Mathematics Commons^™

Consensus-Type Stochastic Approximation Algorithms, Yu Sun

Wayne State University Dissertations

This work is concerned with asymptotic properties of consensus-type algorithms for networked systems whose topologies switch randomly. The regime-switching process is modeled as a discrete-time Markov chain with a nite state space. The consensus control is achieved by designing stochastic approximation algorithms. In the setup, the regime-switching process (the Markov chain) contains a rate parameter

"Ε> 0 in the transition probability matrix that characterizes how frequently the topology switches. On the other hand, the consensus control algorithm uses a step-size Μ that denes how fast the network states are updated. Depending on their relative values, three distinct scenarios emerge. Under …

Note On Hilbert-Type Inequalities, Predrag Vukovic

Turkish Journal of Mathematics

The main objective of this paper is to prove Hilbert-type and Hardy-Hilbert-type inequalities with a general homogeneous kernel, thus generalizing a result obtained in [Namita Das and Srinibas Sahoo, A generalization of multiple Hardy-Hilbert's integral inequality, Journal of Mathematical Inequalities, 3(1), (2009), 139--154].

An Oscillation Theorem For Second-Order Nonlinear Differential Equations Of Euler Type, Asadollah Aghajani, Vahid Roomi

Turkish Journal of Mathematics

We consider the nonlinear equation t^2x'' + g(x) = 0, where g(x) satisfies xg(x) > 0 for x \ne 0, but is not assumed to be sublinear or superlinear. We study the problem whether all nontrivial solutions of the equation are oscillatory in some critical cases.

A Generalization Of Banach's Contraction Principle For Some Non-Obviously Contractive Operators In A Cone Metric Space, Yingxin Guo

Turkish Journal of Mathematics

This paper investigates the fixed points for self-maps of a closed set in a space of abstract continuous functions. Our main results essentially extend and generalize some fixed point theorems in cone metric spaces. An application to differential equations is given.

Warped Product Submanifolds Of A Kenmotsu Manifold, Siraj Uddin, Viqar Azam Khan, Khalid Ali Khan

Turkish Journal of Mathematics

In the present paper, we study warped product semi-slant submanifolds of a Kenmotsu manifold. We obtain some results on the existence of such type warped product submanifolds of a Kenmotsu manifold with an example.

Geodesicity And Isoclinity Properties For The Tangent Bundle Of The Heisenberg Manifold With Sasaki Metric, Simona Luiza Druta, Paola Piu

Turkish Journal of Mathematics

We prove that the horizontal and vertical distributions of the tangent bundle with the Sasaki metric are isocline, the distributions given by the kernels of the horizontal and vertical lifts of the contact form \omega on the Heisenberg manifold (H_3,g) to (TH_3,g^S) are not totally geodesic, and the distributions F^H=L(E_1^H,E_2^H) and F^V=L(E_1^V,E_2^V) are totally geodesic, but they are not isocline. We obtain that the horizontal and natural lifts of the curves from the Heisenberg manifold (H_3,g), are geodesics on the tangent bundle endowed with the Sasaki metric (TH_3,g^s), if and only if the curves considered on the base manifold are …

Eulerian Polynomials And B-Splines, Tian-Xiao He

Scholarship

Here presented is the interrelationship between Eulerian polynomials, Eulerian fractions and Euler-Frobenius polynomials, Euler-Frobenius fractions, B-splines, respectively. The properties of Eulerian polynomials and Eulerian fractions and their applications in B-spline interpolation and evaluation of Riemann-zeta function values at odd integers are given. The relation between Eulerian numbers and B-spline values at knot points are also discussed.

Testing Irreducibility Of Trinomials Over Gf(2), Steven Hayman

Honors Projects

The focus of this paper is testing the irreducibility of polynomials over finite fields. In particular there is an emphasis on testing trinomials over the finite field GF(2). We also prove a the probability of a trinomial satisfying Swan's theorem is asymptotically 5/8 as n goes to infinity.

Effects Of Visual, Auditory, And Kinesthetic Imagery Interventions On Dancers’ Plié Arabesques, Teresa Heiland, Robert Rovetti

Mathematics, Statistics and Data Science Faculty Works

The goal of this study was to examine the influence of visual, auditory, and kinesthetic delivery modes of Franklin Method images (anatomical bone rhythms, metaphorical image, and tactile aid, respectively) on the performance of college dancers’ Plié Arabesques by assessing its influence on three measures: plié depth; maintenance of rotation; and simultaneous use of hip, knee, and ankle (Tri-fold). Eighteen participants performed a series of Plié Arabesques during three visits over a period of two months; at each visit, pliés were performed before and after an image intervention, and the change in mean Likert scale rating was calculated for each …

Tensor Products Of Vector Seminormed Spaces, John William Dever

Electronic Theses and Dissertations

A vector seminormed space is a triple consisting of a vector space, a Dedekind complete Riesz space, and a vector valued seminorm, called a vector seminorm, defined on the vector space and taking values in the Riesz space. The collection of vector seminormed spaces with suitably defined morphisms is shown to be a category containing finite products. A theory of vector seminorms on the tensor products of vector seminormed spaces is developed in analogy with the theory of tensor products of Banach spaces. Accordingly, a reasonable cross vector seminorm, or simply tensor seminorm, is defined such that a vector seminorm …

Characterizations Of Zero Divisor Graphs Determined By Equivalence Classes Of Zero Divisors, Amanda Catherine Acosta

Electronic Theses and Dissertations

We study zero divisor graphs of commutative rings determined by equivalence classes of zero divisors, specifically for a Noetherian ring R. We study the classification of these graphs. Specifically, we add more criteria to the list of characterizations that disqualify a graph as the zero divisor graph of a ring. We also briefly discuss Sage, a mathematical software, which was an aid in providing visual pictures for the graphs under study.

New Results In Finite Geometries Pertaining To Albert-Like Semifields, Angela Michelle Brown

Mathematics Dissertations - Archive

One of the most widely studied class of semifields are the generalized twisted fields defined by Albert in the 50s and 60s. The collineation groups of generalized twisted field planes have been completely described. In a series of papers Cordero and Figueroa studied semifields with an autotopism that acts transitively on one side of the autotopism triangle, equivalently the plane admits an autotopism which induces a permutation on a side of the autotopism triangle of order a p-primitive divisor of pr - 1. They showed that with some minor exceptions the plane is a generalized twisted field plane. These planes …

Composition Operators On A Class Of Analytic Function Spaces Related To Brennan's Conjecture, Valentin Matache, Wayne Smith

Mathematics Faculty Publications

Brennan’s conjecture in univalent function theory states that if τ is any analytic univalent transform of the open unit disk D onto a simply connected domain G and −1/3 < p < 1, then 1/(τ′) p belongs to the Hilbert Bergman space of all analytic square integrable functions with respect to the area measure. We introduce a class of analytic function spaces L2a(μp) on G and prove that Brennan’s conjecture is equivalent to the existence of compact composition operators on these spaces for every simply connected domain G and all p∈(−1/3,1) . Motivated by this result, we study the boundedness and compactness of composition operators in this setting.

On Projection-Invariant Subgroups Of Abelian P-Groups, Brendan Goldsmith

Articles

A subgroup P of an Abelian p-group G is said to be projection-invariant in G if Pf is contained in P for all idempotent endomorphisms f. Clearly fully invariant subgroups are projection invariant, but the converse is not true in general. Hausen and Megibben have shown that in many familiar situations these two concepts coincide. In a different direction, the authors have previously introduced the notions of socle-regular and strongly socle-regular groups by focussing on the socles of fully invariant and characteristic subgroups of p-groups. In the present work the authors examine the socles of projection-invariant subgroups of Abelian p-groups.

An Immersed Interface Method For A 1d Poroelasticity Problem With Discontinuous Coefficients, Maranda Lee Bean

Open Access Theses & Dissertations

Poroelastic models deal with the coupling of changes in stress and fluid pressure in some porous medium. For physical reasons, some of the coefficients used in the models may have discontinuities. This project focuses on applying the immersed interface method to the one dimensional Biot model, in order to handle these discontinuities. This method is applied on a staggered grid. Using the immersed interface method allows us to alter only a small number of irregular grid points surrounding a discontinuity. For most of the grid points, a standard finite difference method is used. However at the irregular grid points, the …

Analysis Of Intermittence And Log-Periodicity Of Foreign Exchange Rates Near A Crash, Arturo Casillas

Open Access Theses & Dissertations

Many believe that financial indices near a crash exhibit a type of critical point characterized by log-periodic signatures. Models have been developed based on these ideas in an attempt to mathematically characterize financial data about to crash. Few of these models consider the property of intermittency. Intermittency is a concept borrowed from fluid dynamics that essentially implies that a system alternates between a stable, or predictable, state and unstable state. One model that attempts to characterize crashes incorporates intermittency in the form of log-stationary intervals. It models the asset price as a step function that follows an underlying power law. …

A Generalized Cholera Model And Epidemic-Endemic Analysis, Jin Wang, Shu Liao

Mathematics & Statistics Faculty Publications

The transmission of cholera involves both human-to-human and environment-to-human pathways that complicate its dynamics. In this paper, we present a new and unified deterministic model that incorporates a general incidence rate and a general formulation of the pathogen concentration to analyse the dynamics of cholera. Particularly, this work unifies many existing cholera models proposed by different authors. We conduct equilibrium analysis to carefully study the complex epidemic and endemic behaviour of the disease. Our results show that despite the incorporation of the environmental component, there exists a forward transcritical bifurcation at R₀ = 1 for the combined human-environment epidemiological …

Set Ideal Topological Spaces, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors for the first time introduce a new type of topological spaces called the set ideal topological spaces using rings or semigroups, or used in the mutually exclusive sense. This type of topological spaces use the class of set ideals of a ring (semigroups). The rings or semigroups can be finite or infinite order. By this method we get complex modulo finite integer set ideal topological spaces using finite complex modulo integer rings or finite complex modulo integer semigroups. Also authors construct neutrosophic set ideal toplogical spaces of both finite and infinite order as well as …

Homogeneous Besov Spaces On Stratified Lie Groups And Their Wavelet Characterization, Hartmut Fuhr, Azita Mayeli

Publications and Research

We establish wavelet characterizations of homogeneous Besov spaces on stratified Lie groups, bothin terms of continuous and discrete wavelet systems. We first introduce a notion of homogeneous Besov space ̇Bsp,qin terms of a Littlewood-Paley-type decomposition, in analogy to the well-known characterization of the Euclidean case. Such decompositions can be defined via the spectral measure of a suitably chosen sub-Laplacian. We prove that the scale of Besov spaces is independent of the precise choice of Littlewood-Paley decomposition. In particular, different sub-Laplacians yield the same Besov spaces. We then turn to wavelet characterizations, first via continuous wavelet transforms which can be viewed …

Equivariant Degenerations Of Spherical Modules For Groups Of Type A, Stavros Argyrios Papadakis, Bart Van Steirteghem

Publications and Research

Let G be a complex reductive algebraic group. Fix a Borel subgroup B of G and a maximal torus T in B. Call the monoid of dominant weights L+ and let S be a finitely generated submonoid of L+. V. Alexeev and M. Brion introduced a moduli scheme MS which classifies affine G-varieties X equipped with a T-equivariant isomorphism SpecC[X]U → SpecC[S], where U is the unipotent radical of B. Examples of MS have been obtained by S. Jansou, P. Bravi and S. Cupit-Foutou. In this paper, we prove that MS is isomorphic to an affine space when S is …