Dissertations / Theses on the topic 'Mean Value Theorem'

Les travaux de cette thèse portent sur l’estimation et la commande décentralisée des systèmes de grande dimension. L’objectif est de développer des capteurs logiciels pouvant produire une estimation fiable des variables nécessaires pour la stabilisation des systèmes non linéaires interconnectés. Une décomposition d’un tel système de grande dimension en un ensemble de n sous-systèmes interconnectés est primordiale. Ensuite, en tenant compte de la nature du sous-système ainsi que les fonctions d’interconnexions, des lois de commande décentralisées basées observateurs ont été synthétisées. Chaque loi de commande est associée à un sous-système qui permet de le stabiliser localement, ainsi la stabilité du système global est assurée. L’existence d’un observateur et d’un contrôleur stabilisant le système dépend de la faisabilité d’un problème d’optimisation LMI. La formulation LMI, basée sur l’approche de Lyapunov, est élaborée par l’utilisation de principe de DMVT sur la fonction d’interconnexion non linéaire supposée bornée et incertaine. Ainsi des conditions de synthèse non restrictives sont obtenues. Des méthodes de synthèse de loi de commande décentralisée basée observateur ont été proposées pour les systèmes non linéaires interconnectés dans le cas continu et dans le cas discret. Des lois de commande robuste H1 décentralisées sont élaborées pour les systèmes non linéaires interconnectés en présence de perturbations et des incertitudes paramétriques. L’efficacité et la validation des approches présentées sont testées sur un modèle de réseaux électriques composé de trois générateurs interconnectés
This thesis focuses on the decentralized estimation and control for large scale systems. The objective is to develop software sensors that can produce a reliable estimate of the variables necessary for the interconnected nonlinear systems stability analysis. A decomposition of a such large system into a set of n interconnected subsystems is paramount for model simplification. Then, taking into account the nature of the subsystem as well as the interconnected functions, observer-based decentralized control laws have been synthesized. Each control law is associated with a subsystem which allows it to be locally stable, thus the stability of the overall system is ensured. The existence of an observer and a controller gain matrix stabilizing the system depends on the feasibility of an LMI optimization problem. The LMI formulation, based on Lyapunov approach, is elaborated by applying the DMVT technique on the nonlinear interconnection function, assumed to be bounded and uncertain. Thus, non-restrictive synthesis conditions are obtained. Observer-based decentralized control schemes have been proposed for nonlinear interconnected systems in the continuous and discrete time. Robust Hinfini decentralized controllers are provided for interconnected nonlinear systems in the presence of perturbations and parametric uncertainties. Effectiveness of the proposed schemes are verified through simulation results on a power systems with interconnected machines

Thesis (M.S.)--University of Akron, Dept. of Mathematics, 2007.
"May, 2007." Title from electronic thesis title page (viewed 4/28/2009) Advisor, Ali Hajjafar; Faculty readers, Linda Marie Saliga, Lala Krishna; Department Chair, Joseph W. Wilder; Dean of the College, Ronald F. Levant; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.

The phenomenon of financial bubbles is known to have impacted various markets since the seventeenth century. Such bubbles are known to form when the market drastically overvalues the price of an asset, causing its market value to increase hyperbolically, only to suddenly collapse once the untenable perceived future prospects of the asset are realized. Hence, it remains crucial for investors to be able to sell off assets residing within a bubble before they burst and their value is significantly diminished. Thus, portfolio optimization methods capable of accounting for financial bubbles in stock dynamics is a field of great value and interest for market participants. Portfolio optimization with respect to the mean-field is a relatively novel approach to accounting for the bubble-phenomenon. Hence, this paper investigates a previously unattempted method of portfolio optimization, providing a mean-field solution to the mean-variance trade-off problem, as well as providing new definitions of stock dynamics capable of diverting investors from bubbles.
Finansiella bubblor är ett fenomen som har påverkat marknader sedan 1600-talet. Bubblor tenderar att skapas när marknaden kraftigt övervärderar en tillgång vilket orsakar en hyperbolisk tillväxt i marknadspriset. Detta följs av en plötslig kollaps. Därför är det viktigt för investerare att kunna minska sin exponering mot aktier som befinner sig i en bubbla, så att risken för stora plötsliga förluster reduceras. Således är portföljoptimering där aktiedynamiken tar hänsyn till bubblor av högt intresse för marknadsdeltagare. Portföljoptimering med avseende på medelfältet är ett relativt nytt tillvägagångssätt för att behandla bubbelfenomen. Av denna anledning undersöks i detta arbete en hittills oprövad lösningsmetod som möjliggör en medelfältslösning till avvägningen mellan förväntad avkastning och risk. Där-utöver presenteras även ett antal nya modeller för aktier som kan bortleda investerare från bubblor.

Diese Dissertation präsentiert Modelle zur Lösung von Verhandlungsproblemen mit diskreten Strukturen. Hauptgrundlage der Betrachtung ist dabei die Erweiterung und Anwendung von Theorien der kooperativen Spieltheorie. Insbesondere der Shapley-Wert spielt eine wichtige Rolle. Als erste Problemklasse werden kooperative Spiele präsentiert, bei denen einige Spiele feste Auszahlungen erhalten. Als zweite Problemklasse werden kooperative Spiele untersucht, deren Lösungen ausschließlich ganzzahlig sein dürfen.

The main target of this thesis is to summarize and explain the specifics of power markets and test application of models, which might be used especially in risk management area. Thesis starts with definition of market subjects, typology of traded contracts and description of market development with focus on Czech Republic. Thesis continues with development of theoretical concepts of short term/spot electricity markets and potential link between spot and forward electricity markets. After deriving of those microeconomic fundamental models we continue with stochastic models (Jump Diffusion Mean Reverting process and Extreme Value Theory) in order to depict patterns of spot and forward power contracts price volatility. Last chapter deals with credit risk specifics of power trading and develops model (using concept known as Credit Value Adjustment) to compare economic efficiency of OTC and exchange power trading. Developed and described models are tested on selected power markets, again with focus on Czech power market data set.

Portfolio selection has a long tradition in financial economics and plays an integral role in investment management. Portfolio selection provides the framework to determine optimal portfolio choice from a universe of available investments. However, the asset weightings from portfolio selection are optimal only if the empirical characteristics of asset returns do not violate the portfolio selection model assumptions. This thesis explores the empirical characteristics of traditional assets and hedge fund returns and examines their effects on the assumptions of linearity-in-the-mean testing and portfolio selection. The encompassing theme of this thesis is the empirical interplay between traditional assets and hedge fund returns. Despite the paucity of hedge fund research, pension funds continue to increase their portfolio allocations to global hedge funds in an effort to pursue higher risk-adjusted returns. This thesis presents three empirical studies which provide positive insights into the relationships between traditional assets and hedge fund returns. The first two empirical studies examine an emerging body of literature which suggests that the relationship between traditional assets and hedge fund returns is non-linear. For mean-variance investors, non-linear asset returns are problematic as they do not satisfy the assumption of linearity required for the covariance matrix in portfolio selection. To examine the linearity assumption as it relates to a mean-variance investor, a hypothesis test approach is employed which investigates the linearity-in-the-mean of traditional assets and hedge funds. The findings from the first two empirical studies reveal that conventional linearity-in-the-mean tests incorrectly conclude that asset returns are nonlinear. We demonstrate that the empirical characteristics of heteroscedasticity and autocorrelation in asset returns are the primary sources of test mis-specification in these linearity-in-the-mean hypothesis tests. To address this problem, an innovative approach is proposed to control heteroscedasticity and autocorrelation in the underlying tests and it is shown that traditional assets and hedge funds are indeed linear-in-the-mean. The third and final study of this thesis explores traditional assets and hedge funds in a portfolio selection framework. Following the theme of the previous two studies, the effects of heteroscedasticity and autocorrelation are examined in the portfolio selection context. The characteristics of serial correlation in bond and hedge fund returns are shown to cause a downward bias in the second sample moment. This thesis proposes two methods to control for this effect and it is shown that autocorrelation induces an overallocation to bonds and hedge funds. Whilst heteroscedasticity cannot be directly examined in portfolio selection, empirical evidence suggests that heteroscedastic events (such as those that occurred in August 1998) translate into the empirical feature known as tail-risk. The effects of tail-risk are examined by comparing the portfolio decisions of mean-variance analysis (MVA) versus mean-conditional value at risk (M-CVaR) investors. The findings reveal that the volatility of returns in a MVA portfolio decreases when hedge funds are included in the investment opportunity set. However, the reduction in the volatility of portfolio returns comes at a cost of undesirable third and fourth moments. Furthermore, it is shown that investors with M-CVaR preferences exhibit a decreasing demand for hedge funds as their aversion for tail-risk increases. The results of the thesis highlight the sensitivities of linearity tests and portfolio selection to the empirical features of heteroscedasticity, autocorrelation and tail-risk. This thesis contributes to the literature by providing refinements to these frameworks which allow improved inferences to be made when hedge funds are examined in linearity and portfolio selection settings.

With extensive use of information systems in day-to-day business operations, many organizations are facing challenges to develop robust computer-based information systems that are secure and widely used by the user community. In order to develop information systems that are secure and useful, understanding what stakeholders consider important and value about the security and usability is critical. Security refers to confidentiality, integrity and availability and usability refers to efficiency, effectiveness and user satisfaction. Using Value Focused Thinking approach, this research first proposes the usability objectives based on the values of system developers and users. Using the security objectives proposed by Dhillon & Torkzadeh (2006) and the usability objectives, this research proposes hierarchies with the overall/over-arching goals of security (confidentiality, integrity, availability) and/or usability (efficiency, effectiveness and satisfaction). This research also analyzes a case of computer hacking and identifies which of the security and usability objectives that have not been met in that case study. The research contributions which include the usability objectives and security and usability hierarchies can be useful for theoretical as well as practical purposes.

L'objectif de cette thèse est de développer des méthodes de synthèses d'observateurs et des contrôleurs basés sur un observateur pour les systèmes à retard. Différentes classes de systèmes ont été traitées avec différents types de retard. Trois méthodes ont été développées. La première méthode traite des systèmes non linéaires avec des non-linéarités lipschitziennes et consiste à transformer le système d'origine à un système LPV grâce à une reformulation de la propriété classique de Lipschitz. Cette technique est formulée pour les cas continu et discret, respectivement. Nous avons démontré, à travers des exemples numériques, que cette technique offre des conditions de synthèse moins restrictives par rapport aux résultats existants dans la littérature. La seconde méthode est développée pour une classe de systèmes singuliers avec des perturbations. La principale difficulté résidait dans la présence des dérivées des perturbations qui entravent l'analyse de la stabilité et pour laquelle deux approches ont été proposées: une approche Hinf en utilisant une fonctionnelle de Lyapunov-Krasovskii spéciale dépendante des perturbations et une approche basée sur l'utilisation d'un critère de performance W1;2. La dernière méthode est basée sur l'utilisation des matrices de pondération libres pour résoudre le problème de contrôle des systèmes non-linéaires à retards inconnus. La solution proposée fournit une condition de synthèse LMI garantissant la stabilisation du système en boucle fermée malgré la présence du retard inconnu, au lieu d'une inégalité matricielle linéaire itérative ILMI trouvée habituellement dans la littérature.

Purpose – This study aims to explore, and suggest solutions to, the gap between the supply of information from organic meat producers and the demand of information from consumers regarding traceable characteristics (attributes) of meat in a limited geographical area in order to maximize the utilization and value of collected data. Design/methodology/approach – A mixed methods research design is applied to collect both quantitative data from consumers and qualitative data from suppliers to produce empirical results of the supply and demand of information. A theoretical framework of organic food purchase intent is used for the quantitative study as well as the correlation between consumers’ perceived importance of attributes and their willingness-to-pay for meat. The results of the empirical studies are compared to each other in an effort to expose a possible gap using a gap analysis. Findings – Meat is shifting from a price based commodity to a product based on characteristics. This study reveals that there is now a gap between the information made available by organic meat producers and the demand of information from consumers that needs to be recognized in order to maximize the value of collected data. Information regarding environmental impact of raising and transporting the animals is not extensively collected. A substantial amount of data about attributes of perceived importance, such as safety and handling, animal welfare and medication or other treatments is collected but not extensively shared with consumers. Research limitations/implications – The small sample size in a unique area and the scope of the survey data does not provide a result that can be truly generalized. It is therefore suggested that future studies produce results from a larger sample that incorporates the perceived accessibility of important information for consumers. Practical implications – This contributes to the emerging literature of organic food production by comparing both the supply and the demand of information regarding attributes of meat. This information is valuable to organic meat producers and marketers as well as developers of agricultural systems and databases that should shift their focus to consumer oriented traceability systems. Originality/value – This study goes beyond the substantial body of literature regarding attributes of organic food and consumers preferences by comparing these factors to the available supply of information by meat producers and by suggesting solutions to bridge the gap between them. Keywords – Organic meat, Organic agriculture, e-Agriculture, Traceability, Traceability systems, Consumer oriented, Consumer behavior, Willingness-to-pay, Supply and demand, Information gap, Gap analysis, Business development, United States of America, Sense-making theory, Mixed methods Paper type – Research paper, Bachelor’s thesis

A CONWIP (Constant Work-In-Progress) system is basically a hybrid system with a PUSH-PULL interface at the first machine in the line. This research addresses the most general case of a cyclic CONWIP system by incorporating two additional constraints over earlier studies namely; stochastic processing times and limited intermediate storage. One of the main issues in the design of a CONWIP system is the WIP level 'M', to be maintained. This research proposes an iterative procedure to determine this optimal level. The second main issue is the optimization of the line by determining an appropriate job sequence. This research assumes a 'permutational' scheduling policy and proposes an iterative approach to find the best sequence. The approach utilizes a controlled enumerative approach called the Fast Insertion Heuristic (FIH) coupled with a method to appraise the quality of every enumeration at each iteration. This is done by using a modified version of the Floyd's algorithm, to determine the cycle time (or Flow time) of a partial/full solution. The performance measures considered are the Flow time and the Interdeparture time (inverse of throughput). Finally, both the methods suggested for the two subproblems, are tested through computer implementations to reveal their proficiency.
Master of Science

Recommender systems provide new opportunities for retrieving personalized information on the Internet. Due to the availability of big data, the fitness industries are now focusing on building an efficient recommender system for their end-users. This thesis investigates the possibilities of building an efficient recommender system for gym users. BRP Systems AB has provided the gym data for evaluation and it consists of approximately 896,000 customer interactions with 8 features. Four different matrix factorization methods, Latent semantic analysis using Singular value decomposition, Alternating least square, Bayesian personalized ranking, and Logistic matrix factorization that are based on implicit feedback are applied for the given data. These methods decompose the implicit data matrix of user-gym group activity interactions into the product of two lower-dimensional matrices. They are used to calculate the similarities between the user and activity interactions and based on the score, the top-k recommendations are provided. These methods are evaluated by the ranking metrics such as Precision@k, Mean average precision (MAP) @k, Area under the curve (AUC) score, and Normalized discounted cumulative gain (NDCG) @k. The qualitative analysis is also performed to evaluate the results of the recommendations. For this specific dataset, it is found that the optimal method is the Alternating least square method which achieved around 90\% AUC for the overall system and managed to give personalized recommendations to the users.

Souvent prônée au regard de l’abondant discours politique et juridique dont elle fait l’objet, mais en même temps fréquemment et subtilement « torpillée », « combattue », la transparence des élections est l’une de ces notions-méridien des temps modernes.La présente thèse lève ainsi le voile sur ce que, quelle qu’en soit la forme, cette notion est tout logiquement reprise − et tant bien que mal consolidée ou en voie de consolidation − dans l’ordre juridique interne des différents États, notamment africains et tente de faire prendre conscience que, à l’analyse, une telle consécration, ou le cas échéant une telle consolidation, apparait bien plus embarrassée. En sus de cela, d’un point de vue de théorie et de pratique juridiques, naissent des incertitudes, au double regard de sa nature et de sa portée juridiques, instaurant ainsi un climat d’insécurité juridique dont il devient donc impérieux de sortir. Sans doute est-ce parce que, assez récente dans un domaine lui-même en quête d’autonomie : le droit électoral, cette notion se révèle très redoutable à cerner. Cette modeste contribution tente-t-elle justement de répondre à l’ensemble de ces préoccupations. Dans cette perspective, le travail pionnier de la Cour constitutionnelle du Bénin qui a érigé la transparence électorale en un principe à valeur constitutionnelle mérite d’être poursuivi. Elle est donc davantage un « construit » qu’un « donné ». En tout état de cause, un tel approfondissement assurerait une cohérence au droit public et renforcerait la sécurité juridique. Cette exigence est donc un terreau fertile à l’éclosion et au triomphe de la démocratie libérale. À y voir de près, elle est à même de réaliser la révolution juridique chère à Montesquieu et que n’a pu, malheureusement, pérenniser le principe de séparation des pouvoirs : la modération du pouvoir politique dans l’État
Often advocated in view of the abundant political and legal discourse of which it is the object, but at the same time and often subtly "torpedoed", “fought”, transparent elections are one of these meridian notions of modern times.Whatever form it may take, this Thesis is lifting the veil on this notion which is logically repeated, and somehow not well consolidated or being consolidated - in the internal legal order of the various States, particularly African States and which tries to make people aware that, in the analysis, such a consecration, or if any such consolidation, appears more embarrassed. In addition to this, a point of view of legal theory and practice, uncertainties arise, the double view of its nature and scope of legal, thus creating a climate of legal insecurity that it becomes imperative to quit Without any doubt, this recently field is seeking itself autonomy, and this concept , electoral law proves to be very formidable to understand. This modest contribution, consequently tries to answer all these concerns. In this perspective, the pioneering work of the Constitutional Court of Benin which erected electoral transparency principle to a value worth pursuing. Therefore, it is more of “a constructed” than a "given”. In any event, such a deepening should ensure coherence to public law and enhance legal certainty. This requirement is a fertile ground for the emergence and triumph of liberal democracy. A close look at it, it is able to perform the legal revolution dear to Montesquieu who could not, unfortunately, perpetuate the principle of separation of powers: the moderation of political power in the state

碩士
國立中興大學
應用數學系所
102
In this thesis, we derive the mean value theorems for the super-harmonic, sub-harmonic and harmonic solutions on square domains. Moreover, we consider the mesh functions on the mesh squares and establish the discrete mean value theorem by using the Green’s identities on rectangles in R2. From the discrete mean value theorem, we obtain that the value of a discrete harmonic function at a mesh point (x0, y0) is the average of any discrete square which has center at this mesh point (x0, y0) . For further research, it is interesting to extend the result here to n-dimensional space.

碩士
國立臺北大學
統計學系
94
In the study of the behavior of probability density function of continuous random variable, if the functions are differentiable or piecewise differentiable, usually, one can apply the method of calculus to determine the monotonically, concavity, points of inflection and asymptotes of these functions to attain some properties of the probability distributions. Most of the tools in calculus are consequences of the Mean Value Theorem for Derivatives. It is a theorem about functions continuous in bounded closed intervals and differentiable in the interior of the intervals. In general, continuous probability density functions are not necessarily differentiable everywhere, typical examples such as continuous piecewise linear distributions and double exponential distributions, but they have both left and right derivatives at the points where they are not differentiable. In this thesis, we shall consider one-sided differential functions defined on some intervals in the real number system and attain a Mean Value Theorem for One-sided Derivatives by an elementary proof. We also apply the result to discuss the monotonically and concavity of functions by examine some probability density functions.

A small group of profit seeking publishers dominates the American textbook market and guides the learning of the majority of our nation’s calculus students. The College Board’s AP Calculus curriculum is a de facto national standard for this gateway course that is critically important to 21st century STEM careers. A multi-representational understanding of calculus is a central pillar of the AP curriculum. This dissertation asks whether this multi-representational vision is manifest in popular calculus textbooks. This dissertation began with a survey of all AP Calculus AB Examination free response items, 2002-2011, and found that students score worse on items characterized by numerical anchors or verbal targets. Based on previously elucidated models, a new cognitive model of five levels and six principles is developed for the purpose of calculus textbook task analysis. This model explicates complexity as a function of representational input and output. Eight popular secondary calculus textbooks were selected for study based on Amazon sales rank data. All verbally anchored mathematical tasks (n=555) from sections of those books concerning the mean value theorem and all AP Calculus AB prompts (n=226) were analyzed for cognitive complexity and representational diversity using the model. The textbook study found that calculus textbooks underrepresented the numerical anchor and verbal target. It found that the textbooks were both explicitly and implicitly less cognitively complex than the AP test. The article suggested that textbook tasks should be less dense, avoid cognitive attenuation, move away from the stand-alone item, juxtapose anchor representations, scaffold student solutions, incorporate previously considered overarching concepts and include more profound follow-up questions. To date there have been no studies of calculus textbook content based on established research on cognitive learning. Given the critical role that their calculus course plays in the lives of hundreds of thousands of students annually, it is incumbent upon the College Board to establish a textbook review process at the very least in the same vain as the teacher syllabus auditing process established in recent years.

碩士
元培醫事科技大學
資訊管理系數位創新管理碩士班
105
There are more and more coffee making products in market to fulfill the increment of domestic coffee requirement. Coffee lovers tend to have their own preference making their own coffee and these preferences can vary from different individual whereas the technique adopted by coffee making machine can decide quality of coffee brewed. With the growing needs to coffee, drinking coffee has become a fashion. This study will focus on identifying customer’s core value for certain attributes based on their thoughts and requirements to the leading model of capsule coffee machine in market. Open-ended questionnaire will be used to collect customer's opinion on capsule coffee machine, find out customer preference, requirements and satisfaction, and identify the connection between customer’s thoughts and personal value. Applying Content analysis to analyze the relativity of attributes－consequences－values to individual end user, and provide manufacturer / distributer reasonable results for future product value design / marketing strategy recommendations and customer purchasing behavior reference.

MV is the traditional method to treat international portfolio selection problems, which bases its theory on the assumption of Normal Distribution. However, during economy recession the portfolio return turns out to be a fat tail distribution. Therefore, in this sense, we explore Roy’s SF criterion and apply the extreme theory to the historical data. We demonstrate how such portfolios would perform during the Asian Crisis, IT Bubble Bust and the Financial Crisis separately. We also compare the SF portfolio’s performance to the MV portfolio’s performance, therefore to check, SF and MV portfolio, which will outperform during bust and boom of the economy. The Asian Crisis was marked with great currency devaluation and lower currency return on equity. The Dot.Com Bubble Busts was known for its sharp plummet in the stock market, while, the Financial Crisis was known as the large falls in the US stock market and elsewhere. They are the extreme events of the world capital markets, which in some way contribute to the non-normal distribution. Simulated results over the 1997-2010 period which include six busts and booms: the Asian Crisis, period after Asian Crisis, IT Bubble Bust, period after IT Bubble Bust, The Financial Crisis and period after The Financial Crisis, indicate that SF portfolio outperforms MV portfolio during most of the times, this result is especially obvious for Indonesian and Thailand.

Le sujet principal de cette thèse est l’étude des valeurs moyennes et corrélations de fonctions multiplicatives. Les résultats portant sur ces derniers sont subséquemment appliqués à la résolution de plusieurs problèmes. Dans le premier chapitre, on rappelle certains résultats classiques concernant les valeurs moyennes des fonctions multiplicatives. On y énonce également les théorèmes principaux de la thèse. Le deuxième chapitre consiste de l’article “Mean values of multiplicative functions over the function fields". En se basant sur des résultats classiques de Wirsing, de Hall et de Tenenbaum concernant les fonctions multiplicatives arithmétiques, on énonce et on démontre des théorèmes qui y correspondent pour les fonctions multiplicatives sur les corps des fonctions Fq[x]. Ainsi, on résoud un problème posé dans un travail récent de Granville, Harper et Soundararajan. On décrit dans notre thése certaines caractéristiques du comportement des fonctions multiplicatives sur les corps de fonctions qui ne sont pas présentes dans le contexte des corps de nombres. Entre autres, on introduit pour la première fois une notion de “simulation” pour les fonctions multiplicatives sur les corps de fonctions Fq[x]. Les chapitres 3 et 4 comprennent plusieurs résultats de l’article “Correlations of multiplicative functions and applications". Dans cet article, on détermine une formule asymptotique pour les corrélations X n6x f1(P1(n)) · · · fm(Pm(n)), où f1, . . . ,fm sont des fonctions multiplicatives de module au plus ou égal à 1 ”simulatrices” qui satisfont certaines hypothèses naturelles, et P1, . . . ,Pm sont des polynomes ayant des coefficients positifs. On déduit de cette formule plusieurs conséquences intéressantes. D’abord, on donne une classification des fonctions multiplicatives f : N ! {−1,+1} ayant des sommes partielles uniformément bornées. Ainsi, on résoud un problème d’Erdos datant de 1957 (dans la forme conjecturée par Tao). Ensuite, on démontre que si la valeur moyenne des écarts |f(n + 1) − f(n)| est zéro, alors soit |f| a une valeur moyenne de zéro, soit f(n) = ns avec iii Re(s) < 1. Ce résultat affirme une ancienne conjecture de Kátai. Enfin, notre théorème principal est utilisé pour compter le nombre de représentations d’un entier n en tant que somme a+b, où a et b proviennent de sous-ensembles multiplicatifs fixés de N. Notre démonstration de ce résultat, dû à l’origine à Brüdern, évite l’usage de la “méthode du cercle". Les chapitres 5 et 6 sont basés sur les résultats obtenus dans l’article “Effective asymptotic formulae for multilinear averages and sign patterns of multiplicative functions," un travail conjoint avec Alexander Mangerel. D’après une méthode analytique dans l’esprit du théorème des valeurs moyennes de Halász, on détermine une formule asymptotique pour les moyennes multidimensionelles x−l X n2[x]l Y 16j6k fj(Lj(n)), lorsque x ! 1, où [x] := [1,x] et L1, . . . ,Lk sont des applications linéaires affines qui satisfont certaines hypothèses naturelles. Notre méthode rend ainsi une démonstration neuve d’un résultat de Frantzikinakis et Host avec, également, un terme principal explicite et un terme d’erreur quantitatif. On applique nos formules à la démonstration d’un phénomène local-global pour les normes de Gowers des fonctions multiplicatives. De plus, on découvre et explique certaines irrégularités dans la distribution des suites de signes de fonctions multiplicatives f : N ! {−1,+1}. Visant de tels résultats, on détermine les densités asymptotiques des ensembles d’entiers n tels que la fonction f rend une suite fixée de 3 ou 4 signes dans presque toutes les progressions arithmétiques de 3 ou 4 termes, respectivement, ayant n comme premier terme. Ceci mène à une généralisation et amélioration du travail de Buttkewitz et Elsholtz, et donne un complément à un travail récent de Matomäki, Radziwiłł et Tao sur les suites de signes de la fonction de Liouville.
The main theme of this thesis is to study mean values and correlations of multiplicative functions and apply the corresponding results to tackle some open problems. The first chapter contains discussion of several classical facts about mean values of multiplicative functions and statement of the main results of the thesis. The second chapter consists of the article “Mean values of multiplicative functions over the function fields". The main purpose of this chapter is to formulate and prove analog of several classical results due to Wirsing, Hall and Tenenbaum over the function field Fq[x], thus answering questions raised in the recent work of Granville, Harper and Soundararajan. We explain some features of the behaviour of multiplicative functions that are not present in the number field settings. This is accomplished by, among other things, introducing the notion of “pretentiousness" over the function fields. Chapter 3 and Chapter 4 include results of the article “Correlations of multiplicative functions and applications". Here, we give an asymptotic formula for correlations X n_x f1(P1(n))f2(P2(n)) · · · · · fm(Pm(n)) where f . . . ,fm are bounded “pretentious" multiplicative functions, under certain natural hypotheses. We then deduce several desirable consequences. First, we characterize all multiplicative functions f : N ! {−1,+1} with bounded partial sums. This answers a question of Erdos from 1957 in the form conjectured by Tao. Second, we show that if the average of the first divided difference of multiplicative function is zero, then either f(n) = ns for Re(s) < 1 or |f(n)| is small on average. This settles an old conjecture of Kátai. Third, we apply our theorem to count the number of representations of n = a + b where a,b belong to some multiplicative subsets of N. This gives a new "circle method-free" proof of the result of Brüdern. Chapters 5 and Chapter 6 are based on the results obtained in the article “Effective asymptotic formulae for multilinear averages and sign patterns of multiplicative functions," joint with Alexander Mangerel. Using an analytic approach in the spirit of Halász’ mean v value theorem, we compute multidimensional averages x−l X n2[x]l Y 16j6k fj(Lj(n)) as x ! 1, where [x] := [1,x] and L1, . . . ,Lk are affine linear forms that satisfy some natural conditions. Our approach gives a new proof of a result of Frantzikinakis and Host that is distinct from theirs, with explicit main and error terms. As an application of our formulae, we establish a local-to-global principle for Gowers norms of multiplicative functions. We reveal and explain irregularities in the distribution of the sign patterns of multiplicative functions by computing the asymptotic densities of the sets of integers n such that a given multiplicative function f : N ! {−1, 1} yields a fixed sign pattern of length 3 or 4 on almost all 3- and 4-term arithmetic progressions, respectively, with first term n. The latter generalizes and refines the work of Buttkewitz and Elsholtz and complements the recent work of Matomaki, Radziwiłł and Tao. We conclude this thesis by discussing some work in progress.

碩士
亞洲大學
休閒與遊憩管理學系碩士在職專班
100
The purpose of this study is to examine the relationships among spectator sport attributes, benefits and values. Additionally, this study attempts to identify the major connections of spectator sport attribute-benefit-value. The mediating effects of benefits on the relationship between attributes and values are also examined. This study used a survey. Questionnaires were administered in the middle of Taiwan to the 6th grade, middle-school, high-school and college students who have ever watched NBA. A total of valid 713 questionnaires were collected. The statistical analyses showed that the most important attribute was “Sportsmanship” and the least important attribute was the “Team history.” However, those attributes which could bring the highest values were "Favorite players," "Favorite team," "Star players," "Level of competition," "Skills." The greatest benefit in watching NBA was "Learning sportsmanship." The self-reported values most highly associated with watching NBA were "Conformity," "Power," and "Enjoyment," whereas the highest associated values acquired through NBA attributes and watching benefits were "enjoyment," "achievement," and "sociability." The strongest connections among attributes-benefits -values were “Favorite Teams, Can Support Favorite Players, Enjoyment,” “Favorite Players, Can Support Favorite Players, Enjoyment.” Experienced benefits in watching NBA partly mediated the relationship between spectator sport attributes and values.

Stochastic approximation algorithms encompass a class of iterative schemes that converge to a sought value through a series of successive approximations. Such algorithms converge even when the observations are erroneous. Errors in observations may arise due to the stochastic nature of the problem at hand or due to extraneous noise. In other words, stochastic approximation algorithms are self-correcting schemes, in that the errors are wiped out in the limit and the algorithms still converge to the sought values. The rst stochastic approximation algorithm was developed by Robbins and Monro in 1951 to solve the root- nding problem. In 1977 Ljung showed that the asymptotic behavior of a stochastic approximation algorithm can be studied by associating a deterministic ODE, called the associated ODE, and studying it's asymptotic behavior instead. This is commonly referred to as the ODE method. In 1996 Bena•m and Bena•m and Hirsch [1] [2] used the dynamical systems approach in order to develop a framework to analyze generalized stochastic approximation algorithms, given by the following recursion: xn+1 = xn + a(n) [h(xn) + Mn+1] ; (1) where xn 2 Rd for all n; h : Rd ! Rd is Lipschitz continuous; fa(n)gn 0 is the given step-size sequence; fMn+1gn 0 is the Martingale difference noise. The assumptions of [1] later became the `standard assumptions for convergence'. One bottleneck in deploying this framework is the requirement on stability (almost sure boundedness) of the iterates. In 1999 Borkar and Meyn developed a unified set of assumptions that guaranteed both stability and convergence of stochastic approximations. However, the aforementioned frameworks did not account for scenarios with set-valued mean fields. In 2005 Bena•m, Hofbauer and Sorin [3] showed that the dynamical systems approach to stochastic approximations can be extended to scenarios with set-valued mean- fields. Again, stability of the fiterates was assumed. Note that stochastic approximation algorithms with set-valued mean- fields are also called stochastic recursive inclusions (SRIs). The Borkar-Meyn theorem for SRIs [10] As stated earlier, in many applications stability of the iterates is a hard assumption to verify. In Chapter 2 of the thesis, we present an extension of the original theorem of Borkar and Meyn to include SRIs. Specifically, we present two different (yet related) easily-verifiable sets of assumptions for both stability and convergence of SRIs. A SRI is given by the following recursion in Rd: xn+1 = xn + a(n) [yn + Mn+1] ; (2) where 8 n yn 2 H(xn) and H : Rd ! fsubsets of Rdg is a given Marchaud map. As a corollary to one of our main results, a natural generalization of the original Borkar and Meyn theorem is seen to follow. We also present two applications of our framework. First, we use our framework to provide a solution to the `approximate drift problem'. This problem can be stated as follows. When an experimenter runs a traditional stochastic approximation algorithm such as (1), the exact value of the drift h cannot be accurately calculated at every stage. In other words, the recursion run by the experimenter is given by (2), where yn is an approximation of h(xn) at stage n. A natural question arises: Do the errors due to approximations accumulate and wreak havoc with the long-term behavior (convergence) of the algorithm? Using our framework, we show the following: Suppose a stochastic approximation algorithm without errors can be guaranteed to be stable, then it's `approximate version' with errors is also stable, provided the errors are bounded at every stage. For the second application, we use our framework to relax the stability assumptions involved in the original Borkar-Meyn theorem, hence making the framework more applicable. It may be noted that the contents of Chapter 2 are based on [10]. Analysis of gradient descent methods with non-diminishing, bounded errors [9] Let us consider a continuously differentiable function f. Suppose we are interested in nding a minimizer of f, then a gradient descent (GD) scheme may be employed to nd a local minimum. Such a scheme is given by the following recursion in Rd: xn+1 = xn a(n)rf(xn): (3) GD is an important implementation tool for many machine learning algorithms, such as the backpropagation algorithm to train neural networks. For the sake of convenience, experimenters often employ gradient estimators such as Kiefer-Wolfowitz estimator, simultaneous perturbation stochastic approximation, etc. These estimators provide an estimate of the gradient rf(xn) at stage n. Since these estimators only provide an approximation of the true gradient, the experimenter is essentially running the recursion given by (2), where yn is a `gradient estimate' at stage n. Such gradient methods with errors have been previously studied by Bertsekas and Tsitsiklis [5]. However, the assumptions involved are rather restrictive and hard to verify. In particular, the gradient-errors are required to vanish asymptotically at a prescribed rate. This may not hold true in many scenarios. In Chapter 3 of the thesis, the results of [5] are extended to GD with bounded, non-diminishing errors, given by the following recursion in Rd: xn+1 = xn a(n) [rf(xn) + (n)] ; (4) where k (n)k for some fixed > 0. As stated earlier, previous literature required k (n)k ! 0, as n ! 1, at a `prescribed rate'. Sufficient conditions are presented for both stability and convergence of (4). In other words, the conditions presented in Chapter 3 ensure that the errors `do not accumulate' and wreak havoc with the stability or convergence of GD. Further, we show that (4) converges to a small neighborhood of the minimum set, which in turn depends on the error-bound . To the best of our knowledge this is the first time that GD with bounded non-diminishing errors has been analyzed. As an application, we use our framework to present a simplified implementation of simultaneous perturbation stochastic approximation (SPSA), a popular gradient descent method introduced by Spall [13]. Traditional convergence-analysis of SPSA involves assumptions that `couple' the `sensitivity parameters' of SPSA and the step-sizes. These assumptions restrict the choice of step-sizes available to the experimenter. In the context of machine learning, the learning rate may be adversely affected. We present an implementation of SPSA using `constant sensitivity parameters', thereby `decoupling' the step-sizes and sensitivity parameters. Further, we show that SPSA with constant sensitivity parameters can be analyzed using our framework. Finally, we present experimental results to support our theory. It may be noted that contents of Chapter 3 are based on [9]. b(n) a(n) Stochastic recursive inclusions with two timescales [12] There are many scenarios wherein the traditional single timescale framework cannot be used to analyze the algorithm at hand. Consider for example, the adaptive heuristic critic approach to reinforcement learning, which requires a stationary value iteration (for a fixed policy) to be executed between two policy iterations. To analyze such schemes Borkar [6] introduced the two timescale framework, along with a set of sufficient conditions which guarantee their convergence. Perkins and Leslie [8] extended the framework of Borkar to include set-valued mean- fields. However, the assumptions involved were still very restrictive and not easily verifiable. In Chapter 4 of the thesis, we present a generalization of the aforementioned frameworks. The framework presented is more general when compared to the frameworks of [6] and [8], and the assumptions involved are easily verifiable. A SRI with two timescales is given by the following coupled iteration: xn+1 = xn + a(n) un + Mn1+1 ; (5) yn+1 = yn + b(n) vn + Mn2+1 ; (6) where xn 2 R d and yn 2 R k for all n 0; un 2 h(xn; yn) and vn 2 g(xn; yn) for all n 0, where h : Rd Rk ! fsubsets of Rdg and g : Rd Rk ! fsubsets of Rkg are two given Marchaud maps; fa(n)gn 0 and fb(n)gn 0 are the step-size sequences satisfying ! 0 as n ! 1; fMn1+1gn 0 and fMn2+1 gn 0 constitute the Martingale noise terms. Our main contribution is in the weakening of the key assumption that `couples' the behavior of the x and y iterates. As an application of our framework we analyze the two timescale algorithm which solves the `constrained Lagrangian dual optimization problem'. The problem can be stated as thus: Given two functions f : Rd ! R and g : Rd ! Rk, we want to minimize f(x) subject to the condition that g(x) 0. This problem can be stated in the following primal form: inf sup f(x) + T g(x) : (7) 2R 2R0 x d k Under strong duality, solving the above equation is equivalent to solving it's dual: sup inf f(x) + T g(x) : (8) 2Rk x2Rd 0 The corresponding two timescale algorithm to solve the dual is given by: xn+1 = xn a(n) rx f(xn) + nT g(xn) + Mn2+1 ; (9) n+1 = n + b(n) f(xn) + nT g(xn) + Mn1+1 : r We use our framework to show that (9) converges to a solution of the dual given by (8). Further, as a consequence of our framework, the class of objective and constraint functions, for which (9) can be analyzed, is greatly enlarged. It may be noted that the contents of Chapter 4 are based on [12]. Stochastic approximation driven by `controlled Markov' process and temporal difference learning [11] In the field of reinforcement learning, one encounters stochastic approximation algorithms that are driven by Markov processes. The groundwork for analyzing the long-term behavior of such algorithms was laid by Benveniste et. al. [4]. Borkar [7] extended the results of [4] to include algorithms driven by `controlled Markov' processes i.e., algorithms where the `state process' was in turn driven by a time varying `control' process. Another important extension was that multiple stationary distributions were allowed, see [7] for details. The convergence analysis of [7] assumed that the iterates were stable. In reinforcement learning applications, stability is a hard assumption to verify. Hence, the stability assumption poses a bottleneck when deploying the aforementioned framework for the analysis of reinforcement algorithms. In Chapter 5 of the thesis we present sufficient conditions for both stability and convergence of stochastic approximations driven by `controlled Markov' processes. As an application of our framework, sufficient conditions for stability of temporal difference (T D) learning algorithm, an important policy-evaluation method, are presented that are compatible with existing conditions for convergence. The conditions are weakened two-fold in that (a) the Markov process is no longer required to evolve in a finite state space and (b) the state process is not required to be ergodic under a given stationary policy. It may be noted that the contents of Chapter 5 are based on [11].

碩士
國立政治大學
資訊管理學系
104
While online shopping websites are facing the difficulties of price and low-quality competition, cross-border online shopping is on a vigorous development trend, showing that cross-border online shopping is an important trend of online shopping field. Due to the complexity of cross-border online shopping is much higher than the traditional domestic online shopping, so understanding the value of cross-border online shopping consumers is the most important success factors. Companies want to develop new markets abroad, must understand the local consumer’s behavior and their decision-making process in order to make good business strategies. This study uses means-end chain to construct Taiwanese cross-border online shopping consumers’ hierarchical value map, and also apply to Maslow’s hierarchy of needs, then sorting these value elements’ importance by their position in hierarchy of needs. After obtained the reason why consumers use cross-border online shopping service and what values they got in this service. Researcher can predict and analyze the evolution and development of cross-border online shopping, provide reference for future online shopping academic studies and online shopping industry’s decision-making.

碩士
中國文化大學
國際貿易學系
107
According to a report released by the Taiwan Network Information Center (TWNIC), Taiwan has an internet population of 17.38 million over the age of 12 and an entire internet population of 18.66 million with overall surfing rate of 79.2% in 2018, these statistics indicated that the infrastructure of Taiwan is well-developed and the condition required for the development of digital learning is also matured. The devel-opment and prevailing use of personal computer provided better opportunity for people in access to digital learning. Digital learning is usually presented in combination with gaming so as to make learning more interesting, game makers also provide content fea-turing active interaction mechanisms so that people could experience different roles and interaction in the environment designed in the games. In this study, the complete simulation of the digital game, “Marketing-Winner” was taken as an example, coupled with the use of the Means-End Chains as the founda-tion to explore the kinds of positive and negative elements of gaming. Laddering inter-view was adopted in this study for data collection with the results from 29 respondents collected. These data were subject to content analysis for systematic and objective clas-sification with summarization of the content of essential information. The findings from this study indicated that of all the positive elements of games, users tended to incline to information analysis, production and operation management, simulation, marketing management, human resource management, game economic cycle as the attributes for gaming. The benefits to the users from the results are the learning of professional knowledge, input to career development in the future, improvement of de-cision-making, discussion and communication, ranking upgrade, system thinking and observation, eventually, the result also helps users in advancing the targeted value of enjoyment of life, sense of achievement, sense of security, sense of belonging, self-actualization, warm interpersonal relation, adventure and excitement, and self-esteem. As for the negative elements of games, the users mentioned interface, hardware, monotony, vague information, and fuzziness, others such as decision bias, no data storage, waste of time, insufficient time, discourage the mood of gaming, confuse thinking, retardant are also brought to the users. Finally, the negative emotion brought to the users is frustration, abhorrence, wrath, sadness, fear, anxiety, and nervousness.

碩士
國立勤益科技大學
企業管理系
105
Recently decade, the food and beverage industries have developed rapidly in Taiwan, and the baking manufacturers already grown nearly doubled from 2008 to 2015. The baking D.I.Y (Do it yourself) workshops which let consumers possess the diversified consumption experiences such as learning cooking skill, leisure, enjoying handmade desserts, senses, thinking, acts, and so on, and already became a new and innovative consumption model by following the experience marketing perspective and many on-line cooking shows that were emphasized and promoted in current years. However, investigations about the business model, service processes and the customers’ concerned values of baking workshops in baking industries are rarely explored in domestic or international research papers at present. Hence, this study explores the most important attributes of service and commodity, the resulted interest of consumption, and the customer's perceived value for baking D.I.Y workshops based on the theoretical view of means-end chains theory and adopted the soft laddering technique and the purposively sampling method to conduct interviews of 60 consumers that ever participated the baking D.I.Y workshops within one year. The study analyzed these transcripts of interview through the content analyses method, and in order to confirm the consistency of data classification by calculating the reliability of classification and the internal consistency. In addition, this study also used the implication matrix and the hierarchical value map to show the strength or weakness relationships and explained the theoretical conclusions and practical meaning among the concepts of classification. The study results found consumers gained these mainly consequences or benefits (getting the steps to explain the process, clear classification, problem assistance and resolution, improving food safety, improving the preservation of finished products) and the mainly final values (giving the customer a sense of security, a sense of belonging, being respected), were through the important attributes (all kinds of ingredients, serious staffs, science and technology auxiliary teaching). Finally, the results of this study are expected to as an important managerial reference and assist the baking D.I.Y workshop operators to plan marketing promotion strategies, to improve service processes, or to design related products in the further.

碩士
國立臺灣海洋大學
教育研究所
99
The research aims to enhance elementary students’ attitude and behaviors at marine environmental protection through Value-Belief-Norm Theory. To design marine environmental protection teaching by the VBN theory, investigating after the VBN marine environmental protection teaching, elementary students’ marine environmental protection attitude and behaviors change situation. The research objects are 10 second grade students in new Taipei city. After the cycle of action research, implementation and reflection, the results are described as follows: (1)The relative values discussion can surge elementary students’ marine environmental protection attitude and behaviors. (2)Elementary students’ marine environmental protection attitude and behaviors will accumulate gradually along with the curriculum. (3)Grasping the VBN Theory core concept to design the different teaching situation is able to promote the result. (4)VBN marine environmental protection teaching is helpful in raises elementary students’ marine environmental protection attitude and behaviors. (5)The values of marine environmental protection will affect elementary students’ marine environmental protection attitude and behaviors. (6)Elementary students’ fondness will affect the marine environmental protection attitude and the behaviors performance.

>Magister Scientiae - MSc
In this thesis, we discuss methods for optimising the expected rate of return of a portfolio with minimal risk. As part of the work we look at the Modern Portfolio Theory which tries to maximise the portfolio's expected rate of return for a cer- tain amount of risk. We also use Quadratic Programming to optimise portfolios. Generally it is recognised that portfolios with a high expected return, carry higher risk. The Modern Portfolio Theory assists when choosing portfolios with the lowest possible risk. There is a nite number of assets in a portfolio and we therefore want to allocate them in such a way that we're able to optimise the expected rate of return with minimal risk. We also use the Markowian approach to allocate these assets. The Capital Asset Pricing Model is also used, which will help us to reduce our e cient portfolio to a single portfolio. Furthermore we use the Black-Litterman model to try and optimise our portfolio with a view to understanding the current market conditions, as well as considering how the market will perform in the future. An additional tool we'll use is Value at Risk. This enables us to manage the market risk. To this end, we follow the three basic approaches from Jorion [Value at Risk. USA: McGraw-Hills, 2001]. The Value at Risk tool has become essential in calcu- lating a portfolio's risk over the last decade. It works by monitoring algorithms in order to nd the worst possible scenarios within the portfolio. We perform several numerical experiments in MATLAB and Microsoft Excel and these are presented in the thesis with the relevant descriptions.

Modern financial asset pricing theory is a broad, and at times, complex field. The literature review in this study covers many of the asset pricing techniques including factor models, random walk models, correlation models, Bayesian methods, autoregressive models, moment-matching models, stochastic jumps and mean reversion models. An important topic in finance is portfolio opti-misation with respect to risk and reward such as the mean variance optimisation introduced by Markowitz (1952). This study covers optimisation techniques such as single period mean variance optimisation, optimisation with risk aversion, multi-period stochastic programs, two-fund separa- tion theory, downside optimisation techniques and multi-period optimisation such as the Bellman dynamic programming model. The question asked in this study is, in the context of investing for South African individuals in a multi-asset portfolio, whether an active investment strategy is signi cantly di erent from a passive investment strategy. The passive strategy is built using stochastic programming with moment matching methods for non-Gaussian asset class distributions. The strategy is optimised in a framework using a downside risk metric, the conditional variance at risk. The active strategy is built with forward forecasts for asset classes using the time-varying transitional-probability Markov regime switching model. The active portfolio is finalised by a dynamic optimisation using a two-stage stochastic programme with recourse, which is solved as a large linear program. A hypothesis test is used to establish whether the results of two strategies are statistically different. The performance of the strategies are also reviewed relative to multi-asset peer rankings. Lastly, we consider whether the findings reveal information on the degree of effi ciency in the market place for multi-asset investments for the South African investor.
Operations Management
M. Sc. (Operations Research)