Related papers: Quasi-Minimal, Pseudo-Minimal Systems and Dense Or…
We introduce and study weak o-minimality in the context of complete types in an arbitrary first-order theory. A type $p\in S(A)$ is weakly o-minimal if for some relatively $A$-definable linear order, $<$, on $p(\mathfrak{C})$ every…
"Weak measurements" -- involving a weak unitary interaction between a quantum system and a meter followed by a projective measurement -- are investigated when the system has a non-Hermitian Hamiltonian. We show in particular how the…
Quasi-polar spaces are sets of points having the same intersection numbers with respect to hyperplanes as classical polar spaces. Non-classical examples of quasi-quadrics have been constructed using a technique called pivoting [5]. We…
Quasinormal modes describe the ringdown of compact objects deformed by small perturbations. In generic theories of gravity that extend General Relativity, the linearized dynamics of these perturbations is described by a system of coupled…
We show that all countable subsets of any pseudocompact quasitopological group in the form of a Korovin orbit are closed, discrete, and $C^\ast$-embedded. Consequently, any infinite pseudocompact Korovin orbit is not homeomorphic to a…
It is proven that the orbit-equivalence class of any essentially free probability-measure-preserving action of a free group $G$ is weakly dense in the space of actions of $G$.
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of…
In this paper, we introduce quasi-convex subsets in Alxandrov spaces with lower curvature bound, which include not only all closed convex subsets without boundary but also all extremal subsets. Moreover, we explore several essential…
We extend the restricted phase space formalism for spherically symmetric black hole solutions of Einstein-Maxwell theory to the quasi-local regime, with the static observers located at a finite radial distance. The first law and Euler…
In this paper we consider the existence and regularity of weakly polyharmonic almost complex structures on a compact almost Hermitian manifold $M^{2m}$. Such objects satisfy the elliptic system weakly $[J, \Delta^m J]=0$. We prove a very…
By virtue of a weak comparison principle in small domains we prove axial symmetry in convex and symmetric smooth bounded domains as well as radial symmetry in balls for regular solutions of a class of quasi-linear elliptic systems in…
In this paper, we give two elementary constructions of homogeneous quasi-morphisms defined on the group of Hamiltonian diffeomorphisms of certain closed connected symplectic manifolds (or on its universal cover). The first quasi-morphism,…
We construct here two new examples of non-orientable, non-compact, hyperbolic 4-manifolds. The first has minimal volume $v_m = 4{\pi}^2/3$ and two cusps. This example has the lowest number of cusps among known minimal volume hyperbolic…
This work explores the dynamic properties of test particles surrounding a distorted, deformed compact object. The astrophysical motivation was to choose such background, which could constitute a more reasonable model of a real situation…
Although the hyperbolic metric possesses many remarkable properties, it is not defined on arbitrary subdomains of $\mathbb{R}^n$ with $n \geq 2$. This article introduces a new hyperbolic-type metric that provides an alternative approach to…
We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For…
We propose a notion of cusp forms on semisimple symmetric spaces. We then study the real hyperbolic spaces in detail, and show that there exists both cuspidal and non-cuspidal discrete series. In particular, we show that all the spherical…
In this paper, we prove that the product of strongly quasi-nonexpansive $\Delta$-demiclosed mappings is also a strongly quasi-nonexpansive orbital $\Delta$-demiclosed mapping in Hadamard spaces. Additionally, we establish the…
Photometric observations and analysis of twelve previously poorly studied contact binary systems is presented. All show total eclipses and have extremely low mass ratios ranging from 0.072 to 0.15. Also, all show characteristics of orbital…
In this paper, we use the concept of proximal quasi-normal structure (P. Q-N. S) to study the existence of best proximity points for cyclic mappings, cyclic contractions, relatively Kannan nonexpansive mappings, as well as for orbitally…