The present work focusses on the rational and complex use of land and water transport, depending of the type of goods, technical characteristics of particular transport facilities (speed, capacity, environmental pollution, fuel consumption) and the particular meand of transport (automobiles, rail transport or ships).

The present work focusses on the rational and complex use of land and water transport, depending on the type of goods, technical charakteristics of particular transport facilieties (speed, capacity, environmental pollution, fuel consumption, etc.) and the particular means of transport (automobiles, rail transport or ships).

The most widely used variable reluctance and permanent magnet stepper motors of different design types are discussed in the theoretical part of this work. It also overviews a constructional diversity of these motors, the fundamentals of operating modes and characteristics. This part discuses features of stepper motors as a part of automation control system, presents the main counting equations and applications with stepper motors. The practical part includes the mathematical model of stepper motor and the Simulink model that was developed for software package “Matlab”. Those models formed the basis for analysis of stepper motor dynamic characteristics in various operating modes (wave drive, full step drive, half step drive, microstepping, reversing, braking).

Savo magistriniame darbe nagrinėju vienos draudimo kompanijos KASKO sistemos funkcionavimą. Visų pirma sukonstruoju KASKO draudimo sistemos matematinį modelį. Tuomet atlieku išsamias analizes polisų sutartims, draudiminiams įvykiams, įmokoms ir išmokoms, bei jų kitimo dinamikai. Apskaičiuoju 2006 m. kiekvieno mėnesio pelno pasikliovimo intervalus ir padarau prognozę 2007 metams. Galiausiai patikrinu draudimo kompanijos padalinių ir filialų darbo efektyvumą. / My work analyses CASCO insurance system’s behavior of one insurance company. At first I made a mathematical model of CASCO insurance. Then I properly described analyses of policies’ contracts, insurance events, insurance premiums and payouts. Later I estimated approximate confidence intervals of profit and made a forecast for 2007 year. And finally I analysed the work efficiency of subdivisions and branches. The mathematical model of CASCO insurance system let us to do various experiments in mathematical space when we analyses incomes of insurance company.

Konstruojant modelį, susiduriama su optimalios architektūros parinkimo problema. Optimalus modelis reiškia optimalų netiesinės regresijos komponenčių skaičių ir svorių reikšmes su kuriomis modelis „geriausiai“ prognozuoja tirpalo koncentracijas. Optimaliam komponenčių skaičiui nustatyti pasitelkiame pažingsninės regresijos metodą. Skaičiavimams buvo pasirinkta netiesinės regresijos sigmoidinė aktyvacijos funkcija, šis pasirinkimas buvo pagrįstas P.L. Bartlet [1] darbo rezultatais. Modelyje taip pat taikomas nepilnai apibūdintų duomenų analizės metodas, pagrįstas Volker Tresp [3] darbo rezultatais. Šis metodas yra plačiai taikomas šiuolaikinėje informacinėse technologijose bei matematinių modelių konstravime, kai turima pilna informacija apie modelių įėjimus tačiau išėjimo duomenys yra žinomi ne visais atvejais. Mūsų atveju, yra žinomi tikslūs amperometro parodymai – srovės stipris tam tikru laiko momentu (realybėje šiuos duomenis nesunku pamatuoti), tačiau duomenys apie tikslias tirpalų koncentracijas yra žinomi ne visi. Panaudojome pagrindinių komponenčių analizės metodą (PCA) ir sumažinome turimų duomenų rinkinius, taip išsaugodami didžiąją dalį informacijos apie tuos duomenis. Tam tikri modelio parametrai : , buvo parenkami bandymų keliu, stebint modelio vidurkių kvadratų sumą(MSE). Gauti rezultatai rodo, kad sukurtas regresijos modelis pakankamai gerai klasifikuoja duomenis, tačiau tiksliems koncentracijų prognozavimams reikalingi papildomi tyrimai. / The purpose of this work is to create non liner regression model with optimal number of coefficients and optimal values of these coefficients, and predict liquor concentration having values of amperimetric data. The main task of the work: • To use Semi-supervised learning algorithm while creating the model (Kai Yu, Volker Tresp [4]) • To apply P.L. Bartlet [1] idea, that in non-linear regression model the value of the weights is more important than number of these weights. • To create mathematical model that could calculate optimal non-liner regression’ weights using stochastic search, and could determine the concentration of liquor according biosensors response curve While creating the model, we met model optimization problem. The optimal model means the optimal number of model’ weights and the values of weights with whom the model best predicts the concentration of the liquor. We used step wise regression method to determine the optimal number of weights. For the calculations we choose non-liner regressions sigmoid function according P.L. Bartlet [1] work results. We also implemented semi supervised data analysis method that was chosen based on Volker Tresp [3] work results. These methods are widely applied in the mathematical modeling and information technologies. What is more, we also applied partial component analysis and reduced the data sets of response curve, without loosing significant information about these data. The parameters , of the model we chosen in... [to full text]

Šiame darbe nagrinėjama geležinkelio vagonų, reikalingų tam tikros apimties krovinių vežimams, poreikio problema. Ypatingas dėmesys atkreipiamas į vagonų parko rezervo sudarymą. Pagal pateiktas matematines formules, įvertinus visas vagonų eksploatavimo sąnaudas, nustatomas reikalingų vagonų skaičius. Taip pat yra aprašomas „MS Excel“ programa sudarytas matematinis modelis operatyviniam bei planiniam vagonų poreikiui apskaičiuoti. Šiuo modeliu apskaičiuota reikšmė yra optimali ir yra 1,4 % mažesnė, negu vagono poreikio reikšmė, apskaičiuota remiantis praėjusių metų statistiniais rezultatais. Siekiant visapusiškai išnagrinėti problemą, papildomai buvo tiriamas prekinių vagonų parko amžius, atlikta vagonų prastovų laiko analizė, nustatyti prekinių vagonų poreikio ekonominiai aspektai. / This paper considers the need of the rail cars for the determined volume of the freight traffic. The special attention is drawn to the composition of the railway wagon reserve park. The mathematical equations evaluating the operational elements of the wagons are determined. An experimental mathematical model which describes the operational need of wagons is calculated using supportive software Excel; the model estimates that the optimized need for wagons are by 1.4 % lower then the need has been calculated by last year statistical data. Furthermore the work also observes the performance and the age of the freight Wagon Park. The analysis performed to analyze the wagons idle time and other economic issues concerning the matter of the freight wagons are observed.

Magistrinio darbo tikslas yra sukurti kompiuterinį amperometrinio biojutiklio su chemiškai modifikuotu elektrodu modelį ir ištirti jo savybes. Modelis papildo egzistuojančius modelius mediatoriaus sluoksniu. Mediatoriaus koncentracija sluoksnyje nėra konstanta, tirpsta biojutiklio veikimo eigoje. Darbe apžvelgiama medžiaga apie amperometrinius biojutiklius, biojutiklio modeliavimo aspektus, mediatoriaus tirpimo priežastis ir veikimo principus. Vėliau suformuluojamas pasirinkto biojutiklio matematinis modelis. Matematiniame modelyje pateikiamos diferencialinės lygtys su dalinėmis išvestinėmis, aprašančios biojutiklyje vykstančias reakcijas ir difuzijas. Pagal matematinį modelį yra sudaromas skaitinis modelis. Pagal žinomus analizinius sprendimus modelis yra ratifikuojamas. Remiantis skaitiniu modeliu buvo sukurta programinė įranga įgyvendinanti diferencialinių lygčių su dalinėmis išvestinėmis sprendimo metodą (išreikštinę baigtinių skirtumų schemą) ir simuliuojanti biojutiklio veikimą. Programinė įranga yra karkasas, leidžiantis nagrinėti sumodeliuoto biojutiklio savybes bei charakteristikas. Buvo ištirtos substrato ir mediatoriaus koncentracijų, mediatoriaus, fermento, difuzijos sluoksnių, bei mediatoriaus sluoksnio difuzijos koeficiento įtakos biojutiklio generuojamos srovės tankiui. Be to gauti dviejų modelių palyginimo rezultatai parodė sumodeliuoto biojutiklio modelio skirtumus ir panaudojimo prasmingumą. / The aim of master thesis is to model amperometric biosensor with chemically modified electrode, introducing into existing model one more additional mediator layer. Mediator concentration inside the layer is changing during the biosensor action. Master thesis content consists of: enzyme kinetics introduction, biosensor modeling peculiarities exploration, chemically modified electrode information, biosensor action aspects description. Following chapter concentrates on mathematical modeling of particular biosensor type. Mathematical model represents differential equations with partial derivatives describing the reactions and diffusion inside biosensor. Next, numerical model is formulated. The explicit method technique was used. Based on numerical model software was made and validated. Using software the biosensor action was simulated in order to investigate biosensor properties and characteristics. In this work several properties were analyzed: impact of substrate and mediator concentrations, size of mediator, enzyme and diffusion layers, mediator layer diffusion coefficient on biosensor response. This model was compared with previous introduced model and it was shown that there is some difference between them and there is a reason to use new model.

The suspension of the motor vehicle is one of the most important elements of the flexible mounted and inflexible mounted masses of the vehicle bodywork, and most attention is paid to its exploration and improvement. Analysis of models of equivalent oscillation systems of motor vehicles testifies that the evaluation of motor vehicle oscillations and modelling of its motion modes is still very topical and requires further research. Suspension models of motor vehicles offered in publications regard only the influence of road irregularities, and the modernisation of these models is directed towards the improvement of passengers’ comfort. However not much research has been done on the influence of oscillations of flexible mounted and inflexible mounted masses of the bodyworks of vehicles in the process of braking; also there is not much investigation of the post-accident identification of the vehicle’s movement mode corresponding to the deformations of the suspension and the longitudinal pitch of the bodywork. Research of oscillations in the conditions of emergency braking is primarily important for the work in two practical directions: 1) improvement of calculation methods of motor vehicle’s response to external impact in the conditions of real operation; 2) further improvement of research methods on the road, and analysis of fait accompli road accidents related to oscillations in the emergency braking. Methodology defining the oscillations occurring in the braking may be applied... [to full text]

The suspension of the motor vehicle is one of the most important elements of the flexible mounted and inflexible mounted masses of the vehicle bodywork, and most attention is paid to its exploration and improvement. Analysis of models of equivalent oscillation systems of motor vehicles testifies that the evaluation of motor vehicle oscillations and modelling of its motion modes is still very topical and requires further research. Suspension models of motor vehicles offered in publications regard only the influence of road irregularities, and the modernisation of these models is directed towards the improvement of passengers’ comfort. However not much research has been done on the influence of oscillations of flexible mounted and inflexible mounted masses of the bodyworks of vehicles in the process of braking; also there is not much investigation of the post-accident identification of the vehicle’s movement mode corresponding to the deformations of the suspension and the longitudinal pitch of the bodywork. Research of oscillations in the conditions of emergency braking is primarily important for the work in two practical directions: 1) improvement of calculation methods of motor vehicle’s response to external impact in the conditions of real operation; 2) further improvement of research methods on the road, and analysis of fait accompli road accidents related to oscillations in the emergency braking. Methodology defining the oscillations occurring in the braking may be applied... [to full text]