Mathematics Commons^™

Levy-Like Continuity Theorems For Convergence In Distribution, Theodore P. Hill, Ulrich Krengel

Research Scholars in Residence

Levy’s classical continuity theorem states that if the pointwise limit of a sequence of characteristic functions exists, then the limit function itself is a characteristic function if and only if the limit function satisfies a single universal limit condition (in his case, the limit at zero is one), in which case the underlying measures converge weakly to the probability measure represented by the limit function. It is the purpose of this article to give a number of direct analogs of L´evy’s theorem for other probability-representing functions including moment sequences, maximal moment sequences, mean-residual-life functions, Hardy-Littlewood maximal functions, and failure-rate functions. …

Random Probability Measures With Given Mean And Variance Running Title: Random Probability Measures, Lisa Bloomer, Theodore P. Hill

Research Scholars in Residence

This article describes several natural methods of constructing random probability measures with prescribed mean and variance, and focuses mainly on a technique which constructs a sequence of simple (purely discrete, finite number of atoms) distributions with the prescribed mean and with variances which increase to the desired variance. Basic properties of the construction are established, including conditions guaranteeing full support of the generated measures, and conditions guaranteeing that the final measure is discrete. Finally, applications of the construction method to optimization problems such as Plackett’s Problem are mentioned, and to experimental determination of average-optimal solutions of certain control problems.

Vertex-Unfoldings Of Simplicial Manifolds, Erik D. Demaine, David Eppstein, Jeff Erickson, George W. Hart, Joseph O'Rourke

Computer Science: Faculty Publications

We present an algorithm to unfold any triangulated 2-manifold (in particular, any simplicial polyhedron) into a non-overlapping, connected planar layout in linear time. The manifold is cut only along its edges. The resulting layout is connected, but it may have a disconnected interior; the triangles are connected at vertices, but not necessarily joined along edges. We extend our algorithm to establish a similar result for simplicial manifolds of arbitrary dimension.

On Locally Pre-C^{*}-Algebra Structures In Locally M-Convex H^{*}-Algebras, A. El-Kinani

Turkish Journal of Mathematics

We endow any locally m-convex H^{*}-algebra \left( E,\tau \right) with a locally pre-C^{*}-topology weaker than \tau. Examples and applications are provided.

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.

One Sided Banach Algebras, A. El Kinani, A. Najmi, Mohamed Oudadess

Turkish Journal of Mathematics

Many properties of two-sided algebras remain valid for one-sided algebras. Namely, any one sided Banach algebra is commutative modulo its Jacobson radical.

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.

Flat Marcinkiewicz Integral Operators, Hussain Al-Qassem, Ahmad Al-Salman

Turkish Journal of Mathematics

In this paper, we study Marcinkiewicz integral operators with rough kernels supported by surfaces of revolutions. We prove that our operators are bounded on L^p under certain convexity assumptions on our surfaces and under very weak conditions on the kernel.

On Some Properties Connecting Infinite Series, B. K. Lahiri, Pratulananda Das

Turkish Journal of Mathematics

We prove several theorems connecting infinite series of real terms in relation to Borel and Baire classification of sets and functions, connectedness of mappings, porosity character of sets etc.

On The Spectral Properties Of The Regular Sturm-Liouville Problem With The Lag Argument For Which Its Boundary Conditions Depends On The Spectral Parameter, Mehmet Bayramoğlu, Kevser Özden Köklü, Oya Baykal

Turkish Journal of Mathematics

In this paper, the asymptotic expression of the eigenvalues and eigenfunctions of the Sturm-Liouville equation with the lag argument y''(t) + \lambda^2 y(t) + M(t)y (t - \Delta(t)) = 0 and the spectral parameter in the boundary conditions \lambda y(0) +y'(0) = 0 \lambda^{2}y(\pi) + y'(\pi) = 0 y(t - \Delta(t)) = y(0)\varphi(t - \Delta(t)), t - \Delta(t) < 0 has been founded in a finite interval, where M(t) and \Delta(t) \geq 0 are continuous functions on [0, \pi], \lambda > 0 is a real parameter, \varphi(t) is an initial function which is satisfied with the condition \varphi(0) = 1 and continuous in the initial set.

Field Extensions Having The Unique Subfield Property, And G-Cogalois Extensions, Toma Albu

Turkish Journal of Mathematics

We present a short proof, based on Cogalois Theory, of a result due to Acosta de Orozco and Vélez (1982, J. Number Theory 15, 388-405) characterizing separable simple radical field extensions with the unique subfield property, and prove that these extensions are precisely the simple G--Cogalois extensions with a cyclic Kneser group.

Studying The Functional Genomics Of Stress Responses In Loblolly Pine With The Expresso Microarray Experiment Management System, Lenwood S. Heath, Naren Ramakrishnan, Ronald R. Sederoff, Ross W. Whetten, Boris I. Chevone, Craig Struble, Vincent Y. Jouenne, Dawei Chen, Leonel Van Zyl, Ruth Grene

Mathematics, Statistics and Computer Science Faculty Research and Publications

Conception, design, and implementation of cDNA microarray experiments present a variety of bioinformatics challenges for biologists and computational scientists. The multiple stages of data acquisition and analysis have motivated the design of Expresso, a system for microarray experiment management. Salient aspects of Expresso include support for clone replication and randomized placement; automatic gridding, extraction of expression data from each spot, and quality monitoring; flexible methods of combining data from individual spots into information about clones and functional categories; and the use of inductive logic programming for higher-level data analysis and mining. The development of Expresso is occurring in parallel with …

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 …

A Sufficient Condition For The Uniqueness Of Positive Steady State To A Reaction Diffusion System, Joon Hyuk Kang, Yun Oh

Faculty Publications

In this paper, we concentrate on the uniqueness of the positive solution for the general elliptic system { Δu + u(g1(u) - g 2(v)) = 0 in R+ × Ω, Δν + v(h 1(u) - h2(v)) = 0 u|∂Ω = v| ∂Ω = 0. This system is the general model for the steady state of a competitive interacting system. The techniques used in this paper are upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.

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 …

Monoidal Extensions Of A Cohen-Macaulay Unique Factorization Domain, William J. Heinzer, Aihua Li, Louis J. Ratliff, David E. Rush

Department of Mathematics Faculty Scholarship and Creative Works

Let A be a Noetherian Cohen-Macaulay domain, b, c1,...,cg an A-sequence, J = (b, c1,...,cg) A, and B = A[J/b]. Then B is Cohen-Macaulay, there is a natural one-to-one correspondence between the sets AssB(B/bB) and AssA(A/J), and each q ∈ AssA(A/J) has height g + 1. If B does not have unique factorization, then some height-one prime ideals P of B are not principal. These primes are identified in terms of J and P∩A, and we consider the question of how far from principal they can be. If A is integrally closed, necessary and sufficient conditions are given for B …

Geometric Integrators For Hamiltonian Pdes, Dmitry Karpeev

Computer Science Theses & Dissertations

We consider methods for systematic construction of algorithms for a class of time-dependent PDEs with Hamiltonian structure. These systems possess phase space geometry and constants of the motion that need to be preserved by the integration algorithm to reflect the qualitative features of the system.

We exploit the structure of Hamiltonian systems, in particular their variational formulation based on a Lagrangian, and the dual covariant formulation, to expose the geometric features of the system that have natural analogs when discretized. We emphasize the local space-time approach to the constructions, making them amenable to parallelization and preconditioning using domain decomposition methods, …

C-Closed Sets In L-Fuzzy Topological Spaces And Some Of Its Applications, Ali̇ Ahmed Nouh

Turkish Journal of Mathematics

We introduce and study the notion of C-closed sets in L-fuzzy topological spaces. Then, C-convergence theory for nets and ideals is established in terms of C-closedness. Finally, we give a new concept of C-continuity on L-fuzzy topological space by means of L-fuzzy C-closedness and investigate some of its properties and its relationships with other L-fuzzy mappings introduced previously. Then we systematically study the characterizations of this notion with the aid of the C-convergence of L-fuzzy nets and L-fuzzy ideals.

A Note On Interpolation In The Generalized Schur Class. I. Applications Of Realization Theory, Daniel Alpay, T. Constantinescu, A. Dijksma, J. Rovnyak, A. Dijksma

Mathematics, Physics, and Computer Science Faculty Articles and Research

Realization theory for operator colligations on Pontryagin spaces is used to study interpolation and factorization in generalized Schur classes. Several criteria are derived which imply that a given function is almost the restriction of a generalized Schur function. The role of realization theory in coefficient problems is also discussed; a solution of an indefinite Carathéodory-Fejér problem is obtained, as well as a result that relates the number of negative (positive) squares of the reproducing kernels associated with the canonical coisometric, isometric, and unitary realizations of a generalized Schur function to the number of negative (positive) eigenvalues of matrices derived from …

Some Extensions Of Loewner's Theory Of Monotone Operator Functions, Daniel Alpay, Vladimir Bolotnikov, A. Dijksma, J. Rovnyak, A. Dijksma

Mathematics, Physics, and Computer Science Faculty Articles and Research

Several extensions of Loewner’s theory of monotone operator functions are given. These include a theorem on boundary interpolation for matrix-valued functions in the generalized Nevanlinna class. The theory of monotone operator functions is generalized from scalar- to matrix-valued functions of an operator argument. A notion of -monotonicity is introduced and characterized in terms of classical Nevanlinna functions with removable singularities on a real interval. Corresponding results for Stieltjes functions are presented.

Ideal Theory In Prüfer Domains - An Unconventional Approach, Edward Mosteig

Mathematics, Statistics and Data Science Faculty Works

In Prüfer domains of finite character, ideals are represented as finite intersections of special ideals which are proper generalizations of the classical primary ideals. We show that representations of ideals as shortest intersections of primal or quasi-primary ideals exist and are unique. Moreover, every non-zero ideal is the product of uniquely determined pairwise comaximal quasi-primary ideals. Semigroups of primal and quasi-primary ideals with fixed associated primes are also investigated in arbitrary Prüfer domains. Their structures can be described in terms of the value groups of localizations.

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.

[Introduction To] Generalized Analytic Continuation, William T. Ross, Harold S. Shapiro

Bookshelf

The theory of generalized analytic continuation studies continuations of meromorphic functions in situations where traditional theory says there is a natural boundary. This broader theory touches on a remarkable array of topics in classical analysis, as described in the book. This book addresses the following questions: (1) When can we say, in some reasonable way, that component functions of a meromorphic function on a disconnected domain, are "continuations" of each other? (2) What role do such "continuations" play in certain aspects of approximation theory and operator theory? The authors use the strong analogy with the summability of divergent series …

[Introduction To] Data Structures With Java: A Laboratory Approach, Joe Kent, Lewis Barnett Iii

Bookshelf

This book is designed to present the key topics in the second course for computer science students using the Java programming language. For convenience, we cover exceptions and file operations in Java, although this may have been covered in the first course. We also cover material on the binary representation of data and Java's bitwise operations, with applications.These are topics needed for computer organization an operating systems courses.

Like A Bridge Over Colored Water: A Mathematical Review Of The Rainbow Bridge: Rainbows In Art, Myth, And Science, John A. Adam

Mathematics & Statistics Faculty Publications

Commenting on a recent book, the author discusses various views of the rainbow: its role in culture, its scientific description, and its mathematical theory.

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 …