The purpose of this study is to examine variances in the case of distributions obtained by truncating a given distribution at various points. In particular, the truncated distributions are restricted to nested increasing intervals, and the question is posed whether the variances of these distributions are monotonically increasing. The answer to this question is relevant to the use of conditional information for purposes of estimation and prediction. Several tables are presented in the thesis which provide evidence of the property of monotonic variance for nested increasing intervals of truncation in the case of univariate distributions., The Monte Carlo procedure is used to determine a table of standard deviations for the standard normal distribution with the same points of truncation reported by Clark(2). Clark's table is given intact, and it is used in comparison with the new table reported here as a check on the Monte Carlo procedure used in the present study. Distributions other than the standard normal distribution are examined as well, namely, a Pearson U-shaped distribution and a bimodal distribution consisting of a mixture or two Pearson distributions. Graphs of the U-shaped and bimodal distributions are given. A section is given in which dispersion for a bivariate case is examined in terms of the bivariate normal distribution. An interesting trend among the covariance matrices is observed in the data reported in that section. A separate computer program for each type of distribution was written and used to calculate the variances of the truncated distributions. FORTRAN programs and flow charts are presented in the Appendix. Explanation of the tables and procedures used to calculate the entries in the body of each table are given in each section as well as some discussion of the results presented. / Master of Science

In recent years the use of inflatable dams has become more widespread throughout the world. Various people have done studies on the shape and membrane tension of these structures; however, only a few authors have considered dynamic behavior. Due to the nature of the applications and the material composition of these structures, a study considering the dynamic response of an inflatable dam is warranted. In this study, the equation of motion for an air-inflated dam is derived, then solved using the Galerkin approximation method. The solution is performed for a one-term approximation and a two-term approximation, where both solutions use a sine function to approximate the deflected shape of the dam. Frequencies and amplitudes are calculated and presented in tables and plots for the first four modes, and three different values of the central angle of the dam. Comparisons to the results of other studies are presented at the conclusion of this study. / Master of Science

The time optimal slewing problem for flexible spacecraft is considered. We study single-axis rotational maneuvers for a simple flexible system, consisting of a rigid hub with an elastic appendage. The equations of motions are derived by Hamilton’s Principle, and a discrete nonlinear model is obtained by the assumed modes method. The problem is first solved in a discrete linearized space by parameter optimization. Optimality is verified by Pontryagin’s Maximum Principle. The linear solutions are then used to obtain time optimal solutions for the non-linear problem by a multiple-shooting algorithm. Although this approach is applicable to arbitrary boundary conditions, this work is confined, almost exclusively, to rest-to-rest maneuvers. These maneuvers are shown to possess some interesting symmetric and asymptotic properties. The problem is further analyzed in infinite-dimensional space, and the convergence of the finite-dimensional approximations is studied. Finally, a soft version of the time optimal slewing problem is considered, where the control is bounded only by a penalty term in the cost functional. A perturbation technique is applied to further simplify this problem. / Ph. D.

The computer algebra system MACSYMA is used to derive the nonlinear expression for the Lagrangian and the nonlinear equations of motion of composite plates undergoing large deformations by using a higher-order shear-deformation theory. When computer algebra is not used, the derivation of these equations is very involved and time consuming. A time-averaged-Lagrangian technique is developed for the nonlinear analysis of the response of a wide variety of physical systems. It is a perturbation method that produces accurate second-order approximate solutions in the neighborhoods of different resonances. As an application of the technique, the nonlinear response of a fluid-relief valve is discussed in detail. The different resonances are studied, and in each case the responses are compared to those obtained by using the Galerkin procedure. The shortcomings of the latter procedure are pointed out. The time-averaged-Lagrangian technique is implemented in a MACSYMA code that produces second-order perturbation solutions. The effects of the quadratic nonlinearities are incorporated into the solution and different cases of resonances are fully investigated. First-order differential equations are derived for the evolution of the amplitudes and phases for the following resonances: primary resonance, subharmonic resonance of order one-half, and superharmonic resonance of order two. The evolution equations are used to determine the fixed point or constant solutions and the results are then used to obtain representative frequency-response and force-response curves for each case. The stability of the fixed points is investigated. The results show that stable and unstable solutions may coexist when multi-valued solutions are possible, the initial conditions determine which describes the response. The multi-valuedness of the solutions lead to the jump phenomenon. The results show that subharmonic resonances of order one-half cannot be activated unless the excitation amplitude exceeds a threshold value. Lastly, a numerical-perturbation approach is used to study modal interactions in the response of the surface of a liquid in a cylindrical container to a principal parametric resonant excitation in the presence of a two-to-one internal (autoparametric) resonance. The force-response curves exhibit saturation, jumps, and Hopf bifurcations. They also show that the response does not start until a certain threshold level of excitation is exceeded. The frequency-response curves exhibit jumps, pitchfork bifurcations, and Hopf bifurcations. For certain parameters and excitation frequencies between the Hopf bifurcation values, limit-cycle solutions of the modulation equations are found. As the excitation frequency changes, the limit-cycles deform and lose their stability through either pitchfork or cyclic-fold (saddie-node) bifurcations. Some of these saddle-node bifurcations cause a transition to chaos. The pitchfork bifurcations break the symmetry of the limit cycles. Period-three motions are observed over a narrow range of excitation frequencies. / Ph. D.

Yes / Blind-testing is an important tool that should be used by all analytical fields as an approach for validating method. Several fields do this well outside of archaeological science. It is unfortunate that many applied methods do not have a strong underpinning built on, what should be considered necessary, blind-testing. Historically lithic microwear analysis has been subjected to such testing, the results of which stirred considerable debate. However, putting this aside, it is argued here that the tests have not been adequately exploited. Too much attention has been focused on basic results and the implications of those rather than using the tests as a powerful tool to improve the method. Here the tests are revisited and reviewed in a new light. This approach is used to highlight specific areas of methodological weakness that can be targeted by developmental research. It illustrates the value in having a large dataset of consistently designed blind-tests in method evaluation and suggests that fields such as lithic microwear analysis would greatly benefit from such testing. Opportunity is also taken to discuss recent developments in quantitative methods within lithic functional studies and how such techniques might integrate with current practices.

In this paper we will present two different approaches to the development of product measures. In the second chapter we follow the lead of H. L. Royden in his book Real Analysis and develop product measure in the context of outer measure. The approach in the third and fourth chapters will be the one taken by N. Dunford and J. Schwartz in their book Linear Operators Part I. Specifically, in the fourth chapter, product measures arise almost entirely as a consequence of integration theory. Both developments culminate with proofs of well known theorems due to Fubini and Tonelli.

The purpose of the study was to compare traditional functional analysis procedures (isolated contingencies) to functional analysis procedures which are modified to include nuanced environmental variables (synthesized contingencies) for children in an outpatient setting in order to determine sensitivity to the isolated or synthesized contingencies. A multi-element design embedded into a multi-treatment design was used to evaluate differentiated rates of challenging behavior across the two analyses for three children exhibiting challenging behaviors. The results supported the utility of the traditional functional analysis (FA) procedures when compared to that of the interview informed synthesized contingency analysis (IISCA) for one of three participants.

A critical first step in addressing problem behavior is to identify the function of the problem, or reason for engaging in the problem behavior, using systematic assessment procedures known as a functional analysis (FA). The literature consistently demonstrates the effectiveness of FAs, and variations of FAs (e.g., trial-based functional analysis [TBFA]) for assessing a variety of topographies of problem behaviors across populations, age groups, and settings; however, the use of TBFAs for assessing the function of inappropriate mealtime behavior (IMB) has been documented in the literature only once. The purpose of the current study was to contribute to the research examining the efficacy of using TBFAs to identify functions of IMB. Results from the current study are mixed. TBFAs lead to the identification of functions of IMB for 1 out of 3 participants. When comparing TBFA results to traditional FA results, partial correspondence was observed for one participant, and no correspondence was observed for the other two participants. Future research should continue to evaluate the efficacy of TBFAs for IMB as well as evaluate the validity of TBFAs for IMB when results yield evidence of functional relationships.

An analysis of interrater agreement across multiple respondents on anecdotal assessments and correspondence between functional analysis outcomes was completed. Experiment I evaluated overall agreement among multiple respondents (direct-care staff) on the hypothesized function of each residents (28 adults with mental retardation) problematic behavior using the Motivational Assessment Scale (MAS) and the Functional Analysis Screening Tool (FAST). Results of the questionnaires indicated that respondents agreed on the function of the problematic behavior for 10 of the 28 residents. Experiment II examined whether, for selected cases in which 4 out of 5 respondents agreed on the function of the problematic behavior, correspondence occurred between functional analyses and anecdotal assessments outcomes. Two of the 6 functional analyses did not evoke the problematic behavior. However, 4 functional analyses did produce corresponding outcomes suggesting that, when the functional analyses produced interpretable data, the results of the functional analyses corresponded with those of the anecdotal assessments.

Atmospheric monitoring is a vital part of environmental management. Monitoring temporal changes in atmospheric pollution on a local, regional and global scale is important in order to mitigate adverse effects on health and the environment. Currently there is general agreement that atmospheric pollution should be monitored, however, less emphasis is often placed on what should be achieved and the specific monitoring that should be included. Atmospheric pollution monitoring is often hampered by geographically restricted and site specific effects resulting in inefficient or ineffective information transfer to the local manager. The scientific community in the developed world often underestimate problems associated with the maintenance of comprehensive atmospheric measurement stations in Africa. A holistic approach is needed to optimise atmospheric monitoring according to specifications set out by system design; this includes site selection, site design, maintenance and quality control. The aim of this dissertation is to apply the Systems Engineering approach to a case study, the Welgegund atmospheric measurement station (WAMS), to offer a holistic view of interaction between different operational systems and the complexity behind their management in order to be informative to students and personnel from a non-engineering background. A knowledge gap exists that links practical industry related sciences such as engineering to more fundamental and theoretical sciences. In this dissertation the customer need was determined and an operational concept was developed for the WAMS system. The high level goals of the WAMS were derived and stated as applicable to other new as well as established measurement stations. Technical and fundamental requirements such as trained staff for appropriate logistical support and a broad spatial coverage of air quality monitoring were identified. The system boundaries and operational constraints were established for the WAMS, exposing weaknesses and proposing solutions to ensure long term sustainability. Weaknesses include irregular funding periods and retention of expertise (trained students leave academia for industry) whereas a possible solution included overlapping projects and contracts. Functional analysis highlighted the design and establishment process of the WAMS. Physical architectures and interfaces were explored and finally the success of the establishment of the WAMS was evaluated by a reliability block diagram. The reliability of the WAMS system was calculated to be 96.6 %. This agrees well with the percentage data coverage calculated for the gaseous (95.9 %), aerosol (93.4 %) and meteorological (94.6 %) systems (15 min averages). The reliability of the national grid to supply power to the WAMS was found to be the main restrictive component. It may be a challenge interacting and coordinating projects with different disciplines, branches or sectors outside of a speciality project. This study has bridged the gap between industry related sciences such as engineering to more fundamental and theoretical sciences. A framework has been provided that highlights the techniques of Systems Engineering and provides an understanding for the need and process of atmospheric monitoring. / MIng (Development and Management Engineering), North-West University, Potchefstroom Campus, 2015