arXiv preprints from January 1, 2026 through September 8, 2026 — 09:06:18 EST
We illustrate how the recent theory of Spectral Submanifolds (SSM) can capture global bifurcations and complex dynamics in mechanical systems even under delay and spatial discretization. Specifically, we build a parameter-dependent SSM-reduced model that predicts global heteroclinic and local bifurcations in a Furuta pendulum under...
We compute the quantum isometry groups of Cuntz-Krieger algebras endowed with the spectral triples coming from the Ahlfors regular structure of the underlying topological Markov chain. This allows us to exhibit a new family of compact quantum groups, mixing features from quantum automorphism groups of graphs and easy quantum groups....
Les perturbations de faible rang de matrices aléatoires ont été au cœur de nombreux travaux ces vingt dernières années. En particulier, les cas non-hermitiens, moins représentés dans la littérature en règle générale, font ici l'objet d'une attention spéciale en raison de leurs applications à la physique et à l'étude des réseaux de...
Motivated by Varadhan's theorem, we introduce Varadhan functions, variances, and means on compact Riemannian manifolds as smooth approximations to their Fréchet counterparts. Given independent and identically distributed samples, we prove uniform laws of large numbers for their empirical versions. Furthermore, we prove central limit...
Community detection seeks to recover mesoscopic structure from network data that may be binary, count-valued, signed, directed, weighted, or multilayer. The stochastic block model (SBM) explains such structure by positing a latent partition of nodes and block-specific edge distributions. In Bayesian SBMs, standard MCMC alternates...
In this article, we deal with the uniform effective disjunction property and the uniform effective interpolation property, which are weaker versions of the classical effective disjunction property and the effective interpolation property.\\ The main result of the paper is as follows: Suppose the proof system $EF$ (Extended Frege) has...
We introduce a new class of operators, called Berezin sectorial operators, which generalizes classical sectorial operators. We provide examples on the Hardy-Hilbert space showing that there exist operators that are Berezin sectorial but not sectorial and that the Berezin sectorial index can be strictly smaller than the classical one....
Bayesian network models (Erdos Renyi, stochastic block models, random dot product graphs, graphons) are widely used in neuroscience, epidemiology, and the social sciences, yet real networks are sparse, heterogeneous, and exhibit higher-order dependence. How stable are network-based decisions, model selection, and policy...
Alessandro Figà-Talamanca (1938-2023) was an influential Italian mathematician, scientific leader of the Italian group of harmonic analysis for many years. Since the late 1970ies, his interest focussed on harmonic analysis on free groups and trees. In the later years of his scientific work he became also interested in diffusion...
The authors recently introduced a new construction of a knot as an extended symmetric union of a knot with a single tangle region. In this paper, we generalize the construction to include multiple tangle regions. The constructed knot $K$ with a partial knot $\hat{K}$ and multiple tangle regions satisfies the following two properties:...
We study an optimization problem in which the objective is given as a sum of logarithmic-polynomial functions. This formulation is motivated by statistical estimation principles such as maximum likelihood estimation, and by loss functions including cross-entropy and Kullback-Leibler divergence. We propose a hierarchy of moment...
In combinatorial optimization, ordinal costs can be used to model the quality of elements whenever numerical values are not available. When considering, for example, routing problems for cyclists, the safety of a street can be ranked in ordered categories like safe (separate bike lane), medium safe (street with a bike lane) and unsafe...
In this paper, we establish Liouville-type theorems for the steady compressible Navier-Stokes system. Assuming a smooth solution \(u \in L^p(\mathbb{R}^3)\), \(3 \le p \le \frac{9}{2}\), with bounded density, one obtains \(u \equiv0\). This generalizes the result of Li-Yu \cite{Li-Yu} by removing the Dirichlet condition...
In this article, we examine an approximate version of Koldobsky-Blanco-Turnšek theorem (namely, Property P) in the space of vector-valued integrable functions. More precisely, we prove that the Lebesgue-Bochner spaces $L^p(μ,X),\;(1\leq p<\infty)$, do not have Property P under certain conditions on $μ$ and the Banach space $X$.
Let $S(n)$, for $n \in \mathbb{N}$, be the infinite-type surface of infinite genus with $n$ ends, each accumulated by genus. Although the mapping class groups of these surfaces are not countably generated,they are Polish groups and hence admit a countable topological generating set. We study minimal topological generating sets for...
Based on the recent works of Radziwill-Soundararajan and Roberts, we establish a rate of convergence in Bourgade's central limit theorem for shifted Dirichlet $L$-functions. Our results also indicate that the dependence structure in the components of a random vector could have a dramatic impact on the rate of convergence in such a...
In this paper, we determine the automorphism groups of generalized Kausz compactifications $\mathcal T_{s,p,n}$. By establishing the (semi-)positivity of the anticanonical bundles of $\mathcal T_{s,p,n}$, we also determine the automorphism groups of generalized spaces of complete collineations $\mathcal M_{s,p,n}$. The results in this...
We prove explicit rational stable splittings of equivariant complex projective spaces $\mathbb{C}P(V)$ and Grassmannians $Gr_n(V)$, for complex representations $V$. When $V$ is a sum of one-dimensional representations, both $\mathbb{C}P(V)$ and $Gr_n(V)$ are rationally a wedge of representation spheres. For general finite groups $G$...
We prove an analog of Rudolph's theorem for actions of countable amenable groups, which asserts that among invariant measures with entropy at least c on the $G$-shift $(Λ^G,σ)$, a typical measure has entropy $c$ and is Bernoulli. We also address a relative version of this theorem.
In this article, we prove that, on the diffusive time scale, condensing zero-range processes converge to a dimension-decaying diffusion process on the simplex \[ Σ= \{(x_1,\dots,x_S) : x_i \ge 0,\; \sum_{i\in S} x_i = 1\}, \] where $S$ is a finite set. This limiting diffusion has the distinctive feature of being absorbed at the...
Three points uniformly selected on the unit circle form a triangle containing a point $X$ at distance $r \in [0; 1]$ from its center with probability $P(r) = \frac{1}{4} - \frac{3}{2 π^2}\textrm{Li}_2(r^2)$, where $\textrm{Li}_2$ is the dilogarithm function (Jeremy Tan Jie Rui, 2018). In this paper we present an alternative proof of...
Characteristic earlier results were of the form CON$(2^{\aleph_0} \to [λ]^2_{n, 2})$, with $2^{\aleph_0} $ an ex-large cardinal, in the best case the first weakly Mahlo cardinal. Characteristic new results are CON$((2^{\aleph_0} = \aleph_m) + \aleph_l \to [\aleph_k]^2_{n, 2})$, for suitable $k < l < m$. So we improve in three...
Following the definition of perturbed metric space, in this paper, some fixed point theorems are established for $ F $-perturbed mappings in complete perturbed metric spaces and justify the result by counter example. Finally, an application of this theorem for the existence of a solution for the second-order boundary value problem is given.
In 1934, Ramaswami proved a number of curious translation formulae satisfied by the Riemann zeta function. Such translation formulae, in turn give the meromorphic extension of the Riemann zeta function. In 1954, Apostol extended those identities to establish a family of such similar translation formulae. In this article, we establish...
Recently, Jiang et al. \cite{JIANG2025102522} obtained several classes of Permutation Polynomial of the form $x+γ\operatorname{Tr}_q^{q^2}(h(x))$ over finite fields $\mathbb{F}_{q^2},q=2^n$. In this paper, we find the compositional inverse of six classes of permutation polynomials of this form.