Advances in mathematics research Volume 8 / Albert R. Baswell, editor.

Format:

Book

Contributor:

Baswell, Albert R.

Series:

Advances in Mathematics Research

Advances in mathematics research ; 8

Language:

English

Subjects (All):

Mathematics.

Mathematics--Research.

Physical Description:

1 online resource (382 p.)

Edition:

1st ed.

Place of Publication:

Hauppauge, NY : Nova Science Publishers Inc., c2009.

Language Note:

English

Summary:

'Advances in Mathematics Research' presents original research results on the leading edge of mathematics research. Each article has been carefully selected in an attempt to present substantial research results across a broad spectrum.

Contents:

Intro

ADVANCES IN MATHEMATICSRESEARCH,VOLUME 8

ADVANCES IN MATHEMATICS RESEARCH, VOLUME 8

CONTENTS

PREFACE

THE METHOD OF CHARACTERISTICSFOR THE NUMERICAL SOLUTION OF HYPERBOLICDIFFERENTIAL EQUATIONS

Abstract

1. Introduction

2. The Fractional Step Method Applied to the Vlasov Equation

2.1. The Fractional Step Method Applied to the Vlasov-Poisson System inOne Spatial Dimension

2.2. The Vlasov-Poisson System in Higher Phase-Space Dimensions:the Problem of the Formation of an Electric Field at a Plasma Edgein a Slab Geometry

2.3. Vlasov-Maxwell Equations for Laser-Plasma Interaction

3. Problems Involving the Interpolation along the CharacteristicCurves in Two Dimensions

3.1. Solution of the Guiding-Center or Euler Equations

3.2. The Vlasov-Poisson System in Higher Phase-Space Dimensions:Formation of an Electric Field at a Plasma edge in a CylindricalGeometry

3.3. One-Dimensional Fully Relativistic System for the Problem of Laser-Plasma Interaction

3.4. Numerical Solution of a Reduced Model for the Collisionless MagneticReconnection

4. Application of the Method of Characteristics to Fluid Equations

4.1. Numerical Solution of the Shallow Water Equations

4.2. Two-Dimensional Magnetohydrodynamic Flows

5. Conclusion

Acknowledgments

Appendix AThe Shift Operator Using the Cubic Spline

Appendix BInterpolation Using the Cubic Spline

Appendix CInterpolation Using the Cubic B-spline

References

NEGOTIATING MATHEMATICS AND SCIENCE SCHOOLSUBJECT BOUNDARIES:THE ROLE OF AESTHETIC UNDERSTANDING

Introduction

Comparing Mathematics and Science as Secondary SchoolSubjects

Relationship between Subject Culture and the Individual

The Aesthetic in Education

Methodology

Research Methods

Teacher Profiles

Donna

Pauline

Rose.

Looking for the Aesthetic in the Relationship between SubjectCulture and Pedagogy

Compelling and Dramatic Nature of Understanding

Aesthetic, Passion and the Subject

Learning that Brings Unification or Coherence to Aspects of theWorld or the Subject

Aesthetic, Coherence and the Subject

Perceived Transformation of the Person and the World

Rose's Transformation

Pauline's Identity Crisis as She Negotiates Subject Boundaries

Aesthetic, Identity and the Subject

Insights and Implications

Appreciation for the Aesthetic in the Teaching Act

The Aesthetic in the Negotiation of Subject Boundaries

Conclusion

THE MATHEMATICAL BASIS OF PERIODICITYIN ATOMIC AND MOLECULAR SPECTROSCOPY

Combinatorial Periodicity in MolecularElectronic and Atomic Spectroscopy

Combinatorial Periodicity in Molecular and NMR Spectroscopies

Periodicity of Double Groups and Electronic States

Acknowledgement

MATHEMATICAL MODELLING OF THERMOMECHANICALDESTRUCTION OF POLYPROPYLENE

Conclusions

A DESIGN-BASED STUDY OF A COGNITIVE TOOLFOR TEACHING AND LEARNING THE PERIMETEROF CLOSED SHAPES

Cognitive Inflexibility

The Study

The Theory-Driven Design of the Cognitive Tool

The Empirical Study

Evaluation Methods

Results and Discussions

Learning Outcome of Students from Pre-Test-Post-Test Instruments

Feedback of Teachers from Interviews

Feedback of Students from Questionnaire Survey

Implications of the Empirical Study

MODELING ASYMMETRIC CONSUMERBEHAVIOR AND DEMAND EQUATIONSFOR BRIDGING GAPS IN RETAILING1

Related Contributions

Customer Value and Choice Probabilities

Behavioral Asymmetry and Customer Choice

Organizational Influences on Customer Values.

Objectives and Design of Model

Construct of Model

Choice Variability and Demand Equation

Consumer Choice for New Products

Customer Value Enhancement

Conclusion and Managerial Implications

HIGHER EDUCATION: FEDERAL SCIENCE,TECHNOLOGY, ENGINEERING, AND MATHEMATICSPROGRAMS AND RELATED TRENDS*

Why This Study?

Abbreviations

Results in Brief

Background

More than 200 Federal Education Programs are Designed to Increase theNumbers of Students and Graduates or Improve Educational Programs inSTEM Fields, but Most Have Not Been Evaluated

Federal Civilian Agencies Reported Sponsoring over 200 STEM EducationPrograms and Spending Billions in Fiscal Year 2004

Federal Agencies Reported Most STEM Programs Had Multiple Goals andWere Targeted to Multiple Groups

Agency Officials Reported That Evaluations Were Completed or under Wayfor about Half of the Federal Programs

A Subcommittee Was Established in 2003 to Help Coordinate STEMEducation Programs among Federal Agencies

Numbers of Students, Graduates, and Employees in STEM Fields GenerallyIncreased, but Percentage Changes Varied

Numbers of Students in STEM Fields Grew, but This Increase Varied byEducation Level and Student Characteristics

Total Numbers of Graduates with STEM Degrees Increased, but NumbersDecreased in Some Fields, and Percentages of Minority Graduates at theMaster's and Doctoral Levels Did Not Change

STEM Employment Rose, but the Percentage of Women Remained Aboutthe Same and Minorities Continued to be Underrepresented

University Officials and Others Cited Several Factors That InfluenceDecisions about Participation in STEM Fields and Suggested Ways toEncourage Greater Participation

Teacher Quality and Mathematics and Science Preparation Were Cited asKey Factors Affecting Domestic Students' STEM Participation Decisions.

Mentoring Cited as a Key Factor Affecting Women's and Minorities' STEMParticipation Decisions

International Students' STEM Participation Decisions Were Affected byOpportunities Outside the United States and the Visa Process

Several Suggestions Were Made to Encourage More Participation in theSTEM Fields

Concluding Observations

Agency Comments and Our Evaluation

Appendix I: Objectives, Scope, and Methodology

Objectives

Scope and Methodology

Survey

Analyses of Student, Graduate, and Employee Data

College and University Visits

Reviews of Reports and Studies

Interviews

Appendix II: List of 207 Federal STEM Education Programs

Appendix III: Federal STEM Education ProgramsFunded at 10 Million or More

Appendix IV: Data on Students and Graduates in STEM Fields

Appendix V: Confidence Intervals for Estimates of Students atthe Bachelor's, Master's, and Doctoral Levels

Appendix VI: Confidence Intervals for Estimates of STEMEmployment by Gender, Race or Ethnicity, and Wages andSalaries

Appendix VII: Comments from the Department of Commerce

Appendix VIII: Comments from theDepartment of Health and Human Services

Appendix IX: Comments from the National Science Foundation

Appendix X: Comments from the National Scienceand Technology Council

Bibliography

Appendix I

SCIENCE, TECHNOLOGY, ENGINEERING,AND MATHEMATICS (STEM) EDUCATION ISSUESAND LEGISLATIVE OPTIONS*

STEM Education in the United States

Elementary and Secondary Education

Assessments of Math and Science Knowledge

U.S. Students Compared to Students in Other Nations

Math and Science Teacher Quality

Postsecondary Education

STEM Degrees Awarded in the United States

U.S. Degrees Awarded to Foreign Students

International Postsecondary Educational Attainment.

International Comparisons in STEM Education

Federal Programs that Promote STEM Education

Government Accountability Office Study

Description of Selected Federal STEM Programs

NIH National Research Service Awards

NSF Graduate Research Fellowships

NSF Mathematics and Science Partnerships

NSF Research Experiences for Undergraduates

NASA Minority University Research Education Program

ED Mathematics and Science Partnerships

Proposals to Improve STEM Education

Recommendations by the Scientific Community

Legislation in the 109th Congress

Secondary School Math and Science Preparation

Recruiting and Retaining New STEM Teachers

Upgrading the STEM Skills of Current Teachers

Increase STEM Baccalaureate Degree Attainment

Graduate Research and Early-Career Scholarship

Federal Program Coordination

ON COMPUTATIONAL MODELSFOR THE HYPERSPACE

2. Background

3. TheWeightable Quasi-metric Space (B(CX), qHd)

4. Properties from Topological Algebra

PERIODIC-TYPE SOLUTIONS OF DIFFERENTIALINCLUSIONS

2. Preliminaries

3. Periodic-Type Maps, Multivalued Maps and Their Selections

3.1. Periodic Maps

3.2. Anti-periodic Maps

3.3. Quasi-periodic Maps

3.4. Almost-periodic Maps

3.5. Derivo-periodic Maps

4. Primer of Periodic-Type Oscillations

4.1. Linear Systems with Constant Coefficients

4.2. Linear Systems with Time-Variable Coefficients

4.3. Nonlinear Scalar Equations

4.4. Nonlinear Planar Systems

4.5. Nonlinear Systems in Rn

5. General Theorems for Periodic-Type Solutions

5.1. Bounded Solutions

5.2. Periodic Solutions

5.3. Anti-periodic Solutions

5.4. Almost-periodic Solutions

5.5. Derivo-periodic Solutions

6. Concluding Remarks

INDEX.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-61209-811-8

OCLC:

923660441