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User segmentation is one the most important problems in online advertiting. The use of online latent Dirichlet allocation model for analysing big datasets for this purpose is proposed in this paper. The relationship between the number of segments and segmentation quality metrics is analized and criteria for assigning ads to user segments are proposed.

Multiple criteria decision-making (MCDM) methods designed for evaluation of attractiveness of available alternatives, whenever used in decision-aid systems, imply active participation of experts. They participate in all stages of evaluation: casting a set of criteria, which should describe an evaluated process or an alternative; estimating level of importance of each criterion; estimating values of some criteria and sub-criteria. Social and economic processes are prone to laws of statistics,which are described and could be forecasted using the theory of probability. Weights of criteria, which reveal levels of their importance, could rarely be estimated with the absolute level of precision. Uncertainty of evaluation is characterised by a probability distribution. Aiming to elicit evaluation from experts we have to find either a distribution or a density function. Statistical simulation method can be used for estimation of evaluation of weights and/or values of criteria by experts. Alternatively, character of related uncertainty can be estimated by an expert himself during the survey process. The aim of this paper is to describe algorithms of expert evaluation with estimation of opinion uncertainty, which were applied in practice. In particular, a new algorithm was proposed, where an expert evaluates criteria by probability distributions.

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.

Chronic non-communicable diseases are caused by a combination of multilocus genetic risk factors. The genetic risk assessment companies, e.g. Navigenics and 23andMe, calculate a lifetime risk of a disease by the use of strong assumptions on the total impact of the multiple SNPs genotype. The object of the paper is to compare such risk assessment methods. The theoretical disease model that describes both environmental and genetic factors has been used for evaluation of assessment methods. The system of nonlinear equations for tuning model’s parameters to real statistical parameters of the disease has been developed. The Receiver Operating Characteristic curve has been used to evaluate the quality of the methods as predictive tests.

It is often the case that data used for the systems reliability assessment comes from more than one information source. Whether they are power plants at different geographical locations, gas transmission pipelines operating in different environment or power transmission networks deployed within various areas. Therefore, different operating conditions, varying maintenance programs and efficiencies have its share in influencing the vulnerability and variability of reliability data. However, in practice it is usually the case that this heterogeneity is neglected leading to the underestimation of underlying uncertainty of the data. Bayesian models are capable of dealing with this kind of uncertainty as opposed to the frequentists statistical methods. Hierarchical Bayesian modelling technique provides means to quantify not only within-source, but also between-source uncertainties. Even in the case of small data samples it performs well, unlike for example the classical likelihood method which may provide degenerate estimates. In this paper authors investigate the possibility to incorporate this kind of uncertainty into the systems reliability and vulnerability assessment through the Bayesian framework in several cases: gas transmission networks and power transmission grids.

Mathematics teacher Juozas Baltūsis (1900–1994) started his pedagogical activities in the 20th years of the 20th century and retired on a pension in the 70th years of the century. Within over 40-year period of his pedagogical activities, he taught many future mathematicians and engineers; he worked individually with gifted pupils and encouraged them to participate mathematical contests. The teacher took a great interest in integration of the teaching mathematics with the real life and other school subjects. In the prewar period, he compiled 3 course-books and in the postwar period – 3 papers; in the said works, he implemented the ideas on integration in practice.

The purpose of using quantitative multiple criteria decision making (MCDM) methods is to identify the best alternative from the ones considered, or to rank the min order of preference in terms of a chosen objective of evaluation. One of major steps of framework of these methods is estimation of weights of criteria, which will be accounted in the research. The reason for using weights is difference of importance of criteria in terms of the objective of evaluation. In the paper different subjective methods of estimation of weights of criteria are discussed, objective and cumulative weights are covered as well.

Data mining systems suitable for data mining teaching have been investigated in the paper. Ussualy, such systems as SPSS Modeler (Clementine), Statistica, SAS/STAT are used in the mathematical statistics courses. However, they are not always suitable for data mining teaching. WEKA, Orange, KNIME, RapidMiner systems are more appropriate for this purpose.

Providing Klaipeda University Marine Sciences and Technology Centre instruments which are developed for seafloor digital image analysis, object recognition in the heterogeneous environment, and evaluate the results of work. The paper describes a robotic-submarine gathered image enhancement, underwater image mosaic texture and colours description, area segmentation and filtering algorithms and their software components.

In the paper, challenges and problems of information technology teacher education have been investigated. Some reasons affecting a small number of applicants for programs, which leads to the right to work as information technology teachers have been analysed.

In this paper, the projection evaluation measures such as stress function, Spearman’s rho, Konig’s topology preservation, silhouette and Renyi entropy have been analyzed. The principal component analysis (PCA) and part–linear multidimensional projection (PLMP) techniques are used to reduce the dimensionality of the initial data set. The experiments have been carried out with seven real and artificial datasets. The experimental investigation has shown that several quality evaluation measures have to be used when dimension reduction problem is solved.

In this paper we investigate the nullity of second order discrete problem with two nonlocal conditions. The classification of nullity with respect to rows and columns of discrete problem matrix is presented. The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014).

Many real applications are using uncertain data This include expert decisions based on their subjective opinions, The uncertainty can be evaluated applying fuzzy sets theory or the methods of mathematical statistics. In this paper it is proposed to use the Bayesian approach by different distribution functions defining the expert opinion and some prior information. The results are illustrated evaluating the quality of distant education courses.

It is known that traditional techniques used to ensure termination of a decision procedure in non-classical logics are based on loop-checking, in general. Nowadays, effective loop-check techniques based on histories are used instead of unrestricted loop-check. These techniques are widely and successfully applied also for non-classical logics containing induction-like axioms. These induction-like axioms create new type loops (“good loops”) along with ordinary “bad loops”. In this paper, some loop-check free saturation-like decision procedure based on some technique of marks is proposed. This saturation procedure terminates when special type marked sequents are obtained. This procedure is demonstrated for propositional linear temporal logic (PLTL) with temporal operators “next” and “always”.

The article examines the dependencies of individual sectoral stock price indices of OMX Baltic security market on sectoral indicators of Lithuania economy, using econometric methods. Regression models are constructed using quarterly time series of 2005–2013 years. VAR models obtained in the [3] paper have been extended to verify if the inclusion of sectoral economy indicators improves the ability to provide a higher level of accuracy in estimating the growth of sectoral price index. These indicators significantly improve the predictive power compared with the benchmark VAR model. The short-term forecasts of the investigated models are obtained. Econometric analysis of OMX Baltic security market proves the hypothesis that the set of sectoral regressors may vary considerably depending on the individual sector’s price indices.

Quantitative multiple criteria decision aid (MCDA) methods of evaluation gain increasing popularity among researchers. The idea of the methods is to comprise values ofcriteria characterising each object into a single non-dimensional cumulative criterion, which reflects attractiveness or position of the object in view of an objective chosen. Normalisation of weights is a compulsory procedure whenever criteria of different dimensions are present. There several methods of normalisation available. Nevertheless, each method may introduce distortions into transformed data. The paper is devoted to exploration of problems related to such distortions and reveals particular cases.

This paper presents a one-dimensional-in-space mathematical model of the amperometric biosensor with porous membrane influenced by the presence of interfering species. The model is based on diffusion equations. Various effects regarding amperometric bias, caused by the presence of interfering species, have been analyzed.

GeoGebra as cost-free, multi-platform mathematics software, dynamically connecting concepts in geometry, algebra and calculus is applied in different school’s levels, and primary school is no exception. The aim of the paper is to present a theoretical approach of application of GeoGebra in Lithuanian’s primary math education. It analyzes features of GeoGebra, its possible integration into primary school education according to Educational Plan and Programme. Also some examples how this software can be effectively incorporated into teaching and learning are presented. With a view to evaluate GeoGebra’s suitability to primary education primary school teachers were interviewed and results of that exploratory study are presented. Also the study seeks to identify the conditions to successfully support teachers in using GeoGebra and learning objects prepared by it in their teaching process including organisational and technical support required.

The demand for the nature science, mathematics and technologies teachers in Lithuania has been forecasted in this paper. This forecasting is a complex process because it is affected by many factors, such as the birth rate, staff numbers, teachers age, immigration and emigration, etc. The forecast is based on data from the Statistics Lithuanian, the register of teachers, the labour exchange. It is taking into account the current and predicted emigration, the wastage of the number of pupils, moving from a lower to a higher class, as well as the number of teachers in training.

This paper provides an overview of the definitions of real numbers. We pose the axiomatic definition of correctness question. Provided examples of sets that are consistent with some definitions of real numbers, but not in with us usual set of real numbers. Attention is drawn to the mathematical analysis of teaching beginning and claims proof of clearance.

Inspector problem represents an economic duel of inspector and law violator and is formulated as a bimatrix game. In general, bimatrix game is NP-complete problem. The inspector problem is a special case where the equilibrium can be found in polynomial time. In this paper, a generalized version of the Inspector Problem is described with the aim to represent broader family of applied problems, including the optimization of security systems. The explicit solution is provided and the Modified Strategy Elimination algorithm is introduced.

This paper is designated for normal approximation to the distribution function of the compound mixed Poisson process taking into consideration large deviations both in the Cramér and power Linnik zones.

This paper presents a one-dimensional-in-space mathematical model of the amperometric sensors influenced by the presence of interfering species. The model is based on diffusion equations. Various effects regarding amperometric bias, caused by the presence of interfering species, have been analyzed.

The aim of the paper is twofold. On the one hand, it reflects the experience gained supervising master and doctoral theses/dissertations in various Lithuania universities and highlights some common challenges and concerns. On the other hand, it acknowledges with some advanced library research methods and that facilitate writing of postgraduate literature reviews.

This paper presents some new results on the spectrum for the second order dif-ferential problem with one integral type nonlocal boundary condition (NBC). We investigate how the spectrum of this problem depends on the integral nonlocal boundary condition pa-rameters γ, ξ and the symmetric interval in the integral. Some new results are given on the complex spectra of this problem. Many results are presented as graphs of real and complex characteristic functions.

This paper presents systematic and classified achievements of eighth grade students’ in the field of algebra and functions. The authors analyze different student skills of satisfactory, basic and advanced achievement levels in particulars themes: expressions, equations, inequalities, simulation and proportionality. Author’s suggestions on how to improve the curriculum are based on the qualitative analysis of the tasks and the statistical analysis of students’ work. Data collect from 8904 country’s students test books and analyze 134 tasks. The authors would like to thank the National Examination Centre for access to the student database.

The homogeneus almost product structure on the Finsler space have Lieviu Popescu studied. In this paper we study the integrability conditions for the homogeneus product structure in Cartan space with Miron connection.

In this paper, we analyze the Sturm–Liouville problem with one classical first type boundary condition and the other Samarskii–Bitsadze type nonlocal boundary condition. We investigate how the spectrum of this problem depends on the parameters γ and ξ of the nonlocal boundary condition. Some new results are given as graphs of the characteristic function.

The aim of this paper is to highlight the features of the improvement of student’s professional competencies in the final stage of the pedagogical studies in the Lithuanian University of Educational Sciences. 84 students of the fourth year studies of mathematics and computer science specialty were interviewed using questionnaire. The research methods: statistical quantitative analysis of empirical data; qualitative analysis of students’ reports of carried out teaching practice. The results revealed: the studies of mathematics didactics and teaching practice effectively helped students develop their professional competencies; the experience gained during the teaching practice determinated student’s choosing of teaching career mostly.

In this paper we investigate the relation between the matrix nullity of the second order discrete boundary value problem and nonlocal boundary conditions. The obtained classification and examples are also presented.

This paper presents nonparametric statistical estimation of distribution density. The Monte Carlo method is used to show the effects of kernel function for multimodal kernel density estimation. Here it is shown that the novel kernel function is effective for asymmetrical heavy tails distributions.

This paper discusses the use of complete sequent calculi for reflexive common knowledge logic. Description of language and complete infinitary calculus for RCL is presented. Then finitary calculi RCLI and RCLL are introduced and completeness of finitary calculi RCLI and RCLL is proven.

In the papers some aspects of possibly challenging and remarkably nice reflections of small homeland (or any other familiar environment corresponding "small fatherland" as the place where the given person feels itself home) via literary adopted math problems together with the possible advantages of the method are discussed.

In this paper we consider the proper orthogonal decomposition (POD) method for one-dimensional Schrödinger equation. We begin of the review of basic ideas of POD. Later this method is applied to study the linear Schrödinger equation. The generation of optimal basis using POD and model reduction questions are discussed. Also the errors between the POD approximate solutions and the exact problems solutions are calculated. The results of two numerical examples for standing and travelling Gaussian wave are presented and analyzed.

A substantial amount of practical problems are solved by using multiple criteria optimisation methods, e.g. evaluation and comparison of social and economic development of counties of a country, choice of the optimal technology project, comparison of investment or innovation projects, ratings of universities, choice of the best strategy, and many similar tasks. The solution of the problem is to determine the best alternative from several available ones, or ranking of alternatives in accordance with the chosen pursued objective. Nevertheless, often a set of alternatives to choose from is not available, and a single object must be evaluated. This could be a unique technology, innovation, or investment project, enterprise. The aim of this paper is to apply principles, ideas, and philosophy of multiple criteria methods, and to propose evaluation methods for evaluation of a single object.

The paper describes a computer simulation experiment of knowledge assessment test when item’s characteristic functions are power functions and knowledge level of the population has uniform or normal distribution. The inversions of the conditional means were calculated and probability distributions of the numbers of inversions were simulated. In practice of construction of knowledge tests for checking their suitability (validity) observed values of inversions are compared with reference values obtained byMonte Carlo experiments.

We consider three sequent calculi for propositional linear temporal logic (PLTL) which allow us to formalize the properties of operator “always”. The main new results presented in the paper are: (1) introduction of the calculus with looping axioms; (2) the direct proof that the presented calculi are equivalent; (3) the proof of completeness of the calculi with looping axioms and with invariant-like rule based on completeness of the calculus with the infinitary $\omega$-type rule.

This article is intended for math and computer science subjects study deepening and understanding of multidimensional computer graphics environment. The paper describes multidimensional numeric arrays visualization using object-oriented programming tools. The method allows the multidimensional numeric arrays stored data to simulate virtual reality products which, in turn, can become the reference now intensively developed new embedded system components. Shown an another option to simulate the multidimensional visual objects that may be transformed from capturing or graphically present on the computer screen using a new computational mathematics packages for solving advanced computer graphics tasks. It seems comfortable to use new estimated mathematics programs and packages, which already are enriched with digital image processing tools, allowing create a various objects of the real world.

Based on recent researches of mine concerning history and epistemology of sciences (physics and mathematics) one side and foundations of sciences within my physics and mathematics teaching other side, in this paper I briefly discuss and report the role played by history of science within physics and mathematics teaching. Some case-study on the relationship between mathematics, physics and logics in the history and teaching process are presented, as well.

The Strategy Elimination (SE) algorithm was proposed in [2] and implemented by a sequence of Linear Programming (LP) problems. In this paper an efficient explicit solution is developed and the convergence to the Nash Equilibrium is proven. Keywords: game theory, polynomial algorithm, Nash equilibrium.

In this paper the sensitive problems of school mathematics teaching and mathematics teachers training are analysed. Are degree programs, preparing mathematics and informatics teachers, provides enough knowledge that graduates are able to be good teachers? These and other issues, related to realities, an attempt to answer in the article.

Teaching mathematics real life and vizualization in periodical between the two word wars are introduced in article This paper analyzes the interwar Lithuanian periodicals emphasis in mathematics teaching in real life. Much attention in the interwar Lithuania pedagogical periodical offered for pupils to develop independence. This article discusses what proposals teaching mathematics in real life and visualization present A. Nemickas, S. Vainberg, A. King, B. Ketarauskas, V. Augustauskas, K. Budrys et al.

This paper considers some issues of the rhythmical semantic analysis of the text of the letter written by Tatyana Larina, presented in the third chapter of A. S. Pushkin’s novel Eugene Onegin. Previous work in this area has been devoted to studying the structural and compositional peculiarities of the text, as well as to rhythmical and expressive aspects of the reader’s perception of Tatyana’s letter. The present study continues the selected method of analysis in a way related to the specific nature of this letter: the fragment of the novel is viewed as a separate text “inserted” into the whole, which can and should be read separately from the general course of the poetic narrative. The chosen approach allows us to examine the process of perception of Tatyana’s letter by the addressee, Onegin, and, at the same time, makes it possible to clarify Pushkin’s reasons for hiding the text of the letter from readers for so long, as though looking for the best time and place to present it. The study shows that the method of reading Tatyana’s letter as “separate” reveals that at the centre of the emotionally expressive perception of this text is the word “hope.” This fact helps to yield new evidence pointing to the reasons for Onegin’s ruthless and seemingly inadequate response to Larina’s letter.

In the paper, a weighted limit theorem for weakly convergent probability measures on the complex plane for the periodic Hurwitz zeta function is obtained.

The goal of this paper is to determine whether the VLE Moodle 2.2 is a sufficient for successful learning inresponse to appropriate learning activities suitable to particular learning style. The survey showed that the majorityof these tools are applied in Moodle. The problem is that it is quite difficult for the learner to identify all these tools while working in VLE, and use them in a proper way. Therefore, it is recommended to constructand install semanticsearch engine for learning toolsinto VLE. The engine will facilitate the search processby optimizing workloads, thereby improving learner’s satisfaction and improving the efficiency andeffectiveness of the learning process.

The paper is aimed to analyse learning scenario personalization according to learning styles. In order to do that swarm intelligence technique is discussed and modified ant colony optimization method is suggested. Computer simulation is carried out to verify its suitability to the problem of learning scenario personalization. The results of the computer simulation is presented and parameters custamization, long cold-start problems are discuseed.

In this paper we consider the interaction of ligands and receptors on the plane and in the space.

In this paper proper orthogonal decomposition method for 1D parabolic type equations is described. First basic ideas of method are presented and application scheme for compiutations is derived. Later the sensitivity of proper orthogonal decomposition method is analyzed depending on the diffusion coefficient and source function. The obtained numerical results are presented in figures and tables.

In this paper we use the pluged-in Bayes discriminant function (PBDF) for classification of spatial Gaussian data into one of two populations specified by different parametric mean models and common geometric anisotropic covariance function. The pluged-in Bayes discriminant function is constructed by using ML estimators of unknown mean and anisotropy ratio parameters. We focus on the asymptotic approximation of expected error rate (AER) and our aim is to investigate the effects of two different spatial sampling designs (based on increasing and fixed domain asymptotics) on AER.

Method which describes destribution af elements of the finite set to disjoint groups, allowing to obtain of elements in the sense of proposed criterion, is described in the paper. The methodology is based on some combinatorial algorithm and can be useful for social science problems solving, when statistical methods application complicated.