Education Commons^™

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 …

Information Security Newsletter

Information Security Newsletter

No abstract provided.

Information Security Newsletter

Information Security Newsletter

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Information Security Newsletter

Information Security Newsletter

No abstract provided.

Information Security Newsletter

Information Security Newsletter

No abstract provided.

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 …

2012 Georgia Scholarship Of Stem Teaching And Learning Conference Program, Georgia Scholarship Of Stem Teaching And Learning Conference

Interdisciplinary STEM Teaching & Learning Conference (2012-2019)

Conference Program

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.

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.

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.

Restricted Sum Formula Of Alternating Euler Sums, Jianqiang Zhao

Department of Mathematical Sciences Faculty Publications

In this paper, we study restricted sum formulas involving alternating Euler sums which are defined by ζ(s1,…,sd;ε1,…,εd)=∑n1>⋯>nd≥1εn11⋯εnddns11⋯nsdd,

for all positive integers s 1,…,s d and ε 1=±1,…,ε d =±1 with (s 1,ε 1)≠(1,1). We call w=s 1+⋯+s d the weight and d the depth. When ε j =−1 we say the jth component is alternating. We first consider Euler sums of the following special type: ξ(2s1,…,2sd)=ζ(2s1,…,2sd;(−1)s1,…,(−1)sd).

For d≤n, let Ξ(2n,d) be the sum of all ξ(2s 1,…,2s d ) …

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.

Labeling And Comparison Of Isomeric Tree-Like Polyphenyl Systems, Tabitha Williford, Alex Collins, Shainaz Landge, Hua Wang

Department of Mathematical Sciences Faculty Publications

Tree-like polyphenyl systems form an important class of compounds in chemistry, in particular material science and polymers. The importance can be seen in LEDs, transmitters, and electronics. In recent years, many extremal results regarding such systems under specific constraints have been reported. More specifically are the sub-categories of such systems with extremal Wiener indices. In this article, we provide a labelling of the vertices on each hexagon (i.e., the corresponding benzene ring), which facilitates the illustration of a treelike polyphenyl system with its corresponding tree structure. This approach helps to characterize the extremal tree-like polyphenyl systems with respect to the …

Cohen Factorizations: Weak Functoriality And Applications, Saeed Nasseh, Sean Sather-Wagstaff

Department of Mathematical Sciences Faculty Publications

We investigate Cohen factorizations of local ring homomorphisms from three perspectives. First, we prove a “weak functoriality” result for Cohen factorizations: certain morphisms of local ring homomorphisms induce morphisms of Cohen factorizations. Second, we use Cohen factorizations to study the properties of local ring homomorphisms (Gorenstein, Cohen–Macaulay, etc.) in certain commutative diagrams. Third, we use Cohen factorizations to investigate the structure of quasi-deformations of local rings, with an eye on the question of the behavior of CI-dimension in short exact sequences.

Existence Of Solutions For A Variable Exponent System Without Ps Conditions, Li Yin, Yuan Liang, Qihu Zhang, Chunshan Zhao

Department of Mathematical Sciences Faculty Publications

In this article, we study the existence of solution for the following elliptic system of variable exponents with perturbation terms − div |∇u| p(x)−2∇u) + |u| p(x)−2u = λa(x)|u| γ(x)−2u + Fu(x, u, v) in R N , − div |∇v| q(x)−2∇v) + |v| q(x)−2 v = λb(x)|v| δ(x)−2 v + Fv(x, u, v) in R N , u ∈ W1,p(·) (R N ), v ∈ W1,q(·) (R N ), where the corresponding functional does not satisfy PS conditions. We obtain a sufficient condition for the existence of solution and also present a result on asymptotic behavior of solutions at …

Density Of Gallai Multigraphs, Colton Magnant

Department of Mathematical Sciences Faculty Publications

Diwan and Mubayi asked how many edges of each color could be included in a 33-edge-colored multigraph containing no rainbow triangle. We answer this question under the modest assumption that the multigraphs in question contain at least one edge between every pair of vertices. We also conjecture that this assumption is, in fact, without loss of generality.

A New Class Of Generalized Power Lindley Distribution With Applications To Lifetime Data, Marvis Pararai, Gayan Warahena-Liyanage, Broderick O. Oluyede

Department of 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, …

Graphs Obtained From Collections Of Blocks, Colton Magnant, Pouria Salehi Nowbandegani, Hua Wang

Department of 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 …

Kumaraswamy Lindley-Poisson Distribution: Theory And Applications, Mavis Pararai, Broderick O. Oluyede, Gayan Warahena-Liyanage

Department of 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 …

Log-Concavity And Symplectic Rows, Yi Lin, Álvaro Pelayo

Department of Mathematical Sciences Faculty Publications

The Duistermaat-Heckman measure of a Hamiltonian torus action on a symplectic manifold (M,ω) is the push forward of the Liouville measure on M by the momentum map of the action. In this paper we prove the logarithmic concavity of the Duistermaat-Heckman measure of a complexity two Hamiltonian torus action, for which there exists an effective commuting symplectic action of a 2-torus with symplectic orbits. Using this, we show that given a complexity two symplectic torus action satisfying the additional 2-torus action condition, if the fixed point set is non-empty, then it has to be Hamiltonian. This implies a classical result …

The Log-Generalized Lindley-Weibull Distribution With Applications, Broderick O. Oluyede, Fedelis Mutiso, Shujiao Huang

Department of 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.

A Generalized Class Of Kumaraswamy Lindley Distribution With Applications To Lifetime Data, Broderick O. Oluyede, Tiantian Yang, Bernard Omolo

Department of 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 …