Physical Sciences and Mathematics Commons^™

Injective Simplicial Maps Of The Arc Complex, Elmas Irmak, John D. Mccarthy

Turkish Journal of Mathematics

In this paper, we prove that each injective simplicial map of the arc complex of a compact, connected, orientable surface with nonempty boundary is induced by a homeomorphism of the surface. We deduce, from this result, that the group of automorphisms of the arc complex is naturally isomorphic to the extended mapping class group of the surface, provided the surface is not a disc, an annulus, a pair of pants, or a torus with one hole. We also show, for each of these special exceptions, that the group of automorphisms of the arc complex is naturally isomorphic to the quotient …

An Expansion Result For A Sturm-Liouville Eigenvalue Problem With Impulse, Şeri̇fe Faydaoğlu, Gusein Sh. Guseinov

Turkish Journal of Mathematics

The paper is concerned with an eigenvalue problem for second order differential equations with impulse. Such a problem arises when the method of separation of variables applies to the heat conduction equation for two-layered composite. The existence of a countably infinite set of eigenvalues and eigenfunctions is proved and a uniformly convergent expansion formula in the eigenfunctions is established.

Notes On Null Curves In Minkowski Spaces, Makoto Sakaki

Turkish Journal of Mathematics

We show a correspondence between the evolute of a null curve and the involute of a certain spacelike curve in the 4-dimensional Minkowski space. Also we characterize pseudo-spherical null curves in the n-dimensional Minkowski space in terms of the curvature functions.

A Short Survey On Mathematical Work Of Cemal Koç, İsmai̇l Şuayi̇p Güloğlu

Turkish Journal of Mathematics

No abstract provided.

On Abelian Rings, Nazim Agayev, Abdullah Harmanci, Sai̇t Halicioğlu

Turkish Journal of Mathematics

Let \alpha be an endomorphism of an arbitrary ring R with identity. In this note, we introduce the notion of \alpha-abelian rings which generalizes abelian rings. We prove that \alpha-reduced rings, \alpha-symmetric rings, \alpha-semicommutative rings and \alpha-Armendariz rings are \alpha-abelian. For a right principally projective ring R, we also prove that R is \alpha-reduced if and only if R is \alpha-symmetric if and only if R is \alpha-semicommutative if and only if R is \alpha-Armendariz if and only if R is \alpha-Armendariz of power series type if and only if R is \alpha-abelian.

On Weakly M-Supplemented Primary Subgroups Of Finite Groups, Long Miao, Wolfgang Lempken

Turkish Journal of Mathematics

A subgroup H of a group G is said to be weakly M-supplemented in G if there exists a subgroup B of G provided that (1) G=HB, and (2) if H_1/H_G is a maximal subgroup of H/H_G, then H_1B=BH_1

Statistical Convergence Of Max-Product Approximating Operators, Oktay Duman

Turkish Journal of Mathematics

In this study, using the notion of statistical convergence, we obtain various statistical approximation theorems for a general sequence of max-product approximating operators, including Shepard type operators, although its classical limit fails. We also compute the corresponding statistical rates of the approximation.

On Construction Of Coherent States Associated With Homogeneous Spaces, Ali Akbar Arefijamaal

Turkish Journal of Mathematics

In this article, assume that G=H\times_{\tau} K is the semidirect product of two locally compact groups H and K, respectively and consider the quasi regular representation on G. Then for some closed subgroups of G we investigate an admissible condition to generate the Gilmore-Perelomov coherent states. The construction yields a wide variety of coherent states, labelled by a homogeneous space of G.

Order-Isomorphism And A Projection's Diagram Of C(X), Ahmed S. Al-Rawashdeh, Sultan M. Al-Suleiman

Turkish Journal of Mathematics

A mapping between projections of C^*-algebras preserving the orthogonality, is called an orthoisomorphism. We define the order-isomorphism mapping on C^*-algebras, and using Dye's result, we prove in the case of commutative unital C^*-algebras that the concepts; order-isomorphism and the orthoisomorphism coincide. Also, we define the equipotence relation on the projections of C(X); indeed, new concepts of finiteness are introduced. The classes of projections are represented by constructing a special diagram, we study the relation between the diagram and the topological space X. We prove that an order-isomorphism, which preserves the equipotence of projections, induces a diagram-isomorphism; also if two diagrams …

Complete Systems Of Differential Invariants Of Vector Fields In A Euclidean Space, Djavvat Khadjiev

Turkish Journal of Mathematics

The system of generators of the differential field of all G-invariant differential rational functions of a vector field in the n-dimensional Euclidean space R^n is described for groups G=M(n) and G=SM(n), where M(n) is the group of all isometries of R^n and SM(n) is the group of all euclidean motions of R^n. Using these results, vector field analogues of the first part of the Bonnet theorem for groups Aff(n), M(n), SM(n) in R^n are obtained, where Aff(n) is the group of all affine transformations of R^n. These analogues are given in terms of the first fundamental form and Christoffel symbols …

Mathematical Modeling And Control Of Nonlinear Oscillators With Shape Memory Alloys, Mohamed Bendame

Theses and Dissertations (Comprehensive)

Shape memory alloys (SMAs) belong to an interesting type of materials that have attracted the attention of scientists and engineers over the last few decades. They have some interesting properties that made them the subject of extensive research to find the best ways to utilize them in different engineering, biomedical, and scientific applications. In this thesis, we develop a mathematical model and analyze the behavior of SMAs by considering a one degree of freedom nonlinear oscillator consisting of a mass connected to a fixed frame through a viscous damping and a shape memory alloy device. Due to the nonlinear and …

Stochastic Orders In Heterogeneous Samples With Applications, Maochao Xu

Dissertations and Theses

The statistics literature has mostly focused on the case when the data available is in the form of a random sample. In many cases, the observations are not identically distributed. Such samples are called heterogeneous samples. The study of heterogeneous samples is of great interest in many areas, such as statistics, econometrics, reliability engineering, operation research and risk analysis.

Stochastic orders between probability distributions is a widely studied concept. There are several kinds of stochastic orders that are used to compare different aspects of probability distributions like location, variability, skewness, dependence, etc.

In this dissertation, most of the work is …

Spatial Isomorphisms Of Algebras Of Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia, Warren R. Wogen

Department of Math & Statistics Faculty Publications

We examine when two maximal abelian algebras in the truncated Toeplitz operators are spatially isomorphic. This builds upon recent work of N. Sedlock, who obtained a complete description of the maximal algebras of truncated Toeplitz operators.

Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, And Similarity, William T. Ross, Joseph A. Cima, Stephan Ramon Garcia, Warren R. Wogen

Department of Math & Statistics Faculty Publications

A truncated Toeplitz operator Aᵩ : K_Ɵ → K_Ɵ is the compression of a Toeplitz operator Tᵩ : H² → H² to a model space K_Ɵ := H² ⊖ ^ƟH². For Ɵ inner, let T_Ɵ denote the set of all bounded truncated Toeplitz operators on K_Ɵ. Our main result is a necessary and sufficient condition on inner functions Ɵ₁ and Ɵ₂ which guarantees that T_Ɵ1 and T_Ɵ2 are spatially isomorphic. (i.e., UT_Ɵ1 = T_Ɵ2 U for some unitary U : K_{Ɵ1 …}

New Year Tidings, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Leading Learning Within A Plc: Implementing New Mathematics Content, Ann Heirdsfield, Janeen Lamb, Gayle Spry

The Mathematics Enthusiast

This paper does two things. Firstly, it examines the literature that coalesces around theoretical models of teacher professional development (PD) within a professional learning community (PLC). Secondly, these models are used to analyse support provided to two year 3 teachers, while implementing the draft Queensland mathematics syllabus. The findings from this study suggest that the development of this small PLC extended the teachers’ Zone of Enactment which in turn led to teacher action and reflection. This was demonstrated by the teachers leading their own learning as well as that of their students.

Tme Volume 7, Number 1

The Mathematics Enthusiast

No abstract provided.

Families Of Symmetries As Efficient Models Of Resource Binding, Vincenzo Ciancia, Alexander Kurz, Ugo Montanari

Engineering Faculty Articles and Research

Calculi that feature resource-allocating constructs (e.g. the pi-calculus or the fusion calculus) require special kinds of models. The best-known ones are presheaves and nominal sets. But named sets have the advantage of being finite in a wide range of cases where the other two are infinite. The three models are equivalent. Finiteness of named sets is strictly related to the notion of finite support in nominal sets and the corresponding presheaves. We show that named sets are generalisd by the categorical model of families, that is, free coproduct completions, indexed by symmetries, and explain how locality of interfaces gives good …

Eleventh Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics

Kenneth C. Schraut Memorial Lectures

No abstract provided.

Every Time I Turn Around There's Dr. Schraut Or You Can't Take Mathematics Out Of A U. D. Mathematics Major (Abstract), Eugene Steuerie

Kenneth C. Schraut Memorial Lectures

In this lecture, Gene Steurele, a math major from the 1968 graduating class, will discuss the many ways that mathematics & statistics crop up in almost every major public policy debate in which he has participated.

Snort: A Combinatorial Game, Keiko Kakihara

Theses Digitization Project

This paper focuses on the game Snort, which is a combinatorial game on graphs. This paper will explore the characteristics of opposability through examples. More fully, we obtain some neccessary conditions for a graph to be opposable. Since an opposable graph guarantees a second player win, we examine graphs that result in a first player win.

The Wright Message, 2010, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Department Alumni and Friends
-- 2010 - 2011 Tenure-Stream Faculty
-- Spotlight on Undergraduates
-- Projects and Grants
-- Secondary Mathematics Education Programs
-- UNI I-Teach
-- Crane Scholarship
-- Actuarial Science and the Actuarial Science Fund
-- Alliance Project
-- Mathematics Contribution Form
-- Additional Mathematics Funds
-- Around Wright Hall
-- In Memoriam
-- Dr. Ridenhour Retires

Radiographic Imagery Of A Variable Density 3d Object, Justin Stottlemyer

Undergraduate Journal of Mathematical Modeling: One + Two

The purpose of this project is to develop a mathematical model to study 4D (three spatial dimensions plus density) shapes using 3D projections. In the model, the projection is represented as a function that can be applied to data produced by a radiation detector. The projection is visualized as a three-dimensional graph where x and y coordinates represent position and the z coordinate corresponds to the object's density and thickness. Contour plots of such 3D graphs can be used to construct traditional 2D radiographic images.

On The Socles Of Characteristic Subgroups Of Abelian P-Groups, Brendan Goldsmith, Peter Danchev

Articles

Fully invariant subgroups of an Abelian p-group have been the object of a good deal of study, while characteristic subgroups have received somewhat less attention. Recently the socles of fully invariant subgroups have been studied and this led to the notion of a socle-regular group. The present work replaces the fully invariant subgroups with characteristic ones and leads in a natural way to the notion of a strongly socle-regular group. A surprising relationship, mirroring that between transitive and fully transitive groups, is obtained.

EΠi + 1=0: The History & Development, Dawne Charters-Nelson

Undergraduate Review

I have on occasion run across the equation in books, articles and in conversation with other mathematicians. In each of these encounters the person alluded to a fascination with this equation which links the five most important constants in the whole of analysis:

• 0 = The additive identity
• 1 = The multiplicative identity
• π = The circular constant
• e = The base of the natural logarithms
• i = The imaginary unit

Being a novice mathematician, I wondered how all these fundamental constants could end up in one equation and what it meant. Along with this thought came the realization that …

An Examination Of The Association Of Selected Toxic Metals With Total And Central Obesity Indices: Nhanes 99-02, Miguel A. Padilla, Mai Elobeid, Douglas M. Ruden, David B. Allison

Psychology Faculty Publications

It is conceivable that toxic metals contribute to obesity by influencing various aspects of metabolism, such as by substituting for essential micronutrients and vital metals, or by inducing oxidative stress. Deficiency of the essential metal zinc decreases adiposity in humans and rodent models, whereas deficiencies of chromium, copper, iron, and magnesium increases adiposity. This study utilized the NHANES 99-02 data to explore the association between waist circumference and body mass index with the body burdens of selected toxic metals (barium, cadmium, cobalt, cesium, molybdenum, lead, antimony, thallium, and tungsten). Some of the associations were significant direct relationships (barium and thallium), …

Ethnomathematics For Capacity Building In Mathematics Education, Catherine P. Vistro-Yu

Mathematics Faculty Publications

The Mathematics Framework for Philippine Basic Education (MATHTED and SEI, in press), a document that aims to guide the development of curricular contents in mathematics, identifies cultural-rootedness as one of the cognitive values that mathematics education in the Philippines must inculcate. Cultural-rootedness is defined as ?appreciating the cultural value of mathematics and its origins in many cultures, its rich history and how it has grown and continues to evolve?. Ethnomathematics, described as the ?mathematics which is practiced among identifiable cultural groups, such as national tribal societies, labor groups, children of a certain age bracket, professional classes and so on? (D?Ambrosio, …

The Influence Of Inclusion On Langauge Arts Literacy And Math Achievement On Non-Disabled Middle School Students, Faye Brady

Seton Hall University Dissertations and Theses (ETDs)

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Categorical Approaches To Non-Commutative Fuzzy Logic, Lawrence Stout

Scholarship

In this paper we consider what it means for a logic to be non-commutative, how to generate examples of structures with a non-commutative operation * which have enough nice properties to serve as the truth values for a logic. Inference in the propositional logic is gotten from the categorical properties (products, coproducts, monoidal and closed structures, adjoint functors) of the categories of truth values. We then show how to extend this view of propositional logic to a predicate logic using categories of propositions about a type A with functors giving change of type and adjoints giving quantifiers. In the case …

Lifting Module Maps Between Different Noncommutative Domain Algebras, Jonathan Von Stroh

Electronic Theses and Dissertations

The classical Carathéodory interpolation problem is the following: let n be a natural number, a₀, a₁, . . . , a_N be complex numbers, and D the unit disk. When does there exist an analytic function F : D → C and complex numbers a_N+1, a_N+2, . . . such that F(z) = a₀ + a₁z + a₂z² + . . . + a_Nz^N + a_N+1z^N+1 + . . . and ||F||_∞ < 1? In 1967, Sarason used operator theory techniques to give an elegant solution to the Carathéodory interpolation problem. In 1968, Sz.-Nagy and Foias extended Sarason's approach into a commutant lifting theorem. Both the theorem and the technique of the proof have become standard tools in control theory. In particular, the commutant lifting theorem approach lends itself to a wide range of generalizations. This thesis concerns one such generalization.

Arias presented generalizations of the original …