Mathematics Commons^™

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

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 …

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

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

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

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

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.

Restricted Sum Formula Of Alternating Euler Sums, Jianqiang Zhao

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 ) …

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

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 …

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

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 …

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

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.

Density Of Gallai Multigraphs, Colton Magnant

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.

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 …

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, 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, 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, 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, …

A Family Of Multiple Harmonic Sum And Multiple Zeta Star Value Identities, Erin Linebarger, Jianqiang Zhao

Mathematical Sciences: Faculty Publications

In this paper we present a new family of identities for multiple harmonic sums which generalize a recent result of Hessami Pilehrood et al [Trans. Amer. Math. Soc. (to appear)]. We then apply it to obtain a family of identities relating multiple zeta star values to alternating Euler sums. In such a typical identity the entries of the multiple zeta star values consist of blocks of arbitrarily long 2-strings separated by positive integers greater than two while the largest depth of the alternating Euler sums depends only on the number of 2-string blocks but not on their lengths.

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

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 …

New Families Of Weighted Sum Formulas For Multiple Zeta Values, Yuan Zhao, Jianqiang Zhao

Mathematical Sciences: Faculty Publications

In this paper we use the generating functions and the double shuffle relations satisfied by the multiple zeta values to derive some new families of identities.

Primary Spaces, Mackey's Obstruction, And The Generalized Barycentric Decomposition, Patrick Iglesias-Zemmour, Francois Ziegler

Mathematical Sciences: Faculty Publications

We call a hamiltonian N-space primary if its moment map is onto a single coadjoint orbit. The question has long been open whether such spaces always split as (homogeneous) x (trivial), as an analogy with representation theory might suggest. For instance, Souriau's barycentric decomposition theorem asserts just this when N is a Heisenberg group. For general N, we give explicit examples which do not split, and show instead that primary spaces are always flat bundles over the coadjoint orbit. This provides the missing piece for a full "Mackey theory" of hamiltonian G-spaces, where G is an overgroup in which N …

Properly Colored Notions Of Connectivity - A Dynamic Survey, Xueliang Li, Colton Magnant

Mathematical Sciences: Faculty Publications

Sheehan conjectured in 1975 that every Hamiltonian regular simple graph of even degree at least four contains a second Hamiltonian cycle. We prove that most claw-free Hamiltonian graphs with minimum degree at least 3 have a second Hamiltonian cycle and describe the structure of those graphs not covered by our result. By this result, we show that Sheehan’s conjecture holds for claw-free graphs whose order is not divisible by 6. In addition, we believe that the structure that we introduce can be useful for further studies on claw-free graphs.

Second Hamiltonian Cycles In Claw-Free Graphs, Hossein Esfandiari, Colton Magnant, Pouria Salehi Nowbandegani, Shirdareh Haghighi

Mathematical Sciences: Faculty Publications

Sheehan conjectured in 1975 that every Hamiltonian regular simple graph of even degree at least four contains a second Hamiltonian cycle. We prove that most claw-free Hamiltonian graphs with minimum degree at least 3 have a second Hamiltonian cycle and describe the structure of those graphs not covered by our result. By this result, we show that Sheehan’s conjecture holds for claw-free graphs whose order is not divisible by 6. In addition, we believe that the structure that we introduce can be useful for further studies on claw-free graphs.

Functions On Adjacent Vertex Degrees Of Trees With Given Degree Sequence, Hua Wang

Mathematical Sciences: Faculty Publications

In this note we consider a discrete symmetric function f(x, y) where f(x; a) + f(y, b) ≥ f(y, a) + f(x, b) for any x ≥ y and a ≥ b, associated with the degrees of adjacent vertices in a tree. The extremal trees with respect to the corresponding graph invariant, defined as Σ _uv∈E(T) f(deg(u), deg(v)), are characterized by the “greedy tree” and “alternating greedy tree”. This is achieved through simple generalizations of previously used ideas on similar questions. As special cases, the already known extremal structures of the Randić index follow as corollaries. The extremal structures for …

Symplectic Mackey Theory, Francois Ziegler

Mathematical Sciences: Faculty Publications

Many years ago Kazhdan, Kostant and Sternberg defined the notion of inducing a hamiltonian action from a Lie subgroup. In this paper, we develop the attendant imprimitivity theorem and Mackey analysis in the full generality needed to deal with arbitrary closed normal subgroups.

Synthetic Lethality As A Promising Approach For Targeted Cancer Prevention, Wei Tu, Hua Wang, Guang Peng

Mathematical Sciences: Faculty Publications

Carcinogenesis is recognized as a multistep process. It occurs over a relative long span of time, which offers intervention opportunities for cancer prevention [1] . Using drugs to prevent cancer rather than treat cancer is the major research goal in the field of ‘chemoprevention’. Tremendous research efforts have been devoted toward using natural, synthetic or biological agents to prevent, suppress or delay the initiation and or the progression of premalignant cells to cancer [1] . However a big challenge for effective cancer prevention is to identify chemoprevention agents with demonstrable efficacy and safety for healthy general …

Fast Inverse Distance Weighting-Based Spatiotemporal Interpolation: A Web-Based Application Of Interpolating Daily Fine Particulate Matter Pm2.5 In The Contiguous U.S. Using Parallel Programming And K-D Tree, Lixin Li, Travis Losser, Charles Yorke, Reinhard E. Piltner

Mathematical Sciences: Faculty Publications

Epidemiological studies have identified associations between mortality and changes in concentration of particulate matter. These studies have highlighted the public concerns about health effects of particulate air pollution. Modeling fine particulate matter PM2.5exposure risk and monitoring day-to-day changes in PM2.5 concentration is a critical step for understanding the pollution problem and embarking on the necessary remedy. This research designs, implements and compares two inverse distance weighting (IDW)-based spatiotemporal interpolation methods, in order to assess the trend of daily PM2.5 concentration for the contiguous United States over the year of 2009, at both the census block group level and county level. …

Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva, James P. Braselton

Mathematical Sciences: Faculty Publications

Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator-prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.

Fejér And Suffridge Polynomials In The Delayed Feedback Control Theory, Dmitriy Dmitrishin, Anna Khamitova, Anatolii Korenovskyi, Alexander M. Stokolos

Mathematical Sciences: Faculty Publications

A remarkable connection between optimal delayed feedback control (DFC) and complex polynomial mappings of the unit disc is established. The explicit form of extremal polynomials turns out to be related with the Fejer polynomials. The constructed DFC can be used to stabilize cycles of one-dimensional non-linear discrete systems.

Existence Of Positive Solutions For P(X)-Laplacian Equations With A Singular Nonlinear Term, Jingjing Liu, Qihu Zhang, Chunshan Zhao

Mathematical Sciences: Faculty Publications

In this article, we study the existence of positive solutions for the p(x)-Laplacian Dirichlet problem −∆_p(x)u = λf(x, u) in a bounded domain Ω ⊂ R^N. The singular nonlinearity term f is allowed to be either f(x, s) → +∞, or f(x, s) → +∞ as s → 0+ for each x ∈ Ω. Our main results generalize the results in [15] from constant exponents to variable exponents. In particular, we give the asymptotic behavior of solutions of a simpler equation which is useful for finding supersolutions of differential equations with variable exponents, which is of independent …

Generalizations Of The Inverse Weibull And Related Distributions With Applications, Broderick O. Oluyede, Tao Yang

Mathematical Sciences: Faculty Publications

In this paper, the generalized inverse Weibull distribution including the exponentiated or proportional reverse hazard and Kumaraswamy generalized inverse Weibull distributionsare presented. Properties of these distributions including the behavior of the hazard and reverse hazard functions, moments, coefficients of variation, skewness, andkurtosis, entropy, Fisher information matrix are studied. Estimates of the model parameters via method of maximum likelihood (ML), and method of moments (MOM) are presented for complete and censored data. Numerical examples are also presented.

Localized Quantum States, Francois Ziegler

Mathematical Sciences: Faculty Publications

Let X be a symplectic manifold and Aut(L) the automorphism group of a Kostant-Souriau line bundle on X. *Quantum states for X*, as defined by J.-M. Souriau in the 1990s, are certain positive-definite functions on Aut(L) or, less ambitiously, on any "large enough" subgroup G of Aut(L). This definition has two major drawbacks: when G=Aut(L) there are no known examples; and when G is a Lie subgroup the notion is, as we shall see, far from selective enough. In this paper we introduce the concept of a quantum state *localized at Y*, where Y is a coadjoint orbit of a …