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1
Nhangumbe, Clarinda Vitorino. "Lie Analysis for Partial Differential Equations in Finance." Master's thesis, Faculty of Science, 2019. https://hdl.handle.net/11427/31817.
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Weather derivatives are financial tools used to manage the risks related to changes in the weather and are priced considering weather variables such as rainfall, temperature, humidity and wind as the underlying asset. Some recent researches suggest to model the amount of rainfall by considering the mean reverting processes. As an example, the Ornstein Uhlenbeck process was proposed by Allen [3] to model yearly rainfall and by Unami et al. [52] to model the irregularity of rainfall intensity as well as duration of dry spells. By using the Feynman-Kac theorem and the rainfall indexes we derive the partial differential equations (PDEs) that governs the price of an European option. We apply the Lie analysis theory to solve the PDEs, we provide the group classification and use it to find the invariant analytical solutions, particularly the ones compatible with the terminal conditions.
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Bujok, Karolina Edyta. "Numerical solutions to a class of stochastic partial differential equations arising in finance." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:d2e76713-607b-4f26-977a-ac4df56d54f2.
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We propose two alternative approaches to evaluate numerically credit basket derivatives in a N-name structural model where the number of entities, N, is large, and where the names are independent and identically distributed random variables conditional on common random factors. In the first framework, we treat a N-name model as a set of N Bernoulli random variables indicating a default or a survival. We show that certain expected functionals of the proportion LN of variables in a given state converge at rate 1/N as N [right arrow - infinity]. Based on these results, we propose a multi-level simulation algorithm using a family of sequences with increasing length, to obtain estimators for these expected functionals with a mean-square error of epsilon 2 and computational complexity of order epsilon−2, independent of N. In particular, this optimal complexity order also holds for the infinite-dimensional limit. Numerical examples are presented for tranche spreads of basket credit derivatives. In the second framework, we extend the approximation of Bush et al. [13] to a structural jump-diffusion model with discretely monitored defaults. Under this approach, a N-name model is represented as a system of particles with an absorbing boundary that is active in a discrete time set, and the loss of a portfolio is given as the function of empirical measure of the system. We show that, for the infinite system, the empirical measure has a density with respect to the Lebesgue measure that satisfies a stochastic partial differential equation. Then, we develop an algorithm to efficiently estimate CDO index and tranche spreads consistent with underlying credit default swaps, using a finite difference simulation for the resulting SPDE. We verify the validity of this approximation numerically by comparison with results obtained by direct Monte Carlo simulation of the basket constituents. A calibration exercise assesses the flexibility of the model and its extensions to match CDO spreads from precrisis and crisis periods.
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Oladiran, Oladun Solomon, and Scott J. KIrkby. "Computational Studies of the Spin Trapping Behavior of Melatonin and its Derivatives." Digital Commons @ East Tennessee State University, 2019. https://dc.etsu.edu/asrf/2019/schedule/186.
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The presence of excess free radicals in the body can result in severe health consequences because of oxidative damage to cells. Spin traps may be used as a probe to examine radical reactions in cells, but there is a need for less toxic and more lipid soluble examples. Melatonin is one of the numerous antioxidants used to scavenge free radicals in the body and reportedly one of the most efficient radical scavengers known. It is relatively nontoxic and easily crosses the lipid bilayer in cell membranes. Melatonin is thought to undergo a multistep oxidation process and this work investigates the potential for it to be used as a spin trap. The presence of electron withdrawing or donating groups added to melatonin may stabilize an intermediate and allow it to function as a spin trap.
The essence of this study is to conduct a computational inquiry into the relative stability of melatonin, selected derivatives, and the partial oxidation products formed from the scavenging of hydroxyl radical. To determine this, geometries were optimized for each molecule at the DFT/B3LYP/6-31G(d) and HF/6-31G(d) levels of theory.
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Guimarães, Pedro Henrique Engel. "Uma resenha sobre modelos de apreçamento de derivativos." reponame:Repositório Institucional do FGV, 2012. http://hdl.handle.net/10438/10298.
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I present here an approach that unify a variety of derivative pricing models that consists of attaining a Partial Differential Equation(PDE) by intuitive arguments and give its solution by Feynman-Kac method as a conditinal expectation of a markovian process. The expectation is taken in a risk neutral world(or risk neutral measure) where all the assets grow at the risk free rate. I also present how to make this specific change of measure, connecting the real world to the risk neutral world, and show that the relevant element for the measure change is the market price of factor risk. When the market is complete the market price of risk is unique and when the market is incomplete there is a variety of possible prices to the market price of factor risks that satisfy no arbitrage arguments. In the latter case the parameters are usually chosen to calibrate the model to market data.
Apresento aqui uma abordagem que unifica a literatura sobre os vários modelos de apreçamento de derivativos que consiste em obter por argumentos intuitivos de não arbitragem uma Equação Diferencial Parcial(EDP) e através do método de Feynman-Kac uma solução que é representada por uma esperança condicional de um processo markoviano do preço do derivativo descontado pela taxa livre de risco. Por este resultado, temos que a esperança deve ser tomada com relação a processos que crescem à taxa livre de risco e por este motivo dizemos que a esperança é tomada em um mundo neutro ao risco(ou medida neutra ao risco). Apresento ainda como realizar uma mudança de medida pertinente que conecta o mundo real ao mundo neutro ao risco e que o elemento chave para essa mudança de medida é o preço de mercado dos fatores de risco. No caso de mercado completo o preço de mercado do fator de risco é único e no caso de mercados incompletos existe uma variedade de preços aceitáveis para os fatores de risco pelo argumento de não arbitragem. Neste último caso, os preços de mercado são geralmente escolhidos de forma a calibrar o modelo com os dados de mercado.
5
Valenta, Václav. "Moderní metody řešení eliptických parciálních diferenciálních rovnic." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2009. http://www.nusl.cz/ntk/nusl-236712.
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Partial differential equations solution and methods for transformation to a large sets of ordinary equations is described in this work. Taylor series method is important for this work. This method needs higher derivatives for correct work. Ways how to compute higher derivatives are also discused in this work.
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Rosa, Vitor Sales Dias da. "Análise de sensibilidade topológica do modelo de flexão de placas de Reissner-Mindlin." Laboratório Nacional de Computação Científica, 2015. https://tede.lncc.br/handle/tede/222.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Capes)
The topological derivative concept has been proved to be useful in many relevant applications such as topology optimization, inverse problems, image processing, multi-scale constitutive modeling, fracture mechanics and damage evolution modeling. The topological asymptotic analysis has been fully developed for a wide range of problems modeled by partial di erential equations. On the other hand, the topological derivatives associated with coupled problems have been derived only in their abstract forms. In this paper, therefore, we deal with the Reissner-Mindlin plate bending model, which is written in the form of a coupled system of partial di erential equations. In particular, the topological asymptotic analysis of the associated total potential energy is developed and the topological derivative with respect to the nucleation of a circular inclusion is derived in its closed form.Finally, we provide the estimates for the remainders of the topological asymptotic expansion and perform a complete mathematical justi cation for the derived formulas.
O conceito de derivada topológica tem se mostrado útil em muitas aplicações, tais como otimização topológica, problemas inversos, processamento de imagens, modelagem constitutiva multi-escala, mecânica da fratura e modelagem da evolução de dano. A análise assintótica topológica foi amplamente desenvolvida para uma grande variedade de problemas modelados por equações diferenciais parciais. Por outro lado, a derivada topológica associada a problemas acoplados é conhecida apenas em sua forma abstrata. Neste trabalho, portanto, considera-se o modelo de flexão de placa de Reissner-Mindlin, que é escrito na forma de um sistema acoplado de equações diferenciais parciais. Em particular, a análise assintótica topológica da energia potencial total associada é desenvolvida e a derivada topológica com relação a nucleação de uma inclusão circular é obtida na sua forma fechada. Finalmente, os resíduos da expansão assintótica topológica são estimados e uma justificativa matemática completa para a derivada topológica é apresentada.
7
Varner, Christopher Champion. "DGPS carrier phase networks and partial derivative algorithms." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0027/NQ49546.pdf.
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Önskog, Thomas. "The Skorohod problem and weak approximation of stochastic differential equations in time-dependent domains." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-25429.
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This thesis consists of a summary and four scientific articles. All four articles consider various aspects of stochastic differential equations and the purpose of the summary is to provide an introduction to this subject and to supply the notions required in order to fully understand the articles. In the first article we conduct a thorough study of the multi-dimensional Skorohod problem in time-dependent domains. In particular we prove the existence of cádlág solutions to the Skorohod problem with oblique reflection in time-independent domains with corners. We use this existence result to construct weak solutions to stochastic differential equations with oblique reflection in time-dependent domains. In the process of obtaining these results we also establish convergence results for sequences of solutions to the Skorohod problem and a number of estimates for solutions, with bounded jumps, to the Skorohod problem. The second article considers the problem of determining the sensitivities of a solution to a second order parabolic partial differential equation with respect to perturbations in the parameters of the equation. We derive an approximate representation of the sensitivities and an estimate of the discretization error arising in the sensitivity approximation. We apply these theoretical results to the problem of determining the sensitivities of the price of European swaptions in a LIBOR market model with respect to perturbations in the volatility structure (the so-called ‘Greeks’). The third article treats stopped diffusions in time-dependent graph domains with low regularity. We compare, numerically, the performance of one adaptive and three non-adaptive numerical methods with respect to order of convergence, efficiency and stability. In particular we investigate if the performance of the algorithms can be improved by a transformation which increases the regularity of the domain but, at the same time, reduces the regularity of the parameters of the diffusion. In the fourth article we use the existence results obtained in Article I to construct a projected Euler scheme for weak approximation of stochastic differential equations with oblique reflection in time-dependent domains. We prove theoretically that the order of convergence of the proposed algorithm is 1/2 and conduct numerical simulations which support this claim.
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Leonhard, Claudine [Verfasser]. "Derivative-free numerical schemes for stochastic partial differential equations / Claudine Leonhard." Lübeck : Zentrale Hochschulbibliothek Lübeck, 2017. http://d-nb.info/1135168091/34.
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Liu, Boan. "Analytical approximationof the solution of ordinary and partial derivative equations with artificial neural networks." Toulouse 3, 2000. http://www.theses.fr/2000TOU30225.
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Villanueva, Salas Jose Antonio. "Partially substituted calix[4]arene derivatives : synthesis, characterisation and binding properties." Thesis, University of Surrey, 2005. http://epubs.surrey.ac.uk/843388/.
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This thesis concerns the synthesis, characterisation and binding properties of partially substituted calix[4]arene amino derivatives in non-aqueous media. Thus, 5,11,17,23 - tetrakis - (1,1-dimethyl ethyl) - 25,27 - bis - [2 -(diethyl amino) ethoxy] calix[4]arene (L3) was structurally (1H NMR and X-ray crystallography) characterised and its interaction with metal cations and the proton has been investigated by several techniques. Information about the active sites of interaction of this ligand with ionic species was obtained from 1H NMR measurements. Conductance measurements were used to establish the composition of the metal-ion complexes in protic and dipolar aprotic solvents. Potentiometric measurements using two electrodes systems (mercury and glass electrodes) were carried out to determine quantitatively the strength of ligand-ion interactions in acetonitrile at 298.15 K. 2D NMR techniques were used to investigate the predominant processes (complexation or protonation) taking place in solution. The medium effect on the interaction of L3 with metal cations and the proton was assessed using a dipolar aprotic (acetonitrile) and a protic (methanol) solvent. In acetonitrile, L3 interacts with mercury (II), lead (II), cadmium (II), and magnesium (II) forming complexes of 1:1 stoichiometry while two protons are taking up per unit of ligand. No interaction was observed between L3 and alkali-metal cations in this solvent. In CD3OD the 1H NMR data show that the interaction is limited to mercury (II), lead (II) and magnesium (II) and protonation of L3 also occurs in methanol. In both solvents, the stoichiometry of the interaction of aluminium (III) and L3 was not clearly defined. It is concluded that both processes, complexation and protonation are taking place during the interaction of partially substituted calix[4]arene amino derivatives with metal cations in acetonitrile.
12
Geldmacher, Astrid. "Immunogenicity of hantavirus Dobrava nucleocapsid protein derivatives in mice." Doctoral thesis, [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=977995550.
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Chaplin, David Andrew. "The application of biotransformations to the synthesis of partially protected sugar derivatives." Thesis, University of Warwick, 1991. http://wrap.warwick.ac.uk/108830/.
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This thesis describes the use of enzymes to partially deprotect or deprotect sugars. The advantages of this technique are that mild conditions may be used for the protections and that enzymatic catalysis may allow derivatives to be made which involve multi-step procedures or cannot be made using standard methods. These protected sugars can then be used to synthesise interesting derivatives. The particular aim of this project at the outset was to use biotransformations to make partially protected derivatives for the synthesis of a novel artificial sweetener, l',4,6'-trichloro-r,4,6'-trideoxy-ga/acto- sucrose, known as sucralose. The analysis of the products from a deacetylation reaction is a potential problem due to the number of possible products that may be formed. A new approach to this problem is discussed in Chapter Two. A combination of n.m.r. and mass spectrometry is used to analyse the products after they have first been perdeuterioacetylated by treatment with d6-acetic anhydride. The analysis is therefore carried out on one compound, the starting material, now containing deuteriated acetate groups in place of those that were hydrolysed during the reaction. The technique was used initially to analyse the deacetylation of sucrose octaacetate catalysed by yeast esterase. The selectivity of the enzyme for certain positions of the sugar may be determined in this way but little information can be found about the individual species that are formed. The technique can be considerably enhanced by the introduction of a chromatographic separation step. The separation of the deacetylation mixture into classes, according to the number of acetate groups, allows a much more detailed analysis of the individual components to be carried out. If the reaction shows a certain amount of selectivity then it is possible to determine the quantity of each of the individual species. This technique is used to analyse the deacetylation of glucose pentaacetate catalysed by Aspergillus niger lipase. The deacetylation of sucrose octaacetate catalysed by yeast esterase is also analysed in the same way. Chapter Three describes the conversion of N-acetyl- glucosamine to N-acetyl-galactosamine. This is of interest due to the importance of this sugar in biological systems and its high cost relative to the starting material. The synthesis involves the use of an enzyme catalysed deesterification to make a partially protected intermediate, demonstrating the practical application of biotransformations in the synthesis of sugar derivatives.
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Vidal, Jose Antonio. "Partially fluorinated crown ether derivatives : synthesis, phase transfer catalysis and recycling studies." Thesis, University of Leicester, 2007. http://hdl.handle.net/2381/29999.
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A series of N,N'-dialkyl-4,13-diaza-18-crown-6 derivatives containing C8H17 [2.6], (CH2) 3C8F17 (2.36), (CH2) 3C10F21 [2.37], and (CH2) 2C8F17 [2.19] sidearms were synthesized in good yields by N-alkylation of 4, 1-diaza-18-crown-6 [ 2.7]. Potassium picrate could be extracted form an aqueous solution into an organic phase by all of the perfluoroalkylated macrocycles demonstrating their potential to be used as phase transfer catalysts. They each gave higher catalytic activities under solid-liquid than under liquid-liquid phase-transfer conditions. The light fluorous macrocycles gave similar, if not better, catalytic activity compared to the present, non-fluorinated phase-transfer catalyst [2.6] under solid-liquid conditions in conventional organic solvents in both an aliphatic and an aromatic nucleophilic substitution. N,N' -Bis(1H,1H,2H,2 H,3H,3H-perfluoro-undecyl)-4,13-diaza-18-crown-6 [2.36] was recycled six times in the iodide displacement reaction of 1-bromooctane and four times in the fluoride displacement reaction of 2,4-dinitrochlorobenzene using fluorous solid-phase extraction without any loss in activity.;A series of functionalized dibenzo-18-crown-6 derivatives possessing C7H15 [4.17], (CH2)2C 6F13 [4.26], (CH2)2C 8F17 [4.27], NHC17F15 [4.31a-b], and NHCH2C6F13 [ 4.35a-b] sidearms were synthesized following different approaches. All of the non-fluorinated and partially-fluorinated dibenzo-18-crown-6 derivatives showed their potential to act as phase transfer catalysts by extracting potassium and sodium picrate from an aqueous solution into dichloromethane. By adding perfluoroalkyl sidearms to a dibenzo-18-crown-6 type structure, [4.26 ] and [4.27], the phase transfer catalytic activity was improved significantly. Bis(1H,1 H,2H,2H-perfluorooctyl)dibenzo-18-crown-6 [4.26] was recycled four times in the iodide displacement reaction of 1-bromooctane using supported fluorous phase catalysis and four times in the fluoride displacement reaction of 2,4-dinitrochlorobenzene using fluorous solid-phase extraction without any loss in activity.
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Liu, Jiaqi. "Global Well-posedness for the Derivative Nonlinear Schrödinger Equation Through Inverse Scattering." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/50.
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We study the Cauchy problem of the derivative nonlinear Schrodinger equation in one space dimension. Using the method of inverse scattering, we prove global well-posedness of the derivative nonlinear Schrodinger equation for initial conditions in a dense and open subset of weighted Sobolev space that can support bright solitons.
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Marques, Leandro. "Sobre a utilização do livro didático no estudo de derivadas parciais." Pontifícia Universidade Católica de São Paulo, 2009. https://tede2.pucsp.br/handle/handle/11396.
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Previous issue date: 2009-06-22Secretaria da Educação do Estado de São Paulo
The objective of this work is to show how the Engineer course students use the didatic book to study the Partial Derivates. It s known the importance of the Calculus subject in the courses linked to the exact sciences, in which students show heavily burdens, while learning this subject. A lot has been researched about the use of technologies of information in the classroom, trying to make the teaching process more effective, but in practice, the levels of dismissing and failure show that it is not been very satisfactory. The new technologies are making the book a more efficient tool, and you can have it in hands easier than the other technologic tools. Like this, we developed our research with the propose to investigate how students manipulate the books, looking for information and what contributions the use of this tool for the learning of the topic about Partial Derivates. To look for evidences that show us how it happened, we elaborated a research tool with elementary questions based in the Raymond Duval s Theory of the Registers of Semiotics Representation that was used with students from different levels from the mechanic engineering from a private university in São Paulo. The research reveled that the students have as a priority the algebraic records in their resolutions and this representation is known as a valid answer and other representations are just auxiliaries. Most of the students showed a relative good work dealing with the functions treatment of two varieties in their algebraic representation, but they showed some hardship when they are expressed in their natural language. Bother groups show us similarities when using the book for the exploration of the topics. The way some questions were solved told us the book was an efficient tool for the learning process
O trabalho tem por objetivo mostrar como estudantes de um curso de Engenharia mobilizam o livro didático no estudo de derivadas parciais. Sabe-se da importância da disciplina de Cálculo nos cursos ligados à ciências exatas e que muitos alunos apresentam sérias dificuldades na aprendizagem dos conteúdos que a compõem. Muito se tem pesquisado sobre o uso de tecnologias da informação em sala de aula, para tentar tornar o ensino e a aprendizagem mais eficaz, porém na prática, os índices de abandono e repetência indicam que isso não está ocorrendo de maneira satisfatória. As novas tecnologias vêm tornando o livro didático uma ferramenta cada vez mais eficiente e que se pode tê-lo à mão de modo relativamente mais fácil do outras ferramentas tecnológicas. Assim desenvolvemos nossa pesquisa no intuito de investigar como os alunos manipulam o livro didático, na busca por informações e quais contribuições que a utilização dessa ferramenta pode trazer para a aprendizagem do tópico sobre Derivadas Parciais. Para buscar indícios que nos apontassem como isso ocorria, elaboramos um instrumento de pesquisa com questões fundamentadas na Teoria dos Registros de Representação Semiótica de Raymond Duval, que foi aplicado a alunos em estágios distintos do curso de engenharia mecânica de uma universidade particular da cidade de São Paulo. A pesquisa revelou que os alunos priorizam o registro algébrico em suas resoluções e que esta representação é tida como resposta válida e que outras representações são apenas auxiliares . A maioria dos alunos apresentou relativamente bom desempenho no tratamento de funções de duas variáveis na sua representação algébrica, porém demonstraram dificuldades quando elas são expressas no registro da língua natural. Os dois grupos apresentaram similaridades na manipulação do livro para a exploração conteúdo. A forma como foram resolvidas algumas questões indicou que o livro foi uma ferramenta eficaz para o processo de aprendizagem
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Dimitry, Johan. "A mathematical study of convertible bonds." Thesis, KTH, Farkost och flyg, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-151312.
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A convertible bond (CB) is a financial derivative, a so called hybrid security. It is an issued contract from a company or a government, which is paid for up-front. The contract yields a known amount at the specified maturity date, unless the holder chooses to convert it into an amount of the underlying asset. This kind of financial products can have complex features affecting the contract price and the optimal exercising situation. The partial differential equation (PDE) approach used for pricing financial derivatives makes it possible to describe convertible bonds with a physical model, a reversed diffusion described by a parabolic PDE. One can sometimes find both analytical and numerical solutions for this type of PDEs and interpret the solutions from a financial point of view, as they suggest predictable behaviour of the contract price.
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Ozonder, Sener. "Viable Higher Derivative Theories." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608468/index.pdf.
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In this thesis, higher derivative theories are investigated. Ostrogradskian instability of higher derivative theories is examined both at the classical and quantum levels.
It is shown that avoiding the instability in nondegenerate higher derivative theories is impossible. Moreover, the degenerate model of relativistic particle with a curvature
term is studied as a viable higher derivative theory.
Most of the work we present here is not original. We give a review of the literature and compile various detached works that already exist.
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Imafuku, Roberto Seidi. "Sobre a passagem do estudo de função de uma variável real para o caso de duas variáveis." Pontifícia Universidade Católica de São Paulo, 2008. https://tede2.pucsp.br/handle/handle/11354.
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Previous issue date: 2008-10-17Secretaria da Educação do Estado de São Paulo
This research was developed with the goal of verifying the difficulties and the knowledge shown by students related to the transition of the study of functions of one variable to the case of two variables, regarding dependent and independent variables well as the interdependence between them, to the dominion and the graphic, to the relation between the graphic of the dominion of the function and also which manifestations are revealed in the study of the partial derivatives of the first order. In order to do so we developed two questionnaires based upon the Theory of the Registers of Semiotic Representation of Raymond Duval, the questionnaires having been answered by students of the fourth and fifth term of the course of Mathematics of a private university in the greater São Paulo area. The first questionnaire was applied to students of the fourth term and it made possible to verify not only one first analysis of their difficulties, but also how pertinent the questions were, as well as how fitting the wording was. It has been found that some of the questions needed rephrasing, and also that the addition of new questions was necessary, which contributed to the making of a new questionnaire, which was answered by students of the fifth term. This research revealed some difficulties that students show when studying functions of two variables, such as the comprehension of the system of the 3D axis, the lack of clarity when determining and representing the dominium of the function, difficulty when performing the conversion from the representation of the natural language to the algebric language in contextualised situations, the confusion between the graphic representation of the dominion and the function, and the obstacles for the interpretation of the graphic of a function of two variables, difficulties that have negative effect on the study of partial derivatives. The registers of semiotic representation proved themselves an efficient tool for the explanation of the knowledge and the complexity that the study of functions with two variables represent for students
Esta pesquisa foi desenvolvida com o objetivo de verificar as dificuldades e saberes manifestados por estudantes relativos à transição do estudo das funções de uma variável para o caso de duas, no que diz respeito às variáveis dependentes e independentes e à interdependência entre elas, ao domínio e o gráfico, à relação entre o gráfico do domínio e o gráfico da função e, também quais manifestações são reveladas no estudo das derivadas parciais de primeira ordem. Para isso, elaboramos dois questionários fundamentados na Teoria dos Registros de Representação Semiótica de Raymond Duval, os quais foram aplicados a estudantes do quarto e quinto semestre de um curso de Licenciatura em Matemática de uma universidade particular da grande São Paulo. O primeiro questionário foi aplicado a alunos do quarto semestre e possibilitou, além de uma primeira análise das dificuldades, verificar a pertinência das questões, bem como a adequação dos enunciados. Foi constatado que algumas questões necessitavam de uma reestruturação e, também, que era necessário o acréscimo de novas questões, o que contribuiu na elaboração do questionário definitivo, que foi aplicado a estudantes do quinto semestre. Esta pesquisa revelou algumas dificuldades que os alunos apresentam quando estudam as funções de duas variáveis, como: a não compreensão do sistema de eixos 3D, a falta de clareza na determinação e representação do domínio da função, a dificuldade em realizar a conversão do registro da língua natural para o algébrico em situações contextualizadas, a confusão entre o registro gráfico do domínio e da função, e os obstáculos para a interpretação do gráfico de uma função de duas variáveis, dificuldades estas que se refletem negativamente no estudo das derivadas parciais. Os registros de representação semiótica se mostraram uma eficaz ferramenta para a explicitação dos saberes e da complexidade que o estudo de funções de duas variáveis representa para os alunos
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Heuer, Christof. "High-order compact finite difference schemes for parabolic partial differential equations with mixed derivative terms and applications in computational finance." Thesis, University of Sussex, 2014. http://sro.sussex.ac.uk/id/eprint/49800/.
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This thesis is concerned with the derivation, numerical analysis and implementation of high-order compact finite difference schemes for parabolic partial differential equations in multiple spatial dimensions. All those partial differential equations contain mixed derivative terms. The resulting schemes have been applied to equations appearing in computational finance. First, we develop and study essentially high-order compact finite difference schemes in a general setting with option pricing in stochastic volatility models on non-uniform grids as application. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In the numerical study we obtain high-order numerical convergence also for non-zero correlation and non-smooth payoffs which are typical in option pricing. In all numerical experiment a comparative standard second-order discretisation is significantly outperform. We conduct a numerical stability study which indicates unconditional stability of the scheme. Second, we derive and analyse high-order compact schemes with n-dimensional spatial domain in a general setting. We obtain fourth-order accuracy in space and second-order accuracy in time. A thorough von Newmann stability analysis is performed for spatial domain with dimensions two and three. We prove that a necessary stability condition holds unconditionally without additional restrictions on the choice of the discretisation parameters for vanishing mixed derivative terms. We also give partial results for non-vanishing mixed derivative terms. As first example Black-Scholes Basket options are considered. In all numerical experiments, where the initial conditions were smoothened using the smoothing operators developed by Kreiss, Thomée and Widlund, a comparative standard second-order discretisation is significantly outperformed. As second example the multi-dimentional Heston basket option is considered for n independent Heston processes, where for each Heston process there is a non-vanishing correlation between the stock and its volatility.
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Marteau, Benjamin. "Paramétrisation et optimisation sans dérivées pour le problème de calage d’historique." Thesis, Versailles-St Quentin en Yvelines, 2015. http://www.theses.fr/2015VERS014V/document.
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Dans cette thèse, on s’intéresse à un problème inverse classique en ingénierie pétrolière, àsavoir le calage d’historique. Plus précisément, une nouvelle méthode de paramétrisation géostatistiqueainsi qu’un nouvel algorithme d’optimisation sans dérivées adaptés aux particularitésdu problème sont présentés ici. La nouvelle méthode de paramétrisation repose sur les principes des méthodes de déformation graduelle et de déformation de domaines. Comme la déformation graduelle locale, elle consiste àcombiner à l’intérieur de zones préalablement définies deux réalisations ou plus de modèle avec lapossibilité supplémentaire de modifier dynamiquement la forme des zones choisies. La flexibilitéapportée par cette méthode dans le choix des zones a ainsi permis de garantir l’obtention d’unbon point initial pour l’optimisation. Concernant l’optimisation, l’hypothèse que les paramètres locaux dans le modèle de réservoir n’influent que faiblement sur les données de puits distants conduit à considérer que la fonction àoptimiser est à variables partiellement séparables. La nouvelle méthode d’optimisation développée,nommée DFO-PSOF, de type région de confiance avec modèle quadratique d’interpolation,exploite alors au maximum cette propriété de séparabilité partielle. Les résultats numériquesobtenus sur plusieurs cas de réservoir valident à la fois l’hypothèse effectuée ainsi que la qualitéde l’algorithme pour le problème de calage d’historique. En complément de cette validation numérique,un résultat théorique de convergence vers un point critique est prouvé pour la méthoded’optimisation construiteWe worked in this thesis on a classical inverse problem in the petroleum industry, historymatching. We proposed a new geostatistical parameterization technique as well as a new derivativefree optimization algorithm adapted to the problem specificities. The parameterization method is based on two approaches found in the literature, the local gradual deformation method and the domain deformation method. Similarly to the local gradual deformation method, our method combines two or more model realizations inside previouslydefined zones. Moreover, our method adds the possibility to dynamically update the shape ofthe zones during the optimization process. This property substantially improves its robustnesswith regard to the initial choice of the zones. Thus, the greater flexibility brought by our methodallowed us to develop an initialization methodology which garantees a good initial point for theoptimization. To reduce the number of evaluations needed to minimize the objective function, we madethe assumption that a local parameter does not influence the production data of a distantwell. With this hypothesis, the objective function is then considered partially separable. Theoptimization algorithm we developped, called DFO-PSOF, is a trust region algorithm basedon quadratic interpolation models which exploits this partial separability property. Numericalresults obtained on some reservoir test cases validate both the hypothesis and the quality of ouralgorithm for the history matching problem. Moreover, a theoretical convergence result towardsa first order critical point, is proved for this new optimization method
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Vaičiulytė, Ingrida. "Vienos išsigimstančios dalinių išvestinių diferencialinių lygčių sistemos sprendinių struktūra." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2009. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2009~D_20090827_111608-87412.
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Šiame darbe išnagrinėta išsigimstanti keturių pirmos eilės dalinių išvestinių diferencialinių lygčių sistema. Dalinių išvestinių diferencialinių lygčių sistemai spręsti pritaikytas apibendrintų laipsninių eilučių metodas. Rasti analiziniai šios sistemos sprendiniai ir ištirtos jų savybės išsigimimo daugdaros taškų aplinkoje. Apibendrintų laipsninių eilučių metodas gali būti pritaikytas sprendžiant panašios struktūros dalinių išvestinių diferencialines lygtis, kurių eilė išsigimsta. Darbe gauti rezultatai gali būti pritaikomi modeliuojant ir tiriant realius procesus.In this work the system of four degenerating differential equations with partial derivatives of first order was studied. For the solution of system of differential equations with partial derivatives the method of generalized power series was applied. Analytical solutions of this system were found and properties of solutions on neighbourhood of points of degeneration manifold were investigated. The method of generalized power series can be applied to the solution of systems of differential equations with partial derivatives of similar structure, which order is degenerating. The results, which were obtained in this work, can be applied to modelling and studying the real processes.
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Wang, Kunlun. "Design and Synthesis of Novel Liquid Crystals and Organic Semiconductors." Kent State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=kent1492881173762306.
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Wissmann, Rasmus. "Expansion methods for high-dimensional PDEs in finance." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:c791d5e9-dfa3-4bd1-86ec-82e29839aea9.
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We develop expansion methods as a new computational approach towards high-dimensional partial differential equations (PDEs), particularly of such type as arising in the valuation of financial derivatives. The proposed methods are extended from [41] and use principal component analysis (PCA) of the underlying process in combination with a Taylor expansion of the value function into solutions to low-dimensional PDEs. They enable calculation of highly accurate approximate solutions with computational complexity polynomial in the number of dimensions for PDEs with a low number of dominant principal components. For the case of PDEs with constant coefficients, we show existence of expansion solutions and prove theoretical error bounds. We give a precise characterisation of when our methods can be applied and construct specific examples of a first and second order version. We provide numerical results showing that the empirically observed convergence speeds are in agreement with the theoretical predictions. For the case of PDEs with varying coefficients, we give a heuristic motivation using the Parametrix approach and empirically test the methods' accuracy for a range of variable parameter stock models. We demonstrate the applicability of our expansion methods to real-world securities pricing problems by considering path-dependent and early-exercise options in the LIBOR market model. Using the example of Bermudan swaptions and Ratchet floors, which are considered difficult benchmark problems, we give a careful analysis of the numerical accuracy and computational complexity. We are able to demonstrate that for problems with medium to high dimensionality, around 60-100, and moderate time horizons, the presented PDE methods deliver results comparable in accuracy to benchmark state-of-the-art Monte Carlo methods in similar or (significantly) faster run time.
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Rakotonasy, Solonjaka Hiarintsoa. "Modèle fractionnaire pour la sous-diffusion : version stochastique et edp." Phd thesis, Université d'Avignon, 2012. http://tel.archives-ouvertes.fr/tel-00839892.
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Ce travail a pour but de proposer des outils visant 'a comparer des résultats exp'erimentaux avec des modèles pour la dispersion de traceur en milieu poreux, dans le cadre de la dispersion anormale.Le "Mobile Immobile Model" (MIM) a été à l'origine d'importants progrès dans la description du transport en milieu poreux, surtout dans les milieux naturels. Ce modèle généralise l'quation d'advection-dispersion (ADE) e nsupposant que les particules de fluide, comme de solut'e, peuvent ˆetre immo-bilis'ees (en relation avec la matrice solide) puis relˆachées, le piégeage et le relargage suivant de plus une cin'etique d'ordre un. Récemment, une version stochastique de ce modèle a 'eté proposée. Malgré de nombreux succès pendant plus de trois décades, le MIM reste incapable de repr'esenter l''evolutionde la concentration d'un traceur dans certains milieux poreux insaturés. Eneffet, on observe souvent que la concentration peut d'ecroˆıtre comme unepuissance du temps, en particulier aux grands temps. Ceci est incompatible avec la version originale du MIM. En supposant une cinétique de piégeage-relargage diff'erente, certains auteurs ont propos'e une version fractionnaire,le "fractal MIM" (fMIM). C'est une classe d''equations aux d'eriv'ees par-tielles (e.d.p.) qui ont la particularit'e de contenir un op'erateur int'egral li'e'a la variable temps. Les solutions de cette classe d'e.d.p. se comportentasymptotiquement comme des puissances du temps, comme d'ailleurs cellesde l''equation de Fokker-Planck fractionnaire (FFPE). Notre travail fait partie d'un projet incluant des exp'eriences de tra¸cageet de vélocimétrie par R'esistance Magn'etique Nucl'eaire (RMN) en milieuporeux insatur'e. Comme le MIM, le fMIM fait partie des mod'eles ser-vant 'a interpréter de telles exp'eriences. Sa version "e.d.p." est adapt'eeaux grandeurs mesur'ees lors d'exp'eriences de tra¸cage, mais est peu utile pour la vélocimétrie RMN. En effet, cette technique mesure la statistiquedes d'eplacements des mol'ecules excit'ees, entre deux instants fixés. Plus précisément, elle mesure la fonction caractéristique (transform'ee de Fourier) de ces d'eplacements. Notre travail propose un outil d'analyse pour ces expériences: il s'agit d'une expression exacte de la fonction caract'eristiquedes d'eplacements de la version stochastique du mod'ele fMIM, sans oublier les MIM et FFPE. Ces processus sont obtenus 'a partir du mouvement Brown-ien (plus un terme convectif) par des changement de temps aléatoires. Ondit aussi que ces processus sont des mouvement Browniens, subordonnéspar des changements de temps qui sont eux-mˆeme les inverses de processusde L'evy non d'ecroissants (les subordinateurs). Les subordinateurs associés aux modèles fMIM et FFPE sont des processus stables, les subordinateursassoci'es au MIM sont des processus de Poisson composites. Des résultatsexp'erimenatux tr'es r'ecents on sugg'er'e d''elargir ceci 'a des vols de L'evy (plusg'en'eraux que le mouvement Brownien) subordonnés aussi.Le lien entre les e.d.p. fractionnaires et les mod'eles stochastiques pourla sous-diffusion a fait l'objet de nombreux travaux. Nous contribuons 'ad'etailler ce lien en faisant apparaˆıtre les flux de solut'e, en insistant sur une situation peu 'etudiée: nous examinons le cas o'u la cinétique de piégeage-relargage n'est pas la mˆeme dans tout le milieu. En supposant deux cinétiques diff'erentes dans deux sous-domaines, nous obtenons une version du fMIMavec un opérateur intégro-diff'erentiel li'e au temps, mais dépendant de la position.Ces r'esultats sont obtenus au moyen de raisonnements, et sont illustrés par des simulations utilisant la discrétisation d'intégrales fractionnaires etd'e.d.p. ainsi que la méthode de Monte Carlo. Ces simulations sont en quelque sorte des preuves numériques. Les outils sur lesquels elles s'appuient sont présentés aussi.
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Cotton, John, and n/a. "The privilege against self-incrimination in civil proceedings between private parties in Australia and New Zealand : is derivative use immunity the answer?" University of Otago. Faculty of Law, 2007. http://adt.otago.ac.nz./public/adt-NZDU20070815.094307.
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This thesis addresses the problem of the privilege against self-incrimination ("the privilege") in civil proceedings between private parties in Australia and New Zealand. This problem has been recognised by judges, law reform bodies and legislators in both countries for twenty years. However, the legislative response has been inadequate.
The privilege is easily confused with other related concepts, particularly the right to silence in criminal proceedings. The reasons for the privilege in civil proceedings are not necessarily the same as for the right to silence. Care is therefore taken to define the terminology and scope of the thesis. It sets out the modern law on the privilege in civil proceedings between private parties. It describes how the privilege causes particular problems in those proceedings. It surveys the literature, finding that most of it concerns the right to silence.
The thesis draws heavily on the history of the privilege. It argues that, although witness privilege came from the common law, the privilege in interlocutory civil proceedings had its origins in the discretionary remedies devised by the courts of equity. They were sensitive to abuse of their remedies. For the same reason, modern prosecutors should not be encouraged to rely excessively upon evidence acquired through compulsory powers.
Derivative use immunity is one of several substitutes suggested for the privilege. The thesis looks at the various substitutes. It concludes that derivative use immunity is the only satisfactory substitute for the privilege in civil proceedings.
Derivative use immunity originated in the United States. The thesis looks closely at the American experience. The history and scope of the Fifth Amendment are discussed in detail, particularly the supposed removal of its protection from documents. This will show that the removal of the privilege from documents is not as simple as law reform bodies in Australia and New Zealand suggest.
Exaggerated claims have been made by Australian prosecutors about the problems caused by derivative use immunity. The claims are examined in the light of American case-law. This shows that an impossible burden is not imposed on prosecutors. The same point emerges when the thesis examines the operation of derivative use immunity under Australian certification procedures since 1995.
Particular procedural and legislative difficulties need to be addressed, particularly when derivative use immunity replaces the privilege in interlocutory proceedings. However, certification by the court has an important advantage. The court�s exercise of its discretion provides the flexibility which automatic statutory immunity lacks.
The question in the title is therefore answered in the affirmative. Derivative use immunity under a statutory certification procedure can provide the answer. Cooperation between the Commonwealth and States may be needed to overcome constitutional difficulties, but most other problems can be overcome if derivative use immunity is given a sound statutory basis.
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Andreevska, Irena. "Mathematical modeling and analysis of options with jump-diffusion volatility." [Tampa, Fla.] : University of South Florida, 2008. http://purl.fcla.edu/usf/dc/et/SFE0002343.
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Schwarz, Daniel Christopher. "Price modelling and asset valuation in carbon emission and electricity markets." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:7de118d2-a61b-4125-a615-29ff82ac7316.
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This thesis is concerned with the mathematical analysis of electricity and carbon emission markets. We introduce a novel, versatile and tractable stochastic framework for the joint price formation of electricity spot prices and allowance certificates. In the proposed framework electricity and allowance prices are explained as functions of specific fundamental factors, such as the demand for electricity and the prices of the fuels used for its production. As a result, the proposed model very clearly captures the complex dependency of the modelled prices on the aforementioned fundamental factors. The allowance price is obtained as the solution to a coupled forward-backward stochastic differential equation. We provide a rigorous proof of the existence and uniqueness of a solution to this equation and analyse its behaviour using asymptotic techniques. The essence of the model for the electricity price is a carefully chosen and explicitly constructed function representing the supply curve in the electricity market. The model we propose accommodates most regulatory features that are commonly found in implementations of emissions trading systems and we analyse in detail the impact these features have on the prices of allowance certificates. Thereby we reveal a weakness in existing regulatory frameworks, which, in rare cases, can lead to allowance prices that do not conform with the conditions imposed by the regulator. We illustrate the applicability of our model to the pricing of derivative contracts, in particular clean spread options and numerically illustrate its ability to "see" relationships between the fundamental variables and the option contract, which are usually unobserved by other commonly used models in the literature. The results we obtain constitute flexible tools that help to efficiently evaluate the financial impact current or future implementations of emissions trading systems have on participants in these markets.
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Wu, Yue. "Pathwise anticipating random periodic solutions of SDEs and SPDEs with linear multiplicative noise." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/15991.
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In this thesis, we study the existence of pathwise random periodic solutions to both the semilinear stochastic differential equations with linear multiplicative noise and the semilinear stochastic partial differential equations with linear multiplicative noise in a Hilbert space. We identify them as the solutions of coupled forward-backward infinite horizon stochastic integral equations in general cases, and then perform the argument of the relative compactness of Wiener-Sobolev spaces in C([0, T],L2Ω,Rd)) or C([0, T],L2(Ω x O)) and Schauder's fixed point theorem to show the existence of a solution of the coupled stochastic forward-backward infinite horizon integral equations.
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Cantero, Guardeño Juan Carlos. "Transport equations via smooth kernels." Doctoral thesis, Universitat Autònoma de Barcelona, 2021. http://hdl.handle.net/10803/673726.
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En aquesta tesi estudiem l’equació del transport no lineal i no local. Aquesta equació en derivades parcials descriu l’evolució d’un escalar que es transporta seguint un camp de velocitats. El camp i l’escalar estan relacionats mitjançant la convolució d’aquest últim amb un nucli escollit. La principal aportació és que, en general, permetem que aquesta elecció faci que el camp de velocitats resultant tingui divergència no nul·la (a diferència del cas de l’equació d’Euler) i fins i tot no fitada (a diferència del cas de l’equació de l’agregació).
La tesi es divideix en tres blocs.
Al primer bloc, que conté els capítols 1 i 2, veiem que el problema de Cauchy de l’equació per una dada inicial Hölder contínua i amb suport compacte està ben posat. Així, al capítol 1 considerem una família de nuclis a l’espai euclidià n-dimensional on cada component és una combinació lineal de derivades de la solució fonamental del laplacià. Al capítol 2 treballem al pla complex, la qual cosa ens permet considerar una família de nuclis encara més ampla.
El segon bloc és la part central de la tesi. Estudiem el problema del pegat de densitat, és a dir, quan l’escalar considerat és la funció característica d’un domini. Es recupera el resultat de conservació de la regularitat de la frontera d’un domini estudiat per Chemin i Constantin-Bertozzi l’any 1993 per l’equació d’Euler i també el mateix resultat de Bertozzi-Garnett-Laurent-Verdera l’any 2016 per l’equació de l’agregació. Aconseguim aquí una generalització d’aquests dos resultats per les mateixes famílies de nuclis del primer bloc: al capítol 3 ho fem a dimensió arbitrària i al capítol 4 al pla complex.
El tercer bloc és el més petit i es correspon amb l’últim capítol de la tesi. S’estudia el comportament límit (per temps infinit) d’un pegat de densitat unidimensional, en aquest cas per l’equació de l’agregació, que es transforma en una equació del transport mitjançant un canvi de variable adient.En esta tesis estudiamos la ecuación del transporte no lineal y no local. Esta ecuación en derivadas parciales describe la evolución de un escalar que se transporta siguiendo un campo de velocidades. El campo y el escalar están relacionados mediante la convolución de este último con un núcleo escogido. La principal aportación es que, en general, permitimos que esta elección haga que el campo de velocidades resultante tenga divergencia no nula (a diferencia del caso de la ecuación de Euler) e incluso no acotada (a diferencia del caso de la ecuación de la agregación). La tesis se divide en tres bloques. En el primer bloque, que contiene los capítulos 1 y 2, vemos que el problema de Cauchy de la ecuación para un dato inicial Hölder continuo y con soporte compacto está bien puesto. De esta manera, en el capítulo 1 consideramos una familia de núcleos en el espacio euclídeo n-dimensional donde cada componente es una combinación lineal de derivadas de la solución fundamental del laplaciano. En el capítulo 2 trabajamos en el plano complejo, lo cual nos permite considerar una familia de núcleos aún más general. El segundo bloque es la parte central de la tesis. Estudiamos el problema del pegado de densidad, es decir, cuando el escalar considerado es la función característica de un dominio. Se recupera el resultado de conservación de la regularidad de la frontera de un dominio estudiado por Chemin y Constantin-Bertozzi en el año 1993 para la ecuación de Euler y también el mismo resultado de Bertozzi-Garnett-Laurent-Verdera del año 2016 para la ecuación de la agregación. Conseguimos aquí una generalización de estos dos resultados para las mismas familias de núcleos del primer bloque: en el capítulo 3 lo hacemos en dimensión arbitraria y en el capítulo 4 en el plano complejo. El tercer bloque es el más breve y se corresponde con el último capítulo de la tesis. Se estudia el comportamiento límite (para tiempo infinito) de un pegado de densidad unidimensional, en este caso para la ecuación de la agregación, que se transforma en una ecuación del transporte mediando un cambio de variables adecuado.
In this thesis we study the non-linear non-local transport equation. This partial differential equation describes the evolution of a scalar which is transported by a velocity field. The field and the scalar are related through the convolution of the latter with a chosen kernel. The main contribution is that, in general, we allow this choice to yield a velocity field having non-zero divergence (unlike the case of the Euler equation) and even non-bounded divergence (unlike the case of the aggregation equation). The thesis is divided into three blocks. In the first block, which contains chapters 1 and 2, we study the well-posedness of the equation for a Hölder continuous and compactly supporter initial data. Thus, in chapter 1 we consider a family of kernels in the n-dimensional Euclidean space where each component is a linear combination of derivatives of the fundamental solution of the laplacian. In chapter 2 we work in the complex plane, which allows us to consider an even more general family of kernels. The second block is the central part of the thesis. We study the problem of density patches, i.e. when the scalar under consideration is the characteristic function of a domain. We recover the result of conservation of the regularity of the boundary of a domain studied by Chemin and Constantin-Bertozzi in 1993 for the Euler equation and also the same result of Bertozzi-Garnett-Laurent-Verdera in 2016 for the aggregation equation. We achieve here a generalisation of these two results for the same families of kernels of the first block: in chapter 3 we do it in arbitrary dimension and in chapter 4 in the complex plane. The third block is the shortest and corresponds to the last chapter of the thesis. We study the limit behaviour (for infinite time) of a one-dimensional density patch, in this case for the aggregation equation, which is transformed into a transport equation by means of an appropriate change of variables.
Universitat Autònoma de Barcelona. Programa de Doctorat en Matemàtiques
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Mata, Sara Mayeth. "Design and Synthesis of TLR2 and TLR6 Heterodimer Ligands, a Triply Functionalized α-GalCer Derivative for Identifying Proteins Involved in Glycolipid Trafficking, and the Disaccharide of Staphylococcus aureus CP8 Towards a Self-Adjuvanting Vaccine." BYU ScholarsArchive, 2019. https://scholarsarchive.byu.edu/etd/7580.
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Toll like receptors (TLRs) are found on B cells, macrophages, monocytes, and dendritic cells, and these cells belong to the innate immune system that recognizes antigens and induces multiple cell responses through the release of cytokines. TLR1, TLR2 and TLR6 function as heterodimers, either as TLR1/TLR2 or TLR2/TLR6 to recognize lipopeptides. TLR1/2 dimer activation releases inflammatory cytokines, while TLR2/TLR6 dimer activation releases immunomodulatory cytokines. Based on the size of the binding pocket between TLR2 and TLR6, it was hypothesized that lipopeptides, such as FSL1, could be simplified while keeping overall activity. FSL1 is a lipopeptide first isolated from Mycoplasma salivarum that activates macrophages at picomolar concentrations. It is expected that synthetic lipopeptides mimicking immunostimulatory molecules such as FSL1 will allow development of better ways to stimulate or modulate the immune system. Therefore, novel synthetic TLR2/6 ligands were synthesized replacing the polylysine chain with a polyamine chain showing activation of the immune cells in a manner like FSL1. Natural killer T-cell (NKT) antigens, such as α-galactosylceramide (α-GalCer), are carried through the body by lipid transfer proteins before they interact with the NKT cells. Not all the proteins involved in glycolipid transportation have been characterized. The synthesis of an α-GalCer analogue, termed CD1d-Triceps was designed to help find additional proteins involved in glycolipid trafficking. CD1d-Triceps has three functionalities: the first is the α-GalCer structure, and the other two are on C6 of the sugar: biotin, which helps tag the molecule for its purification, and a photoactive tag that, upon UV light activation, will cross-link with neighboring proteins. Antibiotic-resistant strains of Staphylococcus aureus (SA) are a growing health problem worldwide. Serotype 5 and 8 are the most common SA pathogens. Loading the serotype 5 or 8 disaccharides onto Qβ-particles that are linked to an NKT cell activator yield a vaccine that is expected to trigger adaptive immunity to the disaccharide. Previous similar studies showed production of antibodies with high affinity against Streptococcus pyogenes oligosaccharides in a similar vaccine.
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Zinck, Guillaume. "Reconstruction d'hypersurfaces de champs de normales sous contraintes : application à l'analyse stratigraphique des images sismiques." Thesis, Bordeaux 1, 2012. http://www.theses.fr/2012BOR14705/document.
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Cette thèse traite de la reconstruction d'hypersurfaces au sein de champs de normales en dimension quelconque et trouve des applications dans l’analyse des empreintes digitales (lignes dermiques), des images satellites météorologiques (lieux de turbulence) et astrophysiques (bras de galaxies) ainsi que dans l’analyse stratigraphique des images sismiques (horizons). Les méthodes développées s’appuient sur la minimisation d’une équation aux dérivées partielles non linéaire reliant une hypersurface au pendage déduit d’un champ de normales. Elles prennent en compte des contraintes diverses telles que des points de passages, des frontières, des bornes et des discontinuités. La contribution principale de la thèse réside dans l’introduction d’un changement d’espace du pendage qui permet de reconstruire aussi bien des hypersurfaces exprimées sous des formes implicites dans les repères de définition des champs de normales que des horizons sismiques de manière rapide et interactive. Deux schémas de reconstruction d’horizons sismiques unidimensionnels présentant une discontinuité d’amplitude et de lieu inconnus sont également proposésThis thesis deals with the reconstruction of hypersurfaces from a finite-dimensional normal vector field. Application scopes can be found in the analysis of fingerprints (epidermal ridges), meteorological images (eddies and cyclones), astrophysical images (galaxy arms) and in the stratigraphic analysis of seismic images (horizons). The hypersurfaces are obtained by solving a non-linear partial derivative equation relied on the local dip deduced from a normal vector field. Several constraints such as boundaries, bounds, points belonging to the hypersurface or discontinuities can be considered.The major contribution of this thesis consists in a local dip transformation which allows to reconstruct implicit hypersurfaces as well as seismic horizons by a fast and interactive method. Two schemes dedicated to the reconstruction of discontinuous one-dimensional seismic horizons are also proposed when the discontinuity location and jump are unknown
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Lindensjö, Kristoffer. "Essays in financial mathematics." Doctoral thesis, Handelshögskolan i Stockholm, Institutionen för Finansiell ekonomi, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:hhs:diva-2145.
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López, Muñoz Laura. "Homology modeling and structural analysis of the antipsychotic drugs receptorome." Doctoral thesis, Universitat Pompeu Fabra, 2010. http://hdl.handle.net/10803/7228.
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Classically it was assumed that the compounds with therapeutic effect exert their action interacting with a single receptor. Nowadays it is widely recognized that the pharmacological effect of most drugs is more complex and involves a set of receptors, some associated to their positive effects and some others to the side effects and toxicity. Antipsychotic drugs are an example of effective compounds characterized by a complex pharmacological profile binding to several receptors (mainly G protein-coupled-receptors, GPCR). In this work we will present a detailed study of known antipsychotic drugs and the receptors potentially involved in their binding profile, in order to understand the molecular mechanisms of the antipsychotic pharmacologic effects.The study started with obtaining homology models for all the receptors putatively involved in the antipsychotic drugs receptorome, suitable for building consistent drug-receptor complexes. These complexes were structurally analyzed and compared using multivariate statistical methods, which in turn allowed the identification of the relationship between the pharmacological properties of the antipsychotic drugs and the structural differences in the receptor targets. The results can be exploited for the design of safer and more effective antipsychotic drugs with an optimum binding profile.
Tradicionalmente se asumía que los fármacos terapéuticamente efectivos actuaban interaccionando con un único receptor. Actualmente está ampliamente reconocido que el efecto farmacológico de la mayoría de los fármacos es más complejo y abarca a un conjunto de receptores, algunos asociados a los efectos terapéuticos y otros a los secundarios y toxicidad. Los fármacos antipsicóticos son un ejemplo de compuestos eficaces que se caracterizan por unirse a varios receptores simultáneamente (principalmente a receptores unidos a proteína G, GPCR). El trabajo de la presente tesis se ha centrado en el estudio de los mecanismos moleculares que determinan el perfil de afinidad de unión por múltiples receptores de los fármacos antipsicóticos.
En primer lugar se construyeron modelos de homología para todos los receptores potencialmente implicados en la actividad farmacológica de dichos fármacos, usando una metodología adecuada para construir complejos fármaco-receptor consistentes. La estructura de estos complejos fue analizada y se llevó a cabo una comparación mediante métodos estadísticos multivariantes, que permitió la identificación de asociaciones entre la actividad farmacológica de los fármacos antipsicóticos y diferencias estructurales de los receptores diana. Los resultados obtenidos tienen interés para ser explotados en el diseño de fármacos antipsicóticos con un perfil farmacológico óptimo, más seguros y eficaces.
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Schäfer, Carsten. "Asset Dividing Appraisal Model (ADAM) - Direct Real Estate Investment Evaluation." Doctoral thesis, Vysoká škola ekonomická v Praze, 2012. http://www.nusl.cz/ntk/nusl-191784.
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The Asset Dividing Appraisal Model (ADAM) enables the appraisal of cash flows resulting from direct real estate investments. The model is an evaluation tool, which takes capital markets and the specific characteristics of real estate as an asset (heterogeneity, site-dependency, eternal land-yield, etc.) into consideration, while also considering different ownership approaches of real estate in the European Union. Thus, it contributes to the harmonization of capital markets and of direct real estate investment evaluation as intended by the "European Directive on Markets in Financial Instruments 2004/39/EC". ADAM is based on financial mathematical instruments and on the property valuation methods of different cultural areas. It combines continental European (Germ an Gross Rental-Method) and international (Discounted Cash Flow-Method) property valuation approaches. Although it is scientifically reasonable to take property valuation approaches into account, the aim of the model is not to valuate a property or to quantify an objective market value but to evaluate cash-flows resulting from direct real estate investments. A mathematical analysis based on empirical market data confirmed the validity of the methodology of the model. In the course of the analysis the major input variables that determine the results of the model and how the model reacts to marginal deviations of input data, were quantified. This was done using partial derivations and a simulation study. In Czech Republic a building isn't actually considered as a part of the underlying plot. Consequently, differing persons or institutions can be owner of the building, as of the appropriate plot. From 2014 on, a suitable reformation of the Czech Civil Code is supposed to cause a consolidation of real estate property. Czech law is going to be adjusted to German law, which considers plot and building as an economic entity. This consolidation of real estate could be an approach of the introduced model.
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Sebastianutti, Marco. "Geodesic motion and Raychaudhuri equations." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18755/.
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The work presented in this thesis is devoted to the study of geodesic motion in the context of General Relativity. The motion of a single test particle is governed by the geodesic equations of the given space-time, nevertheless one can be interested in the collective behavior of a family (congruence) of test particles, whose dynamics is controlled by the Raychaudhuri equations. In this thesis, both the aspects have been considered, with great interest in the latter issue. Geometric quantities appear in these evolution equations, therefore, it goes without saying that the features of a given space-time must necessarily arise. In this way, through the study of these quantities, one is able to analyze the given space-time. In the first part of this dissertation, we study the relation between geodesic motion and gravity. In fact, the geodesic equations are a useful tool for detecting a gravitational field. While, in the second part, after the derivation of Raychaudhuri equations, we focus on their applications to cosmology. Using these equations, as we mentioned above, one can show how geometric quantities linked to the given space-time, like expansion, shear and twist parameters govern the focusing or de-focusing of geodesic congruences. Physical requirements on matter stress-energy (i.e., positivity of energy density in any frame of reference), lead to the various energy conditions, which must hold, at least in a classical context. Therefore, under these suitable conditions, the focusing of a geodesics "bundle", in the FLRW metric, bring us to the idea of an initial (big bang) singularity in the model of a homogeneous isotropic universe. The geodesic focusing theorem derived from both, the Raychaudhuri equations and the energy conditions acts as an important tool in understanding the Hawking-Penrose singularity theorems.
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Li, Cheng-Chang, and 李承璋. "Error Bounds for Partial Derivatives of Bernstein Approximation." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/34417182802171001282.
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碩士輔仁大學
數學系研究所
95
Bernstein polynomials of two variables are used to approximate certain class of functions. Approximation error is the main point to be explored in this work. We deduce the error bounds for first and second partial derivatives of the approximation.
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Sheppard, Roelof. "Pricing equity derivatives under stochastic volatility : A partial differential equation approach." Thesis, 2008. http://hdl.handle.net/10539/5772.
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Chen, Huang-Yu, and 陳皇宇. "Root n estimates of integrated squared density partial derivatives and applications." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/71059641421011423382.
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博士國立成功大學
統計學系碩博士班
95
Based on a random sample of size $n$ from an unknown $d$-dimensional density $f$, the nonparametric estimation of integrated squared density partial derivatives is considered. These functionals are important in a number of contexts. The proposed estimator is constructed in the frequency domain by using the sample characteristic function. It is known that the sample characteristic function at high frequency is dominated by sample variation and does not contain much information about $f$. Hence, the variation of the estimator can be reduced by modifying the sample characteristic function beyond some cut-off frequency. It is proposed to select adaptively the cut-off frequency by a generalization of cross-validation. For every $d$ and sufficiently smooth $f$, the information bounds of estimating integrated squared density partial derivatives are established. Furthermore, for sufficiently smooth $f$ and kernel function, it is shown that the proposed estimator is asymptotically normal, attains the optimal $sqrt{n}$ convergence rate and achieves the information bound. In simulation studies the superior performance of the proposed procedures is clearly demonstrated. Finally, an application based on the plug-in method of bandwidth selection in kernel estimation of $f$ is also considered.
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"Model study and partial synthesis of prehispanolone and derivatives from hispanolone." Chinese University of Hong Kong, 1994. http://library.cuhk.edu.hk/record=b5895462.
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En Si Wang.Thesis (Ph.D.)--Chinese University of Hong Kong, 1994.
Includes bibliographical references (leaves 126-140 (2nd gp.)).
Acknowledgements --- p.i
Contents --- p.ii
Abstract --- p.iv
List of Acronyms and Abbreviations --- p.vi
introduction --- p.1
Chapter I. --- "Platelet Activating Factor (PAF)´ؤPast, Present, and Future" --- p.1
Chapter I-1. --- What is PAF? --- p.1
Chapter I-2. --- Biochemistry of PAF --- p.2
Chapter I-2-1. --- Metabolic Cycle of PAF --- p.3
Chapter I-2-1-A. --- Biosynthesis of PAF --- p.4
Chapter I-2-1 -B. --- Inactivation of PAF --- p.6
Chapter I-2-2. --- Role of Endogenous PAF in Cell --- p.7
Chapter I-3. --- Chemistry of PAF --- p.8
Chapter I-4. --- Pathobiology of PAF --- p.9
Chapter II. --- PAF Receptor --- p.10
Chapter II-1. --- Presence and Characteristics of PAF Receptor --- p.10
Chapter II-l-l. --- Solubilization of PAF Receptor --- p.10
Chapter II-1-2. --- G-Protein Involvement --- p.11
Chapter II-1-3. --- Species Differences --- p.11
Chapter II-1-4. --- Multiple Conformational States of PAF Receptor --- p.12
Chapter II-1-5. --- PAF Receptor Heterogeneity --- p.12
Chapter II-2. --- Putative Conformation of PAF Membrane Binding Sites --- p.13
Chapter II-3. --- Recent Progress in PAF Receptor Research --- p.15
Chapter III. --- PAF Receptor Antagonist --- p.18
Chapter III-1. --- Classification of PAF Antagonists --- p.18
Chapter III-2. --- Inhibition Types of PAF Receptor Antagonists --- p.19
Chapter III-2-1. --- Nonspecific Inhibition of the Effects of PAF --- p.21
Chapter III-2-2. --- Specific Inhibition of PAF --- p.22
Chapter III-3. --- Recent Progress in PAF Receptor Antagonist Research --- p.22
Chapter IV. --- Pharmacology and Syntheses of Spiro-Ether Structural Units --- p.26
Chapter IV-1. --- Natural Products Containing Spiro-Ether and Related Structural Units --- p.30
Chapter IV-1-1. --- Labdane Diterpenoids Containing Spiro-Ether Structural Units --- p.30
Chapter IV-1-2. --- Leucodrin and Related Derivatives --- p.32
Chapter IV-2. --- Synthetic Methods of Spiro-Ethers and Related Derivatives --- p.34
Chapter V. --- Aim of the Present Work --- p.45
RESULTS AND DISCUSSION --- p.47
Chapter I. --- Isolation and Structure Elucidation of Prehispanolone (1) and Preleoheterin (3) --- p.47
Chapter I-1. --- Material and Isolation --- p.47
Chapter I-2. --- Structure Elucidation of Prehispanolone (1) and Preleoheterin (3) --- p.47
Chapter II. --- Synthesis of Model Compounds --- p.53
Chapter II-l. --- "Synthesis of 2-Methyl-1,7-dioxaspiro[4.4]nonane (137)" --- p.53
Chapter II-2. --- "Synthesis of 2,2-Dimethyl-l,7-dioxaspiro[4.4]nonane (139)" --- p.68
Chapter II-3. --- "Synthesis of 2,2-Diphenyl-1,7-dioxaspiro[4.4]nonane (141) and 2,2-Diphenyl-l,7-dioxaspiro[4.4]non-8-ene (142)" --- p.72
Chapter III. --- "Partial Synthesis of 13R, 14,15-Dihydroprehispanolone (5)，13S,14,15-Di- hydroprehispanolone (135) and prehispanolone (1)" --- p.76
CONCLUSION --- p.89
EXPERIMENTAL SECTION --- p.91
REFERENCES --- p.126
APPENDIX --- p.141
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Tseng, Chun-Ren, and 曾俊仁. "Computing the Partial Derivatives of an Unknown Function Using Fuzzy Network." Thesis, 1996. http://ndltd.ncl.edu.tw/handle/98850716449115161338.
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碩士國立交通大學
控制工程系
84
In this thesis, we use a fuzzy neural network (FNN) system to approximatelycompute the partial derivative of an unknown function. Since the FNN is a universal approximator and is differentiable when its membership functions areall differentiable, we will use its partial derivatives to substitute the partial derivatives of an unknown function. From the proposed FNN structure, the derivative of any order can be easily obtained by only changing its membership functions. As we know, a slight modeling error may cause a large sensitivity error. This error is reduced by canceling the redundant rules which are negligible on the function value but are important on the derivative. Furthermore, this proposed method is also illustrated by solving an optimization problem and obtaining the sensitivity of the unknown system on adaptive control.
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Chih-YuanHsu and 許志遠. "Bandwidth selectors for kernel estimation of density partial derivatives and mode estimates of multivariate data." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/59743997547569053256.
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博士國立成功大學
統計學系碩博士班
101
Based on a random sample of size n from an unknown multivariate density f, two research topics are investigated: (i) bandwidth selection in multivariate kernel density partial derivatives, and (ii) mode estimation of a multivariate density. On the topic (i), a bandwidth selector is proposed, which extends the ones of Wu (1997) and Wu and Tsai (2004). The bandwidth selector is asymptotically normal with the optimal root n relative convergence rate and achieves the (conjectured) “lower bound” on the covariance matrix. On the topic (ii), two mode estimates are proposed. The first one is a multivariate extension to the one of Bickel (2003), which is an application of the joint Box-Cox transform. Also, we show that the estimate is quite efficient when the sample size n is relatively small. However, the first one may not be consistent due to the restriction of the transform method. To solve the non-consistent problem, the second estimate is proposed, which is based on a weighted average of a parametric density estimate and a nonparametric density estimate. It is shown that the estimate not only keeps the strengths of the first one at small n but also overcomes the non-consistent drawback at large n.
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Dang, Duy Minh. "Modeling Multi-factor Financial Derivatives by a Partial Differential Equation Approach with Efficient Implementation on Graphics Processing Units." Thesis, 2012. http://hdl.handle.net/1807/42485.
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This thesis develops efficient modeling frameworks via a Partial Differential Equation (PDE) approach for multi-factor financial derivatives, with emphasis on three-factor models, and studies highly efficient implementations of the numerical methods on novel high-performance computer architectures, with particular focus on Graphics Processing Units (GPUs) and multi-GPU platforms/clusters of GPUs. Two important classes of multi-factor financial instruments are considered: cross-currency/foreign exchange (FX) interest rate derivatives and multi-asset options. For cross-currency interest rate derivatives, the focus of the thesis is on Power Reverse Dual Currency (PRDC) swaps with three of the most popular exotic features, namely Bermudan cancelability, knockout, and FX Target Redemption. The modeling of PRDC swaps using one-factor Gaussian models for the domestic and foreign interest short rates, and a one-factor skew model for the spot FX rate results in a time-dependent parabolic PDE in three space dimensions. Our proposed PDE pricing framework is based on partitioning the pricing problem into several independent pricing subproblems over each time period of the swap's tenor structure, with possible communication at the end of the time period. Each of these subproblems requires a solution of the model PDE. We then develop a highly efficient GPU-based parallelization of the Alternating Direction Implicit (ADI) timestepping methods for solving the model PDE. To further handle the substantially increased computational requirements due to the exotic features, we extend the pricing procedures to multi-GPU platforms/clusters of GPUs to solve each of these independent subproblems on a separate GPU. Numerical results indicate that the proposed GPU-based parallel numerical methods are highly efficient and provide significant increase in performance over CPU-based methods when pricing PRDC swaps. An analysis of the impact of the FX volatility skew on the price of PRDC swaps is provided.
In the second part of the thesis, we develop efficient pricing algorithms for multi-asset options under the Black-Scholes-Merton framework, with strong emphasis on multi-asset American options. Our proposed pricing approach is built upon a combination of (i) a discrete penalty approach for the linear complementarity problem arising due to the free boundary and (ii) a GPU-based parallel ADI Approximate Factorization technique for the solution of the linear algebraic system arising from each penalty iteration. A timestep size selector implemented efficiently on GPUs is used to further increase the efficiency of the methods. We demonstrate the efficiency and accuracy of the proposed GPU-based parallel numerical methods by pricing American options written on three assets.
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Trabulsi, Manal. "Effect of enamel matrix derivatives (EMD) on collagen GTR-based root coverage procedure a thesis submitted in partial fulfillment ... for the degree of Master of Science in Periodontics ... /." 2003. http://catalog.hathitrust.org/api/volumes/oclc/68962689.html.
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Lee, Tze-Kei, and 李澤愷. "Higher Derivative Particle Theory as String Theory." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/42247661673455980389.
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碩士國立臺灣大學
物理研究所
95
We study higher derivative theory with Lagrangian admitting symmetry group which is locally equivalent to conformal group in two dimensions and find there exists a tower of classes of such theory. We propose that new consistent background of string theory could be found in those classes. To demostrate such possiblity, we show that there are Lagrangian corresponding to open and closed string.
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Lee, Tze-Kei. "Higher Derivative Particle Theory as String Theory." 2007. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0001-1207200715460200.
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Jhang, Dingshun, and 張登順. "Kan-Li Hexagram Multiple Symplectic Derivative Synchronization by Partial Region Stability Theory." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/76887242977897768068.
Full textAbstract:
碩士國立交通大學
機械工程學系
100
“Tai Ji”, the great one, is the combination of Yin and Yang, and Tai Ji chaotic system is the combination of “Yang” chaotic system and “Yin” chaotic system. Yang system represents contemporary system, and Yin system means historical system. The eight trigrams, a part of Chinese philosophy, is advance of “Tai Ji”, and they have their own directions, figures, and representations. Trigram synchronization uses three different chaos systems by the figures, and multiple symplectic derivative synchronization is used. Hexagram, advance of the eight trigrams, has two parts, upper and low, which both represent a trigram, and the hexagram synchronization is advance of trigram synchronization. The generalized synchronization is that there exists a functional relationship between the states of the master and those of the slave. A new type of chaotic synchronization, multiple chaotic symplectic synchronization, is obtained with the state variables of the original system and of another different order system as constituents of the functional relation of “partners”. Numerical simulations are provided to verify the effectiveness of the scheme.
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黃啟任. "Kun-Zhen Hexagram Multiple Symplectic Derivative Synchronization by Partial Region Stability Theory." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/12589518613219888449.
Full textAbstract:
碩士國立交通大學
機械工程學系
100
The generalized synchronization is that there exists a functional relationship between the states of the master and those of the slave. A new type of chaotic synchronization, multiple chaotic symplectic derivative synchronization, is obtained with the state variables of the original system and of another different order system as constituents of the functional relation of “partners”. Numerical simulations are provided to verify the effectiveness of the proposed scheme. In Chinese philosophy, Yin means negative, historical, or feminine principle while Yang is positive, contemporary, or masculine principle. Yin and Yang are two fundamental opposites in Chinese philosophy, and “Tai Ji”, the great one, is the combination of Yin and Yang, which maybe the origin of Cosmos. The eight trigrams is a part of Chinese philosophy, and they have their own direction, figure, and representation. In this thesis,as examples,Kun trigram and Zhen trigram are studied. Combining Kun trigram in upper place and Zhen trigram in lower place can get Kun-Zhen hexagram. Kun-Zhen hexagram can be annotated by chaos and its synchronization.
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Ji, Ting-Yu, and 紀亭宇. "Gen-Xun Hexagram Multiple Symplectic Derivative Synchronization by Partial Region Stability Theory." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/12752047445357649001.
Full textAbstract:
碩士國立交通大學
機械工程學系
100
Yin and Yang are two fundamental opposites in Chinese philosophy. Chaos of contemporary Chen system, i.e. Yang chaos of Chen system, has been investigated completely. In this proposal, chaos of historical Chen system, i.e. Yin chaos of Chen system, is studied with comparison to that of Yang chaos by time histories of states, phase portraits, bifurcation diagrams and Lyapunov exponents. Furthermore, by Chinese philosophy, Tai Ji chaos, i.e. Great One chaos, which consists of Yin chaos and Yang chaos, of Chen system is studied firstly. The generalized synchronization is that there exists a functional relationship between the states of the master and those of the slave. A new strategy to achieve chaos generalized synchronization and multiple symplectic derivative synchronization, is obtained with the state variables of the original system and of another different order system as constituents of the functional relation of “partners”. Finally, numerical simulations are given to verify the effectiveness of the proposed scheme examples. “The Book of Changes” is a classic text of Chinese culture. In this thesis, the trigram consisted by three broked lines or unbroken lines forms various chaos synchronization. Numerical simulations in examples of Gen and Xun trigram generalized synchronization are given to verify the effectiveness of the proposed scheme. Finally, combining Gen trigram in upper place and Xun trigram in lower place can get Gen-Xun hexagram. Gen-Xun hexagram can be annotated by Chaos and its synchronization.
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Li, Chienhua, and 李健華. "Qian-Dui Hexagram Multiple Symplectic Derivative Synchronization by Partial Region Stability Theory." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/62707617572238141376.
Full textAbstract:
碩士國立交通大學
機械工程學系
100
The generalized synchronization is that there exists a functional relationship between the states of the master and those of the slave. A new type of chaotic synchronization, multiple chaotic symplectic derivative synchronization, is obtained with the state variables of the original system and of another different order system as constituents of the functional relation of “partners”. Numerical simulations are provided to verify the effectiveness of the proposed scheme. In Chinese philosophy, Yin means negative, historical, or feminine principle while Yang is positive, contemporary, or masculine principle. Yin and Yang are two fundamental opposites in Chinese philosophy, and “Tai Ji”, the great one, is the combination of Yin and Yang, which maybe the origin of Cosmos. The eight trigrams is a part of Chinese philosophy, and they have their own direction, figure, and representation. In this thesis, as examples, Qian trigram and Dui trigram are studied, combining Qian trigram in upper place and Dui trigram in lower place can get Qian-Dui hexagram. Qian-Dui hexagram can be annotated by chaos and its synchronization..