arXiv preprints from January 1, 2026 through September 8, 2026 — 19:31:13 EST
We examine certain phenomena in $C^1$-dynamics from a viewpoint of shadowing and improve a known result on hyperbolic sets. We also review a result on the stability of attractor boundaries from the same viewpoint and derive several additional results.
We study the plastic Burgers equation in one space dimension, i.e., the Burgers equation featuring an additional term formally given by the p-Laplacian with p=1, or rather, by the multivalued subdifferential of the total variation functional. Our study highlights that the interplay of the advection term with the stresses given by the...
In this paper we study the connection between Herzog ideals (i.e., ideals with a squarefree Gröbner degeneration) and $F$-singularities. More precisely, we show that, in positive characteristic, homogeneous Herzog ideals define $F$-anti-nilpotent rings, and we inquire, in characteristic 0, on a surprising relationship between being...
We introduce a {\it non-linear} generalization of the classical Dobrushin-Lanford-Ruelle (DLR) framework by developing the concept of a $q$-specification and the associated $q$-equilibrium measures. These objects arise naturally from a family of non-linear $q$-stochastic operators acting on the space of probability measures. A...
For a purely $N$-periodic continued fraction $ξ=[\overline{a_0,a_1,\dots,a_{N-1}}]=[a_0,a_1,\cdots]$, with $a_k=a_{k+N}$ for all $k\ge 0$, and convergents $h_n/k_n=[a_0,a_1,\dots,a_n]$, we obtain explicit expressions for the weighted error sums $f_ξ(s)=\sum a_{n+1}\lvert h_n-ξk_n\rvert^s$ for $s>1$. A key observation is that, for each...
We introduce pseudofinite W*-probability spaces. These are W*-probability spaces that are elementarily equivalent to Ocneanu ultraproducts of finite-dimensional von Neumann algebras equipped with arbitrary faithful normal states. We are particularly interested in the case where these finite-dimensional von Neumann algebras are full...
The author has been interested in regions surrounded by cylinders of real algebraic hypersurfaces and their shapes and polynomials associated to them. Here, we formulate and investigate natural decompositions into such cylinders of real algebraic hypersurfaces. Especially, intersections of these cylinders of real algebraic...
This paper is devoted to the investigation of multidimensional analogues of refined Bohr-type inequalities for bounded holomorphic mappings on the unit polydisc $\mathbb{D}^n$. We establish a sharp extension of the classical Bohr inequality, proving that the Bohr radius remains $R_n = 1/(3n)$ for the family of holomorphic functions...
Motivated by Khintchin's 1923 conjecture, refuted by Marstrand in 1970, we study the Khintchin class of functions associated to a given increasing sequence of integers. When the Khintchin class contains L^p(\mathbb{T}), we call the sequence a L^p-Khintchin sequence. We establish basic properties of Khintchin sequences, provide several...
We provide error bounds on the traces and norms of the derivative of the $L^2$ projection of an $H^{k}$ function onto the space of polynomials of degree $\leq p$. The bounds are explicit in the order of differentiation and the polynomial degree $p$.
We establish necessary and sufficient condition for existence of solutions for a class of semilinear Dirichlet problems with the linear part at resonance at eigenvalues of multiplicity two. The result is applied to give a condition for unboundness of all solutions of the corresponding semilinear heat equation.
In this paper, we design and apply novel inexact adaptive algorithms to deal with minimizing difference-of-convex (DC) functions in Hilbert spaces. We first introduce I-ADCA, an inexact adaptive counterpart of the well-recognized DCA (difference-of-convex algorithm), that allows inexact subgradient evaluations and inexact solutions to...
The study of global-in-time dynamics of vacuum is crucial for understanding viscous flows. In particular, physical vacuum, characterized by a moving boundary with nontrivial finite normal acceleration, naturally arises in the motion of shallow water. The corresponding large-data problems for multidimensional spherically symmetric...
Given a contact fibration, we construct smooth families of Szegö projections on the fibers. This allows us to define smooth families of Toeplitz operators. We apply these operators to construct a deformation quantization of prequantizable symplectic fibrations, recovering a result of Kravchenko in an analytic way. We also derive a...
Consider an $(n+1)$-dimensional circular cone with opening angle $α\in (0,π)$. Using a free-boundary adaptation of the classical calibration method, we prove that, for $n \geq 4$, there exists a threshold $\barα(n) \in (0,π)$ such that if $α\geq \barα(n)$, that is, the cone is wide enough, the intersection of the cone with an axial...
We consider $C$-pseudo-cones, that is, closed convex sets $K \subset{\mathbb R}^n$ with $o\notin K\subset C$, for which $C$ is the recession cone. Here $C$ is a given closed convex cone in ${\mathbb R}^n$, pointed and with nonempty interior. We define a class of measures for such pseudo-cones and show how they can be interpreted as...
We study the semantic relationship between Gödel-Dummett logic $\mathsf{GL}$ and bounded-depth-2 logic $\mathsf{BD_2}$, two well-known intermediate logics. While $\mathsf{GL}$ imposes linearity on Kripke frames, $\mathsf{BD_2}$ bounds their depth to two. We prove these logics are incomparable (neither contains the other) through...
We introduce FlagAlgebraToolbox, an extension of SageMath capable of automating flag algebra calculations and optimizations. FlagAlgebraToolbox has a simple interface, can handle a wide range of combinatorial theories, can numerically optimize extremal combinatorial problems and round the results to produce exact proofs. We present...
A band is a semigroup in which each element is idempotent. In recent years, there has been a lot of activity on the representation theory of the subclass of left regular bands due to connections to Markov chains associated to hyperplane arrangements, oriented matroids, matroids and CAT(0) cube complexes. We prove here that the...
The aim of this article is to investigate central-valued identities involving pairs of endomorphisms on prime rings equipped with an involution of the second kind. Extending the recent contributions of Mir et al. (2020) and Boua et al. (2024), we establish several new commutativity criteria for such rings in the presence of two...
A new approach to the semantics of identity types in intensional Martin-Löf type theory is proposed, assuming only a category with finite limits and an interval. The specification of \emph{extensional} identity types in the original presentation of natural models paralleled that of the other type formers $Σ$ and $Π$, but the treatment...
In this note, we study Einstein manifolds whose curvature operator of the second kind $\mathring{R}$ satisfies the cone condition \[ α^{-1}\big(\sum_{i=1}^{[α]} λ_i+ (α- [α] ) λ_{[α] + 1} \big) \ge -θ\barλ \] for some real number $α\in [1, (n+2)(n-1)/2)$. Here $[α] :=\max\{ m \in \mathbb{Z}: m \leq α\}$, $θ>-1$ and $λ_1 \le \cdots \le...
Homology of non degenerate real projective quadrics was studied by Steenrod and Tucker. We Compute the rational and the $\mathbb{Z}/2\mathbb{Z}$ homology of degenerate real projective quadrics. This allows to determine the integer homology of these quadrics.
The purpose of this thesis is to introduce two new kinds of hyperplane arrangements, inspired by the graphic arrangements and $q$-deformations of graphic arrangements. In this thesis, the author extends the definition of $q$-deformation to simplicial complexes, with the conjecture by Nian, Tsujie, Uchiumi and Yoshinaga. The author...
Score-based diffusion models have become a powerful framework for generative modeling, with score estimation as a central statistical bottleneck. Existing guarantees for score estimation largely focus on light-tailed targets or rely on restrictive assumptions such as compact support, which are often violated by heavy-tailed data in...