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arXiv:2504.00854v2 Announce Type: replace Abstract: For curves singularities the dimension of smoothing components in the deformation space is an invariant of the singularity, but in general the deformation space has components of different dimensions. We are interested in the question of what the generic singularities are above these components. To this end we revisit the known examples of non-smoothable singularities and study their def....
arXiv:2504.04181v3 Announce Type: replace Abstract: We study a vectorial $L^\infty$-variational problem of second order, where the supremal functional depends on the vector function $u$ through a linear elliptic operator in divergence form. We prove existence and uniqueness of the minimiser $u_\infty$ under prescribed Dirichlet boundary conditions, together with a characterisation of $u_\infty$ as solution of a specific system of PDEs. Our..
arXiv:2504.10019v3 Announce Type: replace Abstract: This paper extends the article of the Bruns and Conca on SAGBI bases and their computation (J. Symb. Comput. 120 (2024)) in two directions. (i) We describe the extension of the Singular library sagbiNormaliz.sing to the computation of defining ideals of subalgebras of polynomial rings. (ii) We give a complete classification of the algebras of minors for which the generating set is a SAGBI..
arXiv:2504.10633v5 Announce Type: replace Abstract: Currently, there is no general theory for deriving diffusion approximations of queueing systems with high- or infinite-dimensional state descriptors. In this paper, we explore one path for deriving diffusion limit equations of queueing models. The method hinges on a martingale decomposition of dynamics driven by time-changed renewal processes, which are a common feature of many queueing m....
arXiv:2504.11603v4 Announce Type: replace Abstract: The dynamics of weighted translation operators on Lebesgue spaces, Orlicz spaces, and in general on solid Banach function spaces have been studied in numerous papers. Recently, the dynamics of weighted translations on weighted Orlicz spaces have also been studied by Chen and others. The main idea of this paper is to obtain a generalization of these results to the case of general weighted ..
arXiv:2504.14455v3 Announce Type: replace Abstract: We extend the topological results of Lytchak-Nagano and Lytchak-Nagano-Stadler for CAT(0) spaces to the setting of Busemann spaces of nonpositive curvature, i.e., BNPC spaces. We give a characterization of locally BNPC topological manifolds in terms of their links and show that the singular set of a locally BNPC homology manifold is discrete. We also prove that any (globally) BNPC topolog..
arXiv:2504.19273v2 Announce Type: replace Abstract: In this paper, we first study the sharp weak estimate for the $p$-adic $n$-dimensional fractional Hardy operator from $L^p$ to $L^{q,\infty}$. Secondly, we study the sharp bounds for the $m$-linear $n$-dimensional $p$-adic integral operator with a kernel on $p$-adic weighted spaces $H_{\alpha}^{\infty}( \mathbb{Q} _{p}^{n} )$. As an application, the sharp bounds for $p$-adic Hardy and Hil..
arXiv:2504.20549v3 Announce Type: replace Abstract: The Pappas--Rapoport coherence conjecture, proved by Zhu, states that the dimensions of spaces of sections of certain line bundles coincide. The two sides of the equality correspond to line bundles on spherical Schubert varieties in affine Grassmannians and to line bundles on unions of Schubert varieties in affine flag varieties. Algebraically, the claim can be reformulated as an equality..
arXiv:2505.07128v2 Announce Type: replace Abstract: In this first work in a series, we prove the local-in-time well-posedness of the IBVP for the vacuum Einstein equations with Dirichlet boundary data on a finite timelike boundary, provided the Brown- York stress tensor of the boundary is a Lorentz metric of the same signature (up to an overall sign) as the induced Lorentz metric on the boundary. This is a convexity-type assumption which i..
arXiv:2505.07352v2 Announce Type: replace Abstract: We establish a Brownian extension to Selberg's central limit theorem for the Riemann zeta function. This implies various limiting distributions for $\zeta$, including an analogue of the reflection principle for the maximum of the Brownian motion: as $T$ diverges, for any $u>0$ we have \[ \frac{1}{T}\cdot {\rm meas}\Big\{0\leq t\leq T:\max_{\sigma\geq \tfrac{1}{2}}\log|\zeta(\sigma+i t)|\g..
arXiv:2505.10809v3 Announce Type: replace Abstract: We prove tilting equivalence for the finite almost derived algebraic cobordism spectrum $\mathrm{dMGL}^{a,fin}$ of perfectoid algebras. More precisely, for any perfectoid algebra, the tilting functor induces a weak equivalence on the corresponding finite almost derived algebraic cobordism spectra. This invariant is a finite-syntomic, derived, and non-$\msthbb{A}^1$-local version of algebr..
arXiv:2505.17707v2 Announce Type: replace Abstract: In this paper, we first obtain the operator norms of the $n$-dimensional Hardy-Littlewood-P\'{o}lya operator $\mathcal{H}$ from weighted Lebesgue spaces $L^p( \mathbb{R} ^n,| x |^{\beta} ) $ to weighted weak Lebesgue spaces $L^{q,\infty}(\mathbb{R} ^n,|x|^{\gamma})$. Next, we obtain the weak bounds for the $m$-linear $n$-dimensional integral operator.
arXiv:2505.23293v3 Announce Type: replace Abstract: Mediangle graphs are a common generalization of median graphs (1-sekeleta of CAT(0) cube complexes) and Coxeter graphs (Cayley graphs of Coxeter systems). Answering a question motivated from geometric group theory, we show that these graphs can be endowed with the structure of a contractible cell complex. We further show that the cells of this complex are products of simplices and simplic..
arXiv:2505.23562v2 Announce Type: replace Abstract: In 1996, Youngs proved that any quadrangulation of the real projective plane is not 3-chromatic. This result has been extended in various directions over the years, including to other non-orientable closed surfaces, higher-dimensional analogues of quadrangulations and circular colorings. In this paper, we provide a generalization which yields some of these extensions of Youngs' theorem.
arXiv:2506.01217v2 Announce Type: replace Abstract: We define two stochastic analogs of a geometric flow on even-dimensional manifolds called $Q$-curvature flow, and use the theory of Dirichlet forms to construct weak solutions to both. The first of these flows, which we call the normalized $Q$ flow (NQF), preserves the intrinsic volume normalization from the deterministic setting. The second, which we call the Liouville $Q$ flow (LQF), ha..
arXiv:2506.02340v3 Announce Type: replace Abstract: In this paper, we obtain an explicit formula for the heat kernel on the Cayley graph of the modular group $PSL_2(Z)$, given by the presentation $\langle a,b\mid a^2=1, b^3=1\rangle$. Our approach extends a method of Chung--Yau by observing that the Cayley graph strongly and regularly covers a weighted infinite line. We solve the spectral problem on this line to obtain an integral expressi..
arXiv:2506.05747v3 Announce Type: replace Abstract: This paper proposes asymmetric perturbation, where only one player's payoff function is perturbed, for solving bilinear saddle-point optimization problems, commonly arising in minimax problems, game theory, and constrained optimization. Symmetric perturbation is known to require decreasing its strength to ensure convergence to a solution, i.e., an equilibrium in the original game, resulti....
arXiv:2506.09267v3 Announce Type: replace Abstract: The problem of estimating the slope parameter in regression between two spatial processes under confounding by an unmeasured spatial process has received widespread attention in the recent statistical literature. Yet, a fundamental question remains unresolved: when is this slope consistently estimable under spatial confounding, with existing insights being largely empirical or estimator-s....
arXiv:2506.11118v2 Announce Type: replace Abstract: The classical Banach-Mazur game characterizes sets of first category in a topological space. In this work, we show that an effectivized version of the game yields a characterization of sets of effective first category. Using this, we give a proof for the effective Banach Category Theorem. Further, we provide a game-theoretic proof of an effective theorem in dynamical systems, namely the c..
arXiv:2506.15340v2 Announce Type: replace Abstract: This work presents a mathematical model for the optimal control of thin-film flows over a flexible substrate influenced by an external force. The objective is to find the optimal distributed force acting on the topography that minimises the differences between actual and desired thin-film profiles. A nonlinear lubrication equation governing the fluid dynamics and appropriate functional se....
arXiv:2506.17895v2 Announce Type: replace Abstract: We study the joint distribution of two randomly weighted sums. Inspired by the practical applications, we assume that the main random variables follow the non-standard bivariate regular variation, symbolically BRV , to put emphasis to the value of inhomogeneity of the risk distribution tails, while the random weights are weakly dependent with main random variables. Under some moment condi....
arXiv:2506.21025v3 Announce Type: replace Abstract: This work develops novel energy-stable parametric finite element methods (ES-PFEM) for the Willmore flow and curvature-dependent geometric gradient flows of surfaces in three dimensions. The key to achieving the energy stability lies in the use of two novel geometric identities: (i) a reformulated variational form of the normal velocity field, and (ii) incorporation of the temporal evolut....
arXiv:2507.01623v4 Announce Type: replace Abstract: In this paper, we present a qualitative and bifurcation analysis of the three-parameter FitzHugh-Nagumo system and its compactified formulation. The study is structured according to three parameter-dependent regimes, for which the associated phase portraits are characterized. In one of these regimes, the system exhibits a double-zero bifurcation with $Z_2$ symmetry, corresponding to a co....
arXiv:2507.02552v4 Announce Type: replace Abstract: This paper investigates the detection and estimation of a single change in high-dimensional linear models. We derive minimax lower bounds for the detection boundary and the estimation rate, which uncover a phase transition governed by the sparsity of the covariance-weighted differential parameter. This form of "inherent sparsity" captures a delicate interplay between the covariance struct....
arXiv:2507.05008v2 Announce Type: replace Abstract: We construct a new quantization $K_t(\mathcal{O}^{sh}_{\mathbb{Z}})$ of the Grothendieck ring of the category $\mathcal{O}^{sh}_{\mathbb{Z}}$ of representations of shifted quantum affine algebras (of simply-laced type). We establish that our quantization is compatible with the quantum Grothendieck ring $K_t(\mathcal{O}^{\mathfrak{b},+}_{\mathbb{Z}})$ for the quantum Borel affine algebra, ....
arXiv:2507.08608v2 Announce Type: replace Abstract: We investigate equidecomposability in the ring of polygons with sides restricted to given directions and using only translations. Extending classical results of Dehn and Hadwiger, we prove that equidecomposability in these rings is equivalent to the equality of some translation invariant simple valuations. We also consider the algebraic structure of direction sets. We show that under mild..
arXiv:2507.10144v2 Announce Type: replace Abstract: The Lanczos method is a fast and memory-efficient algorithm for solving large-scale symmetric eigenvalue problems. However, its rapid convergence can deteriorate significantly when computing clustered eigenvalues due to a lack of cluster robustness. A promising strategy to enhance cluster robustness -- without substantially compromising convergence speed or memory efficiency -- is to use ....
arXiv:2507.10816v2 Announce Type: replace Abstract: We pursue an old conjecture of John Roe about the algebraic K-theory of the algebra of finite propagation, locally trace-class operators, namely that transgressing the algebraic coarse character map on this algebra to a Higson dominated corona coincides with the usual Chern character on the corona.
arXiv:2507.10937v3 Announce Type: replace Abstract: A \emph{matching} from a finite subset \( A \) of an abelian group \( G \) to another subset \( B \) is a bijection \( f : A \to B \) such that \( af(a) \notin A \) for all \( a \in A \). The study of matchings began in the 1990s and was motivated by a conjecture of E.~K.~Wakeford on canonical forms for homogeneous polynomials. The theory was later extended to the linear setting of vector..
arXiv:2507.11365v2 Announce Type: replace Abstract: We classify representations of the mapping class group of a surface of genus $g$ (with at most one puncture or boundary component) up to dimension $3g-3$. Any such representation is the direct sum of a representation in dimension $2g$ or $2g+1$ (given as the action on the (co)homology of the surface or its unit tangent bundle) with a trivial representation. As a corollary, any linear syst..
arXiv:2507.13000v2 Announce Type: replace Abstract: This paper develops a geometric framework for the stability analysis of differential inclusions governed by maximally monotone operators. A key structural decomposition expresses the operator as the sum of a convexified limit mapping and a normal cone. However, the resulting dynamics are often difficult to analyze directly due to the absence of Lipschitz selections and boundedness. To ove....
arXiv:2507.20902v2 Announce Type: replace Abstract: We study sequences of modular representations of the symplectic and special linear groups over finite fields arising from the first homology of congruence subgroups of mapping class groups and automorphism groups of free groups, as well as from the module of coinvariants for the abelianization of the Torelli group. In each case, we determine the composition factors and their multiplicitie..
arXiv:2507.22147v5 Announce Type: replace Abstract: This work focuses on the frequency-domain modeling of a control system with a flexible beam and a rigid body. A simply supported beam is equipped with a spring-loaded control actuator and possesses local damping effect. Using Hamilton's variational principle, the equations of motion are derived in the state space form taking into account interface conditions involving lumped control and l..
arXiv:2508.01973v4 Announce Type: replace Abstract: This article demonstrates how recent developments in the theory of empirical processes allow us to construct a new family of asymptotically distribution-free smooth tests. Their distribution-free property is preserved even when the parameters are estimated, model selection is performed, and the sample size is only moderately large. A computationally efficient alternative to the classical ..
arXiv:2508.08873v2 Announce Type: replace Abstract: We consider a new class of Parareal algorithms, which use ideas from localized reduced basis methods to construct the coarse solver from truncated SVD approximations of the transfer operators mapping initial values for a given time interval to the solution at the end of the interval. By leveraging randomized singular value decompositions, these low-rank approximations are obtained embarra..
arXiv:2508.11073v3 Announce Type: replace Abstract: This paper addresses stochastic optimization of Lipschitz-continuous, nonsmooth and nonconvex objectives over compact convex sets, where only noisy function evaluations are available. While gradient-free methods have been developed for smooth nonconvex problems, extending these techniques to the nonsmooth setting remains challenging. The primary difficulty arises from the absence of a Tay....
arXiv:2508.16047v2 Announce Type: replace Abstract: For site percolation on the triangular lattice, we define two lattice fields that form a logarithmic pair in the sense of conformal field theory. We show that, at the critical point, their two- and three-point correlation functions have well-defined scaling limits, whose structure agrees with that predicted for logarithmic field theories. One of the two fields can be identified with the p..
arXiv:2508.20730v2 Announce Type: replace Abstract: We study the global macroscopic limits associated with kinetic-fluid interaction models for sprays. Motivated by the Vlasov-Navier-Stokes system under the monokinetic ansatz, we consider the pressureless Euler-Navier-Stokes (Euler-NS) system in $\mathbb{R}^{d}$ ($d\geq2$) coupled through the singular drag force $\frac{1}{\tau} \rho (u-v)$, where $\tau$ is the Stokes relaxation time. For i....
arXiv:2508.21515v2 Announce Type: replace Abstract: In this note, we reveal a relation between the weight distribution of a concatenated code ensemble based on the Plotkin construction and those of its component codes. The relation may find applications in the calculation of the ensemble weight distributions for many codes, including Reed-Muller (RM)-like codes.
arXiv:2509.01191v2 Announce Type: replace Abstract: Local log-regular rings are Cohen-Macaulay local domains introduced by Kazuya Kato to expand the theory of toric varieties without a base. In this note, we show that local rings of monoid algebras over regular rings are log-regular. As a corollary, we show that monoid algebras are log-regular rings.
arXiv:2509.02107v2 Announce Type: replace Abstract: We develop high-order numerical schemes to solve random hyperbolic conservation laws using linear programming. The proposed schemes are high-order extensions of the existing first-order scheme introduced in [{\sc S. Chu, M. Herty, M. Luk\'a\v{c}ov\'a-Medvi{\softd}ov\'a, and Y. Zhou}, SIAM J. Sci. Comput., 48 (2026)], where a novel structure-preserving numerical method using a concept of g....
arXiv:2509.04614v2 Announce Type: replace Abstract: We study cluster algebras over $\mathbb{F}_2$. By the Laurent phenomenon there is a map from the set of seeds of the cluster algebra to the corresponding cluster variety. We show that in type $A$, fibers of this map can be described in terms of certain edges of the universal polytope of triangulations of a polygon. Moreover, we show that there is a section of this map giving seeds whose c..
arXiv:2509.06248v2 Announce Type: replace Abstract: Hardy's $Z$-function $Z(t)$ is a real-valued function of the real variable $t$, and whose zeros correspond exactly to the zeros of the Riemann zeta-function on the critical line. In 2012, K. Matsuoka showed that for every non-negative integer $k$, there exists a $T=T(k)>0$ such that $Z^{(k+1)}(t)$ has exactly one zero between consecutive zeros of $Z^{(k)}(t)$ for $t\ge T$ under the Rieman..
arXiv:2509.06527v3 Announce Type: replace Abstract: The aim of this article is to study basic structures and interrelations of $\delta$-rings, perfectoid towers, and lim Cohen--Macaulay sequences over Noetherian rings in positive or mixed characteristic. We also discuss the deformation of perfectoid purity via perfectoid towers. In the latter part of this paper, we discuss some methods for constructing perfectoid towers, dealing with $p$-t..
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