Thesis PlanB (M.S.)--University of Wisconsin--Stout, 2007. / Includes bibliographical references.

This thesis is a study of the affect of differences in the density of a fluid on the mixing regions of jets, which may be laminar or turbulent. These differences in density are present for three main reasons, namely; when the speed of the fluid is of the same order of magnitude as the local speed of sound; when there are large temperature differences in the fluid; and when the fluid consists of a mixture of components the relative proportions of which vary from point to point. Three problems are considered. These are: the flow far from the orifice of a plane and of a round jet and the mixing region on the surface of the core of a plane jet near the orifice. This last problem is idealised as the mixing of two semi-infinite streams. For flows of jet type, the assumption of a coefficient of eddy kinematic viscosity in turbulent flow leads to the possibility of combining in one the equations for laminar and turbulent motion. The method used is to expand the stream function in a Rayleigh-Jansen series. The first term of this series corresponds to the stream function when the fluid is of constant density. The series is developed in powers of a small parameter whose magnitude depends on the density differences in the fluid. Only the second term of this series is found explicitly. This term gives the first order effect that changes in density have on the flow. The solutions of all examples considered are, with on exception, given in analytical form. The last appendix to the the thesis shows the connection between Stewartson's (1957) approach to the problem of finding uniformly valid approximate solutions to the boundary layer equations and Lighthill's (1948) method. This connection is shown by working out one of the problems considered by Stewartson, namely, the wake past a flat plate, using Lighthill's method.

In this dissertation we study the routing problem for multi-commodity survivable network ows, with splittable demands, and propose end-to-end path-based solutions where maximum link utilization is minimized, in order to improve resilience in existing telecommunication networks. We develop mixed integer programming models, and demonstrate that, when the selection of disjoint paths is part of the optimization problem (rather than when k-shortest paths are pre-selected, as in earlier works), maximum link utilization is reduced and the overall network also balances out. We find that three paths are usually enough to reap the benefits of a multipath approach. A reduction in maximum link utilization also provides a margin by which demand values can grow without causing congestion. We also prove that the disjoint multipath selection problem is NPcomplete, even for the case of one node-pair. This warrants a recourse to effi- cient solution methods within ILP (such as decomposition), and to matheuristics. Our literature survey of applications of heuristic techniques, and those combining heuristics with exact methods, shows a research gap, which we attempt to bridge through a novel heuristic algorithm. The heuristic works well and, in several cases, yields better solutions than ILP (in a given time limit), or provides solutions for problems where ILP could not even find one valid solution in the given time limit. We also study this problem within a decomposition methods framework: i.e., column generation. The pricing sub-problem is a mixed non-linear programme, for which we propose an ILP formulation. We find some lower bounds for missing dual values and use them as surrogates. We then show that the lower bounds are valid and present examples where the proposed pricing is applied to path generation for self-protecting multipath routing.

<p> The Program for International Assessment tested students in mathematics from 41 countries and found that students in the United States ranked in the lowest percentile. This struggle with math among youth in the United States prompted this quasi-experimental quantitative study about using interactive technology to engage and motivate 9^th grade students in an Algebra classroom. The theoretical basis of this study was a constructivist perspective, using the Piagetian concept of action as an intellect builder. A convenience sample of 76 students was divided into 4 groups: Group 1, the control group, used no technology and consisted of 21 students; Group 2 used the TI Nspires calculators and consisted of 17 students; Group 3 used the TI Nspire calculators with the TI Navigator and consisted of 20 students; and Group 4 used the TI Nspire calculators, the TI Navigator, and the clickers. The participants were given 45 instructional classes that covered a 9-week period. All groups took the Motivated Strategy for Learning Questionnaire (MSLQ) and the State of Texas Assessment of Academic Readiness test (STAAR) before and after the treatment of interactive technologies. A paired <i>t</i> test and a factorial repeated ANOVA were conducted, revealing no significant effect for the MSLQ based on the use of technology. However, the use of technology with the STAAR did show a significant difference in test scores for 2 treatment groups: Group 3, which used the calculator and the TI navigator; and Group 4, which used the calculator, the TI navigator, and the clickers. These results support the use of additional technology that is needed in the mathematics classroom to support the use of the calculators. </p>

The examination timetabling (exam-timeslot-room assignment) problem involves assigning exams to a specific or limited number of timeslots and rooms, with the aim of satisfying the hard constraints and the soft constraints as much as possible. Most of the techniques reported in the literature have been applied to solve simplified examination benchmark datasets, available within the scientific literature. In this research we bridge the gap between research and practice by investigating a problem taken from the Universiti Malaysia Pahang (UMP), a real world capacitated examination timetabling problem. This dataset has several novel constraints, in addition to those commonly used in the literature. Additionally, the invigilator scheduling problem (invigilator assignment) was also investigated as it has not received the same level of research attention as the examination scheduling (although it is just as important to educational institutions). The formal models are defined, and constructive heuristics was developed for both problems in which the overall problems are solved with a two-phase approach which involves scheduling the exam to timeslot and room, and follows with scheduling the invigilator. During the invigilator assignment, we assume that there is already an examination timetable in place (i.e. previously generated). It reveals that the invigilator scheduling solution dependent on the number of rooms selected from the exam-timeslot-room assignment phase (i.e. a lesser number of used rooms would minimises the invigilation duties for staff), this encourages us to further improve the exam-timeslot-room timetable solution. An improvement on the result was carried out using modified extended great deluge algorithm (modified-GDA) and multi-neighbourhood GDA approach (that use more than one neighbourhood during the search). The modified-GDA uses a simple to understand parameter and allows the boundary that acts as the acceptance level, to dynamically change during the search. The propose approaches able to produce good quality solution when compared to the solutions from the proprietary software used by UMP. In addition, our solutions adhere to all hard constraints which the current systems fail to do. Finally, we extend our research onto investigating the Second International Timetabling Competition (ITC2007) dataset as it also contains numerous constraints much similar to UMP datasets. Our propose approach able to produce competitive solutions when compared to the solutions produced by other reported works in the literature.

This thesis is concerned with automated personnel scheduling in healthcare organisations; in particular, nurse rostering. Over the past forty years the nurse rostering problem has received a large amount of research. This can be mostly attributed to its practical applications and the scientific challenges of solving such a complex problem. The benefits of automating the rostering process include reducing the planner’s workload and associated costs and being able to create higher quality and more flexible schedules. This has become more important recently in order to retain nurses and attract more people into the profession. Better quality rosters also reduce fatigue and stress due to overwork and poor scheduling and help to maximise the use of leisure time by satisfying more requests. A more contented workforce will lead to higher productivity, increased quality of patient service and a better level of healthcare. Basically stated, the nurse rostering problem requires the assignment of shifts to personnel to ensure that sufficient employees are present to perform the duties required. There are usually a number of constraints such as working regulations and legal requirements and a number of objectives such as maximising the nurses working preferences. When formulated mathematically this problem can be shown to belong to a class of problems which are considered intractable. The work presented in this thesis expands upon the research that has already been conducted to try and provide higher quality solutions to these challenging problems in shorter computation times. The thesis is broadly structured into three sections. 1) An investigation into a nurse rostering problem provided by an industrial collaborator. 2) A framework to aid research in nurse rostering. 3) The development of a number of advanced algorithms for solving highly complex, real world problems.

The thesis considers the one-dimensional cutting stock problem, the bin-packing problem, and their relationship. The duality gap of the former is investigated and a characterisation of a class of cutting stock problems with the next round-up property is given. It is shown that worst-case bounds for bin-packing heuristics can be and are best expressed in terms of the linear programming relaxation of the corresponding cutting stock problem. The concept of recurrency is introduced for a bin-packing heuristic, which allows a more natural derivation of a measure for the worst-case behaviour. The ideas are tested on some well known bin-packing heuristics and (slightly) tighter bounds for these are derived. These new bounds (in terms of the linear programming relaxation) are then used to make inferences about the duality gap of the cutting stock problem. In particular; these bounds allow à priori, problem-specific bounds. The thesis ends with conclusions and a number of suggestions to extend the analysis to higher dimensional problems.

<p> With the advent of smart phone technologies, the healthcare industry finds it challenging to keep up with technology demands. In the medical domain, patients are experiencing longer wait times for medical treatment. A basis of dissatisfaction with healthcare, often observed by patients, is the amount of time they wait during a visit. The wait times have a greater delay within medical emergency facilities. Current medical wait time applications may encourage patients to be seen quickly but does not necessarily offer quality care or other aspects of their visits. The amount of time a patient experiences in an emergency facility could influence the patient's perspective and could be contingent upon other qualities. We sought to investigate the association between patient perception of the hospital, time to reach the hospital, patient wait time, patient reviews, and average service time of various North Carolina hospitals using product moment correlation analysis. Analyses were performed of the various hospitals based upon each parameter. In this thesis, we propose a smart phone based service to optimize travel time to a medical facility utilizing patient wait time, service time, time to reach the hospital, patient reviews, and patient perception of the facility and Global Positioning System (GPS) data. Various hospitals were compared ranking in according to the parameters individually, relative to other hospitals in neighboring counties and cities. Each constraint is assigned a weight to be used in the overall ranking of the hospital. We have established relationships about correlation parameters. The parameters were assessed to determine correlations between any two given parameters.</p>

<p> The United States has a serious problem in Science, Technology, Engineering, and Mathematics. The STEM disciplines are suffering from a `Quiet Crisis'[1]. The problem is that African Americans, Latino/a, Native American, and other ethnic minority students are choosing careers in the STEM disciplines at lower percentages than their white and Asian counterparts [2]. We refer to this disparity as underrepresentation. This work focuses on the use of the Culturally Situated Design Tools (CSDTs, <b>http://csdt.rpi.edu</b>) as a means to counter this underrepresentation. The programmable set of CSDTs represents the development of this software from being focused on ethnomathematics, to ethnocomputing. Ethnocomputing is the reproduction of cultural artifacts in simulation. The CSDTs are part of the constructionist genre of programmable software that seeks to teach computer science concepts to students as they construct these cultural artifacts. Development work on the programmable CSDT software has provided the opportunity to examine the challenges that occur in cross cultural software development using the Agile method. This work includes ethnographic user and developer stories that have informed the development of the pCSDT software. Among the challenges of developing this software has been negotiating the controversy of what we have come to term "The Content Agnostic Position". This is the notion that all software with objects in simulation, regardless of what those objects are, possesses equal value in teaching students. This position, however, often results in the commercial or violent colonization of user spaces by corporate produced media objects and simulated gun violence. It is our view that this colonization can be diminished through the use of cultural objects in simulation, such as those found in the CSDTs. Our work is intended to create a decolonized space for mathematics and computing education. This work also reports the findings of a quasi-experiment conducted with junior high school students in Kumasi, Ghana, West Africa during the summer of 2014.</p>

<p> Today's economy is driven by information technology (IT). Education and business should come to an agreement that functional technology skills should be integrated with core academic courses to create an educational system that truly prepares workers for the 21st Century. The business realm theoretical foundation for this study laid on the match/mismatch established between technology&mdash;math education and business' readiness&mdash;[math] skills. The level of education and skills of workers needed by business and industry has increased. Nonetheless, scholars underlined the belief that the skills workers possess are generally not sufficient for the demands of the more sophisticated jobs in today's economy. With this study this researcher pretended to fill the gap in the literature by examining the hypothesis that poor education results in low skills is hampering U.S. businesses and the disparity between what employers need and what workers offer is getting serious enough. Within this investigation the researcher tested for first time three theories: the AST/TML theory, the TAM theory, and the Constructivist theory, whereas having behind scenes K-12's mathematics arena. This study found that "there is no statistically significant relationship between the degree to which teachers accept new technologies and technology usage in mathematics instruction" and that "teachers' individual affective reactions to technology toward integrating computers and technology into math instruction are not related to readiness skills." However, a Post Hoc analysis demonstrated that at least for one of the individual predictors, problem solving construct scores, the null hypothesis was rejected. It means in a long path to academic success, small waves of effectiveness in education are penetrating the sandy beaches of skills. Additionally, this researcher confirmed some scholars' assertion about Confirmatory Factor Analysis, which described that sample sizes smaller than 100 as dangerous and recommended using sample sizes larger than 200 for safe conclusions. Finally, the researcher tested and validated the Technology-Mediated Learning (TML) theory while adding his research positive conclusion(s) to the body of knowledge.</p>