Jorgensen's inequality for non-Archimedean metric spaces.

Jørgensen’s inequality gives a necessary condition for a non-elementary group of Möbius transformations to be discrete. In this paper we generalise this to the case of groups of Möbius transformations of a non-Archimedean metric space. As an application, we give a version of Jørgensen’s inequality for SL(2, ℚ p )

Low carbon global economy: Scenarios of sustainable development, power consumption and greenhouse gas emission control

This paper is devoted to problems of a gradual transfer to renewable energy sources and decarbonization of power systems. It presents the analysis of the structure and the trend in global power consumption, greenhouse gas emissions, and target values of decreased emissions by the largest greenhouse gas emitters. A trend in renewable energy sources in total global power consumption is analyzed. The authors study a potential for carbon capture and storage as an instrument of CO2 emission neutralization in power and industrial processes. The paper contains indicators to evaluate efficiency of power resource utilization and greenhouse gas emission control. © 2019 IOP Publishing Ltd. All rights reserved

НЕЙРОННЫЕ СЕТИ КОНЕЧНОГО КОЛЬЦА НА ОСНОВЕ РЕДУКЦИОННОЙ СХЕМЫ ПОЗИЦИОННО-МОДУЛЯРНОГО КОДОВОГО ПРЕОБРАЗОВАНИЯ

The article studies the problem of creating a neural network of modular computing structures for highperformance expressions in the field of information security. The main attention is paid to the reduction technology of position-modular transformation of scalable integers, which serves as the basis for constructing the so-called neural networks of the finite ring (NNFR). To increase the speed of convergence of the reduction scheme used to reduce the number of elements of the generated sequence of residues, an effective tabular method is proposed. The developed approach makes it possible to reduce the number of iterations of the reduction process to a theoretical minimum. This is achieved through flexible adaptive mechanism check botheration deductions to a special range, allowing a tabular decomposition of its elements into pairs of residues in modules of the modular number system. On the basis of a modified reduction method there was synthesized a fast algorithm and a parallel structure of the NNFR with feedback, which ensures the implementation of the reduction scheme in a time order (S(⌈log2b⌉+1) +2)tsum, were S – the number of iterations, b – the bit width of the input number, – the duration of the addition operation of two deductions. Рассматривается проблема создания нейросетевых модулярных вычислительных структур для высокопроизводительных выражений в области защиты информации. Главное внимание уделяется редукционной технологии позиционно-модулярного преобразования масштабируемых целых чисел, которая служит основой для построения так называемых нейронных сетей конечного кольца (НСКК). Для повышения скорости сходимости используемой редукционной схемы понижения разрядности элементов формируемой последовательности вычетов предложен эффективный табличный метод. Разработанный подход позволяет свести к теоретическому минимуму количество итераций редукционного процесса. Это достигается за счет применения гибкого адаптивного механизма проверки принадлежности поитерационных вычетов к специальному диапазону, допускающему табличную декомпозицию его элементов на пары остатков по модулям модулярной системы счисления. На базе модифицированного редукционного метода синтезированы быстрый алгоритм и параллельная структура НСКК с обратной связью, обеспечивающая реализацию редукционной схемы за время (S(⌈log2b⌉+1) +2)tсл , где S – число итераций, b – разрядность входного числа, – длительность операции сложения двух вычетов

Применение нейросетевой вычислительной технологии для расчета интервально-индексной характеристики минимально избыточного модулярного кода

The article is devoted to the problem of creation of high-speed neural networks (NN) for calculation of interval-index characteristics of a minimally redundant modular code. The functional base of the proposed solution is an advanced class of neural networks of a final ring. These neural networks perform position-modular code transformations of scalable numbers using a modified reduction technology. A developed neural network has a uniform parallel structure, easy to implement and requires the time expenditures of the order (3[log2b]+ [log2k]+6tsum  close to the lower theoretical estimate. Here b and k is the average bit capacity and the number of modules respectively; t sum is the duration of the two-place operation of adding integers. The refusal from a normalization of the numbers of the modular code leads to a reduction of the required set of NN of the finite ring on the (k – 1) component. At the same time, the abnormal configuration of minimally redundant modular coding requires an average k-fold increase in the interval index module (relative to the rest of the bases of the modular number system). It leads to an adequate increase in hardware expenses on this module. Besides, the transition from normalized to unregulated coding reduces the level of homogeneity of the structure of the NN for calculating intervalindex characteristics. The possibility of reducing the structural complexity of the proposed NN by using abnormal intervalindex characteristics is investigated.Сообщение посвящено проблеме создания высокоскоростных нейронных сетей (НС) для расчета интервально-индексных характеристик минимально избыточного модулярного кода. Функциональную базу предлагаемого решения составляет расширенный класс НС конечного кольца, осуществляющих позиционно-модулярные кодовые преобразования масштабируемых чисел с применением модифицированной редукционной технологии. Разработанная НС для вычисления интервально-индексных характеристик имеет однородную параллельную структуру, проста в реализации и требует близких к теоретической нижней оценке временных затрат порядка (3[log2b]+ [log2k]+6tсл где b и k – соответственно средняя разрядность и количество модулей; t сл – длительность двухместной операции сложения целых чисел. Отказ от нормировки цифр модулярного кода приводит к сокращению необходимого набора НС конечного кольца на (k – 1) компонент. Вместе с тем ненормированная конфигурация минимально избыточного модулярного кодирования требует в среднем k-кратного увеличения модуля интервального индекса (по отношению к остальным основаниям модулярной системы счисления), что ведет к адекватному повышению аппаратурных затрат по данному модулю. Кроме того, переход от нормированного к ненормированному кодированию снижает уровень однородности структуры НС для расчета интервально-индексных характеристик. Исследована возможность снижения структурной сложности предложенной НС за счет использования ненормированных интервально-индексных характеристик

Finite Intersection Property and Dynamical Compactness

[EN] Dynamical compactness with respect to a family as a new concept of chaoticity of a dynamical system was introduced and discussed in Huang et al. (J Differ Equ 260(9):6800-6827, 2016). In this paper we continue to investigate this notion. In particular, we prove that all dynamical systems are dynamically compact with respect to a Furstenberg family if and only if this family has the finite intersection property. We investigate weak mixing and weak disjointness by using the concept of dynamical compactness. We also explore further difference between transitive compactness and weak mixing. As a byproduct, we show that the -limit and the -limit sets of a point may have quite different topological structure. Moreover, the equivalence between multi-sensitivity, sensitive compactness and transitive sensitivity is established for a minimal system. Finally, these notions are also explored in the context of linear dynamics.Wen Huang and Sergii Kolyada acknowledge the hospitality of the School of Mathematical Sciences of the Fudan University, Shanghai. Sergii Kolyada also acknowledges the hospitality of the Max-Planck-Institute fur Mathematik (MPIM) in Bonn, the Departament de Matematica Aplicada of the Universitat Politecnica de Valencia, the partial support of Project MTM2013-47093-P, and the Department of Mathematics of the Chinese University of Hong Kong. We thank the referees for careful reading and constructive comments that have resulted in substantial improvements to this paper. Wen Huang was supported by NNSF of China (11225105, 11431012); Alfred Peris was supported by MINECO, Projects MTM2013-47093-P and MTM2016-75963-P, and by GVA, Project PROMETEOII/2013/013; and Guohua Zhang was supported by NNSF of China (11671094).Huang, W.; Khilko, D.; Kolyada, S.; Peris Manguillot, A.; Zhang, G. (2018). 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Topological chaos: what may this mean ?

We confront existing definitions of chaos with the state of the art in topological dynamics. The article does not propose any new definition of chaos but, starting from several topological properties that can be reasonably called chaotic, tries to sketch a theoretical view of chaos. Among the main ideas in this article are the distinction between overall chaos and partial chaos, and the fact that some dynamical properties may be considered more chaotic than others

Проблема корректности порогового метода модулярного разделения секрета с маскирующим преобразованием

The article formulates the principles of constructing threshold cryptographic schemes for secret sharing based on a modular coding and a linear masking function with an additive variational component of pseudo-random type. The main attention is paid to the correctness problem of schemes of the considered class within the limits of the accepted model. The congruent condition in the module of the secret-original ring of the masking function values in full and partial modular number systems is obtained. On the basis of the above-said, the method of correct implementation of the threshold principle of secret information sharing is developed. The proposed approach to solving the problem under study is demonstrated by specific numerical examples.Сформулированы принципы построения пороговых криптосхем разделения секрета, базирующихся на модулярном кодировании и линейной маскирующей функции с аддитивной вариационной компонентой псевдослучайного типа. Главное внимание уделено проблеме корректности схем рассматриваемого класса в рамках принятой модели. Для пороговых криптосхем модулярного разделения секрета получено необходимое и достаточное условие равноостаточности по модулю кольца принадлежности секрета-оригинала значений функции маскирования и отвечающих им элементов диапазонов, определяемых наборами оснований числом, меньшим порогового значения. На базе установленного условия разработан метод корректной реализации порогового принципа разделения секретной информации. Предложенный подход к решению исследуемой проблемы демонстрируется на конкретных числовых примерах