Mathematics Commons^™

A Note On The Application Of Ec2sls And Ec3sls Estimators In Panel Data Models, Badi H. Baltagi, Long Liu

Center for Policy Research

Baltagi and Li (1992) showed that for estimating a single equation in a simultaneous panel data model, EC2SLS has more instruments than G2SLS. Although these extra instruments are redundant in White (1986) terminology, they may yield different estimates and standard errors in empirical studies with finite N and T. We illustrate this using the crime data of Cornwell and Trumbull (1994). We show that the standard errors of EC2SLS are smaller than those of G2SLS for this example. In general, we prove that the asymptotic variance of G2SLS differs from that of EC2SLS by a positive semi-definite matrix. Although this …

Topology And Infinite Graphs, Nicholas Blackburn Lowery

Honors Papers

The main focus of this paper will be on two very different areas in which topology is relevant to the study of infinite graphs. The first is the mechanics of compactness proofs, which use a particular group of lemmas to extend results about finite subgraphs to apply to an entire infinite graph. We will explore these results by using them to prove a result of de Bruijn and Erdos, that an infinite graph is k-colorable if its finite subgraphs are k-colorable, in several different ways.

The second area is a relatively new area of study pioneered by Diestel which redefines …

Common Cyclic Vectors For Unitary Operators, William T. Ross, Warren R. Wogen

Department of Math & Statistics Faculty Publications

In this paper, we determine whether or not certain natural classes of unitary multiplication operators on L²(dƟ) have common cyclic vectors. For some classes which have common cyclic vectors, we obtain a classification of these vectors.

A Nonlinear Extremal Problem On The Hardy Space, William T. Ross, Stephan Ramon Garcia

Department of Math & Statistics Faculty Publications

We relate some classical extremal problems on the Hardy space to norms of truncated Toeplitz operators and complex symmetric operators

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 …

Complementary Responses To Mean And Variance Modulations In The Perfect Integrate-And-Fire Model, Joanna R. Wares, Todd W. Troyer

Department of Math & Statistics Faculty Publications

In the perfect integrate-and-fire model (PIF), the membrane voltage is proportional to the integral of the input current since the time of the previous spike. It has been shown that the firing rate within a noise free ensemble of PIF neurons responds instantaneously to dynamic changes in the input current, whereas in the presence of white noise, model neurons preferentially pass low frequency modulations of the mean current. Here, we prove that when the input variance is perturbed while holding the mean current constant, the PIF responds preferentially to high frequency modulations. Moreover, the linear filters for mean and variance …

Biology In Mathematics At The University Of Richmond, Lester Caudill

Department of Math & Statistics Faculty Publications

In an effort to meet the needs of science students for modeling skills, three new courses have been created at the University of Richmond: Scientific Calculus I and II, and Mathematical Models in Biology and Medicine. The courses are described, and lessons learned and future directions are discussed.

Meaningful Distributed Instruction— Developing Number Sense, Edward C. Rathmell

Faculty Work

What Is Number Sense?

The primary goal for elementary and middle school mathematics is to help students learn to use numbers meaningfully, reasonably and flexibly in everyday life. This means that students must develop a deep understanding of

-- numbers and operations,
-- when operations can appropriately be used to solve problems, and
-- judging the reasonableness of their solutions to problems.

They also need to develop attitudes so they

-- believe they can make sense of mathematics, and
-- habitually try to make sense of mathematics.

In other words, students need to develop number sense.

Understandings Needed for Number …

The Iowa Core Curriculum And Me: How My Teaching Of Mathematics Methods Will Change, Catherine M. Miller

Faculty Work

It is an exciting time to be a mathematics educator in Iowa! We are joining the other 49 states by having a set of state standards. In fact, Iowa is exceeding federal expectations by having a curriculum to inform the work of teachers and school administrators. Because of this, we enter an era of change in Iowa and, as we know, change is never easy. To succeed in implementing the Iowa Core Curriculum (ICC) in mathematics all teachers need to learn about it and have help in implementing its core ideas and content. This includes teachers who will begin their …

Skittles Chocolate Mix Color Distribution: A Chi-Square Experience, David R. Duncan, Bonnie H. Litwiller

Faculty Work

In teaching statistical processes, it is important that there be application to realworld settings and activities. When this is done, students are more likely to see the meaning of the steps being developed.

One such activity involves using the Chi-Square statistical test and its applications to counting Skittles Chocolate Mix candies. Many students are aware that these candies come in five different flavors: Brownie Batter (BB), Vanilla (V), Chocolate Caramel (CC), S’mores (S), and Chocolate Pudding (CP).

Problem-Based Instructional Tasks, Larry Leutzinger

Faculty Work

No abstract provided.

Conceptual Previews In Preparation For The Next Unit Of Instruction, Michele Carnahan, Bridgette Stevens

Faculty Work

Understanding meanings of operations and how they relate to one another is an important mathematical goal for students in fourth grade (National Council of Teachers of Mathematics, 2000). Using pictures, diagrams, or concrete materials to model multiplication helps students learn about factors and how their products represent various contexts. The foundation of understanding how operations of multiplication and division relate to one another deepens the understanding of the composition of numbers. Discussing different types of problems that can be solved using multiplication and division is important, along with the ability to decompose numbers. When students can work among these relationships …

An Investigation Of The Ends Of Finitely Generated Groups, Daniel T. Murphree

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Geometric group theory is a relatively new branch of mathematics, studied as a distinct area since the 1990's. It explores invariant properties of groups based on group actions defined on topological or geometrical spaces. One of the pioneering works in geometric group theory is the article "Topological Methods in Group Theory" by Peter Scott and Terry Wall, written in 1977. This article was an overview of revised notes from an advanced course give in Liverpool in the same year. This report is an attempt to make these notes more accessible to lower level graduate students in the fields of topology …

Positive Solutions For The (N, P) Boundary Value Problem, Bo Yang

Faculty Articles

We consider the (n, p) boundary value problem in this paper. Some new upper estimates to positive solutions for the problem are obtained. Existence and nonexistence results for positive solutions of the problem are obtained by using the Krasnosel'skii fixed point theorem. An example is included to illustrate the results.

Simulation Studies On Estimation Of Variance Components For Multilevel Models, Sara Vakilian

Theses and Dissertations (Comprehensive)

With the presence of unequal sampling in a multilevel model, the weight inflated estimators for variance components can be biased even though the use of survey weights results in design consistent estimators of the parameters. In this thesis I will carry out a simulation study to examine the performance of current existing methods and I will examine the resampling method for correcting bias of estimators of variance components of a multilevel model with covariates. This study will be based on these three papers: “Weighting for Unequal Selection Probabilities in Multilevel Models” by D. Pfeffermann , C. J. Skinner, D.J. Holmes, …

First-Passage Time Models With A Stochastic Time Change In Credit Risk, Hui Li

Theses and Dissertations (Comprehensive)

Many authors have used a time-changed Brownian motion as a model of log-stock returns. Using a Levy process as a stochastic time change, one obtains well known asset price models such as the variance gamma (VG) and normal inverse Gaussian (NIG) models. Following on the heels of these asset price models, it is natural to extend structural credit models by using a time-changed geometric Brownian motion and other jump-diffusion processes to model the value of a firm. To avoid the difficulties that arise in computing the associated first passage time distribution and in analogy to the time-changed Markov chain models, …

Stack-Sortable Permutations And Polynomials, İsmai̇l Ş. Güloğlu, Cemal Koç

Turkish Journal of Mathematics

The Catalan numbers show up in a diverse variety of counting problems. In this note we give yet another characterization of the Catalan number C(n). It is characterized as the dimension of a certain space of multilinear polynomials by exhibiting a basis.

Values Of The Carmichael Function Equal To A Sum Of Two Squares, William D. Banks, Ahmet M. Güloğlu

Turkish Journal of Mathematics

In this note, we determine the order of growth of the number of positive integers n \le x such that \lambda(n) is a sum of two square numbers, where \lambda(n) is the Carmichael function.

On \Phi-Recurrent Kenmotsu Manifolds, Uday Chand De, Ahmet Yildiz, Funda Yaliniz

Turkish Journal of Mathematics

The object of this paper is to study \phi-recurrent Kenmotsu manifolds. Also three-dimensional locally \phi-recurrent Kenmotsu manifolds have been considered. Among others it is proved that a locally \phi-recurrent Kenmotsu spacetime is the Robertson-Walker spacetime. Finally we give a concrete example of a three-dimensional Kenmotsu manifold.

Lebesgue-Stieltjes Measure On Time Scales, Asli Deni̇z, Ünal Ufuktepe

Turkish Journal of Mathematics

The theory of time scales was introduced by Stefan Hilger in his Ph. D. thesis in 1988, supervised by Bernd Auldbach, in order to unify continuous and discrete analysis [5]. Measure theory on time scales was first constructed by Guseinov [4], then further studies were made by Guseinov-Bohner [1], Cabada-Vivero [2] and Rzezuchowski [6]. In this article, we adapt the concept of Lebesgue-Stieltjes measure to time scales. We define Lebesgue-Stieltjes \Delta and \nabla-measures and by using these measures, we define an integral adapted to time scales, specifically Lebesgue-Stieltjes \Delta-integral. We also establish the relation between Lebesgue-Stieltjes measure and Lebesgue-Stieltjes \Delta-measure, …

Korovkin Type Error Estimates For Positive Linear Operators Involving Some Special Functions, Ogün Doğru, Esra Erkuş-Duman

Turkish Journal of Mathematics

In the present paper, we introduce a new sequence of linear positive operators with the help of generating functions. We obtain some Korovkin type approximation properties for these operators and compute rates of convergence by means of the first and second order modulus of continuities and Peetre´s K-functional. In order to obtain explicit expressions for the first and second moment of our operators, we obtain a functional differential equation including our operators. Furthermore, we deal with a modification of our operators converging to integral of function f on the interval (0,1).

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.

Cartan Calculus On The Quantum Space R_Q^3, Sali̇h Çeli̇k, E. Mehmet Özkan, Ergün Yaşar

Turkish Journal of Mathematics

To give a Cartan calculus on the extended quantum 3d space, the noncommutative differential calculus on the extended quantum 3d space is extended by introducing inner derivations and Lie derivatives.

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 …

Geodesics Of The Cheeger-Gromoll Metric, Ari̇f A. Salimov, S. Kazimova

Turkish Journal of Mathematics

The main purpose of the paper is to investigate geodesics on the tangent bundle with respect to the Cheeger-Gromoll metric.

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.

On \Tau-Lifting Modules And \Tau-Semiperfect Modules, Mustafa Alkan

Turkish Journal of Mathematics

Motivated by [1], we study on \tau-lifting modules (rings) and \tau-semiperfect modules (rings) for a preradical \tau and give some equivalent conditions. We prove that; i) if M is a projective \tau-lifting module with \tau(M) \subseteq \delta(M), then M has the finite exchange property; ii) if R is a left hereditary ring and \tau is a left exact preradical, then every \tau-semiperfect module is \tau--lifting; iii) R is \tau-lifting if and only if every finitely generated free module is \tau-lifting if and only if every finitely generated projective module is \tau-lifting; iv) if \tau (R) \subseteq \delta (R), then R …

Perturbation Of Closed Range Operators, Mohammad Sal Moslehian, Ghadir Sadeghi

Turkish Journal of Mathematics

Let T, A be operators with domains D(T) \subseteq D(A) in a normed space X. The operator A is called T-bounded if Ax \leq a x +b Tx for some a, b\geq 0 and all x \in D(T). If A has the Hyers--Ulam stability then under some suitable assumptions we show that both T and S: = A+T have the Hyers--Ulam stability. We also discuss the best constant of Hyers--Ulam stability for the operator S. Thus we establish a link between T-bounded operators and Hyers--Ulam stability.

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.