Dissertations / Theses: 'Analytical Mathematics'

1

Leung, Kung-shing. "The impact of teaching of analytical skills on the mathematics achievement of Form three students." Hong Kong : University of Hong Kong, 1986. http://sunzi.lib.hku.hk/hkuto/record.jsp?B1803553X.

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2

Poolasap, Naowarat. "Analytical Pyrolysis of Thai Lignites." TopSCHOLAR®, 1985. https://digitalcommons.wku.edu/theses/2729.

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Samples of four different Thai lignites were utilized to study the effects of ceiling temperature and heating rate on the overall yield and product distribution by the technique of analytical pyrolysis (pyrolysis-gas chromatography). Ceiling temperatures of 450°, 550°, 650°, 750°, 850°, and 950°C, a heating rate of 500°C/sec and pyrolysis intervals of 20 seconds were investigated. The results were reported in terms of percentage high-volatile product and low-volatile product fraction, weight-loss (% by weight), and total yield (counts per milligram). One sample which showed the highest sensitivity to changing ceiling temperature was selected to study the effect of heating rate on overall yield and product distribution. Heating rates of 500°C/sec and 100°C/sec (for an interval of 20 seconds) and 500°C/sec for one minute and 300°C/min for two minutes were employed in the study, at a ceiling temperature of 750°C. The results of the above investigation may be summarized as follows: All four samples are lignite A (rank) but give different pyrograms as a result of differences in maceral concentrations and chemical structure of each of the coals. The total yield, high-volatile product, and weight-loss increase with increasing ceiling temperatures. Heating rates in the range studied have no significant effect on the total yield and product distribution. High -volatile product yield increases with increasing pyrolysis interval because of secondary cracking reactions but the overall product yield remains essentially constant.

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3

Wessels, Gert Jermia Cornelus. "A numerical and analytical investigation into non-Hermitian Hamiltonians." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/2894.

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Thesis (MSc (Physical and Mathematical Analysis))--University of Stellenbosch, 2009.
In this thesis we aim to show that the Schr odinger equation, which is a boundary eigenvalue problem, can have a discrete and real energy spectrum (eigenvalues) even when the Hamiltonian is non-Hermitian. After a brief introduction into non-Hermiticity, we will focus on solving the Schr odinger equation with a special class of non-Hermitian Hamiltonians, namely PT - symmetric Hamiltonians. PT -symmetric Hamiltonians have been discussed by various authors [1, 2, 3, 4, 5] with some of them focusing speci cally on obtaining the real and discrete energy spectrum. Various methods for solving this problematic Schr odinger equation will be considered. After starting with perturbation theory, we will move on to numerical methods. Three di erent categories of methods will be discussed. First there is the shooting method based on a Runge-Kutta solver. Next, we investigate various implementations of the spectral method. Finally, we will look at the Riccati-Pad e method, which is a numerical implemented analytical method. PT -symmetric potentials need to be solved along a contour in the complex plane. We will propose modi cations to the numerical methods to handle this. After solving the widely documented PT -symmetric Hamiltonian H = p2 􀀀(ix)N with these methods, we give a discussion and comparison of the obtained results. Finally, we solve another PT -symmetric potential, illustrating the use of paths in the complex plane to obtain a real and discrete spectrum and their in uence on the results.

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4

Moorhead, Katherine Tracey. "Design and Implementation of Analytical Mathematics for SIFT-MS Medical Applications." Thesis, University of Canterbury. Mechanical Engineering, 2009. http://hdl.handle.net/10092/2898.

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Selected Ion Flow Tube-Mass spectrometry (SIFT-MS) is an analytical measurement technology for the real-time quantification of volatile organic compounds in gaseous samples. This technology has current and potential applications in a wide variety of industries, although the focus of this research is in medical science. In this field, SIFT-MS has potential as a diagnostic device, capable of determining the presence of a particular disease or condition. In addition, SIFT-MS can be used to monitor the progression of a disease state, or predict deviations from expected behaviour. Lastly, SIFT-MS can be used for the identification of biomarkers of a particular disease state. All these possibilities are available non-invasively and in real-time, by analysing breath samples. SIFT-MS produces an extensive amount of data, requiring specific mathematical methods to identify biomarker masses that differ significantly between populations or time-points. Two classification methods are presented for the analysis of SIFT-MS mass scan data. The first method is a cross-sectional classification model, intended to differentiate between the diseased and non-diseased state. This model was validated in a simple test case. The second method is a longitudinal classification model, intended to identify key biomarkers that change over time, or in response to treatment. Both of these classification models were validated in 2 clinical trials, investigating renal function in humans and rats. The first clinical trial monitored changes in breath ammonia, TMA and acetone concentrations over the course of dialysis treatment. Correlations with the current gold standard plasma creatinine, and blood urea nitrogen were reported. Finally, biomarkers of renal function were identified that change predictably over the course of treatment. The second trial induced acute renal failure in rats, and monitored the change in renal function observed during recovery. For comparison and validation of the result, a 2-compartment model was developed for estimating renal function via a bolus injection of a radio-labelled inulin tracer, and was compared with the current gold standard plasma creatinine measurement, modified using the Cockcroft-Gault equation for rats. These two methods were compared with SIFT-MS monitoring of breath analytes, to examine the potential for non-invasive biomarkers of kidney function. Results show good promise for the non-invasive, real-time monitoring of breath analytes for diagnosis and monitoring of kidney function, and, potentially, other disease states.

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5

Rozenblum, G. "On some analytical index formulas related to operator-valued symbols." Universität Potsdam, 2000. http://opus.kobv.de/ubp/volltexte/2008/2581/.

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For several classes of pseudodifferential operators with operator-valued symbol analytic index formulas are found. The common feature is that uasual index formulas are not valid for these operators. Applications are given to pseudodifferential operators on singular manifolds.

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6

Matthews, John V. III. "An Analytical and Numerical Study of Granular Flows in Hoppers." NCSU, 2000. http://www.lib.ncsu.edu/theses/available/etd-20001106-164836.

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This work investigates the characteristics of a steady state flow of granular material,under the influence of gravity, in two and three dimensional hoppers of simple geometry.Simulations of such flows are of particular interest to various industries, such as the foodand mining industries, where the handling of large quantities of granular materials in hop-persand silos is routine. While understanding and simulation of time-dependent phenomenaare the ultimate goals in this field, those phenomena are still poorly understood and thustheir study is beyond the scope of this research. It has been observed that steady flowscan provide reasonable approximations, and the corresponding steady state model has con-sequentlybeen the focus of a great deal of research. Historically, these steady state modelshave been approached using only smooth radial fields, and even today most practical hop-perdesign uses these fields as their basis. Our work represents the first time that qualitynumerical methods have been brought to bear on the model equations in their original form,without assuming smoothness of the resulting fields. Two different, yet related, models forstress/velocity consisting of systems of hyperbolic conservation laws and algebraic relationsare considered and discussed. The radial stress and velocity fields, and the stability of thosefields, are studied briefly with both analytical and numerical results presented. More im-portantly,a Runge-Kutta Discontinuous Galerkin method is implemented and applied tovarious boundary value problems involving perturbed stress and velocity fields arising fromdiscontinuous changes in parameters such as hopper wall angle or hopper wall friction.

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7

Hagspihl, Christoph. "A comparison of three analytical approximations for basket option valuation." Master's thesis, University of Cape Town, 2013. http://hdl.handle.net/11427/18690.

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Three prominent analytical approximations for pricing basket options,by Levy (1992), Ju (2002) and Deelstra et aI. (2004), are tested for performance and accuracy. Sensitivity analysis shows that all three have greater errors in high volatility and long maturity environments, while Deelstra has weaknesses with small correlation and baskets with few stocks. Deelstra and Levy show tendencies to underprice and overprice respectively, while Ju's errors are more consistently around the true price. A mathematical understanding of the three techniques is also developed.

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8

Erker, Joseph A. "Boundary value problems in electrophoresis, with applications to separations and colloid science." Diss., The University of Arizona, 2003. http://hdl.handle.net/10150/280277.

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The topic of this thesis is investigation of models applied to different aspects of separations and colloid science. Many tools are used for solving the models, which are manifested as boundary value problems. The problems are to determine the equilibrium electrostatics of a fluid droplet, the electrokinetics of such, the (nonuniform) temperature profile of an electrophoresis capillary due to Joule heating, and the temperature at the wall of the capillary. In the fluid drop model, special attention given to a drop that, in addition to the surrounding fluid, supports electrolytes. Matched asymptotic expansions based on thin double layers are applied to the equilibrium electrostatics problem. Attention is given to how conditions on the interface of the drop, such as discontinuity of equilibrium potential and the presence of surface excesses of solutes, affect the electrokinetics. A perturbation scheme is used to formulate a problem for the electrophoretic mobility of a droplet. An approximate solution for the mobility of a drop is derived, based on small interfacial potentials. The formula encompasses those of several past theoretical studies. A regular perturbation is used to determine heating effects in capillary electrophoresis, based on a small power input to the system. The resulting expression for temperature in the capillary is then used implicitly to determine the temperature at the wall of the capillary. Some of the results are compared with experimental data. For the drop electrophoresis problem, the electrophoretic mobility formula is compared with measured mobility of oil drops and drops in aqueous two-phase systems. In the study of heating in capillary electrophoresis, the implicit expression is used to make reasonable estimates of the wall temperature based on published operating conditions. Accuracy of all analytic estimates of the problems are tested against numerical solutions, taken to be exact. In all cases, the analytic approximations are satisfactorily accurate under appropriate conditions.

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9

Nel, W. J. F. "Analytical approximations of surface fields induced on convex scatters by exteriorly incident scalar fields." Doctoral thesis, University of Cape Town, 1989. http://hdl.handle.net/11427/22216.

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The boundary value problems for the Helmholtz equation give rise to boundary integral equations for the unknown surface field or its normal derivative. These integral equations involve the Helmholtz surface potentials in the form of weakly singular surface integrals. This thesis is based on a method of parameterisation of the surface integrals which removes the weak singularities provided that the surface satisfies certain convexity conditions. Firstly this method of parameterisation is applied to investigate the properties of the Helmholtz surface potentials on convex surface elements, and some new proofs are given. The theory is then applied to the boundary integral equations which arise when a scalar field is incident on a bounded scatterer. The surface integrals in these integral equations are Helmholtz potentials and can be regularised by suitable parameterisation. It is assumed that the unknoWn density function is an analytical function on the boundary of the scatterer, and can therefore be expanded as a Taylor series at any point of the surface. If this expansion is substituted into the regularised integral equation and if the operations of integration and summation are formally interchanged, then the end result is a partial differential equation of infinite order involving only the field coordinates and having analytical coefficients. However, if the Taylor expansions are truncated then partial differential equations of finite orders result. The view is taken that analytical solutions of such differential equations of finite orders can serve as _approximations for the surface field or its normal derivative provided that suitable initial conditions are imposed to ensure uniqueness. On the other hand the general solution of such a differential equation can serve as a local approximation at any point on the surface. Some basic properties of the differential equations and their solutions, called analytical approximations, are discussed and the theory is then applied to the problem of acoustic scattering from a sound hard sphere.

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10

Petrack, S. B. "Analytical and algebraic equivariant cohomology and the free loop space." Thesis, University of Oxford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.370268.

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11

Schober, Constance Marie. "Numerical and analytical studies of the discrete nonlinear Schroedinger equation." Diss., The University of Arizona, 1991. http://hdl.handle.net/10150/185595.

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Certain conservative discretizations of the Nonlinear Schroedinger (NLS) Equation can produce irregular behavior. We consider the diagonal discretization as a conservative perturbation of the integrable discretization and study the homoclinic crossings in its nonlinear spectrum. We find that irregularity sets in for the two unstable mode regime and, in this case, many and continual homoclinic crossings occur throughout the irregular time series. We undertake an analysis to determine the mechanism that causes the "chaotic" behavior to appear in this conservatively perturbed NLS equation. This analysis involves the construction of explicit formulas for the homoclinic orbit, a description of the relevant finite dimensional phase space and a Melnikov analysis for the various regimes studied.

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12

Mehmet, Mohammed. "The Korteweg-de Vries equation and its homologues III analytical structure." Thesis, City University London, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.276627.

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13

Leung, Kung-shing, and 梁拱城. "The impact of teaching of analytical skills on the mathematics achievement of Form three students." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1986. http://hub.hku.hk/bib/B31955575.

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14

Muniswamy, Sowmya. "Analytical and Numerical Approach to Caputo Fractional Differential Equations via Generalized Iterative Schemes with Applications." Thesis, University of Louisiana at Lafayette, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3622948.

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Natural lower and upper solutions for initial value problems guarantees the interval of existence. However, coupled lower and upper solutions used as initial approximation in generalized iterative method are very useful since the iterates can be computed without any extra assumption. Generalized monotone method, along with the method of lower and upper solutions, has been used to develop the coupled lower and upper solutions on an extended interval for both scalar and system of Caputo fractional differential equations. This method yields linear convergence. Generalized quasilinearization method, along with the method of lower and upper solutions, was used to compute the coupled minimal and maximal solutions, if coupled lower and upper solutions existed for the scalar Caputo fractional differential equations. This method yielded quadratic convergence. Also, a mixed method of monotone method and quasilinearization method was developed to compute the coupled minimal and maximal solutions, if coupled lower and upper solutions existed, for the scalar Caputo fractional differential equations. This mixed method was used to compute the coupled lower and upper solutions on the desired interval, which yielded superlinear convergence. Numerical examples have been provided as an application of the analytical results.

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15

Shepherd, David. "Optimisation of iterative multi-user receivers using analytical tools /." View thesis entry in Australian Digital Theses Program, 2008. http://thesis.anu.edu.au/public/adt-ANU20081114.221408/index.html.

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16

Torain, David S. II. "An analytical approach to the bio-economic dynamics of a fishery which includes simultaneous harvesting of other species." DigitalCommons@Robert W. Woodruff Library, Atlanta University Center, 2006. http://digitalcommons.auctr.edu/dissertations/1663.

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This bio-economic model reduces essentially to a set of parametric coupled nonlinear differential equations. The major difficulty stems from the fact that sixteen external parameters appear in various places in the equations. As of today, only numerical methods have been developed to investigate this problem. The practical impossibility to handle such large parametric space obscures the understanding ofthe main features of the solutions of the equations. A new approach that is analytical and not numerical is proposed. This approach is based on the remark that when one of the sixteen parameters is sent to infmity, the general solution, involving the remaining fifteen parameters can be expressed in terms of elementary functions. This is made possible because, in this limit, besides the time invariance group, an exact invariance scaling group exists. Then the traditional perturbation method of relatively bounded operators can be applied to the exactly solvable previous equations. Furthermore, it seems that the value of the perturbation parameter corresponding to real world fisheries is itself very large. We, therefore, expect excellent results to be achieved with only a first order perturbation. In order to obtain a global view of the harvesting problem modeled by these types of equations, we have made a dimensional analysis of the sixteen parameters appearing in the equations. We have been able, in all generality, to reduce them to three fundamental dimensionless parameters that carry all the features of the system. This allows making a full analytical study of the fixed points or stationary points of the system. Besides the standard fIXed point, two "catastrophic" new fIXed points have been studied. These are called "catastrophic" because they lead to an exhaustion of the biomass. A global study of the relevance of each stationary fixed point over the range of the dimensionless parameters is presented.

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17

Ramli, Nabilah Binti. "Analytical modelling of sound transmission in a lined duct." Thesis, University of Southampton, 2013. https://eprints.soton.ac.uk/361186/.

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The focus of this thesis is on the prediction of sound attenuation through a lined duct, based on a mathematical model. Ducts with a single section as well as multi-segmented sections are discussed. The duct of interest has a rectangular cross-section as normally used for ventilation purposes. The mean flow in a ventilation duct is very low and can be neglected. In this thesis, two-dimensional analytical models are developed for sound transmission in a series of different duct configurations. Two models of the lining behaviour are considered, either locally-reacting or bulk-reacting. The models are used first to obtain the transverse and axial wavenumbers of various modes of the duct. The required finite numbers of wavenumbers are tracked using Müller’s method. The wavenumbers are traced from a very low frequency to high frequency using small frequency steps. It is found that, for a duct with a bulk-reacting lining, the number of modes with a transverse wavenumber below a particular value may exceed the corresponding number of modes in a duct with a locally-reacting lining. These additional modes are termed lining modes. The number of lining modes depends on the lining thickness. Dispersion curves are presented for both types of lining. The transmission of sound through the duct is then calculated using the mode-matching technique. The mode-matching model allows analysis of multi-modal wave propagation in the duct. The model is first developed for an infinitely long rigid duct with a finite length of lined insert. The estimation from the locally reacting model, that is widely available in the literature, is compared with the estimation from the newly developed bulk-reacting model. Although the locally reacting model often overestimates the performance of a bulk-reacting lining it is found that this is not always the case, especially for a small lining thickness and at lower frequencies where the locally reacting model may under-estimate the performance. The analytical model is then extended to a multi-segmented lining where the lined section is uniformly segmented with rigid walled sections in a periodic manner. For a bulk-reacting lining, the segmented arrangement renders the lining more similar to the behaviour of a duct with a locally-reacting lining and improves the peak attenuation. Little improvement is found in the case of a multi-segmented locally-reacting lining. The effect of duct height, lining thickness and lining flow resistivity on sound attenuation is studied using the analytical model. Experiments are presented which validate the analytical model.

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18

Ryve, Andreas. "Approaching Mathematical Discourse : Two analytical frameworks and their relation to problem solving interactions." Doctoral thesis, Västerås : Department of Mathematics and Physics, Mälardalen University, 2006. http://www.diva-portal.org/mdh/theses/abstract.xsql?dbid=137.

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19

Dallin, Joshua Jeffrey. "Analytical Comparison of Bovine Parentage Single Nucleotide Polymorphisms." DigitalCommons@USU, 2015. https://digitalcommons.usu.edu/etd/4450.

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Often on cattle operations and dairy farms, where multiple bulls are exposed to cows either by live cover or artificial insemination, error can be present in parentage record keeping for breed registries or production use. Research has evolved to the integration of using single nucleotide polymorphisms (SNPs) to answer questions where cases of unknown parentage may exist. With the evolution of the research, differentiated panels have been created specifically for parentage analysis. Our objective was to complete an analytical comparison between two specific panels, a proven 88 parentage SNP panel and a recently developed 25 SNP panel. A smaller panel would be beneficial in a parentage test as the smaller panel would reduce time and costs associated with the parentage analysis. In this study, nearly 4,000 cattle samples were collected and prepared from offspring, sires, and dams. Parentage calling software was used to identify the parentage assignments of the samples. Through these procedures and comparisons, it was determined that the smaller 25 SNP panel did not have the magnitude or strength necessary to be able to correctly identify cattle in the same manner as the 88 SNP panel.

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20

Shok, Aiad Mohamed. "An analytical study of selected aspects of the secondary school mathematics teacher education programme in Libya." Thesis, Cardiff University, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.296654.

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21

Pavaputanon, Lha. "Design and implementation of hypermedia learning environments that facilitate the construction of knowledge about analytical geometry." Thesis, Queensland University of Technology, 2007. https://eprints.qut.edu.au/16453/1/Lha_Pavaputanon_Thesis.pdf.

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This study aimed to develop a teaching and learning model, based on principles derived from the fields of constructivist theory, schema theory, critical literacy theory, and design theory, to inform the development of hypermedia-mediated learning environments that facilitate the construction of mathematical knowledge by secondary school students in Thailand. In this study, the participants were a group of three secondary school students from the Demonstration school attached to the Faculty of Education at Khon Kaen University (Thailand). In order to ascertain how mathematical learning could be facilitated by the process of designing a web page that could be used to introduce other students to analytic geometry, all three participants were asked to work collaboratively to design an analytic geometry web page. The process of designing the web page was informed by a theoretical model derived from an analysis and synthesis from the research literature on constructivist theory, schema theory, critical literacy theory, and design theory. Findings from the study indicated that the creation of a web page facilitated and enhanced the Thai students' learning about analytic geometry. The major outcomes from the study are a revised theoretical framework to inform the integration of the design of mathematical web pages into Thai mathematics classrooms and a conceptual map framework to assess qualitative and quantitative changes to students' repertoires of knowledge about analytic geometry that emerge during the process of designing a webpage.

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22

Pavaputanon, Lha. "Design and implementation of hypermedia learning environments that facilitate the construction of knowledge about analytical geometry." Queensland University of Technology, 2007. http://eprints.qut.edu.au/16453/.

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This study aimed to develop a teaching and learning model, based on principles derived from the fields of constructivist theory, schema theory, critical literacy theory, and design theory, to inform the development of hypermedia-mediated learning environments that facilitate the construction of mathematical knowledge by secondary school students in Thailand. In this study, the participants were a group of three secondary school students from the Demonstration school attached to the Faculty of Education at Khon Kaen University (Thailand). In order to ascertain how mathematical learning could be facilitated by the process of designing a web page that could be used to introduce other students to analytic geometry, all three participants were asked to work collaboratively to design an analytic geometry web page. The process of designing the web page was informed by a theoretical model derived from an analysis and synthesis from the research literature on constructivist theory, schema theory, critical literacy theory, and design theory. Findings from the study indicated that the creation of a web page facilitated and enhanced the Thai students' learning about analytic geometry. The major outcomes from the study are a revised theoretical framework to inform the integration of the design of mathematical web pages into Thai mathematics classrooms and a conceptual map framework to assess qualitative and quantitative changes to students' repertoires of knowledge about analytic geometry that emerge during the process of designing a webpage.

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23

Too, Gee-Pinn James. "Analytical and numerical approaches for finite amplitude sound beams radiated from a circular baffled piston." Diss., Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/16917.

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24

Evans, James Alexander. "Some analytical techniques for partial differential equations on periodic structures and their applications to the study of metamaterials." Thesis, Cardiff University, 2016. http://orca.cf.ac.uk/94875/.

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The work presented in this thesis is a study of homogenisation problems in electromagnetics and elasticity with potential applications to the development of metamaterials. In Chapter 1, I study the leading order frequency approximations of the quasi-static Maxwell equations on the torus. A higher-order asymptotic regime is used to derive a higher-order homogenised equation for the solution of an elliptic second-order partial differential equation. The equivalent variational approach to this problem is studied which leads to an equivalent higher-order homogenised equation. Finally, the derivation of higher-order constitutive laws relating the fields to their inductions is presented. In Chapter 2, I study the governing equations of linearised elasticity where the periodic composite material of interest is made up of a "critically" scaled "stiff" rod framework with the voids in between filled in with a "soft" material which is in high-contrast with the stiff material. Using results from two-scale convergence theory, a well posed homogenised model is presented with features reminiscent of both high-contrast and thin structure homogenised models with the additional feature of a linking relation of Wentzell type. The spectrum of the limiting operator is investigated and the establishment of the convergence of spectra from the initial problem is derived. In the final chapter, I investigate brie y three additional homogenisation problems. In the first problem, I study a periodic dielectric composite and show that there exists a critical scaling between the material parameter of the soft inclusion and the period of the composite. In the second problem, I use of two-scale convergence theory to derive a homogenised model for Maxwell's equations on thin rod structures and in the final problem I study Maxwell's equations in R^3 under a chiral transformation of the coordinates and derive a homogenised model in this special geometry.

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25

Bertel, Jeffrey D. "Analytical study of the spectral-analysis-of-surface-waves method at complex geotechnical sites." Diss., Columbia, Mo. : University of Missouri-Columbia, 2006. http://hdl.handle.net/10355/4625.

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Thesis (M.S.) University of Missouri-Columbia, 2006.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on August 21, 2007) Includes bibliographical references.

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Ezertas, Ahmet Alper. "Sensitivity Analysis Using Finite Difference And Analytical Jacobians." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12611067/index.pdf.

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The Flux Jacobian matrices, the elements of which are the derivatives of the flux vectors with respect to the flow variables, are needed to be evaluated in implicit flow solutions and in analytical sensitivity analyzing methods. The main motivation behind this thesis study is to explore the accuracy of the numerically evaluated flux Jacobian matrices and the effects of the errors in those matrices on the convergence of the flow solver, on the accuracy of the sensitivities and on the performance of the design optimization cycle. To perform these objectives a flow solver, which uses exact Newton&rsquo
s method with direct sparse matrix solution technique, is developed for the Euler flow equations. Flux Jacobian is evaluated both numerically and analytically for different upwind flux discretization schemes with second order MUSCL face interpolation. Numerical flux Jacobian matrices that are derived with wide range of finite difference perturbation magnitudes were compared with analytically derived ones and the optimum perturbation magnitude, which minimizes the error in the numerical evaluation, is searched. The factors that impede the accuracy are analyzed and a simple formulation for optimum perturbation magnitude is derived. The sensitivity derivatives are evaluated by direct-differentiation method with discrete approach. The reuse of the LU factors of the flux Jacobian that are evaluated in the flow solution enabled efficient sensitivity analysis. The sensitivities calculated by the analytical Jacobian are compared with the ones that are calculated by numerically evaluated Jacobian matrices. Both internal and external flow problems with varying flow speeds, varying grid types and sizes are solved with different discretization schemes. In these problems, when the optimum perturbation magnitude is used for numerical Jacobian evaluation, the errors in Jacobian matrix and the sensitivities are minimized. Finally, the effect of the accuracy of the sensitivities on the design optimization cycle is analyzed for an inverse airfoil design performed with least squares minimization.

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27

Nyqvist, Robert. "Algebraic Dynamical Systems, Analytical Results and Numerical Simulations." Doctoral thesis, Växjö : Växjö University Press, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1142.

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28

Gali, Prasad. "Identification of Optimal Conditions for Dry Drilling (Analytical Approach to Prediction of the Occurrence of BUE)." DigitalCommons@USU, 2003. https://digitalcommons.usu.edu/etd/7147.

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Lubrication is used during the drilling of aluminum to counter the formation of a built-up-edge (BUE), among other reasons. The elimination of the use of lubricants in drilling of aluminum is important because of the associated high costs of cleaning and disassembly involved in lubrication. The optimal conditions sought in this work include the elimination of the use of lubricants along with the possible attainment of a high material removal rate, which could help in reduction of cost and increase productivity at the same time. BUE has been found to be almost always present in the process of metal cutting at low to moderate speeds. It has been found that a necessary condition for the formation of a BUE is the presence of a negative stress gradient away and normal to the tool rake face. The quantitative equivalence of the effects of temperature and strain rate on flow stress described by the Zener-Hollomon parameter (Z) [5]. The relationship between the Zener-Hollomon parameter (Z) and chip flow stress implies that a negative Z gradient could be considered equivalent to a negative stress gradient. A series of computer simulations with varied cutting conditions were analyzed to determine the combination of machining variables which yielded a low predicted BUE preferably with a high material removal rate. The results presented here include cases which have a low predicted BUE as well as a high material removal rate.

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Zavareh, Alireza. "Analytical and Numerical methods for a Mean curvature flow equation with applications to financial Mathematics and image processing." Thesis, Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-2132.

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This thesis provides an analytical and two numerical methods for solving a parabolic equation of two-dimensional mean curvature flow with some applications. In analytical method, this equation is solved by Lie group analysis method, and in numerical method, two algorithms are implemented in MATLAB for solving this equation. A geometric algorithm and a step-wise algorithm; both are based on a deterministic game theoretic representation for parabolic partial differential equations, originally proposed in the genial work of Kohn-Serfaty [1].
+46-767165881

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30

Fatemi-Badi, Seyed Mohammad. "Predicting the Self-Heating Potential of Coal." TopSCHOLAR®, 1985. https://digitalcommons.wku.edu/theses/2320.

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Self-heating in coal has been studied for well over one hundred years, yet there is no accurate or reliable method for predicting the potential of certain coals to undergo self-heating. Fires caused by self-heating, and eventually spontaneous combustion, have occurred in the high wall of surface mines, in underground mines, in coal stockpiles, and on trains, barges and ships. Self-heating in coal is brought about through a complex interplay of conditions depending on the specific properties of the coal as well as many external factors involved in the mining and handling of coal. In a study supported by the United States Department of Transportation and monitored by the United States Coast Guard, data on over 2000 barges of coal was incorporated into a data bank. Results from the evaluation of these data and from a barging study, in which a research crew accompanied a tow of barges from western Kentucky to the New Orleans area, were used to make recommendations to minimize self-heating in barged coal. An inexpensive adiabatic calorimeter (accelerating rate calorimeter) was constructed and used to obtain supporting laboratory data on coal samples collected in the barging study. There is very good agreement between the results obtained with the calorimeter concerning the reactivity of coals and susceptibility of the coals to undergo selfheating as would be predicted using chemical and physical data from the data bank.

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Mikaelyan, Anna. "Analitical study of the Schönbucher-Wilmott model of the feedback effect in illiquid markets." Thesis, Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-3587.

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This master project is dedicated to the analysis of one of the nancialmarket models in an illiquid market. This is a nonlinear model. Using analytical methods we studied the symmetry properties of theequation which described the given model. We called this equation aSchonbucher-Wilmott equation or the main equation. We have foundinnitesimal generators of the Lie algebra, containing the informationabout the symmetry group admitted by the main equation. We foundthat there could be dierent types of the unknown function g, whichwas located in the main equation, in particular four types which admitsricher symmetry group. According to the type of the function gthe equation was split up into four PDEs with the dierent Lie algebrasin each case. Using the generators we studied the structure ofthe Lie algebras and found optimal systems of subalgebras. Then weused the optimal systems for dierent reductions of the PDE equationsto some ODEs. Obtained ODEs were easier to solve than the correspondingPDE. Thereafter we proceeded to the solution of the desiredSchonbucher-Wilmott equation. In the project we were guided by thepapers of Bank, Baum [1] and Schonbucher, Wilmott [2]. In these twopapers authors introduced distinct approaches of the analysis of thenonlinear model - stochastic and dierential ones. Both approaches leadunder some additional assumptions to the same nonlinear equation - the main equation.

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32

Olande, Oduor. "Students' narratives from graphical artefacts : Exploring the use of mathematics tools and forms of expression in students' graphicacy." Doctoral thesis, Mittuniversitetet, Avdelningen för ämnesdidaktik och matematik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-19710.

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Holman, Benjamin Robert. "Analytical Study and Numerical Solution of the Inverse Source Problem Arising in Thermoacoustic Tomography." Diss., The University of Arizona, 2016. http://hdl.handle.net/10150/612954.

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In recent years, revolutionary "hybrid" or "multi-physics" methods of medical imaging have emerged. By combining two or three different types of waves these methods overcome limitations of classical tomography techniques and deliver otherwise unavailable, potentially life-saving diagnostic information. Thermoacoustic (and photoacoustic) tomography is the most developed multi-physics imaging modality. Thermo- and photo-acoustic tomography require reconstructing initial acoustic pressure in a body from time series of pressure measured on a surface surrounding the body. For the classical case of free space wave propagation, various reconstruction techniques are well known. However, some novel measurement schemes place the object of interest between reflecting walls that form a de facto resonant cavity. In this case, known methods cannot be used. In chapter 2 we present a fast iterative reconstruction algorithm for measurements made at the walls of a rectangular reverberant cavity with a constant speed of sound. We prove the convergence of the iterations under a certain sufficient condition, and demonstrate the effectiveness and efficiency of the algorithm in numerical simulations. In chapter 3 we consider the more general problem of an arbitrarily shaped resonant cavity with a non constant speed of sound and present the gradual time reversal method for computing solutions to the inverse source problem. It consists in solving back in time on the interval [0, T] the initial/boundary value problem for the wave equation, with the Dirichlet boundary data multiplied by a smooth cutoff function. If T is sufficiently large one obtains a good approximation to the initial pressure; in the limit of large T such an approximation converges (under certain conditions) to the exact solution.

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Hamdan, Suzana. "Studies of the Preparations and Use of Sol-Gel for Enzyme Immobilization and Analytical Applications." Digital Commons @ East Tennessee State University, 2009. https://dc.etsu.edu/etd/1802.

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Much attention has been paid to immobilization of enzymes to improve enzyme stability and permit its reuse. Glucose oxidase entrapment in different kinds of silica sol-gel matrices was investigated. The enzyme showed stable activity for 11 uses in the sol-gel with tetramethyl orthosilicate (TMOS) as precursor, and at least 7 uses in the sol-gel induced electrochemically with tetraethyl orthosilicate (TEOS) as precursor. The sol-gel made with TEOS as precursor and HCl as catalyst showed stability in enzyme activity for 11 uses but the activity decreases on the same sol-gel when modified with silica nanoparticles. Factors such as optimal incubation time of glucose solution, the reproducibility between different sol-gels, and the storage time were investigated. Good linearity and analytical results on real samples were obtained. The detection method was based on a colorimetric method for determining the concentration of hydrogen peroxide produced from the oxidation reaction of glucose.

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Rodrigues, José Maria 1956. "Geometria analítica com enfoque vetorial no ensino médio." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306436.

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Orientador: Roberto Andreani
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
Made available in DSpace on 2018-08-27T14:31:28Z (GMT). No. of bitstreams: 1 Rodrigues_JoseMaria_M.pdf: 2051932 bytes, checksum: 1425a4f7da552244084e91e7f7dad4bb (MD5) Previous issue date: 2015
Resumo: A Geometria Analítica é ministrada de diferentes modos nas escolas do Brasil, resultado de inúmeras reformas nos programas estaduais de ensino. Em alguns lugares a apresentação da Geometria Analítica se faz com tratamento vetorial, o que não ocorre em outras localidades. Nessas localidades, os vetores ficaram restritos ao universo da Física. Nossa proposta, apesar de não ter o mérito da inovação, se alinha ao desejo de inúmeros profissionais da matemática, considera a possibilidade de repatriar os vetores para o domínio da matemática no Ensino Médio
Abstract: The Analytical Geometry is taught in differents ways in Brazilian Schools, as a result of numerous reforms of state educational programs. In some places the presentation of the Analytical Geometry is done by a vectorial treatment, whereas in other this does not occur. In these places, the vectors are restricted to the universe of Physics. Our proposal, despite having no innovation merit, is aligned to the whishes of numerous professionals of mathematics, considering the possibility to repatriate the vectors to the mathematics domain in High School
Mestrado
Matemática em Rede Nacional
Mestre

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36

Novaes, André Luís 1981. "Geometria analítica e vetores : uma proposta para melhoria do ensino da geometria espacial." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306435.

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Orientador: Roberto Andreani
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
Made available in DSpace on 2018-08-27T16:15:41Z (GMT). No. of bitstreams: 1 Novaes_AndreLuis_M.pdf: 1374002 bytes, checksum: df1be15bc4f4e102fedb945375b21959 (MD5) Previous issue date: 2015
Resumo: Esta dissertação tem por objetivo introduzir as definições e os conceitos básicos sobre vetores no R2 e no R3 no ensino básico, junto com as propriedades e operações e através deste conhecimento mostrar, com vários exemplos e aplicações, como isto simplifica e facilita o entendimento das atividades propostas nesta parte da educação matemática. Além disso estudar de forma conjunta a álgebra e a geometria, partindo de um lugar geométrico e então encontrando sua equação ou partindo de uma equação e então encontrando o lugar geométrico, esses que são os dois aspectos recíprocos do princípio fundamental da geometria analítica estudada em grande escala por Descartes e Fermat, dois dos grandes matemáticos que deram uma grande e significativa contribuição à matemática
Abstract: The objective of this thesis is to introduce the definitions and basic concepts about vectors on R² and R³ in basic education with proprieties, operations and beyond this knowledge explain with many examples and applications how this thesis simplifies the understanding of this activity which was proposed in this part of mathematics teaching and further to study jointly algebra and geometric starting from a geometric point and to finding your equation and then finding your geometric place. This two aspects are reciprocal from the fundamental principle of analytic geometry studied on a large scale by Descartes and Fermat, two of the biggest mathematicians
Mestrado
Matemática em Rede Nacional
Mestre

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37

Bengtsson, Martin. "Analytical Expressions for the Hawking Mass in slowly rotating Kerr and Kerr-Newman Space-times." Thesis, Linköping University, Department of Mathematics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-9246.

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Penrose's inequality which relates the total mass of a space-time containing a black hole with the area of the event horizon, is a yet unproven condition that is required for the cosmic censorship hypothesis. It is believed that the inequality could be proved by using properties of the Hawking mass. This thesis gives analytical expressions for the Hawking mass in slowly rotating Kerr and Kerr-Newman space-times. It is also shown that the expressions are monotonically increasing, a result that does not contradict Penrose's inequality.

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38

Mossberg, Eva. "Some numerical and analytical methods for equations of wave propagation and kinetic theory." Doctoral thesis, Karlstad : Fakulty of Technology and Science, Mathematics, Karlstads universitet, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-1848.

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39

Pfeiffer, Philip Edward. "A System for Determining the Statistical Significance of the Frequency of Short DNA Motif Matches in a Genome - An Analytical Approach." University of Dayton / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=dayton1304599225.

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40

Winters, Neva S. "Determination of Select Metal Ions in Commercially Available Conventional and Organic Baby Foods." Digital Commons @ East Tennessee State University, 2011. https://dc.etsu.edu/etd/1354.

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The goal of this study is to determine whether or not there is an appreciable difference between concentrations of various metal ions present in conventionally grown and processed and organically grown and processed baby foods. Two prominent, commercially available brands were chosen to undergo comparative studies between both their own conventional and organic varieties of second stage green beans and carrots. Samples were tested for cadmium, calcium, iron, lead, nickel, and zinc. Two containers of each variety of baby food were sampled in triplicate, with purchases of foods being made in separate areas to ensure that each set came from different batches. Samples were digested with nitric acid, appropriately diluted, and analyzed for metal content by flame atomic absorption spectroscopy with the regular standard calibration curve and standard addition method. There was little overall difference in metal content between the conventional and organic foods tested.

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41

Konda, Sai Sriharsha Manoj. "Computational Investigation of Spin Traps Using Hybrid Solvation Models." Digital Commons @ East Tennessee State University, 2009. https://dc.etsu.edu/etd/1801.

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The cyclic nitrone 5,5-dimethyl-1-pyrroline-N-oxide (DMPO), and the lesser known linear phenyl-N-tert-butylnitrone (PBN) and its phosphorylated analogues have been used as spin traps for the investigation of free radicals in biological systems. Theoretical work on these molecules suggests that there are important differences in their properties between biological systems and isolated molecules in the gas phase, most likely resulting from intra and intermolecular hydrogen bonding. Most dielectric solvation models such as the polarized continuum model and COSMO are incapable of direct determination of solvent-spin trap chemical interactions. To examine this, hybrid models incorporating COSMO for long range effects and discrete solvent molecules for short range effects, at the DFT/B3LYP/6-31G* level of theory, have been used to study the stabilization and alteration of the spin trap molecules properties in protic and aprotic polar solvents. The hybrid models have been successfully implemented to support the prominent role played by hydrogen bonding interactions in the stabilization of spin traps.

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42

Covert, Kyle John. "Roaming Transition States and Highly Accurate Thermochemistry: A PEPICO Study of Two Small Combustion Systems." Scholarly Commons, 2019. https://scholarlycommons.pacific.edu/uop_etds/3624.

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Two small combustion systems, methyl hydroperoxide (CH3OOH) and 2-propanol ((CH3)2CHOH), were studied using imaging photoelectron photoion coincidence spectroscopy (iPEPICO), which combines photoelectron spectroscopy and photoionization mass spectrometry to detect coincident photoelectron-photoion pairs. In the photon energy range of 11.4–14.0 eV, energy selected CH3OOH+ ions dissociate into CH2OOH+, HCO+, CH3+, and H3O+ ions. The lowest-energy dissociation channel is the formation of the cation of the smallest “QOOH” radical, CH2OOH+. A statistical rate model fitted to the experimental data yields a 0 K appearance energy of 11.647 ± 0.005 eV for the CH2OOH+ ion, and a 74.2 ± 2.6 kJ mol–1 mixed experimental-theoretical 0 K heat of formation for the CH2OOH radical. The proton affinity of the Criegee intermediate, CH2OO, was also obtained from the heat of formation of CH2OOH+ (792.8 ± 0.9 kJ mol–1) to be 847.7 ± 1.1 kJ mol–1, reducing the uncertainty of the previously available computational value by a factor of 4. RRKM modeling of the higher-energy fragmentation processes, supported by Born–Oppenheimer molecular dynamics simulations, found that the HCO+ fragment ion is produced through a roaming transition state; H3O+ is formed in a consecutive process from the CH2OOH+ fragment ion; and direct C–O fission of the molecular ion leads to the methyl cation. Experimentally, 2-propanol has been found to dissociate primarily into CH2CHOH+, CH3CHOH+, CH3CHCH3+, and, as a minor product, into (CH3)2COH+ ions within a photon energy range of 10.0–13.1eV. There are interesting dissociation dynamics involving breaking the C–¬C bond: the lowest energy product (CH3 loss) is quickly outcompeted by a kinetically favored CH4 loss. At low internal energies of < 0.3 eV, the loss of CH4 dominates through a roaming pathway, when the leaving CH3 abstracts a hydrogen atom from the other methyl group. At higher energy, the direct loss of CH3• quickly takes over as its transition state is much less tight and, thus, it is kinetically favored. The statistical model fitted to the experimental data yielded the appearance energy corresponding to the thermochemical limit for the CH3-loss dissociation and the 0 K heats of formation of the CH3CHOH+ ion was found to be in good agreement with ATcT values and with our previous study on ethanol.

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43

Ghann, William Emmanuel. "Studies of Surfactants Effect on Riboflavin Fluorescence and Its Determination in Commercial Food Products and Vitamin Tablets." Digital Commons @ East Tennessee State University, 2008. https://dc.etsu.edu/etd/2000.

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A simple and economical fluorometer using blue LEDs excitation sources and simple PMT detection had been built, assembled, optimized, and employed for measurement of fluorescence from riboflavin (vitamin B2). Surfactants have been known to enhance the intensity of fluorescence of fluorescent compounds. Fluorescence analysis of riboflavin in the presence of various anionic, cationic, and nonionic surfactants was also conducted to determine if they could improve analysis. However, the surfactants employed did not seem to have any meaningful enhancement; in fact, some actually diminished the fluorescence intensity of riboflavin. The procedure was linear for riboflavin from 0.01 to 2.5 μg/mL. Reproducibility expressed as relative standard deviation was about 2%. The recoveries obtained range from 91.3% to 100.21% for the samples determined. The proposed method was successfully applied to the analysis of riboflavin in commercial vitamin tablets and cereal products. The results obtained were consistent with expected values as provided by the manufacturers. The method is simple, sensitive, economical, and rapid.

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Muchena, John Kailemia. "Studies of Capsaicinoids Contents of Locally Grown and Commercial Chilies Using Reversed-Phase High Performance Liquid Chromatography." Digital Commons @ East Tennessee State University, 2009. https://dc.etsu.edu/etd/1800.

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Capsaicinoids are a class of compounds responsible for the "heat" of hot peppers. Capsaicin and dihydrocapsaicin have the highest burning effect. The aim of this work is to separate and quantify the two major capsaicinoids in fruits harvested at different stages of development and at different seasons. Simple and rapid HPLC method involves 73:27% methanol water mobile phase with C18 stationary phase and UV-Vis detector set at 210 nm. The method showed good reproducibility with 1.74% - 4.72% relative standard deviations, a linear response within 0.65–45.5 and 0.25-17.5 μg/mL for capsaicin and dihydrocapsaicin, respectively. The method achieved average recovery of 106% for capsaicin and 102% dihydrocapsaicin. Determination of capsaicinoids in four naturally grown chili and commercial source habanero were analyzed. The amount in the sample ranged from 1184-8156 μg/g for capsaicin and 430-3299 μg/g for dihydrocapsaicin.

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45

Liu, Fuyou. "Determination of Hydroquinone in Cosmetic Creams by High Performance Liquid Chromatography." Digital Commons @ East Tennessee State University, 2007. https://dc.etsu.edu/etd/2114.

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Hydroquinone is a most commonly used whitening agent in cosmetics. A high performance liquid chromatography method was developed and validated for the quantitative determination of hydroquinone in creams. Validation parameters such as linearity, precision, accuracy, and limit of detection and limit of quantitation were determined. HPLC was carried by reverses phase technique on a RP-C18 column with a mobile phase of water and methanol (pH 5.0) 70:30. The linearity in the range of 2.0-40.0 μg/mL presents a correlation coefficient of 0.9998. The LOD and LOQ were 0.16 and 0.53 μg/mL, respectively. The precision of the method was found to be satisfactory with a coefficient of variation below 2.2%. The recovery values were in the range of 92.4 to 99.0%. The method is sensitive, fast, and simple. It has been successfully applied to the determination of hydroquinone in cosmetic creams. The results obtained agreed well with the percentages given by the manufacturers.

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46

Yu, Zhonghua Walter. "Characterization of irreversible inhibition of proteases by mass spectroscopy." Scholarly Commons, 1995. https://scholarlycommons.pacific.edu/uop_etds/2805.

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Proteases are present in all living organisms and are involved in various biological processes. Inhibition of protease activities in disease-causing agents is one strategy for rational drug design. Characterization of the protease inhibition processes is essential for understanding the inhibition mechanisms and for developing efficient therapeutics. This work represents a major challenge in analytical biochemistry. In this study, a strategy based on mass spectrometry has been developed to characterize irreversible inhibition of proteases. Five proteases representing three of the four protease classes were irreversibly inhibited by various irreversible inhibitors, some of which are potential drug candidates. In all the cases, the stoichiometry of each of the protease/inhibitor complexes was determined by electrospray ionization mass spectrometry through measurement of the complex's molecular weight. The inhibited proteases were then enzymatically cleaved and the resulting peptides isolated for further characterization by high performance tandem mass spectrometry. Attention was focused on the determination of the site(s) of the modification and the reaction mechanisms involved. High energy collision induced dissociation mass spectra of each modified peptide provided information on the exact modification site(s) and the detailed chemical nature of the covalent complex. The serine protease trypsin, the cysteine protease cruzain, and the aspartic proteases, HIV-2 protease and SIV protease, were covalently modified only at one amino acid residue, while the aspartic protease, HIV-1 protease, was found to be modified at three sites by the haloperidol derivative compounds. In addition, mass spectrometry has been applied to characterize the plasma glycoprotein, biotinidase, and to obtain partial peptide sequences of a membrane-bound protein, UDP-GalNac:polypeptide N-acetylgalactosaminyl transferase, using a low picomole quantity of sample.

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Klein, Mark Stephen. "The Determination of Lead and Cadmium in Tobacco Using High Performance Liquid Chromatography and Dithiocarbamate Derivitization." Digital Commons @ East Tennessee State University, 2011. https://dc.etsu.edu/etd/1240.

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A reversed phase-high performance liquid chromatography method has been developed that is capable of resolving lead and cadmium diethyldithiocarbamate complexes. The method does not require the presence of hazardous solvents to optimize peak shape and resolution; the mobile phase consists of methanol, water, and a surfactant. Tobacco samples were chemically oxidized and reacted with sodium diethyldithiocarbamate reagent prior to analysis using the HPLC method. The lead diethyldithiocarbamate determination was compromised by the presence of a significant interference in the analysis; lead determinations in 10 foreign and domestic tobacco samples ranged from 27.14 to 134.84 μg/g. The cadmium diethyldithiocarbamate determination was not adversely affected by interferences. Cadmium determinations in 10 foreign and domestic tobacco samples ranged from 0.89 to 6.96 μg/g. The tobacco samples were also analyzed using atomic absorption spectrometry. Foreign tobacco brands that contained clove as a spice showed lower levels of cadmium and lead.

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Dixon, Daniel Wayne. "Characterization of Commercial Pectin Preparations by Spectroscopic and Chromatographic Techniques." Digital Commons @ East Tennessee State University, 2008. https://dc.etsu.edu/etd/1910.

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Pectin has a long history as a food additive. However, elucidation of its fine structural and property relationships remains elusive. Recent research has focused on pectin's ability to complex with divalent heavy metals to aid in characterizing it. Commercial pectins of unknown composition were obtained from local grocers. Purified pectin samples from orange peel, lemon peel, and apple pomace, each of low and high levels of methyl esterification and of unknown distribution pattern were also purchased. Instead of metal complexation, several highly absorbing dyes such as Ruthenium Red, Nile Blue, and Acridine Orange were used to complex with the pectins and their resulting UV-Vis spectral patterns were employed to determine if one can characterize the different pectins. Chemometric methods are also included to aid in distinguishing them apart.

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Regmi, Suresh Chandra. "Monitoring Metal Containing Particulates Distribution on a College Campus Using Dandelion (Taraxacum officinale) Leaves as Receptors." Digital Commons @ East Tennessee State University, 2008. https://dc.etsu.edu/etd/1976.

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This study aims to determine the distribution of particulates carrying heavy metals at selected sites on a college campus using dandelion leaves as collectors. As a comparison, sites far away from the campus surrounding Bristol Motor Speedway Car Racing Stadium were also monitored. To reduce the probability of memory effects from the long-term atmospheric deposition or absorption of metals from soil a seasonal plant, dandelion, was used to monitor the metal contents. The metals monitored are cadmium, calcium, copper, chromium, iron, lead, and zinc. Fourteen sites were monitored and samples were collected once a week initially (growing time of the plant), and later at 4-week interval from 28th March to 31st August of 2007. The metal contents of the nitric acid digested and appropriately diluted samples were determined by flame atomic absorption spectrometry using the regular standard calibration curve and also the standard addition method. From the results obtained, and the careful log of the weather and human activities at the different sites, it is concluded that human activities played a major role in the distribution of metal-laden particulates. Also dandelion leaves were proven to be viable collectors of these particulates without memory effects and as indicators of current particulates generated rather than a long-term cumulative one.

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Affadu-Danful, George. "Immobilization of Gold Nanoparticles on Nitrided Carbon Fiber Ultramicroelectrodes by Direct Reduction." Digital Commons @ East Tennessee State University, 2018. https://dc.etsu.edu/etd/3446.

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Due to enhanced properties such as large surface area-to-volume ratio, metal nanoparticles are often employed as catalysts for various applications. However, most studies involving nanoparticle catalysts have been conducted on collections of particles rather than single nanoparticles. Results obtained for ensemble systems can be difficult to interpret due to variations in particle loading and interparticle distance, which are often challenging to control and characterize. In this study, two immobilization strategies for incorporating gold nanoparticles (AuNPs) on carbon fiber ultramicroelectrodes (UMEs) were compared with the goal of extending these techniques to nanoelectrodes for studies of single AuNPs. Both layer-by-layer deposition of AuNPs on natural carbon fiber UMEs and direct reduction of AuNPs on nitrided carbon fiber UMEs were explored. Although both methods proved feasible, the direct reduction method seemed to be more effective and should better enable direct comparisons of bare and capped AuNPs.

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Dissertations / Theses on the topic 'Analytical Mathematics'

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