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Inspired by the concept of coherent frozen waves, this paper introduces one possible theoretical framework of its partially coherent version, a frozen spatial coherence, in which a desired two-point correlation structure of an optical field…

In this letter we discuss a method for generating synchrony-optimized coupling architectures of Kuramoto oscillators with a heterogeneous distribution of native frequencies. The method allows us to relate the properties of the coupling…

We prove that some quantized Arnold cat maps are entropic K-systems. This result was formulated by H. Narnhofer[1], but the fact that the optimal decomposition for the multi-channel entropy constructed there is not strictly local was not…

Any unitary operation in quantum information processing can be implemented via a sequence of simpler steps - quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, seeking for…

Let $X$ be a compact Hausdorff space, with uniformity $\mathscr{U}$, and let $f \colon X \to X$ be a continuous function. For $D \in \mathscr{U}$, a $D$-pseudo-orbit is a sequence $(x_i)$ for which $(f(x_i),x_{i+1}) \in D$ for all indices…

We establish an optimal gluing construction for general relativistic initial data sets. The construction is optimal in two distinct ways. First, it applies to generic initial data sets and the required (generically satisfied) hypotheses are…

I demonstrate that the chart based approach to the study of the global structure of Lorentzian manifolds induces a homeomorphism of the manifold into a topological space as an open dense set. The topological boundary of this homeomorphism…

We give the first deterministic fully polynomial-time approximation scheme (FPTAS) for computing the partition function of a two-state spin system on an arbitrary graph, when the parameters of the system satisfy the uniqueness condition on…

Recently, an open geometry Fourier modal method based on a new combination of an open boundary condition and a non-uniform $k$-space discretization was introduced for rotationally symmetric structures providing a more efficient approach for…

Following up on the systematic compactification of the two-channel Kondo model (and its multichannel extensions; arXiv:2308.03569 (companion paper I)) and the demonstration of its validity over the past proposal of compactification, we…

Here is an English summary of the abstract: This research investigates a geometric dynamical mechanism within a specific class of domains that contain a fixed convex core. By using a radial structure that links the boundaries of the core…

A modified Kuramoto model of synchronization in a finite discrete system of locally coupled oscillators is studied. The model consists of N oscillators with random natural frequencies arranged on a ring. It is shown analytically and…

In this text we show, that the notion of a "good pair" that was introduced in the paper "Digital Manifolds and the Theorem of Jordan-Brouwer" has actually known models. We will show, how to choose cubical adjacencies, the generalizations of…

A system of equations that serves as a model for the Einstein field equation in generalised harmonic gauge called the good-bad-ugly system is studied in the region close to null and spatial infinity in Minkowski spacetime. This analysis is…

Fine-grained complexity theory is the area of theoretical computer science that proves conditional lower bounds based on the Strong Exponential Time Hypothesis and similar conjectures. This area has been thriving in the last decade, leading…

Let X be a Banach space. Given a subset A of the dual space X* denote by $A_{(1)}$ the weak* sequential closure of A, i.e., the set of all limits of weak*-convergent sequences in A. The study of weak* sequential closures of linear subspaces…

This article focuses on the optimization of a complex system which is composed of several subsystems. On the one hand, these subsystems are subject to multiple objectives, local constraints as well as local variables, and they are…

Given a measure space and a totally ordered ordered collection of measurable sets, called an ordered core, the notion of a core decreasing function is introduced and used to define the down space of a Banach function space. This is done…

Classical objects in computational geometry are defined by explicit relations. Several years ago the pioneering works of T. Asano, J. Matousek and T. Tokuyama introduced "implicit computational geometry", in which the geometric objects are…

Using methods from ergodic theory along with properties of the Furstenberg measure we obtain conditions under which certain classes of plane self-affine sets have Hausdorff or box-counting dimensions equal to their affinity dimension. We…