Advances in mathematics research, Vol.08

Title\n......Page 4
CONTENTS......Page 6
PREFACE......Page 8
1. Introduction......Page 12
2. The Fractional Step Method Applied to the Vlasov Equation......Page 16
2.1. The Fractional Step Method Applied to the Vlasov-Poisson System in One Spatial Dimension......Page 17
2.2. The Vlasov-Poisson System in Higher Phase-Space Dimensions: the Problem of the Formation of an Electric Field at a Plasma Edge in a Slab Geometry......Page 24
2.3. Vlasov-Maxwell Equations for Laser-Plasma Interaction......Page 32
3. Problems Involving the Interpolation along the Characteristic Curves in Two Dimensions......Page 40
3.1. Solution of the Guiding-Center or Euler Equations......Page 41
3.2. The Vlasov-Poisson System in Higher Phase-Space Dimensions: Formation of an Electric Field at a Plasma edge in a Cylindrical Geometry......Page 47
3.3. One-Dimensional Fully Relativistic System for the Problem of Laser-Plasma Interaction......Page 51
3.4. Numerical Solution of a Reduced Model for the Collisionless Magnetic Reconnection......Page 58
4.1. Numerical Solution of the Shallow Water Equations......Page 66
4.2. Two-Dimensional Magnetohydrodynamic Flows......Page 78
5. Conclusion......Page 89
Appendix A: The Shift Operator Using the Cubic Spline......Page 90
Appendix B: Interpolation Using the Cubic Spline......Page 91
Appendix C: Interpolation Using the Cubic B-spline......Page 93
References......Page 95
Abstract......Page 100
Introduction......Page 101
Comparing Mathematics and Science as Secondary School Subjects......Page 102
Relationship between Subject Culture and the Individual......Page 105
The Aesthetic in Education......Page 106
Methodology......Page 108
Research Methods......Page 109
Rose......Page 111
Compelling and Dramatic Nature of Understanding......Page 112
Aesthetic, Passion and the Subject......Page 113
Learning that Brings Unification or Coherence to Aspects of the World or the Subject......Page 114
Aesthetic, Coherence and the Subject......Page 115
Rose’s Transformation......Page 116
Pauline’s Identity Crisis as She Negotiates Subject Boundaries......Page 117
Aesthetic, Identity and the Subject......Page 118
Appreciation for the Aesthetic in the Teaching Act......Page 119
The Aesthetic in the Negotiation of Subject Boundaries......Page 120
Conclusion......Page 121
References......Page 122
Introduction......Page 126
Combinatorial Periodicity in Molecular Electronic and Atomic Spectroscopy......Page 128
Combinatorial Periodicity in Molecular and NMR Spectroscopies......Page 134
Periodicity of Double Groups and Electronic States......Page 145
References......Page 150
Abstract......Page 152
References......Page 155
Introduction......Page 156
Cognitive Inflexibility......Page 157
The Study......Page 160
The Theory-Driven Design of the Cognitive Tool......Page 161
The Empirical Study......Page 162
Learning Outcome of Students from Pre-Test—Post-Test Instruments......Page 164
Feedback of Teachers from Interviews......Page 166
Implications of the Empirical Study......Page 168
Conclusion......Page 169
References......Page 170
Introduction......Page 172
Customer Value and Choice Probabilities......Page 173
Behavioral Asymmetry and Customer Choice......Page 174
Organizational Influences on Customer Values......Page 175
Objectives and Design of Model......Page 176
Choice Variability and Demand Equation......Page 177
Consumer Choice for New Products......Page 180
Customer Value Enhancement......Page 183
Conclusion and Managerial Implications......Page 185
References......Page 186
Why This Study?......Page 188
Abbreviations......Page 189
Results in Brief......Page 191
Background......Page 193
More than 200 Federal Education Programs are Designed to Increase the Numbers of Students and Graduates or Improve Educational Programs in STEM Fields, but Most Have Not Been Evaluated......Page 195
Federal Civilian Agencies Reported Sponsoring over 200 STEM Education Programs and Spending Billions in Fiscal Year 2004......Page 196
Federal Agencies Reported Most STEM Programs Had Multiple Goals and Were Targeted to Multiple Groups......Page 198
A Subcommittee Was Established in 2003 to Help Coordinate STEM Education Programs among Federal Agencies......Page 200
Numbers of Students, Graduates, and Employees in STEM Fields Generally Increased, but Percentage Changes Varied......Page 201
Numbers of Students in STEM Fields Grew, but This Increase Varied by Education Level and Student Characteristics......Page 202
Total Numbers of Graduates with STEM Degrees Increased, but Numbers Decreased in Some Fields, and Percentages of Minority Graduates at the Master’s and Doctoral Levels Did Not Change......Page 204
STEM Employment Rose, but the Percentage of Women Remained About the Same and Minorities Continued to be Underrepresented......Page 208
University Officials and Others Cited Several Factors That Influence Decisions about Participation in STEM Fields and Suggested Ways to Encourage Greater Participation......Page 210
Teacher Quality and Mathematics and Science Preparation Were Cited as Key Factors Affecting Domestic Students’ STEM Participation Decisions......Page 211
International Students’ STEM Participation Decisions Were Affected by Opportunities Outside the United States and the Visa Process......Page 213
Several Suggestions Were Made to Encourage More Participation in the STEM Fields......Page 215
Concluding Observations......Page 216
Agency Comments and Our Evaluation......Page 217
Scope and Methodology......Page 219
Survey......Page 220
Analyses of Student, Graduate, and Employee Data......Page 221
College and University Visits......Page 224
Reviews of Reports and Studies......Page 225
Interviews......Page 226
Appendix II: List of 207 Federal STEM Education Programs......Page 227
Appendix III: Federal STEM Education Programs Funded at $10 Million or More......Page 232
Appendix IV: Data on Students and Graduates in STEM Fields......Page 237
Appendix V: Confidence Intervals for Estimates of Students att he Bachelor’s, Master’s, and Doctoral Levels......Page 241
Appendix VI: Confidence Intervals for Estimates of STEM Employment by Gender, Race or Ethnicity, and Wages and Salaries......Page 246
Appendix VII: Comments from the Department of Commerce......Page 248
Appendix VIII: Comments from the Department of Health and Human Services......Page 250
Appendix IX: Comments from the National Science Foundation......Page 251
Appendix X: Comments from the National Science and Technology Council......Page 253
Bibliography......Page 254
References......Page 255
Appendix I......Page 257
Abstract......Page 258
Introduction......Page 259
Assessments of Math and Science Knowledge......Page 260
U.S. Students Compared to Students in Other Nations......Page 262
Math and Science Teacher Quality......Page 266
STEM Degrees Awarded in the United States......Page 267
U.S. Degrees Awarded to Foreign Students......Page 269
International Comparisons in STEM Education......Page 270
Government Accountability Office Study......Page 272
NIH National Research Service Awards......Page 274
NSF Mathematics and Science Partnerships......Page 275
NASA Minority University Research Education Program......Page 277
ED Mathematics and Science Partnerships......Page 278
Recommendations by the Scientific Community......Page 279
Legislation in the 109th Congress......Page 280
Secondary School Math and Science Preparation......Page 281
Recruiting and Retaining New STEM Teachers......Page 282
Increase STEM Baccalaureate Degree Attainment......Page 283
Graduate Research and Early-Career Scholarship......Page 284
Federal Program Coordination......Page 286
1. Introduction......Page 288
2. Background......Page 289
3. The Weightable Quasi-metric Space (B(CX), qHd)......Page 292
4. Properties from Topological Algebra......Page 297
5. Conclusion......Page 302
References......Page 303
1. Introduction......Page 306
2. Preliminaries......Page 307
3.1. Periodic Maps......Page 309
3.2. Anti-periodic Maps......Page 312
3.3. Quasi-periodic Maps......Page 314
3.4. Almost-periodic Maps......Page 316
3.5. Derivo-periodic Maps......Page 321
4.1. Linear Systems with Constant Coefficients......Page 325
4.2. Linear Systems with Time-Variable Coefficients......Page 326
4.4. Nonlinear Planar Systems......Page 328
4.5. Nonlinear Systems in Rn......Page 329
5.1. Bounded Solutions......Page 332
5.2. Periodic Solutions......Page 339
5.3. Anti-periodic Solutions......Page 343
5.4. Almost-periodic Solutions......Page 349
5.5. Derivo-periodic Solutions......Page 354
6. Concluding Remarks......Page 357
References......Page 358
INDEX......Page 366