A Julia set for a complex function 𝑓 is the set of all points in the complex plane where the iterates of 𝑓 do not form a normal family. A picture of the Julia set for a function can be generated with a computer by coloring pixels (which we consider to be small squares) based on the behavior of the point at the center of each pixel. We consider the accuracy of computer generated pictures of Julia sets. Such a picture is said to be accurate if each colored pixel actually contains some point in the Julia set. We extend previous work to show that the pictures generated by an algorithm for the family λe² are accurate, for appropriate choices of parameters in the algorithm. We observe that the Julia set for meromorphic functions with polynomial Schwarzian derivative is the closure of those points which go to infinity under iteration, and use this as a basis for an algorithm to generate pictures for such functions. A pixel in our algorithm will be colored if the center point becomes larger than some specified bound upon iteration. We show that using our algorithm, the pictures of Julia sets generated for the family λtan(z) for positive real λ are also accurate. We conclude with a cautionary example of a Julia set whose picture will be inaccurate for some apparently reasonable choices of parameters, demonstrating that some care must be exercised in using such algorithms. In general, more information about the nature of the function may be needed. / Ph. D.

Emulation of computer experiments via surrogate models can be difficult when the number of input parameters determining the simulation grows any greater than a few dozen. In this dissertation, we explore dimension reduction in the context of computer experiments. The active subspace method is a linear dimension reduction technique which uses the gradients of a function to determine important input directions. Unfortunately, we cannot expect to always have access to the gradients of our black-box functions. We thus begin by developing an estimator for the active subspace of a function using kernel methods to indirectly estimate the gradient. We then demonstrate how to deploy the learned input directions to improve the predictive performance of local regression models by ``undoing" the active subspace. Finally, we develop notions of sensitivities which are local to certain parts of the input space, which we then use to develop a Bayesian optimization algorithm which can exploit locally important directions. / Doctor of Philosophy / Increasingly, scientists and engineers developing new understanding or products rely on computers to simulate complex phenomena. Sometimes, these computer programs are so detailed that the amount of time they take to run becomes a serious issue. Surrogate modeling is the problem of trying to predict a computer experiment's result without having to actually run it, on the basis of having observed the behavior of similar simulations. Typically, computer experiments have different settings which induce different behavior. When there are many different settings to tweak, typical surrogate modeling approaches can struggle. In this dissertation, we develop a technique for deciding which input settings, or even which combinations of input settings, we should focus our attention on when trying to predict the output of the computer experiment. We then deploy this technique both to prediction of computer experiment outputs as well as to trying to find which of the input settings yields a particular desired result.

The development and introduction of financial derivatives have great impact on modern finance. Option pricing theory has become a powerful tool to value and to understand these innovations. It is also an indispensable tool to calculate hedge ratios for risk measurement and management. On the one hand, the introduction of new financial derivatives has been blamed for making financial market more volatile and risky as evidenced in the financial markets of the USA and Japan, especially during the expiration of index futures and index options, On the other hand, the applicability of new pricing models to hedging strategies is essential in monitoring and managing option positions. This study tries to give some answers on first: whether the expiration of financial derivatives increases the volatility of the Hong Kong stock market; second: whether we can better hedge by straightly applying more elaborated option valuation models replacing the standard Black-Scholes model, which market participants commonly employed for hedging option positions. Part I of this article addresses the first question while Part II studies the second question. / Yung Hei Ming. / Source: Dissertation Abstracts International, Volume: 62-09, Section: A, page: 3138. / Supervisor: Zhang Hua. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Leksiniai sinonimai – skirtingai skambantys, tos pačios ar artimos reikšmės žodžiai, kurie skiriasi semantinėmis, emocinėmis, stilistinėmis ypatybėmis. Darybiniais sinonimais laikomi skirtingų darybos afiksų bendrašakniai dariniai, turintys tapačią arba artimą leksinę ir darybinę reikšmę. Į leksinių sinonimų eiles dažnai įeina ir darybinių sinonimų eilės. Antano Lyberio Sinonimų žodyne (2002) pateiktose leksinių sinonimų eilėse rastas 4471 daiktavardžių, būdvardžių, veiksmažodžių darinys, iš kurių sudarytos 1836 darybinių sinonimų eilės. Bendrašakniai dariniai, kaip ir leksiniai sinonimai, gali sutapti ar skirtis stilistinėmis ypatybėmis. Daugumas sinonimiškai santykiaujančių darinių yra artimos semantikos žodžiai. Analizuojant darybinius sinonimus leksinių sinonimų eilėse pastebėta, kad ne visi žodžiai, esantys Lietuvių kalbos žodyne ir Dabartinės lietuvių kalbos žodyne, yra įtraukti į A. Lyberio Sinonimų žodyną. Remiantis šių žodynų medžiaga, į Sinonimų žodyną siūloma įtraukti 800 žodžių ir pratęsti 82 leksinių sinonimų eiles. Iš į Sinonimų žodyną neįtrauktų darinių sudarytos 123 naujos darybinių sinonimų eilės: į 94 eilių sudėtį įeina Sinonimų žodyne fiksuotas darinys, 29 darybinių sinonimų eilės sudarytos vien iš naujų darinių. Sinonimų žodyne rasta žodžių, kurie nefiksuojami nei Lietuvių kalbos žodyne, nei Dabartinės lietuvių kalbos žodyne, todėl nėra aišku, kokiu kriterijumi remiantis jie buvo įtraukti į žodyną. / Lexical synonyms are differently sounding words of the same or close meaning that are different by semantic, emotional or stylistic features. Derivative synonyms are structures of different affix with identical or close lexical and derivation meaning. Lexical synonyms rows often included derivative synonyms rows. Dictionary of Synonyms (Sinonimų žodynas, 2002) by Antanas Lyberis submitted lexical synonyms rows were found 4471 noun, adjective and verb derivatives, which were made 1836 derivative synonyms rows. Conjugate structures, as well as lexical synonyms, may be the same or vary by stylistic features. Most of the derivatives, having synonymous relationships, are close semantic words. Analysis of derivative synonyms in lexical synonym rows noted that not all the words in Lithuanian Language Dictionary (Lietuvių kalbos žodynas), Current Lithuanian Dictionary (Dabartinės lietuvių kalbos žodynas) are included in Dictionary of Synonyms by Antanas Lyberis. According to these dictionaries material, it is proposed to include 800 words extend 82 lexical synonym rows in Dictionary of Synonyms. Were made 123 new derivative synonym rows from the words that were not included into Dictionary of Synonyms: 94 rows containing fixed derivatives of Dictionary of Synonyms, 29 derivative synonym rows consisting entirely of new structures. In Dictionary of Synonyms were found words not included into Lithuanian Language Dictionary, Current Lithuanian Dictionary, so it is not clear by which... [to full text]

Nominalisation is being considered as one of the tendencies of the contemporary German. The diploma thesis focuses not only on noun derivatives. This diploma thesis deals with the nominal style in general, which is rich on the derivative nouns and different kinds of noun-verb combinations. In contrary to verbal style, the nominal style occurs primarily in the written and professional language. However, some features are to be found even on level A1 and A2 and are used in everyday spoken language. The goal of this thesis is to analyse the textbooks for children and young adults and to find in what level occur the features of the nominal style in textbooks for secondary schools.

Submitted by MARCIA ROVADOSCHI (marciar@unifra.br) on 2018-08-20T17:53:01Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_JaniceRachelli.pdf: 4818944 bytes, checksum: 0c02a81d2b4c04364b21e1ddddc2fe58 (MD5) / Made available in DSpace on 2018-08-20T17:53:01Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_JaniceRachelli.pdf: 4818944 bytes, checksum: 0c02a81d2b4c04364b21e1ddddc2fe58 (MD5) Previous issue date: 2017-10-03 / The present study is on the field of Mathematics Education in higher education and is focused on the teaching and learning of Calculus concepts, specifically related to the concepts of classical derivative and weak derivative. The work, developed in the context of a qualitative research, aims to investigate how some students of the Master degree course in Teaching Mathematics of a community institution in Rio Grande do Sul comprehend the concepts of classical derivative and weak derivative. The APOS theory serves as a theoretical and methodological reference for the elaboration of the genetic decomposition in which the possible mental constructions used by the students were described in what the understanding of the concepts of classical derivative and weak derivative concern. We proposed some activities on the historical constructions of the classical concept, the derivative in the present times, and the passage from the classical derivative to the weak derivative. The teaching situations were developed in the classroom in the second semester of 2016, within the subject of Fundamentals of Differential and Integral Calculus. The basis for these activities was the ACE teaching cycle. The results obtained by analyzing the students' records in the proposed activities and the observations recorded in the field diary indicate that the students were able to coordinate actions and processes in order to obtain the derivative and verify if a function is differentiable. They could also coordinate the interpretations of the derivative, such as slope of the tangent line, instantaneous velocity and rate of variation, besides using mechanisms of generalization and reversibility in the analysis of the graphs of functions and their derivatives and encapsulating the processes necessary for a satisfactory understanding of the concept of the classical derivative. By means of the integral equation, the integration formula by parts, and the fundamental theorem of Calculus, the students were able to coordinate the function and intervals, the functions with compact support by means of internalizing actions and processes for the encapsulation of the mathematical object and weak derivative. Although there are some errors in these processes, there is evidence that the concepts of classical derivative and weak derivative have been understood by the students. These evidences developed mental mechanisms of reflective abstraction that allowed the construction of the mental structures of action, process, object and scheme present in the genetic decomposition that allowed them to understand the concepts. Moreover, the treatment with the historical context of the derivative and the collaborative work of the students were significant factors to obtain the results of the research. / O presente estudo se situa no campo da Educação Matemática no ensino superior e se insere na linha de investigação voltada ao ensino e aprendizagem de conceitos do Cálculo, especificamente ligados aos conceitos de derivada clássica e derivada fraca. O trabalho, desenvolvido no contexto de uma pesquisa qualitativa, teve como objetivo investigar como se dá a compreensão dos conceitos de derivada clássica e derivada fraca por estudantes de um curso de mestrado em Ensino de Matemática de uma instituição comunitária do Rio Grande do Sul. Tendo a teoria APOS como referencial teórico e metodológico, elaborou-se a decomposição genética, em que foram descritas as possíveis construções mentais utilizadas pelos estudantes para a compreensão dos conceitos de derivada clássica e derivada fraca. Foram organizadas situações de ensino compostas por atividades sobre as construções históricas do conceito clássico, a derivada nos tempos atuais e a passagem da derivada clássica para a derivada fraca. As situações de ensino foram desenvolvidas em sala de aula, no segundo semestre de 2016, na disciplina de Fundamentos de Cálculo Diferencial e Integral, tendo como base o ciclo de ensino ACE. Os resultados obtidos, por meio da análise dos registros dos alunos nas atividades propostas e das observações anotadas no diário de campo, indicam que os estudantes foram capazes de coordenar ações e processos para obter a derivada e verificar se uma função é diferenciável, coordenar as interpretações da derivada como inclinação da reta tangente, velocidade instantânea e taxa de variação, além de, utilizar mecanismos de generalização e reversibilidade na análise dos gráficos das funções e suas derivadas e de encapsular os processos necessários para a compreensão, de forma satisfatória, do conceito da derivada clássica. Por meio da equação integral, da fórmula de integração por partes e do teorema fundamental do Cálculo, os alunos coordenaram a função e os intervalos, funções com suporte compacto, interiorizando ações e processos para a encapsulação do objeto matemático, derivada fraca. Embora com alguns erros cometidos nesses processos, há evidências de que houve compreensão dos conceitos de derivada clássica e derivada fraca pelos estudantes. Estes evidenciaram desenvolver mecanismos mentais de abstração reflexionante que possibilitaram a construção das estruturas mentais de ação, processo, objeto e esquema presentes na decomposição genética que lhes permitiu compreender os conceitos. Além do mais, o trato com o contexto histórico da derivada e o trabalho colaborativo dos alunos foram fatores significativos para a obtenção dos resultados da pesquisa.

The international financial environment has become riskier due to the recent developments in product offerings and failure of regulation to keep abreast with these changes. The Global Financial Crisis exposed inadequacies of regulation, thus consensus on the need for comprehensive and uniform regulation was made by G-20 member states. Imposing exchange trading, clearing, reporting and capital requirements on the derivatives market are some of the ways of dealing with the problems caused by lax regulatory oversight. In this study, through the comparative analysis of derivatives regulation in South Africa, Brazil, India and Turkey, it was established that emerging countries are taking active steps to implement the G-20 agreement. Uniformity in the core rules was noted, with differences in the supportive legislation. Country specific rules which support the macroeconomic factors that are faced by these countries and the infrastructure available for regulatory execution are used amongst countries. The study concluded that current regulation in emerging countries is accommodative and regulatory differences are in line with economic factors in each country.

Linear Evolution Equations (LEE) have been studied extensively over many years. Their extension in the field of fractional calculus have been defined by Dαu(x, t) = Au(x, t), where α is the fractional order and Dα is a generalized differential operator. Two types of generalized differential operators were applied to the LEE in the state-of-the-art, producing the Riemann-Liouville and the Caputo time fractional evolution equations. However the extension of the new Caputo-Fabrizio derivative (CFFD) to these equations has not been developed. This work investigates existing fractional derivative evolution equations and analyze the generalized linear evolution equations with non-singular ker- nel derivative. The well-posedness of the extended CFFD linear evolution equation is demonstrated by proving the existence of a solution, the uniqueness of the existing solu- tion, and finally the continuous dependence of the behavior of the solution on the data and parameters. Extended evolution equations with CFFD are applied to kinetics, heat diffusion and dispersion of shallow water waves using MATLAB simulation software for validation purpose. / Mathematical Science / M Sc. (Applied Mathematics)

[pt] Os dados adquiridos nos experimentos físicos e nas imagens geométricas ou médicas são tipicamente discretas. Esses dados são interpretados como amostras de uma função desconhecida, porém cujas derivadas servem para caracterizar o dado. Por exemplo, o movimento de um fluido é descrito por um campo de velocidades, uma curva é caracterizada pela evolução da sua curvatura, as imagens médicas são geralmente segmentadas por estimativas de gradiente, entre outros. É possível obter derivadas coerentes a partir de filtragem dos dados. Porém, em dados multi-dimensionais, os filtros usuais privilegiam direções alinhadas com os eixos, o que pode gerar problemas quando essas derivadas são interpretadas geometricamente. Por exemplo, a curvatura estimada dependeria da orientação da curva, perdendo o sentido geométrico da curvatura. O objetivo do presente trabalho é melhorar a invariância geométrica dos filtros de derivadas. / [en] Typical data acquired in physical experiments or in geometrical or medical imaging are discrete. This data is generally interpreted as samples of an unknown function, whose derivatives still serve for the data characterisation. For example, the movement of a fluid is described as a velocity field, a curve is characterised by the evolution of its curvature, images used in medical sciences are usually segmented by estimates of their gradients, among others. It is possible to obtain coherent derivatives by filtering the data. However, with multidimensional data, the usual filters present a bias towards to favor directions aligned with the axis, which may induce problems when the derivatives are interpreted geometrically. For example, the estimated curvature would depend on the orientation of the curve, loosing the geometric meaning of the curvature. The goal of the present work is to improve the geometric invariance of derivative filters.

by Ng Hon Sun, Stephen & Poon Ming Him. / Thesis (M.B.A.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 50-52). / ABSTRACT --- p.ii / TABLE OF CONTENTS --- p.iv / LIST OF TABLES --- p.v / LIST OF FIGURES --- p.v / ACKNOWLEDGEMENT --- p.vi / Chapter I. --- INTRODUCTION --- p.1 / Chapter II. --- CHARACTERISTICS OF WARRANTS AND THE NATURE OF HK WARRANT MARKET --- p.5 / Chapter II (i) --- Warrants Versus Call Options --- p.5 / Chapter II (ii) --- Historical Development of Warrants in Hong Kong --- p.6 / Chapter II (iii) --- Equity Warrants --- p.7 / Chapter II (iv) --- Derivative Warrants --- p.8 / Chapter II (v) --- The Risks of Derivative Warrants --- p.10 / High Inherent Risks --- p.10 / Complex Exercise Conditions and Conversion Adjustments --- p.10 / Chapter II (vi) --- Regulatory Environment of Derivative Warrants --- p.12 / Chapter III. --- LITERATURE REVIEW --- p.14 / Chapter IV. --- DATA AND METHODOLOGY EMPLOYED --- p.19 / Chapter IV (i) --- Date Employed --- p.19 / Chapter IV (ii) --- Methodology Employed --- p.24 / Chapter V. --- EMPIRICAL RESULTS AND INTERPRETATION --- p.28 / Chapter V (i) --- Market Trend Before and After Listing --- p.37 / Chapter V (ii) --- Trading Volume --- p.38 / Chapter V (iv) --- Volatility --- p.39 / Chapter VI. --- CONCLUSIONS --- p.44 / APPENDIXES --- p.46 / APPENDIX A STOCKS SELECTED FOR STUDY --- p.46 / APPENDIX B CONSTITUENT STOCKS OF HANG SENG INDEX --- p.47 / APPENDIX C HANG SENG INDEX 1993-1994 --- p.48 / APPENDIX D HANG SENG INDEX RETURN AND SELECTED STOCK UNADJUSTED MEAN RETURN --- p.49 / REFERENCES --- p.50 / LIST OF TABLES / TABLE 1 DERIVATIVE STOCK WARRANTS LISTING IN 1993 -1 994 --- p.21 / TABLE 2 COMPARISON OF PRE- AND POST- LISTING RETURNS --- p.28 / TABLE 3 EXCESS MARKET RATE OF RETURN AND CUMULATIVE EXCESS MARKET RATE OF RETURN --- p.32 / TABLE 4 MARKET MODEL RATE OF RETURN AND CUMULATIVE MARKET MODEL RATE OF RETURN --- p.33 / TABLE 5 β'S CALCULATED ON THE UNDERLYING STOCK --- p.33 / TABLE 6 MARKET TREND BEFORE AND AFTER LISTING OF DERIVATIVE WARRANTS --- p.37 / TABLE 7 EFFECTS OF DERIVATIVE WARRANT LISTING ON RISK CHARACTERISTICS OF UNDERLYING STOCKS --- p.41 / LIST OF FIGURES / FIGURE 1 SUMMARY OF THE REGULATIONS ON DERIVATIVE WARRANTS --- p.13 / FIGURE 2 WARRANT LISTINGS DISTRIBUTION MAP --- p.23 / FIGURE 3 CUMULATIVE RETURN % (ADJUSTED AND UNADJUSTED) --- p.31 / FIGURE 4 IMPACT OF LISTING ON VARIANCE --- p.40