions for a subset $X \subseteq F_n$ to generate $F_n$, and provide an algorithm which verifies these conditions when $X$ is finite. As an application, we answer a question of Aiello and Nagnibeda, motivated by Savchuk's problem on..
arXiv:2606.00865v1 Announce Type: new Abstract: It is shown that any hyponormal operator on an infinite-dimensional separable Hilbert space that admits a decomposition \( T = R + V \), where \( R \) is tridiagonal and \( V \) is trace-class, has nontrivial closed hyperinvariant subspaces provided $T$ is not a multiple of the identity. We further discuss implications of this result for the invariant subspace problem of hyponormal operators ..
arXiv:2606.00868v1 Announce Type: new Abstract: We study the distribution of indecomposable elements in Euclidean lattices. A positive element in a lattice is called indecomposable if it cannot be represented as a sum of two other positive nonzero elements. The set of all indecomposables in a lattice forms the Hilbert basis for the positive lattice semigroup. We classify lattices that contain only finitely many indecomposables versus those..
arXiv:2606.00870v1 Announce Type: new Abstract: We consider natural Hamiltonian systems with potentials that are $C^0$ or $C^1$ on a hypersurface and $C^{\infty}$-smooth in the complement and introduce and study corresponding notions of their integrabilty and non-integrability. As a motivating example, we derive and analyze models of bungee jumping. We provide prototype examples of the Liuoville-Arnol'd theorem for $C^0$ and $C^1$ Hamilton..
arXiv:2606.00876v1 Announce Type: new Abstract: In this article, we study the space of smooth genus one curves on del Pezzo threefolds of degree 4 and 5. We describe the irreducible components of the Kontsevich moduli space generically parametrizing genus one stable maps with irreducible domains and classify the irreducible components of the morphism space from general elliptic curves. Our result verifies the Geometric Manin's conjecture f..
arXiv:2606.00879v1 Announce Type: new Abstract: Corresponding to weak almost contact metric structures (defined recently by Rovenski and Wolak), we introduce and study here weak almost contact structures with B-metric, which generalize the classical almost contact structures with Norden metric (B-metric). Several geometric properties are obtained, some special classes are investigated and a lot of examples are constructed throughout this w..
arXiv:2606.00885v1 Announce Type: new Abstract: In this paper, we develop the theory for the two-phase Stefan problem with finite energy, possibly non-empty mushy region, and space-dependent melting temperature. Specifically, we prove the existence of weak solutions with an elliptic regularization scheme. Our existence theorem provides information about the regularity of the solutions: we prove that the temperature of weak solutions is in ..
arXiv:2606.00895v1 Announce Type: new Abstract: This paper presents a fast, recursive neural solver for the J2-perturbed Lambert problem based on Tiny Recursive Models (TRM), termed the TRM-Perturbed Lambert (TRM-PL) model. TRM is a weight-shared architecture whose effective capacity emerges from iteration depth rather than parameter count: a compact reasoning module is applied repeatedly within a two-level latent hierarchy, refining a can....
arXiv:2606.00896v1 Announce Type: new Abstract: Globalization has enabled companies to leverage cost efficiencies; however, it has increased exposure to disruption risks that threaten supply stability. Among these, export bans have emerged as a systemic challenge, often arising as a secondary effect of conventional supply capacity disruptions. The pharmaceutical industry is particularly vulnerable to bans because of the criticality of keep....
arXiv:2606.00897v1 Announce Type: new Abstract: In the paper, we prove a rather general characterization of higher-order Sobolev spaces. We show that the $k\mathrm{th}$-order regularity, where $k \in \mathbb{N}$, is captured via inequalities involving $2^k$-tuples of points. In fact, in full generality, the obtained results characterize higher-order Sobolev spaces based on Banach function spaces. Moreover, we show an analogous characteriza..
arXiv:2606.00899v1 Announce Type: new Abstract: In this work, we study the well-posedness of a quasilinear first-order-in-time system with memory arising in nonlinear acoustics. The model features a memory kernel describing the fractional damping and covers, as special cases, first-order formulations of Kuznetsov- and Westervelt-type equations. For completely monotone convolution kernels, we prove that the Westervelt-type system admits un....
arXiv:2606.00903v1 Announce Type: new Abstract: We identify the quadratic symmetry algebra of the two-dimensional Smorodinsky--Winternitz II system with a Laguerre-type confluent Heun algebra. The system is separable in Cartesian and parabolic coordinates. The complementary Cartesian separation operator \[ Y=\partial_y^2-\omega^2y^2+\frac{1/4-c^2}{y^2} \] is of Laguerre type, while the parabolic integral \(W=L_2\) is its algebraic Heun pa..
arXiv:2606.00905v1 Announce Type: new Abstract: In this work, we are concern with the wave equation subjected to a nonlinear feedback of logarithmic type and nonlinear polynomial source. To achieve a comprehensive understanding of this novel damping mechanism, we start with studying the well-posedness and the uniqueness of the problem. Then we establish the blow-up result of the problem under suitable initial data with negative initial ene..
arXiv:2606.00908v1 Announce Type: new Abstract: Let $\mathcal{A}$ be a Grothendieck category. In this paper we classify subcategories of $\mathcal{A}$ via a support notion defined by Krause \cite{Kr2024} based on the spectral category of $\mathcal{A}$. We show that this aligns with Nemman's support \cite{Ne1992}, and thereby extends earlier classifications of subcategories of the category of modules over a commutative noetherian ring and s..
arXiv:2606.00912v1 Announce Type: new Abstract: We study frames for Hardy spaces generated by orbits of multiplication operators. We characterize the symbols $\varphi \in H^\infty(\mathbb{T}^N)$ for which the multiplication operator $M_\varphi$ admits a frame of orbits on $H^2(\mathbb{T}^N)$. We also show that, in this setting, the existence of a frame is equivalent to the existence of a Parseval frame. Moreover, for $N=1$ we prove that fi..
arXiv:2606.00916v1 Announce Type: new Abstract: We introduce the overflow semiring $S = A \oplus_{\operatorname{ord}} L$, extending a positive information algebra $A$ by a join-semilattice $L$, where elements of $L$ dominate $A$ and arithmetic in $L$ reduces to the join. This models saturation or overflow in computational systems and generalizes the transition from finite to infinite cardinal arithmetic. We characterize the idempotent elem..
arXiv:2606.00945v1 Announce Type: new Abstract: In this survey, we extend conclusions on the hexagonal lattice to 3-12 lattice: the connective constant for the 3-12 lattice can be derived from the connective constant for the hexagonal lattice; the conformal invariance of the Ising model and of the percolation on the 3-12 lattice can be derived from their conformal invariance on the hexagonal lattice.
arXiv:2606.00952v1 Announce Type: new Abstract: This is the second of a pair of papers where we construct and investigate a closed monoidal structure on the category of generalized algebraic theories (in the sense of Cartmell). Having presented the tensor product of theories in a syntactic way, we now study the same structure from the perspective of contextual categories. We define the exponential $\mathcal A^\mathcal B$ between two conte....
arXiv:2606.00958v1 Announce Type: new Abstract: The square-and-multiply algorithm, also known as binary exponentiation or repeated squaring, is a technique for fast exponentiation commonly used in modern cryptography and computational number theory. Despite its prominence, the historical origins of the algorithm are not known with certainty. This paper critically examines the origins and formalization of the algorithm through primary sourc....
arXiv:2606.00961v1 Announce Type: new Abstract: We show that the conflated expression graph for an arbitrary permutation has a unique minimal element and a unique maximal element, and every reduced expression sits on a maximal chain from the source to the sink. This generalizes the work of Manin-Schechtman regarding higher Bruhat orders, and gives an independent and self-contained proof of certain results in Hothem. In addition, we give ex..
arXiv:2606.00964v1 Announce Type: new Abstract: We construct a mean curvature flow with surgery starting with any compact mean convex hypersurface in $\mathbb{R}^{n+1}$, extending previous results of Huisken-Sinestrari, Brendle-Huisken, and Haslhofer-Kleiner for 2-convex flows. In contrast with previous constructions of mean curvature flow with surgery, the topological surgeries are performed by the flow itself through nondegenerate cylind..
arXiv:2606.00969v1 Announce Type: new Abstract: In this paper, we introduce a higher-order averaging theory and method for a wide range of nonsmooth systems that are generally characterized by the classical averaging canonical form. Utilizing tools from generalized derivatives theory, we provide a nonsmooth near-identity transformation analogous to the one in smooth averaging theory. Additionally, we exploit sharp calculus rules from lexic....
arXiv:2606.00976v1 Announce Type: new Abstract: An edge-colored graph is called rainbow if all its edges have distinct colors. For a fixed graph $H$, the rainbow Tur\'an number $\exstar(n, H)$ is the maximum number of edges in a properly edge-colored graph with $n$ vertices that does not contain a rainbow subgraph isomorphic to $H$. A $t$-fan $\Ft$ ($t \geq 2$) is a graph formed by $t$ triangles sharing a common vertex. A wheel graph $\Wn$....
arXiv:2606.00978v1 Announce Type: new Abstract: This paper studies two problems that are motivated by combining two novel approaches, namely DNA composite and rank modulation. The recent approach of composite DNA takes advantage of the DNA synthesis property which generates a huge number of copies for every synthesized strand. Under this paradigm, every composite symbols does not store a single nucleotide but a mixture of the four DNA nucl..
arXiv:2606.00983v1 Announce Type: new Abstract: We formulate a program to prove the categorical local Langlands conjecture (CLLC) of Fargues-Scholze, for all quasisplit $p$-adic groups where the Fargues-Scholze $L$-parameters agree with the semisimplification of a known "automorphic" local Langlands parametrization. A key working hypothesis - which we expect to prove elsewhere jointly with Hamann - is the compatibility of the enhanced Whit....
arXiv:2606.00993v1 Announce Type: new Abstract: In this paper we study the Stokes phenomenon of the quantum confluent hypergeometric supersystem, certain meromorphic linear system of ordinary differential equation with a second order pole, associated to the Lie superalgebra $\mathfrak{gl}_{m|n}$. We prove that its Stokes supermatrices satisfy the Yang-Baxter equation, and thus give rise to the quantum supergroup $U_q(\mathfrak{gl}(m|n))$.
arXiv:2606.01001v1 Announce Type: new Abstract: We show that axisymmetric Willmore surfaces admit a first-order formulation obtained by combining two independent first integrals. If $\rho$ denotes the distance from the axis of revolution and $\Psi=\sin\psi$, where $\psi$ is the tangent angle of the generating curve, then the profile satisfies \begin{equation*} \frac{\left[\Psi(\rho\Psi'-\Psi)^2+2(\rho\Psi'-\Psi)+2C_1\rho\right]^2}{1-\Psi^2..
arXiv:2606.01011v1 Announce Type: new Abstract: This paper studies conditional independence testing under the Gaussian additive noise model (GANM), where two variables are modeled as nonlinear functions of covariates with independent bivariate Gaussian regression errors. Under this framework, conditional independence can be characterized by the correlation coefficient of the regression errors, which motivates a test based on the Pearson co....
arXiv:2606.01017v1 Announce Type: new Abstract: Thurston constructed codimension one foliations on $S^3$ thereby proved that the homomorphism $gv: \pi_3(B\overline{\Gamma}^\infty_1)\rightarrow \mathbb{R}$ induced by the Godbillon-Vey invariant is surjective. By another real analytic construction, he proved that the homomorphism $gv: H_3(B\overline{\Gamma}^\omega_1)\rightarrow \mathbb{R}$ is also surjective where $B\overline{\Gamma}^\omega_....
arXiv:2606.01035v1 Announce Type: new Abstract: We utilize multi-virtual knot theory where there are a multiplicity of virtual crossings to study strict virtual linkoids. In strict virtual linkoid theory, local moves define all virtual moves and Reidemeister moves. In the strict equivalence, no moves, classical or virtual, can transfer an arc across a linkoid endpoint. By taking closures of strict virtual linkoids that are multi-virtual kn..
arXiv:2606.01037v1 Announce Type: new Abstract: Let $n\geq 0$ be an integer and $q$ a prime power. The polynomial $g_{n,q}$ was introduced in [10] with the purpose of finding new classes of permutation polynomials over finite fields. We investigate the permutation behaviour of the polynomial $g_{n,q}(X)$ over finite fields of even characteristic. We introduce the multivariate case of the polynomial $g_{n,q}$, and study the permutation poly..
arXiv:2606.01040v1 Announce Type: new Abstract: Fix $1 \leq n < m, k = m-n.$ The Grassmannian $Gr(n,m)$ is a compact $kn$-dimensional manifold with a unique rotation invariant probability measure $\sigma_n.$ For $W \in Gr(n,m)$, $P_W : \mathbb R^m \mapsto W$ is orthogonal projection. A lattice subset $L \subset \mathbb Z^m \subset \mathbb R^m$ is called $k$-dense if it intersects $C(O) := \bigcup_{V \in O} V\backslash \{0\}$ for every none..
arXiv:2606.01055v1 Announce Type: new Abstract: Bilevel optimization is a fundamental framework for hierarchical decision-making, but its solution is challenging due to the implicit and typically set-valued nature of the lower-level optimality condition. In this paper, we study bilevel optimization problems through an exact-penalty reformulation based on the $\ell_1$-norm of the lower-level gradient. Under suitable regularity assumptions,....
arXiv:2606.01058v1 Announce Type: new Abstract: This paper investigates the infinite-horizon classical stochastic optimal control problem with input delay under an entropy-regularized relaxed control framework. In particular, by constructing a relaxed system and introducing an entropy regularization term, we reformulate the classical optimal control problem into an entropy regularized formulation, and derive the optimal controller that fol..
arXiv:2606.01064v1 Announce Type: new Abstract: In this paper, we study some geometric constants in complete $p$-normed spaces with $0 < p \leq 1$. We introduce a new symmetric geometric constant associated with isosceles orthogonality, establish its sharp bounds, and provide an orthogonal characterization of the generalized von Neumann-Jordan constant in such spaces. We also investigate two Milman-type moduli in complete $p$-normed spaces..
arXiv:2606.01068v1 Announce Type: new Abstract: Let $X$ be a real Banach space and $\lambda \in[0,1]$. Motivated by orthogonal versions of the James constant, we introduce the weighted Birkhoff orthogonal James-type constant $$J_\lambda^{\perp}(X)=\sup \left\{\min \{\|\lambda x+(1-\lambda) y\|,\|\lambda x-(1-\lambda) y\|\}: x, y \in S_X, x \perp_B y\right\},$$ where \(\lambda\in[0,1]\) and $x \perp_B y$ stands for Birkhoff orthogonality. W..
arXiv:2606.01073v1 Announce Type: new Abstract: We study the Riemann problem for the compressible Euler equations with a stationary coupling interface across which a discontinuity in the heat flux is prescribed. This coupling gives rise to non-conservative effects and models heat addition mechanisms such as condensation-induced waves. Without imposing restrictions on sonic states, we analyze the problem in all Mach number regimes. Lax weak....
arXiv:2606.01082v1 Announce Type: new Abstract: We study \(\Gamma_{2^n}(K)\), the least positive number \(\gamma>0\) such that an \(n\)-dimensional convex body \(K\) can be covered by \(2^n\) translates of \(\gamma K\). For \(n\)-simplices \(\Delta_n\), we prove that \(\Gamma_{2^n}(\Delta_n)\), as a sequence in \(n\), tends to \(1/2\). For the cross-polytope \(B_1^n\), we show that \(\Gamma_{2^n}(B_1^n)\leq5/6\) holds for all \(n\geq2\), a..
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