Mathematics Commons^™

Large Deviations Of Stochastic Systems And Applications, Qi He

Wayne State University Dissertations

This dissertation focuses on large deviations of stochastic systems with applications to optimal control and system identification. It encompasses analysis of two-time-scale Markov processes and system identification with regular and quantized data. First, we develops large deviations principles for systems driven by continuous-time Markov chains with twotime scales and related optimal control problems. A distinct feature of our setup is that the Markov chain under consideration is time dependent or inhomogeneous. The use of two time-scale formulation stems from the effort of reducing computational complexity in a wide variety of applications in control, optimization, and systems theory. Starting with a …

Subspace Segmentation And High-Dimensional Data Analysis, Ali Safak Sekmen

Computer Science Faculty Research

This thesis developed theory and associated algorithms to solve subspace segmentation problem. Given a set of data W={w_1,...,w_N} in R^D that comes from a union of subspaces, we focused on determining a nonlinear model of the form U={S_i}_{i in I}, where S_i is a set of subspaces, that is nearest to W. The model is then used to classify W into clusters. Our first approach is based on the binary reduced row echelon form of data matrix. We prove that, in absence of noise, our approach can find the number of subspaces, their dimensions, and an orthonormal basis for each …

Applications Of Extenics To 2d-Space And 3d-Space, Florentin Smarandache, Victor Vladareanu

Branch Mathematics and Statistics Faculty and Staff Publications

In this article one proposes several numerical examples for applying the extension set to 2D- and 3D-spaces. While rectangular and prism geometrical figures can easily be decomposed from 2D and 3D into 1D linear problems, similarly for the circle and the sphere, it is not possible in general to do the same for other geometrical figures.

The Generalised Zakharov-Shabat System And The Gauge Group Action, Georgi Grahovski

Articles

The generalized Zakharov-Shabat systems with complex-valued non-regular Cartan elements and the systems studied by Caudrey, Beals and Coifman (CBC systems) and their gauge equivalent are studied. This study includes: the properties of fundamental analytical solutions (FAS) for the gauge-equivalent to CBC systems and the minimal set of scattering data; the description of the class of nonlinear evolutionary equations, solvable by the inverse scattering method, and the recursion operator, related to such systems; the hierarchies of Hamiltonian structures. The results are illustrated on the example of the multi-component nonlinear Schrodinger (MNLS) equations and the corresponding gauge-equivalent multi-component Heisenberg ferromagnetic (MHF) type …

Various Characterizations Of Modified Weibull And Log Modified Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the well-known modified Weibull and log-modified Weibull distributions are presented. These characterizations are based on a simple relationship between two truncated moments; on the hazard function and on functions of the order statistics.

"Our Research Was Centered On Whether Or Not The Following Changes Made To The Pre-Calculus Algebra Class Positively Affected Student Performance…", Andrea Winchester

Summer Community of Scholars Posters (RCEU and HCR Combined Programs)

No abstract provided.

Math Department Newsletter, 2011-2012 (Year In Review), Mathematics Department

Mathematics Newsletter

No abstract provided.

The History Of Maxwell's Equations, Lindsay Guilmette (Class Of 2012)

Writing Across the Curriculum

An enormous amount of technology is owed to Maxwell's theory of electromagnetism and his perseverance through cultural obstacles to advocate his talent of mathematical interpretation.

Mathematical Competitions In Hungary: Promoting A Tradition Of Excellence & Creativity, Julianna Connelly Stockton

Mathematics Faculty Publications

Hungary has long been known for its outstanding production of mathematical talent. Extracurricular programs such as camps and competitions form a strong foundation within the Hungarian tradition. New types of competitions in recent years include team competitions, multiple choice competitions, and some exclusively for students who are not in a special mathematics class. This study explores some of the recent developments in Hungarian mathematics competitions and the potential implications these changes have for the very competition-driven system that currently exists. The founding of so many new competitions reflects a possible shift in the focus and purpose of competitions away from …

Abelian Groups With Partial Decomposition Bases In LΔ∞Ω, Part Ii, Carol Jacoby, Peter Loth

Mathematics Faculty Publications

We consider abelian groups with partial decomposition bases in L^δ_∞ω for ordinals δ. Jacoby, Leistner, Loth and Str¨ungmann developed a numerical invariant deduced from the classical global Warfield invariant and proved that if two groups have identical modified Warfield invariants and Ulm-Kaplansky invariants up to ωδ for some ordinal δ, then they are equivalent in L^δ_∞ω. Here we prove that the modified Warfield invariant is expressible in L^δ_∞ω and hence the converse is true for appropriate δ.

Finite Factors Of Bernoulli Schemes And Distinguishing Labelings Of Directed Graphs, Andrew Lazowski, Stephen M. Shea

Mathematics Faculty Publications

A labeling of a graph is a function from the vertices of the graph to some finite set. In 1996, Albertson and Collins defined distinguishing labelings of undirected graphs. Their definition easily extends to directed graphs. Let G be a directed graph associated to the k -block presentation of a Bernoulli scheme X . We determine the automorphism group of G , and thus the distinguishing labelings of G . A labeling of G defines a finite factor of X . We define demarcating labelings and prove that demarcating labelings define finitarily Markovian finite factors of X . We use …

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].

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 …

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 …

Secrecy Logic: S-Secrecy Structures, George Voutsadakis

Turkish Journal of Mathematics

Let S = \lan L,\vdash_S\ran be a deductive system. An S-secrecy logic is a quadruple K = \lan Fm_L(V),K,B,S\ran, where Fm_L(V) is the algebra of L-formulas, K,B are S-theories, with B \subseteq K and S \subseteq K such that S \cap B = \emptyset. K corresponds to information deducible from a knowledge base, B to information deducible from the publicly accessible (or browsable) part of the knowledge base and S is a secret set, a set of sensitive or private information that the knowledge base aims at concealing from its users. To provide models for this context, the notion of …

Product Of Graded Submodules, Ameer Jaber

Turkish Journal of Mathematics

Let \Delta be an abelian group. By considering the notion multiplication of \Delta-graded modules (see [7]) over a commutative \Delta-graded ring with unity, we introduce the notion of product of two \Delta-graded submodules which we use to characterize the \Delta-graded prime submodules of a multiplication \Delta-graded module. Finally we proved a graded version of Nakayama lemma for multiplication \Delta-graded modules.

The Character Variety Of A Class Of Rational Links, Khaled Qazaqzeh

Turkish Journal of Mathematics

Let G_n be the fundamental group of the exterior of the rational link C(2n) in Conway's normal form, see [7]. A presentation for G_n is given by \langle a, b (ab)^n = (ba)^n\rangle [3, Thm. 2.2]. We study the character variety in SL(2, C) of the group G_n. In particular, we give the defining polynomial of the character variety of G_n. As an application, we show a well-known result that G_n and G_m are isomorphic only when n = m. Also as a consequence of the main theorem of this paper, we give a basis of the Kauffman bracket skein …