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Lietuvos matematikos rinkinys, Volume 61, pp 1-7; https://doi.org/10.15388/lmr.2020.22466

Abstract:
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.
Linas Aidokas, Laimutis Adolfas Telksnys
Lietuvos matematikos rinkinys, Volume 61, pp 29-37; https://doi.org/10.15388/lmr.2020.22718

Abstract:
The stochastic control system is investigated. The article solves the problem of human-robot humanoid communication. The problem arises in the development of human behavior formation management systems. They describe human behavior in terms of probabilistic characteristics. Such control systems are stochastic. The management system of human behavior formation and its functioning is described quality assessment. The problem is solved by simulation modeling. The software implementing the method is described. The results of experimental research are presented.
Edmundas Mazėtis, Grigorijus Melničenko
Lietuvos matematikos rinkinys, Volume 61, pp 21-28; https://doi.org/10.15388/lmr.2020.22717

Abstract:
The article introduces the reader to some amazing properties of trigonometric functions. It turns out that if the values of the arguments of the functions sin x, cos x, tg x and ctg x, expressed in radians, are algebraic numbers, then the values of these functions are transcendental numbers. Hence, it follows that the values of all angles of the pseudo-Heronian triangle, including the values of all angles of the Pythagoras or Heron triangle, expressed in radians, are transcendental numbers. If the arguments of functions sin x and cos x, expressed in radians, are equal to x = r 2 \pi, where r are rational numbers, then the values of the functions are algebraic numbers. It should be noted that in this case the argument x = r 2\pi is transcendental and, if expressed in degrees, becomes a rational.
Lietuvos matematikos rinkinys, Volume 61, pp 15-20; https://doi.org/10.15388/lmr.2020.22454

Abstract:
As soon as the young Lithuanian state was formed, the international situation was unfavorable (the war of independence took place) and as a result its internal life was burdened by difficulties. Therefore, the Lithuanian intelligentsia (one of their leading mathematicians Z. Žemaitis) took the initiative to organize Higher Courses (AK) in the temporary capital Kaunas. These universal courses, equivalent to the type of higher education institution (university), existed in 1920– 1922. According to the adopted statute, there were six chapters covering the basic sciences - humanities, social sciences and natural or real sciences. The existence of the latter sciences was evidenced by the Department of Mathematics and Physics, where there was an opportunity to study mathematics in Lithuanian. This article shows the circumstances of the establishment of AK, the conditions of their activity, introduces the lecturers of mathematics and shows the composition of the listeners, as well as reveals the content of mathematics studies and names the literature used for studies. During the two years of AK's existence, a solid foundation was laid for the future Lithuanian University (since 1930 – Vytautas Magnus). The staff formed consisted mainly of 1922. the core of the developing university, and the first scientific aids, books and premises were acquired - the base of the higher school. For the first time in its history, AK turned Kaunas into a university city, and the departments operating in them laid the foundations for the establishment of the university, as well as the Faculty of Mathematics.
Rimas Norvaiša
Lietuvos matematikos rinkinys, Volume 61, pp 8-14; https://doi.org/10.15388/lmr.2020.22472

Abstract:
We discuss different alternatives of the content of school mathematics. According to the prevalent public opinion in Lithuania school mathematics can be oriented either to the academic mathematics or to the applications of mathematics. In reality the second alternative means lowering of the level of teaching in the hope that school mathematics will be accessible to all students. While the content oriented to the academic school mathematics is accessible only to gifted students. In this article we describe a middle alternative content which we call school mathematics based on mathematical reasoning. We argue that such school mathematics serves all students and makes acquaintance with mathematical reasoning and with applications of mathematics to the real world. Reasoning makes mathematics reasonable for all.
Ieva Kilienė
Lietuvos matematikos rinkinys, Volume 61, pp 18-24; https://doi.org/10.15388/lmr.2020.22470

Abstract:
Word problems are classified to S problems and P problems by Verschaffel [9], classification is being specified and expanded. Reviewed word problems in Lithuanian first grade textbooks and divided to types. Submitted recommendations to use more varied types word problems, that would let to expand concepts understanding, develop mathematical reasoning, motivate to study word problem.
Jonas Vitkauskas,
Lietuvos matematikos rinkinys, Volume 61, pp 1-6; https://doi.org/10.15388/lmr.2020.22474

Abstract:
Sturm-Liouville problem with nonlocal boundary conditions arises in many scientific fields such as chemistry, physics, or biology. There could be found some references to graph theory in a discrete Sturm-Liouville problem, especially in investigation of spectrum curves. In this paper, relations between discrete Sturm-Liouville problem with nonlocal boundary conditions characteristics (poles, critical points, spectrum curves) and graphs characteristics (vertices, edges and faces) were found.
Arvydas Karbonskis, Eugenijus Manstavičius
Lietuvos matematikos rinkinys, Volume 61, pp 7-12; https://doi.org/10.15388/lmr.2020.22469

Abstract:
The variance of a linear statistics on multisets of necklaces is explored. The upper and lower bounds with optimal constants are obtained
Irma Jankauskienė, Tomas Miliūnas
Lietuvos matematikos rinkinys, Volume 61, pp 13-17; https://doi.org/10.15388/lmr.2020.22468

Abstract:
In this article we are going to analyze market price stability with different market intensity coefficient and delay argument values. Market price is described as a scalar differential equation with a delay argument. In order to find solutions for the transcendental equation we will use method based on Lambert function. We will present examples of the applications of the method.
Gytis Vievesis, Vytautas Janilionis, Antanas Štreimikis
Lietuvos matematikos rinkinys, Volume 61, pp 25-30; https://doi.org/10.15388/lmr.2020.22521

Abstract:
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.
Liudas Kaklauskas, Leonidas Sakalauslas
Lietuvos matematikos rinkinys, Volume 48, pp 314–319-314–319; https://doi.org/10.15388/lmr.2008.18116

Abstract:
The present article deals with statistical university network traffic, by applying the methods of self-similarity and chaos analysis. The object of measurement is Šiauliai University LitNet network node maintaining institutions of education of the northern Lithuania region. Time series of network traffic characteristics are formed by registering amount of information packets in a node at different regimes of network traffic and different values of discretion of registered information are present. Measurement results are processed by calculating Hurst index and estimating reliability of analysis results by applying the statistical method. Investigation of the network traffic allowed us drawing conclusions that time series bear features of self-similarity when aggregated time series bear features of slowly decreasing dependence.
Algimantas Bikelis, Audrius Galinskis
Lietuvos matematikos rinkinys, Volume 48, pp 381–385-381–385; https://doi.org/10.15388/lmr.2008.18126

Abstract:
In this work it is researched H. Bergstrom work about asymptotic behavior of convolutions of probability distributions. We give the theorem about the members of expansion in decreasing order and the remainder term estimation. There we propose apply Levy–Scheffer polynomials and to construct pseudomoments for more profound H. Bergstrom’s asymptotic expansion investigations.
Lietuvos matematikos rinkinys, Volume 48, pp 372–375-372–375; https://doi.org/10.15388/lmr.2008.18124

Abstract:
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.
Lietuvos matematikos rinkinys, Volume 50, pp 140–145-140–145; https://doi.org/10.15388/lmr.2009.25

Abstract:
Mathematics teacher Romualdas Paliokas (1929–1977) worked Mol˙ etai, Ignalina and Anykščiai districts, the city of Panev˙ ežys. He investigated the pupils’ mathematical capabilities and prepared a doctoral thesis. Two major articles were published in pedagogical periodicals. He was unable to defend the thesis, because he died.
Lietuvos matematikos rinkinys, Volume 51, pp 142–144-142–144; https://doi.org/10.15388/lmr.2010.26

Abstract:
In this article, we survey the mathematics contest, which is held for first-year students of Šiauliai College. We discuss on the organize grounding of competition and its perspective, and on the benefit of students motivated for learning. Also, we analyze an example of the tasks and the most common errors made by students.
Olga Suboč
Lietuvos matematikos rinkinys, Volume 57, pp 104–109-104–109; https://doi.org/10.15388/lmr.b.2016.19

Abstract:
In this article are introduced some techniques to present mathematical tasks in puzzle or game form to add variety during lectures and help students to uptake new theoretical knowledge and concepts. Sudoku-type puzzles are constructed using basic problems that students solve during practice lectures. Crosswords of concepts are used to summarize through lectures received theoretical knowledge.
Lietuvos matematikos rinkinys, Volume 56, pp 46–51-46–51; https://doi.org/10.15388/lmr.b.2015.09

Abstract:
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.
Lietuvos matematikos rinkinys, Volume 55, pp 7–11-7–11; https://doi.org/10.15388/lmr.b.2014.02

Abstract:
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.
Lietuvos matematikos rinkinys, Volume 55, pp 96–99-96–99; https://doi.org/10.15388/lmr.b.2014.18

Abstract:
Oosculating sphere have been studied in classical differential geometry [1]. In this article the osculating surfaces of higher order of space curves on surfaces in Euclidean space is considered. We study the intrinsic differential geometry of curves on surfaces by analyzing their contact with surfaces of higher order.
Miglė Morkevičiūtė, Violeta Kravčenkienė
Lietuvos matematikos rinkinys, Volume 60, pp 46-54; https://doi.org/10.15388/lmr.b.2019.15235

Abstract:
This article provides an overview of data from the Ministry of Education, Science and Sport of the Republic of Lithuania on students of Lithuanian higher education institutions. Data from Kaunas University of Technology studies department in 2016–2018 on student graduation, maturity exam and study module results has been analyzed. Using descriptive statistics, correlation, logistic regression analysis, and analyzing student interviews and interviews with the employees from the Faculty of Mathematics and Natural Sciences, it has been clarified how achievements in school influence the final marks of study modules and the success of studies overall.
Birutė Ragalytė, Alma Paukštienė
Lietuvos matematikos rinkinys, Volume 60, pp 63-69; https://doi.org/10.15388/lmr.b.2019.15237

Abstract:
The article compares interwar Lithuanian mathematics programs with Württemberg mathematics programs in German land. The influence of Klein’s ideas on the content of the programs is presented.
Judita Puišo, Dalia Larionovienė
Lietuvos matematikos rinkinys, Volume 60, pp 55-62; https://doi.org/10.15388/lmr.b.2019.15236

Abstract:
Professor Aurel Edmund Voss was a German mathematician, best known for his contributions to application of geometry in natural science and mechanics. The collection of books of professor A.E. Voss was bought and used by Faculty of Matematics and Nature of Univerity of Lithuania. In 1940’s the collection of books of prof. A.E. Voss was transfered to Vilnius University. The aim of the work was to investigate collections of books of libraries of Lithuania and to present books of prof. A.E Voss to scientific society of Lithuania.
Grigorijus Melničenko
Lietuvos matematikos rinkinys, Volume 60, pp 39-45; https://doi.org/10.15388/lmr.b.2019.15234

Abstract:
The factoring natural numbers into factors is a complex computational task. The complexity of solving this problem lies at the heart of RSA security, one of the most famous cryptographic methods. The classical trial division algorithm divides a given number N into all divisors, starting from 2 and to integer part of √N. Therefore, this algorithm can be called the direct trial division algorithm. We present the inverse trial division algorithm, which divides a given number N into all divisors,starting from the integer part of √N to 2.
Romualdas Kašuba, Edmundas Mazėtis
Lietuvos matematikos rinkinys, Volume 60, pp 20-27; https://doi.org/10.15388/lmr.b.2019.15230

Abstract:
Geometry problems are important for training of the mind, imagination and other highly valuable human abilities, however, dealing with geometry tasks is remarkably difficult even for the brightest students. There do not exist, as it seems, universal methods enabling one to solve all or even most of geometry problems. The authors share their life-long experience about some methods of approaching problems, which, when done properly, make some difficult problems not so difficult.
Edmundas Mazėtis, Grigorijus Melničenko
Lietuvos matematikos rinkinys, Volume 60, pp 34-38; https://doi.org/10.15388/lmr.b.2019.15233

Abstract:
We study the connection of Heronian triangles with the problem of the existence of rational cuboids. It is proved that the existence of a rational cuboid is equivalent to the existence of a rectangular tetrahedron, which all sides are rational and the base is a Heronian triangle. Examples of rectangular tetrahedra are given, in which all sides are integer numbers, but the area of the base is irrational. The example of the rectangular tetrahedron is also given, which has lengths of one side irrational and the other integer, but the area of the base is integer.
Lietuvos matematikos rinkinys, Volume 60, pp 1-5; https://doi.org/10.15388/lmr.b.2019.15188

Abstract:
Lithuania and sheds light on attempts by the Lithuanian public to revive higher education studies in Vilnius from 1919 to 1921. According to the remaining sets of documents it is possible to testify about the existing traces of mathematics in the projects of the restored Vilnius University or organized higher education courses.
Arvydas Jokimaitis, Darius Petronaitis
Lietuvos matematikos rinkinys, Volume 60, pp 15-19; https://doi.org/10.15388/lmr.b.2019.15229

Abstract:
The article authors detected distribution estimates of minimum air temperature in Lithuania. Also estimated ultimate minimum temperature record.
Juozas Juvencijus Mačys
Lietuvos matematikos rinkinys, Volume 60, pp 28-33; https://doi.org/10.15388/lmr.b.2019.15232

Abstract:
A complicated system of two equations with two variables is considered. The theory of equations of higher orders required for solution is given. Many different methods of solution are indicated.
Lietuvos matematikos rinkinys, Volume 60, pp 6-10; https://doi.org/10.15388/lmr.b.2019.15207

Abstract:
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.
Lietuvos matematikos rinkinys, Volume 60, pp 11-14; https://doi.org/10.15388/lmr.b.2019.15208

Abstract:
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.
Rimas Norvaiša
Lietuvos matematikos rinkinys, Volume 60, pp 21-26; https://doi.org/10.15388/lmr.a.2019.14957

Abstract:
Due to the changes of education system the school mathematics in Lithua-nia have acquired the elements of commercial-administrative mathematics of ancient times. Among other consequences the opportunities of school children to achieve the standards of mathematical reasoning are limited.
Vytautas Miežys
Lietuvos matematikos rinkinys, Volume 60, pp 15-20; https://doi.org/10.15388/lmr.a.2019.14955

Abstract:
Harel’s [2] notion of intel lectual need is refined by employing Davis’ [1] findingsabout interesting propositions in social sciences. A few hypothetical examples of how thisrevised definition might aid in planning mathematics lessons which provide meaningfulnessfor the students are presented.
Romas Alonderis, Haroldas Giedra
Lietuvos matematikos rinkinys, Volume 60, pp 1-6; https://doi.org/10.15388/lmr.a.2019.14953

Abstract:
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
Rimantas Pupeikis
Lietuvos matematikos rinkinys, Volume 60, pp 33-38; https://doi.org/10.15388/lmr.a.2019.14959

Abstract:
It is assumed that linear time-invariant (LTI) system input signal samples are updated by a sensor in real time. It is urgent for every new input sample or for small part of new samples to update an ordinary convolution as well. The idea is that well-known convolution sum algorithm, used to calculate output signal, should not be recalculated with every new input sample. It is necessary just to modify the algorithm, when the new input sample renew the set of previous samples. Approaches in time and frequency domains are analyzed. An example of computation of the convolution in time area is presented.
Gailė Paukštaitė
Lietuvos matematikos rinkinys, Volume 60, pp 27-32; https://doi.org/10.15388/lmr.a.2019.14951

Abstract:
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.
Jovita Gudan, Alfredas Račkauskas
Lietuvos matematikos rinkinys, Volume 60, pp 7-14; https://doi.org/10.15388/lmr.a.2019.14948

Abstract:
We present a functional data analysis approach to modeling and analyzing daily tax revenues. The main features of daily tax revenue we need to extract are some patterns within calendar months which can be used for prediction. As standard seasonal time series techniques cannot be used due to varying number of banking days per calendar month and presence of seasonality between and within months we interpret monthly tax revenues as curves obtained from daily data. Standard smoothing techniques and registration taking into account time variability are used for data preparation.
Olga Štikonienė,
Lietuvos matematikos rinkinys, Volume 51, pp 385-390; https://doi.org/10.15388/lmr.2010.14665

Abstract:
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 aweighted integral boundary condition in one coordinate direction. We consider the alternatingdirection method for a system of difference equations that approximates Poisson equationwith weighed integral boundary conditions with the fourth-order accuracy. Sufficient conditionsof stability for ADI method are investigated numerically. An analysis of results ofcomputational experiments is presented.
Svetlana Roman,
Lietuvos matematikos rinkinys, Volume 51, pp 379-384; https://doi.org/10.15388/lmr.2010.14664

Abstract:
In this article we investigate a formula for the Green’s function for the n-orderlinear differential equation with n additional conditions. We use this formula for calculatingthe Green’s function for problems with nonlocal boundary conditions.
Lietuvos matematikos rinkinys, Volume 50, pp 340–344-340–344; https://doi.org/10.15388/lmr.2009.14661

Abstract:
In this paper we research Green’s function properties for stationary problem with four-pointnonlocal boundary conditions. Dependence of these functions on values ξ and γ is investigated. Green’sfunctions graphs with various values ξ and γ are presented.
Olga Štikonienė,
Lietuvos matematikos rinkinys, Volume 50, pp 345-350; https://doi.org/10.15388/lmr.2009.14663

Abstract:
The mathematical model of the electrochemical glucose biosensor based on the enzymatic conversionof the substrate and the diffusion of the substrate was used. The influence of the fluctuations of themembrane thickness, the diffusion coefficients and pH were modelled and their impact was evaluated atdifferent modes of an action of the biosensor.
Aleksejus Mihalkovich
Lietuvos matematikos rinkinys, Volume 59, pp 7-12; https://doi.org/10.15388/lmr.a.2018.02

Abstract:
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.
Virginija Klusienė, Bronė Narkevičienė, Judita Puišo
Lietuvos matematikos rinkinys pp 27-34; https://doi.org/10.15388/lmr.b.2018.4

Abstract:
Matematikos ir gamtos fakulteto ištakomis Kaune laikomi 1920-ieji metai, kai buvo įsteigti Lietuvos Aukštieji Kursai, į kurių sudėtį įėjo ir Matematikos-fizikos skyrius. 1922 m. vasario 16~d., įkūrus Lietuvos universitetą Kaune, buvo įsteigtas Matematikos-gamtos fakultetas, kuris vykdė veiklą iki 1940 m. rudens. 1940 m. rugsėjo 1 d. Matematikos-gamtos fakulteto veikla Kaune sustabdyta, jis perkeltas į Vilnių. Visą, nuo Fakulteto įkūrimo iki sustabdymo, veiklos laiką Kaune Fakultetui vadovavo dekanas prof. Zigmas Žemaitis. 1993 m. rugsėjo 1 d. Kauno technologijos universitete Aukštosios matematikos (pakeičiant pavadinimą į Taikomosios matematikos), Bendrosios matematikos ir Fizikos katedrų pagrindu įsteigtas Fundamentaliųjų mokslų fakultetas, 2014 m. sausio 1 d. (at)gavęs istorinį Matematikos ir gamtos mokslų fakulteto pavadinimą ir skaičiuojantis jau 25-uosius savo veiklos metus.
Viktorija Sičiūnienė
Lietuvos matematikos rinkinys pp 82-86; https://doi.org/10.15388/lmr.b.2018.12

Abstract:
Straipsnyje pristatoma revizuota Bloom-o taksonomija ir jos taikymo patirtys išsivysčiusiose pasaulio šalyse. Taip pat gvildenama kognityvinių gebėjimų ugdymo Lietuvoje situacija. Išryškinama Bloom-o taksonomijos taikymo visose švietimo sistemos grandyse svarba, siekiant aukštesnių mokinių pasiekimų. Artimiausiu laiku Švietimo ir mokslo ministerijoje suplanuoti Bendrojo ugdymo programų naujinimo darbai. Aiškūs ugdymo taikiniai padėtų kokybiškai pertvarkyti įvairias mokymo programas, todėl matematikų bendruomenė neturėtų likti nuošalyje, kai jie bus svarstomi. Tikimasi, kad straipsnyje išdėstytos mintys padės priimti kokybiškesnius sprendimus.
Juvencijus Mačys, Jurgis Sušinskas, Juozas Juvencijus Mačys
Lietuvos matematikos rinkinys pp 54-60; https://doi.org/10.15388/lmr.b.2018.8

Abstract:
Some problems of Lithuanian school mathematical olympiad 2018 and Vilnius University mathematicalolympiad 2018 are considered. Different methods of solution are compared. Some usefulcommon advices for solving mathematical problems are given.
Bronė Narkevičienė, Regina Novikienė
Lietuvos matematikos rinkinys pp 67-75; https://doi.org/10.15388/lmr.b.2018.10

Abstract:
The article presents the results of the analysis of the science didactics of mathematics situation atthe state, social and institutional levels, and recommendations for improvement of the situation isgiven.
Karolina Piaseckienė
Lietuvos matematikos rinkinys pp 76-81; https://doi.org/10.15388/lmr.b.2018.11

Abstract:
The article deals with the analysis of the results of problem solution during the mathematics olympiadsof fifth grade students (stage 2) held in Šiauliai city in 2015–2018.
Romualdas Kašuba
Lietuvos matematikos rinkinys pp 20-26; https://doi.org/10.15388/lmr.b.2018.3

Abstract:
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.
Loreta Mačėnaitė
Lietuvos matematikos rinkinys pp 40-45; https://doi.org/10.15388/lmr.b.2018.6

Abstract:
In this article the case study method and its application in mathematical education are presented.
Edmundas Mazėtis, Grigorijus Melničenko
Lietuvos matematikos rinkinys pp 61-66; https://doi.org/10.15388/lmr.b.2018.9

Abstract:
The problem of existence of rational cuboids is considered in the article. Equivalent statements ofthis problem are obtained which lead to the existence of Heron’s triangles whose lengths are integralsquares and satisfy other additional conditions. Also, the connections between Euler bricks and theHeron triangles are obtained, which correspond to additional conditions.
Juvencijus Mačys, Jurgis Sušinskas, Juozas Juvencijus Mačys
Lietuvos matematikos rinkinys pp 46-53; https://doi.org/10.15388/lmr.b.2018.7

Abstract:
Rather unexpectably all real equations of the fourth degree are solvable by real means. So we canclassify all real equations of the third and fourth degree. In this article we classify real cubics. Thereal quartics will be classified in another article.
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