Sequential injection has, over the past eight years, developed into a viable alternative to flow-injection, but its full potential has not yet been fully realized. It developed out of existing flow-injection methods when a need for mechanically simple and robust flow-injection methodology arose. In this study the development of this method is discussed with its numerous advantages and disadvantages over existing flow-injection methods. The theoretical basis on which this technique is based is outlined as well as parameters that influence the design of the manifold. With the manifold design principles established, the manifold is evaluated using real sample analysis, with liquid fertilizer as the source of selected elements. Adjustments made to existing flow-injection methods, for the determination of nitrite with sequential injection analysis, are discussed, while a new method is proposed for nitrate determination. The viability of solid-phase reductors and in situ preparation of reagents, combined with sequential injection analysis, is also studied. / Dissertation (MSc (Chemistry))--University of Pretoria, 2006. / Chemistry / unrestricted

This dissertation examines the Carnap-Quine debate on analyticity with the objective of identifying exactly what is at stake. Close scrutiny of Quine’s criticism of the definitions of analyticity reveals that most of his objections are convincing only if they are considered in relation to the definitions of analyticity in natural language. Carnap, however, defines analyticity in artificial languages. The dissertation also shows that Carnap can meet the objections to his definitions by using a perspective based within his own philosophy. After examining the presumptions of each party to the debate, the dissertation concludes that the disagreement between Carnap and Quine on the notion of analyticity is rooted in their different approaches to empiricism and that there is nothing said by either philosopher which proves that one approach has ultimate advantages over the other. It is thus impossible to identify a winner in the Carnap-Quine debate on analyticity. The process of arriving at this conclusion starts with a discussion in the first three chapters of Carnap’s philosophy followed by a critical and detailed discussion of his syntactical and semantical definitions of analyticity and the advantages and disadvantages of each. Chapter Four examines Quine’s objections to Carnap’s definitions of essential predication and shows that his objections do not undermine Carnap’s definitions of this notion in artificial languages. It also shows how vital providing a proper definition of essential predication in natural language is for Carnap’s philosophy and examines whether or not he is able to do so. Chapter Five analyzes Quine’s objections to Carnap’s definitions of logical truth and demonstrates that Carnap is able to respond to all of them when the discussion is situated within his philosophical system. Again, Quine’s objections to definitions of logical truth are meaningful only if they are considered in relation to natural language, which is not Carnap’s concern. The dissertation concludes by showing that both Carnap and Quine arrived at their conclusions with respect to the nature of logical sentences, based not on the arguments in their debate on analyticity, but on their philosophical considerations regarding the principle of empiricism: for Carnap, logical sentences are out of the realm of knowledge and independent of matters of fact whereas, for Quine, these are as empirical as other sentences. Nothing either says in their debate can convince the other to accept a different viewpoint.

Finite quantum systems with d-dimension Hilbert space, where position x and momentum p take values in Zd(the integers modulo d) are studied. An analytic representation of finite quantum systems, using Theta function is considered. The analytic function has exactly d zeros. The d paths of these zeros on the torus describe the time evolution of the systems. The calculation of these paths of zeros, is studied. The concepts of path multiplicity, and path winding number, are introduced. Special cases where two paths join together, are also considered. A periodic system which has the displacement operator to real power t, as time evolution is also studied. The Bargmann analytic representation for infinite dimension systems, with variables in R, is also studied. Mittag-Leffler function are used as examples of Bargmann function with arbitrary order of growth. The zeros of polynomial approximations of the Mittag-Leffler function are studied. / Libyan Cultural Affairs

No description available.

No description available.

In recent years it has been shown that the folding pattern of an RNA molecule plays an important role in its function, likened to a lock and key system. γ-structures are a subset of RNA pseudoknot structures filtered by topological genus that lend themselves nicely to combinatorial analysis. Namely, the coefficients of their generating function can be approximated for large n. This paper is an investigation into the length-spectrum of the longest block in random γ-structures. We prove that the expected length of the longest block is on the order n - O(n^1/2). We further compare these results with a similar analysis of the length-spectrum of rainbows in RNA secondary structures, found in Li and Reidys (2018). It turns out that the expected length of the longest block for γ-structures is on the order the same as the expected length of rainbows in secondary structures. / Master of Science / Ribonucleic acid (RNA), similar in composition to well-known DNA, plays a myriad of roles within the cell. The major distinction between DNA and RNA is the nature of the nucleotide pairings. RNA is single stranded, to mean that its nucleotides are paired with one another (as opposed to a unique complementary strand). Consequently, RNA exhibits a knotted 3D structure. These diverse structures (folding patterns) have been shown to play important roles in RNA function, likened to a lock and key system. Given the cost of gathering data on folding patterns, little is known about exactly how structure and function are related. The work presented centers around building the mathematical framework of RNA structures in an effort to guide technology and further scientific discovery. We provide insight into the prevalence of certain important folding patterns.

by Law Huk-yuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 235-243). / ACKNOWLEDGEMENTS --- p.ii / ABSTRACT --- p.iii / LIST OF TABLES --- p.x / LIST OF FIGURES --- p.xii / Chapter CHAPTER 1 --- INTRODUCTION --- p.1 / Chapter 1.1 --- Background of the Study --- p.1 / Chapter 1.2 --- Purpose and Significance of the Study --- p.2 / Chapter CHAPTER 2 --- REVIEW OF LITERATURE --- p.5 / Chapter 2.1 --- Research in Mathematics Education : A Cognitive Science Perspective --- p.7 / Chapter 2.1.1 --- Issues in mathematics education --- p.8 / Chapter 2.1.2 --- The cognitive science perspective --- p.13 / Chapter 2.1.2a --- Task-based interviews --- p.16 / Chapter 2.1.2b --- Information-processing framework --- p.18 / Chapter 2.1.2c --- The knowledge structure --- p.21 / Chapter 2.1.2d --- The nature of concepts --- p.23 / Chapter 2.1.3 --- The psychological studies of mathematical concepts --- p.25 / Chapter 2.2 --- Mental Models and Conceptual Knowledge --- p.29 / Chapter 2.3 --- Expert-Novice Discrepancies in Knowledge Representation --- p.32 / Chapter 2.4 --- Assessing Mathematical Understanding --- p.38 / Chapter 2.4.1 --- Assessing knowledge structure --- p.39 / Chapter 2.4.2 --- Test validation --- p.41 / Chapter 2.5 --- Summary --- p.42 / Chapter CHAPTER 3 --- RESEARCH METHOD --- p.44 / Chapter 3.1 --- Research Questions --- p.44 / Chapter 3.2 --- Subjects --- p.45 / Chapter 3.3 --- Design and Procedures --- p.46 / Chapter 3.3.1 --- Phase 1. : Initial testing for conceptual knowledge --- p.46 / Chapter 3.3.2 --- Phase 2 : Task-based interviewing --- p.47 / Chapter 3.3.3 --- Phase 3: Revised testing for conceptual knowledge --- p.48 / Chapter 3.3.4 --- Model for assessing conceptual understanding --- p.49 / Chapter 3.4 --- Data Analysis --- p.51 / Chapter 3.5 --- Time Frame --- p.52 / Chapter CHAPTER 4 --- RESULTS AND DISCUSSION --- p.53 / Chapter 4.1 --- Overview --- p.53 / Chapter 4.2 --- Conceptual Knowledge in Coordinate Geometry --- p.54 / Chapter 4.3 --- Phase-one Analysis : Selection of Expert and Novice Students --- p.57 / Chapter 4.3.1 --- The scoring of initial test --- p.58 / Chapter 4.3.2 --- A profile of expert students and novice students --- p.60 / Chapter 4.3.3 --- A preliminary discussion ： Expert students vs. novice students --- p.61 / Chapter 4.4 --- Phase-two Analysis --- p.63 / Chapter 4.4.1 --- Constructing students' knowledge representations --- p.64 / Chapter 4.4.1a --- Mental representation of <PARALLEL LINES> --- p.66 / Chapter 4.4.1b --- Mental representation of <SLOPES> --- p.78 / Chapter 4.4.1c --- Mental representation of <INTERCEPTS> --- p.82 / Chapter 4.4.1d --- Mental representation of <POINT COORDINATES> --- p.85 / Chapter 4.4.1e --- Knowledge representations --- p.92 / Chapter 4.4.2 --- Comparison of expert mental representat ion and novice mental representation --- p.101 / Chapter 4.4.3 --- Generating and testing hypotheses --- p.105 / Chapter 4.5 --- Phase-three Analysis --- p.123 / Chapter 4.5.1 --- Scoring of the revised test --- p.123 / Chapter 4.5.2 --- Test reliability and validation --- p.135 / Chapter 4.6 --- Summary --- p.139 / Chapter CHAPTER 5 --- "CONCLUSIONS, IMPLICATIONS AND SUGGESTIONS FOR FUTURE RESEARCH" --- p.142 / Chapter 5.1 --- Conclusions --- p.142 / Chapter 5.2 --- Limitations --- p.144 / Chapter 5.3 --- Implications --- p.145 / Chapter 5.4 --- Suggestions for Future Research --- p.147 / APPENDICES / Appendix 1. Initial test for conceptual knowledge --- p.149 / Appendix 2. Scoring record of initial test --- p.152 / Appendix 3. Questions for the first interview --- p.153 / Appendix 4. Subjects' protocols of the first interview (the Chinese version) --- p.157 / Appendix 5 . Subjects ' protocols of the first interview (the Knglish- trans1ated version ) --- p.176 / Appendix 6. Questions for the second interview --- p.202 / Appendix 7. Record of subjects' responses to the questions of second interview --- p.208 / Appendix 8. Revised quiz for conceptual knowledge --- p.210 / Appendix 9. Item and score distribution of the two-halves of the revised test --- p.232 / Appendix 10A. Scoring record of Test A ( the first half- test ) --- p.233 / Appendix 10B. Scoring record of Test B (the second half- test ) --- p.234 / REFERENCES --- p.235

Call number: LD2668 .T4 1952 M3 / Master of Science

There has been much recent interest in random graphs sampled uniformly from the set of (labelled) graphs on n vertices in a suitably structured class A. An important and well-studied example of such a suitable structure is bridge-addability, introduced in 2005 by McDiarmid et al. in the course of studying random planar graphs. A class A is bridge-addable when the following holds: if we take any graph G in A and any pair u,v of vertices that are in different components in G, then the graph G′ obtained by adding the edge uv to G is also in A. It was shown that for a random graph sampled from a bridge-addable class, the probability that it is connected is always bounded away from 0, and the number of components is bounded above by a Poisson law. What happens if ’bridge-addable’ is replaced by something weaker? In this thesis, this question is explored in several different directions. After an introductory chapter and a chapter on generating function methods presenting standard techniques as well as some new technical results needed later, we look at minor-closed, labelled classes of graphs. The excluded minors are always assumed to be connected, which is equivalent to the class A being decomposable - a graph is in A if and only if every component of the graph is in A. When A is minor-closed, decomposable and bridge-addable various properties are known (McDiarmid 2010), generalizing results for planar graphs. A minor-closed class is decomposable and bridge-addable if and only if all excluded minors are 2-connected. Chapter 3 presents a series of examples where the excluded minors are not 2-connected, analysed using generating functions as well as techniques from graph theory. This is a step towards a classification of connectivity behaviour for minor-closed classes of graphs. In contrast to the bridge-addable case, different types of behaviours are observed. Chapter 4 deals with a new, more general vari- ant of bridge-addability related to edge-expander graphs. We will see that as long as we are allowed to introduce ’sufficiently many’ edges between components, the number of components of a random graph can still be bounded above by a Pois- son law. In this context, random forests in Kn,n are studied in detail. Chapter 5 takes a different approach, and studies the class of labelled forests where some vertices belong to a specified stable set. A weighting parameter y for the vertices belonging to the stable set is introduced, and a graph is sampled with probability proportional to y*s where s is the size of its stable set. The behaviour of this class is studied for y tending to ∞. Chapters 6 concerns random graphs sampled from general decomposable classes. We investigate the minimum size of a component, in both the labelled and the unlabelled case.

In this thesis we prove several results in analytic number theory. 1. We show that there exist 3-digit palindromic primes in base b for a set of b having density 1 and that if b is sufficiently large then there is a $3$-digit palindrome in base b having precisely two prime factors. 2. We prove various estimates for averages of sums of Kloosterman fractions over primes. The first of these improves previous results of Fouvry-Shparlinski and Baker. 3. By using the q-analogue of van der Corput's method to estimate short Kloosterman sums we study the divisor function in an arithmetic progression to modulus q. We show that the expected asymptotic formula holds for a larger range of q than was previously known, provided that q has a certain factorisation. 4. Let ‖x‖ denote the distance from x to the nearest integer. We show that for any irrational α and any ϴ< 8/23 there are infinitely many n which are the product of two primes for which ‖nalpha‖ ≤ n ^-ϴ. 5. By establishing an improved level of distribution we study almost-primes of the form f(p,n) where f is an irreducible binary form over Z. 6. We show that for an irreducible cubic f ? Z[x] and a full norm form $mathbf N$ for a number field $K/Q$, satisfying certain hypotheses, the variety $$f(t)=mathbf N(x_1,ldots,x_k) e 0$$ satisfies the Hasse principle. Our proof uses sieve methods.