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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.

In the article necessary and sufficient conditions for existence and uniqueness of a right triangle with given bisector and median are established.

It is shown in the article that, in general, it is not possible to draw a triangle using a compass and a straightedge given an angle and a bisector and a median drawn from the vertices of another different angles. It is shown in which particular cases a triangle can be drawn.

Šiame darbe yra apžvelgta programavimo kalbų istorija ir jų raida, pradedant nuo pačios pirmosios programos ir pirmosios programuotojos ir baigiant šiuolaikinėmis programavimo kalbomis. Taip pat apžvelgiama programavimo kalbų filosofija ir jų populiarumas šiuo metu, analizuojamos programų populiarumo pasikeitimo tendencijos. Taip pat yra atlikti anketiniai ir eksperimentiniai tyrimai, parodantys programavimo kalbų populiarumą mokyklose, pateikti mokinių gebėjimų įvertinimai mokinantis skirtingas programavimo kalbas. Mokyklinio kurso lygmenyje išanalizuotos informacinių technologijų valstybiniame brandos egzamine naudojamos programavimo kalbos, jų struktūra, sintaksė ir galimybės. This paper is an overview of the history of programming languages ​​and their evolution, starting from the first program and the first programmer and ending with modern programming languages. It also provides an overview of the programming language and the philosophy of their popularity this time, the popularity of the programs analyzed the change in trend. There are also carried out the survey and experimental studies demonstrating the popularity of programming languages ​​in schools, give students skills assessments in teaching different programming languages. School-level course analysis of information technology in the public examination of maturity used programming languages, their structure, syntax and options.

Magistriniu darbu, kurio tema “Vertikalios ašies vėjo jėginės sparno modeliavimas“, siekiama ištirti mažos galios, paprastos konstrukcijos, vertikalios ašies vėjo jėgainės sparnuotes, atlikti jų kompiuterinį modeliavimą ir analizę. Tema yra aktuali dėl to, kad norint būti energetiškai nepriklausomiems, reikia ieškoti alternatyvių energijos šaltinių, kurie būtų neišsenkantys, prieinami daugeliui vartotojų. Vienas iš tokių - vėjo srauto energija, tačiau gyvenant tankiai užstatytoje, geografiškai šiurkščioje aplinkoje, tenka ieškoti mažų matmenų, mažos galios įrenginių, kurie pajėgtų dirbti esant mažiems vėjo greičiams ir sūkurinėmis sąlygomis, nedarkytų gamtos ar pastatų estetinės išvaizdos, nekeltų triukšmo ir būtų kuo lengviau aptarnaujami. Atliekant tyrimą, VAVJ sparno modelio analizės skaičiavimai buvo daromi remiantis bendrąja hidrodinaminių srautų teorija, naudojant baigtinių elementų analizės, projektavimo ir modeliavimo programą - COMSOL Multiphysics. Atlikti tyrimai parodė, kad didesnį sukimo momentą gausime naudodami uždarų galų rotorius, o įrengus oro srautą kreipiančias mentes, slėgis į rotoriaus sparną ženkliai išauga. Statant šachmatine tvarka keletą VAVJ, didžiausią slėgį į sparnuotes gausime esant 6 kartus didesniam atstumui nei sparnuočių spindulys. The aim of this master's dissertation on the theme of "FEM modeling of vertical wind turbine using CFD solvers" is to investigate the low-power, simple design, vertical axis wind turbine impellers and to carry out their computer simulation and analysis. The theme is of great importance so as to be energectically independent, it is also necessary to look for alternative energy sources that are inexhaustible and accessible to many users. One of them - the wind flow energy, but living in a densely built-up, geographically rough environment forces us to look for small footprints, low-power devices that would be able to work at low wind speeds and eddy terms wouldn't damage natural and aesthetic appearance of the buildings making no noise and also maximize opportunities to be serviced. The study of VAWT wing pattern analysis calculations were made based on the general theory of hydrodynamic flows, using finite element analysis, as well as design and simulation software - COMSOL Multiphysics. Research has shown that we will get bigger torque while using closed ends of the rotors, and the installation of air flow directing vanes, the pressure in the rotor wing significantly increases. Constructing in a checkered order a few VAWT, the greatest pressure on the impellers receives 6 times greater distance than the impeller radius.

Užsibrėžtam tikslui pasiekti, buvo įdiegtos populiariausios „Windows“ operacinės sistemos. Nagrinėjant atskiras sistemų versijas, susipažinta su jų istorija. Palyginus skirtingu laikmečiu sukurtas operacines sistemas įvertinti sąsajos elementai, remiantis vieninga vartotojo aplinka, prieinamumu, natūralia vartotojo sąsaja ir papildyta tikrove. Analizės metu buvo nustatyta, kad keičiantis operacinių sistemų versijoms, išlikdavo tie patys valdymo elementai, buvo įdiegiami pakeitimai, nedarantys įtakos vartotojo sąsajai su operacinių sistemų darbu. The most popular "Windows" operative systems were intalled to achieve the targeted aims. During analysis of single systems versions it was acquainted with their history. After comparison of operating systems that were created in different time, evaluated the interface elements based on the recommendations of common user accer, accessibility, natural user interface and the augmented reality. During the analysis, it was found that replacing the operating system versions, has remained with same controls, there were made changes, without affecting the user interface with the operating system.

Darbe nagrinėjami objektinio programavimo principai. Apžvelgiama Java programavimo kalba, jos platformos, virtualioji mašina, programų tipai. Apžvelgiami Java baziniai paketai, klasės. Aprašyta programavimo aplinka ir vartotojo grafinės sąsajos (interfeiso) kūrimas NetBeans aplinkoje. Aprašyti pagrindiniai swing ir awt paketų komponentai. Programiškai realizuoti ir aprašyti keli uždaviniai NetBeans aplinkoje, kurie demonstruoja vartotojo grafinės sąsajos kūrimą. Darbo tikslas yra NetBeans aplinkos taikymas objektinio programavimo mokymo tikslams. In this work are analyzed objective programming principles. Reviewed JAVA programming language, its platforms, virtual machine (apparatus), program types. Also are overviewed JAVA basic packets, classes. Described programming environment and user graphic interface creation in NetBeans environment. Described main SWING and AWT packets component. Program realized and described few tasks in NetBeans environment which demonstrates user graphic connections creation. Work purpose is NetBeans environment application for studying objective programming.

Šiame darbe supažindinama su kompiuterinių tinklų apsaugos problemomis, pagrindiniais tinklo veikimo principais. Išaiškinti pagrindinai kompiuterinių tinklų struktūros modeliai. Išanalizuotos ir išaiškintos pagrindinės kompiuterių tinklo plėtros, sujungimo, maršrutizavimo, vaizdavimo, valdymo ir monitoringo problemos. Išnagrinėjus esamas kompiuterinių tinklų problemas, buvo sukurtas naujas tinklo modelis, užtikrinantis lengvą ir greitą tinklo išteklių ir vartotojų segmentaciją, pastovų ir nepertraukiamą visų tinklo mazgų darbą, o svarbiausiai užtikrinantis didelį visų kompiuterių tinklo vartotojų ir išteklių apsaugą. Taip pat yra numatyta lengva galimybė dėl naujų ar kitų tinklo segmentų prijungimo ir to paties tinklo augimo ir plėtros. Atlikti eksperimentai su naujų kompiuterių tinklų modeliais, aiškinantis teorinius ir praktinius VLAN tinklų kiekius, kuriuos pasiekus ar viršijus, vertėtų atlikti tinklo segmentaciją ir aiškinantis jų įtaką maršrutizatoriaus apkrovai ir veikimui. In this work you’ll learn about computer network’s problems and basic network operation principles, also the basic computer network’s structure models explained. Analyzed and explained basic problems about computer network development, connection, routers, monitoring and operation. After researching the existing computer network problems there was new network model designed. This model ensures easy and fast users and resources segmentation, constant and continuous work of all the network nodes and above all ensures the reliable protection for computer users and sources. Also there is the opportunity for the new or existing segments to hook up to the main network easily and for its growth and development. There were carried out the experiments with the new models of computer network, which helped to explain the theoretical and practical VLAN numbers. In case of reaching or exciding those VLAN numbers it is necessary to carry out network’s segmentation and clarify its influence on router’s overload and operation.

Darbe nagrinėjama Eclipse programavimo aplinka. Aprašomos jos pagalbinė funkcijos pertvarkant darbinę aplinką bei kuriant Java projektus. Taip pat šias pagalbines funkcijas demonstruoja sukurta video medžiaga. Aprašomi SWT vaizdiniai komponentai. Supažindinama su Eclipse aplinkos papildiniu WindowBuilder. Sukurtų projektų pagalba pateikiamas SWT bei Swing vaizdinių komponentų skirtumas. Eclipse Micro Edition papildinio bei Sun Wireless Toolkit mobiliųjų prietaisų programinės įrangos pagalba pateikiami Midlet projektų kūrimo pavyzdžiai. Aprašomas darbo su MySQL duomenų baze projektas naudojant JDBC. In this thesis we analyze Eclipse integrated development environment in customization and Java projects development contexts and illustrate our research with videos. We also describe graphical SWT components and WindowBuilder plug-in. Differences between SWT and Swing components are shown using specially created projects. Examples of Midlet projects, developed using Eclipse Micro Edition plug-in and Sun Wireless Toolkit for mobile device, are described. We also demonstrate connectivity to MySQL database through JDBC interface.

Šiame darbe yra trumpai aprašomas algoritmas, kuris naudoja nereikalingus skaičiavimus, ieškant iškilojo apvalkalo taškų. Pateikiamas naujas „Artimiausio taško“ algoritmas, kuris iškilojo apvalkalo taškus randa įterpimo būdu. Pateikiamos ir dvi „Artimiausio taško“ algoritmo realizacijos. „Preparata“ bei „Artimiausio taško“ algoritmai, bei „Artimiausio taško“ algoritmo dvi realizacijos realizuojamos skirtingose operacinėse sistemose: Windows ir Linux. Realizavus algoritmus („Preparata“, „Artimiausio taško“) ir dvi „Artimiausio taško“ algoritmo realizacijas, buvo analizuojamas algoritmų atlikimo laikas. This work shortly describes the algorithms, that uses unnecessary calculations for the search of convex hull points. A new algorithm called “Nearest point” is presented in this work. This algorithm founds the points of convex hull by using the method of insertion. Two realisations of the “Nearest point” realisation are presented in the current work.. The “Preparata” algorithm, the “Nearest point” algorithm, and two realisations of the “Nearest point” algorithm were build both for Windows and Linux operating systems. After the realisation of the algorithms (“Preparata” and “Nearest point”) and two versions of the “Nearest point”, the action time of them has been analysed.

Darbe trumpai apžvelgtos figūrų pakavimo ištakos, aprašyti keli figūrų pakavimui naudojami stochastinio modeliavimo algoritmai. Išnagrinėtas perturbacijos metodas, sukurtos dvi šiuo metodu vienetiniame kvadrate vienodus apskritimus pakuojan��ios programos, detaliai aprašyti jų algoritmai. Eksperimentiškai ištirtos programų galimybės: kiekviena programa po 30 kartų buvo pakuojami n apskritimų, kur 3 ≤ n ≤ 15 ir n = 25, 50, 75, 100. Buvo fiksuojami ir apibendrinami pakavimų rezultatai. Pastarieji lyginti tarpusavy ir kartu su Violetos Sabonienės magistriniame darbe ,,Biliardinio modeliavimo algoritmai ieškant talpiausio geometrinių figūrų pakavimo“ biliardiniu metodu atliktais pakavimo rezultatais. Prieduose pateikti programų tekstai ir skaičiavimų lentelės. In this work are examined the sources of figure packing, described the stochastic simulation algorithms of finding the densest packing of geometric figures. Here is analysed the method of perturbation and made two programmes of equal circle packing in unit square and their algorithms are being described in detail. The possibilities of programmes were analysed experimentally: using each programme 30 times. In each experiment were packed n circles, were 3 ≤ n ≤ 15 end n = 25, 50, 75, 100. The results of packing were fixed and summarized. The latter rezults were compared between themselves and also with the results of Violeta Sabonienė master of science work “The billiarding simulation algorithms of finding the densest packing of geometric figures“. The text and the calculation charts of the program are giver in the appendices.

Šiame magistro darbe aptarsime keletą projekcijos metodų: tai pagrindinių komponenčių analizė (Principal Component Analysis (PCA)), daugiamačių skalių (Multidimensional Scaling (MDS)) ir santykinės perspektyvos (relational perspective map (RPM)). Tirsime, kuris iš trijų pradinių projekcijos taškų parinkimo būdų - atsitiktinis, pagrindinių komponenčių ar didžiausių dispersijų garantuoja mažesnę paklaidą RPM algoritme. Atliksime paprasto RPM algoritmo, pasiūlyto autoriaus James Xinzhi Li modifikaciją. Taip pat tirsime parametrus r,a (mokymo greičiai), nustatysime, kaip jie įtakoja RPM algoritmo konvergavimą. Integruosime MDS ir RPM algoritmus į internetinę terpę. Vizualiai vaizduosime daugiamačių duomenų projekcijas. This paper deals with a methods, called the relational perspective map and multidimentional scaling. Relational perspective map that visualizes multidimensional data onto two-dimensional closed plane. It tries to preserve the distances between the multidimensional data in the lowerdimensional space. But the most important feature of the relational perspective map is the ability to visualize data in a non-overlapping manner so that it reveals small distances better than other known visualization methods. In the methods are In this paper, the features of relational perspective map are explored experimentally and some disadvantages are noticed. We have proposed a modification of this method, which enables us to avoid them. Also we have stored RPM and MDS algorithms in php language and included them in web site for testing these methods online. But allow testing only small data, because algorithms in php language works longer that stored in c++ language.

Šiame darbe yra aprašomas optimizavimo paketas SeDuMi Interface ir jam priklausantis skaičiavimo paketas SeDuMi 1.05. Išvardintos paketo savybės, kurios išskiria jį iš kitų optimizavimo paketų. Aprašytos paketo funkcijų reikšmės. Supažindinama su optimizavimo paketų įvairove. Palyginamas pusiau apibrėžtas programavimas su tiesiniu programavimu, kadangi pakete SeDuMi interface realizuoti pusiau apibrėžto programavimo algoritmai. Taip pat lyginami programų skaičiavimų laikai: programų naudojančių SeDuMi paketo funkcijas ir programų su MATLAB funkcijomis. Palyginimui realizuoti, naudojamas klasikinis optimizavimo uždavinys –mažiausių reikšmių elipsoido uždavinys. The optimization software SeDuMi Interface and it‘s calculation packet SeDuMi 1.05 is described in this work. Distinctive software features are listed. and values of packet’s functions are described. Variety of optimization packets is presented. Semidefinite programming is compared with linear programming, since semidefinite programming algorithms are implemented in the SeDuMi interface. Time of execution of the programs has been also compared: programs using SeDuMi software functions has been compared with programs using MATLAB functions. For the comparison classical optimization problem is used – the minimum volume ellipsoid problem.

All possible convex hull (i.e. the minimum area convex polygon containing the planar set) algorithms ever published in scientific press have been analysed in this work. Two new convex hull algorithms created by myself have been presented. The running time of analysed algorithms has been surveyed. Three most popular algorithms (Graham Scan, Jarvis March and Quickhull), the oldest algorithm (Brute Force) as well as the both new ones have been implemented. Efficiency experiments have been carried out with them. The algorithms created by me achieved the best results. In order to raise the efficiency of all the algorithms I suggested a priori filtration of points, which decreases the amount of the original points by almost 50% and, consequently, the speed of algorithms is increased. The major part of this master work will be published in the magazine “Technological and economic development of economy”. Besides, the report of this work has been made in the conference of Lithuanian young scientists, called “Operation analysis and application”.

The presented work discusses and compares these means of learning: the Content Management System and Distant Learning Environment. In the same way the means called MOODLE is studied with great attention in order to discover its opportunities, structure and working principles. http://MOODLE.org/ MOODLE – Modular Object Orentiered Dynamic Learning Environment MOODLE- is based on the theory of Social Constructivism and, from the pedagogical point of view, is considered to be the most flexible means of virtual learning. It approaches both distant learning and a task presentation for those who study in a computer classroom (not exactly Computer Studies). They are such systems as PHP and MySQL (some others, e.g. DB), which are oriented on the main technological standards (for instance, LDAP – users system, SCORM – presentation of learning material). The course is considered to be enough flexible, thus it might be presented in three ways: v Weekly (all the lectures are hold on time, like in the traditional timetable model); v According to the list of topics (topics are taught in consecutive order, it is possible to determine time of learning. However they are not so strict as in a weekly course model); v Social (based on discussions). Also it is worth to mention that there are plenty of various activities. The following ones are used the most often: (a) Lecture; (b) Individual task; (c) Critical estimation of the colleagues (Workshop); (d) Discussions (synchronous and... [to full text]

The present research paper deals with the comparison of static and dynamic data structures: static array, dynamic array, pointers array - class TList (Delphi) and dynamic doubly linked list, created with the help of recursive record.To compare the above mentioned structures, sorting (Bubble) and convex hull creation algorithms (Graham, Endrew) are realized, with the time of their implementation analysed. The algorithm of sorting (Bubble) is realized by four ways: static array, dynamic array, pointers array (class TList) and a dynamic doubly linked list, created with the help of recursive record.The algorithms of convex hull creation (Graham, Endrew) is realized by three ways: static array, dynamic array and pointers array (TList).The research paper also describes the pointers array class TList (Delphi), its properties and methods. The sorting method Sort of this class is compared with the sorting method of a “Bubble”. Using class templates, a universal class MList (C++) was created for work with dynamic linear linked lists.

The electronic magazine has been realized on platform Visual Basic. NET. Therefore work of the master can be divided into two parts: Use Windows of forms,Use Web of forms. Advantage of the given system will be, that the magazine works in real time, that is the program calculates time and what lesson under the schedule now at the teacher who is registered in system.