Darbe analizuojamos dvimačių ir trimačių objektų geometrinės transformacijos. Yra sistemų, kurios pateikia priemones demonstruoti ir atlikti užduotis. Yra galimybė sukurti ir transformuoti figūrą. Bet tokiose sistemose nėra galimybės atlikti kontrolinę užduotį, kurią vėliau galima peržiūrėti ir spręsti apie studento žinias. Analizuojamose sistemose nėra galimybės išsaugoti užduotį. Kuriama sistema turi galimybę sukurti, įtraukti ir išsaugoti naują užduotį. Sistema skirta dviejų tipų vartotojams - paprasti vartotojai ir administratoriai. Paprastas vartotojas gali mokintis transformacijų valdymo ir atlikti kontrolinę užduotį. Administratorius be šių galimybių dar gali kurti naujas užduotis ir valdyti duomenų bazę. / I am analysing the system for two-dimentional and three-dimentional objects transformation in this work. There is the system that serves the purpose to demonstrate and control exercised worksheets. Available systems allows to create and transform the shape. But there is no condition of worksheet, that after accomplished, we could conclude about students‘ knowledge. There is no possibility to save created worksheet in the analysed systems, so there is no chance to resume its data base. My demonstrated system has the tools for creating, saving and including new worksheet to the data base. There are two types of users using the system – ordinary user and administrating user. Administrator has all privilege to control the program. Ordinary user can study or make worksheet.

Darbe analizuojama diskrečioji Le Gall transformacija (DLGT) yra viena iš bangelių transformacijų, kurios naudojamos skaitmeninių vaizdų glaudinime. Vaizdų glaudinimas ypač svarbus, kai kalbama apie vaizdų siuntimą mažo pralaidumo kompiuteriniu kanalu. Šiai problemai spręsti pasitelkiama diskrečioji Le Gall transformacija, bei didelis dėmesys darbe skirtas vaizdo fragmento DLGT spektrui. Šio spektro radimui sukurtas ir realizuotas naujas algoritmas − greitoji procedūra. Palyginamosios analizės metu įrodyta, kad sukurta greitoji procedūra randa vaizdo fragmento DLGT spektrą daugiau nei 50 kartų greičiau nei tiesiogiai taikant DLGT vaizdo fragmentui. Darbo pradžioje aptariamos pagrindinės bangelių ir jų transformacijų savybės. Šių savybių svarba iliustruojama pateiktais pavyzdžiais ir sąsajomis su taikymu praktikoje. Viena iš svarbesnių aptariamų savybių būtų transformacijos lokalizavimas erdvėje. Nors DLGT pilnai netenkina šios savybės, tačiau darbe apžvelgtas dekoreliacijos metodas leidžia išspręsti šią problemą. Be to, pateikiami išsamūs DLGT algoritmai vienmačiams ir dvimačiams vaizdams. Šių algoritmų dėka buvo sukurta programinė įranga, padedanti analizuoti DLGT. Galiausiai darbo pabaigoje pateikiama sukurtos programinės įrangos instrukcija. / In this paper the main attention is dedicated to discrete Le Gall transformation (DLGT), the family of discrete wavelets transformations, which usage in the image compression is quite popular. Image compression is very important when it comes to low bandwidth network and computer channels. To deal with this problem the discrete Le Gall wavelets are brought up and focused on the image fragment DLGT spectrum. For calculation of this spectrum the new fast procedure is suggested and realized. In comparative analysis the fast procedure is proved to work more than 50 times faster than applying DLGT direct to image fragment. In the beginning of this paper the main concepts of wavelets and their transformations are analyzed. An importance of these properties is illustrated by examples and applications in practice. One of the most important properties is localization in space. Even though DLGT does not fully meet this property decorrelation technique, introduced in paper, benefits in solving localization problem. Moreover, DLGT algorithms are proposed for one-dimensional and 2-dimensional images. According to these algorithms the new program was created, which is dedicated for image analysis. Finally, in the end of paper the instructions of program are presented.

The current work has arisen with respect to the growing importance of ontology modelling in Information Systems development. Due to emerging technologies of Semantic Web, it is desirable to use for this purpose the Web Ontology Language OWL. From the other side, the relational database technology has ensured the best facilities for storing, updating and manipulating the information of problem domain. This work covers analysis of the process how ontology of a particular domain described in OWL may be transformed and stored in a relational database. The algorithms for transformation of domain ontology, described in OWL, to relational database are proposed. According this algorithm, ontology classes are mapped to relational tables, properties to relations and attributes, and constraints – to metadata. The proposed algorithm is capable to transform all OWL Lite and part of OWL DL syntax. The further expansion of the algorithm to cover more capabilities of OWL should be based on the same principles. The prototypical tool, performing transformations, has been implemented as add-in for the ontology development tool “Protégé����. The methodology of transformation is illustrated with an example.

Magistro studijų baigiamasis darbas, 53 puslapiai, 12 paveikslų, 6 lentelės, 50 literatūros šaltinių, lietuvių kalba. RAKTINIAI ŽODŽIAI: paslaugų sektorius, užimtumas, užimtumo lygis, poindustrinė visuomenė, transformacija. Tyrimo objektas: paslaugų sektorius kaimo vietovėse. Darbo tikslas: įvertinti paslaugų sektoriaus poveikį užimtumui kaimo vietovėse. Uždaviniai: • atskleisti vyraujančius požiūrius į gyventojų užimtumo teorines nuostatas; • išanalizuoti paslaugų sektorių ir gyventojų užimtumo struktūros transformacijas poindustrinėje visuomenėje; • išanalizuoti gyventojų užimtumo pokyčius kaimo vietovėse; • įvertinti gyventojų užimtumo problemas ir didinimo galimybes kaimo vietovėse; • pateikti paslaugų sektoriaus plėtros perspektyvas kaimo vietovėse . Tyrimo metodai: • gyventojų užimtumo teorinės nuostatos, paslaugų sektorius ir užimtumo struktūros transformacijos poindustrinėje visuomenėje pateikiami naudojant abstrakcinį, mokslinės literatūros, teisinių dokumentų, straipsnių, konferencijų bei interneto puslapiuose surinktos medžiagos analizės metodus; • analizuojant gyventojų užimtumo struktūros pokyčius kaimo vietovėse naudojami statistiniai duomenų rinkimo bei analizės metodai; • statistinės informacijos sisteminimui naudoti grupavimo, palyginimo bei grafinio vaizdavimo metodai. / Final work of Postgradeduate studies, 53 pages, 12 figures, 6 tables, 50 references, Lithuanian language. KEY WORDS: service sector, employment, employment rate, post-industrial society, transformation. The object of research: service sector in rural areas. The aim of work: evaluate the impact of service sector on employment in rural areas. Objectives: • to reveal the dominating theoretical attitudes of population employment; • to analyse the service sector and the structure transformations of population employment in post-industrial society; • to analyse the changes of population employment in rural areas; • to evaluate the problems and possibilities of population employment in rural areas; • to prefer the perspectives of development of service sector in rural areas. Research methods: • theoretical attitudes of population employment, service sector and the transformations of employment structure in post-industrial society are preferred according to such analysis methods as abstractic, nonfictions, legal documents, articles, conferences and internet material; • analysing the changes of population employment structure in rural areas are used the statistical accumulation and analysis of data methods; • the methods of grouping, comparison and graphic depiction are used for statistical systematize of information.

Disertacijoje gautas Dirichlė L funkcijų modifikuotosios Melino transformacijos pratęsimas į visą kompleksinę plokštumą. / In the thesis a meremorphic continuation of Dirichlet L- functions to the whole complex plane have been obtained.

In the thesis moromorphic continuation of modified Mellin transforms of Dirichlet L-functions to the whole complex plane have been obtained. / Disertacijoje gauta modifikuotosios Melino transformacijos L- funkcijai meromorfinis pratęsimas į visą kompleksinę plokštumą.

<p>Jedan od najvažnijih parametara kvaliteta električne energije u<br />distributivnoj mreži je harmonijski sastav naponskih i strujnih<br />signala. U disertaciji je razmatrano integrisano merilo harmonika,<br />na principu stohastičke rezonance. Uopštenje postojećeg teorijskog<br />modela rada merila, ostvareno je ukidanjem pojedinih pretpostavki o<br />idealizovanim uslovima rada: idealni intervali merenja, poznata i<br />nepromenljiva osnovna učestanost, idelane diterske sekvence. Na<br />osnovu teorijske analize, simulacija i praktičnih merenja, date su<br />procene reda veličine za svaku od navedenih grešaka. Na kraju je dato<br />šest preporuka za modifikaciju hardvera i načine obrade rezultata<br />merenja, koje mogu značajno poboljšati metrološke performanse<br />budućih generacija ovih merila.</p> / <p>One of the most important power quality indicators in power grids is the<br />harmonic composition of voltage and current signals. In this thesis an<br />integrated harmonic instrument has been considered, which operates on the<br />principle of the stochastic resonance. Generalization of the existing<br />theoretical model of the instrument was realized by terminating several<br />idealistic assumptions: perfect measurement intervals, known and stable<br />fundamental frequency, ideal dithering sequences. Based on the performed<br />theoretical analysis, simulations and practical measurements, estimates have<br />been given for each of the measurement error sources. Finally, six<br />recommendations were given for the modification of the hardware and the<br />results processing in order to achieve significantly better metrological<br />performances in future generations of this instrument.</p>

<p style="text-align: justify;">In this doctoral dissertation several integral transforms are discussed.The first one is the Short time Fourier transform (STFT). We present continuity theorems for the STFT and its adjoint on the test function space <em>K</em>₁(ℝⁿ) and the topological tensor product <em>K</em>₁(ℝⁿ) &otimes; <em>U</em>(<strong>ℂ</strong>ⁿ), where <em>U</em>(<strong>ℂ</strong>ⁿ) is the space of entirerapidly decreasing functions in any horizontal band of&nbsp;<strong>ℂ</strong>ⁿ. We then use such continuity results to develop a framework for the STFT on K&#39;₁(ℝⁿ). Also, we devote one section to the characterization of <em>K</em>&rsquo;₁(ℝⁿ) and related spaces via modulation spaces. We also obtain various Tauberian theorems for the short-time Fourier transform.</p><p style="text-align: justify;">Part of the thesis is dedicated to the ridgelet and the Radon transform. We define and study the ridgelet transform of (Lizorkin) distributions and we show that the ridgelet transform and the ridgelet synthesis operator can be extended as continuous mappings <em>R</em>_{<em>&psi;&nbsp;</em>}: <em>S</em>&rsquo;₀(ℝⁿ) &rarr; <em>S</em>&rsquo;(<strong>Y</strong>ⁿ⁺¹) and <em>R^t</em>_{<span style="vertical-align: sub;">&psi;</span>}: <em>S</em>&rsquo;(<strong>Y</strong>ⁿ⁺¹) &rarr; <em>S</em>&rsquo;₀(ℝⁿ). We then use our results to develop a distributional framework for the ridgelet transform that is, we treat the ridgelet transform on <em>S</em>&rsquo;₀(ℝⁿ) via a duality approach. Then, the continuity theorems for the ridgelet transform are applied to discuss the continuity of the Radon transform on these spaces and their duals. Finally, we deal with some Abelian and Tauberian theorems relating the quasiasymptotic behavior of distributions with the quasiasymptotics of the its Radon and ridgelet transform.</p><p style="text-align: justify;">The last chapter is dedicated to the MRA of M-exponential distributions. We study the convergence of multiresolution expansions in various test function and distribution spaces and we discuss the pointwise convergence of multiresolution expansions to the distributional point values of a distribution. We also provide a characterization of the quasiasymptotic behavior in terms of multiresolution expansions and give an MRA sufficient condition for the existence of &alpha;-density points of positive measures.</p> / <p>U ovoj doktorskoj disertaciji razmotreno je nekoliko integralnih transformacija. Prva je short time Fourier transform (STFT). Date su i dokazane teoreme o neprekidnosti STFT i njena sinteza na prostoru test funkcije <em>K</em>₁(ℝⁿ) i na prostoru <em>K</em>₁(ℝⁿ) &otimes; <em>U</em>(ℂⁿ), gde je&nbsp;<em>U</em>(ℂⁿ) prostor od celih brzo opadajućih funkcija u proizvoljnom horizontalnom opsegu na ℂⁿ. Onda, ovi rezultati neprekidnosti su iskori&scaron;teni za razvijanje teorije STFT na prostoru <em>K</em>&rsquo;₁(ℝⁿ). Jedno poglavlje je posvećeno karakterizaciji&nbsp;<em>K</em>&rsquo;₁(ℝⁿ) sa srodnih modulaciskih prostora. Dokazani su i različiti Tauberovi rezultata za STFT. Deo teze je posvećen na ridglet i Radon transformacije. Ridgelet transformacija je definisana na (Lizorkin) distribucije i pokazano je da ridgelet transformacija i njen operator sinteze mogu da se pro&scaron;ire kako neprekidna preslikava <em>R</em>_&psi; : <em>S</em>&rsquo;₀(ℝⁿ) &rarr; <em>S</em>&rsquo;(<strong>Y</strong>ⁿ⁺¹) and <em>R</em>^t_&Psi;: <em>S</em>&rsquo;(<strong>Y</strong>ⁿ⁺¹) &rarr; <em>S</em>&rsquo;₀(ℝⁿ).&nbsp;Ridgelet transformacija na <em>S</em>&rsquo;₀(ℝⁿ) je data preko dualnog pristupa. Na&scaron;e teoreme neprekidnosti ridgelet transformacije su primenjene u dokazivanju neprekidnosti Radonove transformacije na Lizorkin test prostorima i njihovim dualima. Na kraju, dajemo Abelovih i Tauberovih teorema koji daju veze izmedju kvaziasimptotike distribucija i kvaziasimptotike rigdelet i Radonovog transfomaciju.<br />Zadnje poglavje je posveceno multirezolucijskog analizu M - eksponencijalnih distrubucije. Proucavamo konvergenciju multirezolucijkog razvoja u razlicitih prostori test funkcije i distribucije i razmotrena je tackasta konvergencija multirezolucijkog razvoju u tacku u distributivnog smislu. Obezbedjena je i karakterizacija kvaziasimptotike u pogled multirezolucijskog razvoju i dat dovoljni uslov za postojanje &alpha;-tacka gustine za pozitivne mere.</p>

<p>In the thesis are introduced and investigated spaces of Burling and of Roumieu type tempered ultradistributions, which are natural generalization of the space of Schwartz&rsquo;s tempered distributions in Denjoy-Carleman-Komatsu&rsquo;s theory of ultradistributions.&nbsp; It has been proved that the introduced spaces preserve all of the good properties Schwartz space has, among others, a remarkable one, that the Fourier transform maps continuposly the spaces into themselves.<br />In the first chapter the necessary notation and notions are given.<br />In the second chapter, the spaces of ultrarapidly decreasing ultradifferentiable functions and their duals, the spaces of Beurling and of Roumieu tempered ultradistributions, are introduced; their topological properties and relations with the known distribution and ultradistribution spaces and structural properties are investigated;&nbsp; characterization of&nbsp; the Hermite expansions&nbsp; and boundary value representation of the elements of the spaces are given.<br />The spaces of multipliers of the spaces of Beurling and of Roumieu type tempered ultradistributions are determined explicitly in the third chapter.<br />The fourth chapter is devoted to the investigation of&nbsp; Fourier, Wigner, Bargmann and Hilbert transforms on the spaces of Beurling and of Roumieu type tempered ultradistributions and their test spaces.<br />In the fifth chapter the equivalence of classical definitions of the convolution of Beurling type ultradistributions is proved, and the equivalence of, newly introduced definitions, of ultratempered convolutions of Beurling type ultradistributions is proved.<br />In the last chapter is given a necessary and sufficient condition for a convolutor of a space of tempered ultradistributions to be hypoelliptic in a space of integrable ultradistribution, is given, and hypoelliptic convolution equations are studied in the spaces.<br />Bibliograpy has 70 items.</p> / <p>U ovoj tezi su proučavani prostori temperiranih ultradistribucija Beurlingovog&nbsp; i Roumieovog tipa, koji su prirodna uop&scaron;tenja prostora Schwarzovih temperiranih distribucija u Denjoy-Carleman-Komatsuovoj teoriji ultradistribucija. Dokazano je ovi prostori imaju sva dobra svojstva, koja ima i Schwarzov prostor, izmedju ostalog, značajno svojstvo da Furijeova transformacija preslikava te prostore neprekidno na same sebe.<br />U prvom poglavlju su uvedene neophodne oznake i pojmovi.<br />U drugom poglavlju su uvedeni prostori ultrabrzo opadajucih ultradiferencijabilnih funkcija i njihovi duali, prostori Beurlingovih i Rumieuovih temperiranih ultradistribucija; proučavana su njihova topolo&scaron;ka svojstva i veze sa poznatim prostorima distribucija i ultradistribucija, kao i strukturne osobine; date su i karakterizacije Ermitskih ekspanzija i graničnih reprezentacija elemenata tih prostora.<br />Prostori multiplikatora Beurlingovih i Roumieuovih temperiranih ultradistribucija su okarakterisani u trećem poglavlju.<br />Četvrto poglavlje je posvećeno proučavanju Fourierove, Wignerove, Bargmanove i Hilbertove transformacije na prostorima Beurlingovih i Rouimieovih temperiranih ultradistribucija i njihovim test prostorima.<br />U petoj glavi je dokazana ekvivalentnost klasičnih definicija konvolucije na Beurlingovim prostorima ultradistribucija, kao i ekvivalentnost novouvedenih definicija ultratemperirane konvolucije ultradistribucija Beurlingovog tipa.<br />U poslednjoj glavi je dat potreban i dovoljan uslov da konvolutor prostora temperiranih ultradistribucija bude hipoeliptičan u prostoru integrabilnih ultradistribucija i razmatrane su neke konvolucione jednačine u tom prostoru.<br />Bibliografija ima 70 bibliografskih jedinica.</p>

Pagrindinė šio darbo koncepcija ir tikslas – nagrinėti šeimos ir santuokos klausimus per vertybių prizmę. Nagrinėjant santuokos kaip vertybės silpnėjimą buvo apsiribota keturiais pagrindiniais veiksniais: pripažinimu ir įtvirtinimu naujų gyvenimo kartu formų, asmens saviraiškos svarba, karjeros ir tvirti materialinio pagrindo siekimu bei įpareigojimų ir atsakomybės vengimu. / The main concept of this work and the aim - to examine the family and marriage issues through the prism of values. The examination of marriage as the values decline was confined to four major factors: the recognition and establishment of new life forms, to express the importance of personal, career and solid material basis for the achievement of the obligations and liability avoidance.