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.
Author(s): Albert R. Baswell
Series: Advances in Mathematics Research, 31
Publisher: Nova Science Publishers
Year: 2022
Language: English
Pages: 216
City: New York
Advances in Mathematics Research
Advances in Mathematics Research
Contents
PREFACE
Chapter 1THE MAPLE COMPUTER ALGEBRA SYSTEMIN TEACHING THE BASICS OF SET THEORY
ABSTRACT
INTRODUCTION
Set Theory and Its Study
Information Technologies in Teaching Mathematics
The Maple Computer Algebra System in Teaching Mathematics
ANALYTICAL FRAMEWORK
Literature Review
The Hypothesis of Using Maple in the Study of Set Theory
METHOD
Visualization in Maple
Analytical Testing
Setting the Set
Ways to Define Sets in the Maple Computer Algebra System
Setting Sets Using a Worksheet
Setting Sets Using Maplet
Operations on Sets and Knowledge Control of PerformingOperations on Sets
Control of Knowledge of the Order of Operations on Sets
Control of Knowledge of Performing Operations on Text Sets
The Laws of Set Theory and Verification of the Validityof the Laws (Properties) of Sets
Checking the Validity of the Laws (Properties) of Sets Using theTable of Occurrences
Checking the Validity of the Laws (Properties) of Sets Based on theExecution of Procedures
Checking the Validity of the Laws (Properties) of Sets Basedon the Expression of Operations on Sets through LogicalOperations
Construction of Euler- to Venn-Diagram with Maple
The Use of Maple CAS for Solving Problems in Set Theory
RESULTS AND DISCUSSION
Descriptive Statistics
CONCLUSION
REFERENCES
BIOGRAPHICAL SKETCHES
Alexander Anatolievich Olenev
Publications from the Last 3 Years
Ksenia Alexandrovna Kirichek
Publications from the Last 3 Years
Ekaterina Valentinovna Potekhina
Publications from the Last 3 Years
Chapter 2MULTILEVEL MEDIATION ANALYSISWITH CATEGORICAL OUTCOMES:CONDUCTING CAUSAL INFERENCE BYTHE MSEM FRAMEWORK
ABSTRACT
INTRODUCTION
MEDIATION ANALYSIS IN THE FRAMEWORK OFMULTILEVEL STRUCTURAL EQUATION MODELING(MSEM)
EMPIRICAL EXAMPLES OF MULTILEVEL MEDIATIONANALYSIS CONDUCTED WITH THE MSEMFRAMEWORK
MEASUREMENT
Individual-Level Variables
Outcome Variable
Mediator
Predictor Variable
Control Variables
School-Level Variables
Predictor Variable
Control Variables
Estimation of MSEM Modeling Procedures
RESULTS
DISCUSSION
APPENDIX 1. MPLUS AND R CODES FOR THE NULLMSEM MODEL PREDICTING COLLEGE GRADUATIONOF IMMIGRANT YOUTHS WITH THE DATA FROM CILS
APPENDIX 2. MPLUS AND R CODES FOR THE MSEMMODEL PREDICTING COLLEGE GRADUATION ANDACADEMIC ASPIRATION OF IMMIGRANT YOUTHSWITH THE DATA FROM CILS
APPENDIX 3. MPLUS AND R CODES FOR THE 1-1-1MEDIATION MSEM MODEL PREDICTING COLLEGEGRADUATION BY THE INDIRECT EFFECT OFACADEMIC ASPIRATION OF IMMIGRANT YOUTHSFROM FAMILY SES WITH THE DATA FROM CILS
APPENDIX 4. MPLUS AND R CODES FOR THE 2-1-1MEDIATION MSEM MODEL PREDICTING COLLEGEGRADUATION BY THE INDIRECT EFFECT OFACADEMIC ASPIRATION OF IMMIGRANT YOUTHSFROM SCHOOL LOCATION WITH THE DATA FROMCILS
REFERENCES
Chapter 3LOCAL EXISTENCE AND REGULARITY OFSOLUTIONS IN -NORM FOR SOMEPARTIAL FUNCTIONALINTEGRODIFFERENTIAL EQUATIONS INBANACH SPACES
Abstract
1. INTRODUCTION
2. PRELIMINARY RESULTS
3. EXISTENCE, GLOBAL CONTINUATION ANDBLOWING UP OF SOLUTIONS
4. EXISTENCE OF STRICT SOLUTIONS
5. APPLICATION
CONCLUSION
ACKNOWLEDGMENTS
REFERENCES
Chapter 4SIMPLE EQUATIONS METHOD (SESM)FOR OBTAINING EXACT SOLUTIONS OFNONLINEAR DIFFERENTIAL EQUATIONS
Abstract
1. INTRODUCTION
2. SIMPLE EQUATIONS METHOD - SESM
3. EXAMPLE 1
4. EXAMPLE 2
CONCLUSION
REFERENCES
Chapter 5STABILITY OF WEAK SOLUTIONS OFTHE BAROTROPIC VORTICITY EQUATIONON A SPHERE
Abstract
1. INTRODUCTION
2. HILBERT SPACES
3. VORTICITY EQUATION
4. MODONS
5. DISTANCE BETWEEN TWO DIPOLE MODONS
6. THE CASE OF TWO MODONS MOVING ALONGTHE SAME LATITUDINAL CIRCLE
7. STATIONARY SOLUTIONS
8. CONSERVATION LAW FOR INFINITESIMALPERTURBATIONS
9. NECESSARY CONDITIONS FOR INSTABILITY
10. MAIN PROPERTIES OF UNSTABLE MODES
11. LYAPUNOV INSTABILITY OF DIPOLE MODONS
CONCLUSION
APPENDIX A. EULER ANGLES
APPENDIX B. PROOF OF LEMMA 3
ACKNOWLEDGMENTS
REFERENCES
Chapter 6INTERRELATION OF THE EQUATION OFRSJ MODEL OF JOSEPHSON JUNCTIONAND THE SPECIAL DOUBLE CONFLUENTHEUN EQUATION
Abstract
INTRODUCTION
TRANSITION OF EQ. (1) TO COMPLEX DOMAIN
OPERATOR LC
EIGENFUNCTIONS OF THE OPERATOR LC ANDTHEIR PROPERTIES
EXPLICIT REPRESENTATIONS OFEIGENFUNCTIONS OF LC
SELF-CONJUGATION PROPERTY OFEIGENFUNCTIONS OF THE OPERATOR LC
REPRESENTATION OF GENERAL SOLUTION TOTHE EQUATION OF RSJ MODEL IN TERMS OFSOLUTIONS TO SPECIAL DOUBLE CONFLUENTHEUN EQUATION
CONCLUSION
REFERENCES
CONTENTS OF EARLIER VOLUMES
INDEX
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