Education Commons^™

Eccentricity Sum In Trees, Heather Smith, Laszlo A. Szekely, Hua Wang

Department of Mathematical Sciences Faculty Publications

The eccentricity of a vertex, eccT(v)=maxu∈TdT(v,u), was one of the first, distance-based, tree invariants studied. The total eccentricity of a tree, Ecc(T), is the sum of eccentricities of its vertices. We determine extremal values and characterize extremal tree structures for the ratios Ecc(T)/eccT(u), Ecc(T)/eccT(v), eccT(u)/eccT(v), and eccT(u)/eccT(w) where u,w are leaves of T and v is in the center of T. In addition, we determine the tree structures that minimize and maximize total eccentricity among trees with a given degree sequence.

Dagum-Poisson Distribution: Model, Properties And Application, Broderick O. Oluyede, Galelhakanelwe Motsewabagale, Shujiao Huang, Gayan Warahena-Liyanage, Marvis Pararai

Department of Mathematical Sciences Faculty Publications

A new four parameter distribution called the Dagum-Poisson (DP) distribution is introduced and studied. This distribution is obtained by compounding Dagum and Poisson distributions. The structural properties of the new distribution are discussed, including explicit algebraic formulas for its survival and hazard functions, quantile function, moments, moment generating function, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of order statistics and R\'enyi entropy. Method of maximum likelihood is used for estimating the model parameters. A Monte Carlo simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators and width of the …

Improved Full-Newton-Step Infeasible Interior-Point Method For Linear Complementarity Problems, Goran Lesaja, Mustafa Ozen

Department of Mathematical Sciences Faculty Publications

We present an Infeasible Interior-Point Method for monotone Linear Complementarity Problem (LCP) which is an improved version of the algorithm given in [13]. In the earlier version, each iteration consisted of one feasibility step and few centering steps. The improved version guarantees that after one feasibility step, the new iterate is feasible and close enough to the central path thanks to the much tighter proximity estimate which is based on the new lemma introduced in [18]. Thus, the centering steps are eliminated. Another advantage of this method is the use of full-Newton-steps, that is, no calculation of the step size …

Research And Evaluation Of The Effectiveness Of E-Learning In The Case Of Linear Programming, Ljiljana Miletić, Goran Lesaja

Department of Mathematical Sciences Faculty Publications

The paper evaluates the effectiveness of the e-learning approach to linearprogramming. The goal was to investigate how proper use of information andcommunication technologies (ICT) and interactive learning helps to improve high schoolstudents’ understanding, learning and retention of advanced non-curriculum material.The hypothesis was that ICT and e-learning is helpful in teaching linear programmingmethods. In the first phase of the research, a module of lessons for linear programming(LP) was created using the software package Loomen Moodle and other interactivesoftware packages such as Geogebra. In the second phase, the LP module was taught asa short course to two groups of high school students. …

Beta Linear Failure Rate Geometric Distribution With Applications, Broderick O. Oluyede, Ibrahim Elbatal, Shujiao Huang

Department of Mathematical Sciences Faculty Publications

This paper introduces the beta linear failure rate geometric (BLFRG) distribution, which contains a number of distributions including the exponentiated linear failure rate geometric, linear failure rate geometric, linear failure rate, exponential geometric, Rayleigh geometric, Rayleigh and exponential distributions as special cases. The model further generalizes the linear failure rate distribution. A comprehensive investigation of the model properties including moments, conditional moments, deviations, Lorenz and Bonferroni curves and entropy are presented. Estimates of model parameters are given. Real data examples are presented to illustrate the usefulness and applicability of the distribution.

Applying Linear Controls To Chaotic Continuous Dynamical Systems, James P. Braselton, Yan Wu

Department of Mathematical Sciences Faculty Publications

In this case-study, we examine the effects of linear control on continuous dynamical systems that exhibit chaotic behavior using the symbolic computer algebra system Mathematica. Stabilizing (or controlling) higher-dimensional chaotic dynamical systems is generally a difficult problem, Musielak and Musielak, [1]. We numerically illustrate that sometimes elementary approaches can yield the desired numerical results with two different continuous higher order dynamical systems that exhibit chaotic behavior, the Lorenz equations and the Rössler attractor.

Topological Contact Dynamics Iii: Uniqueness Of The Topological Hamiltonian And C0-Rigidity Of The Geodesic Flow, Stefan Müller, Peter Spaeth

Department of Mathematical Sciences Faculty Publications

We prove that a topological contact isotopy uniquely defines a topological contact Hamiltonian. Combined with previous results from [MS11], this generalizes the classical one-to-one correspondence between smooth contact isotopies and their generating smooth contact Hamiltonians and conformal factors to the group of topological contact dynamical systems. Applications of this generalized correspondence include C0 -rigidity of smooth contact Hamiltonians, a transformation law for topological contact dynamical systems, and C0 -rigidity of the geodesic flows of Riemannian manifolds.

Directed Proper Connection Of Graphs, Colton Magnant, Patrick R. Morley, Sarabeth A. Porter, Pouria Salehi Nowbandegani, Hua Wang

Department of Mathematical Sciences Faculty Publications

An edge-colored directed graph is called properly connected if, between every pair of vertices, there is a properly colored directed path. We study some conditions on directed graphs which guarantee the existence of a coloring that is properly connected. We also study conditions on a colored directed graph which guarantee that the coloring is properly connected.

Path Partitions Of Almost Regular Graphs, Colton Magnant, Hua Wang, Shuai Yuan

Department of Mathematical Sciences Faculty Publications

The path partition number of a graph is the minimum number of paths required to partition the vertices. We consider upper bounds on the path partition number under minimum and maximum degree assumptions.

A New Class Of Generalized Power Lindley Distribution With Applications To Lifetime Data, Broderick O. Oluyede, Tiantian Yang, Boikanyo Makubate

Department of Mathematical Sciences Faculty Publications

In this paper, a new class of generalized distribution called the Kumaraswamy Power Lindley (KPL) distribution is proposed and studied. This class of distributions contains the Kumaraswamy Lindley (KL), exponentiated power Lindley (EPL), power Lindley (PL), generalized or exponentiated Lindley (GL), and Lindley (L) distributions as special cases. Series expansion of the density is obtained. Statistical properties of this class of distributions, including hazard function, reverse hazard function, monotonicity property, shapes, moments, reliability, quantile function, mean deviations, Bonferroni and Lorenz curves, entropy and Fisher information are derived. Method of maximum likelihood is used to estimate the parameters of this new …

The Beta Lindley-Poisson Distribution With Applications, Broderick O. Oluyede, Gayan Warahena-Liyanage, Mavis Pararai

Department of Mathematical Sciences Faculty Publications

The beta Lindley-Poisson (BLP) distribution which is an extension of the Lindley-Poisson Distribution 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 expansion of the density function, hazard rate function, moments and moment generating function, skewness and kurtosis are explored. Renyi entropy and the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters and finally applications of the model to real data sets are presented for the illustration of the usefulness …

Mathematical Writing Assignment For Deeper Understanding And Process Writing, Colton Magnant, Saeed Nasseh, Teresa Flateby

Department of Mathematical Sciences Faculty Publications

Brief Description: The broad goals of this writing assignment are two-fold: 1) To delve deeper into the inner workings of a chosen proof and explore fundamental motivation of the chosen result. 2) To enhance student learning in the area of academic writing in the discipline of mathematics.

By walking the students through a process of academic writing, we address the following DQP proficiencies: Specialized Knowledge, Applied and Collaborative Learning and Intellectual Skills - Use of Information Resources, Mathematics-Specific Intellectual and Practical Skills and Communicative Fluency.

Background and context: This assignment has been used in a Mathematical Structures (introduction-to-proofs) course and …

Extended Lindley Poisson Distribution, Mavis Pararai, Gayan Warahena-Liyanage, Broderick O. Oluyede

Department of Mathematical Sciences Faculty Publications

The Extended Lindley Poisson (ELP) distribution which is an extension of the extended Lindley distribution [2] 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, hazard rate functions, moments, Bonferroni and Lorenz curves are explored. 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, we present applications …

Tight Super-Edge-Graceful Labelings Of Trees And Their Applications, Alex Collins, Colton Magnant, Hua Wang

Department of Mathematical Sciences Faculty Publications

The concept of graceful labeling of graphs has been extensively studied. In 1994, Mitchem and Simoson introduced a stronger concept called super-edge-graceful labeling for some classes of graphs. Among many other interesting pioneering results, Mitchem and Simoson provided a simple but powerful recursive way of constructing super-edge-graceful trees of odd order. In this note, we present a stronger concept of “tight” super-edge-graceful labeling. Such a super-edge graceful labeling has an additional constraint on the edge and vertices with the largest and smallest labels. This concept enables us to recursively construct tight super-edge-graceful trees of any order. As applications, we provide …

On The Stability Of Cycles By Delayed Feedback Control, Dmitriy Dmitrishin, Paul Hagelstein, Anna Khamitova, Alexander M. Stokolos

Department of Mathematical Sciences Faculty Publications

We present a delayed feedback control (DFC) mechanism for stabilizing cycles of one dimensional discrete time systems. In particular, we consider a delayed feedback control for stabilizingT-cycles of a differentiable functionf:R→Rof the form

x(k+1)=f(x(k))+u(k)

where

u(k)=(a₁−1)f(x(k))+a₂f(x(k−T))+...+a_Nf(x(k−(N−1)T)),

with a₁+...+a_N=1. Following an approach of Morgül, we construct a map F:R^T+1→R^T+1 whose fixed points correspond to T-cycles of f. We then analyze the local stability of the above DFC mechanism by evaluating the stability of the corresponding equilibrum points of F. We associate to each periodic orbit of f an …

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Information Security Newsletter

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A New Class Of Generalized Modified Weibull Distribution With Applications, Broderick O. Oluyede, Shujiao Huang, Tiantian Yang

Department of Mathematical Sciences Faculty Publications

A new five parameter gamma-generalized modified Weibull (GGMW) distribution which includes exponential, Rayleigh, modified Weibull, Weibull, gamma-modified Weibull, gamma-modified Rayleigh, gamma-modified exponential, gamma-Weibull, gamma-Rayleigh, and gamma-exponential distributions as special cases is proposed and studied. Some mathematical properties of the new class of distributions including moments, distribution of the order statistics, and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to a real datasets to illustrates the usefulness of the proposed class of models are presented.

Gorenstein Flat Preenvelopes, Alina Iacob

Department of Mathematical Sciences Faculty Publications

We consider a two sided noetherian ring R such that the character modules of Gorenstein injective left R-modules are Gorenstein flat right R-modules. We then prove that the class of Gorenstein flat right R-modules is preenveloping. We also show that the class of Gorenstein flat complexes of right R-modules is preenevloping in Ch(R).

In the second part of the paper we give examples of rings with the property that the character modules of Gorenstein injective modules are Gorenstein flat. We prove that any two sided noetherian ring R with i.d.Rop R < 1 has the desired property. We also prove that if R is a two sided noetherian ring with a dualizing bimodule R VR and such that R is left n-perfect for some positive integer n, then the character modules of Gorenstein injective modules are Gorenstein flat.

Contracting Endomorphisms And Dualizing Complexes, Saeed Nasseh, Sean Sather-Wagstaff

Department of Mathematical Sciences Faculty Publications

We investigate how one can detect the dualizing property for a chain complex over a commutative local Noetherian ring R. Our focus is on homological properties of contracting endomorphisms of R, e.g., the Frobenius endomorphism when R contains a field of positive characteristic. For instance, in this case, when R is F-finite and C is a semidualizing R-complex, we prove that the following conditions are equivalent: (i) C is a dualizing R-complex; (ii) C ∼RHomR(nR,C) for some n > 0; (iii) GC-dimnR < ∞ and C is derived …

A Survey Of Mathematical Models Of Dengue Fever, James P. Braselton, Iurii Bakach

Department of Mathematical Sciences Faculty Publications

In this paper, we compare and contrast five models of dengue fever, a serious illness that affects tropical and subtropical areas around the world. We evaluate each model using different scenarios and identify the strengths and weakness of each of the models. The goal of our analysis is to indicate the strengths and weaknesses of current mathematical models of dengue fever that should assist future researchers in forming models that accurately measure the variables they are studying that affect the spread and progression of the disease.

Homology Over Trivial Extensions Of Commutative Dg Algebras, Luchezar L. Avramov, Srikanth B. Iyengar, Saeed Nasseh, Sean Sather-Wagstaff

Department of Mathematical Sciences Faculty Publications

Conditions on the Koszul complex of a noetherian local ring R guarantee that TorRi(M,N) is non-zero for infinitely many i, when M and N are finitely generated R-modules of infinite projective dimension. These conditions are obtained from results concerning Tor of differential graded modules over certain trivial extensions of commutative differential graded algebras.

Meander Graphs And Frobenius Seaweed Lie Algebras Ii, Vincent Coll, Matthew Hyatt, Colton Magnant, Hua Wang

Department of Mathematical Sciences Faculty Publications

We provide a recursive classification of meander graphs, showing that each meander is identified by a unique sequence of fundamental graph theoretic moves. This sequence is called the meander’s signature and can be used to construct arbitrarily large sets of meanders, Frobenius or otherwise, of any size and configuration. In certain special cases, the signature is used to produce an explicit formula for the index of seaweed Lie subalgebra of sl(n) in terms of elementary functions.

On The Generalized Linear And Non-Linear Dfc In Non-Linear Dynamics, Dmitriy Dmitrishin, Anna Khamitova, Alexander M. Stokolos

Department of Mathematical Sciences Faculty Publications

The article is devoted to investigation of robust stability of the generalized linear control of the discrete autonomous dynamical systems. Sharp necessary conditions on the size of the set of multipliers that guaranty robust stabilization of the equilibrium of the system are provided. Surprisingly enough it turns out that the generalized linear delayed feedback control has same limitation as the classical Pyragas DFC. This generalized Ushio 1996 DFC limitation statement. Note that in scalar case a generalized non-linear control can robustly stabilize an equilibrium for any admissible range of multipliers. In the current article similar result is obtained in the …

Bohr Density Of Simple Linear Group Orbits, Roger Howe, Francois Ziegler

Department of Mathematical Sciences Faculty Publications

We show that any non-zero orbit under a non-compact, simple, irreducible linear group is dense in the Bohr compactification of the ambient space.

Families Of Weighted Sum Formulas For Multiple Zeta Values, Li Guo, Peng Lei, Jianqiang Zhao

Department of Mathematical Sciences Faculty Publications

Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper, we prove a family of identities involving Bernoulli numbers and apply them to obtain infinitely many weighted sum formulas for double zeta values and triple zeta values where the weight coefficients are given by symmetric polynomials. We give a general conjecture in arbitrary depth at the end of the paper.

Estimation In The Exponentiated Kumaraswamy Dagum Distribution With Censored Samples, Broderick O. Oluyede, Shujiao Huang

Department of Mathematical Sciences Faculty Publications

In a recent note, Huang and Oluyede (2014) proposed a new model called the exponentiated Kumaraswamy Dagum (EKD) distribution with applications to income and lifetime data. In this note, this distribution is shown to be a very competitive model for describing censored observations in lifetime reliability problems. This work shows that in certain cases, the EKD distribution performs better than other parametric model such as the exponentiated Kumaraswamy Weibull distribution and its sub-models, which include some of the commonly used models in survival analysis and reliability analysis, such as the exponentiated Weibull, Weibull and exponential distributions.

Local Well-Posedness Of Periodic Fifth Order Kdv-Type Equations, Yi Hu, Xiaochun Li

Department of Mathematical Sciences Faculty Publications

In this paper, the local well-posedness of periodic fifth order dispersive equation with nonlinear term P1(u)∂xu + P2(u)∂xu∂xu. Here P1(u) and P2(u) are polynomials of u. We also get some new Strichartz estimates.