Continuous Dependence of Attractors on Parameters of Non-Autonomous Dynamical Systems and Infinite Iterated Function Systems

The paper is dedicated to the study of the problem of continuous dependence of compact global attractors on parameters of non-autonomous dynamical systems and infinite iterated function systems (IIFS). We prove that if a family of non-autonomous dynamical systems depending on a parameter is uniformly contracting (in the generalized sense), then each system of this family admits a compact global attractor. As an application we give a generalization of well known Theorem of Bransley concerning the continuous dependence of fractals on parameters

Compact Global Attractors of Discrete Inclusions

The paper is dedicated to the study of the problem of the existence of compact global attractors of discrete inclusions and to the description of its structure. We consider a family of continuous mappings of a metric space W into itself; on the metric space W we consider a discrete inclusion. We give sufficient conditions for the existence of a compact global attractor. If the family consists of a finite number of maps, then the corresponding compact global attractor is chaotic. We study this problem in the framework of non-autonomous dynamical systems (cocyles)

Application of method of heat vision generalization for the estimation of terms of accumulation of hydrocarbons in the Western desert of Egypt

The article presents results of an innovative technologies application – the thermal imaging generalization method for environments assessing that make possible the accumulation of hydrocarbon in the Western Desert of Egypt. This method was first applied in the cumulative desert in new modification, which applies not only the field of thermal radiation, but also an indicator of relative water saturation. It gives an opportunity to confirm and specify the discovered contours of oil and gas deposits and similar to them to discover some new, which are predicted for the first time

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)

On the stability of gradient-like systems

Качественная теория дифференциальных уравнени

Preservation of the High Quality Factor and Accelerating Gradient of Nb3Sn-coated Cavity During Pair Assembly

Two CEBAF 5-cell accelerator cavities have been coated with Nb3Sn film using the vapor diffusion technique. One cavity was coated in the Jefferson Lab Nb3Sn cavity coating system, and the other in the Fermilab Nb3Sn coating system. Both cavities were measured at 4 K and 2 K in the vertical dewar test in each lab and then assembled into a cavity pair at Jefferson Lab. Previous attempts to assemble Nb3Sn cavities into a cavity pair degraded the superconducting properties of Nb3Sn-coated cavities. This contribution discusses the efforts to identify and mitigate the pair assembly challenges and will present the results of the vertical tests before and after pair assembly. Notably, one of the cavities reached the highest gradient above 80 mT in the vertical test after the pair assembly.Comment: 21st Intl Conf Radio Frequency Superconductivity (SRF 2023

Asymptotic behaviour of random tridiagonal Markov chains in biological applications

Discrete-time discrete-state random Markov chains with a tridiagonal generator are shown to have a random attractor consisting of singleton subsets, essentially a random path, in the simplex of probability vectors. The proof uses the Hilbert projection metric and the fact that the linear cocycle generated by the Markov chain is a uniformly contractive mapping of the positive cone into itself. The proof does not involve probabilistic properties of the sample path and is thus equally valid in the nonautonomous deterministic context of Markov chains with, say, periodically varying transitions probabilities, in which case the attractor is a periodic path.Comment: 13 pages, 22 bibliography references, submitted to DCDS-B, added references and minor correction

Stochastic attractors for shell phenomenological models of turbulence

Recently, it has been proposed that the Navier-Stokes equations and a relevant linear advection model have the same long-time statistical properties, in particular, they have the same scaling exponents of their structure functions. This assertion has been investigate rigorously in the context of certain nonlinear deterministic phenomenological shell model, the Sabra shell model, of turbulence and its corresponding linear advection counterpart model. This relationship has been established through a "homotopy-like" coefficient $\lambda$ which bridges continuously between the two systems. That is, for $\lambda=1$ one obtains the full nonlinear model, and the corresponding linear advection model is achieved for $\lambda=0$. In this paper, we investigate the validity of this assertion for certain stochastic phenomenological shell models of turbulence driven by an additive noise. We prove the continuous dependence of the solutions with respect to the parameter $\lambda$. Moreover, we show the existence of a finite-dimensional random attractor for each value of $\lambda$ and establish the upper semicontinuity property of this random attractors, with respect to the parameter $\lambda$. This property is proved by a pathwise argument. Our study aims toward the development of basic results and techniques that may contribute to the understanding of the relation between the long-time statistical properties of the nonlinear and linear models

ВПЧ-СТАТУС РАКА МОЧЕВОГО ПУЗЫРЯ, МОРФОЛОГИЧЕСКИЕ ХАРАКТЕРИСТИКИ ОПУХОЛИ И КЛИНИЧЕСКИЕ ОСОБЕННОСТИ ЗАБОЛЕВАНИЯ

The data of medical records of 101 patients with urothelial bladder cancer (BC) were compared with the results of laboratory detection of human papillomaviruses (HPV) in the tumor tissue samples taken from these patients during transurethral resection. DNA of HPV 16, the major type of the virus responsible for the occurrence of cervical cancer, was previously detected in 38 samples; and oncogenes E6 and E7 mRNA and HPV 16 E7 oncoprotein were found in 13 of these samples. Comparison of HPV-positive and HPV-negative groups revealed that HPV-positive BC showed higher cell anaplasia than HPV-negative one; moreover, primary cancer was HPV-positive more frequently than recurrent cancer. Sex, age, muscular layer invasion did not correlate with the HPV positivity of BC. Проведено сопоставление данных историй болезни 101 больного уротелиальным раком мочевого пузыря (РМП) с результатами лабораторной детекции вирусов папиллом человека (ВПЧ) в образцах опухолевой ткани, взятой у этих пациентов во время транс-уретральной резекции. Ранее ДНК ВПЧ-16, основного типа вируса, ответственного за возникновение рака шейки матки, была обнаружена в 38, а мРНК онкогенов Е6 и Е7 и онкобелок Е7 ВПЧ-16 – в 13 из этих образцов. При сравнении групп «ВПЧ-положительные» и «ВПЧ-отрицательные» выявлено, что ВПЧ-положительный РМП характеризуется более высокой степенью анаплазии клеток, чем ВПЧ-отрицательный, при этом первичный рак бывает ВПЧ-положительным чаще, чем рецидивный. Пол, возраст и инвазия в мышечный слой не коррелируют с ВПЧ-положительностью РМП.