<p>H-mere i H-distribucije su mikrolokalni objekti koji se koriste za ispitivanje jake konvergencije slabo konvergentnog niza u prostorima Lebega i prostorima Soboljeva. H-mere su uveli Tartar i&nbsp; Zerar (koji ih zove mikrolokalne mere defekta), u radovima [34] i [19]. H-mere su Radonove mere koje daju informacije o mogu &acute; cim oblastima jake konvergencije slabo konvergentnog<em> L</em>² niza. Da bismo mogli da posmatramo i slabo konvergentne<em> L</em>^p nizove za 1 &lt; p &lt; &infin;, Antonić&nbsp; i Mitrović u radu [11] uvode H-distribucije.</p><p>U disertaciji dajemo konstrukciju H-distribucija za slabo konvergentne nizove u <em>W</em>^-k,p prostorima, kad je 1 &lt; p &lt; &infin;, k &isin; ℕ&nbsp;i pokazujemo da kada je H-distribucija pridružena slabo konvergetnim nizovima jednaka nuli za sve test funkcije, onda imamo lokalno jaku konverenciju datog niza.</p><p>Takođe je pokazan i lokalizacijski princip, koji nam daje oblast u kojoj imamo lokalno jaku&nbsp; konvergenciju slabo konvergentnog niza. H-mere i H-distribucije deluju na test funkcije &phi;&nbsp;i &psi;&nbsp;(odgovarajuće regularnosti) koje su definisane na ℝ^d i S^d-1 (jedinična sfera u ℝ^d), pri&nbsp; čemu je funkcija &psi;, koju zovemo množilac, ograničena. U disertaciji uvodimo i H-distribucije sa neograničenim simbolom, pri čemu posmatramo slabo&nbsp; konvergentne nizove u Beselovim H^p_-s prostorima, gde je 1 &lt; p &lt; &infin;; s &isin; ℝ. U ovom delu koristimo teoriju pseudo-diferencijalnih operatora i dokazujemo kompaktnost komutatora [<i>A</i>_&psi;, T_&phi;] za razne klase množioca &psi;,&nbsp; &scaron;to je potrebno za dokaz postojanja H-distribucija. Takođe pokazujemo odgovarajuću verziju lokalizacijskog principa.</p> / <p>H-measures and H-distributions are microlocal tools that can be used to investigate strong conver-gence of weakly convergent sequences in the Lebesgue and Sobolev spaces.</p><p>H-measures are introduced by Tartar and G&eacute;rard (as microlocal defect measures) in papers [34] and [19]. H-measures are Radon measures and they provide information about the set of points where given weakly convergent sequence in <em>L</em>² converges strongly. In paper [11], Antonić and Mitrović introduced&nbsp; H-distributions in order to work with weakly convergent <em>L</em>^p sequences.</p><p>In this thesis we give construction of H-distributions for weakly convergent <em>W^-</em>^k,p sequences, where 1 &lt; p &lt; &infin;; k &isin;&nbsp;N. We show that if the H-distribution corresponding to given weakly convergent sequence is equal to zero, then we have locally strong convergence of the sequence. We also prove localization principle.</p><p>H-measures and H-distributions act on test functions &phi; and &psi;&nbsp;(regular enough) which are defined on ℝ^d and ^d-1 (unit sphere in ℝ^d ) and the function &psi;, which is called multiplier, is bounded. We also introduce H-distributions with unboundedmultipliers and in this&nbsp; case we assume that weakly convergent sequences are in Bessel potential spaces H^p_-s , where 1 &lt; p &lt; &infin;, s &isin; ℝ. Theory of pseudo-differential operators is used in construction of H-distributions with unbounded multipliers. We prove compactness of the commutator [<em>A</em>_{<em>&psi;</em>},T_&phi; ] for different classes of multipliers y and appropriate version of localization principle.</p>

<p>Disertacija se bavi iterativnim postupcima za simultano određivanje nula polinoma. Glavna pažnja je posvećena problemu izbora početnih aproksimacija koje omogućavaju sigurnu konvergenciju razmatranih postupaka. Koristeći originalne metode zasnovano na teoremama o lokalizaciji nula polinoma i konvergenciji nizova, konstruisani su računski proverljivi početni uslovi koji garantuju konvergenciju najče&scaron;će kori&scaron;ćenih simultanih postupaka.</p> / <p>Dissertation deals with iterative methods for simultaneous determination of polynomial zeros. The main attention is devoted to the problem of the choice of initial approximations which provide a safe convergence of the considered methods. Using original methods based on suitable localization theorems for polynomial zeros and the convergence of sequences, computationally verifiable initial conditions that guarantee convergence of the most frequently used simultaneous methods are constructed.</p>

Magistro baigiamojo darbo tema yra aktuali, nes Europos Sąjungos bendrosios pinigų politikos sukūrimas bei funkcionavimas yra ypatingai svarbus žingsnis Europos integracijoje, atveriantis kelią galutiniam politiniam valstybių narių suartėjimui. Todėl detali šios Europos Sąjungos politikos srities studija yra būtina siekiant pažinti ateities integracinių procesų galimybes bei iššūkius. Paskutinė euro zonos plėtra įvyko 2009 m. sausio 1 d., kuomet Slovakijoje įvesta euro valiuta. Europos Bendrijos valiutą naudojančių ES valstybių narių skaičius padidėjo ik šešiolikos. Nors Estija kol kas dar nėra pasiekusi visiškos integracijos EPS procese, tačiau 2010 m. gegužės mėn. Europos Komisija oficialiai pasiūlė Estijai nuo ateinančių metų sausio 1 d. prisijungti prie euro zonos. Tyrimo tikslas – įvertinti Slovakijos ir Estijos ekonominę ir teisinę konvergenciją. Atsižvelgiant į tyrimo tikslą ir iškeltus uždavinius, darbe teoriniu aspektu apžvelgiami Europos ekonominės ir pinigų sąjungos kūrimo etapai, išryškinami dalyvavimo ekonominėje ir pinigų sąjungoje privalumai ir trūkumai; išanalizuojama Europos centrinio banko bei kitų Europos Sąjungos institucijų politika euro zonos plėtros procese; įvertinamas Slovakijos ir Estijos makroekonominių rodiklių atitikimas Mastrichto konvergencijos kriterijams bei Europos Sąjungos ir šių šalių nacionalinės teisės harmonizavimas, bei pateikiamas Slovakijos naudos euro zonoje įvertinimas ir Estijos pasiruošimas prisijungti prie ekonominės ir pinigų... [toliau žr. visą tekstą] / Subject of the final master’s thesis is topical, because development and functioning of the common European Union monetary policy is especially important step in European integration, opening the way for final political approach of the member states. Thus a detailed study of this sphere of the European Union politics is necessary striving to cognize possibilities and challenges of the future integration processes. The last expansion in the Euro-area happened on 1 January 2009, when the euro was introduced in Slovakia. A number of the EU member states that use the currency of the European Union increased up to sixteen. Though Estonia still hasn’t reached complete integration in the EMU process, yet in May 2010 European Commission officially suggested Estonia to join the Euro-area from 1 January 2011. Objective of the research is to assess Slovakia’s and Estonia’s economic and legal convergence. Considering the objective of the research and set tasks, stages of development of the Economic and Monetary Union in Europe are covered in the work in theoretical aspect, advantages and disadvantages of participation in the Economic and Monetary Union are highlighted; policy of the European Central Bank and other institutions of the European Union in the process of euro-area expansion is analysed; conformity of Slovakia’s and Estonia’s macroeconomic indices to criteria of Maastricht convergence and harmonization of the European Union Law and national law of the mentioned countries and... [to full text]

Lietuvoje privatūs asmenys (spekuliantai) vis dažniau pasirenka įvairesnes investicijos formas. Viena iš sparčiai populiarėjančių investicijos formų – prekyba akcijomis Lietuvos vertybinių popierių biržoje tarpininkaujant finansų maklerių įmonėms. Investuotojai/spekuliantai norėtų žinoti, ar teorijoje aprašyta techninė analizė gali suteikti pakankamai informacijos, kad būtų galima apsispręsti, pirkti ar parduoti akcijas. Darbo tikslas yra nustatyti ar taikytini yra techninės analizės matematiniai modeliai Lietuvos vertybinių popierių rinkoje. Buvo taikomi penki pagrindiniai techninės analizės matematiniai modeliai: - paprastąjį slankųjį vidurkį (SMA); - eksponentinį slankųjį vidurkį (EMA); - slankaus vidurkio konvergencijos ir divergencijos indikatorių (MACD); - santykinio stiprumo indeksą (RSI); - stochastinį indikatorių; Buvo sukurta programinė įranga kuri, analizuodama pagal statistinius duomenis matematinių modelių generuojamus pirkimo pardavimo signalus, skaičiavo prekybos rezultatus. Tyrimo rezultatai parodė, kad krypties indikatorių SMA, EMA bei MACD naudojimas Lietuvos vertybinių popierių rinkoje pasitvirtino. Osciliatorių naudojimas Lietuvos vertybinių popierių rinkoje davė arba prastus arba neigiamus rezultatus. / There are more and more private persons (speculators) who a choosing different types of investment in Lithuania. More people are willing to participate in the stock trade in the Lithuanian stock market with brokers mediation. Investors/speculators are willing to know if technical analysis, that is well described in the theory, can give enough information that could lead to decision to buy or sell the stock. The goal of this study is to identify if the mathematical models, that are described by technical analysis, are possible to use in Lithuanian stock market. The mathematical models are: - simple moving average, SMA; - exponential moving average, EMA; - moving average convergence and divergence, MACD; - relative strength indicator, RSI; - Stochastic oscillator. The software was developed to calculate the result of all possible trades. All trades were made after receiving the signals according to mathematical calculations when statistic data where entered. The result of the study proved with positive results the use of trend indicators like SMA, EMA and MACD in Lithuanian stock market. The use of oscillators is not offered to use in Lithuanian stock market according to study results.

<p>U tezi se istražuje uniformna konvergencija Galerkinovog postupka konačnih elemenata na mrežama različitog tipa za dvoparametarske singularno&nbsp;perturbovane probleme.</p><p>Uvedene su slojno-adaptivne mreže za probleme konvekcije-reakcije-difuzije: &nbsp;Bahvalovljeva, Duran-&Scaron;i&scaron;kinova i Duranova za jednodimenzionalni i&nbsp;Duran-&Scaron;i&scaron;kinova i Duranova mreža za dvodimenzionalni problem. Za pomenute&nbsp;probleme na svim ovim mrežama analizirane su gre&scaron;ke interpolacije,&nbsp;diskretizacije i gre&scaron;ka u energetskoj normi i dokazana je uniformna konvergencija&nbsp;Galerkinovog postupka konačnih elemenata. Sva teorijska tvrđenja su&nbsp;potvrđena numeričkim eksperimentima.<br />&nbsp;</p> / <p>The thesis explores the uniform convergence for Galerkin nite element<br />method on various meshes for two parameter singularly perturbed problems.<br />Layer-adapted meshes are introduced for convection-reaction-diusion<br />problems: Bakhvalov, Duran-Shishkin and Duran meshes for a one dimensional<br />and Duran-Shishkin and Duran meshes for a two dimensional problem.<br />We analyze the errors of interpolation, discretization and error in the energy<br />norm and prove the parameter uniform convergence for Galerkin nite element<br />method on mentioned meshes. Numerical experiments support theoretical<br />ndings.<br />&nbsp;</p>

<p>Algorithmic trading is an automated process of order execution on electronic stock markets. It can be applied to a broad range of financial instruments, and it is&nbsp; characterized by a signicant investors&#39; control over the execution of his/her orders, with the principal goal of finding the right balance between costs and risk of not (fully) executing an order. As the measurement of execution performance gives information whether best execution is achieved, a signicant number of diffeerent benchmarks is&nbsp; used in practice. The most frequently used are price benchmarks, where some of them are determined before trading (Pre-trade benchmarks), some during the trading&nbsp; day (In-traday benchmarks), and some are determined after the trade (Post-trade benchmarks). The two most dominant are VWAP and Arrival Price, which is along with other pre-trade price benchmarks known as the Implementation Shortfall (IS).</p><p>We introduce Negative Selection as a posteriori measure of the execution algorithm performance. It is based on the concept of Optimal Placement, which represents the ideal order that could be executed in a given time win-dow, where the notion of ideal means that it is an order with the best execution price considering&nbsp; market &nbsp;conditions&nbsp; during the time window. Negative Selection is dened as a difference between vectors of optimal and executed orders, with vectors dened as a quantity of shares at specied price positionsin the order book. It is equal to zero when the order is optimally executed; negative if the order is not (completely) filled, and positive if the order is executed but at an unfavorable price.</p><p>Negative Selection is based on the idea to offer a new, alternative performance measure, which will enable us to find the&nbsp; optimal trajectories and construct optimal execution of an order.</p><p>The first chapter of the thesis includes a list of notation and an overview of denitions and theorems that will be used further in the thesis. Chapters 2 and 3 follow with a&nbsp; theoretical overview of concepts related to market microstructure, basic information regarding benchmarks, and theoretical background of algorithmic trading. Original results are presented in chapters 4 and 5. Chapter 4 includes a construction of optimal placement, definition and properties of Negative Selection. The results regarding the properties of a Negative Selection are given in [35]. Chapter 5 contains the theoretical background for stochastic optimization, a model of the optimal execution formulated as a stochastic optimization problem with regard to Negative Selection, as well as original work on nonmonotone line search method [31], while numerical results are in the last, 6th chapter.</p> / <p>Algoritamsko trgovanje je automatizovani proces izvr&scaron;avanja naloga na elektronskim berzama. Može se primeniti na &scaron;irok spektar nansijskih instrumenata kojima se trguje na berzi i karakteri&scaron;e ga značajna kontrola investitora nad izvr&scaron;avanjem njegovih naloga, pri čemu se teži nalaženju pravog balansa izmedu tro&scaron;ka i rizika u vezi sa izvr&scaron;enjem naloga. S ozirom da se merenjem performasi izvr&scaron;enja naloga određuje da li je postignuto najbolje izvr&scaron;enje, u praksi postoji značajan broj različitih pokazatelja. Najče&scaron;će su to pokazatelji cena, neki od njih se određuju pre trgovanja (eng. Pre-trade), neki u toku trgovanja (eng. Intraday), a neki nakon trgovanja (eng. Post-trade). Dva najdominantnija pokazatelja cena su VWAP i Arrival Price koji je zajedno sa ostalim &quot;pre-trade&quot; pokazateljima cena poznat kao Implementation shortfall (IS).</p><p>Pojam negative selekcije se uvodi kao &quot;post-trade&quot; mera performansi algoritama izvr&scaron;enja, polazeći od pojma optimalnog naloga, koji predstavlja idealni nalog koji se&nbsp; mogao izvrsiti u datom vremenskom intervalu, pri ćemu se pod pojmom &quot;idealni&quot; podrazumeva nalog kojim se postiže najbolja cena u trži&scaron;nim uslovima koji su vladali&nbsp; u toku tog vremenskog intervala. Negativna selekcija se defini&scaron;e kao razlika vektora optimalnog i izvr&scaron;enog naloga, pri čemu su vektori naloga defisani kao količine akcija na odgovarajućim pozicijama cena knjige naloga. Ona je jednaka nuli kada je nalog optimalno izvr&scaron;en; negativna, ako nalog nije (u potpunosti) izvr&scaron;en, a pozitivna ako je nalog izvr&scaron;en, ali po nepovoljnoj ceni.</p><p>Uvođenje mere negativne selekcije zasnovano je na ideji da se ponudi nova, alternativna, mera performansi i da se u odnosu na nju nađe optimalna trajektorija i konstrui&scaron;e optimalno izvr&scaron;enje naloga.</p><p>U prvom poglavlju teze dati su lista notacija kao i pregled definicija i teorema&nbsp; neophodnih za izlaganje materije. Poglavlja 2 i 3 bave se teorijskim pregledom pojmova i literature u vezi sa mikrostrukturom trži&scaron;ta, pokazateljima trgovanja i algoritamskim trgovanjem. Originalni rezultati su predstavljeni u 4. i 5. poglavlju. Poglavlje 4 sadrži konstrukciju optimalnog naloga, definiciju i osobine negativne selekcije. Teorijski i praktični rezultati u vezi sa osobinama negativna selekcije dati su u [35]. Poglavlje 5 sadrži teorijske osnove stohastičke optimizacije, definiciju modela za optimalno izvr&scaron;enje, kao i originalni rad u vezi sa metodom nemonotonog linijskog pretraživanja [31], dok 6. poglavlje sadrži empirijske rezultate.</p>

<p>The Ph.D. thesis addresses a comprehensive study of the bee colony<br />optimization meta-heuristic method (BCO). Theoretical analysis of the<br />method is conducted with the tools of probability theory. Necessary and<br />sufficient conditions are presented that establish convergence of the BCO<br />method towards an optimal solution. Three parallelization strategies and five<br />corresponding implementations are proposed for BCO for distributed-memory<br />systems. The influence of method&rsquo;s parameters on the performance of the<br />BCO algorithm for two combinatorial optimization problems is analyzed<br />through the experimental study.</p> / <p>Докторска дисертације се бави испитивањем метахеуристичке методе<br />оптимизације колонијом пчела. Извршена је теоријска анализа<br />асимптотске конвергенције методе посматрањем конвергенције низа<br />случајних променљивих. Установљени су довољни и потребни услови<br />за које метода конвергира ка оптималном решењу. Предложене су три<br />стратегије паралелизације и пет одговарајућих имплементација конст-<br />руктивне варијанте методе за рачунаре са дистрибуираном меморијом.<br />Извршено је експериментално испитивање утицаја параметара методе<br />на њене перформансе за два различита комбинаторна проблема:<br />проблем распоређивања и проблем задовољивости.</p> / <p>Doktorska disertacije se bavi ispitivanjem metaheurističke metode<br />optimizacije kolonijom pčela. Izvršena je teorijska analiza<br />asimptotske konvergencije metode posmatranjem konvergencije niza<br />slučajnih promenljivih. Ustanovljeni su dovoljni i potrebni uslovi<br />za koje metoda konvergira ka optimalnom rešenju. Predložene su tri<br />strategije paralelizacije i pet odgovarajućih implementacija konst-<br />ruktivne varijante metode za računare sa distribuiranom memorijom.<br />Izvršeno je eksperimentalno ispitivanje uticaja parametara metode<br />na njene performanse za dva različita kombinatorna problema:<br />problem raspoređivanja i problem zadovoljivosti.</p>

In this masterwork author presents a concept of the European monetary union, main features and steps of creating this union; also defines benefits and costs of entering the euro zone. The legal regulation of economic convergence requirements and its practice are analyzed comprehensively. In this work author detects harmonization areas of legal acts between European Community and national legal acts, presents a necessity and ways of this harmonization and reviews the most important regulations in Lithuania, witch must be harmonized.

<p>U doktorskoj diseratciji posmatrani su singularni nelinearni problemi. U prvom&nbsp;poglavlju predstavljene su oznake i osnovne definicije i teoreme koje se koriste u&nbsp;disertaciji. U drugom poglavlju prikazani su poznati postupci i njihovo pona&scaron;anje&nbsp;u slučajevima da je re&scaron;enje regularno ili singularno. Takođe su pokazane poznate&nbsp;modifikacije ovih postupaka kako bi se pobolj&scaron;ala konvergencija. Posebno su&nbsp;predstavljena četiri kvazi-Njutnova metoda i predložene njihove modifikacije u&nbsp;slučaju singularnosti re&scaron;enja. U trećem poglavlju predstavljeni su teorijski okvir&nbsp;pri definisanju graničnih sistema i neki poznati algoritmi za njihovo re&scaron;avanje i&nbsp;definisan je novi algoritam koji je podjednako efikasan ali jeftiniji za rad jer ne&nbsp;uključuje izračunavanje izvoda. Takođe, predložena je kombinacija definisanog&nbsp;algortitma sa metodom negativnog gradijenta, kao i algoritam koji predstavlja&nbsp;primenu poznatog algoritma na definisani granični sistem. U četvrtom poglavlju&nbsp;predstavljeni su numerički rezultati dobijeni primenom definisanih algoritama na&nbsp;relevantne primere i potvrđeni su teorijski dobijeni rezultati.</p> / <p>In this doctoral thesis nonlinear singular problems were observed. The first&nbsp;chapter presents basic definitions and theorems that are used in the thesis. The&nbsp;second chapter presents several methods that are commonly used and their&nbsp;behavior if the solution is regular or singular. Also, some known modifications to&nbsp;these methods are presented in order to improve convergence. In addition four&nbsp;quasi-Newton methods and their modifications in the case the singularity of the&nbsp;solution. The third chapter consists of the theoretical foundation for defining the&nbsp;bordered system, some known algorithms for solving them and new algorithm is&nbsp;defined to accelerate convergence to a singular solution. New algorithm is&nbsp;efficient but cheaper for the use since there is no derivative evaluations in it. It is&nbsp;presented synthesis of new algorithm with negative gradient method and using&nbsp;one of well known method on the bordered system as well. The fourth chapter&nbsp;presents the numerical results obtained by the defined algorithms on the relevant&nbsp;examples and theoretical results are confirmed.</p>

<p>The linear complementarity problems (LCP) arise from linear or quadratic programming, or from a variety of other particular application problems, like boundary problems, network equilibrium problems,contact problems, market equilibria problems, bimatrix games etc. Recently, many people have focused on the solver of LCP with a matrix having some kind of special property, for example, when this matrix is an H+-matrix, since this property is a sufficient condition for the existence and uniqueness of the soluition of LCP. Generally speaking, solving LCP can be approached from two essentially different perspectives. One of them includes the use of so-called direct methods, in the literature also known under the name pivoting methods. The other, and from our perspective - more interesting one, which we actually focus on in this thesis,<br />is the iterative approach. Among the vast collection of iterative solvers,our choice was one particular class of modulus based iterative methods.Since the subclass of modulus based-methods is again diverse in some sense, it can be specialized even further, by the introduction and the use of matrix splittings. The main goal of this thesis is to use the theory of H -matrices for proving convergence of the modulus-based multisplit-ting methods, and to use this new technique to analyze some important properties of iterative methods once the convergence has been guaranteed.</p> / <p>Problemi linearne komplementarnosti (LCP) se javljaju kod problema linearnog i kvadratnog programiranja i kod mnogih drugih problema iz prakse, kao &scaron;to su, na&nbsp; primer, problemi sa graničnim slojem, problemi mrežnih ekvilibrijuma, kontaktni problemi, problemi određivanja trži&scaron;ne ravnoteže, problemi bimatričnih igara i mnogi drugi. Ne tako davno, veliki broj autora se bavio razvijanjem postupaka za re&scaron;avanje LCP sa matricom koja ispunjava neko specijalno svojstvo, na primer, da pripada klasi H+-matrica, budući da je dobro poznato da je ovaj uslov dovoljan da obezbedi egzistenciju i jedinstvenost re&scaron;enja LCP. Uop&scaron;teno govoreći, re&scaron;avanju LCP moguce&nbsp; je pristupiti dvojako. Prvi pristup podrazumeva upotrebu takozvanih direktnih metoda, koje su u literaturi poznate i pod nazivom metode pivota. Drugoj kategoriji, koja je i sa stanovi&scaron;ta ove teze interesantna, pripadaju iterativni postupci. S obzirom da je ova kategorija izuzetno bogata, mi smo se opredelili za jednu od najznačajnijih varijanti, a&nbsp; to je modulski iterativni postupak. Međutim, ni ova odrednica nije dovoljno adekvatna, budući da modulski postupci obuhvataju nekolicinu različitih pravaca. Zato smo se odlučili da posmatramo postupke koji se zasnivaju na razlaganjima ali i vi&scaron;estrukim razlaganjima matrice. Glavni cilj ove doktorske disertacije jeste upotreba teorije H -matrica u teoremama o konvergenciji modulskih metoda zasnovanih na multisplitinzima matrice i kori&scaron;ćenje ove nove tehnike, sa ciljem analize bitnih osobina, nakon &scaron;to je konvergencija postupka zagarantovana.</p>