The purpose of this paper was to prove the equivalence of the following completeness axioms. This purpose was carried out by first defining an ordered field and developing some basic theorems relative to it, then proving that lim [(u+u)*]^n = z (where u is the multiplicative identity, z is the additive identity, and * indicates the multiplicative inverse of an element), and finally proving the equivalence of the five axioms.

In this thesis, information completeness and credibility in web auction environment is the mainly question to find out. By using focus group research method, three discussions were held. In the first discussion, there were six interviewers joined, and the discussing purpose was to understand the concept of information completeness and credibility in e-commerce. In the second discussion, two sellers were invited to demonstrate and to explain how to sell in online auction. In the third discussion, eight buyers were asked to introducing themselves, and discussing themselves cases about online shopping. Finally using oral analysis skills, the research framework was constructed. The research suggests that information completeness and credibility includes all about product information, retailers¡¦ information, transaction information, information representation and third parties information. Each has its different degree of credibility, and buyers usually retrieve information they need to reduce their perceived risk.

In this paper we seek to answer the following question: How complete is the Swespineregister? In order to answer this question we believe that in a register that has the ambitionto follow-up patients throughout a specified period of time, two types of completeness haveto be defined: external and internal completeness. In our opinion, the correct assessment ofa register’s level of completeness, results in an increase in its credibility, revealing whetherthe register has met its desired level of quality.By defining the register’s target population we came to the conclusion that the methodused by Swespine to calculate external completeness yielded misleading results. We definedanother method of assessing external completeness and concluded that our questioncannot be answered.We have also found an appropriate way to calculate the register’s internal completenesslevel. Since the internal completeness decreases as the follow-up period increases, wesought to discover which groups of patients are more likely to respond to the follow-upquestionnaire. For this a Logistic Regression Method was applied.

Kant famously claims his table of judgments is complete. However, Kant does not provide a demonstration of his claim of completeness. In fact, he does not seem to think that a proof of completeness is necessary. I argue that we can reconstruct a demonstration that Kant would accept once we reflect upon his notion of a disjunctive judgment.

This dissertation presents and responds to the following problem. For Kant a field of enquiry can be a science only if it is systematic. Most sciences achieve systematicity through having a unified content and method. Physics, for example, has a unified content, as it is the science of matter in motion, and a unified method because all claims in physics must be verified through empirical testing. In order for metaphysics to be a science it also must be systematic. However, metaphysics cannot have a unified content or method because metaphysicians lack a positive conception of what its content and method are. On Kant's account, metaphysicians can say with certainty what metaphysics does not study and what methods it cannot use, but never how it should proceed. Without unified content and method systematicity can only be guaranteed by some either means, namely, completeness. Without completeness metaphysics cannot have systematicity and every science must be systematic. Completeness can only be achieved if we severely limit the scope of metaphysics so that it contains only the conditions for the possibility of experience. This dissertation defends the claims made about the centrality of completeness in understanding Kant's conception of metaphysics as a science in two ways. First, the first two chapters point to a substantial body of textual evidence that supports the idea that Kant was directly concerned about the notion of completeness and links it to his conception of metaphysics as a science. Chapters 3 and 4 consider some possible objections to thinking that metaphysics as a science can be complete, giving special consideration to Gödel's incompleteness theorem. Chapter 5 explains why, if this position is as clear as this dissertation has argued, previous scholars have failed to acknowledge it. Giving a full answer to this question requires considering the general neglect of the "Doctrine of Method" section of Kant's primary theoretical text, The Critique of Pure Reason. The Doctrine of Method contains many of the passages which most directly support my thesis. Chapter 6 explains why scholars have ignored this important passage and argues that they should not continue to do so.

Poor quality data such as data with errors or missing values cause negative consequences in many application domains. An important aspect of data quality is completeness. One problem in data completeness is the problem of missing individuals in data sets. Within a data set, the individuals refer to the real world entities whose information is recorded. So far, in completeness studies however, there has been little discussion about how missing individuals are assessed. In this thesis, we propose the notion of population-based completeness (PBC) that deals with the missing individuals problem, with the aim of investigating what is required to measure PBC and to identify what is needed to support PBC measurements in practice. To achieve these aims, we analyse the elements of PBC and the requirements for PBC measurement, resulting in a definition of the PBC elements and PBC measurement formula. We propose an architecture for PBC measurement systems and determine the technical requirements of PBC systems in terms of software and hardware components. An analysis of the technical issues that arise in implementing PBC makes a contribution to an understanding of the feasibility of PBC measurements to provide accurate measurement results. Further exploration of a particular issue that was discovered in the analysis showed that when measuring PBC across multiple databases, data from those databases need to be integrated and materialised. Unfortunately, this requirement may lead to a large internal store for the PBC system that is impractical to maintain. We propose an approach to test the hypothesis that the available storage space can be optimised by materialising only partial information from the contributing databases, while retaining accuracy of the PBC measurements. Our approach involves substituting some of the attributes from the contributing databases with smaller alternatives, by exploiting the approximate functional dependencies (AFDs) that can be discovered within each local database. An analysis of the space-accuracy trade-offs of the approach leads to the development of an algorithm to assess candidate alternative attributes in terms of space-saving and accuracy (of PBC measurement). The result of several case studies conducted for proxy assessment contributes to an understanding of the space-accuracy trade-offs offered by the proxies. A better understanding of dealing with the completeness problem has been achieved through the proposal and the investigation of PBC, in terms of the requirements to measure and to support PBC in practice.

In this thesis, three fluid dynamical problems are studied. First in chapter 2 we investigate, via both theoretical and experimental methods, the swimming motion of a magnetotactic bacterium having the shape of a prolate spheroid in a viscous liquid under the influence of an imposed magnetic field. The emphasis of the study is placed on how the shape of the non-spherical magnetotactic bacterium, marked by the size of its eccentricity, affects the pattern of its swimming motion. It is revealed that the pattern/speed of a swimming spheroidal magnetotactic bacterium is highly sensitive not only to the direction of its magnetic moment but also to its shape. Secondly, an important unanswered mathematical question in the theory of rotating fluids has been the completeness of the inviscid eigenfunctions which are usually referred to as inertial waves or inertial modes. In chapter 3 we provide for the first time a mathematical proof for the completeness of the inertial modes in a rotating annular channel by establishing the completeness relation, or Parseval’s equality, for any piecewise continuous, differentiable velocity of an incompressible fluid. Thirdly, in chapter 4 we investigate, through both asymptotic analysis and direct numerical simulation, precessionally driven flow of a homogeneous fluid confined in a fluid-filled circular cylinder that rotates rapidly about its symmetry axis and precesses about a different axis that is fixed in space. A particular emphasis is placed on the spherical-like cylinder whose diameter is nearly the same as its length. An asymptotic analytical solution in closed form is derived in the mantle frame of reference for describing weakly precessing flow in the spherical-like cylinder at asymptotically small Ekman numbers. We also construct a three-dimensional finite element model, which is checked against the asymptotic solution, in attempting to elucidate the structure of the nonlinear flow.

The purpose of this thesis is to study the concept of completeness in an ordered field. Several conditions which are necessary and sufficient for completeness in an ordered field are examined. In Chapter I the definitions of a field and an ordered field are presented and several properties of fields and ordered fields are noted. Chapter II defines an Archimedean field and presents several conditions equivalent to the Archimedean property. Definitions of a complete ordered field (in terms of a least upper bound) and the set of real numbers are also stated. Chapter III presents eight conditions which are equivalent to completeness in an ordered field. These conditions include the concepts of nested intervals, Dedekind cuts, bounded monotonic sequences, convergent subsequences, open coverings, cluster points, Cauchy sequences, and continuous functions.

Neste trabalho, estudamos algumas formas de combinar sistemas de Lógica Modal, analisando quando a combinação preserva propriedades como correção, completude e decidibilidade. Estendemos um estudo já realizado sobre combinações de sistemas de Lógica Modal Normal para sistemas de Lógica Modal Não-normal. O principal resultado deste trabalho é a preservação de completude da aplicação externa de um sistema de Lógica Modal Não-normal M em um sistema lógico L. Outro resultado importante é um exemplo de interação forte na combinação independente, ou fusão, de dois sistemas de Lógica Modal Não-normal. / In this work, we study a few ways of combining Modal Logic systems, analysing when the combination preserves properties like soundness, completeness and decidability. We extend a study of the combination of Normal Modal Logic systems to Non-normal Modal Logic systems. The main result of this work is the completeness preservation in the external application of a Non-normal Modal Logic system M to a logic system L. Another important result is an example of strong interations arising in the fusion of two Non-normal Modal Logic system.

We present an extension of Geodesics in Lorentzian Manifolds (Semi-Riemannian Manifolds or pseudo-Riemannian Manifolds ). A geodesic on a Riemannian manifold is, locally, a length minimizing curve. On the other hand, geodesics in Lorentzian manifolds can be viewed as a distance between ``events''. They are no longer distance minimizing (instead, some are distance maximizing) and our goal is to illustrate over what time parameter geodesics in Lorentzian manifolds are defined. If all geodesics in timelike or spacelike or lightlike are defined for infinite time, then the manifold is called ``geodesically complete'', or simply, ``complete''. It is easy to show that the magnitude of a geodesic is constant, so one can characterize geodesics in terms of their causal character: if this magnitude is negative, the geodesic is called timelike. If this magnitude is positive, then it is spacelike. If this magnitude is 0, then it is called lightlike or null. Geodesic completeness can be considered by only considering one causal character to produce the notions of spacelike complete, timelike complete, and null or lightlike complete. We illustrate that some of the notions are inequivalent.