Mathematics Commons^™

Longitudinal Investigation Of The Curricular Effect: An Analysis Of Student Learning Outcomes From The Liecal Project In The United States, Jinfa Cai, Ning Wang, John Moyer, Chuang Wang, Bikai Nie

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this article, we present the results from a longitudinal examination of the impact of a Standards-based or reform mathematics curriculum (called CMP) and traditional mathematics curricula (called non-CMP) on students’ learning of algebra using various outcome measures. Findings include the following: (1) students did not sacrifice basic mathematical skills if they are taught using a Standards-based or reform mathematics curriculum like CMP; (2) African American students experienced greater gain in symbol manipulation when they used a traditional curriculum; (3) the use of either the CMP or a non-CMP curriculum improved the mathematics achievement of all students, including …

Products Of Multiplication, Composition And Differentiation Between Weighted Bergman-Nevanlinna And Bloch-Type Spaces, Ajay K. Sharma

Turkish Journal of Mathematics

Let \varphi and \psi be holomorphic maps on D such that \varphi ( D ) \subset D . Let C_{\varphi} , M_{\psi} and D be the composition, multiplication and differentiation operators, respectively. In this paper, we consider linear operators induced by products of these operators from Bergman-Nevanlinna spaces A^{\beta}_N to Bloch-type spaces. In fact, we prove that these operators map A^{\beta}_N compactly into Bloch-type spaces if and only if they map A^{\beta}_N boundedly into these spaces.

Some Products Involving The Fourth Greek Letter Family Element \Tilde{\Delta}_S In The Adams Spectral Sequence, Xiu-Gui Liu, He Wang

Turkish Journal of Mathematics

Let p be an odd prime and A be the mod p Steenrod algebra. For computing the stable homotopy groups of spheres with the classical Adams spectral sequence, we must compute the E_2-term of the Adams spectral sequence, Ext_A^{\ast,\ast} (Z_p,Z_p). In this paper we prove that in the cohomology of A, the product k_0 h_n \tilde \delta _{s + 4} \in Ext_A^{s + 7, t(s,n) + s} (Z_p, Z_p), is nontrivial for n \geq 5, and trivial for n=3, 4, where \tilde\delta_{s + 4} is actually \tilde\alpha_{s + 4}^{(4)} described by Wang and Zheng, p \geq 11, 0 \leq s < p - 4 and t(s,n)=2(p-1)[(s + 2) + (s + 4)p + (s + 3)p^2 + (s + 4)p^3 + p^n].

Pseudo Pq-Injective Modules, Zhanmin Zhu

Turkish Journal of Mathematics

A module M_R is called Pseudo PQ-injective (or PPQ-injective for short) if every monomorphism from a principal submodule of M to M extends to an endomorphism of M. Some characterizations and properties of this class of modules are investigated, PPQ-injective modules with some additional conditions are studied, semisimple artinian rings are characterized by PPQ-injective modules.

B. Y. Chen Inequalities For Submanifolds Of A Riemannian Manifold Of Quasi-Constant Curvature, Ci̇han Özgür

Turkish Journal of Mathematics

In this paper, we prove B. Y. Chen inequalities for submanifolds of a Riemannian manifold of quasi-constant curvature, i.e., relations between the mean curvature, scalar and sectional curvatures, Ricci curvatures and the sectional curvature of the ambient space. The equality cases are considered.

Top Generalized Local Cohomology Modules, Amir Mafi

Turkish Journal of Mathematics

Let (R,m) be a commutative Noetherian local ring and M, N two non-zero finitely generated R-modules with d(M)=n

Minimal And Symmetric Global Partition Polynomials For Reproducing Kernel Elements, Mario Jesus Juha

USF Tampa Graduate Theses and Dissertations

The Reproducing Kernel Element Method is a numerical technique that combines finite element and meshless methods to construct shape functions of arbitrary order and continuity, yet retains the Kronecker-δ property. Central to constructing these shape functions is the construction of global partition polynomials on an element. This dissertation shows that asymmetric interpolations may arise due to such things as changes in the local to global node numbering and that may adversely affect the interpolation capability of the method. This issue arises due to the use in previous formulations of incomplete polynomials that are subsequently non-affine invariant. This dissertation lays out …

Problems In Classical Potential Theory With Applications To Mathematical Physics, Erik Lundberg

USF Tampa Graduate Theses and Dissertations

In this thesis we are interested in some problems regarding harmonic functions. The topics are divided into three chapters.

Chapter 2 concerns singularities developed by solutions of the Cauchy problem for a holomorphic elliptic equation, especially Laplace's equation. The principal motivation is to locate the singularities of the Schwarz potential. The results have direct applications to Laplacian growth (or the Hele-Shaw problem).

Chapter 3 concerns the Dirichlet problem when the boundary is an algebraic set and the data is a polynomial or a real-analytic function. We pursue some questions related to the Khavinson-Shapiro conjecture. A main topic of interest is …

Parametric And Bayesian Modeling Of Reliability And Survival Analysis, Carlos A. Molinares

USF Tampa Graduate Theses and Dissertations

The objective of this study is to compare Bayesian and parametric approaches to determine the best for estimating reliability in complex systems. Determining reliability is particularly important in business and medical contexts. As expected, the Bayesian method showed the best results in assessing the reliability of systems.

In the first study, the Bayesian reliability function under the Higgins-Tsokos loss function using Jeffreys as its prior performs similarly as when the Bayesian reliability function is based on the squared-error loss. In addition, the Higgins-Tsokos loss function was found to be as robust as the squared-error loss function and slightly more efficient. …

Enumeration Of Inequivalent Cycle Decompositions, William J. Laffin

Dissertations, Master's Theses and Master's Reports - Open

A k-cycle decomposition of order n is a partition of the edges of the complete graph on n vertices into k-cycles. In this report a backtracking algorithm is developed to count the number of inequivalent k-cycle decompositions of order n.

Parallel Algorithm For Solving Integer Linear Programs, David O. Torrey Jr.

Dissertations, Master's Theses and Master's Reports - Open

Linear programs, or LPs, are often used in optimization problems, such as improving manufacturing efficiency of maximizing the yield from limited resources. The most common method for solving LPs is the Simplex Method, which will yield a solution, if one exists, but over the real numbers. From a purely numerical standpoint, it will be an optimal solution, but quite often we desire an optimal integer solution. A linear program in which the variables are also constrained to be integers is called an integer linear program or ILP. It is the focus of this report to present a parallel algorithm for …

Neutrosophic Interpretation Of The Analects Of Confucius, Florentin Smarandache, Fu Yuhua

Branch Mathematics and Statistics Faculty and Staff Publications

This book is the companion volume of "Neutrosophic Interpretation of Tao Te Ching,” its purpose is to extend the foundation and application range of “The Analects of Confucius.” The reasons for this are as follows. Firstly, we are willing to point out that The Analects of Confucius already has some limitations, because many questions we are interested in cannot be answered within “The Analects of Confucius.” For example, The Analects of Confucius basically discussed the matters in China, however considering all possible situations it should matter in foreign countries as well, i.e. the “global village.” This was impossible in Confucian …

Covering Systems Of Polynomial Rings Over Finite Fields, Michael Wayne Azlin

Electronic Theses and Dissertations

In 1950 Paul Erdos observed that every integer belonged to a certain system of congruences with distinct moduli. He called such systems of congruences covering systems. Utilizing his covering system, he disproved a conjecture of de Polignac asking, “for every odd k, is there a prime of the form 2n + k?” Examples of covering systems of the integers are presented along with some brief history and a sketch of the disproof by Erd?s. Open conjectures concerning covering systems and best known results of attempts to prove these conjectures are given. Analogies are drawn between the integers and Fq[x], and …

Asymptotics Of Carleman Polynomials For Level Curves Of The Inverse Of A Shifted Joukowsky Transformation, Michael Carr Northington

Electronic Theses and Dissertations

Let L be a level curve of the inverse of the shifted Joukowsky transformation w [special characters omitted] w − 1 + (w − 1) –1, that is, [special characters omitted]In this thesis we investigate the asymptotic properties of the sequence of polynomials that are orthonormal over the interior domain of L with respect to the area measure. We establish strong asymptotic formulas describing the behavior of these polynomials (as their degree increases) at every point of the complex plane.

Traveling Wave Solutions Of Burgers’ Equation For Power-Law Non- Newtonian Flows, Dongming Wei, Harry Borden

Mathematics Faculty Publications

In this work we present some analytic and semi-analytic traveling wave solutions of a generalized Burgers' equation for unidirectional flow of power-law non-Newtonian fluids. The solutions include the corresponding well-known traveling wave solution of the Burgers' equation for Newtonian flows. We also derive estimates of shock thickness for the power-law flows.

Iteratively Reweighted Least Squares Minimization With Prior Information A New Approach, Dmitriy Popov

Electronic Theses and Dissertations

Iteratively reweighted least squares (IRLS) algorithms provide an alternative to the more standard 1 l -minimization approach in compressive sensing. Daubechies et al. introduced a particularly stable version of an IRLS algorithm and rigorously proved its convergence in 2010. They did not, however, consider the case in which prior information on the support of the sparse domain of the solution is available. In 2009, Miosso et al. proposed an IRLS algorithm that makes use of this information to further reduce the number of measurements required to recover the solution with specified accuracy. Although Miosso et al. obtained a number of …

Prediction Of Survival Of Early Stages Lung Cancer Patients Based On Er Beta Cellular Expressions And Epidemiological Data, Evgeny Martinenko

Electronic Theses and Dissertations

We attempted a mathematical model for expected prognosis of lung cancer patients based on a multivariate analysis of the values of ER-interacting proteins (ERbeta) and a membrane bound, glycosylated phosphoprotein MUC1), and patients clinical data recorded at the time of initial surgery. We demonstrate that, even with the limited sample size available to use, combination of clinical and biochemical data (in particular, associated with ERbeta and MUC1) allows to predict survival of lung cancer patients with about 80% accuracy while prediction on the basis of clinical data only gives about 70% accuracy. The present work can be viewed as a …

Zero Divisor Graphs And Poset Decomposition, Bette Catherine Putnam

Electronic Theses and Dissertations

A graph is associated to any commutative ring R where the vertices are the non-zero zero divisors of R with two vertices adjacent if x · y = 0. The zero-divisor graph has also been studied for various algebraic stuctures such as semigroups and partially ordered sets. In this paper, we will discuss some known results on zero-divisor graphs of posets as well as the concept of compactness as it relates to zero-divisor graphs. We will dicuss equivalence class graphs defined on the elements of various algebraic structures and also the reduced graph defined on the vertices of a compact …

A Statistical Analysis Of The Factors Affecting University Endowments, Lisa M. Stoecken

Honors Program Theses

The purpose of this study was to discover which, if any, institutional characteristics had a significant impact upon a university's endowment size. This study further explored whether the success of a university's athletic program had an impact on endowment size. The results from the study indicated two variables, operating revenues and student selectivity, were significant at a 99 percent confidence level; and, two additional variables, appropriations and a binary research university variable, were significant at a 95 percent confidence level. The results indicated that an additional one million dollars in total operating revenues and appropriations would decrease the endowment size …

Weak-Projective Dimensions, Mohammad Javad Nikmehr, Zahra Poormahmood, Reza Nikandish

Turkish Journal of Mathematics

In this paper, the notions of weak-projective modules and weak-projective dimension over commutative domain R are given. It is shown that over semisimple rings with weak global dimension 1, these modules are equivalent to weak-injective modules. The weak-projective dimension measures how far away a domain is from being a Prüfer domain. Several properties of these modules are also presented.