Physical Sciences and Mathematics Commons^™

Renewal Theory For Uniform Random Variables, Steven Robert Spencer

Theses Digitization Project

This project will focus on finding formulas for E[N(t)] using one of the classical problems in the discipline first, and then extending the scope of the problem to include overall times greater than the time t in the original problem. The expected values in these cases will be found using the uniform and exponential distributions of random variables.

Egyptian Fractions, Jodi Ann Hanley

Theses Digitization Project

Egyptian fractions are what we know as unit fractions that are of the form 1/n - with the exception, by the Egyptians, of 2/3. Egyptian fractions have actually played an important part in mathematics history with its primary roots in number theory. This paper will trace the history of Egyptian fractions by starting at the time of the Egyptians, working our way to Fibonacci, a geologist named Farey, continued fractions, Diophantine equations, and unsolved problems in number theory.

Variables Related To The Successful Completion Of The First Course In Business Calculus At Three Jamaican Universities, Martin Nkhrama Richards

Dissertations

Problem. Many students at all levels of the education system in Jamaica perform poorly at mathematics. In particular, the results of both the Caribbean Examinations Council and Business Calculus 1 at the university level have reflected a declining trend in mathematics performance in recent years. Consequently, this study sought to investigate the variables related to the successful completion of the first course in business calculus at Jamaican universities. To this end, the study looked at perceptions of students and their professors regarding students' cognitive, affective, and professor effectiveness variables impacting success.

Method. The sample for this study consisted of 389 …

The Evolution Of Cell Colonies In Volvocacean Algae : Investigation By Theoretical Analysis And Computer Simulation., Frank Noe

Theses

This thesis presents a mathematical analysis and computational simulation which is used to investigate the evolution of cell colonies. The evolutionary transition from unicellular to cell colony form is a prerequesite for multicellular life as it exists abundantly on earth. This transition has occured numerous times independently so that we expect a high selective advantage to be associated with it. The photosynthetic green algae order Volvocaceae is an appropriate set of model organisms for the study of the evolution of cell colonies since it comprises living unicellular organisms, cell colonies, and multicellular organisms of different shapes, sizes and levels of …

N-Commutator Groups, A. A. Mehrvarz, K. Azizi

Turkish Journal of Mathematics

A sufficient condition such that any element of G' (the commutator subgroup of G) can be represented as a product of n commutators, was studied in \cite{GAL62}. In this article we study a necessary and sufficient condition such that any element of G' can be represented as a product of n commutators, Let n be the smallest nature number such that any element of finite group G can be represented as a product of n commutators. A group G with this property will be called an n -commutator group, and n will be denoted by c(G) . Then \frac{\ln( G' …

A Macwilliams Type Identity, İrfan Şi̇ap

Turkish Journal of Mathematics

A MacWilliams identity for a \rho complete weight enumerator of linear spaces of matrices with entries from the ring F_q[u]/(u^r-a), where a \in F_q, endowed with a non-Hamming metric is proved.

Analytically Continued Hypergeometric Expression Of The Incomplete Beta Function, Jack C. Straton

Physics Faculty Publications and Presentations

The Incomplete Beta Function is rewritten as a Hypergeometric Function that is the analytic continuation of the conventional form, a generalization of the finite series, which simpifies the Stieltjes transform of powers of a monomial divided by powers of a binomial.

Numerical Solution And Convergence Speed Of Variational Formulation For Linear Schrödinger Equation, Murat Subaşi, Bünyami̇n Yildiz

Turkish Journal of Mathematics

This paper presents a numerical solution of an optimal control problem for linear parabolic equations. The estimates for the error of the difference scheme and the speed of convergence have been established. Numerical results are reported on test problems.

On Summand Sum And Summand Intersection Property Of Modules, Mustafa Alkan, Abdullah Harmanci

Turkish Journal of Mathematics

R will be an associative ring with identity and modules M will be unital left R- modules. In this work, extending modules and lifting modules with the SSP (or SIP) are studied. A necessary and sufficient condition for a module M to have the SSP is that for every decomposition M = A\oplus B and f\in Hom(A,B), Im(f) is a direct summand of B. Among others it is shown also that a (C_3) module with the SIP has the SSP, and a (D_3) module with SSP has the SIP.

Asymptotic Formulas For The Eigenvalues Of The Schrodinger Operator, Şi̇ri̇n Atilgan, Sedef Karakiliç, Oktay A. Veliev

Turkish Journal of Mathematics

In this paper, we obtain asymptotic formulas for the eigenvalues of the d-dimensional Schrodinger operator L=-\Delta +q(x) in d-dimensional parallelepiped F with Dirichlet and Neumann boundary conditions.

Remarks On Bounded Operators In Köthe Spaces, P. B. Djakov, T. Terzi̇oğlu, M. Yurdakul, V. P. Zahariuta

Turkish Journal of Mathematics

We prove that if \lambda(A),\lambda(B) and \lambda(C) are Köthe spaces such that L(\lambda(A),\lambda(B)) and L(\lambda(C),\lambda(A)) consist of bounded operators then each operator acting on \lambda(A) that factors over \lambda(B)\widehat\otimes_{\pi} \lambda(C) is bounded.

Vaccination Strategies And Backward Bifurcation In Age-Since-Infection Structured Model, Christopher Kribs, Maia Martcheva

Mathematics Faculty Publications

We consider models for a disease with acute and chronic infective stages, and variable infectivity and recovery rates, within the context of a vaccination campaign. Models for SIRS and SIS disease cycles exhibit backward bifurcations under certain conditions, which complicate the criteria for success of the vaccination campaign by making it possible to have stable endemic states when R0 < 1. We also show the extent to which the forms of the infectivity and recovery functions affect the possibility of backward bifurcations. SIR and SI models examined do not exhibit this behavior.

Transverse Group Actions On Bundles, Ian M. Anderson, Mark E. Fels

Mathematics and Statistics Faculty Publications

An action of a Lie group G on a bundle is said to be transverse if it is projectable and if the orbits of G on E are diffeomorphic under π to the orbits of G on M. Transverse group actions on bundles are completely classified in terms of the pullback bundle construction for G-invariant maps. This classification result is used to give a full characterization of the G invariant sections of E for projectable group actions.

Nonparametric Estimation Of A Distribution Subject To A Stochastic Precedence Constraint, Miguel A. Arcones, Paul H. Kvam, Francisco J. Samaniego

Department of Math & Statistics Faculty Publications

For any two random variables X and Y with distributions F and G defined on [0,∞), X is said to stochastically precede Y if P(X≤Y) ≥ 1/2. For independent X and Y, stochastic precedence (denoted by X≤_spY) is equivalent to E[G(X–)] ≤ 1/2. The applicability of stochastic precedence in various statistical contexts, including reliability modeling, tests for distributional equality versus various alternatives, and the relative performance of comparable tolerance bounds, is discussed. The problem of estimating the underlying distribution(s) of experimental data under the assumption that they obey a …

Proceedings Of The First International Conference On Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability And Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In 1960s Abraham Robinson has developed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, that rigorously defines the infinitesimals. Informally, an infinitesimal is an infinitely small number. Formally, x is said to be infinitesimal if and only if for all positive integers n one has xxx < 1/n. Let &>0 be a such infinitesimal number. The hyper-real number set is an extension of the real number set, which includes classes of infinite numbers and classes of infinitesimal numbers. Let’s consider the non-standard finite numbers 1+ = 1+&, where “1” is its standard part and “&” its non-standard part, …

Randomness And Optimal Estimation In Data Sampling, Florentin Smarandache, Mohammad Khosnevisan, Housila P. Singh, S Saxena, Sarjinder Singh

Branch Mathematics and Statistics Faculty and Staff Publications

The purpose of this book is to postulate some theories and test them numerically. Estimation is often a difficult task and it has wide application in social sciences and financial market. In order to obtain the optimum efficiency for some classes of estimators, we have devoted this book into three specialized sections: Part 1. In this section we have studied a class of shrinkage estimators for shape parameter beta in failure censored samples from two-parameter Weibull distribution when some 'apriori' or guessed interval containing the parameter beta is available in addition to sample information and analyses their properties. Some estimators …

Modal Predicates And Coequations, Alexander Kurz, Jiří Rosický

Engineering Faculty Articles and Research

We show how coalgebras can be presented by operations and equations. This is a special case of Linton’s approach to algebras over a general base category X, namely where X is taken as the dual of sets. Since the resulting equations generalise coalgebraic coequations to situations without cofree coalgebras, we call them coequations. We prove a general co-Birkhoff theorem describing covarieties of coalgebras by means of coequations. We argue that the resulting coequational logic generalises modal logic.

Flow Patterns In A Two-Roll Mill, Christopher Hills

Articles

The two-dimensional flow of a Newtonian fluid in a rectangular box that contains two disjoint, independently-rotating, circular boundaries is studied. The flow field for this two-roll mill is determined numerically using a finite-difference scheme over a Cartesian grid with variable horizontal and vertical spacing to accommodate satisfactorily the circular boundaries. To make the streamfunction numerically determinate we insist that the pressure field is everywhere single-valued. The physical character, streamline topology and transitions of the flow are discussed for a range of geometries, rotation rates and Reynolds numbers in the underlying seven-parameter space. An account of a preliminary experimental study of …

Some Irrational Generalised Moonshine From Orbifolds, Rossen Ivanov, Michael Tuite

Articles

We verify the Generalised Moonshine conjectures for some irrational modular functions for theMonster centralisers related to the Harada-Norton, Held, M12 and L3(3) simple groups based on certain orbifolding constraints. We find explicitly the fixing groups of the hauptmoduls arising in each case.

Rational Generalized Moonshine From Abelian Orbifoldings Of The Moonshine Module, Rossen Ivanov, Michael Tuite

Articles

We consider orbifoldings of the Moonshine Module with respect to the abelian group generated by a pair of commuting Monster group elements with one of prime order p = 2, 3, 5, 7 and the other of order pk for k = 1 or k prime. We show that constraints arising from meromorphic orbifold conformal field theory allow us to demonstrate that each orbifold partition function with rational coefficients is either constant or is a hauptmodul for an explicitly found modular fixing group of genus zero. We thus confirm in the cases considered the Generalised Moonshine conjectures for all rational …

Preface, Alexander Kurz

Engineering Faculty Articles and Research

No abstract provided.

Asymptotic Analysis Of Singularly Perturbed Abstract Evolution Equations In Banach And Hilbert Spaces, Dialla Konate

Turkish Journal of Mathematics

In the current paper, we are concerned with the study of abstract linear evolution equations in Banach spaces in which the time derivative term is multiplied by a small parameter, say \epsilon. Such equations arise in the study of radiative transfer and neutron transport in Nuclear Physics. Following works by Krein (cf [9]) and others, Mika (cf [12,13,14,15]) using either the Hilbert method or the Compressed method has shown that the solution of the given singularly perturbed equation may be approximated upto any prescibed order by a sum of two asymptotic expansions that are the outer expansion that is valid …

The Fine Spectra Of The Rhaly Operators On C_{0}, Mustafa Yildirim

Turkish Journal of Mathematics

In 1975, Wenger [3] determined the fine spectra of Cesàro operator C_{1} on c, the space of convergent sequences. In [6], the spectrum of the Rhaly operators on c_{0} and c, under the assumption that {\displaystyle\lim_{n \rightarrow \infty}(n+1)a_{n} }=L\neq 0, has been determined. This paper presents the fine spectra of the Rhaly matrix R_{a} as an operator on the space c_{0}, with the same assumption.

On Some Class Of Hypersurfaces In \Bbb{E}^{N+1} Satisfying Chen's Equality, Ci̇han Özgür, Kadri̇ Arslan

Turkish Journal of Mathematics

In this paper we study pseudosymmetry type hypersurfaces in the Euclidean space \Bbb{E}^{n+1} satisfying B. Y. Chen's equality.

On The Modular Curve X(6) And Surfaces Admitting Genus 2 Fibrations, Gülay Karadoğan

Turkish Journal of Mathematics

In this paper, we study the moduli spaces of surfaces admitting nonsmooth genus 2 fibrations with slope \lambda = 6 (necessarily) over curves of genus \geq 1. We determine the structure of each connected component of these moduli spaces. Our results fill the gap of earlier work in the literature to complete the picture of the moduli spaces of genus 2 fibrations over curves of genus \geq 2 except for the case of \lambda = 4.

On Derivations Of Prime Gamma Rings, Mehmet Ali̇ Öztürk, Young Bae Jun, Kyung Ho Kim

Turkish Journal of Mathematics

We consider some results in a \Gamma-ring M with derivation which is related to Q, and the quotient \Gamma-ring of M.

Ten Day Pre-Calc Syllabus, Douglas J. Shaw

Faculty Publications

No abstract provided.

Fundamental Theorem Of Algebra, Paul Shibalovich

Theses Digitization Project

The fundamental theorem of algebra (FTA) is an important theorem in algebra. This theorem asserts that the complex field is algebracially closed. This thesis will include historical research of proofs of the fundamental theorem of algebra and provide information about the first proof given by Gauss of the theorem and the time when it was proved.

1p Spaces, Anh Tuyet Tran

Theses Digitization Project

In this paper we will study the 1p spaces. We will begin with definitions and different examples of 1p spaces. In particular, we will prove Holder's and Minkowski's inequalities for 1p sequence.

Common Cause Failure Prediction Using Data Mapping, Paul H. Kvam, J. Glenn Miller

Department of Math & Statistics Faculty Publications

To estimate power plant reliability, a probabilistic safety assessment might combine failure data from various sites. Because dependent failures are a critical concern in the nuclear industry, combining failure data from component groups of different sizes is a challenging problem. One procedure, called data mapping, translates failure data across component group sizes. This includes common cause failures, which are simultaneous failure events of two or more components in a group. In this paper, we present methods for predicting future plant reliability using mapped common cause failure data. The prediction technique is motivated by discrete failure data from emergency diesel generators …