Mathematics Commons^™

Some Results On Derivation Groups, Murat Alp

Turkish Journal of Mathematics

In this paper we describe a share package XMOD of functions for computing with finite, permutation crossed modules, their morphisms and derivations; cat$^1$-groups, their morphisms and their sections, written using the GAP \cite{GAP} group theory programming language. We also give some mathematical results for derivations. These results are suggested by the output produced by the XMOD package.

Strongly Prime Ideals In Cs-Rings, Gonca Güngöroğlu

Turkish Journal of Mathematics

We study and characterize strongly prime right ideals in CS-rings.

On Non-Homogeneous Riemann Boundary Value Problem, Kadi̇r Kutlu

Turkish Journal of Mathematics

In this paper we consider non-homogeneous Riemann boundary value problem with unbounded oscillating coefficients on a class of open rectifiable Jordan curve.

A Remark On The Asymptotic Properties Of Positive Homogeneous Maps On Homogeneous Lattices, Alp Eden

Turkish Journal of Mathematics

An abstract version of Lyapunov exponents is defined for positive homogeneous maps on Homogeneous Lattices and a sufficient condition is given for the asymptotic stability of the map.

Multipliers Between Orlicz Sequence Spaces, P. B. Djakov, M. S. Ramanuan

Turkish Journal of Mathematics

Let $M, N $ be Orlicz functions, and let $D(\ell_M , \ell_N ) $ be the space of all diagonal operators (that is multipliers) acting between the Orlicz sequence spaces $\ell_M$ and $\ell_N$. We prove that the space of multipliers $D(\ell_M , \ell_N )$ coincides with (and is isomorphic to) the Orlicz sequence space $ \ell_{M_N^{*}} ,$ where $ M_N^{*} $ is the Orlicz function defined by $M_N^{*}(\lambda ) = \sup \{ N(\lambda x) - M(x), \; x \in (0,1) \}$.

Three-Dimensional Computer Simulation Of Liquid Drop Evaporation, Mark Korlie

Department of Mathematics Faculty Scholarship and Creative Works

We use molecular dynamics simulation to describe a method that can be used to model liquid drop evaporation. For application, the liquid is taken to be water. Using the properties of the liquid and a Lennard-Jones potential, we derive dynamical equations, which are used to describe the gross dynamical behavior of the liquid-vapor molecular system. The resulting dynamical equations are solved numerically by a time stepping, numerical method. The evaporation of the liquid to the vapor phase is described.

3-D Particle Modeling Of Gas Bubbles In A Liquid, Mark Korlie

Department of Mathematics Faculty Scholarship and Creative Works

We use a molecular aggregate approach and classical, molecular dynamics type formulas to simulate the motion of gas bubbles within a liquid. For application, the liquid is taken to be water while the gas is taken to be carbon dioxide. The resulting dynamical equations are large systems of second-order, nonlinear, ordinary differential equations which are solved by a time-stepping numerical method. The rise of the bubbles and the motion of the water near the bubbles are described and discussed.

Development Of Multiple Channels Edf Lasers, Muhammad Zamzuri Abdul Kadir

Student Works (2000-2009)

This thesis presents the research work carried out on the development and analysis of single wavelength EDFL and multiple wavelength EDFL. Two types of single wavelength EDF ring laser were studied namely a fixed signal wavelength system and a tuneable signal wavelength system. However, emphasis was given to the first case. The analyses made, were based on the following parameters: pump and signal stability, pump power, reflectivity, EDF length and cavity loss. The influence of each cavity component such as isolator, polarisation controller, attenuator and tuneable filter were also investigated and reported here. Only one type of multiple wavelength EDFL …

[Introduction To] The Backward Shift On The Hardy Space, William T. Ross, Joseph A. Cima

Bookshelf

Shift operators on Hilbert spaces of analytic functions play an important role in the study of bounded linear operators on Hilbert spaces since they often serve as models for various classes of linear operators. For example, "parts" of direct sums of the backward shift operator on the classical Hardy space H2 model certain types of contraction operators and potentially have connections to understanding the invariant subspaces of a general linear operator.

This book is a thorough treatment of the characterization of the backward shift invariant subspaces of the well-known Hardy spaces Hp. The characterization of the backward shift …

Understanding Of The Limit Of Functions Among College Students, Logesh K. Sivapakianathan

Student Works (2000-2009)

This study explored concept images and concept definitions of college students on limits of functions. Their views concerning the attainability of the limit and the extent to which they understood the stand taken by the formal view on this matter were also probed on. The sample comprised 10 students who had completed the Calculus and Analytic Geometry 1 course in the School of American University Studies at a private college in the Klang Valley. A questionnaire on beliefs about limits was administered to them and 4 students were then selected for a task-based interview on the attainability of the limit. …

On Strongly N-Regular And Strongly Regular Rings, Huey Voon Chen

Student Works (2000-2009)

Let R be an associative ring with identity 1 (not equal to) 0. An element x E R is said to be right (or left) regular if there exists yin R such that x² y = x (or y.x² = x). If x is both left and right regular, then it is said to be strongly regular. The ring R is said to be strongly regular if every element of R is strongly regular. We say that x is a left -π-regular element if there exist an integer n > 0 and an element y E R such that yx n+1 …

A Brief Biography Of Professor L.C. Hsu (Lizhi Xu), Tian-Xiao He

Scholarship

No abstract provided.

On Some Length Biased Inequalities For Reliability Measures, Broderick O. Oluyede

Mathematical Sciences: Faculty Publications

In this note, inequalities for length biased and the original residual life function and equilibrium distribution function with monotone hazard rate and mean residual life functions are derived. We also obtain estimates of the length biased probability density function and hazard function under random censoring. Finally, the Bayesian exponential reliability estimate under length biased sampling using a conjugate prior for the scale parameter is given.

Boundary Controllability Of Thermoelastic Plates Via The Free Boundary Conditions, George Avalos, Irena Lasiecka

Department of Mathematics: Faculty Publications

Controllability properties of a partial differential equation (PDE) model describing a thermoelastic plate are studied. The PDE is composed of a Kirchoff plate equation coupled to a heat equation on a bounded domain, with the coupling taking place on the interior and boundary of the domain. The coupling in this PDE is parameterized by α > 0. Boundary control is exerted through the (two) free boundary conditions of the plate equation and through the Robin boundary condition of the temperature. These controls have the physical interpretation of inserted forces and moments and prescribed temperature, respectively, all of which act on the …

Two-Groups With Few Conjugacy Classes, Nigel Boston, Judy L. Walker

Department of Mathematics: Faculty Publications

An old question of Brauer asking how fast numbers of conjugacy classes grow is investigated by considering the least number c_n of conjugacy classes in a group of order 2ⁿ. The numbers c_n are computed for n ≤ 14 and a lower bound is given for c₁₅. It is observed that c_n grows very slowly except for occasional large jumps corresponding to an increase in coclass of the minimal groups G_n. Restricting to groups that are 2-generated or have coclass at most 3 allows us to extend these computations.

Translation Theorems For Fourier-Feynman Transforms And Conditional Fourier-Feynman Transforms, Seung Jun Change, Chull Park, David Skough

Department of Mathematics: Faculty Publications

Translation theorems for Wiener integrals were given by Cameron and Martin in [3] and by Cameron and Graves in [2]. Translation theorems for analytic Feynman integrals were given by Cameron and Storvick in [4], [7] and translation theorems for Feynman integrals on abstract Wiener and Hilbert spaces were given by Chung and Kang in [12].

[Introduction To] Schaum's Outline Programming With C++, John R. Hubbard

Bookshelf

Tough Test Questions? Missed Lectures? Not Enough Time?

Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you

• Practice problems with full explanations that reinforce knowledge
• Coverage of the most up-to-date developments in your course field
• In-depth review of practices …

[Introduction To] Mathematics Calculus Bc, John R. Hubbard, David R. Arterburn, Michael A. Perl

Bookshelf

This book gives you the tools to prepare effectively for the Advanced Placement Examination in Mathematics: Calculus BC. These tools include a concise topical review and six full-length practice tests. Our review succinctly covers areas considered most relevant to this exam. Following each of our tests is an answer key complete with detailed explanations designed to clarify the material for you.

Collected Papers Vol. Iii, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Algebra În Exercijii Şi Probleme Pentru Liceu, Florentin Smarandache, Ion Goian, Raisa Grigor, Vasila Marin

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Definitions, Solved And Unsolved Problems, Conjectures, And Theorems In Number Theory And Geometry, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Florentin Smarandache, an American mathematician of Romanian descent has generated a vast variety of mathematical problems. Some problems are easy, others medium, but many are interesting or unsolved and this is the reason why the present book appears. Here, of course, there are problems from various types. Solving these problems is addictive like eating pumpkin seed: having once started, one cannot help doing it over and over again.

An Extension Of Zermelo's Model For Ranking By Paired Comparisons, Christopher P. Grant, Gregory R. Conner

Faculty Publications

In 1929, Zermelo proposed a probabilistic model for ranking by paired comparisons and showed that this model produces a unique ranking of the objects under consideration when the outcome matrix is irreducible. When the matrix is reducible, the model may yield only a partial ordering of the objects. In this paper, we analyse a natural extension of Zermelo's model resulting from a singular perturbation. We show that this extension produces a ranking for arbitrary (nonnegative) outcome matrices and retains several of the desirable properties of the original model. In addition, we discuss computational techniques and provide examples of their use.

A Mathematical Model For Spatially Varying Extracellular Matrix, J. C. Dallon, J. A. Sherratt

Faculty Publications

Orientation of extracellular matrix fibers in the skin is a key ingredient of tissue appearance and function, and differences in fiber alignment are one of the main distinctions between scar tissue and normal skin. In this paper, the authors develop a mathematical model for alignment of collagen fibers and the fibroblast cells that remodel them; the model extends previous work in which spatial variation was excluded. Numerical simulations of the model are presented, which show spatial variations in alignment over long transients, but with spatially uniform behavior in the long term. This is investigated further via asymptotic analysis, using the …