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The discourse presented here is aimed at examining the justification of applications of current analysis to real world problems.

Over that past three decades, power sector reform has been a key pillar of policy agendas in more than half of the countries across the world. This thesis specifically concerns the empirical investigation of the economic performance of the international electricity generation industry. Drawing on the stochastic frontier analysis techniques, the thesis considers the influence of reform as exogenous factors in shifting frontier technology as well as shaping inefficiency function directly -determinants and heteroscedasticity variables. The first essay uses an extensive panel dataset of 91 countries over the period 1980 to 2010 to measure the impact of deregulation on efficiency and total productivity growth using stochastic input distance frontier (SIDF). Three specific issues are addressed in the first essay: (1) the relationship between deregulation and technical efficiency, (2) the extent of the rank correlation of the country intercepts with deregulation via their position on the frontier, (3) the trend of total factor productivity and its components. We establish a positive impact of deregulation on efficiency and some compelling evidence suggesting that the country intercepts equally account for the influence of deregulation aside efficiency. In particular, the technical efficiency index from the first paper reveals that most OECD European countries are consistently efficient. Building on this finding, the second essay investigates the performance in term of cost efficiency for electricity generation in OECD power sector while accounting for the impact of electricity market product regulatory indicators. Empirical models are developed for the cost function as a translog form and analysed using panel data of 25 countries during the period 1980 to 2009. We show that it is necessary to model latent country-specific heterogeneity in addition to time-varying inefficiency. The estimated economies of scale are adjusted to take account of the importance of the quasi-fixed capital input in determining cost behaviour, and adjusted economies of scale are verified for the OECD generation sector. The findings suggest there is a significant impact of electricity market regulatory indicators on cost. Cost complementarity between generation and emissions found to be significant, indicating the possibility of reducing emissions without necessarily reducing electricity generation. Finally, the third essay examines the performance of electric power industry s using consistent state-level electricity generation dataset for the US contiguous states from 1998-2014. We estimate stochastic production frontier for five competing models in order to identify the determinants of technical inefficiency and marginal effects. We find evidence of positive impacts of deregulation on technical efficiency across the models estimated. Our preferred model shows that deregulated states are more efficient in electricity generation than non-deregulated states. The result of the marginal effects shows that deregulation has a positive and monotonic effect on the technical efficiency.

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本文利用可以同時捕捉到銀行增加意欲產出、減少投入與減少非意欲產出的方向距離函數，評估台灣銀行業與個別銀行在民國93年至97年的無效率值與生產力變化。設定逾期放款為銀行生產放款時的非意欲產出，以考量銀行的放款品質，也考慮到銀行都會付出成本來提供服務給存戶，因此以交易性存款作為銀行提供服務的替代變數，使銀行的服務包含在效率評估內，並以固定的方向向量作為無效率值加總的基礎，來衡量台灣整體銀行業的無效率。實證結果是台灣銀行業的無效率值隨著雙卡風暴的遠去，有逐年遞減的趨勢，生產力的變化則是退步的情況較多。 / In this paper we estimate Taiwanese banks’ efficiency and productivity change during 2004-2008. The estimates are derived from the directional distance function. We treat non-performing loans as an undesirable output arising from the production of loans to measure the quality of loans. Considering every bank would make costs to serve customers, we choose transaction deposits as an alternative variable to capture the service provided by banks. The way we set the directional vector allows the aggregation of individual bank inefficiency and productivity change to the industry level. Our findings indicate that inefficiencies of Taiwanese banking industry were decreasing after the over of credit and cash card debts. And Taiwanese banking industry experienced productivity regress during this period.

本文採取隨機方向距離函數方法，探討制度變革前、後(第一次金融改革)對台灣銀行業技術效率的影響。資料期間涵蓋1999年至2012年。相較傳統Shephard距離函數，隨機方向距離函數方法最大優點係可同時考量增加意欲產出、減少投入與非意欲產出。本文依循Koutsomanoli-Filippaki et al. (2009a) 模型，並納入考慮非意欲產出。本文採取隨機邊界法進行實證估計，以最大概似法估計方向距離函數，依據Battese and Coelli (1995)的模型將環境變數納入實證模型 (主要模型)，並考量未包含環境變數之模型，與主要模型比較。此外，為凸顯非意欲產出之重要性，本文亦估計未考慮非意欲產出之模型以及傳統距離函數，以茲比較。 實證結果顯示，考慮非意欲產出與環境變數的主要模型，其估計結果相較其他模型之無效率明顯高估。2002年以前，技術無效率逐漸攀升。一次金改期間，技術無效率明顯下降，證明制度變革下，銀行效率獲得改善。惟2004年後反轉向上，尤其在雙卡風暴與次貸風暴期間，技術無效率明顯惡化。此外，本文將資料分群進行分析，發現公營銀行或是金控銀行較有效率。 / This paper aims to gain further insights into whether the policy of First Financial Restructuring (FFR) does improve the technical efficiency of banks in Taiwan during the period 1999-2012 by using the directional technology distance function (DDF). Compared to the conventional distance function, DDF simultaneously allows for the expansion of the desirables and the contraction of the undesirables. We follow Koutsomanoli-Filippaki et al. (2009a), and differing from them, we include undesirable outputs in DDF to depict a bank’s true production activities. We find on average that the banks have a lower technical inefficiency with the main model compared to the other models. However, prior to 2002, the technical inefficiency exhibits a gradual upward trend and then posts a downward trend during the FFR period. These results suggest that the improved efficiency in the FFR period is possibly due to enhanced banking and benefits obtained from compliance with FFR. After the FFR period, the inefficiency scores deteriorate sharply, especially during the “credit card and cash card crisis” in 2006 and “the subprime mortgage crisis” in 2008. Public banks are more efficient than private banks. Banks belonging to a financial holding company (FHC) may operate more efficiently than those belonging to a non-FHC.

La modélisation des équilibres thermodynamiques entre phases est essentielle pour le génie des procédés et le génie pétrolier. L’analyse de la stabilité des phases est un problème de la plus haute importance parmi les calculs d’équilibre des phases. Le calcul de stabilité décide si un système se présente dans un état monophasique ou multiphasique ; si le système se sépare en deux ou plusieurs phases, les résultats du calcul de stabilité fournissent une initialisation de qualité pour les calculs de flash (Michelsen, 1982b), et permettent la validation des résultats des calculs de flash multiphasique. Le problème de la stabilité des phases est résolu par une minimisation sans contraintes de la fonction distance au plan tangent à la surface de l’énergie libre de Gibbs (« tangent plane distance », ou TPD). Une phase est considérée comme étant thermodynamiquement stable si la fonction TPD est non- négative pour tous les points stationnaires, tandis qu’une valeur négative indique une phase thermodynamiquement instable. La surface TPD dans l’espace compositionnel est non- convexe et peut être hautement non linéaire, ce qui fait que les calculs de stabilité peuvent être extrêmement difficiles pour certaines conditions, notamment aux voisinages des singularités. On distingue deux types de singularités : (i) au lieu de la limite du test de stabilité (stability test limit locus, ou STLL), et ii) à la spinodale (la limite intrinsèque de la stabilité thermodynamique). Du point de vue géométrique, la surface TPD présente un point selle, correspondant à une solution non triviale (à la STLL) ou triviale (à la spinodale). Dans le voisinage de ces singularités, le nombre d’itérations de toute méthode de minimisation augmente dramatiquement et la divergence peut survenir. Cet inconvénient est bien plus sévère pour la STLL que pour la spinodale. Le présent mémoire est structuré sur trois grandes lignes : (i) après la présentation du critère du plan tangent à la surface de l’énergie libre de Gibbs, plusieurs solutions itératives (gradient et méthodes d’accélération de la convergence, méthodes de second ordre de Newton et méthodes quasi- Newton), du problème de la stabilité des phases sont présentées et analysées, surtout du point de vue de leurs comportement près des singularités; (ii) Suivant l’analyse des valeurs propres, du conditionnement de la matrice Hessienne et de l’échelle du problème, ainsi que la représentation de la surface de la fonction TPD, la résolution du calcul de la stabilité des phases par la minimisation des fonctions coût modifiées est adoptée. Ces fonctions « coût » sont choisies de telle sorte que tout point stationnaire (y compris les points selle) de la fonction TPD soit converti en minimum global; la Hessienne à la STLL est dans ce cas positif définie, et non indéfinie, ce qui mène a une amélioration des propriétés de convergence, comme montré par plusieurs exemples pour des mélanges représentatifs, synthétiques et naturels. Finalement, (iii) les calculs de stabilité sont menés par une méthode d’optimisation globale, dite de Tunneling. La méthode de Tunneling consiste à détruire (en plaçant un pôle) les minima déjà trouvés par une méthode de minimisation locale, et a tunneliser pour trouver un point situé dans une autre vallée de la surface de la fonction coût qui contient un minimum 9 à une valeur plus petite de la fonction coût; le processus continue jusqu'à ce que les critères du minimum global soient remplis. Plusieurs exemples soigneusement choisis montrent la robustesse et l’efficacité de la méthode de Tunneling pour la minimisation de la fonction TPD, ainsi que pour la minimisation des fonctions coût modifiées. / The thermodynamic phase equilibrium modelling is an essential issue for petroleum and process engineering. Phase stability analysis is a highly important problem among phase equilibrium calculations. The stability computation establishes whether a given mixture is in one or several phases. If a mixture splits into two or more phases, the stability calculations provide valuables initialisation sets for the flash calculations, and allow the validation of multiphase flash calculations. The phase stability problem is solved as an unconstrained minimisation of the tangent plan distance (TPD) function to the Gibbs free energy surface. A phase is thermodynamically stable if the TPD function is non-negative at all its stationary points, while a negative value indicates an unstable case. The TPD surface is non-convex and may be highly non-linear in the compositional space; for this reason, phase stability calculation may be extremely difficult for certain conditions, mainly within the vicinity of singularities. One can distinguish two types of singularities: (i) the stability test limit locus (STLL), and (ii) the intrinsic limit of stability (spinodal). Geometrically, the TPD surface exhibits a saddle point, corresponding to a non-trivial (at the STLL) or trivial solution (at the spinodal). In the immediate vicinity of these singularities, the number of iterations of all minimisation methods increases dramatically, and divergence could occur. This inconvenient is more severe for the STLL than for the spinodal. The work presented herein is structured as follow: (i) after the introduction to the concept of tangent plan distance to the Gibbs free energy surface, several iterative methods (gradient, acceleration methods, second-order Newton and quasi-Newton) are presented, and their behaviour analysed, especially near singularities. (ii) following the analysis of Hessian matrix eigenvalues and conditioning, of problem scaling, as well as of the TPD surface representation, the solution of phase stability computation using modified objective functions is adopted. The latter are chosen in such a manner that any stationary point of the TPD function becomes a global minimum of the modified function; at the STLL, the Hessian matrix is no more indefinite, but positive definite. This leads to a better scheme of convergence as will be shown in various examples for synthetic and naturally occurring mixtures. Finally, (iii) the so-called Tunneling global optimization method is used for the stability analysis. This method consists in destroying the minima already found (by placing poles), and to tunnel to another valley of the modified objective function to find a new minimum with a smaller value of the objective function. The process is resumed when criteria for the global minimum are fulfilled. Several carefully chosen examples demonstrate the robustness and the efficiency of the Tunneling method to minimize the TPD function, as well as the modified objective functions.

<p>Doktorska disertacija izučava primenu fazi operacija, prvenstveno agregacionih operatora na funkcije rastojanja i metrike. Originalan doprinos teze je u konstrukciji novih funkcija rastojanja i metrika primenom agregacionih operatora na neke polazne funkcije rastojanja i metrike. Za neke tipove agregacionih operatora i polaznih funkcija rastojanja i metrika su ispitane osobine ovako konstruisanih funkcija rastojanja i metrika. Za neke od njih su ispitane performanse pri primeni u segmentaciji slike &bdquo;Fuzzy c-means&ldquo; algoritmom.</p> / <p>This thesis studies application of fuzzy operations, especially aggregation operators, on distance functions and metrics. The contribution of the thesis is construction of new distance functions and metrics by application of aggregation operators on some basic distance functions and metrics. For some types of aggregation operators and basic distance functions and metrics, properties of distance functions and metrics constructed in this way are analyzed. For some of them, performances in application in Fuzzy c-means algorithm are analyzed.</p>

The main contribution of this thesis is the implementation of manufacturing constraints in shape and topology optimization. Fabrication limitations related to the casting process are formulated as mathematical constraints and introduced in the optimization algorithm. In addition, based on the same theoretical and modelization tools, we propose a novel formulation for multi-phase optimization problems, which can be extended to the optimization of structures with functionally-graded properties. A key ingredient for the mathematical formulation of most problems throughout our work is the notion of the signed distance function to a domain. This work is divided into three parts. The rst part is bibliographical and contains the necessary background material for the understanding of the thesis' main core. It includes the rst two chapters. Chapter 1 provides a synopsis of shape and topology optimization methods and emphasizes the combination of shape sensitivity analysis and the level-set method for tracking a shape's boundary. In Chapter 2 we give a short description of the casting process, from which all our manufacturing constraints derive. We explain how industrial designers account for these limitations and propose a strategy to incorporate them in shape and topology optimization algorithms. The second part is about the mathematical formulation of manufacturing constraints. It starts with Chapter 3, where the control of thickness is discussed. Based on the signed distance function, we formulate three constraints to ensure a maximum and minimm feature size, as well as a minimal distance between structural members. Then, in Chapter 4, we propose ways to handle molding direction constraints and combine them with thickness constraints. Finally, a thermal constraint coming from the solidi cation of cast parts is treated in Chapter 5 using several thermal models. Multi-phase optimization is discussed in the third part. The general problem of shape and topology optimization using multiple phases is presented in detail in Chapter 6. A "smoothed-interface" approach, based again on the signed distance function, is proposed to avoid numerical di culties related to classical "sharp-interface" problems and a shape derivative is calculated. An extension of this novel formulation to general types of material properties' gradation is shown in the Appendix A.

全球暖化已成為大多數國家近幾年所關心的議題。雖然臺灣政府於2010年5月所核定的「國家節能減碳總計畫」之中，儘管減量目標及原則業已確立，但未充分探討各別產業的面臨碳排放管制時所造成的影響，因此，臺灣各產業或次部門究竟應承擔多大的減量責任仍是混沌不明。 為了更清楚瞭解碳排放管制對於臺灣工業部門之各產業的影響，本文以方向性距離函數，估算工業部門中14個產業367家上市櫃、興櫃和公開發行公司於2005年至2010年，在不同電力消費所產生的CO2之責任歸屬情況下之生產效率及汙染減量成本，以反映各產業於管制下的機會成本，便於鎖定某些產業或公司，來賦予減量責任。結果發現，各產業在實施碳排放管制後的效率水準，會高於未實施碳排放管制時的效率水準，且各產業的平均總汙染減量成本與每噸二氧化碳減量成本相差甚大。而臺灣尚未通過相關法規以規範各產業二氧化碳排放水準，若各產業節能技術或政府相關配套政策未改善，倉促實施碳排放管制，除了對管制對象的產生影響外，也可能間接衝擊未管制對象。政府除了加強輔導各種產業從事節能技術外，也需要適當的公布各產業各公司的各種汙染排放量資訊，以供各界研究碳排放管制或其他汙染排放管制對社會的影響。 / Global warming has become the topic of most countries which concerns things in recent years. Government sets up CO2 reduction objectives and principle in “General National Plan for Energy Saving and Carbon Reduction” in 2010, but the plan doesn’t probe effect of CO2 regulation which different industries. Therefore, it is unknown that different industries should be responsible for the abatement of CO2. In order to clearly understand effect of CO2 regulation for Taiwan industrial sector, this paper use directional distance function to estimate production efficiency and pollution abatement cost of 367 public companies in 14 industries in industrial sector from 2005 to 2010, and to reflect different industries’ opportunity cost under CO2 regulation. Production efficiency of different industries after the implementation of CO2 regulation will be higher than before the implementation of CO2 regulation. On the other hand, different industries have a variety of average pollution abatement cost and pollution abatement cost of CO2 per ton. However, Taiwan has not yet adopted the environment laws to set up industrial CO2 emission level, if the government hurriedly implemented CO2 regulation for Taiwan industrial sector, may be indirectly influence other sectors. Hence, the government should not only urge that industries must be engaged in energy-saving technologies, but also announce companies’ various pollution emission information which provides research institutes to analyze effect of social welfare under CO2 regulation.