Nagrinėjamas funkcijos minimizavimo uždavinys. Išanalizuoti metodai, kuriais remiantis išsprendžiamas funkcijos minimizavimo uždavinys. Išanalizuota Lukaso skaičių įtaka funkcijos optimizavimo uždavinių sprendimui. / The main objective of this work is to find out how Lucas numbers influence unimodal function optimization. Here are analyzed Fibonacci method and golden section method, in this master thesis.

<p>Konačni rezultat koji se odnosi na prvi deo istraživanja u ovoj disertaciji ogleda se<br />u definisanju i evaluaciji modela optimizacije rangiranja op&scaron;tina i katastarskih<br />op&scaron;tina. Predložena metodologija, zasnovana na definisanom modelu, može u<br />značajnoj meri pomoći donosiocu odluke kod izbora op&scaron;tine ili katastarske op&scaron;tine<br />za pokretanje komasacionih projekata. Konačni rezultat koji se odnosi na drugi<br />deo istraživanja u ovoj disertaciji ogleda se u detaljnom definisanju i evaluaciji<br />modela optimizacije radova u fazi planiranja komasacionih projekata, koji<br />omogućava ostvarenje osnovnih ciljeva projekata: da se celokupan obim posla<br />izvr&scaron;i u zahtevanom kvalitetu, u predviđenom vremenu, sa planiranim tro&scaron;kovima i<br />potpunom eliminacijom ili ublažavanjem uticaja rizika na realizaciju projekta.</p> / <p>The final result which is related to the first part of the research in this thesis is<br />reflected in the definition and evaluation of optimization models ranking of<br />municipalities and cadastral municipalities. The proposed methodology is<br />based on a defined model can significantly help the decision maker in the<br />selection of municipalities or cadastral municipalities to start the land<br />consolidation projects. The final result which relates to the second part of the<br />research in this thesis is reflected in the detailed definition of the evaluation<br />model and optimization works in the planning phase of land consolidation<br />projects, which enables the realization of the basic targets of this projects:<br />that the entire scope of work perform in the required quality, in the allotted<br />time, the planned costs and complete elimination or diffusing of the impact of<br />risk on the project.</p>

Baigiamajame darbe atliktas tiltin÷s santvaros, iš metalinių profiliuočių, konstrukcijos formos ir strypų skerspjūvių optimizavimas, esant vienam ir dviems apkrovų variantams. Konstrukcija projektuota atsižvelgiant į STR reikalavimus. Tam buvo spręstas netiesinio programavimo uždavinys. Sudarytos nagrinėjamo modelio pagrindinės priklausomybės taikant pusiausviruosius baigtinius elementus. Jų pagrindu sudaryta konstrukcijos optimizavimo programa MATLAB aplinkoje. Naudojantis ją, nustatyta optimali konstrukcijos struktūra ir optimalūs strypų skerspjūviai, esant minimaliam konstrukcijos tūriui, taikant ir netaikant santvaros aukščio ribojimą. Suformuluotos išvados. Darbą sudaro 6 dalys: įvadas, santvaros skaičiuojamoji schema ir apkrovų deriniai, santvaros įtempių ir deformacijų būvio analizė taikant pusiausviruosius baigtinius elementus, konstrukcijos masės minimizavimo uždavinys,optimizavimo rezultatai, išvados, literatūros sąrašas. Darbo apimtis – 67 p. teksto be priedų, 19 iliustr., 11 lent., 26 bibliografiniai šaltiniai. Atskirai pridedami darbo priedai. / In the work bridge truss made of steel cross sections was optimized. There was both form of truss and cross sections optimized according to one, and two loads combinations. Construction was design by STR (Lithuanian national design codes). For the mathematical nonlinear programing problem was solved. The main equations inequality of structure analyze discrete model was made using finite elements method. Basing on them program for optimization in Matlab language was made. By that program, optimal truss form and cross sections was found by minimizing structure volume. Six projects were found including and not including limitation of truss high. Structure: introduction, truss analytical scheme and load combinations, truss analysis using finite element method, construction mass minimization, optimal structure results, conclusions and suggestions, references. Thesis consist of: 67 p. text without appendixes, 19 pictures, 11 tables, 26 bibliographical entries. Appendixes included.

Disertaciniame darbe aprašyti autoriaus sudaryti geometriškai netiesinių tamprių plastinių statybinių strypinių konstrukcijų skaičiavimo ir optimizavimo uždavinių, ribojant konstrukcijos poslinkius, matematiniai modeliai. Sukurtas geometriškai netiesinių erdvinių strypinių konstrukcijų optimizavimo, ribojant poslinkius, uždavinio sprendimo originalus algoritmas. Disertaciją sudaro įvadas, trys skyriai, rezultatų apibendrinimas, naudotos literatūros ir autoriaus publikacijų disertacijos tema sąrašai bei 8 priedai. Įvadiniame skyriuje aptariama tiriamoji problema, aprašomas tyrimų objektas ir metodai, formuluojamas darbo tikslas bei uždaviniai, aprašomas darbo mokslinis naujumas bei aktualumas, darbo rezultatų praktinė reikšmė. Įvado pabaigoje pristatomos disertacijos tema autoriaus paskelbtos publikacijos ir pranešimai konferencijose bei disertacijos struktūra. Pirmajame skyriuje analizuojamos projektavimo ir konstrukcijų optimizavimo uždavinių sąsajos, pateikiama trumpa konstrukcijų optimizavimo metodų analitinė apžvalga. Nagrinėjama netamprių geometriškai netiesinių plieninių rėminių konstrukcijų optimizavimo ribojant poslinkius problematika. Aprašomos pasirinktos pagrindinės prielaidos ir fizinės priklausomybės bei dydžiai, apibrėžiantys konstrukcijos įtemptąjį-deformuotąjį būvį (ĮDB). Pateikiamas konstrukcijų optimizavimo uždavinio matematinis modelis. Pasiūlomas algoritmas šiam uždaviniui spręsti. Apžvelgiamos optimizavimo uždavinio skaitinės realizacijos galimybės... [toliau žr. visą tekstą] / The optimization mathematical models of geometrically nonlinear elastic plastic frameworks structures optimization under displacement constraints are created in the thesis. Original solution algorithm was created for the optimization of geometrically nonlinear elastic-plastic frameworks structures under displacement constraints. The dissertation consists of introduction, 3 chapters, conclusions, references and 8 annexes. The introduction reveals the investigated problem, the object of research and describes the purpose and tasks of the thesis, research methodology, scientific novelty, the practical significance of results examined in the thesis. The introduction ends in presenting the author’s publications on the subject of the defended dissertation, offering the material of made presentations in conferences and defining the structure of the dissertation. Construction design and structures optimization problems correlation is describing in chapter 1. Short historical review of optimization methods and structures optimization analytical analysis are presented. Reviewing problematic of non-elastic geometrically nonlinear steel frame structures optimization under displacements constraints. Describing basic accepted assumptions and physical dependences and values describing structures real stress-strain state (SSS). Structure optimization problem mathematical model is presented. Algorithm for such optimization problem solution is suggested. Optimization problem numerical... [to full text]

<p>Hemijskim transformacijama se iz biljnih ulja dobijaju vredni &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; derivati, poput epoksidovanih biljnih ulja, koji se<br />koriste u hemijskoj i polimernoj industriji. Kvalitet, pa<br />time i primena epoksidovanih biljnih ulja, zavise od<br />sadržaja epoksidnih grupa u derivatizovanom ulju, koji bi<br />trebalo da je &scaron;to veći. Kako epoksidne grupe nastaju<br />oksidacijom dvostrukih veza u trigliceridima kao<br />dominantnoj grupi jedinjenja u biljnim uljima, pogodna<br />sirovina za epoksidovanje su visoko nezasićena ulja,<br />kakvo je laneno.<br />Proizvodnja epoksidovanih biljnih ulja zahteva izbor<br />takvih procesnih uslova pri kojima bi se postigli &scaron;to<br />potpunija konverzija dvostrukih veza i &scaron;to veća<br />selektivnost procesa u odnosu na epoksidnu grupu. Zato je<br />kao cilj ove doktorske disertacije postavljeno određivanje<br />optimalnih vrednosti procesnih uslova epoksidovanja<br />lanenog ulja persirćetnom kiselinom formiranom in situ iz<br />sirćetne kiseline i 30% vodenog rastvora vodonik<br />peroksida u prisustvu jonoizmenjivačke smole kao<br />katalizatora. Određivanje je izvedeno primenom<br />metodologije odzivne povr&scaron;ine, kao i kori&scaron;ćenjem u ovoj<br />disertaciji predloženih kinetičkih modela ispitivanog<br />reakcionog sistema, u oba slučaja sa maksimumom<br />relativnog prinosa epoksida kao funkcijom cilja.<br />Ispitivanje uticaja procesnih uslova, i to temperature,<br />molskog odnosa reaktanata, količine katalizatora i brzine<br />me&scaron;anja, na tok procesa epoksidovanja je bilo osnov za<br />definisanje graničnih vrednosti procesnih uslova unutar<br />kojih je tražen maksimum prinosa epoksida. Oblast dugih<br />vremena reagovanja, koja nije od interesa za industriju, je<br />izbegnuta adekvatnim izborom temperature.<br />Pri optimalnim vrednostima procesnih uslova<br />epoksidovanja lanenog ulja, određenim primenom<br />metodologije odzivne povr&scaron;ine, postignuto je dobro<br />slaganje očekivane i eksperimentalno određene vrednosti<br />maksimalnog relativnog prinosa epoksida, sa odstupanjem<br />od 3,28%.<br />Za potrebe određivanja optimalnih uslova izvođenja<br />procesa epoksidovanja biljnih ulja kori&scaron;ćenjem kinetičkih<br />modela, razvijena su tri pseudohomogena modela<br />ispitivanog trofaznog multireakcionog sistema. Pored<br />kinetike osnovnih reakcija formiranja persirćetne kiseline i&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; reakcije epoksidovanja dvostrukih veza triglicerida biljnog ulja,&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; kao i kinetike sporedne reakcije otvaranja epoksidne<br />grupe sa sirćetnom kiselinom, u predloženim modelima je<br />uzeta u obzir i raspodela sirćetne i persirćetne kiseline<br />između uljne i vodene faze sistema. Opisan je i uticaj<br />masno-kiselinskog sastava ulja, odnosno broja dvostrukih<br />veza u masno-kiselinskim lancima triglicerida, na kinetiku<br />reakcija. Za koeficijent raspodele sirćetne kiseline između<br />tečnih faza reakcionog sistema predložena je empirijska<br />korelacija koja je dala dobro slaganje izračunatih<br />vrednosti sa eksperimentalnim podacima. Kinetički<br />parametri modela su određeni fitovanjem<br />eksperimentalnih podataka o promenama količina<br />dvostruke veze i epoksidne grupe sa vremenom izvođenja<br />procesa epoksidovanja. Na osnovu statističkih pokazatelja<br />uspe&scaron;nosti fitovanja eksperimentalnih podataka, potvrđena<br />je prepostavka da je pseudohomogeni model publikovan u<br />literaturi unapređen uzimanjem u obzir pomenutih<br />fenomena raspodele komponenata reakcione sme&scaron;e i<br />masno-kiselinskog sastava sirovine pri modelovanju<br />reakcionog sistema epoksidovanja biljnih ulja<br />persirćetnom kiselinom.<br />Kori&scaron;ćenjem predloženih pseudohomogenih modela<br />reakcionog sistema za određivanje optimalnih uslova<br />izvođenja procesa epoksidovanja lanenog ulja in situ<br />formiranom persirćetnom kiselinom u prisustvu<br />jonoizmenjivačke smole, dobijeno je odstupanje od 5,51%<br />očekivane od eksperimentalno određene vrednosti<br />relativnog prinosa epoksida.<br />Bolje slaganje predviđene sa eksperimentalno određenom<br />vredno&scaron;ću relativnog prinosa epoksida u kontrolnom<br />eksperimentu je dobijeno primenom metodologije odzivne<br />povr&scaron;ine u poređenju sa kori&scaron;ćenjem kinetičkih modela pri<br />određivanju optimalnih vrednosti procesnih uslova. To je i<br />očekivano, s obzirom da regresiona jednačina kori&scaron;ćena u<br />okviru metodologije odzivne povr&scaron;ine bolje fituje relativni<br />prinos epoksida. Standardna devijacija relativnog prinos<br />epoksida za regresionu jednačinu je 8,9 puta niža od one<br />izračunate za kinetički model koji najbolje predviđa<br />optimalne procesne uslove epoksidovanja lanenog ulja<br />persirćetnom kiselinom.</p> / <p>Vegetable oils can be transformed into added value<br />products by various chemical modifications, such as<br />epoxidation. The epoxidized vegetable oils have a<br />wide range of applications in the chemical and<br />polymer industry. The quality, and consequently the<br />application, of epoxidized vegetable oil is influenced<br />by the epoxy group content. Since the epoxy groups<br />are formed by the oxidation of double bonds in<br />triglycerides, the main constituent of vegetable oils,<br />highly unsaturated vegetable oils, such as linseed<br />oil, are desirable raw materials.<br />The manufacturing of epoxidized vegetable oils<br />requires the optimization of the process conditions<br />in order to achieve complete conversion of double<br />bonds and high selectivity of the process in respect<br />to the epoxy groups. Therefore, the aim of this<br />doctoral thesis is to determine the optimal process<br />conditions for the epoxidation of linseed oil with<br />peracetic acid, formed in situ from acetic acid and<br />30% hydrogen peroxide in the presence of an ion<br />exchange resin as the catalyst. The optimal process<br />conditions were determined by response surface<br />methodology, as well as by using developed pseudohomogeneous<br />kinetic models that describe the<br />investigated reaction system. For both optimization<br />methods, the relative epoxy yield was selected as an<br />objective function to be maximized.<br />The effects of process conditions, such as<br />temperature, molar ratio of reactants, catalyst<br />amount and steering speed, on the kinetics of the<br />epoxidation were studied in order to define<br />constraints for the optimization. To avoid long<br />reaction times, which are not of interest in<br />manufacturing, an adequate temperature range was<br />selected. Under the optimized process conditions for the<br />epoxidation of linseed oil, which were determined<br />by response surface methodology, good agreement<br />between the calculated and experimentally<br />determined relative epoxy yields was achieved<br />within 3.28%.<br />Three models describing the three-phase multireaction<br />system of vegetable oil epoxidation with<br />peracetic acid were developed and further used for<br />the optimization. The models are pseudohomogeneous<br />with respect to the catalyst. Besides<br />the kinetics of the main reactions of peracetic acid<br />and epoxy group formation, the models take into<br />account the side reaction of the epoxy group opening<br />with acetic acid. The partitioning of the acetic acid<br />and peracetic acid between the oil and aqueous<br />phases is considered. In two proposed models, the<br />effect of fatty acid composition on the kinetics of the<br />process is also described by considering the number<br />of double bonds in the fatty acid chains. The<br />developed empirical correlation for the partition<br />coefficient for acetic acid between the liquid phases<br />shows good agreement between the calculated and<br />experimental data. The kinetic parameters of the<br />proposed pseudo-homogeneous models were<br />determined by fitting the experimentally determined<br />changes of the double bond and epoxy group<br />amounts with reaction time of the epoxidation.<br />Statistical values of the models` parameters<br />determination confirmed the hypothesis that the<br />pseudo-homogeneous model proposed in the<br />literature can be improved by considering the<br />partitioning phenomena and the effect of the oil fatty<br />acid composition on the kinetics of the vegetable<br />oils epoxidation with peracetic acid.<br />Under the optimized process conditions for the<br />epoxidation of linseed oil with peracetic acid formed<br />in situ in the presence of the ion exchange resin,<br />which were determined by using proposed pseudohomogeneous<br />models, the experimentally<br />determined relative epoxy yield was 5.51% lower<br />than the calculated.<br />Better agreement between the calculated and<br />experimentally determined values for the relative<br />epoxy yield, achieved under the optimal process<br />conditions, is obtained when the response surface<br />methodology (RSM) was applied as opposed to<br />when the kinetic models were used for the<br />determination of the optimal process conditions.<br />This is in accordance with better fitting of the<br />relative epoxy yield by RSM regression equation<br />than by kinetics models. Standard deviation of the<br />relative epoxy yield for RSM regression equation is 8.9 times lower than the standard deviation for the<br />most successful kinetic model used for prediction of<br />the optimal process conditions for the epoxidation of<br />the linseed oil by peracetic acid.</p>

<p>Na na&scaron;im prostorima napitak crne kafe veoma je cijenjen i ima dugu tradiciju pripreme i konzumiranja. Izborom optimalnih parametara procesa prženja u industrijskim uslovima proizvodnje i definisanjem recepture, nastoji se postići odgovarajući kvaliteta, odnosno najprihvatljivija senzorska svojstava napitka kafe. Da bi kafa na određenom trži&scaron;tu zadovoljila želje i očekivanja poro&scaron;ača, potrebno je definisati parametre kvaliteta kafe za potrebe svakog ciljnog trži&scaron;ta. Primjenom deskriptivne senzorske analize moguće je dati precizan opis arome, ukusa i boje napitka kafe, kao najvažnijih senzorskih svojstava, sa značajnim uticajem na kvalitet i prihvatljivost kvaliteta.<br />Cilj ove doktorske disertacije je postizanje optimalnog senzorskog kvaliteta napitka crne kafe definisanjem parametara procesa prženja kafe u industrijskim uslovim proizvodnje i definisanjem optimalnog odnosa kafe vrste Arabika i kafe vrste Robuste, kao i definisanje senzorskog profila i sistema senzorskog ocjenjivanja napitka crne kafe koji se priprema na tradicionalan način.<br />Da bi se definisali parametri procesa prženja, neophodno je odrediti optimalnu temperaturu prženja, koja će omogućiti razvoj i formiranje prijatnih senzorskih svojstava u zrnu kafe. Za pripremanje napitka crne kafe na tradicionalan način obično se koriste dvije vrste kafe, Arabika i Robusta u različitom odnosu.<br />Na osnovu rezultata dobijenih hemijsko-fizičkim analizama uzoraka različitih vrsta kafa i mje&scaron;avina na različitim temperaturama prženja i senzorskom analizom napitka kafe pripremljenog od ispitivanih uzoraka kafe na tradicionalan način, sa ciljem pobolj&scaron;anja kvaliteta napitka kafe izborom optimalnih uslova prženja i odnosa različitih vrsta kafe može se zaključiti da uzorci napitka kafe pripremljeni od uzoraka proizvedenih prema proizvođačkoj specifikaciji nemaju očekivani kvalitet napitka kafe, kao i da proizvodnjom uzoraka pojedinačnih vrsta kafe pržene na 167&deg;C i 175&deg;C i njihovih mje&scaron;avina nije postignut optimalni kvaliteta napitka kafe. Takođe je zaključeno da je uzorak napitka kafe pržene na 171&deg;C N1 ocjenjen kao uzorak najboljih senzorskih svojstava (82,35%). Odnos kafa Arabika II klasa, Arabika I klasa i Robusta je bio 34,28%:51,42%:14,30%. Vrijednost titracione kiselosti iznosila je 128,86, sadržaj hlorogenske kiseline 3,77%, sadržaj kofeina 2,29%, sadržaj proteina 13,79%, sadržaj slobodne masti 14,37%, odnosno sadržaj ukupno zasićenih masnih kiselina 42,65%, a sadržaj ukupno nezasićenih masnih kiselina 57,36%, vrijednost pH 5,35 i aktivnost vode 0,102. Antioksidativna aktivnost je iznosila 235,57 &mu;mola TE/g uzorka (DPPH) i 217,62 &mu;mola TE/g uzorka (ABTS).<br />Uzorak U1 napitka kafe pripremljen na tradicionalan način od mje&scaron;avine kafe pržene na 171&deg;C, sitno mljevene okarakterisan je kao veoma prijatan za konzumiranje, sa najskladnijim aromatskim profilom, usagla&scaron;ene gorčine i kiselosti, prijatne i umjerene punoće ukusa i blagog i harmoničnog utiska u ustima. Odnos kafa Arabika II klasa, Arabika I klasa i Robusta u ovom uzorku je bio 34,28%:51,42%:14,30%.</p> / <p>Consumption of black coffee prepared in a traditional way is very popular in our region. By selecting the optimum parameters of roasting in industrial conditions and defining ratio of the individual species of coffee, it aims to achieve the appropriate quality, and the most acceptable sensory properties of a coffee beverage. In order to fulfill consumers expectations, it is necessary to define the parameters of quality coffee for the needs of each target market. Using descriptive sensory analysis it is possible to give a precise description of the aroma, taste and color of coffee beverage, as the most important sensory characteristics, with significant impact on the quality and acceptability of quality.<br />The aim of this PhD thesis was to achieve optimal sensory quality black coffee beverage, by defining the parameters of the coffee roasting within the industrial conditions and defining the optimal ratio of coffee Arabica and Robusta species, as well as defining a sensory profile and the system of sensory analysis black coffee beverage which was prepared on traditional way.<br />In order to define the parameters of the roasting process, it is necessary to determine the optimum temperature of roasting, which will enable the development and formation of pleasant sensory properties of coffee beans. For the preparation of coffee beverage in the traditional way, usually used two species of coffee, Arabica and Robusta in different ratio. Based on the results of chemical and physical analysis of coffee samples (different species and blends) at different roasting temperatures and results of sensory analysis of a coffee beverage prepared from coffee samples in the traditional way, with the aim of improving the coffee beverage quality, by determining optimal conditions of roasting and ratio of different species of coffee, it could be concluded that the samples of coffee beverage prepared from samples produced according to the production specification do not had the expected quality of coffee beverage. It also could be concluded that by production of individual species of coffee samples roasted at 167 and 175&deg; C, and their blends was not reached optimal quality of coffee beverage. It was also concluded that the coffee beverage of sample roasted at 171C, N1 was rated as the sample of the best sensory properties (82.35%). The ratio of coffee Arabica Class II, Arabica Class I and Robusta was 34.28%: 51.42%: 14.30%. Value of titratable acidity was 128.86, chlorogenic acid content was 3.77%, caffeine content was 2.29%, protein content was 13.79%, the content of free fat was 14.37%, total content of saturated fatty acids was 42.65%, and total content of unsaturated fatty acids was 57.36%, pH value was 5.35 and aw value was 0.102. The antioxidant activity was amounted 235.57 &mu;mol TE/g sample (DPPH) and 217.62 &mu;mol TE/g sample (ABTS).<br />Coffee beverage prepared in the traditional way from a sample U1 roasted at 171 &deg;C, finely ground, was characterized as very pleasant, with the most harmonious aromatic profile, pleasant bitterness and acidity, pleasant and moderate body and gentle and harmonious impression in the mouth. The ratio of coffee Arabica Class II, Arabica Class I and Robusta in this sample was 34.28%: 51.42%: 14.30%.</p>

Disertaciniame darbe, pasitelkus deformuojamo kūno mechanikos energinius principus ir matematinio programavimo teoriją, iš vieningų pozicijų išnagrinėtos tiek tamprių, tiek tamprių-plastinių sistemų deformacijų darnos (Sen-Venano) lygtys. Sprendžiant energinio principo apie papildomos energijos minimumą pagrindu sudarytą ekstremumo analizės uždavinį, įrodoma, kad yra tik trys nepriklausomos Sen-Venano lygtys su atitinkamai performuotomis kraštinėmis sąlygomis. Prisitaikomumo teorija nagrinėja tamprių-plastinių konstrukcijų, veikiamų kintamos-kartotinės apkrovos, būvį, pasitelkdama tiek tamprumo, tiek plastiškumo teorijų pagrindines lygtis ir priklausomybes: disertaciniame darbe pavyko, pasinaudojant Kuno ir Takerio optimalumo sąlygomis, metodiškai pagrįstai įjungti į plastinį konstrukcijų skaičiavimą liekamųjų deformacijų darnos lygtis. Taigi, disertacijoje Kuno ir Takerio sąlygos originaliai pritaikytos tamprumo teorijos lygtims įtempiais ir asociatyvinio tekėjimo dėsnio išraiškoms plastiškumo teorijoje gauti. Pasinaudojant gautaisiais rezultatais patobulinta prisitaikančių lenkiamų plokščių optimizavimo teorija ir sukurti nauji tokių uždavinių sprendimo metodai. Netiesinių uždavinių matematiniai modeliai, sudaryti taikant pusiausvirų baigtinių elementų metodą, sprendžiami iteraciniu būdu, pasitelkus Rozeno projektuojamųjų gradientų algoritmą. Darbui būdinga tai, kad matematinio programavimo teorija optimizavimo problemos nagrinėjimą lydi nuo matematinio modelio sudarymo iki... [toliau žr. visą tekstą] / Adapted perfectly elastic-plastic structure satisfies strength conditions and it is safe with respect to cyclic-plastic collapse. But it can do not satisfy its serviceability requirements, for instance, stiffness ones. Therefore, not only strength, but also stiffness conditions-constraints should be included in the discrete mathematical models of bending plate parameter or load variation bound optimization problems (exactly such problems are considered in the dissertation). Using mathematical programming not only new optimization technique of bending plates at shakedown is developed, but also relation between Kuhn-Tucker conditions and strain compatibility (Saint-Venant) equations and dependences of associative yield law of the deformable body mechanics is showed in the dissertation. Mathematical models of nonlinear problems are constructed applying method of equilibrium elements and are solved by iterations using Rosen project gradient algorithm. The feature of this research work is that the theory of mathematical programming accompanies investigation of optimization problem from the construction of the mathematical model up to its numerical solution, at the same time revealing mechanical meaning optimality criterion of applied Rosen algorithm.

Darbo autorius: Vismantas Anglickas Tema: Kaštų valdymo sistemos tobulinimas Prano Anglicko individualios įmonės molio masių gamybos procese. Darbo tikslas: • Geriausios alternatyvos pateikimas molio masių gamybos proceso kaštams mažinti Darbo uždaviniai: • Molio masių gamybos proceso aprašymas ir įvertinimas • Defektų ir jų priežasčių analizavimas • Kontrolės metodų įvertinimas • Priemonių nustatymas gamybos kaštams mažinti • Galimų alternatyvų įvertinimas (pakavimo linijos įdiegimas ir t.t.) Tyrimo metodas: • Reaktyvus stebėjimas nedalyvaujant procese Darbo rezultatai: Šis darbas yra ypatingai vertingas įmonei bei įmonės vadovui. Visa darbo esmė yra pagrįsta alternatyvų analizavimu ir geriausio sprendimo kaštams mažinti radimu. Vadybiniuose sprendimuose pateikta informacija turėtų padėti apsispręsti, kokia linkme įmonė turėtų judėti, kad pasiektų norimų rezultatų. Tinkamas problemos sprendimo būdas leis įmonei sėkmingai paskirstyti kaštus gamybos procese ir padidinti pelną maksimaliai. Gamybos kaštai – (firmos) piniginės išlaidos, būtinos visiems gamybos veiksniams apmokėti, už prekės pagaminimą ar paslaugos teikimą. Alternatyva – tikslas arba veiksmas kuris gali būti pasirinktas. Kokybė – produkto atitikimas jo reikalavimams. Optimizacija – apgalvotas taikymas įvairių metodų, kurie turėtų pagreitinti bei pagerinti programos vykdymą ir rasti kainos atžvilgiu geriausia problemos sprendimą. / Author: Vismantas Anglickas Theme: Improvement of clay process cost management in Prano ceramics company. Aim of work: • Give the best alternative for reducing cost in clay production process Work tasks: • Create a schedule of clay production process and evaluate • Defect and their reason analysis • Control method evaluation • Identify ways how to reduce the production cost • Analyze possible alternatives (packing line establishment and etc.) Research method: • Reactive watch without attendance in the process Work results: This work is very valuable for company and its owner. The main aim of the work is to find the best alternative for reducing cost in clay production process. Decision part has to help finding the way that company have to move. Also how to find the solution to the problem and achieve their results. Only suitable problem solving will help company operate successfully in cost effective way and maximize its profit. Production cost – company expenses to cover all production process cost. Alternative – is an object or action which can be chosen. Quality – the standard of something as measured against other things of a similar kind. Optimization – is the use of specific techniques to determine the most cost effective and efficient solution to a problem or design for a process.

Mokyklų tinklo optimizavimas sukėlė itin prieštaringus vertinimus visuomenėje, tiek pedagogų, tiek mokinių tėvų, tiek ir pačių mokinių akimis. Tinklo pertvarkymas išryškino skirtingą požiūrį į švietimui skirtų lėšų ir kitų išteklių panaudojimą Baigiamajame bakalauro darbe nagrinėjamas mokyklų tinklo optimizavimas didmiestyje ir rajone 1995- 2010 metais. Apžvelgiama švietimo įstaigų tinklo struktūra Vilniaus mieste ir Telšių rajone minėtu laikotarpiu. Lyginami mokyklų tinklo pertvarkos procesai. Atskleista mokyklų tinklo pertvarkos esmė ir raiška: teoriniu aspektu išanalizuota švietimo reformos situacija Lietuvoje ir minėtose savivaldybėse, identifikuojami ją lemiantys veiksniai. Tyrimo metu atskleistas Vilniaus miesto ir Telšių rajono pedagogų, bei mokinių tėvų požiūris į Lietuvos švietimo sistemą. Pateikta studijuotų užsienio ir šalies mokslininkų teorinių darbų analizė apie Lietuvos švietimo reformą, išryškintos pagrindinės sąvokos, apžvelgti gauti tyrimo rezultatai. Apibendrinant darbą suformuluotos išvados, teigiančios, kad mokyklų tinklo pertvarka labai ištęsta ir būtina kuo greičiau pabaigti pradėtus darbus, tam, kad galima būtų siekti užsibrėžtų tikslų. / Optimizations of schools’ network arouse very controversial valuation in society, among teachers, parents of the students, and the students themselves. The reform of the network highlighted diverse opinions about the usage of the funds and other resources designated for the education. In the final work for Bachelor degree, the optimization of schools’ network in city and in district in 1995 – 2010 is being analyzed. It also reviews the structure of educational institutions network in Vilnius city and in Telšiai district during the earlier mentioned period. There the schools’ network reform processes are compared. The essence and expression of the schools’ network reform is revealed: the situation of educational reform in Lithuania and in the earlier mentioned municipalities is analyzed using theoretical aspect, and the factors determining the reform are identified. The research revealed the attitude of the teachers and parents of the students in Vilnius city and Telšiai district towards the system of education in Lithuania. Analysis of the studied theoretical works on the educational reform in Lithuania of foreign and national scientists is provided. The main concepts are highlighted, and the results of the research are reviewed. Summarizing the work the conclusions were formulated, and they state that the reform of the schools’ network is too lengthy and it is essential to finalize the work that had been started, so that the goals set could be achieved.

Globaliojo optimizavimo metodai, pagrįsti Lipšico rėžių apskaičiavimu, yra plačiai taikomi įvairių optimizavimo uždavinių sprendimui. Tačiau Lipšico metodai dažniausiai remiasi prielaida, kad Lipšico konstanta žinoma iš anksto, o tai retas atvejis sprendžiant praktinius uždavinius. Todėl Simonos Talačkaitės magistro darbe yra toliau nagrinėjama aktuali ir svarbi problematika iškylanti realizuojant Lipšico metodus nesiremiančius jokiomis išankstinėmis prielaidomis apie Lipšico konstantą. Praktinio tiriamojo pobūdžio magistro darbe iškeliamas toks pagrindinis tikslas: ištirti daugiamačių simpleksinių globaliojo optimizavimo algoritmų su nežinoma Lipšico konstanta efektyvumą priklausomai nuo naudojamo simplekso centro. Šiam tikslui pasiekti buvo iškelti šie uždaviniai: apžvelgti naujausią literatūrą skirta Lipšico metodams su nežinoma Lipšico konstanta; matematiškai išnagrinėti įvairių daugiamačių simplekso centrų apskaičiavimus bendru atveju bei juos realizuoti Matlab aplinkoje; papildyti simpleksinį globaliojo optimizavimo DISIMPL algoritmą šių simpleksų centrų apskaičiavimo paprogramėmis; eksperimentiškai ištirti pasiūlytų rezultatų praktiškumą sprendžiant testinius optimizavimo uždavinius. / This work analyzes Global optimization objectives, the most important it will be algorithms with simplicial Lipšico constant. Also, this work analyzes multidi- mensional DIRECT algorithm. We will provide dividing in higher dimennsions DIRECT algorithm. Then analyzes two simplex and apply the solutions. The hand simplex to smallerpartitions. Perceive multidimensional DIRECT algorithm division rules. In this work wrote a lot about simplicial center about dividing of hyoer-cube. Finally, the experiment it will be about the best way, how we can …nd circle center ir diferent way. Simplex centers using 8 test funkcions , changing the number of iterations and mistakes number. Create tables and to analyzes them. The purpose of this paper work is to introduce the simplex algorithm for global optimization with unknown Lipšicas constant depending on the e¢ ciency of the division of the rules used in the simplex.