Mathematics Commons^™

A Borsuk-Ulak Theorem For Heisenberg Group Actions, Necdet Güner

Turkish Journal of Mathematics

Let $G=H_{2n+1}$ be a $(2n+1)$-dimensional Heisenberg Lie group acts on $M=C^m-\{0\}$ and $M^{'}=C^{m'}-\{0\}$ exponentially. By using Cohomological Index we proved the following theorem. If $f:M{\to}M^{'}$ is a $G$-equivariant map, then $m{\le}m'$.

On Conjugation In The Mod-P Steenrod Algebra, İsmet Karaca, İlkay Yaslan Karaca

Turkish Journal of Mathematics

In this paper we prove a formula involving the canonical anti-automorphism $\chi$ of the mod-$p$ Steenrod algebra.

On Subspaces Isomorphic To L^Q In Interpolation Of Quasi Banach Spaces, J. A. Lopez Molina

Turkish Journal of Mathematics

We show that every sequence $\{x_n\}_{n=1}^{\infty}$ in a real interpolation space $(E_0,E_1)_{\theta,q}$, $0 < \theta < 1$, $0 < q < \infty,$ of quasi Banach spaces $E_0,E_1,$ which is $0-$convergent in $E_0 + E_1$ but $\inf_n \;\ x_n\ _{(E_0,E_1)_{\theta,q}} > 0,$ has a subsequence which is equivalent to the standard unit basis of $\ell^q.$

The P-Stirling Numbers, Russel Merris

Turkish Journal of Mathematics

The purpose of this article is to introduce \( p \)-Stirling numbers of the first and second kinds.

Some Radius Problem For Certain Families Of Analytic Functions, Yaşar Polatoğlu, Meti̇n Bolcal

Turkish Journal of Mathematics

The aim of this paper is to give bounds of the radius of $\alpha $-convexity for certain families of analytic functions in the unit disc. The radius of $\alpha $-convexity is generalization of the radius of convexity and the radius of starlikeness, and introduced by S.S.Miller; P.T.Mocanu and M.O.Reade [3,4]

On Simplicial Commutative Algebras With Vanishing André-Quillen Homology, James M. Turner

University Faculty Publications and Creative Works

In this paper, we study the André-Quillen homology of simplicial commutative ℓ-algebras, ℓ a field, having certain vanishing properties. When ℓ has non-zero characteristic, we obtain an algebraic version of a theorem of J.-P. Serre and Y. Umeda that characterizes such simplicial algebras having bounded homotopy groups. We further discuss how this theorem fails in the rational case and, as an application, indicate how the algebraic Serre theorem can be used to resolve a conjecture of D. Quillen for algebras of finite type over Noetherian rings, having non-zero characteristic.

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.

[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 …

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 …

Cyclic Dehn Surgery And The A-Polynomial, Patrick Shanahan

Mathematics, Statistics and Data Science Faculty Works

We present a necessary condition for Dehn surgery on a knot in double-struck S sign3 to be cyclic which is based on the A-polynomial of the knot. The condition involves a width of the Newton polygon of the A-polynomial, and provides a simple method of computing a list of possible cyclic surgery slopes. The width produces a list of at most three slopes for a hyperbolic knot which contains no closed essential surface in its complement (in agreement with the Cyclic Surgery Theorem). We conclude with an application to cyclic surgeries along non-boundary slopes of hyperbolic mutant knots.

Finite Type Link Concordance Invariants, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

This paper is a generalization of the author's previous work on link homotopy to link concordance. We show that the only real-valued finite type link concordance invariants are the linking numbers of the components.

Finite Type Link Homotopy Invariants Ii: Milnor's Invariants, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

We define a notion of finite type invariants for links with a fixed linking matrix. We show that Milnor's triple link homotopy invariant is a finite type invariant, of type 1, in this sense. We also generalize the approach to Milnor's higher order homotopy invariants and show that they are also, in a sense, of finite type. Finally, we compare our approach to another approach for defining finite type invariants within linking classes.

The Intersection Graph Conjecture For Loop Diagrams, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

Vassiliev invariants can be studied by studying the spaces of chord diagrams associated with singular knots. To these chord diagrams are associated the intersection graphs of the chords. We extend results of Chmutov, Duzhin and Lando to show that these graphs determine the chord diagram if the graph has at most one loop. We also compute the size of the subalgebra generated by these "loop diagrams."

[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.

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.

[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 …

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 …

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. …

Distribution Of Petrogenic Hydrocarbons In Water, Sediment And Cockles (Anadara Granosa) From Kuala Sungai Sepetang And Kuala Sungai Selangor, Mohd Hilmi Jaafar

Student Works (2000-2009)

In order to assess the level of oil pollution in the cockle culture areas along the Straits of Malacca, water, sediment and cockle samples were collected from the culture beds of Kuala Sepetang and Kuala Selangor, two of the largest cockle producing areas of Malaysia. The samples were analysed for petrogenic hydrocarbons by employing a spectrofluorometric technique which measures the content of polycyclic aromatic hydrocarbons (PAH) in oil. The content of aliphatic straight chain hydrocarbons were measured by using gas chromatography􀀐mass spectrometry (GCMS) which also allowed for the estimation of carbon preference indices and hence providing a means of estimating …

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 …

Nonstationary Panels, Cointegration In Panels And Dynamic Panels: A Survey, Badi H. Baltagi, Chihwa Kao

Center for Policy Research

This paper provides an overview of topics in nonstationary panels: panel unit root tests, panel cointegration tests, and estimation of panel cointegration models. In addition it surveys recent developments in dynamic panel data models.