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2016

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Articles 1081 - 1110 of 1329

Full-Text Articles in Mathematics

The Transmuted Weibull-Pareto Distribution, Ahmed Z. Afify, Haitham M. Yousof, Nadeem Shafique Butt, Gholamhossein G. Hamedani Jan 2016

The Transmuted Weibull-Pareto Distribution, Ahmed Z. Afify, Haitham M. Yousof, Nadeem Shafique Butt, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

A new generalization of the Weibull-Pareto distribution called the transmuted Weibull-Pareto distribution is proposed and studied. Various mathematical properties of this distribution including ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves and order statistics are derived. The method of maximum likelihood is used for estimating the model parameters. The flexibility of the new lifetime model is illustrated by means of an application to a real data set.

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Almost Perfect Restriction Semigroups, Peter R. Jones Jan 2016

Almost Perfect Restriction Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

We call a restriction semigroup almost perfect if it is proper and the least congruence that identifies all its projections is perfect. We show that any such semigroup is isomorphic to a ‘W -product’ W(T,Y)W(T,Y), where T is a monoid, Y is a semilattice and there is a homomorphism from T into the inverse semigroup TIYTIY of isomorphisms between ideals of Y. Conversely, all such W-products are almost perfect. Since we also show that every restriction semigroup has an easily computed cover of this type, the combination yields a ‘McAlister-type’ theorem for all restriction semigroups. …

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An Edge-Swap Heuristic For Finding Dense Spanning Trees, Mustafa Ozen, Hua Wang, Kai Wang, Demet Yalman Jan 2016

An Edge-Swap Heuristic For Finding Dense Spanning Trees, Mustafa Ozen, Hua Wang, Kai Wang, Demet Yalman

Theory & Applications of Graphs

Finding spanning trees under various restrictions has been an interesting question to researchers. A "dense" tree, from a graph theoretical point of view, has small total distances between vertices and large number of substructures. In this note, the "density" of a spanning tree is conveniently measured by the weight of a tree (defined as the sum of products of adjacent vertex degrees). By utilizing established conditions and relations between trees with the minimum total distance or maximum number of sub-trees, an edge-swap heuristic for generating "dense" spanning trees is presented. Computational results are presented for randomly generated graphs and specific …

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The Discontinuous Galerkin Finite Element Method For Ordinary Differential Equations, Mahboub Baccouch Jan 2016

The Discontinuous Galerkin Finite Element Method For Ordinary Differential Equations, Mahboub Baccouch

Mathematics Faculty Publications

We present an analysis of the discontinuous Galerkin (DG) finite element method for nonlinear ordinary differential equations (ODEs). We prove that the DG solution is $(p + 1) $th order convergent in the $L^2$-norm, when the space of piecewise polynomials of degree $p$ is used. A $ (2p+1) $th order superconvergence rate of the DG approximation at the downwind point of each element is obtained under quasi-uniform meshes. Moreover, we prove that the DG solution is superconvergent with order $p+2$ to a particular projection of the exact solution. The superconvergence results are used to show that the leading term of …

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Zeon Roots, Lisa M. Dollar, G. Stacey Staples Jan 2016

Zeon Roots, Lisa M. Dollar, G. Stacey Staples

SIUE Faculty Research, Scholarship, and Creative Activity

Zeon algebras can be thought of as commutative analogues of fermion algebras, and they can be constructed as subalgebras within Clifford algebras of appropriate signature. Their inherent combinatorial properties make them useful for applications in graph enumeration problems and evaluating functions defined on partitions. In this paper, kth roots of invertible zeon elements are considered. More specifically, conditions for existence of roots are established, numbers of existing roots are determined, and computational methods for constructing roots are developed. Recursive and closed formulas are presented, and specific low-dimensional examples are computed with Mathematica. Interestingly, Stirling numbers of the first kind appear …

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Zeons, Orthozeons, And Graph Colorings, G. Stacey Staples, Tiffany Stellhorn Jan 2016

Zeons, Orthozeons, And Graph Colorings, G. Stacey Staples, Tiffany Stellhorn

SIUE Faculty Research, Scholarship, and Creative Activity

No abstract provided.

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On Six-Parameter Fréchet Distribution: Properties And Applications, Haitham M. Yousof, Ahmed Z. Afify, Abd El Hadi N. Ebraheim, Gholamhossein G. Hamedani, Nadeem Shafique Butt Jan 2016

On Six-Parameter Fréchet Distribution: Properties And Applications, Haitham M. Yousof, Ahmed Z. Afify, Abd El Hadi N. Ebraheim, Gholamhossein G. Hamedani, Nadeem Shafique Butt

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper introduces a new generalization of the transmuted Marshall-Olkin Fréchet distribution of Afify et al. (2015), using Kumaraswamy generalized family. The new model is referred to as Kumaraswamy transmuted Marshall-Olkin Fréchet distribution. This model contains sixty two sub-models as special cases such as the Kumaraswamy transmuted Fréchet, Kumaraswamy transmuted Marshall-Olkin, generalized inverse Weibull and Kumaraswamy Gumbel type II distributions, among others. Various mathematical properties of the proposed distribution including closed forms for ordinary and incomplete moments, quantile and generating functions and Rényi and η-entropies are derived. The unknown parameters of the new distribution are estimated using the maximum …

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On The Double Chain Ladder For Reserve Estimation With Bootstrap Applications, Larissa Schoepf Jan 2016

On The Double Chain Ladder For Reserve Estimation With Bootstrap Applications, Larissa Schoepf

Masters Theses

"To avoid insolvency, insurance companies must have enough reserves to fulfill their present and future commitment-refer to in this thesis as outstanding claims towards policyholders. This entails having an accurate and reliable estimate of funds necessary to cover those claims as they are presented. One of the major techniques used by practitioners and researchers is the single chain ladder method. However, though most popular and widely used, the method does not offer a good understanding of the distributional properties of the way claims evolve. In a series of recent papers, researchers have focused on two potential components of outstanding claims, …

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An Analysis Of Charles Fefferman's Proof Of The Fundamental Theorem Of Algebra, Kyle O. Linford Jan 2016

An Analysis Of Charles Fefferman's Proof Of The Fundamental Theorem Of Algebra, Kyle O. Linford

Senior Honors Theses and Projects

Many peoples' first exploration into more rigorous and formalized mathematics is with their early explorations in algebra. Much of their time and effort is dedicated to finding roots of polynomials-a challenge that becomes more increasingly difficult as the degree of the polynomials increases, especially if no real number roots exist. The Fundamental Theorem of Algebra is used to show that there exists a root, particularly a complex root, for any nth degree polynomial. After struggling to prove this statement for over 3 centuries, Carl Friedrich Gauss offered the first fairly complete proof of the theorem in 1799. Further proofs of …

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A Linear Matrix Inequality-Based Approach For The Computation Of Actuator Bandwidth Limits In Adaptive Control, Daniel Robert Wagner Jan 2016

A Linear Matrix Inequality-Based Approach For The Computation Of Actuator Bandwidth Limits In Adaptive Control, Daniel Robert Wagner

Masters Theses

"Linear matrix inequalities and convex optimization techniques have become popular tools to solve nontrivial problems in the field of adaptive control. Specifically, the stability of adaptive control laws in the presence of actuator dynamics remains as an important open control problem. In this thesis, we present a linear matrix inequalities-based hedging approach and evaluate it for model reference adaptive control of an uncertain dynamical system in the presence of actuator dynamics. The ideal reference dynamics are modified such that the hedging approach allows the correct adaptation without being hindered by the presence of actuator dynamics. The hedging approach is first …

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Unequal Edge Inclusion Probabilities In Link-Tracing Network Sampling With Implications For Respondent-Driven Sampling, Miles Q. Ott, Krista J. Gile Jan 2016

Unequal Edge Inclusion Probabilities In Link-Tracing Network Sampling With Implications For Respondent-Driven Sampling, Miles Q. Ott, Krista J. Gile

Statistical and Data Sciences: Faculty Publications

Respondent-Driven Sampling (RDS) is a widely adopted linktracing sampling design used to draw valid statistical inference from samples of populations for which there is no available sampling frame. RDS estimators rely upon the assumption that each edge (representing a relationship between two individuals) in the underlying network has an equal probability of being sampled. We show that this assumption is violated in even the simplest cases, and that RDS estimators are sensitive to the violation of this assumption.

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Analysis Of Employment And Earnings Using Varying Coefficient Models To Assess Success Of Minorities And Women, Amanda Goedeker Jan 2016

Analysis Of Employment And Earnings Using Varying Coefficient Models To Assess Success Of Minorities And Women, Amanda Goedeker

Electronic Theses and Dissertations

The objective of this thesis is to examine the success of minorities (black, and Hispanic/Latino employees) and women in the United States workforce, defining success by employment percentage and earnings. The goal of this thesis is to study the impact gender, race, passage of time, and national economic status reflected in gross domestic product have on the success of minorities and women. In particular, this thesis considers the impact of these factors in Science, Technology, Engineering and Math (STEM) industries. Varying coefficient models are utilized in the analysis of data sets for national employment percentages and earnings.

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Number Knowledge And Error Types Of Elementary Portuguese Students: Implications For Instruction, Silvana Watson, Sharon Judge, João Lopes, Célia Oliveira, Ana Catarina Jesus Jan 2016

Number Knowledge And Error Types Of Elementary Portuguese Students: Implications For Instruction, Silvana Watson, Sharon Judge, João Lopes, Célia Oliveira, Ana Catarina Jesus

Communication Disorders & Special Education Faculty Publications

In the present study, we examined number knowledge skills of 697 Portuguese elementary students from first to fourth grade. Students completed three number knowledge tasks: 1) translating numbers into words, 2) symbolic magnitude (i.e., number comparison), and 3) decomposing numbers. We evaluated students’ answers by means of error analysis using a three-category coding system adopted from specific error types were computed by grade level. Results showed that there were significant differences among grades and that the prerequisite linguistic error type (i.e., pre linguistic rules or principles of the cardinal number system), particularly in the magnitude tasks, significantly contributed to students’ …

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Monte Carlo Approx. Methods For Stochastic Optimization, John Fowler Jan 2016

Monte Carlo Approx. Methods For Stochastic Optimization, John Fowler

Pomona Senior Theses

This thesis provides an overview of stochastic optimization (SP) problems and looks at how the Sample Average Approximation (SAA) method is used to solve them. We review several applications of this problem-solving technique that have been published in papers over the last few years. The number and variety of the examples should give an indication of the usefulness of this technique. The examples also provide opportunities to discuss important aspects of SPs and the SAA method including model assumptions, optimality gaps, the use of deterministic methods for finite sample sizes, and the accelerated Benders decomposition algorithm. We also give a …

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Exploration Of Curvature Through Physical Materials, Lucinda-Joi Chu-Ketterer Jan 2016

Exploration Of Curvature Through Physical Materials, Lucinda-Joi Chu-Ketterer

Pitzer Senior Theses

Parametric equations are commonly used to describe surfaces. Looking at parametric equations does not provide tangible information about an object. Thus through the use of physical materials, an understanding of the limitations of the materials allows someone to gain a broader understanding of the surface. A M$\ddot{o}$bius strip and Figure 8 Klein bottle were created through knitting due to the precision and steady increase in curvature allowed through knitting. A more standard Klein bottle was created through crochet due to the ease in creating quick increases in curvature. Both methods demonstrate the change in curvature for both surfaces where the …

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Refinements Of Some Partition Inequalities, James Mclaughlin Jan 2016

Refinements Of Some Partition Inequalities, James Mclaughlin

Mathematics Faculty Publications

In the present paper we initiate the study of a certain kind of partition inequality, by showing, for example, that if M ≥ 5 is an integer and the integers a and b are relatively prime to M and satisfy 1 ≤ a < b < M/2, and the c(m, n) are defined by 1 (sqa, sqM−a; qM)∞ − 1 (sqb , sqM−b ; qM)∞ := X m,n≥0 c(m, n)s mq n , then c(m, Mn) ≥ 0 for all integers m ≥ 0, n ≥ 0. A similar result is proved for the integers d(m, n) defined by (−sqa , −sqM−a ; q M)∞ − (−sqb , −sqM−b ; q M)∞ := X m,n≥0 d(m, n)s mq n . In each case there are obvious interpretations in terms of integer partitions. For example, if p1,5(m, n) (respectively p2,5(m, n)) denotes the number of partitions of n into exactly m parts ≡ ±1( mod 5) (respectively ≡ ±2( mod 5)), then for each integer n ≥ 1, p1,5(m, 5n) ≥ p2,5(m, 5n), 1 ≤ m ≤ 5n.

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Modeling Rogue Waves In Deep Water, Maria Strawn Jan 2016

Modeling Rogue Waves In Deep Water, Maria Strawn

Electronic Theses and Dissertations

The evolution of surface waves in deep water is governed by the nonlinear Schrodinger (NLS) equation. Spatially periodic breathers (SPBs) and rational solutions of the NLS equation are used as typical models for rogue waves since they exhibit many features of rogue waves. A major component of the dissertation is the stability of solutions of the NLS equation. We address the stability of the rational solutions of the NLS equation used to model rogue waves using squared eigenfunctions of the associated Lax Pair. This allows us to contrast to the existing results for SPBs. The stability of the constant amplitude …

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Building Lax Integrable Variable-Coefficient Generalizations To Integrable Pdes And Exact Solutions To Nonlinear Pdes, Matthew Russo Jan 2016

Building Lax Integrable Variable-Coefficient Generalizations To Integrable Pdes And Exact Solutions To Nonlinear Pdes, Matthew Russo

Electronic Theses and Dissertations

This dissertation is composed of two parts. In Part I a technique based on extended Lax Pairs is first considered to derive variable-coefficient generalizations of various Lax-integrable NLPDE hierarchies recently introduced in the literature. It is demonstrated that the technique yields Lax- or S-integrable nonlinear partial differential equations (PDEs) with both time- and space-dependent coefficients which are thus more general than almost all cases considered earlier via other methods such as the Painleve Test, Bell Polynomials, and various similarity methods. However, this technique, although operationally effective, has the significant disadvantage that, for any integrable system with spatiotemporally varying coefficients, one …

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Rate Of Change 4, Ruth Dover Jan 2016

Rate Of Change 4, Ruth Dover

A Simple Introduction to Rates

No abstract provided.

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1. Monotonic Sequences, Ruth Dover Jan 2016

1. Monotonic Sequences, Ruth Dover

Series

Practice with monotonic sequences.

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Approximations 3, Ruth Dover Jan 2016

Approximations 3, Ruth Dover

Integrals

Understanding Riemann sum approximations, including technology.

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2. Geometric Series, Ruth Dover Jan 2016

2. Geometric Series, Ruth Dover

Series

Quick review of geometric series.

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Series 01, Ruth Dover Jan 2016

Series 01, Ruth Dover

Series

Asks students to create a polynomial function for y = ln(1 + x), extends the polynomial to a series, examines the interval of convergence and error.

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Series 04, Ruth Dover Jan 2016

Series 04, Ruth Dover

Series

A closer examination of y = cosx and y = sinx, including error estimation.

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2. Population, Ruth Dover Jan 2016

2. Population, Ruth Dover

Differential Equations

Introduction to logistic population growth.

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More Limits, Ruth Dover Jan 2016

More Limits, Ruth Dover

Limits

No abstract provided.

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Limits1, Ruth Dover Jan 2016

Limits1, Ruth Dover

Limits

A basic idea to limits and notation.

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2. Intro To Concavity, Ruth Dover Jan 2016

2. Intro To Concavity, Ruth Dover

More on Derivatives

Looking at changes in ƒ’ to understand concavity.

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3. Upper Bounds, Ruth Dover Jan 2016

3. Upper Bounds, Ruth Dover

Series

Understanding upper bounds and a proof of the divergence of the harmonic series.

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Approximating Alternating Series, Ruth Dover Jan 2016

Approximating Alternating Series, Ruth Dover

Series

Error bounds with alternating series.

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