A homework set for learning the International Phonetic Alphabet. Both reading and writing the IPA are used. Note that these .doc files use the old SILDoulos IPA93 font. The set includes the problem set and answer key. / This collection consists of learning objects developed for use in courses offered by the Department of Linguistics. Learning objects include lectures, presentations, quizzes, activities, and more. Access to this collection is restricted to authorized faculty and instructors. For access to this collection, please contact Dr. Amy Fountain, Department of Linguistics, avf@email.arizona.edu.

Individual differences in problem-solving have been studied from both information-processing and developmental psychology perspectives. The purpose of the present research was to use an information-processing approach to investigate the effects of both age and intelligence on the performances by young persons on experimental tasks which required systematic application of appropriate solution rules. Eighty 10- and 15-year-old subjects were assigned to one of eight groups on the bases of their ages, sex, and intelligence levels. The testing condition was the same for all groups. Stimulus materials consisted of a two-pan balance and a variety of different-density cubes. Subjects' responses to the materials were their predictions of equilibrium or imbalance. Correct solutions required understanding of the physical science concepts of volume and density, and the mathematics concept of proportionality. From analysis of variance performed on the data, it was found that males and females did not differ in their abilities to problem-solve. The highly-intelligent subjects had a greater frequency of correct responses in both age groups, and the older subjects outperformed younger subjects. The equilibrium problems presented in the study were of six separate types, and the interaction effects in the data revealed that the six types were of varying levels of difficulty. It was in the analyses of the subjects' patterns of responses to the several types that the most theoretically interesting results appeared. Examination of the response patterns led to assignment of the respondents to categories of probable rule-usage. The less sophisticated problem-solvers did not take density into account and consistently relied on their knowledge of the volume concept in making their decisions. Solvers functioning at higher rule-levels were able to consider density as well before making their predictions, although a substantial number failed to use cues present in the experiment to reckon the respective densities correctly. Fully-functional problem-solvers gave responses which showed their mastery of the mathematics of proportionality. Twenty-four subjects participated in a second experiment which was a short demonstration-oriented training study providing feedback, although the algorithm for correct problem solution was not directly taught. Results were discussed in terms of the efficacy of the rule-usage model.

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This thesis investigates the effect of problem structure on performance and behavioural variety in group problem solving. In addition, it examines the effects of problem solving strategy in group problem solving. <br /><br /> Previous researchers have focused their efforts on individual problem solving with minimal reference to groups. This is due to difficulties such as the presence of distributed information, the coordination of people and the large scale of work that typified group problems. Specifically, the effect of problem structure in group problems has been rarely studied due to the absence of an encompassing theory. <br /><br /> In this thesis, the effect of problem structure on group performance is studied using the fundamental characteristics of structure such as detour, redundancy, abstraction and degree of homogeneity. These characteristics were used in conjunction with existing problem solving theories (such as Information processing system, Gestalt approach and Lewin's lifespace approach) and Heider's balance theory to understand the effects of task structure on group performance and behavioural output. <br /><br /> Balance theory is introduced as a conceptual framework in which the problem solving process is viewed as a dynamic progression from cognitive imbalance towards a state of structural balance corresponding with the solution. This theoretical approach captures both incremental search processes and insight associated with cognitive restructuring, typical of existing problem solving approaches in the literature. It also allowed the development of unique measures for studying the effect of structure in group problem solving. <br /><br /> A Laboratory experiment was conducted using 153 undergraduate and 3 graduate students in groups of 4 subjects. The experiment examined the effect of task structure on groups' performance and behavioural variety. The stimulus used for the experiment was a categorization problem consisting of sixteen cards with two objects each shared equally among four participants. The objective was to form four groups of items with no cards left unused. The groups' performance data was collected and analyzed to verify the postulated hypotheses. <br /><br /> The results indicate that both increased problem structure complexity and the introduction of a restructuring dimension in the problem structure were associated with reduced performance and increased behavioural variety. With respect to problem solving strategy, early discussion in problem solving was associated with better performance and less behavioural variety. Finally, the results support the premise that group problem solving processes tend to be in the direction of attaining higher states of balance.

The Stochastic Diffusion Search (SDS) was developed as a solution to the best-fit search problem. Thus, as a special case it is capable of solving the transform invariant pattern recognition problem. SDS is efficient and, although inherently probabilistic, produces very reliable solutions in widely ranging search conditions. However, to date a systematic formal investigation of its properties has not been carried out. This thesis addresses this problem. The thesis reports results pertaining to the global convergence of SDS as well as characterising its time complexity. However, the main emphasis of the work, reports on the resource allocation aspect of the Stochastic Diffusion Search operations. The thesis introduces a novel model of the algorithm, generalising an Ehrenfest Urn Model from statistical physics. This approach makes it possible to obtain a thorough characterisation of the response of the algorithm in terms of the parameters describing the search conditions in case of a unique best-fit pattern in the search space. This model is further generalised in order to account for different search conditions: two solutions in the search space and search for a unique solution in a noisy search space. Also an approximate solution in the case of two alternative solutions is proposed and compared with predictions of the extended Ehrenfest Urn model. The analysis performed enabled a quantitative characterisation of the Stochastic Diffusion Search in terms of exploration and exploitation of the search space. It appeared that SDS is biased towards the latter mode of operation. This novel perspective on the Stochastic Diffusion Search lead to an investigation of extensions of the standard SDS, which would strike a different balance between these two modes of search space processing. Thus, two novel algorithms were derived from the standard Stochastic Diffusion Search, ‘context-free’ and ‘context-sensitive’ SDS, and their properties were analysed with respect to resource allocation. It appeared that they shared some of the desired features of their predecessor but also possessed some properties not present in the classic SDS. The theory developed in the thesis was illustrated throughout with carefully chosen simulations of a best-fit search for a string pattern, a simple but representative domain, enabling careful control of search conditions.

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This thesis investigates the polynomial collocation method for the numerical solution of Cauchy type integral equations and the use of those equations and the related numerical techniques to solve two practical problem in Acoustics and Aerodynamics. Chapters I and II include the basic background material required for the development of the main body of the thesis. Chapter I discusses a number of practical problems which can be modelled as a singular integral equations. In Chapter II the theory of those equations is given in great detail. In Chapter III the polynomial collocation method for singular integral equations with constant coefficients is presented. A particular set of collocation points, namely the zeros of the first kind Chebyshev polynomials, is shown to give uniform convergence of the numerical approximation for the cases of the index K = 0. 1. The convergence rate for this method is also given. All these results were obtained under slightly stronger assumptions than the minimum required for the existence of an exact solution. Chapter IV contains a generalization of the results in Chapter III to the case of variable coefficients. In Chapter V an example of a practical problem which results in a singular integral equation and which is successfully solved by the collocation method is described in substantial detail. This problem consists of the interaction of a sound wave with an elastic plate freely suspended in a fluid. It can be modelled by a system of two coupled boundary value problems - the Helmholtz equation and the beam equation. The collocation method is then compared with asymptotic results and a quadrature method due to Miller. In Chapter VI an efficient numerical method is developed for solving problems with discontinuous right-hand sides. Numerical comparison with other methods and possible extensions are also discussed.