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 -- Abstract -- 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 -- References -- THE MATHEMATICAL BASIS OF PERIODICITYIN ATOMIC AND MOLECULAR SPECTROSCOPY -- Introduction -- Combinatorial Periodicity in MolecularElectronic and Atomic Spectroscopy -- Combinatorial Periodicity in Molecular and NMR Spectroscopies -- Periodicity of Double Groups and Electronic States -- Acknowledgement -- References -- MATHEMATICAL MODELLING OF THERMOMECHANICALDESTRUCTION OF POLYPROPYLENE -- Abstract -- Conclusions -- References -- A DESIGN-BASED STUDY OF A COGNITIVE TOOLFOR TEACHING AND LEARNING THE PERIMETEROF CLOSED SHAPES -- Abstract -- Introduction -- 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 -- Conclusion -- References -- MODELING ASYMMETRIC CONSUMERBEHAVIOR AND DEMAND EQUATIONSFOR BRIDGING GAPS IN RETAILING1 -- Introduction -- 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 -- References -- 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 -- Acknowledgments -- Bibliography -- References -- Appendix I -- SCIENCE, TECHNOLOGY, ENGINEERING,AND MATHEMATICS (STEM) EDUCATION ISSUESAND LEGISLATIVE OPTIONS* -- Abstract -- Introduction -- 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 -- Abstract -- 1. Introduction -- 2. Background -- 3. TheWeightable Quasi-metric Space (B(CX), qHd) -- 4. Properties from Topological Algebra -- 5. Conclusion -- References -- PERIODIC-TYPE SOLUTIONS OF DIFFERENTIALINCLUSIONS -- 1. Introduction -- 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 -- References -- INDEX.