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This paper deals with problem of automatic keywords assignment for scientific publications. In recent papers proposed identification clouds based classification algorithms are analysed and compared to popular alternavite methods. The efficiency of algorithms is estimated through real data based experiments. Conclusions about practical aspects and applicability of proposed algorithms are drawn.

The paper deals with the design of localization courses for high education. In Lithuania, the localization of software is very important. Localization process is growing. We need a lot of high qualification translators. However, teaching of software localization is not a part of translators’ studies. All localizers are still volunteers. Curricula of localization are discussed in the paper.

This paper is devoted to the development and specification problems of software component ontology. The formalisation of the proposed component ontology is presented, too. The choice of ontology interpretation is motivated. The paper discusses the content of the ontology specification and its development. The mereological theory of software component, one of the constituent parts of a formal component specification, is presented.

This paper will focus on analysis of changing of educational policy of mathematics education at school. The way of changing (from reproductive approach to interpretative one) and the theoretical foundations (constructivist approach: ontological, epistemological, methodological principles; pedagogical and psy­chological provisions) are presented in the paper.

This paper analyses is it meaningful to use ``Geometer's Sketchpad'' to teach and to learn mathematics at general school of Lithuania. First, it looks how this program helps to implement the goals of National Curricula and Standards. After that, the paper analyses to which group of classification of ICT programs ``Geometer's Sketchpad'' can be attached. In addition, it views CD ``Mathematics 9 with geometer's sketch­pad'' which is prepared for teaching and learning math grade 9th.

The paper analyses possibilities to adapt and introduce open source Virtual Learning Environment (VLE) in general schools of Lithuania. First, it looks at general functions of VLE and defines its generic model. After that, the paper analyses four specific aspects of general education in Lithuania: National Curricula and Standards, age range of learners, compulsory attendance of a school, and the level of ICT development in schools. On that basis, it decides, which VLE's functional requirements are the most essential. Later, the paper investigates and compares the main features of eight worldwide popular open source VLEs. It looks, how the VLEs mach the needs of Lithuanian schools. It concludes that Moodle and Caroline software fit the best.

The paper describes quality evaluation procedure and gives example of its application. The purpose of the paper is to propose a way to determine specification language appropriateness for concrete project.

The paper deals with the methods of algorithmical problems solving used in the Lithuanian Student Olympiads of Informatics, Young Programmers School, and comprehensive schools. Difficulties rising in the employment of the evaluation methods are discussed as well. The paper analyzes testing, which is the main method of algorithm evaluation, and the principles of the control tests drafting. The special attention is concentrated on the algorithm culture and the describing of the problems' ideas.

The paper outlines IS development methodology based on reuse ideas developed in knowledge engi­neering and ontology-based system engineering fields. This methodology enables business process reuse. Paper focuses on location of business process in business domain and assignment of business process roles to business domain entities.

In this paper a simulated annealing algorithm for continuous global optimization is considered. There are a lot of theoretical research and very few computer modeling of efficiency of this algori­thm. Modeling results, recommendations for efficiency and accuracy of the SA algorithm are given in the paper.

The paper discusses comparative analysis methods in informatics. It examines nature of each class of methods and presents examples of its application. The purpose of the paper is to propose a classification of comparative analysis methods.

The paper extends the investigations of limit theorems for numbers satisfying a class of triangular arrays. We obtain analytical expressions for the semiexponential generating function the numbers, associated with Hermite polynomials. We apply the results to prove the asymptotic normality of the numbers and specify the convergence rate to the limiting distribution.

This paper deals with the main problem of involving information technologies in education – contents of teachers' training courses. Three directions are presented: preparation of teachers (1), in-service teacher training (2), re-qualification of the speciality (3). The main attention should be paid to the constant in-service teachers' training. The Standard of computer literacy for educators has been developed. It should be the main sources of all teachers' training courses on informa­tion technology. The Standard consists of two parts: technological one and educational one. The technological part is based on ECDL Start modules. The educational part is uniqu: it requires some psychological, social, and pedagogical knowledge referring to information technology usage in education. The main attention of the paper is paid to the analysis and requirements of the educa­tional part of the Standard of computer literacy for educators.

This paper discusses the computer literacy standard of students with respect to the European Computer Driving License (ECDL) and general informatics curricula of comprehensive schools. Some aspects of relations to ECDL Start modules are analyzed. The main attention is paid to discuss the virtue attitude of using the information and communication technology as well as to general capabilities related to computer literacy. The main propositions are presented and motivated. The paper also deals with the main fields of computer literacy topics: Basic principles and concepts of applying computers (1), Basics of information processing (2), Text handling and information presentation (3), Web and electronic mail (4), Introducing spreadsheet and data base (5), Social, juridical and ethical aspects (6).

The main aim of this paper is to identify current major trends in geometry and to discuss perspectives concerning its teaching in schools, for today and for tomorrow. Geometry involves three kinds of cognitive processes which fulfill specific epistemological functions: (1) visualization processes with regard to space representation for the illustration of a statement, for the heuristic exploration of a complex situation, etc.; (2) construction processes by tools: construction of figu­rations can work like a model; (3) reasoning in relationship to discursive processes for extension of knowledge, for proof, for explanation. The paper deals with relationship between geometry and computer technology. Among all school subjects, geometry stands as one which is bound to be influenced most profoundly by the recent progress both in hardware and software development. The purpose is to examine some influence of computer technology in the teaching and learning of geometry.

In this paper, we present models for the analysis of the behavior of the virtual library (VL) users. Unlike the models presented in the literature, they use only the big data that is stored in the log files of virtual library servers and methods of statistics, association rules, and recommendation systems. The proposed models were implemented with R software. Using the proposed models, the analysis of the behavior of VL users of Lithuanian research and study of higher education institutions was performed for the first time. The results showed that the proposed models allow to operatively analyze the behavior of virtual library users using advanced search filters, facets, and provide suggestions for improvement of service quality.

In this paper non-uniform estimate of convergence rate in the min-scheme is obtained. Presented results make the estimates, given in [1] and [2], more precise.

The paper continues the research of the modified Borwein method for the evaluation of the Riemann zeta-function. It provides a different perspective on the derivation of the local limit theorem for coefficients of the method. The approach is based on the ratio method, proposed by Proschan.

In this paper we perform a statistical analysis of the returns of OMX Baltic Benchmark index. We construct symmetric α-stable, non-standardized Student’s t and normal-inverse Gaussian models of daily logarithmic returns of the index, using maximum likelihood method for the estimation of the parameters of the models. The adequacy of the modeling is evaluated with the Kolmogorov-Smirnov tests for composite hypothesis. The results of the study indicate that the normal-inverse Gaussian model outperforms alternative heavy-tailed models for long periods of time, while the non-standardized Student’s t model provides the best overall fit for the data for shorter intervals. According to the likelihood-ratio test, the four-parameter models of the log-returns of OMX Baltic Benchmark index could be reduced to the three-parameter (symmetric) models without much loss.

In this paper, we investigate the best fit solution for the second order differential problem with one initial and other integral conditions. We obtain the representation of that minimizer and present an example.paration.

Various types of calculi (Hilbert, Gentzen sequent, resolution calculi, tableaux) for propositional linear temporal logic (PLTL) have been considered in the literature. Cutfree Gentzen-type sequent calculi are convenient tools for backward proof-search search of formulas and sequents. In this paper we present a cut-free Gentzen type sequent calculus for PLTL with the operator

The present paper deals with a generalization of the alternating-direction implicit (ADI) method for a two dimensional Poisson equation in a rectangle domain with a weighted integral boundary condition in one coordinate direction. We consider the alternating direction method for a system of difference equations that approximates Poisson equation with weighed integral boundary conditions with the fourth-order accuracy. Sufficient conditions of stability for ADI method are investigated numerically. An analysis of results of computational experiments is presented.

In this paper we research Green’s function properties for stationary problem with four-point nonlocal boundary conditions. Dependence of these functions on values ξ and γ is investigated. Green’s functions graphs with various values ξ and γ are presented.

In the paper an attempt to represent some not too easy and in the same time not difficult, accessible, useful and challenging problems used in Lithuanian math events, as well as in training high-scool and University students, is undertaken.

The objective of this paper is to find suitable non-commuting algebraic structure to be used as a platform structure in the so-called matrix power function (MPF). We think it is non-trivial and interesting problem could be useful for candidate one-way function (OWF) construction with application in cryptography. Since the cornerstone of OWF construction using non-commuting algebraic structures is the satisfiability of certain associativity conditions, we consider one of the possible choices, i.e. the group M16, explore its basic properties and construct templates to use in our future work.

Knowledge of agents associated to particles of quantum system has been modelled in the paper. Also analysis of formulas and satisfiability in the model have been done.

In this paper, we investigate the minimizer of the residual for the second order differential problem with one initial and other nonlocal Bitsadze–Samarskii condition. We obtain the representation of the minimizer and present an example.

In this paper two mathematical models of the dimer–dimer reaction on supported catalysts are compared. The PDE model describe the bulk diffusion of both reactants and product, adsorption and desorption, the surface diffusion of adsorbates and intermediate. The ODE model is derived from the first, assuming that all materials are well-mixed. The catalytic reactivity, calculated using the PDE and ODE models, is compared for two variants of reactants adsorption and variuos bulk and surface diffusion.

In this paper, an algorithm is proposed which uses facial landmarks to calculate normalized Euclidean distances between different facial parts and performs faces recognition by using Multilayer Perceptron. In order to determine the most effective model, different neural network parameters have been changed in an experimental way, such as hidden layers and the number of neurons, gradient descent optimization algorithms, error and activation functions, and different sets of distances.

The paper aims to analyse application trends of intelligent multi-agent systems to personalise learning. First of all, systematic literature review was performed. Based on the systematic review analysis, the main trends on applying multi-agent systems to personalise learning were identified. Second, main requirements and components for an educational multi-agent system were formulated. Third, based on these components a model of intelligent personalized system is proposed. The system employs five intelligent agents: (1) learning styles identification software agent, (2) learner profile creation software agent, (3) pedagogical suitability software agent, (4) optimal learning units/scenarios creation software agent, and (5) learning analytics/educational data mining software agent.

The paper aims to suggest a method of using artificial neural for learning personalisation. Learning personalisation consists form learning style identification then linking it to learning activities and objects which correspond to learning style. But the problem is that learning style identified by questionnaire cannot guarantee adequacy and objectivity. In order to overcome this issue we can use artificial neural network which could analyse learner in learning activities and interaction with learning objects and correct learning style and scenarios characteristics according to collected information.

In the paper, a survey on the life and activity of the former and longtime chief of the Lithuanian museum of mathematicians Doc. Henrikas Jasiūnas (1925–2015) is given. The main directions of the museum work in variuos periods are shortly discussed, the public importance of this cultural institution is disclosed.

In the paper, we prove a limit theorem of discrete type on the weak convergence of probability measures on the complex plane for the periodic Hurwitz zeta-function.

The efficiency is a measure of a performance of a decision making units (DMUs can be a firm, a person, an organization). The data envelopment analysis (DEA) is a datadriven non-parametric approach for measuring the efficiency of a set of DMUs. The DEA is a linear programming (LP) based technique which deals with the basic models (CCR, BCC, SBM, additive) of the efficiency evaluation. This paper presents basic solution ellipsoid method approach associated with some problems of initial basic solution and the steps of it.

In the most multiple attribute decision making methods the attribute values are provided to transform into one dimension. The normalization of attribute values is not always needed, but it may be essential. This restructuring is carried out in accordance with appropriate normalization rules. It has been observed that some of multiple attribute methods are used for different normalization rules. In practical calculations it noted that using different normalization rules in the same multiple attribute method produces different alternatives priority line, with the same data. Due to the fact of this paper is to carry out normalization methods affect the ranking of alternatives, study. And find out under what conditions the normalization rules change the ranking of alternatives.

In this paper, we obtain the representation of the nullspace for m-th order discrete linear problems with nonlocal conditions. An example is given. The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014).

In the paper it is illustrated by some examples the difference between a mathematical problem, computer problem and puzzle. It is given detailed solution of the mathematical problem considered.

In this paper we consider Pailler encryption and RSA textbook signature. We show that due to valuable homomorphic property these algorithms can be used together to obtain a valid signature on a certain combination of ciphertexts. Our goal is to show that this combination of algorithms provide security against chosen plaintext and chosen ciphertext attacks.

The paper aims to analyse Educational Data Mining/Learning Analytics application trends to personalise learning. First of all, systematic literature review was performed. Based on the systematic review analysis, the main trends on applying educational data mining methods to personalise learning were identified. Second, three main tendencies on educational data mining/learning analytics application in education were formulated. They are: (a) Educational Data Mining/Learning Analytics support self-directed autonomous learning; (b) Educational Data Mining/Learning Analytics systems become essential tools of educational management; and (c) most teaching is delegated to computers, and Educational Data Mining/Learning Analytics based recommendations become better and more reliable than those that can be produced by even the best-trained teachers.

In this paper, effective utilization of processors in computer cluster is investigated. Generally, a computer cluster is treated as a specially designed system only for solving specific computationally intensive and time consuming problems. Commonly, computers in offices and universities are idle for a considerable proportion of the time. Therefore, in this research, we focus on exploitation of such computational resources. The experimental investigation shows that when executing multiple processes in each CPU core allows to solve computationally intensive problems more precisely compared to the case, where the number of processes is equal to the number of CPU cores, meanwhile the same amount of energy is consumed in both cases.

Let Z(t) = Σ j=1N(t) Xj, t ≥ 0, be a stochastic process, where Xj are independent identically distributed random variables, and N(t) is non-negative integer-valued process with independent increments. Throughout, we assume that N(t) and Xj are independent. The paper considers normal approximation to the distribution of properly centered and normed random variable Zδ =∫0∞e- δt dZ(t), δ > 0, taking into consideration large deviations both in the Cramér zone and the power Linnik zones. Also, we obtain a nonuniform estimate in the Berry–Essen inequality.

In this paper two mathematical methods, McEvoy and Mezzavilla–Ghirotto, were investigated, they are devoted to determine the effective population size. Comparative analysis of two methods, for estimating effective population size, was performed.

In this paper a nonlinear mathematical model of the kinetics of two-molecular heterogeneous catalytic reaction proceeding on a supported catalyst is investigated numerically. The model is based on the Langmuir–Hinshelwood type kinetics of the surface reactions assuming that all species are well-mixed. The effect of the catalytic surface size, adsorbtion rate constants and jump rate via the catalyst-support interface constants on the catalytic reactivity and product concentration is studied for different arrangements of the adsorption sites.