Physical Sciences and Mathematics Commons^™

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.

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.

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.

Why Makik Can "Do" Math: Race And Status In Integrated Classrooms, Jacqueline Leonard, Scott Jackson Dantley

Trotter Review

This case study reports on the small group interactions and achievements of Malik, an African American sixth grader, who attended a Maryland elementary school in 1997. Student achievement was measured by the Maryland Functional Mathematics Test (MFMT-I), which was given on a pre/post basis. Students' scores on the MFMT-I were analyzed using the ANOVA. The analysis revealed a significant difference (F = 3-330, p < .05) between the scores of Caucasian (M = 342.12) and African American students (M = 323-56). However, Malik's MFMT-I score rose from 293 to 353. A passing score is 340. This study examines Malik's interactions to ascertain what factors influenced his achievement. The findings are that Malik had a positive attitude about mathematics and a strong command of mathematical and scientific language. Recommendations are that teachers become cultural brokers to help all children learn the "language" of mathematics and encourage all students to become self-advocates to overcome negative social dynamics in small groups.

High-Stakes Tests Require High-Stakes Pedagogy, Randy Lattimore

Trotter Review

High-stakes mathematics tests continue to gain popularity in the United States, with an increasing number of states setting the passing of such tests as a high school graduation requirement. Consequently, instruction and instructional content have changed, with teachers emphasizing materials on the test while neglecting other important aspects of learning. The tests have become all-consuming, taking over many students' lives. Yet students are often ill prepared for these tests. This is even more true for African-American students whose cultural and social circumstances make their preparation for high-stakes tests inadequate and ineffective. The author examines six such students - their hopes …

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 …

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.

The Local Moduli Of Sasakian 3-Manifolds, Brendan Guilfoyle

Publications

The Newman-Penrose-Perjes formalism is applied to Sasakian 3-manifolds and the local form of the metric and contact structure is presented. The local moduli space can be parameterised by a single function of two variables and it is shown that, given any smooth function of two variables, there exists locally a Sasakian structure with scalar curvature equal to this function. The case where the scalar curvature is constant (η-Einstein Sasakian metrics) is completely solved locally. The resulting Sasakian manifolds include S 3, Nil, and SL˜ 2 (ℝ), as well as the Berger spheres. It is also shown that a conformally flat …

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 …

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 …

An Effective Version Of Belyi's Theorem, Lily S. Khadjavi

Mathematics Faculty Works

We compute bounds on covering maps that arise in Belyi's Theorem. In particular, we construct a library of height properties and then apply it to algorithms that produce Belyi maps. Such maps are used to give coverings from algebraic curves to the projective line ramified over at most three points. The computations here give upper bounds on the degree and coefficients of polynomials and rational functions over the rationals that send a given set of algebraic numbers to the set {0,1,∞} with the additional property that the only critical values are also contained in {0,1,∞}.

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

Mathematics 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.

Valuations And Filtrations, Edward Mosteig

Mathematics Faculty Works

The classical theory of Gröbner bases, as developed by Bruno Buchberger, can be expanded to utilize objects more general than term orders. Each term order on the polynomial ring k[x] produces a filtration of k[x] and a valuation ring of the rational function field k(x). The algorithms developed by Buchberger can be performed by using directly the induced valuation or filtration in place of the term order. There are many valuations and filtrations that are suitable for this general computational framework that are not derived from term orders, even after a change of variables. Here we study how to translate …

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.

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, …

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, …

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.

Stable Refinable Generators Of Shift Invariant Spaces With Certain Regularities And Vanishing Moments, Tian-Xiao He

Tian-Xiao He

In this paper, we discuss the stable refinable functions that generate shift in variant (SI) spaces and possess the largest possible regularities and required vanishing moments. The stability of the corresponding complementary spaces is also discussed.

Logic, Optimization And Constraint Programming, John Hooker

John Hooker

No abstract provided.

Spectra Of Composition Operators On The Bloch And Bergman Spaces, Karen Saxe, B. Maccluer

Karen Saxe

No abstract provided.

Asymptotically Constant Solutions Of Functional Difference Systems, William F. Trench

William F. Trench

No abstract provided.

Analysis And Classification Of Nonlinear Dispersive Evolution Equations In The Potential Representation, Andrei Ludu

Andrei Ludu

No abstract provided.

Dimensionality-Reducing Expansion, Boundary Type Quadrature Formulas, And The Boundary Element Method, Tian-Xiao He

Tian-Xiao He

This paper discusses the connection between boundary quadrature formulas constructed by using solutions of partial differential equations and boundary element schemes.