Education Commons^™

Minimization And Eulerian Formulation Of Differential Geometry Based Nonpolar Multiscale Solvation Models, Zhan Chen

Department of Mathematical Sciences Faculty Publications

In this work, the existence of a global minimizer for the previous Lagrangian formulation of nonpolar solvation model proposed in [1] has been proved. One of the proofs involves a construction of a phase field model that converges to the Lagrangian formulation. Moreover, an Eulerian formulation of nonpolar solvation model is proposed and implemented under a similar parameterization scheme to that in [1]. By doing so, the connection, similarity and difference between the Eulerian formulation and its Lagrangian counterpart can be analyzed. It turns out that both of them have a great potential in solvation prediction for nonpolar molecules, while …

Extension Groups For Dg Modules, Saeed Nasseh, Sean Sather-Wagstaff

Department of Mathematical Sciences Faculty Publications

Let M and N be differential graded (DG) modules over a positively graded commutative DG algebra A. We show that the Ext-groups ExtiA(M,N) defined in terms of semi-projective resolutions are not in general isomorphic to the Yoneda Ext-groups YExtiA(M,N) given in terms of equivalence classes of extensions. On the other hand, we show that these groups are isomorphic when the first DG module is semi-projective.

Rank Of Submatrices Of The Pascal Matrix, Scott N. Kersey

Department of Mathematical Sciences Faculty Publications

In a previous paper, we derived necessary and sufficient conditions for the invertibility of square submatrices of the Pascal upper triangular matrix. To do so, we established a connection with the two-point Birkhoff interpolation problem. In this paper, we extend this result by deriving a formula for the rank of submatrices of the Pascal matrix. Our formula works for both square and non-square submatrices. We also provide bases for the row and column spaces of these submatrices. Further, we apply our result to one-point lacunary polynomial approximation.

A Generalized Class Of Exponentiated Modified Weibull Distribution With Applications, Shusen Pu, Broderick O. Oluyede, Yuqi Qui, Daniel F. Linder

Department of Mathematical Sciences Faculty Publications

In this paper, a new class of five parameter gamma-exponentiated or generalized modified Weibull (GEMW) distribution which includes exponential, Rayleigh, Weibull, modified Weibull, exponentiated Weibull, exponentiated exponential, exponentiated modified Weibull, exponentiated modified exponential, gamma-exponentiated exponential, gamma-exponentiated Rayleigh, gamma-modified Weibull, gamma-modified exponential, gamma-Weibull, gamma-Rayleigh and gamma-exponential distributions as special cases is proposed and studied. Mathematical properties of this new class of distributions including moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to real data sets presented in order to illustrate …

Equivariant Formality Of Transversely Symplectic Foliations And Frobenius Manifolds, Yi Lin, Xiangdong Yang

Department of Mathematical Sciences Faculty Publications

Consider the Hamiltonian action of a compact connected Lie group on a transversely symplectic foliation whose basic cohomology satisfies the Hard Lefschetz property. We establish an equivariant formality theorem and an equivariant symplectic dδ-lemma in this setting. As an application, we show that there exists a natural Frobenius manifold structure on the equivariant basic cohomology of the given foliation. In particular, this result provides a class of new examples of dGBV-algebras whose cohomology carries a Frobenius manifold structure.

Lefschetz Contact Manifolds And Odd Dimensional Symplectic Geometry, Yi Lin

Department of Mathematical Sciences Faculty Publications

In the literature, there are two different versions of Hard Lefschetz theorems for a compact Sasakian manifold. The first version, due to Kacimi-Alaoui, asserts that the basic cohomology groups of a compact Sasakian manifold satisfies the transverse Lefschetz property. The second version, established far more recently by Cappelletti-Montano, De Nicola, and Yudin, holds for the De Rham cohomology groups of a compact Sasakian manifold. In the current paper, using the formalism of odd dimensional symplectic geometry, we prove a Hard Lefschetz theorem for compact K-contact manifolds, which implies immediately that the two existing versions of Hard Lefschetz theorems are mathematically …

The Log-Logistic Weibull Distribution With Applications To Lifetime Data, Broderick O. Oluyede, Susan Foya, Gayan Warahena-Liyanage, Shujiao Huang

Department of Mathematical Sciences Faculty Publications

In this paper, a new generalized distribution called the log-logistic Weibull (LLoGW) distribution is developed and presented. This distribution contain the log-logistic Rayleigh (LLoGR), log-logistic exponential (LLoGE) and log-logistic (LLoG) distributions as special cases. The structural properties of the distribution including the hazard function, reverse hazard function, quantile function, probability weighted moments, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics, L-moments and Renyi entropy are derived. Method of maximum likelihood is used to estimate the parameters of this new distribution. A simulation study to examine the bias, mean square error of the maximum likelihood estimators …

Stabilizing The Lorenz Flows Using A Closed Loop Quotient Controller, James P. Braselton, Yan Wu

Department of Mathematical Sciences Faculty Publications

In this study, we introduce a closed loop quotient controller into the three-dimensional Lorenz system. We then compute the equilibrium points and analyze their local stability. We use several examples to illustrate how cross-sections of the basins of attraction for the equilibrium points look for various parameter values. We then provided numerical evidence that with the controller, the controlled Lorenz system cannot exhibit chaos if the equilibrium points are locally stable.

Invertibility Of Submatrices Of The Pascal Matrix And Birkhoff Interpolation, Scott N. Kersey

Department of Mathematical Sciences Faculty Publications

The infinite upper triangular Pascal matrix is T = [( j )i] for 0 ≤ i, j. It is easy to see that any leading principle square submatrix is triangular with determinant 1, hence invertible. In this paper, we investigate the invertibility of arbitrary square submatrices Tr, c comprised of rows r = [r0, … , rm ] and columns c = c0 , … , cm[] of T. We show that Tr, c is invertible r ≤ c i.e., ri ≤ ci for i = 0, …, m(), or equivalently, iff all diagonal entries are nonzero. To prove this …

Fast Cycles Detecting In Non-Linear Discrete Systems, Dmitriy Dmitrishin, Elena Franzheva, Alexander M. Stokolos

Department of Mathematical Sciences Faculty Publications

In the paper below we consider a problem of stabilization of a priori unknown unstable periodic orbits in non-linear autonomous discrete dynamical systems. We suggest a generalization of a non-linear DFC scheme to improve the rate of detecting T-cycles. Some numerical simulations are presented.

From Chaos To Order Through Mixing, Dmitriy Dmitrishin, I. M. Skrinnik, Alexander M. Stokolos

Department of Mathematical Sciences Faculty Publications

In this article we consider the possibility of controlling the dynamics of nonlinear discrete systems. A new method of control is by mixing states of the system (or the functions of these states) calculated on previous steps. This approach allows us to locally stabilize a priori unknown cycles of a given length. As a special case, we have a cycle stabilization using nonlinear feedback. Several examples are considered.

Note On Vertex And Total Proper Connection Numbers, Emily C. Chizmar, Colton Magnant, Pouria Salehi Nowbandegani

Department of Mathematical Sciences Faculty Publications

This note introduces the vertex proper connection number of a graph and provides a relationship to the chromatic number of minimally connected subgraphs. Also a notion of total proper connection is introduced and a question is asked about a possible relationship between the total proper connection number and the vertex and edge proper connection numbers.

Spatiotemporal Interpolation Methods For The Application Of Estimating Population Exposure To Fine Particulate Matter In The Contiguous U.S. And A Real-Time Web Application, Lixin Li, Xiaolu Zhou, Marc Kalo, Reinhard E. Piltner

Department of Mathematical Sciences Faculty Publications

Appropriate spatiotemporal interpolation is critical to the assessment of relationships between environmental exposures and health outcomes. A powerful assessment of human exposure to environmental agents would incorporate spatial and temporal dimensions simultaneously. This paper compares shape function (SF)-based and inverse distance weighting (IDW)-based spatiotemporal interpolation methods on a data set of PM_2.5 data in the contiguous U.S. Particle pollution, also known as particulate matter (PM), is composed of microscopic solids or liquid droplets that are so small that they can get deep into the lungs and cause serious health problems. PM_2.5 refers to particles with a mean aerodynamic …

Partial Differential Equations And Function Spaces, Shijun Zheng, Simone Secchi, Huoxiong Wu, Nguyen Cong Phuc

Department of Mathematical Sciences Faculty Publications

It is well known that PDEs and the theory of function spaces have played a central role in the mathematical analysis of problems arising from mathematical physics, biology, and other branches of modern applied sciences. This special issue addresses the current advances in these two broad areas; in particular it focuses on the connections and interactions between them. We are happy that this issue has received the attention of active researchers with interesting and valuable contributions in the field. Topics cover areas from existence and nonexistence theorems for degenerate differential operators to multilinear fractional singular integral operators on weighted function …

Example Of An Order 16 Non Symplectic Action On A K3 Surface, Jimmy J. Dillies

Department of Mathematical Sciences Faculty Publications

We exhibit an example of a K3 surface of Picard rank 14 with a non-symplectic automorphism of order 16 which fixes a rational curve and 10 isolated points. This settles the existence problem for the last case of Al Tabbaa, Sarti and Taki's classification.

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.

Using Ipads And Video-Based Instruction To Teach Algebra To High School Students With Disabilities, Elias Clinton, Tom J. Clees

National Youth Advocacy and Resilience Conference

This presentation targets a study in which four high school students with disabilities were taught to solve algebraic equations using iPads and video-based instruction. All students showed immediate increases in accurate responding following the introduction of the video-based intervention. This presentation provides practitioners with a flexible technology-based intervention for students with disabilities in need of grade-level academic instruction. The intervention could be used across a variety of subjects and academic tasks.

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.

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.

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 …

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 …

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 …