Education Commons^™

Inequalities And Exponential Approximations For Residual Life Reliability Functions, Broderick O. Oluyede, Marvis Pararai

Department of Mathematical Sciences Faculty Publications

Given that a unit is of age t, the remaining life after time t is random. The expected value of this random residual life is called the mean residual life at time t. Specifically, if T is the life of a component with distribution function F, then δF (t) = E(T −t|T > t) is called the mean residual life function (MRLF). It is well known that the class of distributions with decreasing mean residual life (DMR) contains the class of distributions with increasing hazard rate (IHR). In this note, …

Harmonic Analysis Related To Schrödinger Operators, Gestur Olafsson, Shijun Zheng

Department of Mathematical Sciences Faculty Publications

In this article, we give an overview of some recent developments in Littlewood-Paley theory for Schrödinger operators. We extend the Littlewood-Paley theory for special potentials considered in our previous work [J. Fourier Anal. Appl. 12 (2006), no. 6, 653–674; MR2275390]. We elaborate our approach by considering a potential in C^∞₀ or the Schwartz class in one dimension. In particular, the low energy estimates are treated by establishing some new and refined asymptotics for the eigenfunctions and their Fourier transforms. We give a maximal function characterization of the Besov spaces and Triebel-Lizorkin spaces associated with H. Then we …

A Note On Extreme Bernoulli And Dependent Families Of Bivariate Distributions, Broderick O. Oluyede, Marvis Pararai

Department of Mathematical Sciences Faculty Publications

The objective and purpose of this note is to generate bivariate distributions via extreme Bernoulli distributions and obtain results on positively and negatively dependent families of bivariate binomial distributions generated by extreme Bernoulli distributions. Some distributional properties and results are presented. The factorial moment generating functions, correlation functions, conditional distributions and the regression functions are given.

A Partition Bijection Related To The Rogers-Selberg Identities And Gordon's Theorem, Andrew Sills

Department of Mathematical Sciences Faculty Publications

We provide a bijective map from the partitions enumerated by the series side of the Rogers–Selberg mod 7 identities onto partitions associated with a special case of Basil Gordon's combinatorial generalization of the Rogers–Ramanujan identities. The implications of applying the same map to a special case of David Bressoud's even modulus analog of Gordon's theorem are also explored.

On The Ordinary And Signed Göllnitz-Gordon Partitions, Andrew Sills

Department of Mathematical Sciences Faculty Publications

A partition of an integer n is a representation of n as an unordered sum of positive integers. In a recent paper [1], Andrews introduced the notion of a "signed partition," that is, a representation of a positive integer as an unordered sum of integers, some possibly negative.

Utilization Of Revoicing Based On Learners‘ Thinking In An Inquiry-Oriented Differential Equations Class, Oh Kwon Nam, Mi Kyung Ju, Chris Rasmussen, Karen A. Marrongelle, Jae Hee Park, Kyoung Hee Cho, Jung Sook Park, Jee Hyun Park

Mathematics and Statistics Faculty Publications and Presentations

Researchers of mathematics education are increasingly interested in a teacher's discursive moves, which refer to deliberate actions taken by a teacher to participate in or influence debate and discussion in the mathematics classroom. This study explored one teacher's discursive moves in an undergraduate inquiry-oriented mathematics class. The data for this study come from four class sessions in which students investigated initial value problems as represented by the phase portrait of a system of differential equations. Through the analysis and a review of the literature, we identified four categories of a teacher's discursive moves: revoicing, questioning/requesting, telling, and managing. This report …

Ua66/1/5 Icset - Institute For Combustion Science & Environmental Technology, Wku Ogden College Of Science & Engineering

WKU Archives Records

History and overview of the work of the WKU Institute for Combustion Science & Environmental Technology through 2008.

Ua1f Wku Archives Vertical File - Wku Information Technology, Wku Archives

WKU Archives Records

Digitized vertical file materials regarding WKU Information Technology.

Fostering Sustainability In Higher Education: A Mixed-Methods Study Of Transformative Leadership And Change Strategies, Kim H. Mcnamara

Antioch University Dissertations & Theses

As evidence of the earth’s limited capacity to sustain human life mounts, institutions of higher education are being looked to for leadership in the effort to educate students about environmental concerns and support the development of sustainable innovations. Colleges and universities are responding to this call for leadership by starting and/or expanding environmental research programs, integrating sustainability issues throughout the curriculum, adopting sustainable operations, and building green facilities. Reflecting upon the sustainability efforts of these institutions, this research study explores the following questions: What factors are essential for initiating and leading a successful change effort to foster sustainability in higher …

Connecting With Nature Through Land Use Decision Making, Cathy Setterlin

Antioch University Dissertations & Theses

This narrative inquiry, which draws on my experience as a land use decision maker, environmental educator, and scholar, examines the complexities of our human-nature relationship as we use and protect the life of the land in local communities. I began this research by interviewing seventeen land use decision makers representing a range of land use perspectives in New Milford, Connecticut, focusing on their views of land as a living community, their connections to land, and their sense of duty and responsibility.

Their responses led me to further inquiry and drew me into a process that transformed my views of both …