Physical Sciences and Mathematics Commons^™

Comparision Of High Achievers With Low Achievers: Discussion Of Juter’S (2007) Article, T. P. Hutchinson

The Mathematics Enthusiast

The use of questionnaires and interviews to compare the responses to a mathematical task of high achievers with low achievers has limitations. The partial information that they have provides a way of comparing high and low achievers. Some references are given here to relevant task formats and theories. An example is given of how examinees’ performance with unusual task formats (specifically, answer-until-correct) may be analysed to throw light on the mathematical description of partial information.

To Publish Or Not To Publish?- That Is The (Editorial) Question, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Statistics Teaching In An Agricultural University: A Motivation Problem, Klara Lokos Toth

The Mathematics Enthusiast

There are many teaching methods and there are various teaching materials even in one university, not to mention different universities specialising in different disciplines. So I cannot talk about Hungarian method in general, but about my experience in teaching statistics. I teach statistics on several levels (BSc, MSc, PhD) and in different faculties (Agriculture and environmental Sciences, Economic and Social Sciences) and in different forms. I find different problems according to the faculties and forms. In this paper I focus on only one of them, which is the most important for me.

Catch Me If You Can!, Steve Humble

The Mathematics Enthusiast

Learning mathematics outside the classroom is not enrichment, it is at the core of empowering an individuals understanding of the subject.

The three activities described in this article can all be used outside the classroom in a maths lesson. Teaching mathematical concepts in this way engages and reinforces learning. It puts the ideas learnt into a setting and allows time for those ideas to be developed without any of the maths hang-ups which can occur in the classroom. By taking maths beyond the classroom, we can more clearly illustrate the connections between the real world and what they are studying …

Special Set Linear Algebra And Special Set Fuzzy Linear Algebra, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

This book for the first time introduces the notion of special set linear algebra and special set fuzzy linear algebra. This is an extension of the book set linear algebra and set fuzzy linear algebra. These algebraic structures basically exploit only the set theoretic property, hence in applications one can include a finite number of elements without affecting the systems property. These new structures are not only the most generalized structures but they can perform multi task simultaneously; hence they would be of immense use to computer scientists. This book has five chapters. In chapter one the basic concepts about …

Calculation Of Equilibrants For Semipositive Matrices, Zheng Tong

Dissertations, Theses, and Masters Projects

No abstract provided.

A New Method For Non-Rigid Registration Of 3d Images, Mehmet Ali Akinlar

Mathematics Dissertations

In this dissertation we present a novel method for the nonrigid registration of 3D images using a well-established mathematical framework mostly known as the deformation based grid generation method. The deformation based grid generation method is able to generate a grid with desired grid density distribution that is free from grid folding. This method gives direct control over the cell size of the adaptive grid and determines the node velocities directly. The adaptive grid system naturally distributes more grids to deprived areas. The positive monitor function disallows grid folding and provides a mean to control the ratio of the areas …

Optimal Control Approach To Image Registration, Stephen Taiwo Salako

Mathematics Dissertations

The purpose of this dissertation is twofold: To present a new method of orthogonal grid generation and to investigate certain theoretical aspects of the optimal control approach to the image registration problem.In the first part of this dissertation, we will present a variational method of orthogonal grid generation which is based on the deformation method and solving Euler-Lagrange equations. Although the concept of grid generation has been studied extensively, the generation of orthogonal grids is still one of the most challenging problems of the grid generation methods.An orthogonal grid should offer significant advantages in the solution of systems of partial …

Authentic Discovery Projects In Statistics, Dianna J. Spence, Robb Sinn

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

We report the activities and findings of a 3-year project, ―Authentic, Career-Specific, Discovery Learning Projects in Introductory Statistics,‖ funded by the National Science Foundation. The project scope includes: 1) development of teaching materials for using discovery learning projects to teach statistics; 2) training secondary teachers to use the materials developed; 3) evaluation of student outcomes, in both content knowledge and attitudes toward statistics; and 4) extending and refining teacher training. With input from an interdisciplinary team of instructors, materials were developed to assist the teacher in facilitating collaborative discovery projects using linear regression techniques and comparison techniques with appropriate t-tests. …

Content Knowledge And Pedagogical Content Knowledge Of Algebra Teachers And Changes In Both Types Of Knowledge As A Result Of Professional Development, Joy W. Black

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

In seeking to improve the mathematics education of all students, it is important to understand the connection between the content knowledge and pedagogical content knowledge of mathematics and how professionals can influence growth in both of these types of knowledge. We do not have an answer about the interplay of content knowledge and pedagogical content knowledge in successful instructional practices in the mathematics classroom. This study involves assessing the content knowledge and pedagogical content knowledge of secondary teachers of Algebra I. In addition, how are these types of knowledge expressed in instructional practices? Last, how do content knowledge, pedagogical content …

Analysis Of Achievement For Understanding Geometry, Annita W. Hunt

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

The purpose of this study was to investigate the effectiveness of a mathematics professional development course. More specifically, in this study we examine whether geometric experiences have an impact on level of performance in mathematics. The van Hiele (Fuys, D., Geddes, D., & Tischler, R., 1988) model of geometric understanding provided a research framework from which to view geometric understanding. This model suggests five levels of understanding that should be taken into consideration when examining levels of geometric thinking: Visual, Descriptive/Analytic, Abstract/Relational, Formal Deduction/Proof, and Rigor. The sample under study was three cohorts of practicing elementary teachers and mathematics coaches …

Characterization Of Compactly Supported Renable Splines With Integer Matrix, Tian-Xiao He, Yujing Guana

Scholarship

Let M be an integer matrix with absolute values of all its eigenvalues being greater than 1. We give a characterization of compactly supported M-refinable splines f and the conditions that the shifts of f form a Riesz basis.

Using Calculus To Model The Growth Of L. Plantarum Bacteria, Erin Carey

Undergraduate Journal of Mathematical Modeling: One + Two

Experimental data for the growth of Lactobacillus plantarum bacteria have been obtained over time, creating the need for mathematical means to model this data. We use the Gompertz model because it is a sigmoid function for a time series, where growth is slowest at the start and end of a time period. The Gompertz model is especially useful because it defines specific parameters that characterize the S-shaped curve. In addition, the Gompertz model uses relative growth, which is the logarithm of the given population compared to the initial population. This reflects the fact that bacteria grow exponentially. The important parameters …

Biodiversity In A Florida Sandhill Ecosystem, Samantha Robertson

Undergraduate Journal of Mathematical Modeling: One + Two

This project compares two transects of land in the University of South Florida's Botanical Gardens for their biodiversity. The transects were chosen to represent a Florida sandhill ecosystem and the individual Longleaf Pine, Saw Palmetto, Turkey Oak, Laurel Oak and Live Oak specimens were counted. All other species above waist height were counted as "other"?. Once the individuals were counted, the Simpson's and Shannon-Wiener indices were calculated. Since the Shannon-Wiener index incorporates several diversity characteristics, it is typically more reliable than Simpson's. However, both biodiversity indices agreed that transect B was more diverse than transect A.

Cycle Equivalence Of Graph Dynamical Systems, Matthew Macauley, Henning S. Mortveit

Publications

Graph dynamical systems (GDSs) generalize concepts such as cellular automata and Boolean networks and can describe a wide range of distributed, nonlinear phenomena. Two GDSs are cycle equivalent if their periodic orbits are isomorphic as directed graphs, which captures the notion of having comparable long-term dynamics. In this paper, we study cycle equivalence of GDSs in which the vertex functions are applied sequentially through an update sequence. The main result is a general characterization of cycle equivalence based on the underlying graph Y and the update sequences. We construct and analyse two graphs C(Y) and D( …

Two Component Integrable Systems Modelling Shallow Water Waves: The Constant Vorticity Case, Rossen Ivanov

Articles

In this contribution we describe the role of several two-component integrable systems in the classical problem of shallow water waves. The starting point in our derivation is the Euler equation for an incompressible fluid, the equation of mass conservation, the simplest bottom and surface conditions and the constant vorticity condition. The approximate model equations are generated by introduction of suitable scalings and by truncating asymptotic expansions of the quantities to appropriate order. The so obtained equations can be related to three different integrable systems: a two component generalization of the Camassa-Holm equation, the Zakharov-Ito system and the Kaup-Boussinesq system. The …

Daemon Decay And Inflation, Emil Prodanov

Articles

In 1971, Hawking suggested [1] that there may be a very large number of gravitationally collapsed charged objects of very low masses, formed as a result of fluctuations in the early Universe. A mass of of these objects could be accumulated at the centre of a star like the Sun. The masses of these collapsed objects are from and above and their charges are up to ±30 electron units [1].

Examining The Accuracy Of The Normal Approximation To The Poisson Random Variable, Wesley Jacob Rich

Master's Theses and Doctoral Dissertations

Because the Poisson distribution is discrete, it is sometimes useful to use the continuous normal distribution as an approximation. In doing so, determining the accuracy of the approximation is important. Some issues of interest include: knowing how the error depends on the Poisson parameter, knowing when the approximation overestimates or underestimates the distribution, bounding the magnitude of the error, and determining if the approximation can be improved. This paper addresses these issues by examining how two types of absolute error measurements are affected by variations in the Poisson parameter; changes in the relative error are also examined. Generally, the error …

Extending The Skill Test For Disease Diagnosis, Shu-Chuan Lin, Paul H. Kvam, Jye-Chyi Lu

Department of Math & Statistics Faculty Publications

For diagnostic tests, we present an extension to the skill plot introduced by Briggs and Zaretski (Biometrics 2008; 64:250–261). The method is motivated by diagnostic measures for osteopetrosis in a study summarized by Hans et al. (The Lancet 1996; 348:511–514). Diagnostic test accuracy is typically defined using the area (or partial area) under the receiver operator characteristic (ROC) curve. If partial area is used, the resulting statistic can be highly subjective because the focus region of the ROC curve corresponds to a set of low false‐positive rates that are chosen by the experimenter. This paper introduces a more …

Existence And Uniqueness Theorem For Slant Immersions In Kenmotsu Space Forms, Pradeep Kumar Pandey, Ram Shankar Gupta

Turkish Journal of Mathematics

In this paper we have obtained a general existence as well as uniqueness theorem for slant immersions into a Kenmotsu-space form.

Hopf Quivers And Nichols Algebras In Positive Characteristic, Claude Cibils, Aaron Lauve, Sarah Witherspoon

Mathematics and Statistics: Faculty Publications and Other Works

We apply a combinatorial formula of the first author and Rosso, for products in Hopf quiver algebras, to determine the structure of Nichols algebras. We illustrate this technique by explicitly constructing new examples of Nichols algebras in positive characteristic. We further describe the corresponding Radford biproducts and some liftings of these biproducts, which are new finite dimensional pointed Hopf algebras.

Analysis And Simulation In Neuron And Fibrosis Models, Humberto D. Perez Gonzalez

Mathematics Dissertations

In this work, we use analysis and numerical simulations to study the change of collective behaviorof two synaptically coupled square bursting systems, the effect of noise inan elliptic bursting system and foreign body reactions.For the square bursters we study its synchronization process as the strength ofcoupling increases. The two cells present chaotic bursting behaviorwhen there is no coupling. As the strength increases and past a certain value,the behavior of two cells, which are uncoupled, becomes synchronized regular burstingmotions. For the elliptic bursting phenomenon we study the distribution of the noise and its effects in the dynamics and the reliability of …

Multiple Positive Solutions For Nonlinear Third-Order Boundary Value Problems In Banach Spaces, Feng Wang, Hai-Hua Lu, Fang Zhang

Turkish Journal of Mathematics

This paper deals with the positive solutions of nonlinear boundary value problems in Banach spaces. By using fixed point index theory, some sufficient conditions for the existence of at least one or two positive solutions to boundary value problems in Banach spaces are obtained. An example illustrating the main results is given.

Stability Of An Euler-Lagrange Type Cubic Functional Equation, Abbas Najati, Fridoun Moradlou

Turkish Journal of Mathematics

In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for an Euler-Lagrange type cubic functional equation 2mf(x+my)+2f(mx-y)=(m^3+m)[f(x+y)+f(x-y)]+2(m^4-1)f(y) in Banach spaces and in left Banach modules over a unital Banach *-algebra for a fixed integer m with m\neq0,\pm1.

Strong Convergence Theorems By An Extragradient Method For Solving Variational Inequalities And Equilibrium Problems In A Hilbert Space, Poom Kumam

Turkish Journal of Mathematics

In this paper, we introduce an iterative process for finding the common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for monotone, Lipschitz-continuous mappings. The iterative process is based on the so-called extragradient method. We show that the sequence converges strongly to a common element of the above three sets under some parametric controlling conditions. This main theorem extends a recent result of Yao, Liou and Yao [Y. Yao, Y. C. Liou and J.-C. Yao, ''An Extragradient Method for Fixed …

On Symmetric Monomial Curves In P^3, Mesut Şahi̇n

Turkish Journal of Mathematics

In this paper, we give an elementary proof of the fact that symmetric arithmetically Cohen-Macaulay monomial curves are set-theoretic complete intersections. The proof is constructive and provides the equations of the surfaces cutting out the monomial curve.

Modules With Unique Closure Relative To A Torsion Theory Ii, Semra Doğruöz, Abdullah Harmanci, Patrick F. Smith

Turkish Journal of Mathematics

We study modules M over a general ring R such that every submodule has a unique closure with respect to a hereditary torsion theory \tau on Mod-R using the fact that the module M satisfies a certain transitivity property on \tau-closed submodules.

Modified Szász-Mirakjan-Kantorovich Operators Preserving Linear Functions, Oktay Duman, Mehmet Ali̇ Özarslan, Biancamaria Della Vecchia

Turkish Journal of Mathematics

In this paper, we introduce a modification of the Szász-Mirakjan-Kantorovich operators, which preserve the linear functions. This type of operator modification enables better error estimation on the interval [1/2,+\infty) than the classical Szász-Mirakjan-Kantorovich operators. We also obtain a Voronovskaya-type theorem for these operators.

Equi-Statistical Extension Of The Korovkin Type Approximation Theorem, Sevda Karakuş, Kami̇l Demi̇rci̇

Turkish Journal of Mathematics

In this paper using equi-statistical convergence, which is stronger than the usual uniform convergence and statistical uniform convergence, we obtain a general Korovkin type theorem. Then, we construct examples such that our new approximation result works but its classical and statistical cases do not work.

Local Fourier Bases And Ultramodulation Spaces, Salti Samarah, Fady Hasan

Turkish Journal of Mathematics

It was proved that local Fourier bases are unconditional bases for modulation spaces M_{p.q}^w. We prove that the local Fourier bases are unconditional bases for ultramodulation spaces M_p^{w_{\gamma}}=M_{p.p}^{w_{\gamma}}, where 0