This dissertation analyzes the Wigner-Poisson system in the presence of an external Coulomb potential. In the first part, the Weyl transform is defined and used to derive an exact quantum mechanical equation for the Weyl transform of the density function ρw (the Wigner function) known as the Wigner equation. This equation holds for any Hamiltonian which is a function of the position and momentum operators. The Wigner-Poisson system is then formally derived by imposing various assumptions on the structure of the Hamiltonian. This system describes the behaviour of an effective one-particle distribution in the presence of a large ensemble of particles. Furthermore, it allows the particles to either attract or repel each other as well as attract or repel as a whole from a fixed Coulomb source located at the origin. The second part details the question of existence and uniqueness for the Wigner-Poisson system. It is shown that provided the initial Wigner function is sufficiently regular [special characters omitted] and is a valid Wigner distribution, then the Wigner-Poisson system has a unique global mild solution [special characters omitted]. This result is independent of both the nature of the external Coulomb potential as well as the interparticle interaction.The proof of this result is accomplished by first transforming the Wigner-Poisson system into a countably infinite set of Schrödinger equations which results in what is referred to as the Schrödinger Poisson system. Using standard semigroup theory arguments, existence and uniqueness of the Schrödinger-Poisson system is established. The properties of the Wigner-Poisson system are then obtained by reversing the transformation step. Regularity results for both the Schrödinger-Poisson and the Wigner-Poisson systems are compared to the case with no external Coulomb potential. In addition, the known regularity results are extended when there is no external field. The results illustrate that the introduction of an external Coulomb potential slightly reduces the regularity of the solution. This confirms a conjecture of Brezzi and Markowich. The third part analyzes the asymptotic behaviour of the Wigner-Poisson system. If the configurational energy Εₐ,ᵦ(t) is positive for all times then by considering the Schrödinger-Poisson system, solutions will decay in the sense of Lᵖ for 2 < p < 6. This generalizes a result of Illner, Lange and Zweifel. Moreover, If the total energy is negative then the solutions will not decay in the sense of Lᵖ for any 2 < p ≤ ∞. This generalizes a result of Chadam and Glassey. Decay estimates for both the Schrödinger-Poisson and the Wigner-Poisson systems are compared to the case with no external Coulomb field. As with the regularity results, the introduction of an external Coulomb field degrades the reported decay rates of the solution. / Graduate

No description available.

No description available.

No description available.

No description available.

As the level of integrated circuit (IC) complexity continues to increase, the post-silicon validation stage is becoming a large component of the overall development cost. To address this, we propose a reconfigurable post-silicon debug infrastructure that enhances the post-silicon validation process by enabling the observation and control of signals that are internal to the manufactured device. The infrastructure is composed of dedicated programmable logic and programmable access networks. Our reconfigurable infrastructure enables not only the diagnoses of bugs; it also allows the detection and potential correction of errors in normal operation. In this thesis we describe the architecture, implementation and operation of our new infrastructure. Furthermore, we identify and address three key challenges arising from the implementation of this infrastructure. Our results demonstrate that it is possible to implement an effective reconfigurable post-silicon infrastructure that is able to observe and control circuits operating at full speed, with an area overhead of between 5% and 10% for many of our target ICs. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

A generalized inclusion (g.i.) frame consists of a set of points (or "worlds") W and an assignment of a binary relation Rw on W to each point w in W. generalized inclusion frames whose Rw are partial orders are called comparison frames. Conditional logics of various comparative notions, for example, Lewis's V-logic of comparative possibility and utilitarian accounts of conditional obligation, model the dyadic modal operator > on comparison frames according to (what amounts to) the following truth condition: oc>13"holds at w" if every point in the truth set of a bears Rw to some point where holds. In this essay I provide a relational frame theory which embraces both accessibility semantics and g.i. semantics as special cases. This goal is achieved via a philosophically significant generalization of universal strict implication which does not assume accessibility as a primitive. Within this very general setting, I provide the first axiomatization of the dyadic modal logic corresponding to the class of all g.i. frames. Various correspondences between dyadic logics and first order definable subclasses of the class of g.i. frames are established. Finally, some general model constructions are developed which allow uniform completeness proofs for important sublogics of Lewis' V. / Arts, Faculty of / Philosophy, Department of / Graduate

No description available.

The structure of our world is given in the grammar of our native tongue. If so people whose native tongue has quite a different grammar must be living in a quite different world. A logic such as Aristotle's may seem universal to the speakers of Greek, in fact it may seem universal to speakers of any Indo-European tongue, but the logic will hold good only for the 'universe' of the language or language-family in question. This implies a relationship between logic and grammar rather like the one Russell and Whitehead -claimed for mathematics and logic. Their Principia Mathematica tried to show that the mathematical notion of number rests on, or arises out of, the logical notion of class, that is, we come to understand what a number is through our grasp of what a class is. This thesis is a kind of Principia Logica: it suggests that the whole framework of common sense logic rests on, or arises out of, the grammatical structure of the language the logic was conceived in or took shape in terms of. And if so logical criteria come into being and take shape inside a language or language-family, and are dependent for their validity and even for their meaning on the structure of the language in question. To test, or to try to test, a mode of thought or an argument form against a logical system would be to put the cart before the horse: the logic only makes sense because the form of argument or mode of thought was there already. If so philosophers and logicians ought to think of the words 'world', 'universe' and 'universal' with tongue in cheek. In so far as a judgment seems to us universally true it is unlikely to hold good for the world of an alien language family. If our world is not the only world anybody writing logic or philosophy down ought to make it clear whose world he has in mind - and to do this it may be enough to make sure it is addressed to somebody in particular. Western philosophers seem to have addressed themselves to the whole world, or to mankind, or God. This thesis shows, if nothing else, how hard it can be to address even one other human being. To sum up with another analogy; it seems to me, as a single man, that the difference between one and two is greater than the difference between any other two numbers. There may be a world of difference between zero and one, but between one and two there's all the difference in the world - and that's the difference that matters. Perhaps the only way 1,000 differs from 1,001, as Frege puts it, is in the expression on its face. / Arts, Faculty of / Philosophy, Department of / Graduate

This study was designed to determine the effectiveness of teaching symbolic logic in the high school. Three hundred eighty-seven students enrolled on the University Programme in grades nine to thirteen at Como Lake High School, in School District No. 43 (Coquitlam), took part in the investigation. The students were grouped according to the mathematics course they were studying. Answers were sought to two specific questions. Do significant differences exist between the means of the final test scores of the students in each of the groups? At which grade levels can this material be effectively mastered? As a criterion for determining this, 75 per cent of the students at a particular level were required to obtain a score of 50 per cent or better on the final test. In order to answer the first question, the results were studied by analysis of covariance with scholastic aptitude being the variable controlled. The answer to the second question was obtained by comparing the performance of each group with the standard outlined. On the basis of this information, decisions were made regarding the suitability of the material for the various grade levels. All of the differences between the means were found to be significant at the one per cent level. The highest mean score was obtained by the students in Mathematics 101, followed in order by those of Mathematics 91, 30, 20, and 10. The students of Mathematics 101, 91 and 30 satisfied the requirement that 75 per cent should obtain a score of 50 per cent or better on the final test. The students of Mathematics 20 and 10 failed to satisfy this requirement. / Education, Faculty of / Graduate