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In this paper hyperbolic system of the first order gas dynamics PDE with initial and boundary conditions is studied. The aim of the paper is to construct the averaged system of differential equations in order to find the uniformly valid in a large domain asymptotical solution. The averaged system is a new object of asymptotical analysis.

This paper discusses the concept of three-dimensional (3D) fractal interpolation and the possibility to use it in modeling 3D surfaces. It is important to notice that this paper treats fractal interpolation only as a numerical tool and not as a model. The purpose of the research is to create a methodology for obtaining models for the given 3D surface and making them similar to it to a certain degree. The set of models then can be investigated as required (3D graphical representation, simulation of particular technological process, quality assessment for bonded surfaces, etc.). Measuring a particular 3D surface and making a set of models is far more cost efficient than performing the measurements many times.

In this paper supervised classification method is proposed. It is based on Bayes discriminant functions (BDF) and it deals with the problem of optimal classification for images, which are corrupted by natural phenomenon such as cloud, smoke or fog. Solving such a problem is very important when we have remotely sensed information, which very often is corrupted by clouds. For example, the remotely sensed images from the territory of Lithuania are very often corrupted by clouds. The idea of classification, using BDF with incorporated spatial dependency between the observation to be classified and the training sample is presented in earlier works of the author. The novelty of this paper is the method how to use these methods for the real situation, i.e. for the remotely sensed image which is naturally covered by clouds. Visual and numerical results are presented in this paper, which show the advantage of this method against BDF ignoring spatial dependency between training sample and observation to be classified and against the method using grey level cooccurrence matrices.

In this paper the stationary Navier–Stokes system with non-homogeneous boundary condition is studied in domain which consists of two connected layers. The extension of the boundary value, which reduces the non-homogeneous boundary problem to the homogeneous one, is constructed in this paper.

The paper deals with the evaluation of the criteria impacting distance learning course content quality. The goal of the paper is to introduce the improved AHP method with Fuzzy triangle numbers used to determine the quality of distance learning courses. In the paper, the interval and discrete methods for weights determination are compared.

In this paper, relations between discrete Sturm--Liouville problem with nonlocal integral boundary condition characteristics (poles, critical points, spectrum curves) and graphs characteristics (vertices, edges and faces) were found. The previous article was devoted to the Sturm--Liouville problem in the case two-points nonlocal boundary conditions.

In this paper the multidimensional scaling, the principal coordinate and principal component methods for the Lithuanian population structure have investigated, taken that the proximity measures are Euclid, Gower, Bray-Curtis, Kulczynski, Jaccard and Morisita. The genome-wide single nucleotide polymorphism genetic data analyzed. A comparative analysis of proximity measures performed. The results of visualization are also presented.

In recent years, a lot of research has focused on understanding the behavior of when synchronous and asynchronous phases occur, that is, the existence of chimera states in various networks. Chimera states have wide-range applications in many disciplines including biology, chemistry, physics, or engineering. The object of research in this paper is a coupled map lattice of matrices when each node is described by an iterative map of matrices of order two. A regular topology network of iterative maps of matrices was formed by replacing the scalar iterative map with the iterative map of matrices in each node. The coupled map of matrices is special in a way where we can observe the effect of divergence. This effect can be observed when the matrix of initial conditions is a nilpotent matrix. Also, the evolution of the derived network is investigated. It is found that the network of the supplementary variable $\mu$ can evolve into three different modes: the quiet state, the state of divergence, and the formation of divergence chimeras. The space of parameters of node coupling including coupling strength $\varepsilon$ and coupling range $r$ is also analyzed in this study. Image entropy is applied in order to identify chimera state parameter zones.

This paper presents an investigation of modeling and solving of differential equations in the study of mechanical systems with holonomic constraints. The 2D and 3D mathematical models of constrained motion are made. The structure of the models consists of nonlinear first or second order differential equations. Cases of free movement and movement with resistance are investigated. Solutions of the Cauchy problem of obtained differential equations were obtained by Runge–Kutta method.

In this paper, spatial data specified by auto-beta models is analysed by considering a supervised classification problem of classifying feature observation into one of two populations. Two classification rules based on conditional Bayes discriminant function (BDF) and linear discriminant function (LDF) are proposed. These classification rules are critically compared by the values of the actual error rates through the simulation study.

Floyd's triangle is often presented to computer science students as an exercise or example to illustrate the concepts of text formatting and loop constructs. The paper proposes to look at an object from a different angle and to examine limit theorems for the numbers of generalized Floyd's triangles. Tasks of this type can be used as exercises in study programs of mathematics and informatics (couses of probability theory and combinatorics). It would help to master the appropriate proof techniques and mathematical apparatus. The article proposes a series of possible problems and their proof schemes.

The paper considers several issues of Russian Verse Theory connected with the architectonics of Lermontov’s Borodino strophe. This rare and unique strophe is characterized by an odd number of lines (seven), peculiar rhyme, and mainly by the different number of syllables in its lines: five lines of the strophe contain nine syllables of iambic tetrameter, while the third and the seventh contain six syllables of iambic trimeter. Such a structure does not allow the use of traditional (statistical) methods of the study of verse rhythmics. To prove that, this paper describes the construction of “stress profiles” for the quatrain in iambic tetrameter, and shows that it is impossible to carry out this procedure for Lermontov’s Borodino strophe. Unlike the traditional approach, our method of rhythmic-harmonic precision imposes no restrictions on the architectonics of verse, which is why it is this method that underlies the analysis of the structural harmony of the Borodino strophe given in this paper. Our analysis compares the rhythmic-harmonic potential of the strophe and the actual values of the rhythmic harmony parameter with iambic and trochaic quatrains and with Onegin’s strophe in Pushkin’s verse. Another task of our work was a rhythmic-conceptual study of the “Borodino” text. This poem was published in 1837; together with the poem “On the Poet’s Death,” it immediately moved Lermontov to the forefront of Russian poets. The main result of our work consists in proving that in its structural-harmonic aspect, the Borodino strophe is unique and, moreover, it turns out to be the perfect verse construction for the expression of a mixed sublime-descending poetic mood: inspiration (in our case, a patriotic rise) and the following disappointment. Our study shows that Lermontov’s great poem “Borodino” not only passes “the trial of harmony with algebra,” but also, from the point of view of its single a rhythm-sense, stands near the best works of the first Russian poet, Pushkin.

In this paper, we consider a compound random variable Z = \sum^N_{j=1} vjXj , where 0 < v < 1, Z = 0, if N = 0. It is assumed that independent identically distributed random variables X1,X2, . . . with mean EX = μ and variance DX =σ2 > 0 are independent of a non-negative integer-valued random variable N. It should be noted that, in this scheme of summation, we must consider two cases: μ\neq 0 and μ = 0. The paper is designated to the research of the upper estimates of normal approximation to the sum ˜ Z = (Z −EZ)(DZ)−1/2, theorems on large deviations in the Cramer and power Linnik zones and exponential inequalities for P( ˜ Z > x).

The paper is aimed to analyse the problems of evaluation of quality of learning scenarios. Multiple criteria analysis principles are applied to form learning scenarios quality model. Several alternatives of learning scenarios that are widely used in Europe are analysed in the paper. These alternatives are evaluated with the help of the created quality model and application of triangular and trapezoidal fuzzy numbers methods. Research results show that both these methods are applicable in practice while evaluating quality of learning scenarios alternatives, and their application shows in principle similar results while comparing different alternatives of learning scenarios.

On overview of pedagogical and methodical activities of Vytautas Magnus University mathematicians in 1940–1943 is given in this paper. Bibliographic data of Vytautas Magnus University mathematicians are supplemented by new facts. An analysis of the first and the third parts of J. Valukonis book “Lectures in High Mathematics” published in 1943 is presented in the paper. The second part of this book has not been found yet in Lithuania.

Secondary school in Lithuania goes over to modules in the mathematics syllabi. Teachers need various proof methods for solving problems of more complicated (olympiad) modules. The paper discusses the module of functional equations. The books and papers dealing with this question are pointed out. Some typical solving errors are discussed.

Paper deals with the nonlinear coupled equations of the well known in the literature Hirota–Satsuma type system. The asymptotic analysis of this system, which is based on the principle of two scales and on averaging of weakly nonlinear hyperbolic systems along characteristics is presented in the paper. The asymptotic analysis shown that the system disintegrates on three independent Korteweg–de Vries equations in the non-resonance case, and the system describes an interaction of periodical nonlinear waves in the resonance case.

The paper is aimed to analyse the learning objects quality evaluation model taking into account learning objects reusability principles. Multiple criteria analysis methods and quality evaluation criteria identification principles are used to create the learning objects quality evaluation model. The portrait of the sets of the learning objects reusability principles and the learning objects quality evaluation criteria is presented in the paper. This portrait shows the bilateral cohesion of these principles and criteria. The presented learning objects quality evaluation model is usable in education institutions while selecting learning objects in the market or free-of-charge repositories.

Several distance learning courses adaptation aspects are analyzed in the paper. Adaptation characteristics of virtual learning environments and distance learning courses are considered very significant quality factors in scientific literature. These factors warrant the better adaptability of distance learning courses to the different learners’ needs, and therefore, the better learning quality. While creating distance learning courses according to “Computer training systems” teaching program for VGTU IV course students, there was an additional course adaptation requirement for the students. The aim of this paper is to analyze the students’ works from courses’ adaptation point of view. The paper is also aimed to analyze which course sequencing rules are the mostly clear and often used by the students.

This paper is a position paper, so it presents not well-established scientific truths but remarks and notices on the phenomena and their generalisations. The paper asserts that current portal design practices are not sound, advocates for an explicit specification of the assumptions about the predicted users’ behaviour, and requires that a specification language to formulate such the assumptions should be based on the formalism of temporal logic of actions.

In the paper a method to check termination of history-free proof for linear modal logic S4.3 is proposed. This method improves the method proposed by the authors for modal logic S4. Analogously as for S4, instead of history we use marks and indices that allow us to eliminate loop checking. The method proposed in this paper specifies some kind of formulas which allow us to check termination of derivations in more effective way in comparison with S4.

The goal of the paper is to use the MUSIC method to estimate the fundamental frequency of signals, and compare the results with the ones obtained by the DFT method. Real speech signals are considered in the paper. Lithuanian vowel sound fundamental frequency is estimated by the MUSIC and DFT methods.

This paper is about ergonomic education process’ organization. Authors analyze main educational principles of ergonomic education process on the basis of individual educational environment creation in the electronic environment. There are given some recommendations in this paper. These recommendations are about ergonomic education material preparation, training process making more effective.

The objective of legal document drafting system is both facilitating the work of legislative drafters and improving the quality of laws. However, currently almost all legislative bodies use general purpose wordprocessing software for the drafting of legal documents, and internet browsers for seaching documents. This is because legal drafting systems have too little facilities so far and are rather difficult for use. The paper discusses specific features of the user interface of a legal document drafting system. It is focused on the functionality of the user interface. User groups are identified as legislative drafters, legislators, experts, system administrators, and knowledge engineers. Usability requirements for these groups are described in the paper.

The paper deals with the survey made on the Strategy for Information and Communication Technology Implementation in Education for 2005–2007. Attention is paid to study the implementation of aims and objectives of the Strategy. Conclusions and some suggestions are presented at the end of the paper.

The number of GIS web services has been essentially increasing in recent years. The services encompass geospatial data providing and processing. GIS web services enable application developers to integrate GIS functionality into their web applications without having to build the functionality or host the mapping data locally. The integration of services from different providers enables creating more sophisticated services and applications. This paper analyzes peculiarities of GIS web services, and discusses ways of their integrating. In order to investigate issues of implementing distributed GIS web services, a prototype of a system was designed and implemented. The system integrates public map services and our specialized GIS Akis-WS services. This paper describes specific features and architecture of this system.

In the paper experience of software localization into Lithuanian is presented. Main attention is paid to the mathematical computer aids and programs. The paper covers such problems as process of translation and adoption to language and culture requirements,mathematical notation,testing, and quality assurance.Ways of problem solutionsare presentedand discussed.All localizationcycle of mathematics computer programs including analysis of the software to be localized, and support of the localized software is presented.

This paper deals with main teaching methods of arithmetics – addition, subtraction, multiplication, and division in different countries: USA, Israel, Germany, Austria, Japan, Egypt, and the Netherlands. Methods of teaching arithmetics basics and methodology of its application have been discussed. The paper reports on a survey conducted on methods of teaching arithmetics actions at the introductory level. It presents some examples of learning objects for teaching aritmetics basic.

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In this paper there are clarified a few principal concepts that are then being used to explain the process of solving and analysing equations and inequalities with parameter. The process of analysing inequalities is conveyed by including a method of areas which means the intervalmethod expanded to the plane.

Algorithm for a fixed charge telephone network approach transmitters placing problem is presented in this paper.

In this paper the problem of classification of an observation into one of two Gaussian populations with different means and common variance is considered in the case when equicorrelated training sample is given. Unknown means and common variance are estimated from training sample and these estimators are pluged in the Bayes discriminant function. The maximum likelihood estimators are used. The approximation of the expected error rate associated with Bayes plug-in discriminant function is derived. Numerical analysis of the accuracy of that approximation for various values of correlation is presented.

In the paper I continue investigations on the self-normalization of simple autoregressive field Xt,s = aXt−1,s + bXt,s−1 + εt,s started in [5]. And extend previous results when the variance of the innovations of the process above are not finite.

The methods for finding Nash equilibrium in bimatrix game are introduced in this paper. Linear optimization model with binary variables for coputation of all equilibrium points in nongenerate bimatrix game is proposed.

The paper addresses the problem of achieving alignment of information system requirements and business strategy and infrastructure. Themost popular strategic alignmentmodels and enterprise architecture frameworks are reviewed. The role of these models and frameworks in the process of requirements definition and the ways to utilize them to achieve the alignment are analyzed.

Programming Style is an important part of program quality and it should be taken into account while assessing programs designedby competitors in informatics. In InternationalOlympiad in Informatics grading is automated and based on testing results only, while programming style is not taken into account. However there exists practice in universities in programming courses where programming style of submitted programs is evaluated automatically. The paper reviews existing experience and discusses possibilities for automated grading of programming style in informatics olympiads.

In the paper the global optimization problem of truss systems is studied. The genetic algorithms are employed for the optimization. As the objective function the structure mass is treated; the constraints include equilibrium, local stability and other requirements. All the truss system characteristics needed for genetic algorithm are obtained via finite element solution. Topology optimization of truss system is performed using original modified genetic algorithm, while the shape optimization – using ordinary genetic algorithm. Numerical solutions are presented. The obtained solutions are compared with global extremes obtained using full search algorithm. All the numerical examples are solved using original software.

This paper presents stress calculationmethod of bending multilayer structural element when bending moment acts in the planes that do not coincident with principal planes, and cross section is symmetric or asymmetric. Carrying the computation of occurring stress values in multilayer beam layers it is necessary to identify coordinates of cross-section stiffness centre, direction of principal axes, and coordinates of specific points regarding principal axes. Having this information and equation which is valid for stress calculation of bending multilayer beams it is possible to identify normal stress values at any point of the beam cross section under skew bending. It is deduced that stress values and the nature of their changes are influenced by the shape of beam cross-section, its asymmetry degree, and the direction of appliedmoment.

The analysis of cutting stock problem and heuristic and metaheuristic algorithms for solving it are presented in this paper.

In this paper we investigate a simple AR(1) model by testing a presence of changed segment in a data. We suggest test statistics based on a behavior of partial sums of residuals.

The paper analyses graph oriented ontology transformation into conceptual data model. A number of methodswere proposed to develop conceptual datamodels, but only fewdealswith knowledge reuse. In this paperwe present an approach for knowledge represented by ontology automatic transformation into conceptual data model. The graph transformation language is presented and adapted for formal transformation of ontology into conceptualmodel. Details and examples of proposed ontology transformation into conceptual data model are presented.

In this paper the key agreement protocol is given and the applicationof it in Braid groups is suggested. The one way of protocol is being justified.

Paper deals with statistical classification of spatial data as a part of widely applicable statistical approach to pattern recognition. Error rates in supervised classification of Gaussian random field observation into one of two populations specified by different constant means and common stationary geometric anisotropic covariance are considered. Formula for the exact Bayesian error rate is derived. The influence of the ratio of anisotropy to the error rates is evaluated numerically for the case of complete parametric certainty.

The object of the paper is to investigate what number of hours was dedicated for mathematics in 1922–1943. The program of mathematics lectured to students of the Faculty of Technology since 1930 is analyzed.

This paper examines the Lithuanian consumer price inflation from 1996 January till 2006 December using a modern non-stationary time series and econometric theory. The multiple regressionmodels are proposed for inflation modeling. The stationarity of Lithuanian inflation and the main explored exogenous variables are analyzed using the augmented Dickey–Fuller test. All indicators are integrated of order one. Vector error correction (VECM) model of Lithuanian inflation processes is investigated and proposed for inflation modeling.

In this paper extreme learning machine and support vector regression are used for biosensors response to mixtures of compounds classification. The results are compared with the results obtained using artificial neural networks and others.

This paper describes several methods for modulating of the stocks volatility through use of variance, EWMA and GARCH models. Results are presented using logarithmic return of the Lithuanian OMXV index.

In this paper,we study a transformationof pure hybrid logic formulae,which do not have binding operator, into an equivalent normal form, which does not have any satisfiability operators in the scope of another satisfiability operator.

In this paper, we discuss the visualization of multidimensional data. A well-known procedure for mapping data from a high-dimensional space onto a lower-dimensional one is Sammon‘s mapping. The paper describes an unsupervised backpropagation algorithm to train a multilayer feed-forward neural network (SAMANN) to perform the Sammon‘s nonlinear projection. In our research the emphasis is put on the optimization of the learning rate to save computation time without losing the mapping quality.

This paper defines decision algorithm for subclass of BKD45DKDIKD logic which is based on known algorithm for temporal BKD45DKDIKD logic [2]. BDI logics are widely used in agent based systems. Such usage of BDI logic can be found in [1]. The original decision algorithm uses loop-check technique for BEL and temporal operators. Applied loop-check technique is not optimized and therefore loop-check takes most of the time used in decision algorithm. Some examples of efficient loop-check applications for logic KT, S4 and some subclasses of intuitionistic logic can be found in [4]. Another efficient loop-check can be found in work [3]. We concentrate on our attitude on loop-check optimization for BEL operator. This paper defines decision algorithm modification, which uses efficient loop-check for BEL operator, but do not effect performance of other parts of algorithm. We define optimization only for BEL operator and therefore we omit temporal operators in this paper.