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Simonas Vainbergas, a teacher of Jewish primary schools in prewar Lithuania (1894?), was one of few his colleagues that actively collaborated with Lithuanian pedagogical journals. He published in them 11 papers in didactics of mathematics about teaching mathematics at primary schools. The said papers helped young teachers of primary schools to improve their qualification. There is a great probability that S. Vainbergas was a victim of holocaust.

One of the ways to improve the accuracy of probability density estimation is multi-mode density treating as the mixture of single-mode one. In this paper we offer to use data clustering in the first place and to estimate density in every cluster separately. To objectively compare the performance, Monte Carlo approximation is used. While using various methods to evaluate the accuracy of probability density estimations we tried to use clustered and not clustered data. In this paper we also tried to reveal the usefulness of using clustering for data generated by single-mode and multi-mode distributions.

BDI logic is widely used to describe agent based systems, since it can express a lot of different real world domains with three main operators: belief, desire and intention. There are lots of works where BDI logic is used as descriptive language, but authors do not talk about implementation issues [5,2,4,8,1]. There is even known general agent implementation scheme, which do not describe howto use formal logic for such scheme implementation [12]. The main aim of this paper is to show the bridge, which connects formal and practical parts of logic. We describe how sequent calculus can be used for implementing some parts of general scheme. In this paper, we show how flexible constraints can be implemented. Sequent calculus usage is illustrated with simple examples.

The paper describes shortly the main principles of representative examples development, provides the essence of the methodology to develop representative examples and an example of its application. The main contribution of the paper is the methodology to develop representative examples that could be used to evaluate the sufficiency of specification language for specification of software system requirements.

In this paper we present separate cases of Sturm–Liouville problem with nonlocal two-point boundary condition. The existence of positive eigenvalues and eigenfunctions is analysed. Obtained results we compare with results that are described in paper [1] and denote that in some cases they don’t coincide.

In this paper authors research the problem of traceability of assumptions in logical derivation. The essence of this task is to trace which assumptions from the available knowledge base of assumptions are necessary to derive a certain conclusion. The paper presents a new derivation procedure for propositional logic, which ensures traceability feature. For the derivable conclusion formula derivation procedure also returns the smallest set of assumptions those are enough to get derivation of the conclusion formula. Verification of the procedure were performed using authors implementation.

The article presents several observations about the examination papers of the state-level Maturity Examinations in Mathematics in the years 2014–2021 in Lithuania. Some inaccuracies were observed in the appendix of the paper titled ``Mathematical formulas'', in the wordings of the problems. Also the issue of proof problems in the examination is discussed. The purpose of these observations is to draw attention to areas for improvement in the examination system. The article presents the subjective opinion of the authors.

The technology for automatization of lecturer’sworkplace is presented in the paper, enhancing and simplifying the preparation of assignments for practical works and their inspection. The main focus of paper is placed on the inspection of students’works. The informational system created and exploited at the department of EngineeringMechanics, Vilnius Gediminas TechnicalUniversity, is described. Similar principles may be employed also for analogical systems of generating of assigments for practical works as well as inspection of them for other subjects (mathematics, informatics, etc).

The essential feature of Internet GIS is the interactivity between the users and the spatial data. Interactive GIS can offer interactive maps rather than static map images on the Web. Users can work with the maps interactively by performing conventionalGIS functions such as zoom, pan, search, etc. However, the interactivity of many InternetGIS is quite limited so far. In this paper, we propose to use AJAX to improve the interactivity of Internet GIS. AJAX design patterns that can be used to this aim are described in the paper. We present the architecture of the Internet GIS with AJAX-based user interface and integration with GIS web services.

In this paper, authors emphasise on the correctness of the transformation. Therefore, types of correctness are analysed here. As a context of transformation, the transformation of PAL constraints in SQL rules is chosen for more details. Formal rules for the transformation of PAL constraints in SQL rules are presented in this paper also. And finally, the analysis of the proposed transformation is checked.

Multiple Criteria Decision Making (MCDM) methods are effectively used in decision making tasks. The weights of criteria are an integral part of MCDM methods. The paper proposes the Bayesian approach to recalculate the weights of the criteria, when the decision-maker takes into account the opinions of other expert groups. Recalculation is relevant when the selection is individualized by the opinion of separate expert group. In this paper the distance learning course was chosen by separate group of experts, using SAW and TOPSIS methods and recounted criteria weights by Bayesian method.

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Copyright of Pedagogy Studies / Pedagogika is the property of Vytautas Magnus University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this research paper, a comprehensive analysis of particulate matter (PM10) and nitrogen dioxide (NO2) pollution concentrations in six different Lithuanian regions is presented. The analysis employs data smoothing, principal component analysis (PCA), exploratory data analysis, hypothesis testing, and time series analysis to provide a thorough examination. Functional data analysis approaches were used to find the origins and effects of these air pollutants by revealing their data patterns. The functional data analysis techniques demonstrate their effectiveness in revealing deep links within large datasets, assisting in the control of air quality problems. This research provides valuable insights into air quality challenges in Lithuanian regions. The study, aimed at comparing air quality across different regions, indicates that there are no significant differences in PM10 and NO2 between the two groups. Notably, reliable forecasts for 2023 data are attainable for PM10 in regions such as Vilnius Old Town, Vilnius Lazdynai, Šiauliai, and Klaipėda. For NO2, successful forecasting can be applied to Vilnius Old Town, Vilnius Lazdynai, and Šiauliai.

Usually, proofs of mathematical statements involve both algebraic rearrangements and logical reasoning. But there are mathematical statements whose truth is obvious at first glance when there is a diagram illustrating that proof. Although the proofs based on the drawing are not necessarily full and complete, but the drawing helps to notice facts that are then easily supported by algebra and logic. The paper presents proofs of mathematical propositions where, upon careful study of the drawing, the main idea of the proof can be seen from the drawing, and the proof itself becomes beautiful and clear.

In this paper we consider a modification of the attack on the classic RSA cryptosystem aimed at factoring the public modulus n, which is a product of three primes. To improve the performance of the modified attack we introduce additional parameters. We present the theoretical upper bound on the search range parameter and define a shifting parameter based on the empirical results. Since these changes make our attack probabilistic, we investigate the dependence of the success on the values of the newly defined parameters.

In this paper the error estimation for n-th order Filon quadrature formula is discussed.

Poisson approximation for the sum of independent random variables is investigates in this paper.

In this paper the local limit theorem for density of k-th maxima of independent identically distributed random variables is proved.

The paper reviews the visualisation problems of genetic sequences and of their analysis results as well as other related problems. A possible formulation of the problem based on similarity, complexity measure (distance) between DNA sequences is proposed. It is solved by making use of multidimensional scaling (MDS) of principal component analysis (PCA) methods.