Abstract: The source data is represented by three-dimensional truth table for 3-demensional functions of binary, ternary and mixed logics. The calculation of values of logic function is performed by geometric interpretations, disjunctive / conjunctive normal forms, non-fully connected artificial neural networks and perceptrons with hidden layer. The article reviews in detail the intermediate results of calculations in all given ways. The authors study properties of mixed logic functions: binary-ternary and 3-2 logics in cases of one, two and three dimensions. The article shows mutually equivalent implementations of logic functions in the form of DNF and non-fully connected artificial neural network. The authors perform replacement of continuous activation function on ternary threshold function. The study uses the methods of DNF constructing; direct synthesis of ANN weight matrices, perceptron is trained using Back Propagation algorithm, some conclusions are made by the laws of mathematical inductions. The paper shows that: Minimizations of neuron quantity in the perceptron hidden layer implicitly leads to the use of multiple-valued logics; Some functions of binary-ternary logics may be used for generating disjunctive forms; There is a decisive way of converting DNF to ANN and vice versa; In the one-dimension  3-2 logics there only 8 functions and all of them are listed; The suggested ANN structure can implement any other function of ternary logics of any dimensions.

Keywords: three-valued logic, 3-2 logic, binary-ternary logic, perfect disjunctive form, activation function, separating hyperplane, perceptron, XOR problem, neural network training, Back Propagation algorithm

Abstract: The subject of the study is to describe the topology of the network by using graph theory. The purpose of the study is to construct the graphic descriptions of a computer network, a mathematical model and notation (language) for storing and processing computer network. All these problems are related and in the study the author focuses on describing the basic topologies "bus", "star", "ring" using graphs for further development and construction of a mathematical model, language notation of mixed network topology using various components. Creating a mathematical model and graphical / symbolic notation of the language is an important step in the task of building a theoretical mathematical apparatus for the creation of computer-aided design and automated control systems for telecommunications networks. The study uses analysis of the existing topology networks, the theory of networks and telecommunication devices, mathematical apparatus of graph theory and the theory of hypergraphs. The problem of constructing computer-aided design of computer networks is relevant since the beginning of the development of computer networks and up to the present time. Invention of new telecommunication technologies and new areas of their application leaves this task up-to-date and requires the development of new approaches. The novelty of the research is in developing methods to describe the classical topology in the context of the task of building a network topology with a complex combination topology. The author describe the classical topologies using graphs, proposes methods for replacements and decomposition. The results can be used in the development of the graph and the symbol models of telecommunication network topology with a complex mixed topology for use in computer-aided design and automated control systems of telecommunication networks. 

Keywords: binary tree, graph, bus network topology, ring network topology, star network topology, network topology, topology, hypergraph, graph theory, CAD

Abstract: The subject of the study is analysis of a sequence of transformations of information about functioning of an educational institution in the simulation of management of its activities as a training and research center. The paper analyzes the structure and functioning of the educational institutions of higher education system within the trends of modernization and quality of education set by legal documents of the educational system of the Russian Federation. In addition, the article presents an example of a developed diagram of the university, which allows searching and predicting the causes of the inefficiency of its activities, and is relevant for choosing ways to achieve the best possible performance. The article describes the developed mathematical model of the university as a dynamic control system for a continuous period of time, allowing to estimate the characteristics of the dynamics of an educational establishment, and also allowing to develop a software system to improve decision-making in the university management. A set of techniques used includes methods of system analysis, expert evaluation methods and functional analysis, methods of the theory of differential equations, methods of mathematical statistics, methods of decision theory, methods of control theory of complex systems, methods of the theory of databases and expert systems, methods of discrete mathematics, the theory of automatic methods management. A list of indicators of the university as an educational and scientific center is formed in terms of indicators to measure the quality of modern functioning education-enforcement agencies. Author impact diagram of components of the university as a dynamic control system. A mathematical model of the educational institution as a dynamic control system for a continuous period of time is given.

Keywords: education system, mathematical modeling, control systems, transformation of information, cause-and-effect diagram, assessment of efficiency, dynamical systems, identification of management facilities, expert assessments, software package

Abstract: The subject of the study is building an information system of electronic documents management for website pages. The developed model of hierarchical storage of web-documents is intended for designing the content management system for web-sites and, also, is a contribution to the development of a methodology of developing content management systems. Object-oriented description of the model of electronic documents storage allows to create the optimal design for the interface for human-computer interaction in comparison with existing content management systems. The research is based on the implementation of object-oriented approach (object-oriented design), prototyping, theory of the object-oriented user interface, graph theory, set theory, theory of formal languages and formal systems and programming languages  development methodology. The existing content management systems (CMS) are build on the base of engineering approach without the attempts to create sufficient mathematical basis. The author tries to form the mathematical basis for building the CMS. The decision to develop a model was made after analyzing the existing content management systems and receiving unsatisfactory ratings in the field of HCI. In order to create the optimal design of the human-users the author decided to create an object-oriented description of the structure of documents.

Keywords: web server, CMS, content management system, graphic user interface, GUI, object-oriented programming, object-oriented approach, prototype approach, graph Model, binary tree

Abstract: The article reviews the informational capabilities of software for professional cost analysis. None of the information agencies from the Russian market proves to have textbooks and manuals on their products for training financiers, analysts and evaluators. The present documentation is brief and fragmented; it does not disclose  important features of the described software, multiple calculation modules, in particular, financial ratio analysis, the calculation of multipliers and many other. At the moment there is a contradiction: on the one hand, information systems are actively developing in Russian educational and financial sectors, installed in the leading universities of the country (HSE, Moscow State University, Financial University under the Government of the Russian Federation), large and medium-sized financial companies and bands, but on the other hand subtends and specialists does not have educational aids to work with. This article consistently discusses the main tasks and requirements for information system for cost analysis, basics and architecture required for building such information system. The author describes  features and functions needed by the financial analyst for the cost valuation. This article for the first time present main trends and possibilities for creating educational materials on information system for teaching students, training of financial analysts and scientists working in the field of finance. The author describes elements of information system meant to be used on each of the major stage of cost analysis and valuation. More than a half of financial Russian information market is occupied by foreign information agencies. Their products due to its large volume are localized into Russian by means of machine translations. Because of the low-quality of translation the working with them is very difficult. The presence of the manuals in Russian is a great help when working with the software. 

Keywords: logical order, journalistic order, chronological order, cost estimate, cost analysis, receiving information, financial ratio analysis, information system, systematization, database