About the book:

The book being offered by the author differs from other existing books on the subject in its nontraditional approach to the course of physics. The principle underlying the preparation of this course can be summarized as follows: “From atom to matter”.

What prompted the author to adopt this approach? Indeed, the creation of new materials with unusual mechanical, thermal, electrical, magnetic, and optical properties requires a microscopic approach to the problem and a clear understanding of the practical significance of the approach “from atom to matter”. This means that the scientists and industrial workers engaged in fields like physical materials science, nuclear and semiconductor engineering, laser

…This book is intended for those who wish to acquire a deeper knowledge of physical phenomena. It can be used by students of physics and mathematical schools, as well as by those who have finished school and are engaged in self- education. A good deal of the material may be useful to teachers delivering lectures on various topics of physics.

…

This is not a textbook, but rather a helpbook that should be used in conjunction with the standard textbooks. Nor is the book intended for a light reading; you have to use a pen and paper, think, analyze, and even compute whenever it is necessary. We shall describe physics here in the way re searchers understand it today.

Physics essentially deals with the fundamental laws of nature. The progress being made at present in all branches of natural science is due, as a rule, to the introduction of physical concepts and techniques in them. This is besides the fact that a knowledge of physical sciences is essential for new industrial ventures lying at the root of technical progress. Physics is fast becoming an important element in the modern civilization.

The book was published by Mir in 1989 and was translated from the Russian by R. S. Wadhwa.

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Front Cover 1

Title Page 5

Preface 7

To The Reader 9

Content 10

Chapter 1. Unity of Nature 16 18

1.1. Hierarchy of Natural Objects 16 18

1.1.1. Elementary Particles 16 18

1.1.2. Nuclei 20 22

1.1.3. Atoms and Molecules 21 23

1.1.4. Macroscopic Bodies 22 24

1.1.5. Planets 23 25

1.1.6. Stars. Galaxies. Universe 25 27

1.2. Four Types of Fundamental Interactions 26 28

1.2.1. Bound Systems of Objects. Interactions 26 28

1.2.2. Gravitational Interactions 26 28

1.2.3. Electromagnetic Interactions 27 29

1.2.4. Strong (Nuclear) Interactions 27 29

1.2.5. Weak Interactions 27 29

1.2.6. Comparative Estimates for the Intensity of All Types of Interactions 29 31

1.2.7. Fields and Matter 29 31

1.3. Space and Time 30 32

1.3.1. Scales of Space and Time in Nature 30 32

1.3.2. Homogeneity of Space and Time 31 33

1.3.3. Free Bodies and Inertial Motion 31 33

1.3.4. Inertial Reference Frames. The Relativity Principle 32 34

Chapter 2. Mechanics of a Material Particle 34 36

2.1. Coordinates, Velocity, Acceleration 34 36

2.2. Galilean Transformations 35 37

2.2.1. Absolute Nature of Dimensions and Time Intervals 36 38

2.2.2. Relative Nature of Velocities and the Law of Their Transformation 37 39

2.2.3. Absolute Nature of Accelerations 37 2.3. Law of Motion in Mechanics 37 41

2.4. Motion of a Material Particle in a Gravitational Field 39 41

2.5. Momentum. Law of Momentum Conservation 42 44

2.6. Law of Energy Conservation. Applications and Universal Nature of ConservationLaws 43 44

2.6.1. Law of Energy Conservation 43 45

2.6.2. Applications of Conservation Laws 46 48

2.6.3. Universal Nature of Conservation Laws. Angular Momentum 52 54

2.7. Ultimate Velocity. Mechanics of High-Energy Particles 54 56

2.7.1. Experiments on Accelerators and Ultimate Velocity 54 56

2.7.2. Lorentz Transformations 55 57

2.7.3. Relativistic Energy and Momentum 58 60

2.7.4. Role of Relativistic Constant c in Physics 61 63

Chapter 3 Electromagnetic Field 63 65

3.1. Electric Charge 63 65

3.2. Method of Field Investigation 64 66

3.2.1. Equation of Motion of a Charge in a Field 64 66

3.2.2. Laws of Field Transformation 64 66

3.3. Laws of Electromagnetic Field 66 68

3.3.1. New Objects and New Mathematics 66 68

3.3.2. First Field Equation. Relation Between Electric Field and Electric Charge 67 69

3.3.3. Second Field Equation. Absence of Magnetic Charges 68 69

3.3.4. Third Field Equation. Relation Be tween Current and “Something” with a Vortex Magnetic Field 68 70

3.3.5. Fourth Field Equation. Relation Between a Varying Magnetic Field and a Vortex Electric Field 71 73

3.3.6. Additional Analysis of the Third Field Equation. Relation Between a Varying Electric Field and a Vortex Magnetic Field 72 74

3.3.7. Maxwell’s Field Equations 73 75

3.4. Constant Electric Field 74 76

3.4.1. Field of a Stationary Point Charge 74 76

3.4.2. Field of Charges Distributed over a Sphere, Line or Plane Surface 74 76

3.4.3. Electrostatic Energy of Charges. Field Potential 77 79

3.4.4. Field of a Dipole. Charge-Dipole and Dipole-Dipole Interactions 80 82

3.5. Constant Magnetic Field 82 84

3.5.1. Magnetic Field of a Direct Current 82 84

3.5.2. Magnetic Field of a Current Surface 82 84

3.5.3. Magnetic Moment and Its Relation with Mechanical (Angular) Momentum 83 85

3.6. Motion of Charges in a Field 85 87

3.6.1. Motion of a Charge in a Constant Uniform Electric Field 85 87

3.6.2. Motion of a Charge in a Constant Uniform Magnetic Field 86 88

3.6.3. Motion of a Charge in a Coulomb Field 86 88

3.7. Fields of Moving Charges. Emission 91 93

3.7.1. Field of a Uniformly Moving Charge 91 93

3.7.2. Emission by a Charge Moving with an Acceleration 95 97

3.7.3. Emission by a Charge Moving Uniformly in a Circle 98 99

3.8. Electromagnetic Waves 100 102

3.8.1. Some Properties of Radiation Fields 100 102

3.8.2. Travelling Waves 100 102

3.8.3. Emission of Electromagnetic Waves by Oscillating Charges. Energy and Momentum of Waves 102 104

3.8.4. Free Oscillations of a Field. Standing Waves 104 106

3.9. Propagation of Light 106 108

3.9.1. Interference of Electromagnetic Waves 106 108

3.9.2. Diffraction of Electromagnetic Waves 107 109

3.9.3. Geometrical Optics 109 111

Chapter 4. Atomic Physics and Quantum Mechanics 112

4.1. Planetary Model of Atom 110 112

4.2. Experiments on Diffraction of Particles 110 112

4.3. The Uncertainty Relation 115 117

4.4. Probability Waves 117 119

4.4.1. Complex Numbers. Euler’s Formula 118 120

4.4.2. Complex Probability Waves. The Superposition Principle 119 121

4.4.3. Limiting Transition to Classical Mechanics 121 123

4.5. Electron in an Atom 123 125

4.5.1. Energy and Its Quantization 123 125

4.5.2. Angular Momentum and Its Quantization 128 130

4.5.3. Probability Amplitudes and Quantum Numbers 130 132

4.6. Many-Electron Atom 132 134

4.6.1. Spin of an Electron 132 134

4.6.2. Systems of Identical Particles. Quantum Statistics 134 136

4.6.3. Atomic Quantum States 137 139

4.7. Quantization of Atomic Radiation 139 141

4.7.1. Quantum Transitions. Line Spectra 139 141

4.7.2. Photon. The Concept of Parity. Selection Rules 140 142

4.8. Photon-Electron Interaction. The Photoelectric Effect. The Compton Effect 146 148

4.9. Simultaneous Measurement of Quantities and the Concept of the Complete Set of Measurable Quantities 150 152

4.10. Molecules 151 153

Chapter 5. Macroscopic Bodies as Aggregates of Particles. Thermal Phenomena 155 157

5.1. The Basic Problem of Statistical Physics 155 157

5.2. Macroscopic Quantities. Fluctuations 157 159

5.3. Statistical Analysis of the Gas Model 159 161

5.3.1. Computer Experiments 159 161

5.3.2. Reversibility of Microscopic Processes in Time and Irreversibility of Macroscopic Processes 160 162

5.4. Entropy 161 163

5.5. Temperature 162 164

5.6. Equilibrium Distribution of Particles in a Body 167 169

5.7. Thermodynamic Relations 172 174

5.8. Ideal Gas 176 178

5.8.1. Matter and Its States 176 178

5.8.2. Classical and Quantum Ideal Gases 176 178

5.8.3. Equation of State for an Ideal Gas 178 180

5.8.4. Heat Capacity of an Ideal Gas 181 183

5.8.5. Reversible Thermal Processes 184 186

5.9. Statistics and Thermodynamics of Radiation 188 190

5.10. Crystals 194 196

5.10.1. Crystal Lattice 194 196

5.10.2. Types of Lattice Bonds 195 197

5.10.3. Mechanical Properties of Crystals 196 198

5.10.4. Electron Energy Spectra of Crystals 204 206

5.10.5. Lattice Heat Capacity 206 206

5.10.6. Electron Gas in Metals 213 215

5.11. Phase Transitions 218 220

Chapter 6. Macroscopic Motion of Media. non Equilibrium Processes 225 227

6.1. Nonequilibrium States of Bodies 225 227

6.2. Macroscopic Motion 226 228

6.3. Equations of Hydrodynamics of an Ideal Liquid 228 230

6.3.1. Matter Conservation Law in Hydrodynamics 228 230

6.3.2. Equation of Motion in Hydrodynamics 231 233

6.4. Hydrodynamic Analysis of Problems on Viscous Flow, Heat Conduction, and Diffusion 233 235

6.4.1. Viscosity 233 235

6.4.2. Flow of a Viscous Liquid Through a Tube 235 237

6.4.3. Heat Conduction 237 239

6.4.4. Heat Transfer Between Two Walls 238 240

6.4.5. Diffusion. Dissolution of a Solid in a Liquid 240 242

6.5. Kinetic Coefficients in Gases and Their Connection with the Molecular Parameters 242 244

6.5.1. The Concept of Mean Free Path of Molecules 243 245

6.5.2. Molecular Treatment of the Diffusion Process 246 248

6.5.3. Diffusion as a Random Motion of Particles 248 250

6.5.4. Relations Between Kinetic Coefficients 251 253

6.6. Resistance to the Motion of Solids in a Liquid 252 254

6.6.1. Similitude Method. The Reynolds Number 252 254

6.6.2. Drag at Low Velocities 254 256

6.6.3. Drag at High (Subsonic) Velocities 257 259

6.7. Instabilities in Hydrodynamics 259 261

6 7.1. Transition from Laminar to Turbulent Flows 259 261

6.7.2. Boundary Layer 260 262

6.7.3. Turbulent Viscosity and Thermal Diffusivity 262 264

6.7.4. Transition from Molecular to Convective Heat Transfer. Solar Granulation 263 265

6.8. Oscillations and Waves in a Liquid 266 268

6.8.1. Various Forms of Wave Motion 266 268

6.8.2. Wave Characteristics 267 269

6.8.3. Linear and Nonlinear Waves 269 271

6.8.4. Solitons and Other Nonlinear Effects 269 271

6.8.5. Highly Perturbed Media 270 272

6.8.6. Oscillations of a Charged Drop and the Fission of Heavy Nuclei 271 273

6.9. Macroscopic Motion of Compressible Media 274 276

6.9.1. Generalized Form of the Bernoulli Equation 274 276

6.9.2. Compressibility Criterion for a Medium and the Velocity of Sound 275 277

6.9.3. Flow in a Tube with a Varying Cross Section 276 278

6.9.4. Laval Nozzle 277 279

6.10. Shock Waves 278 280

6.10.1. Propagation of Perturbations in a Compressible Gas Flow 278 280

6.10.2. General Relations for a Shock Wave 281 283

6.10.3. Shock Waves in an Ideal Gas 285 287

6.10.4. The Problem on a High-Intensity Explosion in the Atmosphere 289 291

6.11. Hydrodynamic Cumulative Effects 290 292

6.11.1. Cumulative Jets 291 293

6.11.2. Bubble Collapse in a Liquid 296 298

6.11.3. Converging Spherical and Cylindrical Shock Waves 297 299

6.11.4. The Role of Instabilities in Suppressing Cumulation 297 299

6.11.5. Emergence of a Shock Wave on the Surface of a Star 298 300

6.12. Cavitation in a Liquid 299 301

6.13. Highly Rarefied Gases 301 303

6.14. Macroscopic Quantum Effects in a Liquid 304 306

6.15. Generalizations of Hydrodynamics 307 309

Chapter 7. Electromagnetic Fields in Media. Electrical, Magnetic, and Optical Properties of Substances 309 311

7.1. Superconductivity 309 311

7.2. Electrical Conductivity of Metals 310 312

7.3. Direct Current 315 317

7.4. Dielectric Conductance 319 321

7.4.1. Electrons and Holes. Exciton States 319 321

7.4.2. Semiconductors 320 322

7.5. Electric Fields in Matter 322 324

7.5.1. Field Fluctuations in a Substance 322 324

7.5.2. Electrostatic Fields in Metals 324 326

7.5.3. Electrostatic Fields in Insulators. Polarization of a Substance 325 327

7.6. A Substance in a Magnetic Field 330 332

7.6.1. Diamagnetic Effect 330 332

7.6.2. Paramagnets. Orientation Magnetization 333 335

7.6.3. Spontaneous Magnetization. Ferromagnetism 335 337

7.6.4. Magnetic Properties of Superconductors. Quantization of Large-Scale Magnetic Flux 338 340

7.7. Alternating Currents and Electromagnetic Waves in a Medium. Optical Properties of Media 342 344

7.7.1. A.C. Fields and a Substance 342 344

7.7.2. Induced EMF 343 345

7.7.3. A.C. Circuits. Solutions of Differential Equations 344 346

7.7.4. Generation of Electromagnetic Waves 353 355

7.7.5. Some Laws of Optics and the Velocity of Propagation of Electromagnetic Waves in a Medium. Reflection and Refraction of Waves 355 357

7.7.6. Refractive Index of Insulators. Dispersion and Absorption of Light 361 363

7.7.7. Refractive Index of Metals. Skin Effect. Transparency of Metals to Hard Radiation 364 366

7.7.8. Nonlinear Optics Effects 365 367

7.7.9. Lasers 369 371

Chapter 8. Plasma 373 375

8.1. General Remarks 373 375

8.2. Quantum Effects in Plasma. Tunneling of Nuclei Through a Potential Barrier 374 376

8.3. Relativistic Effects in Plasma. Mass Defect in Nuclear Fusion and Energy Liberated in the Process 379 381

8.4. Plasma Statistics. Equation of State for Plasma. Thermal Radiation of Plasma 380 382

8.5. Plasma Kinetics. Mobility of Ions and Its Relation with Diffusion. Electrical Conductivity of Plasma 384 386

8.6. Magnetohydrodynamics and Plasma Instabilities. Tokamaks 385 387

8.7. Oscillations and Waves in Plasma. Propagation of Radio Waves in the Ionosphere 388 390

Chapter 9. Stellar and Prestellar States Of Matter 392 394

9.1. State of Matter at Ultrahigh Temperatures and Densities 392 394

9.2. Stars as Gaseous Spheres 394 396

9.2.1. Calculation of Pressure and Temperature at the Centre of a Star 394 396

9.2.2. Temperature of the Surface and the Total Emissive Power of aStar 396 398

9.2.3. Energy Transfer in Stars 396 398

9.3. Sources of Stellar Energy 397 399

9.3.1. Analysis of Possible Sources of Stellar Energy 397 399

9.3.2. Nuclear Reactions of the Proton-Proton Cycle 399 401

9.4. White Dwarfs 401 403

9.4.1. Possible Evolution of Stars of the Type of the Sun 401 403

9.4.2. Density and Size of White Dwarfs 401 403

9.4.3. Limiting Mass of WhiteDwarfs 403 405

9.5. Superdense Neutron Stars 404 406

9.5.1. Size of Neutron Stars 404 406

9.5.2. Rotation and Magnetic Fields of Neutron Stars 405 407

9.5.3. Radio Emission by Pulsars 406 408

9.5.4. Internal Structure of Neutron Stars 406 408

9.5.5. Gravitational Effects in the Vicinity of a Neutron Star 409 411

9.6. Gravitation and Relativity 411 413

9.6.1. Equivalence Principle 411 413

9.6.2. Geometry and Time in Non-inertial Reference Frames 412 414

9.6.3. Einstein’s Equations 413 415

9.7.Expansion of the Universe 413 415

9.7.1. Friedman’s Cosmological Solutions 413 415

9.7.2. Discovery of “Expansion” of the Universe 415 417

9.7.3. Critical Density 416 418

9.8. Hot Universe 418 420

9.8.1. Discovery of Background Thermal Radiation 418 420

9.8.2. Charge-Asymmetric Model of Early Universe 419 421

9.8.3. Change in Density and Temperature of Prestellar Matter in the Process of Cosmological Expansion 421 423

9.8.4. State of Aggregation at Early Stages of Evolution of Hot Universe 422 424

9.9. Fusion of Elements in Stars 425 427

Concluding Remarks 432 434

Appendices 433 435

Subject Index 447 449

About the book:

The question of consciousness, of its relation to being cannot in principle be reduced to a particular scientific problem of the correlation of mental and physiological processes or to a problem of the reception, processing and production of information. The essence of this problem is not what happens under my skull when I calculate the trajectory of a flight to the stars, but what in philosophy is called the question of the identity of thought and being. How is it possible that a person can mentally chart the road to the stars? How and why can he, in his thoughts, conceive of the existence of the Universe? How can the infinity of time and space be contained in the instant of their realisation in consciousness? This is the key question of the human ability to set goals. And unless one knows one’s way through the two thousand years history of solutions to this question, one will have little chance of even framing a correct approach to any particular problem of the relation between mind and brain.

That is why I have called this book The Riddle of the Self. By suggesting that the Self, the Ego presents a riddle I imply that there may be many different ways of tackling it. This book is not a calm and consistent academic exposition of compiled knowledge. It is more like a not very good transcript of a heated debate. And it is not in itself the answer to the riddle, but a discussion of how the problem should be stated. It is about the method that should be used in the search.

The book was published by Progress in 1980 and was translated from the Russian by Robert Daglish. The book was designed by Vadim Kuleshov.

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CONTENTS

Page FOREWORD 7

INTRODUCTION 1

1. Where Is the Self? 11

2. “I” See and “I” Understand 20

CHAPTER ONE. CLEAR APPROACHES AND DEAD-ENDS 25

1. What Is Knowledge 25

2. Something About “Something” 48

3. When Is Kant Right? 72

4. Towards a Solution 82

CHAPTER TWO. SOCIAL AND INDIVIDUAL CONSCIOUSNESS 95

1. Bertrand Russell’s Mistake 95

2. Individual and Social (Hegel versus Russell) 106

3. The End of the Mind-Body Problem 115

4. Dreams of the Kurshskaya 142

5. The Substance of History 156

CHAPTER THREE. MAN AND HIS THOUGHT 181

1. Life Source of the Self 181

2. The Language of Real Life 188

3. When Consciousness Is Conscious of Itself 199

4. The Real Life of Language 211

5. Language and Consciousness 231

THE RIDDLE ANSWERED 250

]]>About the book:

This book presents the first integral treatment of the philosophical views of Albert Einstein and their influence on the origin and interpretation of the theory of relativity. It brings out the specific features of the philosophical com prehension of the theory of relativity m the world and Soviet literature, and analyses the influence of the new relativistic physical ideas in enriching and developing the traditional philosophical categories of matter, space, time, and motion.

The book was first published by Progress Publishers in 1987 and was translated from the Russian by H. Campbell Creighton. The book was designed by Vyacheslav Serebryakov.

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Contents

Preface 11

Part One. Philosophical Problems of the Theory of Relativity in the World and Soviet Literature 13

Part Two. The Evolution of Einstein’s Philosophical Views 65

1. Philosophical Analysis of Classical Mechanics and Metaphysics 67

2. Einstein and the Concepts of Idealist Philosophy 96

3. The Substance of Einstein’s Philosophic views 114

Part Three. The Development of the Theory of Relativity and Philosophy 154

1. The Concept of Matter and the Development of Physics 155

2. Time, Space, and Motion in Physics and Philosophy 178

3. The Genesis of the Special Theory of Relativity and Philosophy 193

4. The Development of the General Theory of Relativity 217

5. The Philosophical Essence of Relativistic Physics 232

Conclusion 244

Bibliography 246

Name Index 250

Subject Index 254

A contemporary of Pushkin and Gogol, the well-known Russian Prince Vladimir Odoyeusky (1804-1869) is the author of many works, including some extremely popular tales for children. Here are two of them, the delightful title story about Misha’s adventures with a musical snuff-box, and “Old Father Frost”, also highly entertaining and instructive.

The book is lavishly illustrated. The illustrations in the first story perhaps reminds one of Tim Burton’s imagery in his movies.

The book was published by Raduga in 1990. The amazing illustrations are by Alexander Koshkin and Natalia Polyanskaya.

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]]>About the book:

The book describes the working of many electronic devices and methods of testing them. Since the book was written in the early 70s, some of the technology presented in the book may be outdated.

The book was translated from the Russian by George Roberts and was first published by Mir in 1972.

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LIST OF SYMBOLS 5

**Chapter One. RADIO PARTS. GENERAL 9
**

1.1. Resistors 9

1.2. Capacitors 13

1.3. Inductance Coils 17

1.4. Transformers and Low-Frequency Chokes 20

Review Questions 22

**Chapter Two. TEMPERATURE MEASURING INSTRUMENTS 23**

2.1. Non-Electrical Measurement of Temperature 23

2.2. Electrical Measurement of Temperature 28

Review Questions 37

**Chapter Three. SEMICONDUCTOR DEVICES AND THEIR APPLICATIONS 38
**

3.1. General 38

3.2. Semiconductor Diodes 44

3.3. Transistors 55

3.4. Photodiodes, Phototransistors, Photoresistors, Phosphide Diodes, and Laser Diodes 64

Review Questions 67

**Chapter Four. SEMICONDUCTOR TECHNOLOGY 68
**

4.1. Technological Cycle 68

4.2. Basic Methods of P-N Junction Formation 73

4.3. Equipment for P-N Junction Fabrication 78

4.4. Photolithographic Processing 81

4.5. Newly-Developed Methods of Semiconductor Production 82

4.6. Selection of Technological Method 85

4.7. Formation of Ohmic Contacts 86

4.8. Fabrication of Semiconductor Wafers and Crystals 88

4.9. Assembly of Medium-Power Junction Diffusion Diodes 90

4. 10. Assembly of High-Frequency Diffusion-Alloy Transistors 92

Review Questions 94

**Chapter Five. Electrical Measuring Circuits 95 **

5.1. Graphical Representation of Measuring Circuit Elements 95

5.2. Rectifiers 97

5.3. Filters 101

5.4. Voltage stabilizers 103

5.5. Amplifiers 105

5.6. Multivibrators 108

5.7. Trigger Circuits 111

5.8. Comparators 113

5.9. Fundamentals of Logical Elements 115

5.10. Measuring Equipment and Wiring 119

5.11. Adjustment of Measuring Equipment 121

Review Questions 122

**Chapter Six. Measurement of Electrical Parameters 124
**

6.1. Purpose and Methods of Measurement 124

6.2. Rectifier Diode Measurements 127

6.3. High-Frequency and Microwave Diodes Measurements 135

6.4. Pulse Diode Measurements 141

6.5. Reference Diode Measurements 142

6.6. Switching Diode Measurements 145

6.7. Transistor Measurements 150

6.8. Measurements of Varicap Diodes, Tunnel Diodes, Photodiodes, Phototransistors, and Photoresistors 160

6.9. Laser Diode Measurements 163

6.10. Automatic Measurements 166

Review Questions 171

**Chapter Seven. Adjustment of Semiconductor Devices 172
**

7.1. Adjustment of Pulse Diodes 173

7.2. Adjustment of High-Frequency Diodes 174

7.3. Adjustment of Tunnel Diodes 175

7.4. Adjustment of Microwave Diodes 177

Review Questions 180

**Chapter Eight. Testing Semiconductor Devices 181
**

8.1. Effect of Ambient Medium on Semiconductor Devices 181

8.2. Classification of Tests 182

8.3. Construction Tests 185

8.4. Electrical Tests 186

8.5. Mechanical Tests 192

8.6. Climatic Tests 195

Review Questions 200

Index 201

]]>About the book:

This publication is the second book. of the “Elements of the Theory of Functions and Functional Analysis,” the first book of which (“Metric and Normed Spaces”) appeared in 1954. In this second book the main role is played by measure theory and the Lebesgue integral. These concepts, in particular the concept of measure, are discussed with a sufficient degree of generality; however, for greater clarity we start with the concept of a Lebesgue measure for plane sets. If the reader so desires he can, having read §1, proceed immediately to Chapter II and then to the Lebesgue integral, taking as the measure, with respect to which the integral is being taken, the usual Lebesgue measure on the line or on the plane.

The theory of measure and of the Lebesgue integral as set forth in this book is based on lectures by A.N. Kolmogorov given by him repeatedly in the Mechanics-Mathematics Faculty of the Moscow State University. The final preparation of the text for publication was carried out by S. V. Fomin.

The two books correspond to the program of the course “Analysis III” which was given for the mathematics students by A. N. Kolmogorov. At the end of this volume the reader will find corrections pertaining to the text of the first volume.

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Translator’s Note. v

Foreword vii

List of Symbols. xi

CHAPTER I Measure Theory

1. Measure of Plane Sets. 1

2. Systems of Sets. 19

3. Measures on Semirings. Continuation of a Measure from a Semiring to the Minimal Ring over it. 26

4. Continuations of Jordan Measures. 29

5. Countable Additivity. General Problem of Continuation of Measures. 35

6. Lebesgue Continuation of Measure, Defined on a Semiring with a Unit. 39

7. Lebesgue Continuation of Measures in the General Case. 45

CHAPTER II Measurable Functions

8. Definition and Basic Properties of Measurable Functions. 48

9. Sequences of Measurable Functions. Different Types of Convergence. 54

CHAPTER III

The Lebesgue Integral

10. The Lebesgue Integral for Simple Functions. 61

11. General Definition and Basic Properties of the Lebesgue Integral. 63

12. Limiting Processes Under the Lebesgue Integral Sign. 69

13. Comparison of the Lebesgue Integral and the Riemann Integral. 75

14. Direct Products of Systems of Sets and Measures. 78

15. Expressing the Plane Measure by the Integral of a Linear Measure and the Geometric Definition of the Lebesgue Integral. 82

16. Fubini’s Theorem. 86

17. The Integral as a Set Function. 90

CHAPTER IV

Functions Which Are Square Integrable

18. The L_2 Space. 92

19. Mean Convergence. Sets in L2 which are Everywhere Complete. 97

20. L_2 Spaces with a Countable Basis. 100

21. Orthogonal Systems of Functions. Orthogonalisation. 104

22. Fourier Series on Orthogonal Systems. Riesz-Fischer Theorem.109

23. The Isomorphism of the Spaces L_2 and l_2. 115

CHAPTER V

The Abstract Hilbert Space. Integral Equations with a Symmetric Kernel

24. Abstract Hilbert Space. 118

25. Subspaces. Orthogonal Complements. Direct Sum. 121

26. Linear and Bilinear Functionals in Hilbert Space. 126

27. Completely Continuous Self-Adjoint Operators in H. 129

28. Linear Equations with Completely Continuous Operators. 134

29. Integral Equations with a Symmetric Kernel. 135

Additions and Corrections to Volume I 138

Subject Index 143

]]>About the book:

In 1979 the scientists of the world marked the centenary of Albert Einstein. This book, written by prominent Soviet specialists in physics and philosophy, purports to repeal Einstein’s influence on the modern scientific view of the world and analyses the most important philosophical problems of 20th century physics. The focus is on the problems of the special and general theory of relativity. Such as the development of the concepts of time and space in relativistic physics, their interconnection, the dimensionality of physical space, and complementarity of physics and geometry. The book deals with Einstein’s views of the philosophical foundations of quantum mechanics and his search for a unified field theory. Special consideration is given to the philosophical problems of relativistic cosmology and its role in the description of the time- space structure of the universe.

The book was first published by Progress Publishers in 1983 and was translated from the Russian by Sergei Syrovatkin. The book was designed by Sergei Zeitsev.

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Front Cover 1

Title Page 5

Content 7

Preface 9

D. P. Gribanov. Einstein’s Philosophical Worldview 12

M. E. Omelyanovsky. Einstein, the Foundations of Modem Physics and Materialist Dialectics 38

B. G. Kuznetsov. Einstein and Classical Science 65

A. D. Alexandrov. On the Philosophical Content of the Relativity Theory 106

Yu. B. Molchanov. The Concept of Simultaneity and the conception of time in the special theory of relativity 126

I. A. Akchurin. M. D. Akhundov. Einstein and the Development of the Concept of Space 148

A. M. Mostepanenko. Complementarity of Physics and Geometry (Einstein and Poincare) 185

V. A. Fok. The Physical Principles of Einstein’s Gravitational Theory 215

M. A. Markov. Modern Problems of the General Theory of Relativity 228

E. M. Chudinov. Einstein and the Problem of the infinity of the Universe 234

V. L. Ginzburg. The Heliocentric System and the General Theory of Relativity (From Copernicus to Einstein) 258

V. S. Barashenkov. The Laws of the General Relativity Theory and the phenomena of the microworld 313

V. I. Rodichev. Methodological Aspects of Unified Field Theory 346

Yu. V. Sachkov. Problems in the Substantiation of Probabilistic Research Methods in Physics 378

S. V. Illarionov. The Einstein Bohr Controversy 401

K. Kh. Delokarov. Einstein and Mach 420

E. M. Chudinov. Einstein and Bridgman’sOperationalism 439

K. Kh. Delokarov. The Theory of Relativity and Soviet Science ( A Historico-Methodological Analysis) 454

Name Index 500

Subject Index 507

Back Cover 520

About the book from the Preface:

A teaching of the biosphere has developed – a science which stands in its own right and cannot be reduced either to geography or biology, but makes use of their advances and results, and, in turn, influences the development of geology. The founder of this science was the brilliant Russian scientist Vladimir Ivanovich Vernadsky (1863-1945).

This book will describe the biosphere and the role of life in geological processes; reading it, you will leam about the scientists who dealt with these problems and, above all about V. I. Vernadsky himself. His name is bound up with the problems treated in this book, just as the name of Albert Einstein is bound up with the theory of relativity. The highest moral qualities of Vernadsky and Einstein also bring them together. And, evidently, it is not by chance that the greatest scientific discoveries of the twentieth century were made by such irreproachable personalities as Vernadsky and Einstein. “To all who knew him, even slightly, he will remain an ideal of a man of high purpose and purity of character and a scientist who never lost his interest in the search for knowledge” -this is what one of Vernadsky’s contemporaries wrote about him.

About the author (from the backcover):

Petrographic Types of Coals of the USSR(Ed. A. A. Lyuber) (USSR: Nedra) andRational Complex of Petrographic and Chemical Methods of Investigations of Coals and Combustible Shales(USSR: Nedra).

The book was translated from the Russian by V. Purto and was first published by Mir in 1982. This book was also reprinted in the Science for Everyone series. The current scan is for the 1982 book and not the SFE series.

PDF | OCR | Cover | Bookmarked | 228 pp. | 12 MB

The Internet Archive link for the book.

*Note:* The scanning of the book was an adventure in itself. The pages of the book and its spine were very brittle. The pages were so brittle that just turning the pages separated them from the spine. At end of the scan, the book was almost separated into individual pages. The physical copy of the book was almost destroyed in the scanning process and I hope the creation of the electronic copy justifies it.

The white images on the cover are from Ernst Haeckel’s Kunstformen der Natur (Art Forms of Nature). Art Forms of Nature is an amazing book, if you have not seen it you must. You may explore these aesthetic and amazing drawings at the Biodiversity Heritage Library.

To the English-speaking Reader 6

Strange Fate (Foreword) 9

Biosphere 17

Living Matter 45

Most Powerful Geological Force 77

Three Factors: Bio-, Eco- and Tapho- 115

Metabiosphere 151 Conclusion 209

Glossary of Special Terms 210

Bibliography 215

Illustrations 217

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About the book:

This book is devoted to some interrelated problems of a new, rapidly developing branch of mathematics called combinatorial geometry. Common to all the problems examined here is the notion of “ cutting” a geometric figure into several “smaller pieces.” There are several different criteria for what constitutes a “ smaller piece” ; hence this book necessarily treats several different problems. All the theorems proved here are very recent; the oldest of them was proved by the Polish mathematician Karol Borsuk about forty years ago. This theorem of Borsuk is the core around which all of the subsequent exposition unfolds. The most recent theorem is barely a year old.

The topics treated in this book are well within the grasp of bright and interested high school students. At the same time, the book intro duces the reader to a number of the unsolved problems of geometry.

This family of problems is the subject of another book by the same authors. Theorems and Problems in Combinatorial Geometry (Nauka, 1965). That book, however, deals chiefly with problems of three- dimensional and higher-dimensional spaces. The present book concerns itself only with problems of plane geometry, and can thus be used by high school mathematics clubs. Theorems and Problems in Combinatorial Geometry will be useful, however, to readers interested in continuing further.

The remarks at the end of the book are intended for the more advanced reader.

The book is part of the series Popular Lectures in Mathematics.

PDF | OCR | Bookmarked | 2.7 MB | 78 pages

All credits to the original uploader.

The Internet Archive link.

Preface vi

1. Division of Figures into Pieces of Smaller Diameter 1

1.1. The Diameter of a Figure 1

1.2. Formulation of the Problem 3

1.3. Borsuk’s Theorem 4

1.4. Convex Figures 7

1.5. Figures of Constant Width 12

1.6. Embedding in a Figure of Constant Width 14

1.7. For Which Figures is a{F) = 3? 19

2. Division of Figures in the Minkowski Plane 26

2.1. A Graphic Example 26

2.2. The Minkowski Plane 28

2.3. Borsuk’s Problem in Minkowski Planes 34

3. The Covering of Convex Figures by Reduced Copies 40

3.1. Formulation of the Problem 40

3.2. Another Formulation of the Problem 41

3.3. Solution of the Covering Problem 42

3.4. Proof of Theorem 2.2 52

4. The Problem of Illumination 55

4.1. Formulation of the Problem 55

4.2. Solution of the Problem of Illumination 57

4.3. The Equivalence of the Last Two Problems 58

4.4. Division and Illumination of Unbounded Convex Figures 63

Remarks 66

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This book is not a textbook in the ordinary sense of the word but rather a reader in the mathematical sciences. Using simple examples taken from physics and a variety of mathematical problems, we have tried to introduce the reader to a broad range of ideas and methods that are found in present-day applications of mathematics to physics, engineering and other fields. Some of these ideas and methods (such as the use of the delta function, the principle of superposition, obtaining asymptotic expressions, etc.) have not been sufficiently discussed in the ordinary run of mathematics textbooks for non-mathematicians, and so this text can serve as a supplement to such textbooks. Our aim has been to elucidate the basic ideas of mathematical methods and the general laws of the phenomena at hand. Formal proofs, exceptions and complicating factors have for the most part been dropped. Instead we have strived in certain places to go deeper into the physical picture of the processes.

The book was first published by Mir in 1976 and was translated from the Russian by George Yankovsky.

PDF | 666 pages | Cover | OCR

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The Internet Archive link for the book.

Contents

PREFACE 9

Chapter 1. Certain Numerical Methods 13

1.1 Numerical integration 14

1.2 Computing sums by means of integrals 20

1.3 Numerical solution of equations 28 Answers and Solutions 36

Chapter 2. Mathematical Treatment of Experimental Results 39

2.1 Tables and differences 39

2.2 Integration and differentiation of tabulated functions 44

2.3 Fitting of experimental data by the least-squares method 49

2.4 The graphical method of curve fitting 55

Answers and Solutions 62

Chapter 3. More on Integrals and Series 65

3.1 Improper integrals 65

3.2 Integrating rapidly varying functions 73

3.3 Stirling’s formula 82

3.4 Integrating rapidly oscillating functions 84

3.5 Numerical series 88

3.6 Integrals depending on a parameter 99

Answers and Solutions 103

Chapter 4. Functions of Several Variables 108

4.1 Partial derivatives 108

4.2 Geometrical meaning of a function of two variables 115

4.3 Implicit functions 118

4.4 Electron tube 126

4.5 Envelope of a family of curves 129

4.6 Taylor’s series and extremum problems 131

4.7 Multiple integrals 139

4.8 Multidimensional space and number of degrees of freedom 150

Answers and Solutions 154

Chapter 5. Functions of a Complex Variable 158

5.1 Basic properties of complex numbers 158

5.2 Conjugate complex numbers 161

5.3 Raising a number to an imaginary power. Euler’s formula 164

5.4 Logarithms and roots 169

5.5 Describing harmonic oscillations by the exponential function of an imaginary argument 173

5.6 The derivative of a function of a complex variable 180

5.7 Harmonic functions 182

5.8 The integral of a function of a complex variable 184

5.9 Residues 190

Answers and Solutions 199

Chapter 6. Dirac’s Delta Function 203

6.1 Dirac’s delta function a(x) 203

6.2 Green’s function 208

6.3 Functions related to the delta function 214

6.4 On the Stieltjes integral 221

Answers and Solutions 223

Chapter 7. Differential Equations 225

7.1 Geometric meaning of a first-order differential equation 225

7.2 Integrable types of first-order equations 229

7.3 Second-order homogeneous linear equations with constant coefficients 236

7.4 A simple second-order nonhomogeneous linear equation 242

7.5 Second-order nonhomogeneous linear equations with constant coefficients 249

7.6 Stable and unstable solutions 256

Answers and Solutions 261

Chapter 8. Differential Equations Continued 263

8.1 Singular points 263

8.2 Systems of differential equations 265

8.3 Determinants and the solution of linear systems with constant coefficients 270

8.4 Lyapunov stability of the equilibrium state 274

8.5 Constructing approximate formulas for a solution 277

8.6 Adiabatic variation of a solution 285

8.7 Numerical solution of differential equations 288

8.8 Boundary-value problems 297

8.9 Boundary layer 303

8.10 Similarity of phenomena 305

Answers and Solutions 309

Chapter 9. Vectors 312

9.1 Linear operations on vectors 313

9.2 The scalar product of vectors 319

9.3 The derivative of a vector 321

9.4 The motion of a material point 324

9.5 Basic facts about tensors 328

9.6 Multidimensional vector space 333

Answers and Solutions 336

Chapter 10. Field Theory 340

10.1 Introduction 340

10.2 Scalar field and gradient 341

10.3 Potential energy and force 345

10.4 Velocity field and flux 351

10.5 Electrostatic field, its potential and flux 356

10.6 Examples 359

10.7 General vector field and its divergence 369

10.8 The divergence of a velocity field and the continuity equation 374

10.9 The divergence of an electric field and the Poisson equation 376

10.10 An area vector and pressure 379

Answers and Solutions 384

Chapter 11. Vector Product and Rotation 388

11.1 The vector product of two vectors 388

11.2 Some applications to mechanics 392

11.3 Motion in a central-force field 396

11.4 Rotation of a rigid body 406

11.5 Symmetric and antisymmetric tensors 408

11.6 True vectors and pseudovectors 415

11.7 The curl of a vector field 416

11.8 The Hamiltonian operator del 423

11.9 Potential fields 426

11.10 The curl of a velocity field 430

11.11 Magnetic field and electric current 433

11.12 Electromagnetic field and Maxwell’s equations 438

11.13 Potential in a multiply connected region 442

Answers and Solutions 445

Chapter 12. Calculus of Variations 450

12.1 An instance of passing from a finite number of degrees of freedom to an infinite number 450

12.2 Functional 456

12.3 Necessary condition of an extremum 460

12.4 Euler’s equation 462

12.5 Does a solution always exist? 468

12.6 Variants of the basic problem 474

12.7 Conditional extremum for a finite number of degrees of freedom 476

12.8 Conditional extremum in the calculus of variations 479

12.9 Extremum problems with restrictions 488

12.10 Variational principles. Fermat’s principle in optics 491

12.11 Principle of least action 499

12.12 Direct methods 503

Answers and Solutions 508

Chapter 13. Theory of Probability 514

13.1 Statement of the problem 514

13.2 Multiplication of probabilities 517

13.3 Analysing the results of many trials 522

13.4 Entropy 533

13.5 Radioactive decay. Poisson’s formula 539

13.6 An alternative derivation of the Poisson distribution 542

13.7 Continuously distributed quantities 544

13.8 The case of a very large number of trials 549

13.9 Correlational dependence 556

13.10 On the distribution of primes 561

Answers and Solutions 567

Chapter 14. Fourier Transformation 573

14.1 Introduction 573

14.2 Formulas of the Fourier transformation 577

14.3 Causality and dispersion relations 585

14.4 Properties of the Fourier transformation 589

14.5 Bell-shaped transformation and the uncertainty principle 597

14.6 Harmonic analysis of a periodic function 602

14.7 Hilbert space 606

14.8 Modulus and phase of spectral density 612

Answer and Solutions 615

Chapter 15. Digital Computers 619

15.1 Analogue computers 619

15.2 Digital computers 621

15.3 Representation of numbers and instructions in digital computers 623

15.4 Programming 628

15.5 Use computers1 634

Answers and Solutions 642

REFERENCES 645

INDEX 696