Limit theorems for random point measures generated by cooperative sequential adsorption

We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity of the model is that the probability distribution of a point depends on previously allocated points. We assume that the dependence vanishes as the concentration of points tends to infinity. Under this assumption the law of large numbers, the central limit theorem and Poisson approximation are proved for the generated sequence of random point measures.Comment: 17 page

Concepts of universal time and multiplicity of times in understanding the existence of past reality

The purpose of the article is to identify and determine the dependence of ontological ideas about the existence of past reality on thinking within the framework of competing concepts of universal time and multiplicity of times. The methods of research were the representation, comparison and ontological analysis of various ideas about the essence and nature of time, synthesis and philosophical criticism of the consequences arising from competing concepts of the multiplicity of times and the concept of a single universal time in relation to the definition of ontological characteristics of past reality. The article gives a representation of several versions of the concepts of multiplicity of times, some of which are based on the theory of relativity, others proceed from ontological differences in the processes of various forms of being — being material, spiritual, personal and social. It has been shown that in some cases, in the concepts of multiplicity of times, time itself and the idea of time as a construct of the mind are mistakenly identified, which serves as the reason for the incorrect attribution of time to atypical paradoxical properties, such as inversion — the possibility of its movement to reverse, the uncertainty of the past, present and future, the variability of the past and others. The author gives critical arguments refuting ideas about the possibility of changing the places of events and states of reality in the time relationship “earlier/later,” that is, in the sequence of their appearance and disappearance, as well as incorrect opinions about the possibility of variability of the past under the influence of processes that take place in the present and have to be in the future. The study justifies the idea that a clear and unambiguous distinction between past and present objective reality is impossible from the point of view of ideas about the multiplicity of times and is possible only in the conceptual field of theories, recognizing the unity of the world and using a single scale of universal time common to processes and events, having different ontological characteristics and flowing in arbitrarily distant places of space in different inertial reference systems

Existence in the present as an ontological problem

The purpose of the article is to develop an ontological understanding and interpretation of the existence of real world objects in the present mode, to determine the essence, properties and ontological status of the Present. The author identifies and analyzes contradictions in various approaches to understanding being and reality in the present. The essence of the problem is the contradiction of the idea of the inactivity of the moment of the present time, which gives rise to its denial («there is no present») and the procedural representation of being, the idea of the duration of the processes, the course of the movement, which, as it is customary to think, in the present. The study is conducted mainly within the framework of realistic ontology, which recognizes the authenticity of the existence of real material things and social objects as single integrations. A phenomenological approach is also used to identify the forms and methods of the primary pre-reflexive given reality of the Present to human consciousness. At the same time, the methods of research are representation, comparison, ontological analysis, interpretation and reinterpretation of various interpretations of the Present and time as a whole. The article presents various interpretations of the essence of the Present. The theoretical contradictions of the concept of the idle Present, presented as one state of existence and its inconsistency with reality, are revealed and shown. The argument is given to the impossibility of realizing the existence of things and the world as a whole on the basis of the idea of the idle Present. The author justifies the idea of the existence of the Past in the present on the basis of a synthesis of various interpretations of the interpenetration of the reality of these temporary modes. The dilemma of the ratio of competing ideas about the inactivity of the Present and the movement taking place in it is solved by the provision that in the Present not a particular state of the world continues (lasts), but the process of changing these states itself, which «moves» the Present to the last place in the non-spatial temporal order of successive states. Scientific novelty in solving the problem is manifested in justifying the modification of the idea of being in the Present within the framework of the dynamic concept of time by the provision on various forms and methods of the existence of the Past in the Present. The author concludes that such synthesis is possible and necessary

Dispersion of Waves in Relativistic Plasmas with Isotropic Particle Distributions

The dispersion laws of Langmuir and transverse waves are calculated in the relativistic non-magnetized formalism for several isotropic particle distributions: thermal, power-law, relativistic Lorentzian $\kappa,$ and hybrid $\beta$. For Langmuir waves the parameters of superluminal undamped, subluminal damped principal and higher modes are determined for a range of distribution parameters. The undamped and principal damped modes are found to match smoothly. Principal damped and second damped modes are found not to match smoothly. The presence of maximum wavenumber is discovered above that no longitudinal modes formally exist. The higher damped modes are discovered to be qualitatively different for thermal and certain non-thermal distributions. Consistently with the known results, the Landau damping is calculated to be stronger for non-thermal power-law-like distributions. The dispersion law is obtained for the single undamped transverse mode. The analytic results for the simplest distributions are provided.Comment: 8 pages, 12 figures, accepted by Physics of Plasma

A model for the distribution of aftershock waiting times

In this work the distribution of inter-occurrence times between earthquakes in aftershock sequences is analyzed and a model based on a non-homogeneous Poisson (NHP) process is proposed to quantify the observed scaling. In this model the generalized Omori's law for the decay of aftershocks is used as a time-dependent rate in the NHP process. The analytically derived distribution of inter-occurrence times is applied to several major aftershock sequences in California to confirm the validity of the proposed hypothesis.Comment: 4 pages, 3 figure

Almost Periodic and Asymptotically Almost Periodic Solutions of Liénard Equations

The aim of this paper is to study the almost periodic and asymptotically almost periodic solutions on (0,+1) of the Li´enard equation x′′ + f(x)x′ + g(x) = F(t), where F : T ! R (T = R+ or R) is an almost periodic or asymptotically almost periodic function and g : (a, b) ! R is a strictly decreasing function. We study also this problem for the vectorial Li´enard equation. We analyze this problem in the framework of general non-autonomous dynamical systems (cocycles). We apply the general results obtained in our early papers [3, 7] to prove the existence of almost periodic (almost automorphic, recurrent, pseudo recurrent) and asymptotically almost periodic (asymptotically almost automorphic, asymptotically recurrent, asymptotically pseudo recurrent) solutions of Li´enard equations (both scalar and vectorial)

Stator current limiting in variable-frequency electrical drive with scalar control system

The problem of stator current limiting of asynchronous electrical drive under overload is reviewed. Task of research is stated. Mathematical model of simplest scalar control system with current limiter and results of mathematical modeling of electrical drives in stator limiting modes are included.Рассматривается проблема ограничения тока статора асинхронного электропривода при перегрузке. Дается постановка задачи исследования. Приводятся математическая модель простейшей скалярной системы с отсечкой по току и результаты математического моделирования процессов электропривода в режимах ограничения тока статора