Abstract: The object of study involves radio frequency planning when designing a radio network.  The frequency allocation within the provided range is one of the key problems in radio networks, since when the frequency is incorrectly provided for the radio station, there may be the radio wave interference effect, and the information transfer becomes distorted.  The article provides an algorithm for frequency planning, which may be used for providing  frequency for the radio stations within radio networks, the algorithm involves circular pattern, known radio station coordinates and the emitted radio power. The development of the algorithm involved experimental theoretical method based upon the known facts regarding radio broadcast and result modeling, as well as use of software. The novelty of the study is due to the development of an algorithm for frequency planning when designing a radio network for a provided frequency resource for a radio station with the circular pattern, known coordinates and emitted radio power. The result of its application involves distribution of radio frequency with their dual use, while excluding interference effect.

Keywords: interference, radio network, frequency planning, mesh network, frequency spectrum control, cellular network, wireless connection, frequency planning algorithm, radio access, frequency division multiple access

Abstract: The object of study in the article is the credit, however it does not concern its economic essence regarding both the creditor, and the borrower. The key aspects of studу concern the mathematical foundations for modeling the  phenomenon of related borrowers. The author stars her research by analyzing economic maintenance of a phenomenon of being related, while directly giving strictly mathematical interpretation to the economic terms, which she employs. Further the author explicitly considers functional and stochastic aspects of coherence of borrowers, showing continuous connection among these aspects. The methodological basis of a research is formed with the set-theoretic and probability-theoretic approaches. Application-oriented aspects of the loan portfolio modeling are explained in terms of the algebraic theory of risk. The graphic illustration of the main results of operation is based on classical submissions of the Cartesian product of finite sets and on traditional (quasi) trees of classification. The key result of this  study is revealing of the complete mathematical list of possible options for the coherence of borrowers in the functional and probability-theoretic contexts. At the same time the article contains detailed descriptions of all possible relation options within the object field of study. This a  novel relation classification. Similar studies are not found among either Russian, or foreign studies so far. Another result of this study is a practical one, since some of the received ratios can be used in order to form efficient algorithms for the direct analysis of risk processes within the complicated systems.

Keywords: affiliate, a group of related entities, a group of related borrowers, credit, independent events, uncertainty, risk, conditional probability, holding, economic relation of the companies

Abstract: The article concerns the computer testing system architecture, possessing the elements of intelligence. The intelligence of the testing system involves adaptability of the testing process, as well as the ability to diagnose and identify errors in the decision process, and it is provided for by the use of the knowledge base of the subject area, the structure of the complexity of case tasks, as well as the expert subsystem and the competency model of students. The subject of the study concerns method and results of implementing an automated assessment of the level of formed subject competencies among the students based upon an analysis of their task decisions generated in accordance with the structure of the level of complication of typical tasks. The options for the use of the intellectual testing system in the context of online learning involve the options of the component architecture of the implemented system as learning subsystems embedded in LMS Moodle, diagrams of the system functioning and usage. The research involves the analysis of the implemented environment architecture for solving learning tasks, as well as and the structure of decision-making concerning the level of the formed subject competencies of the students. The results of introducing a subsystem into a real online course are analyzed. The main results of the study are as follows: the architecture of the subsystem used is sufficiently flexible and makes it possible to provide the registration and logging of decisions for users of the testing system, provides the freedom of the student in the construction of possible solutions; comparative analysis of the solution with the decisions of the agent-experts makes it possible to evaluate the rationality of the solutions; construction of student competency map as overlay model makes it possible to assess the level of the formed subject competencies in accordance with the level of complexity of tasks; it allows organizing adaptive testing that takes into account the individual characteristics of students; the system is open for further development through the introduction of multi-agent and neural network solutions.

Keywords: intelligent testing system, architecture of intelligent system, use case diagrams, user roles, lattice of complication of tasks, agent-oriented environment, levels of formed competencies, classification of students, gaming learning environment, card of formed competencies

Abstract: The researcdh object in this study involves the  multi-level satellite infocommunication networks. The dynamic influence of various factors upon the characteristics of communication lines in different elements of the network causes changes in the distribution of traffic within the studied network, which in turn can lead to a decline in service quality markers, one of which is the average delay in the delivery of information. The article presents the results of the development of the traffic optimization model in the satellite hierarchical communication network based upon the criterion of minimum mean delay time for the purpose of improving the quality of information flows in the studied network. The key method used to develop the optimization model is the node method  for the  tensor analysis of networks, which fits the requirements of accounting for the interaction of the network topology and the processes of servicing information flows, and the used set of initial data. The scientific novelty involves the use of the nodal tensor analysis method in order to optimize the traffic distribution in the hierarchical infocommunication satellite network using the criterion of minimum mean delay time by using an objective function that takes into account the average delay time in each system of the information transmission route and the constraints determined by the tensor equation of behavior of the initial network .

Keywords: satellite networks, average delay, tensor analysis of networks, node method, quality of service, hierarchical networks, network topology, inter-satellite link, system load, Lagrange multipliers method

Abstract: This article concerns the issue of improving performance when processing large amounts of information in data warehouses (storages). The main purpose is to increase the speed of the process of wiping out information in the cache of data warehouses, and, consequently to improve the processing speed of the cached data. The subject of research involves the algorithms of data extortion LRU1 and LRU2, as well as and structural organization of the control table. The article proposes the implementation of algorithms for wiping out information in the data warehouse cache on the basis of an associative data array. The results of a comparative analysis of the basic algorithms of information displacement used in the operational memory of computer systems (LRU, LFU, FIFO, Random) are presented in this article. The results of the development of algorithms for accelerated information extrusion in the cache of data warehouses are also presented. The author construes the systems of canonical equations for these algorithms are. The  mathematical model, which is used by the author,  is an executable formalized specification allowing for a direct transition from the DCS (the system of canonical equations) to the further hardware or software implementation of the proposed algorithms.

Keywords: systems of canonical equations, storages, caching, data wiping algorithms, LRU algorithm, MRU algorithm, ARC algorithm, data processing, automatic models, data storage

Abstract: In their article the authors provide their results on systematization of methods for computational optimization of the transformation of color spaces based upon the application of fixed-point arithmetic. The authors formulate the goals and analyze the key problems arising in the situation of computational optimization in the process of color space formation from the standpoint of the speed of operation increase. The principles of transition from a floating point format to a format with a fixed point are stated. The authors also provide an example for the analysis of computational optimization  for the mutual transformation of RGB and Y709CbCr. In this article the authros consider the method of computational optimization of the transformation of color spaces based on the application of fixed-point arithmetic. When applying the considered principle of practical implementation, the computation time for an image of 4134x2756 on an Intel Core 2 Duo processor becomes 18 times less. This is a very significant increase in productivity. It is not too difficult to apply this approach to other similar calculations, especially on modern 64-bit and 128-bit processors, when the necessary values fit into a single processor register.

Keywords: RGB, format with a floating point, the format with fixed point, computing optimization, mathematical coprocessor, serial processing of images, parallel processing of images, transformation, color space, image processing