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Measures Of Concordance Of Polynomial Type, Heather Edwards
Measures Of Concordance Of Polynomial Type, Heather Edwards
Electronic Theses and Dissertations
A measure of concordance, $\kappa$, is of polynomial type if and only if $\kappa (tA+(1-t)B)$ is a polynomial in $t$ where $A$ and $B$ are 2-copulas. The degree of such a type of measure of concordance is simply the highest degree of the polynomial associated with $\kappa$. In previous work [2], [3], properties of measures of concordance preserving convex sums (equivalently measures of concordance of polynomial type degree one) were established; however, a characterization was not made. Here a characterization is made using approximations involving doubly stochastic matrices. Other representations are provided from this characterization leading naturally to two interpretations …
Macmahon's Master Theorem And Infinite Dimensional Matrix Inversion, Vivian Lola Wong
Macmahon's Master Theorem And Infinite Dimensional Matrix Inversion, Vivian Lola Wong
Electronic Theses and Dissertations
MacMahon's Master Theorem is an important result in the theory of algebraic combinatorics. It gives a precise connection between coefficients of certain power series defined by linear relations. We give a complete proof of MacMahon's Master Theorem based on MacMahon's original 1960 proof. We also study a specific infinite dimensional matrix inverse due to C. Krattenthaler.
Asymptotic Formulas For Large Arguments Of Hypergeometric-Type Functio, Adam Heck
Asymptotic Formulas For Large Arguments Of Hypergeometric-Type Functio, Adam Heck
Electronic Theses and Dissertations
Hypergeometric type functions have a long list of applications in the field of sciences. A brief history is given of Hypergeometric functions including some of their applications. A development of a new method for finding asymptotic formulas for large arguments is given. This new method is applied to Bessel functions. Results are compared with previously known methods.
The Wave Structure Function And Temporal Frequency Spread In Weak To Strong Optical Turbulence, Aaron J. Masino
The Wave Structure Function And Temporal Frequency Spread In Weak To Strong Optical Turbulence, Aaron J. Masino
Electronic Theses and Dissertations
This paper presents analytic expressions for the wave structure function, frequency spread of the temporal frequency spectrum, and the temporal frequency spectrum of optical signals propagating through a random medium, specifically the Earth’s atmosphere. The results are believed to be valid for all optical turbulence conditions. These expressions are developed using the Rytov approximation method. Generally, the validity of statistical quantities obtained via this method is restricted to conditions of weak optical turbulence. However, in this work, by using a modification of the effective atmospheric spectral model presented by Andrews et al. for scintillation index, wave structure function expressions have …
Smoothing Parameter Selection In Nonparametric Functional Estimation, Mohamed Amezziane
Smoothing Parameter Selection In Nonparametric Functional Estimation, Mohamed Amezziane
Electronic Theses and Dissertations
This study intends to build up new techniques for how to obtain completely data-driven choices of the smoothing parameter in functional estimation, within the confines of minimal assumptions. The focus of the study will be within the framework of the estimation of the distribution function, the density function and their multivariable extensions along with some of their functionals such as the location and the integrated squared derivatives.
The Use Of Filters In Topology, Abdellatif Dasser
The Use Of Filters In Topology, Abdellatif Dasser
Electronic Theses and Dissertations
Sequences are sufficient to describe topological properties in metric spaces or, more generally, topological spaces having a countable base for the topology. However, filters or nets are needed in more abstract spaces. Nets are more natural extension of sequences but are generally less friendly to work with since quite often two nets have distinct directed sets for domains. Operations involving filters are set theoretic and generally certain to filters on the same set. The concept of a filter was introduced by H. Cartan in 1937 and an excellent treatment of the subject can be found in N. Bourbaki (1940).
Neural Networks Satisfying Stone-Weiestrass Theorem And Approximating, Pinal Thakkar
Neural Networks Satisfying Stone-Weiestrass Theorem And Approximating, Pinal Thakkar
Electronic Theses and Dissertations
Neural networks are an attempt to build computer networks called artificial neurons, which imitate the activities of the human brain. Its origin dates back to 1943 when neurophysiologist Warren Me Cello and logician Walter Pits produced the first artificial neuron. Since then there has been tremendous development of neural networks and their applications to pattern and optical character recognition, speech processing, time series prediction, image processing and scattered data approximation. Since it has been shown that neural nets can approximate all but pathological functions, Neil Cotter considered neural network architecture based on Stone-Weierstrass Theorem. Using exponential functions, polynomials, rational functions …