Advances in Mathematics Research. Volume 31


Albert R. Baswell (Editor)

Series: Advances in Mathematics Research
BISAC: MAT000000

This volume includes six chapters that detail recent advancements in mathematics research. Chapter One presents various capabilities of the Maple computer algebra system. Chapter Two uses data from the Children of Immigrants Longitudinal Study to demonstrate how to perform multilevel structural equation modeling to investigate if academic aspiration of immigrant youths in late adolescence mediates both the effects of family socioeconomic status and school location at individual and school levels in early adolescence on their later successful college graduation in young adulthood. Chapter Three proves the existence and regularity of solutions in α-norm for some partial functional integrodifferential equations in Banach spaces. Chapter Four discusses a method for obtaining exact solutions of nonlinear partial differential equations. Chapter Five analyzes the linear and nonlinear stability of modons and We-Verkley waves, which are weak solutions of the barotropic vorticity equation. Lastly, Chapter Six provides an explicit representation of the maps interconnecting the sets of solutions to the special double confluent Heun equation and the equation of the RSJ model of overdamped Josephson junction in case of shifted sinusoidal bias.



Table of Contents


Chapter 1. The Maple Computer Algebra System in Teaching the Basics of Set Theory
A. A. Olenev, K. A. Kirichek and E.V. Potechina
Department of Mathematics, Computer Science and Digital Educational Technologies, Stavropol State Pedagogical Institute, Stavropol, Russia

Chapter 2. Multilevel Mediation Analysis with Categorical Outcomes: Conducting Causal Inference by the MSEM Framework
Jerf W. K. Yeung, Hui-Feng Chen, Andrew You Tsang Low, Chi Xu and Leilei Xu
Department of Social and Behavioural Sciences, City University of Hong Kong, Hong Kong, China

Chapter 3. Local Existence and Regularity of Solutions in α-Norm for Some Partial Functional Integrodifferential Equations in Banach Spaces
Djendode Mbainadji and Issa Zabsonré
Université Joseph KI-ZERBO, Unité de Recherche et de Formation en Sciences Exactes et Appliquées, Département de Mathématiques, Ouagadougou, Burkina Faso

Chapter 4. Simple Equations Method (SEM) for Obtaining Exact Solutions of Nonlinear Differential Equations
Nikolay K. Vitanov
Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria

Chapter 5. Stability of Weak Solutions of the Barotropic Vorticity Equation on a Sphere
Yuri N. Skiba
Centro de Ciencias de la Atmósfera, Universidad Nacional Autónoma de México

Chapter 6. Interrelation of the Equation of RSJ Model of Josephson Junction and the Special Double Confluent Heun Equation
Sergey I. Tertychniy
-Russian Metrological Institute of Technical Physics and Radio Engineering, Mendeleevo, Russia


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