圓教是中國佛學獨有的概念，圓主要指圓滿和圓融二義，圓教即圓滿究竟、圓融無礙地總攝一切法的教法。對天台宗來說，這圓教是如何可能的呢﹖智者大師透過教相門與觀心門來講圓教，教相門就是以判教理論，分判、判定有佛一代的說法，何者為權，何者為實，而最後必以天台圓教為實。觀心門就是通過智者大師自心所行法門，點出一念三千的教說，由此一念心即具三千法以明圓教之義。 　　另外，佛性是中土佛教思想的核心概念，主導著整個中國佛學的發展方向，然則在天台圓教浸潤下，會顯出何種形態的佛性理論﹖我們發現，在天台宗之思想中，佛性圓滿無盡地具足一切法，可以說和圓教義理是一致的，實則兩者之關係本來就密不可分。 　　總之，天台圓教和佛性思想表顯著中國佛教哲學的高峰，亦充份地開顯了大乘佛教的精神，實為人類思想文化的一大寶庫。

<p>We derive the equation linking the Weyl tensor with its Lanczos potential, called the Weyl-Lanczos equation, in 1+3 covariant formalism for perfect fluid Bianchi type I spacetime and find an explicit expression for a Lanczos potential of the Weyl tensor in these spacetimes. To achieve this, we first need to derive the covariant decomposition of the Lanczos potential in this formalism. We also study an example by Novello and Velloso and derive their Lanczos potential in shear-free, irrotational perfect fluid spacetimes from a particular ansatz in 1+3 covariant formalism. The existence of the Lanczos potential is in some ways analogous to the vector potential in electromagnetic theory. Therefore, we also derive the electromagnetic potential equation in 1+3 covariant formalism for a general spacetime. We give a short description of the necessary tools for these calculations and the cosmological formalism we are using.</p>

In Chapters 1 and 2, we introduce the definition of interpolating refinable function vectors in dimension one and high dimensions, characterize such interpolating refinable function vectors in terms of their masks, and derive their sum rule structure explicitly. We study biorthogonal refinable function vectors from interpolating refinable function vectors. We also study the symmetry property of an interpolating refinable function vector and characterize a symmetric interpolating refinable function vector in any dimension with respect to certain symmetry group in terms of its mask. Examples of interpolating refinable function vectors with some desirable properties, such as orthogonality, symmetry, compact support, and so on, are constructed according to our characterization results. In Chapters 3 and 4, we turn to the study of general matrix extension problems with symmetry for the construction of orthogonal and biorthogonal multiwavelets. We give characterization theorems and develop step-by-step algorithms for matrix extension with symmetry. To illustrate our results, we apply our algorithms to several examples of interpolating refinable function vectors with orthogonality or biorthogonality obtained in Chapter 1. In Chapter 5, we discuss some possible future research topics on the subjects of matrix extension with symmetry in high dimensions and frequency-based non-stationary tight wavelet frames with directionality. We demonstrate that one can construct a frequency-based tight wavelet frame with symmetry and show that directional analysis can be easily achieved under the framework of tight wavelet frames. Potential applications and research directions of such tight wavelet frames with directionality are discussed. / Applied Mathematics

Perfect simulation  and the EM algorithm are the main topics in this thesis. In paper I, we present coupling from the past (CFTP) algorithms that generate perfectly distributed samples from the multi-type Widom--Rowlin-son (W--R) model and some generalizations of it. The classical W--R model is a point process in the plane or the  space consisting of points of several different types. Points of different types are not allowed to be closer than some specified distance, whereas points of the same type can be arbitrary close. A stick-model and soft-core generalizations are also considered. Further, we  generate samples without edge effects, and give a bound on sufficiently small intensities (of the points) for the algorithm to terminate. In paper II, we consider the  forestry problem on how to estimate  seedling dispersal distributions and effective plant fecundities from spatially data of adult trees  and seedlings, when the origin of the seedlings are unknown.   Traditional models for fecundities build on allometric assumptions, where the fecundity is related to some  characteristic of the adult tree (e.g.\ diameter). However, the allometric assumptions are generally too restrictive and lead to nonrealistic estimates. Therefore we present a new model, the unrestricted fecundity (UF) model, which uses no allometric assumptions. We propose an EM algorithm to estimate the unknown parameters.   Evaluations on real and simulated data indicates better performance for the UF model. In paper III, we propose  EM algorithms to  estimate the passage time distribution on a graph.Data is obtained by observing a flow only at the nodes -- what happens on the edges is unknown. Therefore the sample of passage times, i.e. the times it takes for the flow to stream between two neighbors, consists of right censored and uncensored observations where it sometimes is unknown which is which.       For discrete passage time distributions, we show that the maximum likelihood (ML) estimate is strongly consistent under certain  weak conditions. We also show that our propsed EM algorithm  converges to the ML estimate if the sample size is sufficiently large and the starting value is sufficiently close to the true parameter. In a special case we show that it always converges.  In the continuous case, we propose an EM algorithm for fitting  phase-type distributions to data.

We derive the equation linking the Weyl tensor with its Lanczos potential, called the Weyl-Lanczos equation, in 1+3 covariant formalism for perfect fluid Bianchi type I spacetime and find an explicit expression for a Lanczos potential of the Weyl tensor in these spacetimes. To achieve this, we first need to derive the covariant decomposition of the Lanczos potential in this formalism. We also study an example by Novello and Velloso and derive their Lanczos potential in shear-free, irrotational perfect fluid spacetimes from a particular ansatz in 1+3 covariant formalism. The existence of the Lanczos potential is in some ways analogous to the vector potential in electromagnetic theory. Therefore, we also derive the electromagnetic potential equation in 1+3 covariant formalism for a general spacetime. We give a short description of the necessary tools for these calculations and the cosmological formalism we are using.

The construction industry is a business with an intense flow of both material and information that require well-functioning logistics in order to not suffer from unnecessarily high costs. Suppliers play a big part regarding the costs of the distribution and handling of material and due to this a construction project’s costs are affected a great deal by the suppliers’ actions. Spinnrocken is a construction project in the town center of Norrköping. The real estate company Fastighets AB L E Lundbergs is the client and the construction company Skanska is contracted as sole constructor for the project. Spinnrocken is planned to be finalized in the summer of 2014 and consists of several rental-apartments and some smaller businesses. Spinnrocken and its central location result in major logistic challenges, because of this Lundbergs and Skanska want to analyze and evaluate the project’s logistic performance. The main purpose of this thesis is to measure the order fulfillment of interior materials, the scaffold material Doka and windows at Spinnrocken by using the so-called perfect order fulfillment measure, as defined in Supply Chain Operations Reference Model. Perfect order fulfillment indicates the delivery performance to the construction site.The combined perfect order fulfillment for the three investigated materials is 18 %. A perfect order fulfillment of 18 % means that only one out of five inspected deliveries to Spinnrocken was considered having no faults at all. The effects of a low perfect order fulfillment are disruptions in the short-term time schedule, delayed operations, additional work and that the work space at the construction site is occupied by unnecessary construction material. The resulting effects thereby affects the project’s economy negatively.

El objetivo de esta tesis es definir códigos perfectos sobre diferentes espacios de señal multidimensionales. Para resolver este problema, esta memoria presenta una relación original entre las Teorías de Grafos, Números y Códigos. Uno de nuestros principales resultados es la propuesta de una métrica adecuada sobre constelaciones de señal de tipo cuadrático, hexagonal y cuatro-dimensional. Esta métrica es la distancia entre los vértices de una nueva clase de grafos de Cayley definidos sobre diferentes anillos de enteros, en concreto, los enteros de Gauss, Eisenstein-Jacobi y Lipschitz. Así, resolvemos el problema de Teoría de Grafos conocido como el cálculo del conjunto perfecto dominante sobre las familias de grafos definidas en esta memoria. Para cada caso, daremos una condición suficiente para obtener dicho conjunto. La obtención de estos conjuntos de dominación implica directamente la construcción de códigos perfectos sobre los alfabetos que se consideran.Además, se obtendrán algunos resultados de isomorfía y embebimiento de grafos. En particular, se establecerán las relaciones entre grafos circulantes, toroidales y los que se presentan en este trabajo. Más concretamente, se mostrará que siempre existen órdenes para los cuales un grafo Toro puede ser embebido en un grafo Gaussiano, de Esenstein-Jacobi o de Lipschitz. Esto implica que la conocida distancia de Lee es un caso particular de las métricas presentadas en este trabajo. / The aim of this work is to define perfect codes for different multidimensional signal spaces. To solve this problem, this thesis presents an original relationship among the fields of Graph Theory, Number Theory and Coding Theory. One of our main findings is the proposal of a suitable metric over quadratic, hexagonal and four-dimensional constellations of signal points. This metric is the distance among vertices of a new class of Cayley graphs defined over integer rings, namely Gaussian integers, the Eisenstein-Jacobi integers and the Lipschitz integers.A problem in Graph Theory known as the perfect dominating set calculation is solved over the families of graphs defined in this memory. A sufficient condition for obtaining such a set is given for each case. The obtention of these sets of domination directly yields to the construction of perfect codes for the alphabets under consideration. In addition, some isomorphism and graph embedding results are going to be obtained. Specially, the relations between circulant, toroidal and the graphs presented in this work are stated. In particular, there always exist orders for which a Torus graph can be embedded in Gaussian, Eisenstein-Jacobi and Lipschitz graphs. This implies that the well-known Lee distance is a subcase of the metrics presented in this research.

This thesis is focused on hash families and cover-free families and their application to problems in cryptography. We present new necessary conditions for generalized separating hash families, and provide new explicit constructions. We then consider three cryptographic applications of hash families and cover-free families. We provide a stronger de nition of anonymity in the context of shared symmetric key primitives and give a new scheme with improved anonymity properties. Second, we observe that nding the invalid signatures in a set of digital signatures that fails batch veri cation is a group testing problem, then apply and compare many group testing algorithms to solve this problem e ciently. In particular, we apply group testing algorithms based on cover-free families. Finally, we construct a one-time signature scheme based on cover-free families with short signatures.

This dissertation explores the issues of mixed oligopoly, restructuring, and M&A that occurs in turn on the stages of policy set-up, preparation, and performing when the government attempt to privatize the state-owned enterprises (SOEs). On the policy set-up stage, private firms in domestic market are not necessary confined to originate at home country. Foreign private firms may establish an oversea subsidiary and create a mixed oligopoly market structure at home country. In addition, those foreign private firms may not passively accept all the trade policies that came from the government decision of home country. Mixed oligopoly competition between one domestic public firm and one subsidiary of foreign private firm is been formulated to investigate the following questions: (1) how the agents compete under the cases that home country government adopts policies such as corporate tax rate, repatriation tax rate, and partial offering public stocks; and the foreign private firm implements strategies such as vertical integration and transfer pricing; (2) the impact on social welfare and the decision of optimal public stock-offering ratio while home country government¡¦s policies and foreign private firm¡¦s strategies have changed. New findings include (1) Home country government can not maximize social welfare by simply adopting strategic policies; (2) For home country government, the best strategy for privatizing SOEs maybe partial privatization; (3) For home country government, ¡§mass privatization¡¨ should be avoided as the means of manipulating domestic market shares. On the preparation stage, an incentive scheme model is designed to analyze the governance mechanism for improving SOEs¡¦ situation. First, different types of SOEs are classified according to their own ability and the employees¡¦ attitude for privatization. By offering a sound device of incentive scheme, the government is able to strengthen the SOEs¡¦ ability and employees¡¦ desirability. Within a one-stage symmetric information game framwork, it proves that SOEs with high ability and their employees with high privatization desirability can implement the highest amount of public stock offering ratio. Next, it utilizes a two-stage asymmetric game model for discussing how to improve the SOEs¡¦ ability and how to encourage the employees to support privatization. By providing an incentive contract, the government not only can coerce the SOEs but also can inspire their employees to reveal their true information. The due process of public stock offering is able to strengthen the abilities of SOEs via ¡§restructuring¡¨ on the one hand, and to facilitate the issue of ¡§training subsidies¡¨ for hatching the entrepreneurship of employees on the other hand. Finally, it investigates the impact on public stock offering ratio for the amount of specific grants, and found that the more generosity of incentive contract, the higher the public stock offering ratio. On the performing stage, it adopts the incentive theorem to analyze the outcome of SOEs¡¦ privatization by inviting a named firm. The named firm takes over the SOEs through M&A for the purpose of long-term operation. In order to encourage the employees of the privatized company working more aggressively, the named firm comes up incentive schemes including bonus-sharing and Employees Stock Ownership Plan, ESOP. It found that whether there exists information asymmetry or not between the named firm and the employees of the privatized company will affect the following decision-makings: the level of the employees¡¦ effort, the willingness of the employees¡¦ stock-holding, and the achievement of the named firm¡¦s profit maximizing objective. In particular, it shows that the change of the contents of the incentive schemes will affect the bargaining outcomes between the named firm and the trade union of the SOEs on the issue of working conditions after privatization.

This thesis is focused on hash families and cover-free families and their application to problems in cryptography. We present new necessary conditions for generalized separating hash families, and provide new explicit constructions. We then consider three cryptographic applications of hash families and cover-free families. We provide a stronger de nition of anonymity in the context of shared symmetric key primitives and give a new scheme with improved anonymity properties. Second, we observe that nding the invalid signatures in a set of digital signatures that fails batch veri cation is a group testing problem, then apply and compare many group testing algorithms to solve this problem e ciently. In particular, we apply group testing algorithms based on cover-free families. Finally, we construct a one-time signature scheme based on cover-free families with short signatures.