Physical Sciences and Mathematics Commons^™

Some Inequalities Concerning The Rate Of Growth Of Polynomials, Abdullah Mir, K. K. Dewan, Naresh Singh

Turkish Journal of Mathematics

In this paper we consider a class of polynomials p(z)=a_0+\suml_{v=t}^n a_vz^v, t\ge1, not vanishing in z

Approximation By Certain Linear Operators Preserving X^2, Lucyna Rempulska, Karolina Tomczak

Turkish Journal of Mathematics

We investigate certain positive linear operators L_n preserving the functions e_k (x)=x^k, k=0, 1, and modified operators L_n^* which preserve e_0 and e_2. We show that the error of approximation of f by L_n^* (f) is smaller than for L_n(f).

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.

A New Approach On Constant Angle Surfaces In E^3, Marian Ioan Munteanu, Ana Irina Nistor

Turkish Journal of Mathematics

In this paper we study constant angle surfaces in Euclidean 3--space. Even that the result is a consequence of some classical results involving the Gauss map (of the surface), we give another approach to classify all surfaces for which the unit normal makes a constant angle with a fixed direction.

Applications Of The Golden Ratio On Riemannian Manifolds, Cristina-Elena Hretcanu, Mircea Craşmareanu

Turkish Journal of Mathematics

The Golden Ratio is a fascinating topic that continually generates new ideas. The main purpose of the present paper is to point out and find some applications of the Golden Ratio and of Fibonacci numbers in Differential Geometry. We study a structure defined on a class of Riemannian manifolds, called by us a Golden Structure. A Riemannian manifold endowed with a Golden Structure will be called a Golden Riemannian manifold. Precisely, we say that an (1,1)-tensor field \widetilde{P} on a m-dimensional Riemannian manifold (\widetilde{M}, \widetilde{g}) is a Golden Structure if it satisfies the equation \widetilde{P}^{2}=\widetilde{P}+I (which is similar to that …

Criteria Of Nilpotency And Influence Of Contranormal Subgroups On The Structure Of Infinite Groups, Leonid Andreevich Kurdachenko, Javier Otal, Igor Yakov Subbotin

Turkish Journal of Mathematics

Following J.S. Rose, a subgroup H of a group G is called contranormal if G=H^G. In a certain sense, contranormal subgroups are antipodes to subnormal subgroups. It is well known that a finite group is nilpotent if and only if it has no proper contranormal subgroups. However, for infinite groups this criterion is not valid. There are examples of non-nilpotent infinite groups whose subgroups are subnormal; in particular, these groups have no contranormal subgroups. Nevertheless, for some classes of infinite groups, the absence of contranormal subgroups implies nilpotency of the group. The present article is devoted to the search of …

A Note On The Lévy Constant For Continued Fractions, Ting Zhong

Turkish Journal of Mathematics

In this note, we study the lévy constant of continued fraction expansions. We show that for all x \in [0,1), the upper lévy constant of x is finite except a set with Hausdorff dimension one-half.

Intrinsic Equations For A Generalized Relaxed Elastic Line On An Oriented Surface In The Minkowski 3-Space E_1^3, Cumali̇ Eki̇ci̇, Ali̇ Görgülü

Turkish Journal of Mathematics

H. K. Nickerson and Gerald S. Manning [8] derived the intrinsic equations for a relaxed elastic line on an oriented surface in the Euclidean 3-dimensional space E^3. In this paper, we define a generalized relaxed elastic line and derive the intrinsic equations for a generalized of relaxed elastic line on an oriented surface in the Minkowski 3-dimensional space E_1^3 and give some applications of the result.

On Determining Paint By Numbers Puzzles With Nonunique Solutions, Ryan Mullen

Mathematics Faculty Publications

Paint by Numbers is a classic logic puzzle in which the squares of a p×n grid are to be colored in such a way as to display a picture. The decision on which squares to color is determined by sequences of numbers above each column and to the left of each row. The numbers describe how many consecutive squares are to be colored in that row or column, and multiple numbers represent multiple blocks of colored in squares (with at least one uncolored square in between blocks). Certain natural questions arise. For a given p × n grid, how many …

An A1 Function That Is Not In Lipα For Any Positive Α, Ryan Mullen

Mathematics Faculty Publications

Let A1 be the Banach algebra of all continuous functions on the torus whose Fourier coefficients are in 1, and let Lipα be the Banach algebra of all continuous function f on the torus such that ...

An Introduction To Dsmt, Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or highly conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning. In this introduction, we present a survey of our recent theory of plausible and paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT), developed for dealing with imprecise, uncertain and conflicting sources of information. We focus our presentation on the foundations of DSmT and on its most important rules of combination, rather than on browsing specific applications of DSmT available in literature. Several simple …

A Bayesian Network Approach To Feature Selection In Mass Spectrometry Data, Karl W. Kuschner

Dissertations, Theses, and Masters Projects

One of the key goals of current cancer research is the identification of biologic molecules that allow non-invasive detection of existing cancers or cancer precursors. One way to begin this process of biomarker discovery is by using time-of-flight mass spectroscopy to identify proteins or other molecules in tissue or serum that correlate to certain cancers. However, there are many difficulties associated with the output of such experiments. The distribution of protein abundances in a population is unknown, the mass spectroscopy measurements have high variability, and high correlations between variables cause problems with popular methods of data mining. to mitigate these …

Extremal Problems For Roman Domination, E. W. Chambers, W. Kinnersley, N. Prince, D. B. West

Faculty Publications & Research

A Roman dominating function of a graph G is a labeling f: V(G) →{0,1,2} such that every vertex with a label 0 has a neighbor with label 2. The Roman domination number γ_R(G) of G is the minimum of ∑_ʋϵV(G)f(v) over such functions. Let G be a connected n-vertex graph. We prove that γ_R(G) ≤ 4n/5, and we characterize the graphs achieving equality. We obtain sharp upper and lower bounds for γ_R(G) + …

Polynomial Extension Operators. Part Ii, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl

Mathematics and Statistics Faculty Publications and Presentations

Consider the tangential trace of a vector polynomial on the surface of a tetrahedron. We construct an extension operator that extends such a trace function into a polynomial on the tetrahedron. This operator can be continuously extended to the trace space of H(curl ). Furthermore, it satisfies a commutativity property with an extension operator we constructed in Part I of this series. Such extensions are a fundamental ingredient of high order finite element analysis.

The Derivation Of Hybridizable Discontinuous Galerkin Methods For Stokes Flow, Bernardo Cockburn, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we introduce a new class of discontinuous Galerkin methods for the Stokes equations. The main feature of these methods is that they can be implemented in an efficient way through a hybridization procedure which reduces the globally coupled unknowns to certain approximations on the element boundaries. We present four ways of hybridizing the methods, which differ by the choice of the globally coupled unknowns. Classical methods for the Stokes equations can be thought of as limiting cases of these new methods.

Unified Hybridization Of Discontinuous Galerkin, Mixed, And Continuous Galerkin Methods For Second Order Elliptic Problems, Bernardo Cockburn, Jay Gopalakrishnan, Raytcho Lazarov

Mathematics and Statistics Faculty Publications and Presentations

We introduce a unifying framework for hybridization of finite element methods for second order elliptic problems. The methods fitting in the framework are a general class of mixed-dual finite element methods including hybridized mixed, continu- ous Galerkin, non-conforming and a new, wide class of hybridizable discontinuous Galerkin methods. The distinctive feature of the methods in this framework is that the only globally coupled degrees of freedom are those of an approximation of the solution defined only on the boundaries of the elements. Since the associated matrix is sparse, symmetric and positive definite, these methods can be efficiently implemented. Moreover, the …

Reservation For Other Backward Classes In Indian Central Government Institutions Like Iits, Iims And Aiims – A Study Of The Role Of Media Using Fuzzy Super Frm Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The new notions of super column FRM model, super row FRM model and mixed super FRM model are introduced in this book. These three models are introduced specially to analyze the biased role of the print media on 27 percent reservation for the Other Backward Classes (OBCs) in educational institutions run by the Indian Central Government. This book has four chapters. In chapter one the authors introduce the three types of super FRM models. Chapter two uses these three new super fuzzy models to study the role of media which feverishly argued against 27 percent reservation for OBCs in Central …

Dynamics And Rheology Of Biaxial Liquid Crystal Polymers, Sarthok K. Sircar

Theses and Dissertations

In this thesis we derive a hydrodynamical kinetic theory to study the orientational response of a mesoscopic system of nematic liquid crystals in the presence of an external flow field. Various problems have been attempted in this direction. First, we understand the steady-state behavior of uniaxial LCPs under an imposed elongational flow, electric and magnetic field respectively. We show that (1) the Smoluchowski equation can be cast into a generic form, (2) the external field is parallel to one of the eigenvectors of the second moment tensor, and (3) the steady state probability density function is of the Boltzmann type. …

My Trig Book, Bruce Kessler

Mathematics Faculty Publications

This is the MATH 117 Trigonometry text developed by Dr. Bruce Kessler for the Gatton Academy of Math and Science at Western Kentucky University for the Math and Science sections of the course. The text has also been used in two online course offerings.

Comic Books That Teach Mathematics, Bruce Kessler

Mathematics Faculty Publications

During the 2008--2009 academic year, the author embarked on an extremely non-standard curriculum path: developing comic books with embedded mathematics appropriate for 3rd through 6th grade students. With the help of an education professor to measure impact, an elementary-school principal, and talented undergraduate illustrators, this project came to fruition and the comics were implemented in elementary classrooms at Cumberland Trace Elementary in the Warren County School System in Bowling Green, Kentucky. This manuscript gives the history of this idea, the difficulties of developing the content of the comics and getting them illustrated, and the implementation plan in the school.

My Trig Book, Bruce Kessler

Mathematics Faculty Publications

This is the MATH 117 Trigonometry text developed by Dr. Bruce Kessler for the Gatton Academy of Math and Science at Western Kentucky University for the Academy sections of the course. The text has also been used in two online course offerings.

Gas-Kinetic Schemes For Direct Numerical Simulations Of Compressible Homogeneous Turbulence, Wei Liao, Yan Peng, Li-Shi Luo

Mathematics & Statistics Faculty Publications

We apply the gas-kinetic scheme (GKS) for the direct numerical simulations (DNSs) of compressible decaying homogeneous isotropic turbulence (DHIT). We intend to study the accuracy, stability, and efficiency of the gas-kinetic scheme for DNS of compressible homogeneous turbulence depending on both flow conditions and numerics. In particular, we study the GKS with multidimensional, quasi-one-dimensional, dimensional-splitting, and smooth-flow approximations. We simulate the compressible DHIT with the Taylor microscale Reynolds number Reλ =72.0 and the turbulence Mach number Ma_t between 0.1 and 0.6. We compute the low-order statistical quantities including the total kinetic energy K (t), the dissipation rate ε (t), …

Convergence And The Lebesgue Integral, Ryan Vail Thomas

MSU Graduate Theses

In this paper, we examine the theory of integration of functions of real variables. Background information in measure theory and convergence is provided and several examples are considered. We compare Riemann and Lebesgue integration and develop several important theorems. In particular, the Monotone Convergence Theorem and Dominated Convergence Theorem are considered under both pointwise convergence and convergence in measure.

Converging Flow Between Coaxial Cones, O. Hall, A. D. Gilbert, C. P. Hills

Articles

Fluid flow governed by the Navier-Stokes equation is considered in a domain bounded by two cones with the same axis. In the first, 'non-parallel' case, the two cones have the same apex and different angles θ = α and β in spherical polar coordinates (r, θ, φ). In the second, 'parallel' case, the two cones have the same opening angle α, parallel walls separated by a gap h and apices separated by a distance h/sinα. Flows are driven by a source Q at the origin, the apex of the lower cone in the parallel case. The Stokes solution for the …

Nonaxisymmetric Stokes Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert

Articles

We study the fully three-dimensional Stokes flow within a geometry consisting of two infinite cones with coincident apices. The Stokes approximation is valid near the apex and we consider the dominant flow features as it is approached. The cones are assumed to be stationary and the flow to be driven by an arbitrary far-field disturbance. We express the flow quantities in terms of eigenfunction expansions and allow for the first time for nonaxisymmetric flow regimes through an azimuthal wave number. The eigenvalue problem is solved numerically for successive wave numbers. Both real and complex sequences of eigenvalues are found, their …

Dendrites, Topological Graphs, And 2-Dominance, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

For each positive ordinal α, the reflexive and transitive binary relation of α-dominance between compacta was first defined in our paper [Mapping properties of co-existentially closed continua, Houston J. Math., 31 (2005), 1047-1063] using the ultracopower construction. Here we consider the important special case α =2, and show that any Peano compactum 2-dominated by a dendrite is itself a dendrite (with the same being true for topological graphs and trees). We also characterize the topological graphs that 2-dominate arcs (resp., simple closed curves) as those that have cut points of order 2 (resp., those that are not trees).

Compartmentalized Approach To The Assembly Of Physical Maps, Serdar Bozdag, Timothy J. Close, Stefano Lonardi

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

Physical maps have been historically one of the cornerstones of genome sequencing and map-based cloning strategies. They also support marker assisted breeding and EST mapping. The problem of building a high quality physical map is computationally challenging due to unavoidable noise in the input fingerprint data.

Results

We propose a novel compartmentalized method for the assembly of high quality physical maps from fingerprinted clones. The knowledge of genetic markers enables us to group clones into clusters so that clones in the same cluster are more likely to overlap. For each cluster of clones, a local physical map is first …

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

Faculty Publications

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).

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

Faculty Publications

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 …

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

Faculty Publications

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 …