Physical Sciences and Mathematics Commons^™

A Primer On The Legendre Transformation, Steven J. Kilner, David L. Farnsworth

Articles

Guidance is offered for understanding and using the Legendre transformation and its associated duality among functions and curves. The genesis of this paper was encounters with colleagues and students asking about the transformation. A main feature is simplicity of exposition, while keeping in mind the purpose or application for using the transformation.

Probability Distributions Arising In Connection With The Inspection Paradox For Bernoulli Trials., James E. Marengo, Anne Marino Himes, W. Cade Reinberger, David L. Farnsworth

Articles

In renewal theory, the Inspection Paradox refers to the fact that an interarrival period in a renewal process which contains a fixed inspection time tends to be longer than one for the corresponding uninspected process. We focus on the paradox for Bernoulli trials. Probability distributions and moments for the lengths of the interarrival periods are derived for the inspected process, and we compare them to those for the uninspected case.

The State Of Accessibility In Blackboard: Survey And User Reviews Case Study, Mohamed Wiem Mkaouer, Wajdi Aljedaani, Stephanie Ludi, Mohammed Alkahtani, Marcelo M. Eler, Marouane Kessentini, Ali Ouni

Articles

Context: Nowadays, mobile applications (or apps) have become vital in our daily life, particularly within education. Many institutions increasingly rely on mobile apps to provide access to all their students. However, many education mobile apps remain inaccessible to users with disabilities who need to utilize accessibility features like talkback or screen reader features. Accessibility features have to be considered in mobile apps to foster equity and inclusion in the educational environment allowing to use of such apps without limitations. Gaps in the accessibility to educational systems persist.

Objective: In this paper, we focus on the accessibility of the Blackboard mobile …

Modeling And Fitting Two-Way Tables Containing Outliers, David L. Farnsworth

Articles

A model is proposed for two-way tables of measurement data containing outliers. The two independent variables are categorical and error free. Neither missing values nor replication are present. The model consists of the sum of a customary additive part that can be fit using least squares and a part that is composed of outliers. Recommendations are made for methods for identifying cells containing outliers and for fitting the model. A graph of the observations is used to determine the outliers’ locations. For all cells containing an outlier, replacement values are determined simultaneously using a classical missing-data tool. The result is …

A Mathematical Model Of Juvenile Delinquency In The New York State, Oluwasegun Micheal Ibrahim

Articles

This report presents a mathematical model of juvenile delinquency in the New York State. In particular, we develop a juvenile delinquency system of non-linear differential equations using the mathematical epidemiology framework. In constructing this model, we assume that juvenile delinquency can be studied as a socially infectious disease. The stability of the juvenile delinquency-free equilibrium of the model is examined using the standard non-linear dynamical systems theory technique. We carried out a data fitting based on real-life data from the New York State Criminal Justice Services. The research result reveals that the formulated model conforms with the available data and …