This work uses computational fluid dynamics to study the flowfield around a hypersonic missile with two lateral jets to provide control in place of control surfaces. The jets exhaust an H2-O2 mixture at Mach number of 2.9 with a jet pressure ratio of roughly 10,500. The jets are staggered axially and circumferentially in such a way to produce pitch and yaw. The flowfield of such a jet configuration is characterized at several angles of attack and the corresponding force coefficients and amplification factors are provided. The freestream air and H2-O2 plume is treated as inert for the majority of the calculations. Special cases are treated with finite rate chemical kinetics and compared to the inert flowfield to ascertain the effects that chemical reactions have on the force coefficients. It was found that the flowfield was only slightly altered from the familiar one jet flowfield when the second jet is active. The flow topology and vortex structures tend to shift towards the second jet but the overall structure remains the same. The normal force amplification factors are close to unity over the range of angle of attack due to the thrust being so high with the two jet configuration having a lower amplification factor compared to firing a single jet. Treating the flowfield as chemically reacting did not affect the force values much: the difference being 0.3% for an angle of attack of 0°. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2017. / FAU Electronic Theses and Dissertations Collection

Light, medium and heavy crude oils were studied at three concentrations and with two different sediments in experimental microcosm settings to determine the ability of Spartina alterniflora and associated microbes to breakdown total extractable hydrocarbons (TEH) in the water. It was a baseline experiment designed to quantify the rates of biodegradation under relatively quiescent conditions from different crude oils at moderate doses ranging from 0-150 mg/kg soil. Upon the completion of the experiment there were several key findings: (1) The lethal dosage for Spartina alterniflora was not reached within the 90 day experiment at these dosages, and all plants survived; (2) More than 97% of the total extractable hydrocarbons (TEH) were shown to be degraded by plants and rhizosphere microorganisms within the 90- day experiment; (3) The dose of oil introduced as a slick (simulated spill) on day zero did not significantly affect the results for TEH degradation within the range of dosages from 50-150 mg/g -- these dosages could be degraded by the marsh cord grass system; (4) A sediment type which was acclimated to oil for several months and one which was non-acclimated did not show significantly different results for TEH degradation in the microcosms -- both sediment systems resulted in TEH degradation over the 90-day experiment; and (5) A mathematical model was developed which simulated experiment results quite closely including TEH diffusion from the crude oil slick into the water and subsequent biodegradation.

This paper deals with the applications of symbolic computation of Mathematica 7.0 (Wolfram, 2008) in distribution theory. The purpose of this study is twofold. Firstly, we will implement some functions to extend Mathematica capabilities to handle symbolic computations of the characteristic function for linear combination of independent univariate random variables. These functions utilizes pattern-matching codes that enhance Mathematica's ability to simplify expressions involving the product and summation of algebraic terms. Secondly, characteristic function can be classified into commonly used distributions, including six discrete distributions and seven continuous distributions, via the pattern-matching feature of Mathematica. Finally, several examples will be presented. The examples include calculating limit of characteristic function of linear combinations of independent random variables, and applications of coded functions and illustrate the central limit theorem, the law of large numbers and properties of some distributions.

Mathematica is an extremely powerful and flexible symbolic computer algebra system that enables the user to deal with complicated algebraic tasks. It can also easily handle the numerical and graphical sides. One such task is the derivation of moment generating functions (MGF) and characteristic functions (CF), demonstrably effective tools to characterize a distribution. In this paper, we define some rules in Mathematica to help in computing the MGF and CF for linear combination of independent random variables. These commands utilizes pattern-matching code that enhances Mathematica's ability to simplify expressions involving the product of algebraic terms. This enhancement to Mathematica's functionality can be of particular benefit for MGF and CF. Applications of these rules to determine mean, variance and distribution are illustrated for various independent random variables.

This paper is an analysis of creative opportunities of graphical user interface software of computer mathematics systems. There were two computer mathematics systems chosen: Matlab 7, Maple 10 and Mathematica 5.2 for this work. In order to compare the creative opportunities of graphical user interface software in computer mathematics systems and universal programming languages, C++ Builder 6 system was chosen. In line, there were four application programs groups created in mathematics systems and in C++ Builder system. The process of creating these programs, the peculiarities of the codes and the final result were compared. To sum up, computer mathematics systems may be used for creating application programs. Classical programming tasks may be implemented in these programs. Moreover, computer mathematics systems used for creating software cannot be changed by any other program that needs classical programming constructions, analytic computations and creating of graphical user interface.

We report a class of the mathematics in which an animation technology (calculating and plotting capabilities) of the software Mathematica is utilized. This class is taught for university students in a computer laboratory during a second semester. It is our purpose to make a student realize the usefulness and the importance of mathematics easily through visualization. In addition, we hope that students will acquire a new power of mathematics needed in the 21st century. For several years, we have continued this kind of class, and have continued to investigate the effectiveness that our teaching method (especially visualization) brings in the understanding of the mathematics. In this paper, we present some of this teaching method, which is performed in our class. From the questionnaire survey, it is found that our teaching method not only convinces students that the mathematics is useful or important but also deepens the mathematic understanding of students more.

We report a class of the mathematics in which an animation technology (calculating and plotting capabilities) of the software Mathematica is utilized. This class is taught for university students in a computer laboratory during a second semester. It is our purpose to make a student realize the usefulness and the importance of mathematics easily through visualization. In addition, we hope that students will acquire a new power of mathematics needed in the 21st century. For several years, we have continued this kind of class, and have continued to investigate the effectiveness that our teaching method (especially visualization) brings in the understanding of the mathematics. In this paper, we present some of this teaching method, which is performed in our class. From the questionnaire survey, it is found that our teaching method not only convinces students that the mathematics is useful or important but also deepens the mathematic understanding of students more.

A level set of a function is defined as the region, where the function gets over the specified level. A level set of the probability density function can be considered an alternative to the traditional confidence region because on certain conditions the level set covers the region with minimal volume over all regions with a given confidence level. The benefits of using level sets arise in situations where, for example, the given random variables are multimodal or the given random vectors have strongly correlated components. This thesis describes estimates of the level set by means of a so called plug-in method, which first estimates density from the data set and then specifies the level set from the estimated density. In addition, explicit direct methods are also studied, such as algorithms based on support vectors or dyadic decision trees. Special attention is paid to the nonparametric probability density estimates, which form an essential tool for plug-in estimates. Namely, the second chapter describes histograms, averaged shifted histograms, kernel density estimates and its generalization. A new technique transforming kernel supports is proposed to avoid the so called boundary effect in multidimensional data domains. Ultimately, all methods are implemented in Mathematica and compared on financial data sets.

Analisando o maior exame de acesso ao ensino superior de nosso país, o ENEM, percebe-se que as dimensões do quantitativo de inscritos e importância para os programas educacionais e de acesso as instituições de ensino superior, são surpreendentemente notáveis, tornando-se na segunda maior avaliação do mundo. Desta análise percebemos uma relação das provas de Matemática com a Modelagem Matemática, principalmente na Matriz de Referência do ENEM, permitindo assim um comparativo com as etapas da então denominada Modelação Matemática, ou seja, a Modelagem Matemática usada como metodologia de ensino da Matemática. As etapas da Modelação Matemática são identificadas nas questões de Matemática do ENEM através de inúmeros exemplos de questões resolvidas de edições anteriores. A Modelação Matemática é apresentada como método de ensino e aprendizagem para a resolução das questões de Matemática do ENEM. / Analyzing the greatest exam of access to higher education in our country, ENEM, it was noticed that its dimension, concerning the number of enrollment and importance to educational programs and to the access to higher education institutions, is surprisingly remarkable, making it the second-highest evaluation in the world. From this analysis, we perceive a relation between Mathematics esams and the Mathematical Modeling, mainly on ENEM’s the former reference, thus allowing a comparison of the steps of the so-called Mathematical Molding, that is, the Mathematical Modeling used as a methodology of the teaching of Mathematics. The stages of Mathematical Molding are identified on ENEM’s Mathematics questions through numerous examples of solved questions from previous editions. The Mathematical Molding is presented as a teaching-learning method, which is not necessarily the same as a method or technique for solving ENEM Mathematics questions.

This study presents a theoretical basis for and outlines the method of finding the Lie point symmetries of systems of partial differential equations. It seeks to determine which of five computer algebra packages is best at finding these symmetries. The chosen packages are LIEPDE and DIMSYM for REDUCE, LIE and BIGLIE for MUMATH, DESOLV for MAPLE, and MATHLIE for MATHEMATICA. This work concludes that while all of the computer packages are useful, DESOLV appears to be the most successful system at determining the complete set of Lie symmetries. Also, the study describes REDUCEVAR, a new package for MAPLE, that reduces the number of independent variables in systems of partial differential equations, using particular Lie point symmetries. It outlines the results of some testing carried out on this package. It concludes that REDUCEVAR is a very useful tool in performing the reduction of independent variables according to Lie's theory and is highly accurate in identifying cases where the symmetries are not suitable for finding S/G equations.