Physical Sciences and Mathematics Commons^™

2004 Vol. 1 Table Of Contents, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Past Content

No abstract provided.

Newton-Raphson Versus Fisher Scoring Algorithms In Calculating Maximum Likelihood Estimates, Andrew Schworer, Peter Hovey

Undergraduate Mathematics Day: Past Content

In this work we explore the difficulties and the means by which maximum likelihood estimates can be calculated iteratively when direct solutions do not exist. The Newton-Raphson algorithm can be used to do these calculations. However, this algorithm has certain limitations that will be discussed. An alternative algorithm, Fisher scoring, which is less dependent on specific data values, is a good replacement. The Fisher scoring method converged for data sets available to the authors, that would not converge when using the Newton-Raphson algorithm. An analysis and discussion of both algorithms will be presented. Their real world application on analysis of …

How Not To Get Lost While On A Random Walk, Robert Lewand

Undergraduate Mathematics Day: Past Content

What happens if you go on a random walk? Will you ever return home? Well, sometimes yes (probably) and sometimes no (probably). During this talk we will derive some elementary identities in favor you're not getting lost while on a random walk.

On The Cotorsion Images Of The Baer-Specker Group, Brendan Goldsmith, T. Kelly, S, Wallutis

Articles

No abstract available

Torsion-Free Weakly Transitive Abelian Groups, Brendan Goldsmith, Lutz Strungmann

Articles

We introduce the notion of weak transitivity for torsion-free abelian groups. A torsion-free abelian group G is called weakly transitive if for any pair of elements x, y ∈ G and endomorphisms ϕ, ψ ∈ End(G) such that xϕ = y, yψ = x, there exists an automorphism of G mapping x onto y. It is shown that every suitable ring can be realized as the endomorphism ring of a weakly transitive torsion-free abelian group, and we characterize up to a number-theoretical property the separable weakly transitive torsion-free abelian groups.

The Spectral Function For Sturm-Liouville Problems Where The Potential Is Of Wigner-Von Neumann Type Or Slowly Decaying, Daphne Gilbert, B.J. Harris, S.M. Riehl

Articles

We consider the linear, second-order, differential equation (∗) with the boundary condition (∗∗)

We suppose that q(x) is real-valued, continuously differentiable and that q(x)→0 as x→∞ with q∉L1[0,∞). Our main object of study is the spectral function ρα(λ) associated with () and (). We derive a series expansion for this function, valid for λ⩾Λ0 where Λ0 is computable and establish a Λ1, also computable, such that () and () with α=0, have no points of spectral concentration for λ⩾Λ1. We illustrate our results with examples. In particular we consider the case of the Wigner–von Neumann potential.

[Introduction To] Schaum's Outline Of Programming With Java, 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] Data Structures With Java, John R. Hubbard, Anita Huray

Bookshelf

For a freshman/sophomore-level course in Data Structures in Computer Science. This text teaches the use of direct source code implementations and the use of the Java libraries; it helps students prepare for later work on larger Java software solutions by adhering to software engineering principles and techniques such as the UML and the Java Collections Framework (JCF). Using the spiral approach to cover such topics as linked structures, recursion, and algorithm analysis, this text also provides revealing illustrations, summaries, review questions, and specialized reference sections.

Evaluation Of Multiple Models To Distinguish Closely Related Forms Of Disease Using Dna Microarray Data: An Application To Multiple Myeloma, Johanna S. Hardin, Michael Waddell, C. David Page, Fenghuang Zhan, Bart Barlogie, John Shaughnessy, John J. Crowley

Pomona Faculty Publications and Research

Motivation: Standard laboratory classification of the plasma cell dyscrasia monoclonal gammopathy of undetermined significance (MGUS) and the overt plasma cell neoplasm multiple myeloma (MM) is quite accurate, yet, for the most part, biologically uninformative. Most, if not all, cancers are caused by inherited or acquired genetic mutations that manifest themselves in altered gene expression patterns in the clonally related cancer cells. Microarray technology allows for qualitative and quantitative measurements of the expression levels of thousands of genes simultaneously, and it has now been used both to classify cancers that are morphologically indistinguishable and to predict response to therapy. It is …

The Growth Of Valuations On Rational Function Fields In Two Variables, Edward Mosteig, Moss Sweedler

Mathematics, Statistics and Data Science Faculty Works

Given a valuation on the function field k( x; y), we examine the set of images of nonzero elements of the underlying polynomial ring k[ x; y] under this valuation. For an arbitrary field k, a Noetherian power series is a map z : Q --> k that has Noetherian (i.e., reverse well-ordered) support. Each Noetherian power series induces a natural valuation on k( x; y). Although the value groups corresponding to such valuations are well-understood, the restrictions of the valuations to underlying polynomial rings have yet to be characterized. Let Lambda(n) denote the images under the valuation v of …

A New Proof Of A Theorem Of Phan, Curtis Bennett, Sergey Shpectorov

Mathematics, Statistics and Data Science Faculty Works

We apply diagram geometry and amalgam techniques to give a new proof of a theorem of K.-W. Phan, characterizing the special unitary group as a group generated by certain systems of subgroups SU(2, q(2)).

Tree Diagrams For String Links Ii: Determining Chord Diagrams, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

In previous work, we defined the intersection graph of a chord diagram associated with a string link (as in the theory of finite type invariants). In this paper, we look at the case when this graph is a tree, and we show that in many cases these trees determine the chord diagram (modulo the usual 1-term and 4-term relations).

Higher Dimensional Algebra Vi: Lie 2-Algebra, John C. Baez, Alissa S. Crans

Mathematics, Statistics and Data Science Faculty Works

The theory of Lie algebras can be categorified starting from a new notion of `2-vector space', which we define as an internal category in Vect. There is a 2-category 2Vect having these 2-vector spaces as objects, `linear functors' as morphisms and `linear natural transformations' as 2-morphisms. We define a `semistrict Lie 2-algebra' to be a 2-vector space L equipped with a skew-symmetric bilinear functor [ . , . ] : L x L -> L satisfying the Jacobi identity up to a completely antisymmetric trilinear natural transformation called the `Jacobiator', which in turn must satisfy a certain law of its …

The Theory Of Jacobi Systems And Their Abelian Representations, M. Shahryari, Y. Zamani

Turkish Journal of Mathematics

In this article we introduce a new generalization of the concept of Lie ring which we call Jacobi system and we investigate some elementary properties of these systems and their Abelian representations.

Modules Supplemented Relative To A Torsion Theory, M. Tamer Koşan, Abdullah Harmanci

Turkish Journal of Mathematics

This article introduces the concept of a \tau-supplemented module as follows: Given a hereditary torsion theory in Mod R with associated torsion functor \tau, we say that a module M is \tau-supplemented when for every submodule N of M there exists a direct summand K of M such that K\leq N and N/K is \tau-torsion module. We present here some fundamental properties of this class of modules and study the decompositions of \tau-supplemented modules under certain conditions on modules. The question of which direct sum of \tau-supplemented R-modules are \tau-supplemented is treated here.

On Orthogonal Generalized Derivations Of Semiprime Rings, Nurcan Argaç, Atsushi Nakajima, Emi̇ne Albaş

Turkish Journal of Mathematics

In this paper, we present some results concerning two generalized derivations on a semiprime ring. These results are a generalization of results of M. Bre\u{s}ar and J. Vukman in [2], which are related to a theorem of E. Posner for the product of derivations on a prime ring.

Conjugacy Classes Of Finite Subgroups Of Certain Mapping Class Groups, Michal Stukow

Turkish Journal of Mathematics

We give a complete description of conjugacy classes of finite subgroups of the mapping class group of the sphere with r marked points. As a corollary we obtain a description of conjugacy classes of maximal finite subgroups of the hyperelliptic mapping class group. In particular, we prove that, for a fixed genus g, there are at most five such classes.

On \Theta-Euclidean L-Fuzzy Ideals Of Rings, Ayten Koç, Erol Balkanay

Turkish Journal of Mathematics

In this paper we define a \theta-Euclidean level subset and a \theta-Euclidean level ideal. We also give some properties of a \theta-Euclidean level subset.

New Special Curves And Developable Surfaces, Shyuichi Izumiya, Nobuko Takeuchi

Turkish Journal of Mathematics

We define new special curves in Euclidean 3-space which we call slant helices and conical geodesic curves. Those notions are generalizations of the notion of cylindrical helices. One of the results in this paper gives a classification of special developable surfaces under the condition of the existence of such a special curve as a geodesic. As a result, we consider geometric invariants of space curves. By using these invariants, we can estimate the order of contact with those special curves for general space curves. All arguments in this paper are straight forward and classical. However, there have been no papers …

Groups With Rank Restrictions On Non-Subnormal Subgroups, Leonid Andreevich Kurdachenko, Howard Smith

Turkish Journal of Mathematics

Let G be a group in which every non-subnormal subgroup has finite rank. This paper considers the question as to which extra conditions on such a group G ensure that G has all subgroups subnormal. For example, if G is torsion-free and locally soluble-by-finite then either G has finite 0-rank or G is nilpotent. Several results are obtained on soluble (respectively, locally soluble-by-finite) groups satisfying the stated hypothesis on subgroups.

Ideal Theory In Topological Algebras, A. Najmi

Turkish Journal of Mathematics

Given a simplicial topologically non radical algebra A, we characterize its topological radical, radA. If furthermore A is advertive, then radA coincides with the Jacobson radical RadA. On the other hand, it is shown that every two-sided invertive simplicial topological Gelfand-Mazur algebra has a functional spectrum and for every topologically nonradical simplicial Gelfand-Mazur amits the set \mathcal{X}(A), of all continuous multiplicative linear functionals, is not empty.

On A Certain Class Of Bessel Integrals, Ali A. Al-Jarrah, A. Al-Momani

Turkish Journal of Mathematics

There are many old results of integrals involving Bessel functions, currently available in handbooks, but we found no recourse in the well-known references to how they were established. In this paper, we attempt to have a clear way of proving some of these results. In fact, we consider a certain class of Bessel integrals where we prove that such integrals vanish under certain conditions. To this end some theorems regarding this class of integrals with their proofs are put forward. A computer algorithm is provided to implement some of our results. The result in this paper extend the work in …

Computational Geometry Column 45, Joseph O'Rourke

Computer Science: Faculty Publications

The algorithm of Edelsbrunner for surface reconstruction by "wrapping" a set of points in R³ is described.

A 2-Chain Can Interlock With A K-Chain, Julie Glass, Stefan Langerman, Joseph O'Rourke, Jack Snoeyink, Jianyuan K. Zhong

Computer Science: Faculty Publications

One of the open problems posed in [3] is: what is the minimal number k such that an open, flexible k-chain can interlock with a flexible 2-chain? In this paper, we establish the assumption behind this problem, that there is indeed some k that achieves interlocking. We prove that a flexible 2-chain can interlock with a flexible, open 16-chain.

Analysis Of Social Aspects Of Migrant Labourers Living With Hiv/Aids Using Fuzzy Theory And Neutrosophic Cognitive Maps, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic logic grew as an alternative to the existing topics and it represents a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined-ness, unknown, incompleteness, inconsistency, redundancy and contradiction. Despite various attempts to reorient logic, there has remained an essential need for an alternative system that could infuse into itself a representation of the real world. Out of this need arose the system of neutrosophy and its connected logic, neutrosophic logic. This new logic, which allows also the concept of indeterminacy to play a role in any real-world problem, was introduced first by one of the authors Florentin Smarandache. In this …

A Thermoviscoelastic Beam Model For Brakes, Kenneth Kuttler, J. Bajkowski, J. R. Fernandez, M. Shillor

Faculty Publications

A model for the dynamic thermomechanical behavior of a viscoelastic beam which is in frictional contact with a rigid rotating wheel is presented. It describes a simple braking system in which the wheel comes to a stop as a result of the frictional traction generated by the beam. Friction is modelled with a temperature and slip rate dependent coefficient of friction. Frictional heat generation is taken into account as well as the wheel temperature evolution, and the wear of the beam's contacting end. The model is formulated as a variational inequality. A FEM numerical scheme for the model is described, …

Computational Modeling Of Tumor Angiogenesis, Santanu Chatterjee

Masters Theses

No abstract provided.

Cyclic Rings, Warren K. Buck

Masters Theses

No abstract provided.

Practical Approach To Incorporating Maple Into The Finite Mathematics Course: 3 Modules And 8 Case Studies, Jonica Helene Craft-Mcbride

Masters Theses

No abstract provided.

On Certain Sets Of Matrices: Euclidean Squared Distance Matrices, Ray-Nonsingular Matrices And Matrices Generated By Reflections, Thomas W. Milligan

Dissertations, Theses, and Masters Projects

In this dissertation, we study three different sets of matrices. First, we consider Euclidean distance squared matrices. Given n points in Euclidean space, we construct an n x n Euclidean squared distance matrix by assigning to each entry the square of the pairwise interpoint Euclidean distance. The study of distance matrices is useful in computational chemistry and structural molecular biology. The purpose of the first part of the thesis is to better understand this set of matrices and its different characterizations so that a number of open problems might be answered and known results improved. We look at geometrical properties …