Kravchuk Polynomials And Induced/Reduced Operators On Clifford Algebras,
2015
Southern Illinois University Edwardsville
Kravchuk Polynomials And Induced/Reduced Operators On Clifford Algebras, G. Stacey Staples
SIUE Faculty Research, Scholarship, and Creative Activity
Kravchuk polynomials arise as orthogonal polynomials with respect to the binomial distribution and have numerous applications in harmonic analysis, statistics, coding theory, and quantum probability. The relationship between Kravchuk polynomials and Clifford algebras is multifaceted. In this paper, Kravchuk polynomials are discovered as traces of conjugation operators in Clifford algebras, and appear in Clifford Berezin integrals of Clifford polynomials. Regarding Kravchuk matrices as linear operators on a vector space V, the action induced on the Clifford algebra over V is equivalent to blade conjugation, i.e., reflections across sets of orthogonal hyperplanes. Such operators also have a natural interpretation in …
Clifford Algebra Decompositions Of Conformal Orthogonal Group Elements,
2015
Southern Illinois University Edwardsville
Clifford Algebra Decompositions Of Conformal Orthogonal Group Elements, G. Stacey Staples, David Wylie
SIUE Faculty Research, Scholarship, and Creative Activity
Beginning with a finite-dimensional vector space V equipped with a nondegenerate quadratic form Q, we consider the decompositions of elements of the conformal orthogonal group COQ(V), defined as the direct product of the orthogonal group OQ(V) with dilations. Utilizing the correspondence between conformal orthogonal group elements and ``decomposable'' elements of the associated Clifford algebra, ClQ(V), a decomposition algorithm is developed. Preliminary results on complexity reductions that can be realized passing from additive to multiplicative representations of invertible elements are also presented with examples. The approach here is …
On Representations Of Semigroups Having Hypercube-Like Cayley Graphs,
2015
Southern Illinois University Edwardsville
On Representations Of Semigroups Having Hypercube-Like Cayley Graphs, Cody Cassiday, G. Stacey Staples
SIUE Faculty Research, Scholarship, and Creative Activity
The $n-dimensional hypercube, or n-cube, is the Cayley graph of the Abelian group Z2n. A number of combinatorially-interesting groups and semigroups arise from modified hypercubes. The inherent combinatorial properties of these groups and semigroups make them useful in a number of contexts, including coding theory, graph theory, stochastic processes, and even quantum mechanics. In this paper, particular groups and semigroups whose Cayley graphs are generalizations of hypercubes are described, and their irreducible representations are characterized. Constructions of faithful representations are also presented for each semigroup. The associated semigroup algebras are realized within the context …
Sampling Strategies For Finite Population Using Auxiliary Information,
2015
University of New Mexico
Sampling Strategies For Finite Population Using Auxiliary Information, Florentin Smarandache, Rajesh Singh
Branch Mathematics and Statistics Faculty and Staff Publications
The present book aims to present some improved estimators using auxiliary and attribute information in case of simple random sampling and stratified random sampling and in some cases when non-response is present. This volume is a collection of five papers, written by seven co-authors (listed in the order of the papers): Sachin Malik, Rajesh Singh, Florentin Smarandache, B. B. Khare, P. S. Jha, Usha Srivastava and Habib Ur. Rehman. The first and the second papers deal with the problem of estimating the finite population mean when some information on two auxiliary attributes are available. In the third paper, problems related …
Control, Stability, And Qualitative Theory Of Dynamical Systems 2014,
2015
Eastern Mediterranean University
Control, Stability, And Qualitative Theory Of Dynamical Systems 2014, Nazim I. Mahmudov, Mark A. Mckibben, Sakthivel Rathinasamy, Yong Ren
Mathematics Faculty Publications
No abstract provided.
Further Results On Vanishing Coefficients In Infinite Product Expansions,
2015
West Chester University of Pennsylvania
Further Results On Vanishing Coefficients In Infinite Product Expansions, James Mclaughlin
Mathematics Faculty Publications
We extend results of Andrews and Bressoud on the vanishing of coefficients in the series expansions of certain infinite products. These results have the form that if (q r−tk, qmk−(r−tk) ; q mk)∞ (q r, qmk−r; qmk)∞ =: X∞ n=0 cnq n , for certain integers k, m s and t, where r = sm+t, then ckn−rs is always zero. Our theorems also partly give a simpler reformulation of results of Alladi and Gordon, but also give results for cases not covered by the theorems of Alladi and Gordon. We also give some interpretations of the analytic results in terms …
Integral Representations Of Positive Linear Functionals,
2015
University of Central Florida
Integral Representations Of Positive Linear Functionals, Angela Siple
Electronic Theses and Dissertations
In this dissertation we obtain integral representations for positive linear functionals on commutative algebras with involution and semigroups with involution. We prove Bochner and Plancherel type theorems for representations of positive functionals and show that, under some conditions, the Bochner and Plancherel representations are equivalent. We also consider the extension of positive linear functionals on a Banach algebra into a space of pseudoquotients and give under conditions in which the space of pseudoquotients can be identified with all Radon measures on the structure space. In the final chapter we consider a system of integrated Cauchy functional equations on a semigroup, …
Algebraic Problems And Exercises For High School,
2015
University of New Mexico
Algebraic Problems And Exercises For High School, Florentin Smarandache, Ion Goian, Raisa Grigor, Vasila Marin
Branch Mathematics and Statistics Faculty and Staff Publications
In this book, you will find algebraic exercises and problems, grouped by chapters, intended for higher grades in high schools or middle schools of general education. Its purpose is to facilitate training in mathematics for students in all high school categories, but can be equally helpful in a standalone work. The book can also be used as an extracurricular source, as the reader shall find enclosed important theorems and formulas, standard definitions and notions that are not always included in school textbooks.
On Closed Subsets Of ℝ And Of ℝ2 Admitting Peano Functions,
2015
West Virginia University
On Closed Subsets Of ℝ And Of ℝ2 Admitting Peano Functions, Krzysztof Ciesielski
Faculty & Staff Scholarship
In this note we describe closed subsets of the real line P ⊂ R for which there exists a continuous function from P onto P 2 , called Peano function. Our characterization of those sets is based on the number of connected components of P. We also include a few remarks on compact subsets of R 2 admitting Peano functions, expressed in terms of connectedness and local connectedness.
Graphs Obtained From Collections Of Blocks,
2015
Georgia Southern Universtiy
Graphs Obtained From Collections Of Blocks, Colton Magnant, Pouria Salehi Nowbandegani, Hua Wang
Mathematical Sciences: Faculty Publications
Given a collection of d-dimensional rectangular solids called blocks, no two of which sharing interior points, construct a block graph by adding a vertex for each block and an edge if the faces of the two corresponding blocks intersect nontrivially. It is known that if d ≥ 3, such block graphs can have arbitrarily large chromatic number. We prove that the chromatic number can be bounded with only a mild restriction on the sizes of the blocks. We also show that block graphs of block configurations arising from partitions of d-dimensional hypercubes into sub-hypercubes are at least d-connected. Bounds on …
An Extension Of Herglotz's Theorem To The Quaternions,
2015
Chapman University
An Extension Of Herglotz's Theorem To The Quaternions, Daniel Alpay, Fabrizio Colombo, David P. Kimsey, Irene Sabadini, David P. Kimsey
Mathematics, Physics, and Computer Science Faculty Articles and Research
A classical theorem of Herglotz states that a function n↦r(n) from Z into Cs×s is positive definite if and only there exists a Cs×s-valued positive measure dμ on [0,2π] such that r(n)=∫2π0eintdμ(t)for n∈Z. We prove a quaternionic analogue of this result when the function is allowed to have a number of negative squares. A key tool in the argument is the theory of slice hyperholomorphic functions, and the representation of such functions which have a positive real part in the unit ball of the quaternions. We study in great detail the case of positive definite functions.
Boundary Interpolation For Slice Hyperholomorphic Schur Functions,
2015
Ben Gurion University of the Negev
Boundary Interpolation For Slice Hyperholomorphic Schur Functions, Khaled Abu-Ghanem, Daniel Alpay, Fabrizio Colombo, David P. Kimsey, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
A boundary Nevanlinna-Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers κ1,…,κN, quaternions p1,…,pN all of modulus 1, so that the 2-spheres determined by each point do not intersect and pu≠1 for u=1,…,N, and quaternions s1,…,sN, we wish to find a slice hyperholomorphic Schur function s so that
limr→1r∈(0,1)s(rpu)=suforu=1,…,N,
and
limr→1r∈(0,1)1−s(rpu)su¯¯¯¯¯1−r≤κu,foru=1,…,N.
Our arguments relies on the theory of slice hyperholomorphic functions and reproducing kernel Hilbert spaces.
On Algebras Which Are Inductive Limits Of Banach Spaces,
2015
Chapman University
On Algebras Which Are Inductive Limits Of Banach Spaces, Daniel Alpay, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
We introduce algebras which are inductive limits of Banach spaces and carry inequalities which are counterparts of the inequality for the norm in a Banach algebra. We then define an associated Wiener algebra, and prove the corresponding version of the well-known Wiener theorem. Finally, we consider factorization theory in these algebra, and in particular, in the associated Wiener algebra.
The Log-Generalized Lindley-Weibull Distribution With Applications,
2015
Georgia Southern University
The Log-Generalized Lindley-Weibull Distribution With Applications, Broderick O. Oluyede, Fedelis Mutiso, Shujiao Huang
Mathematical Sciences: Faculty Publications
A new distribution called the log generalized Lindley-Weibull (LGLW) distribution for modeling lifetime data is proposed. This model further generalizes the Lindley distribution and allows for hazard rate functions that are monotonically decreasing, monotonically increasing and bathtub shaped. A comprehensive investigation and account of the mathematical and statistical properties including moments, moment generating function, simulation issues and entropy are presented. Estimates of model parameters via the method of maximum likelihood are given. Real data examples are presented to illustrate the usefulness and applicability of this new distribution.
Kumaraswamy Lindley-Poisson Distribution: Theory And Applications,
2015
Indiana University of Pennsylvania
Kumaraswamy Lindley-Poisson Distribution: Theory And Applications, Mavis Pararai, Broderick O. Oluyede, Gayan Warahena-Liyanage
Mathematical Sciences: Faculty Publications
The Kumaraswamy Lindley-Poisson (KLP) distribution which is an extension of the Lindley-Poisson Distribution [21] is introduced and its properties are explored. This new distribution represents a more flexible model for the lifetime data. Some statistical properties of the proposed distribution including the shapes of the density and hazard rate functions are explored. Moments, entropy measures and the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters and a simulation study is conducted to investigate the performance of the maximum likelihood estimates. Finally some applications of the model with real data …
A Generalized Class Of Kumaraswamy Lindley Distribution With Applications To Lifetime Data,
2015
Georgia Southern University
A Generalized Class Of Kumaraswamy Lindley Distribution With Applications To Lifetime Data, Broderick O. Oluyede, Tiantian Yang, Bernard Omolo
Mathematical Sciences: Faculty Publications
In this paper, we propose a new class of generalized distributions called the Exponentiated Kumaraswamy Lindley (EKL) distribution, as well as related sub-distributions. This class of distributions contains the Kumaraswamy Lindley (KL), generalized Lindley (GL), and Lindley (L) distributions as special cases. A series expansion of the density is obtained. Statistical properties of this class of distributions, including the hazard and reverse hazard functions, monotonicity property, shapes, moments, reliability, quantile function, mean deviations, Bonferroni and Lorenz curves, entropy and Fisher information are derived among others. The method of maximum likelihood is adopted for estimating the model parameters. Two applications to …
A New Class Of Generalized Power Lindley Distribution With Applications To Lifetime Data,
2015
Indiana University of Pennsylvania
A New Class Of Generalized Power Lindley Distribution With Applications To Lifetime Data, Marvis Pararai, Gayan Warahena-Liyanage, Broderick O. Oluyede
Mathematical Sciences: Faculty Publications
A new class of distribution called the beta-exponentiated power Lindley (BEPL) distribution is proposed. This class of distributions includes the Lindley (L), exponentiated Lindley (EL), power Lindley (PL), exponentiated power Lindley (EPL), beta-exponentiated Lindley (BEL), beta-Lindley (BL), and beta-power Lindley distributions (BPL) as special cases. Expansion of the density of BEPL distribution is obtained. Some mathematical properties of the new distribution including hazard function, reverse hazard function, moments, mean deviations, Lorenz and Bonferroni curves are presented. Entropy measures and the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters. Finally, …
Asymptotically Exact Local Discontinuous Galerkin Error Estimates For The Linearized Korteweg-De Vries Equation In One Space Dimension,
2015
University of Nebraska at Omaha
Asymptotically Exact Local Discontinuous Galerkin Error Estimates For The Linearized Korteweg-De Vries Equation In One Space Dimension, Mahboub Baccouch
Mathematics Faculty Publications
We present and analyze a posteriori error estimates for the local discontinuous Galerkin (LDG) method for the linearized Korteweg-de Vries (KdV) equation in one space dimension. These estimates are computationally simple and are obtained by solving a local steady problem with no boundary condition on each element. We extend the work of Hufford and Xing [J. Comput. Appl. Math., 255 (2014), pp. 441-455] to prove new superconvergence results towards particular projections of the exact solutions for the two auxiliary variables in the LDG method that approximate the first and second derivatives of the solution. The order of convergence …
The Influence Of Dynamic Visualization On Undergraduate Calculus Learning,
2015
University of Texas at Arlington
The Influence Of Dynamic Visualization On Undergraduate Calculus Learning, Julie Marie Skinner Sutton
Mathematics Dissertations - Archive
The urgent need in the United States to produce an additional one million graduates in the areas of science, technology, engineering and mathematics and previous research into why students choose to abandon their quest to earn such degrees motivates exploration of the appropriate use of technology that engages students in the first-year calculus classroom. Technology enhances our capacity to incorporate visualization into the teaching of mathematics, yet research suggests that high school mathematics students who prefer to visualize when solving mathematics tasks are not the “super stars” of their classrooms. In this qualitative study, nine students, five of whom prefer …
A Modeling Study In The Regulation Of Stress On Neuronal Plasticity,
2015
University of Texas at Arlington
A Modeling Study In The Regulation Of Stress On Neuronal Plasticity, Pengcheng Xiao
Mathematics Dissertations - Archive
How stress can affect human cognitive functions has been a very popular topic for researchers from different fields including physiology, psychology, biology, neuroscience, and applied mathematics. Hypothalamic−pituitary−adrenal (HPA) axis plays an important role in response to stress by releasing hormones, and level of glucocorticoid has been widely considered to be one key factor to distinguish people with different stress disorder. Emerging evidence has shown that glucocorticoid act on glutamate neurotransmission system and consequently influences neuronal activities’s cognitive function. It changes in the glutamate release and induces synapse plasticity change. Spike-Timing Dependent Plasticity (STDP) is one of the important neuroscience foundations …
