Lietuvos matematikos rinkinys

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 Show More ... ... Show Less

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 Show More ... ... Show Less

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 Show More ... ... Show Less

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 Show More ... ... Show Less

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 Show More ... ... Show Less

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 Show More ... ... Show Less

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 Show More ... ... Show Less

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 Show More ... ... Show Less

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 Show More ... ... Show Less

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. Show More ... ... Show Less

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.  Show More ... ... Show Less

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. Show More ... ... Show Less

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.   Show More ... ... Show Less

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. Show More ... ... Show Less

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. Show More ... ... Show Less

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.   Show More ... ... Show Less

the article authors detected distribution estimates of minimum air temperature in lithuania. also estimated ultimate minimum temperature record. Show More ... ... Show Less

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. Show More ... ... Show Less

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. Show More ... ... Show Less

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 Show More ... ... Show Less

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 Show More ... ... Show Less

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 Show More ... ... Show Less

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 Show More ... ... Show Less

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. Show More ... ... Show Less

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. Show More ... ... Show Less

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 Show More ... ... Show Less

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 Show More ... ... Show Less

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 Show More ... ... Show Less

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 Show More ... ... Show Less

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. Show More ... ... Show Less

šiame straipsnyje remiantis vilniaus universiteto henriko jasiūno vardo matematikų muziejaus fonduose saugomais šaltiniais atskleidžiama lietuvos matematikų draugijos genezė, nurodomos jos ištakos -- ankstesnio meto lietuvių matematikų vienijimosi apraiškos Show More ... ... Show Less

straipsnyje nagrinėjami keli 2018 m. lietuvos mokinių ir vilniaus universiteto matematikos ir informatikos fakulteto matematikos olimpiadų uždaviniai. lyginami jų sprendimo būdai, pateikiama patarimų, naudingų sprendžiant sunkesnius uždavinius Show More ... ... Show Less

straipsnyje pateikiama matematikos didaktikos mokslo situacijos valstybiniame, socialiniame ir instituciniame lygmenyse analizės rezultatai ir išvados – rekomendacijos situacijos pagerinimui Show More ... ... Show Less

zigmas žemaitis (1884-1969) - lietuvos matematikų patriarchu tituluojamas profesorius, klojęs pagrindus visam vasario 16-osios lietuvos respublikos mokslui, paliko ženklų pėdsaką ir pirmųjų aukštosios matematikos vadovėlių lietuvių kalba leidyboje. šiuo straipsniu siekiama aptarti kiek primiršto ,,diferencialinio-integralinio skaičiavimo`` pasirodymo aplinkybes, vadovėlio (konspekto) turinį ir nusakyti leidinio reikšmę įtvirtinant šį dalyką aukštosiose studijose lietuvoje Show More ... ... Show Less

straipsnyje pateikiama šiaulių m. (ii-ojo etapo) 5-os klasės mokinių matematikos olimpiadų (2015--2018 m.) užduočių sprendimo rezultatų analizė Show More ... ... Show Less

šiame straipsnyje nagrinėjami ir aptariami kai kurie uždaviniai, kurie gali būti išspręsti ir beveik nieko neparašius -- tik atsakymą užrašant, nors gali sukelti ir vadinamųjų laikinų sunkumų ir netgi pasirodyti sunkoki Show More ... ... Show Less

šiame straipsnyje pristatomas atvejo analizės metodas ir jo taikymas matematikos mokymosi procese Show More ... ... Show Less

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 Show More ... ... Show Less

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 Show More ... ... Show Less

straipsnyje pristatomas itin gabių mokinių matematinio ugdymo atvejis kauno~ m. tarpdisciplininėje ugdymo programos trečioje klasėje. tokio ugdymo teorinis pagrindas – diferencijuoto mokymo taikymas, naudojant išorinį diferencijavimą – programa skirta viso miesto itin gabiems vaikams. papildomi diferencijuoto mokymo aspektai: mokinių grupavimas pagal gabumų lygmenį, nestandartinio ugdymo turinio parinkimas, komandinis darbas ir individualizuotas vertinimas Show More ... ... Show Less

straipsnyje nagrinėjama iki šiol neišspręsta racionaliųjų kuboidų egzistavimo problema. gauti šiai problemai ekvivalentūs teiginiai, suvedantys ją į herono trikampių, kurių kraštinių ilgiai yra sveikųjų skaičių kvadratai ir kurie tenkina kitas papildomas sąlygas, egzistavimą. taip pat gauti eulerio plytų ryšiai su herono trikampiais, tenkinančiais papildomas sąlygas Show More ... ... Show Less

kadangi paaiškėjo, kad ne tik trečiojo, bet ir ketvirtojo laipsnio lygtys su realiaisiais koeficientais mokykliškai (nesiremiant kompleksinių skaičių teorija) išsprendžiamos realiųjų skaičių aibėje, tapo įmanoma jas suklasifikuoti. šiame straipsnyje pateikta trečiojo laipsnio lygčių klasifikacija (ketvirtojo laipsnio lygčių klasifikacija bus pateikta kitame straipsnyje, rengiamame spaudai Show More ... ... Show Less

the article gives a survey of mathematical life and activities of the lithuanian mathematical society during the past three years Show More ... ... Show Less

ignas saudargas (1902 – 1987) graduated from vytautas magnus university in 1932, he studied mathematics. until the end of world war ii worked as a teacher at gymnasiums of lithuania. he was good teacher, actively participated in  extracurricular activities, always was trying to improve his educational qualifications. after the world war ii, he was invited to teach mathematics in universities of kaunas. i. saudargas was known for high demands for his students Show More ... ... Show Less

the scientist, statesman, academician albinas rimka (1886–1944) is famous in lithuanian historiography as a creator of independent lithuania. first of all, his merits as a politician and economist are to be mentioned. albinas rimka is considered to be the founding father of science of statistics in lithuania in 1920–1940. in the textbooks on fundamentals of statistics and at lectures which albinas rimka delivered at university, the academician based statistical methods upon the main verities of high mathematics including elements of mathematical analysis, theory of probability, and mathematical statistics. in his textbooks, we can find elements of application of mathematics which were not given attention by other researchers (historians and economists) in lithuania. the article tries to fill in the gap in research of origins of science of statistics in lithuania with the help of the analysis of albinas rimka’s textbooks Show More ... ... Show Less