## Reprinting some classics

Edit: Thanks for all the positive responses. Due to the lockdown of the second wave, the printing plans have got delayed a bit, but we should have some updates this month.

Posted in books, meta | 36 Comments

## Theory of Elasticity – Amenzade

In this post, we will see the book Theory Of Elasticity by Yu. A. Amenzade.

The theory of elasticity is concerned with the mechanics of deformable media which, after the removal of the forces producing deformation, completely recover their original shape and give up all the work expended in the deformation.

The first attempts to develop the theory of elasticity on the basis of the concept of a continuous medium, which enables one to ignore its molecular structure and describe macroscopic phenomena by the methods of mathematical analysis, date back to the first half of the eighteenth century.
The fundamental contribution to the classical theory was made by R. Hooke, C. L. M. H. Navier, A. L. Cauchy, G. Lame, G. Green, B. P. E. Clapeyron. In 1678 Hooke established a law linearly con- necting stresses and strains.
After Navier established the basic equations in 1821 and Cauchy developed the theory of stress and strain, of great importance in the development of elasticity theory were the investigations of B. de Saint Venant. In his classical work on the theory of torsion and bending Saint Venant gave the solution of the problems of torsion and bending of prismatic bars on the basis of the general equations of the theory of elasticity. In these investigations Saint Venant devised a semi-inverse method for the solution of elasticity problems, formulated the famous Saint Venant’s principle, which enables one to obtain the solution of elasticity problems. Since then much effort has been made to develop the theory of elasticity and its applications, a number of general theorems have been proved, the general methods for the integration of differential equations of equilibrium and motion have been proposed, many special problems of fundamental interest have been solved. The development of new fields of engineering demands deeper and more extensive studies of the theory of elasticity. High velocities call for the formulation and solution of complex vibrational problems. Lightweight metallic structures draw particular attention to the question of elastic stability. The concentration of stress entails dangerous consequences, which cannot safely be ignored.

The book was translated from Russian by M. Konyaeva and was published in 1979 by Mir.

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## Contents

Notation 9
Introduction 13

Chapter I. ELEMENTS OF TENSOR CALCULUS 15

1. Scalars, Vectors, and Tensors 16
2. Addition, Multiplication, and Contraction of Tensors. The Quotient Law of Tensors 19
3. The Metric Tensor 22
4. Differentiation of Base Vectors. The Christoffel Symbols 28
5. A Parallel Field of Vectors 30
6. The Riemann-Christoffel Tensor. Derivative of a Veetor. The Gauss-Ostrogradsky Formula. The 𝜀-tensor 32

Chapter II. THEORY OF STRESS 39

7. Types of External Forces 39
8. The Method of Sections. The Stress Vector 41
9. The Stress Tensor 43
10. Equations of Motion and Equilibrium in Terms of the Components of the Stress Tensor 44
11. Surface Conditions 47
12. Equations of Motion and Equilibrium Referred to a Cartesian Co-ordinate System 48
13. Equations of Motion and Equilibrium Referred to Cylindrical and Spherical Co-ordinates 49
14. Determination of the Principal Normal Stresses 52

Chapter III. THEORY OF STRAIN 55

15. The Finite Strain Tensor 55
16. The Small Strain Tensor 59
17. Strai Compatibility Equations 60
18. The Strain Tensor Referred to a Cartesian Co-ordinate System 61
19. Components of the Small Strain and Rotation Tensors Referred to Cylindrical and Spherical Co-ordinates 62
20. Principal Extensions 64
21. Strain Compatibility Equations in Some Co-ordinate Systems (Saint Venant’s Conditions) 65
22. Determination of Displacements from the Components of the Small Strain Tensor 66

Chapter IV. STRESS-STRAIN RELATIONS 69

23. Generalized Hooke’s Law 69
24. Work Done by External Forces 70
25. Stress Tensor Potential 71
26. Potential in the Case of a Linearly Elastic Body 75
27. Various Cases of Elastic Symmetry of a Body 75
28. Thermal Stresses 80
29. A Energy Integral for the Equations of Motion of an Elastic Body 80
30. Betti’s Identity 82
31. Clapeyron’s Theorem 82

Chapter V. COMPLETE SYSTEM OF FUNDAMENTAL EQUATIONS IN THE THEORY OF ELASTICITY 84

32. Equations of Elastic Equilibrium and Motion in Terms of Displacements 84
33. Equations in Terms of Stress Components 90
34. Fundamental Boundary Value Problems in Elastostatics. Uniqueness of Solution 93
35. Fundamental Problems in Elastodynamics 95
36. Saint Venant’s Principle (Principle of Softening of Boundary Conditions) 96
37. Direct and Inverse Solutions of Elasticity Problems. Saint Venant’s Semi-inverse Method 98
38. Simple Problems of the Theory of Elasticity 99

Chapter VI. THE PLANE PROBLEM IN THE THEORY OF ELASTICITY 108

39. Plane Strain 108
40. Plane Stress 111
41. Generalized Plane Stress 113
42. Airy’s Stress Function 115
43. Airy’s Function in Polar Co-ordinates. Lamé’s Problem 120
44. Complex Representation of a Biharmonic Function, of the Components of the Displacement Vector and the Stress Tensor 127
45. Degree of Determinancy of the Introduced Functions and Restrictions Imposed on Them 132
46. Fundamental Boundary Value Problems and Their Reduction to Problems of Complex Function Theory 138
47. Maurice Lévy’s Theorem 141
48. Conformal Mapping Method 142
49. Cauchy-type Integral 145
50. Harnack’s Theorem 151
51. Riemann Boundary Value Problem 151
52. Reduction of the Fundamental Boundary Value Problems to Functional Equations 154
53. Equilibrium of a Hollow Circular Cylinder 155
54. Infinite Plate with an Elliptic Hole 159
55. Solution of Boundary Value Problems for a Half-plane 164
56. Some Information on Fourier Integral Transformation 170
57. Infinite Plane Deformed Under Body Forces 174
58. Solution of the Biharmonic Equation for a Weightless Half-plane 177

Chapter VII. TORSION AND BENDING OF PRISMATIC BODIES 182

59. Torsion of a Prismatic Body of Arbitrary Simply Connected Cross Section 182
60. Some Properties of Shearing Stresses 187
61. Torsion at Hollow Prismatic Bodies 188
62. Shear Circulation Theorem 190
63. Analogies in Torsion 191
64. Complex Torsion Function 196
65. Solution of Special Torsion Problems 198
66. Bending of a Prismatic Body Fixed at One End 206
67. The Centre of Flexure 211
68. Bending of a Prismatic Body of Elliptical Cross Section 216

Chapter VIII. GENERAL THEOREMS OF THE THEORY OF ELASTICITY. VARIATIONAL METHODS 219

69. Betti’s Reciprocal Theorem 219
70. Principle of Minimum Potential Energy 220
71. Principle of Minimum Complementary Work—Castigliano’s Principle 222
72. Rayleigh-Ritz Method 224
73. Reissner’s Variational Principle 228
74. Equilibrium Equations and Boundary Conditions for a Geometrically Non-linear Body 230

Chapter IX. THREE-DIMENSIONAL STATIC PROBLEMS 232

75. Kelvin’s and the Boussinesq-Papkovich Solutions 232
76. Doursinesa’s Elementary Solutions of the First and Second Kind 236
77. Pressure on the Surface of a Semi-infinite Body 238
78. Hertz’s Problem of the Pressure Between Two Bodies in Contact 240
79. Symmetrical Deformation of a Bedy of Revolution 246
80. Thermal Stresses 256

Chapter X. THEORY OF PROPAGATION OF ELASTIC WAVES 258

81. Two Types of Waves 258
82. Rayleigh Surface Waves 262
83. Love Waves 265

Chapter XI. THEORY OF THIN PLATES 268

84. Differential Equation for Bending of Thin Plates 268
85. Boundary Conditions 271
86. Bending Equation for a Plate Referred to Polar Co-ordinates 274
87. Symmetrical Bending of a Circular Plate 276
Literature 278
Subject Index 279

## Fundamentals of Radio – Izyumov, Linde

In this post, we will see the book Fundamentals Of Radio by N. Izyumov and D, Linde.

These days radio engineering has become a very important branch of science solving a large number of problems associated with economic, technological and cultural progress. Every year, it finds ever increasing application and the number of people using radio equipment constantly grows. Many of these people have only rudimentary or no knowledge of radio engineering, although modern radio equipment is often so complicated that its effective use is impossible without some training.

The wide sphere of radio application in different branches of science and technology, as well as its close connexion with art and sport has also created a great number of radio amateurs in all countries. Some build radio receivers, tape recorders and TV sets, others design radio controlled models, short and ultra shortwave transmitters or equipment for a fascinating game called “hunting for a fox”, etc.

The book was translated from Russian by A. Ulyanov and was published by Mir in 1976.

You can get the book here.

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## Contents

Foreword 9

Chapter I. PRINCIPLES OF RADIO COMMUNICATION 11

1-1. Basic Properties of Electromagnetic Waves 11
1-2. General Principles of Radio Communication 15
1-3. Electromagnetic Waves Used in Radio Communication 28
1-4. A Brief History of Radio in the USSR 20
1-5. Components Used in Radio Engineering 23

Chapter II. AC CIRCUITS 26

2-1. Sinusoidal Quantities and Their Vector Representation 26
2-2. Basic Components of Radio Circuits and Alternating Currents in Them 28
2-3. AC Power 43
2-4. Steady-State and Transient Processes in Electric Circuits Including Capacitors or Coils 48
2-5. Nonsinusoidal Currents and Their Spectra 55
2-6. Free Oscillations in a Circuit 63
2-7. Forced Oscillations in a Series-Connected Circuit 66
2-8. Forced Oscillations in a Parallel-Connected Circuit 72
2-9. Transient Processes in Oscillatory Circuits 81
2-10. Parallel Circuits with Reactive Elements of Both Types in One of Their Branches 86

Chapter III. COUPLED CIRCUITS 92

3-1. Oscillations in Two Coupled Circuits 92
3-2. Tuning a System of Two Coupled Circuits 104

Chapter IV. ELECTRICAL FILTERS 106

4-1. Purpose of Filters 106
4-2. Filters for DC Supplies 106
4-3. Low-Pass Filters 109
4-4 High-Pass Filters 114
4-5. Bandpass and Band-Elimination Filters 117

Chapter V. TRANSMISSION LINES 120

5-1. Electrical Signals in Ideal Infinitely Long Lines 120
5-2. Signals in Finite Length Lines with Far End Open-Circuited 128
5-3. Signals in Finite Length Lines with Far End Short-Circuited 134
5-4. Signals in Lines with a Reactive Load 136
5-5. Signals in Lines with a Resistive Load 138
5-6. Signals in Lines with a Combined Load 143
5-7. Actual Lines with Losses 145
5-8. Transmission Lines as Reactive Elements and Impedance Transformers 161

Chapter VI. ANTENNAS 169

6-2. Double-Dipole Antennas 172
6-3. Effect of the Ground on Antenna Radiation. Asymmetrical Dipoles 187
6-4. Antenna Resonant Frequencies. Harmonic Antennas 192
6-5. Inphased and Antiphased Antennas. Reflectors and Directors 195
6-6. Ground Effect on Antenna Radiation Patterns 203
6-7. Complex Dipoles 209
6-8. Loop Antennas 212
6-9. Long- and Medium-Wave Antennas 214
6-10.Short-Wave Antennas 217
6-11.Ultrashort-Wave Antennas 225

Chapter VII. RADIO WAVE PROPAGATION 233

7-1. Properties of Atmosphere and Ground Affecting Radio Wave Propagation 233
7-2. Radio Waves Propagating in Atmosphere. General Regularities 245
7-3. Long-Wave Propagation 252
7-4. Medium-Wave Propagation 253
7-5. Short-Wave Propagation 256
7-6. Ultrashort-Wave Propagation 265
7-7. Electromagnetic Waves in Outer Space 272

Chapter VIII. VACUUM AND SEMICONDUCTOR DEVICES 277

8-1. Modern Electronics 277
8-2. Motion of Electrons in Vacuum. Cathodes of Electron Valves 279
8-3. Diodes 290
8-4. Triodes 302
8-5. Multigrid Electron Valves 324
8-6. Electric Conduction in Semiconductors 337
8-7. P-N Junction and Crystal Diodes 343
8-8. Transistors 351
8-9. Miniaturization of Electronic Devices 363
8-10.Cathode-Ray Tubes 365

Chapter IX. PRIMARY-SIGNAL AMPLIFIERS 372

9-1. Purpose and Classification 372
9-2. Audio-Frequency Amplifiers. General 378
9-3. Audio-Frequency Small-Signal Amplifiers 393
9-4. Audio-Frequency Output Amplifiers 403
9-5, Driver Stages. Feedback in Amplifiers 415
9-6. Video Amplifiers 421

Chapter X. WAVE GENERATION 428

10-1. Operating Principles of Valve Oscillators 428
10-2. Separately Excited Oscillators (Amplifiers) 435
10-3. Self-Excited Oscillators 449
10-4. Ultrahigh-Frequency Valve Oscillators 473
10-5. Klystron Amplifiers and Oscillators. 481
10-6. Travelling-Wave Oscillators 488
10-7. Backward-Wave Oscillators 492
10-8. M-type Travelling-Wave Oscillators 496
10-9. Transistor Oscillators and Amplifiers 507
10-10. Negative-Resistance Oscillators 510
10-11. Sinewave RC Oscillators 511
10-12. Frequency Pulling in Self-Oscillators 513
10-13. Self-Oscillator Lock-in 517
10-14. Nonsinewave Oscillators 528

Chapter XI. CONVERSION OF ELECTRIC SIGNALS 532

11-1. Concept of Signal Conversion 532
11-2. Amplitude Modulation 533
11-3. Frequency and Phase Modulation 545
11-4. Pulse Modulation 555
11-5. Detection of Radio Signals 561
11-6. Frequency Converters 565
11-7. Conversion of Electric Pulses 571

12-1. Purpose and Basic Characteristics 579
12-3. High-Frequency Amplifiers 595
12-4. Intermediate-Frequency Amplifiers 607
12-6. Frequency Converters 618
12-9. Examples of Receiver Circuitry 653

Reference Data 659
Index 664

## The Remarkable Sine Functions – Markushevich

In this post, we will see the book The Remarkable Sine Functions by A. I. Markushevich.

In the present book, we shall show how it is possible, by beginning with other curves (such as the equilateral hyperbola or Bernoulli’s lemniscate (a curve having the form of a figure- eight), to define interesting and important functions analogous to the trigonometric functions, similar to them in some respects but possessing certain new characteristics. These functions are called respectively hyperbolic and lemniscate functions. In analogy with them, we shall refer to the trigonometric functions as circular functions.

The reader is assumed to have a familiarity with the ele­ ments of analytic geometry and differential and integral calculus. The necessary material on integration in the complex plane will be given in the present book though proofs will be omitted.

The ultimate purpose of the book is to acquaint the reader not possessing an extensive knowledge of the theory of functions of a complex variable with the simplest representatives of the class of elliptic functions, namely, lemniscate functions and the somewhat more general Jacobian elliptic functions.

In conclusion, we warn the reader that this book is not in­ tended for light reading. He must read it with his pencil in his hand.

The book was translated from Russian by Scripta Technica and was published in 1966.

You can get the book here.

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## Contents

Preface

1. Geometric Definition of Circular, Hyperbolic And Lemniscate Functions 1

2. Generalized Sines 13

3. Integration in the Complex Plane 25

4. Euler’s Method of Deriving the Addition Theorems 41

5. Further Study of Complex Values of the Argument 49

6. Zeros and Poles. Simple and Double Periodicity. The Concept of an Elliptic Function 73

Index 99

## Fibonacci Numbers – Vorob’ev

In this post, we will see the book Fibonacci Numbers by N. N. Vorob’ev. This book is a part of the Popular Lectures In Mathematics series.

In elementary mathematics there are many difficult and interesting problems not connected with the name of an individual, but rather possessing the character of a kind of “mathematical folklore”. Such problems are scattered throughout the wide literature of popular (or, simply, entertaining!) mathematics, and often it is very dif­ ficult to establish the source of a particular problem.

These problems often circulate in several versions. Sometimes several such problems combine into a single, more complex, one, sometimes the opposite happens and one problem splits up into several simple ones: thus it is often difficult to distinguish between the end of one
problem and the beginning of another. We should consider that in each of these problems we are dealing with little mathematical theories, each with its own history, its own complex of problems and its own characteristic methods, all, however, closely connected with the history and methods of “great mathematics”.

The theory of Fibonacci numbers is just such a theory. Derived from the famous “rabbit problem”, going back nearly 750 years, Fibonacci numbers, even now, provide one of the most fascinating chapters of elementary mathe­ matics. Problems connected with Fibonacci numbers occur in many popular books on mathematics, are discussed at meetings of school mathematical societies, and feature in mathematical competitions.

The present booklet contains a set of problems which were the themes of several meetings of the school chil­dren’s mathematical club of Leningrad State University in the academic year 1949-50. In accordance with the wishes of those taking part, the questions discussed at these meetings were mostly number-theoretical, a theme which is developed in greater detail here.
This book is designed to appeal basically to pupils of 16 or 17 years of age in a high school. The concept o a limit is met with only in examples 7 and 8 in chapter III. The reader who is not acquainted with this concept can omit these without prejudice to his understanding of what follows. That applies also to binomial coefficients (I, example 8) and to trigonometry (IV, examples 2 & 3). The elements which are presented of the theory of divisibility and of the theory of continued fractions do not presuppose any knowledge beyond the limits of a school course.

Those readers who develop an interest in the principle of constructing recurrent series are recommended to read the small but full booklet of A.I. Markushevich, “Re­current Sequences” (Vozvratnyye posledovatel’ nosti) (Gostekhizdat, 1950). Those who become interested in facts relating to the theory of numbers are referred to textbooks in this subject*.

The book was translated from Russian by Halina Moss (edited by Ian Sneddon) and was published in 1961.

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## Contents

Foreword vii

Introduction 1

І. The simplest properties оf Fibonacci numbers 6
II. Number-theoretic properties of Fibonacci numbers 25
III. Fibonacci numbers and continued fractions 36
IV. Fibonacci numbers and geometry 55
V. Conclusion 65

## Convex Figures and Polyhedra – Lyusternik

In this post, we will see the book Convex Figures And Polyhedra by L. A. Lyusternik. This book is a part of Topics in Mathematics series.

The theory of convex figures and polyhedra provides an excellent example of a body of mathematical knowledge that offers theorems with elementary formulations and vivid geometric meaning. Despite this simplicity of formulation, the proofs are often not elementary. Thus the area presents a particular challenge to mathematicians, who have investigated convex figures and polyhedra for millenia, and yet have by far not exhausted the subject. Many of the theorems in this volume were in fact proved only a few years ago.

The material in this book will be suitable for study in mathe­matics clubs or by readers with a background of secondary school mathematics only. The topics considered are stimulating and chal­ lenging, and moreover, convexity ideas are valuable in the study of modem higher mathematics. Mathematical analysis, higher geome­ try, and topology each use convexity notions in an essential way.

The book was translated from Russian by Donald L. Barnett and was published in 1966.

You can get the book here.

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## Contents

CHAPTER l. Convex Figures 1

1. Plane convex figures 1
2. Intersections and partitions of plane convex figures 5
3. Supporting lines for two-dimensional convex figures 8
4. Directed convex curves and directed supporting lines 10
5. Vectors; external normals to plane convex figures 13
6. Circuit of a polygon; length of a convex curve 14
7. Convex solids 17
8. Supporting planes and external normals for convex solids 20
9. Central projection; cones 23
10. Convex spherical figures 26
11. Greatest and least widths of convex figures 28
12. Ovals of constant width; Barbier’s Theorem 34

CHAPTER 2. Central-symmetric Convex Figures 39

13. Central symmetry and (parallel) translation 39
14. Partitioning central-symmetric polyhedra 42
15. The greatest central-symmetric convex figure in a lattice of integers; Minkowski’s Theorem 44
16. Filling the plane and space with convex figures 51

CHAPTER 3. Networks and Convex Polyhedra 58

17. Vertices (nodes), faces (regions), and edges (lines); Euler’s Theorem 58
18. Proof of the theorem for connected networks 61
19. Disconnected networks; inequalities 64
20. Congruent and symmetric polyhedra; Cauchy’s Theorem 66
21. Proof of Cauchy’s Theorem 71
22. Steinitz’ correction of Cauchy’s proof 73
23. Abstract and convex polyhedra; Steinitz Theorem 81
24. Development of a convex polyhedron; Aleksandrov’s Theorem 95

CHAPTER 4. Linear Systems of Convex Figures 97

25. Linear operations on points

26. Linear operations on figures; “mixing” figures

27. Linear systems of convex polygons; areas and “mixed areas”
28. Applications
29. Schwarz inequality; other inequalities
30. Relation between areas of Q, Q_{1}, and Q_{S},; the Brunn-Minkowski inequality
31. Relation between areas of plane sections of convex solids
32. Greatest area theorems

CHAPTER 5. Theorems of Minkowski and Aleksandrov for Congruent Convex Polyhedra 132

33. Formulation of the theorems 132
34. A theorem about convex polygons 134
35. Mean polygons and polyhedra 141
36. Proof of Aleksandrov’s Theorem 146

CHAPTER 6. Supplement 150

37. Precise definition of a convex figure 150
38. Continuous mapping and functions 152
39. Regular networks; regular and semiregular polyhedra 153
40. The isoperimetric problem 164
41. Chords of arbitrary continua; Levi’s Theorem 166
42. Figures in a lattice of integers; Blichfeldt’s Theorem 172
43. Topological theorems of Lebesgue and Bol’-Brouwer 175
44. Generalization to n dimensions 182
45. Convex figures in normed spaces 185

Bibliography 191

## Heat And Mass Transfer Vol. 1 – Lykov, Smol’skii ( Eds.)

In this post, we will see the book Heat And Mass Transfer Vol. 1 – A. V. Lykov, B. M. Smol’skii ( Eds.).

Volume 1 Convective Heat Exchange in a Homogeneous Medium edited by: B.S. Petukhov, I.P. Ginzburg, and А. S. Kasperovich

This book comprises reports and communications dealing with the problems of convective heat transfer in a homogeneous medium, and with the heat and mass transfer during the interaction of bodies with liquid and gas streams. Most papers deal with studies based on the boundary layer theory. The papers include theoretical and experimental works on unsteady-state heat transfer, on heat transfer at variable physical properties of liquids and gases, and heat transfer during supersonic flows in dense and rarefied media.

The book was translated from Russian by A. Aladjem and was edited by R. Kondor published in 1967 by Israel Program for Scientific Translations.

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Contents

B.S. PETUKHOV. Convective Heat Transfer in a Homogeneous Medium 1

I. HEAT EXCHANGE AND FRICTION RESISTANCE DURING SUBSTANTIAL CHANGES IN THE PHYSICAL PROPERTIES OF LIQUIDS AND GASES AS A FUNCTION OF TEMPERATURE AND PRESSURE 7

A. A. Gukhman, A. F. Gandel’Sman, Y. Y. Usanov, AND G. N. Shorin.

New Data on the Properties of Trans-sonic Flows 7

V. L. Lel’chuk, G. I. Elfimov, AND Yu. P. Fedotov.

Experimental Study of the Heat Transfer from Pipe Walls to Mono-, Di-, and Triatomic Gases at Large Temperature Gradients 11

L. S. Sterman AND V. V. Petukhov.

Investigation of the Heat Transfer to Organic Liquids 19

E. A. Krasnoshchekov, V. S. Protopopov, Wang Feng, AND I. V. Kuraeva.

Experimental Study of the Heat Transfer in The Supercritical Region of Carbon Dioxide 25

E. N. Dubrovina AND V. P. Skripov.

Convective Heat Transfer In The Supercritical Region of Carbon Dioxide 32

V. N. Popov.

Theoretical Calculation of the Heat Transfer And Friction Resistance for Carbon Dioxide in The Supercritical Region 41

I. Т. Alad’ev, P. I. Povarnin, L. I. Malkina, AND E. Yu. Merkel’.

Investigation of the Cooling Properties of Ethanol At Pressures up to 800.9.8-10^4 N/m^2 49

D. M. Kalachev, I. S. Kudryavtsev, B. L. Paskar’, AND I. I. Yakubovich.

Application of the Method of High-frequency Heating To Liquid- Metal Heat Transfer Media 53

II. HEAT EXCHANGE AND FRICTION RESISTANCE IN PIPES AND CHANNELS OF VARIOUS GEOMETRICAL SHAPES 56

B. S. PETUKHOV AND L.I. Roizen.

Heat Exchange During gas Flow In Pipes With an Annular Cross Section 56

P. I. Puchkov AND O. S. Vinogradov.

Heat Transfer and Hydraulic Resistance in Annular Channels With Smooth and Rough Heat Transfer Surfaces 65

L. M. Zysina-Molozhen AND I. B. Uskov.

Experimental Investigation Of the Heat Transfer on the end Wall of a Blade Channel [In Turbines] 79

Yu. P. Finat’ev.

Calculation of the Hydraulic Resistance Of Annular Channels 88

B. P. Ustimenko, K. A. Zhurgembaev, AND D. A. Nusupbekova.

Calculation of the Convective Heat Transfer for An Incompressible Liquid in Channels With Complicated Shapes 99

I.S. Kochenov, L.I. Baranova, AND V. V. Vasil’ev.

Flow in Channels With Permeable Walls 113

М. E. Podol’Skii.

Attractive Action of a Non-isothermal Lubricating Layer 117

V. N. Zmeikov АND B. P. Ustimenko.

Hydrodynamics and Heat Transfer in a Convoluted Stream Between two Coaxial Cylinders 127

P.N. Romanenko AND A. N. Oblivin.

Experimental Study of The Friction and Heat Transfer During gas Flow in a Diffuser
Channel With Cooled Walls, During Combustion 140

III. INVESTIGATION OF THE HEAT TRANSFER AND [HYDRODYNAMIC] RESISTANCE IN THE ENTRY SECTIONS OF TUBES AND CHANNELS 148

B.S. Petukhov AND Chang-Chéng Yung.

Heat Transfer in The Hydrodynamic Entry Section of a Round Tube During Laminar Liquid Flow 148

A.A. Zhukauskas AND I.I. Zhyugzhda.

Experimental Study of The Heat Transfer and Hydraulic Resistance in the Entry Section of a Flat Channel During Laminar Flow of A
Viscous Liquid 158

E. E. Solodkin AND A. S. Ginevskii.

Turbulent Non-isothermal Flow Of a Viscous Compressible gas in the Entry Sections Of Axisymmetrical and Flat Widening Channels With Zero Pressure Gradient 163

P. N. Romanenko AND N. V. Krylova.

Effect of the Entry Conditions on the Heat Transfer in the Entry Section Of a Tube With Turbulent air Flow 175

IV. STUDIES OF THE INTENSIFICATION OF CONVECTIVE HEAT TRANSFER PROCESSES 184

A. V. Ivanova.

Intensification of the Heat Transfer in An Air-cooled Round Tube 184

E. K. Karasev.

Investigation of the Hydrodynamics And Heat Transfer in a Channel With Turbulizers on The
Heat Transfer Surface 190

A. S. Nevskii, A. V. Arseev, L. A. Chukanova, A. I. Malysehva, AND
T. V. Sharova.

Convective Heat Transfer in Cylindrical Chambers With Recirculation 198

К. Rybáček.

Certain Characteristics of Heat Transfer And Friction in the Case of Longitudinal Flow Around [Fuel] Element 206

V. F. Yudin AND L. S. Tokhtarova,

Investigation of the Heat Transfer and Resistance of Finned, Staggered Banks With Fins of Different Shapes: 215

I. Vampola.

Generalization of the Laws Governing Heat Transfer and Pressure Drop During Transverse Flow Of Gases in Finned Tube Banks 224

A. I. Mitskevich

Efficiency of Heat Transfer Surfaces 232

V. CONVECTIVE HEAT TRANSFER UNDER UNSTEADY-STATE CONDITIONS 239

Yu. L. Rozenshtok.

The Unsteady Laminar Thermal Boundary Layer on a Semi-infinite Plate in a Viscous Liquid Flow 239

Е.K. Kalinin.

Determination of the Stream Temperature and Friction Coefficient in Channels During Unsteady Nonisothermal Flow of a Heat-transfer Medium 249

L. I. Kudryashev and A. A. Smirnov

Accounting for the Effect of Thermal Unsteady State on the Coefficient of Convective Heat Transfer During Flow Round Spherical Bodies at Small Reynolds Numbers 258

I. S. Kochenov AND Yu. N. Kuznetsov.

Explanatory List of Abbreviations 274

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## Low Temperature Properties Of Polymers – Perepechko

In this post, we will see the book Low Temperature Properties Of Polymers by I. Perepechko.

The purpose of this book is to systematize the available material and to delineate the principal trends in the investigation of those closely interrelated properties—thermal (heat capacity, thermal conductivity, thermal expansion), acoustical, dielectric, visco- elastic, etc.—which govern the entire set of important physical properties of polymers at low temperatures. An attempt is made to show how the chemical constitution and the supermolecular
structure influence the physical properties of polymers in the low- temperature region·

All the chapters of this book, except the last two, are organized according to the same plan. Each chapter, devoted to a single physical property, consists'”of three sections. First, the theory of the property under discussion and the related physical phenomena are briefly considered. This is followed by a description of methods of investigation of these properties and phenomena at low temperatures. Finally, systematized data from experimental investigations are presented.

The last three chapters are concerned mainly with studies of the properties of polymers at low temperatures which have been carried out in recent years by the author and his collaborators P .D. Golub and V .E. Sorokin.

The book was translated from Russian by A. Beknazarov and was published in .

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Contents

Chapter 1 Heat Capacity of Polymers at low Temperatures 1

1.1. Basic Concepts of the Heat Capacity of Solids 1
1.2. Basic Concepts of the Heat Capacity of Polymers 8
1.3. Methods of Measuring Heat Capacity 17
1.4. The Heat Capacity of Polymers 20

Chapter 2 Thermal Conductivity of Polymers at low Temperatures 45

2.1. Basic Concepts of the Thermal Conductivity of Dielectrics 45
2.2. Methods of Measuring the Thermal Conductivity of Polymers 56
2.3. Thermal Conductivity of Polymers at low Temperatures 57

Chapter 3 Thermal Expansion of Polymers at low Temperatures 82

3.1. Thermal Expansion of Solids 82
3.2. Equations of State for Solids 83
3.3. Basic Concepts of the Thermal Expansion of Polymers 86
3.4. Methods of Measuring Thermal Expansion Coefficients of Polymers 95
3.5. Thermal Expansion Coefficients of Polymers 97

Chapter 4 Electrical Properties of Polymers at low Temperatures 110

4.1. Basic Concepts of the Electrical Properties of Polymers 110
4.2 Page 112 is Missing
4.3. Phenomenological Relaxation Theory of the Dielectric Properties of Polymers 113
4.4. The Mechanism of Dielectric Relaxation 120
4.5. Methods of Studying the Dielectric Properties of Polymers 124
4.6. Dielectric Properties of Polymers 126

Chapter 5 Nuclear Magnetic Resonance in Polymers at low Temperatures 147

5.1. Basic Concepts of Nuclear Magnetic Resonance in Polymers 147
5.2. Effect of the Structure and Composition of Polymers on Nuclear Magnetic Resonance 154
Page 155 Missing
5.3. Investigation of the Molecular Motion in Polymers at low Temperatures by the nmr Method 164

Chapter 6 Dynamic Mechanical Properties of Polymers at low Temperatures 178

6.1. Effect of Chemical Constitution, Structure and Composition on the Dynamic Mechanical Properties of Polymers. Basic Concepts of Acoustic Spectroscopy of Polymers 178
6.2. Methods of Investigating the Dynamic Mechanical Properties of Polymers 183
6.3. Relaxation Processes in Polymers at low Temperatures 184

Chapter 7 the Acoustical Properties of Polymers at low Temperatures 206

7.1. Propagation of Ultrasonic Waves in Dielectrics 206
7.2. The Phenomenological Theory of Sound Propagation in Polymers 208
7.3. Experimental Methods of Acoustical Measurements in Polymers 211
7.4. Ultrasonic Velocity and Relaxation Processes in Polymers 216
7.5. Ultrasonic Velocity and Relaxation Processes in Linear Crystalline Polymers at Helium Temperatures. the Low-temperature Plateau 218
7.6. Ultrasonic Velocity and Relaxation Processes in Polymers Containing Methyl Groups 228
7.7. Ultrasonic Velocity and Relaxation Processes in Polymers With an Asymmetric Potential Barrier 232
7.8. Effect of Structure on Acoustical Properties 236

Chapter 8 Viscoelastic Parameters of Polymers at low Temperatures 241

8.1. Determination of the Main Viscoelastic Parameters of Polymers from Acoustic Measurements 241
8.2. Dynamic Elastic Moduli of Polymers 243
8.3. Poisson’s Ratio for Polymers Near the Liquid-helium Temperature 249

Chapter 9 Determining the Thermophysical Characteristics of Polymers by Acoustic Measurements at Helium Temperatures

9.1. Debye Temperatures and Heat Capacities Determined by Acoustic Measurements 255
9.2. Determining the Thermal Expansion Coefficients and Grüneisen Constants from Acoustic Measurements 261

Appendix 268

References 275

Name Index 285

Subject Index 297

## Computational Mathematics – Demidov, Maron

In this post, we will see the bookComputational Mathematics by B. P. Demidovich and I. A. Maron.

The basic aim of this book is to give as far as possible a systematic and modern presentation of the most important methods and techniques of computational mathematics on the basis of the general course of higher mathematics taught in higher technical schools. The. book has been arranged so. that the basic portion constitutes a manual for the first .cycle of ·studies in approximate computations for higher technical colleges. The text contains supplementary ma- tetial Which goes beyond the scope of the ordinary college course, but the reader can select those sections which interest him and omit any extra material without loss of continuity. The chapters and sections which may be dropped out in a first reading are marked with an asterisk.

This text makes wide use of matrix calcu]us. The concepts of a vector, matrix, inverse matrix, eigenvalue and eigenvector of a matrix, etc. are workaday tools. The use of matrices offers a number of advantages in presenting the subject matter since they greatly facilitate an understanding of the development of many computations. In this sense a particular gain is achieved in the proofs of the convergence theorems of various numerical processes. Also, modern high-speed computers are nicely adapted to the performance of the basic matrix operations.
For a full comprehension of the contents of this. book, the reader should have a background of linear algebra and the theory of linear vector spaces. With the aim of making the text as self-contained as possible, the authors have included all the necessary starting material in these subjects. The appropriate chapter~ are completely independent of the basic text and can be omitted by readers who have already studied these sections.

A few words about the contents of the book. In the main it is devoted to the following problems: operations involving approximate numbers, computation of functions by means of series and iterative processes, approximate and numerical solution of algebraic ·and transcendental equations, computational methods of linear algebra, interpolation of functions, numerical differentiation and integration of functions, and the Monte Carlo method.

A great deal of attention is devoted to methods of error estimation. Nearly all processes are provided with proofs of convergence theorems, and the presentation is such that the proofs may be omitted if one wishes to confine himself to the technical aspects of the matter. In. certain case?, in order to pictorialize and lighten the presentation, the computational techniques are given as simple recipes.

The basic methods are carried to numerical applications that include computational schemes and numerical examples with de- tailed step.s of solution. To facilitate understanding the essence of the matter at hand, most of the problems are stated in simple form and are of an illustrative nature. References are given at the. end of each chapter and the complete list (in alphabetical order) is given at the end of the book.

The present text offers selected methods in computational mathematics and does not include material that involves empirical formulas, quadratic approximation of functions, approximate solutions of differential equations, etc. Likewise, the book does not include material on programming and the technical aspects of solving mathematical problems on computers. The interested reader must consult the special literature on these subjects.

The book was translated from Russian by George Yankovsky and was published by Mir in 1981.

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Contents

PREFACE 5

INTRODUCTION. GENERAL RULES OF COMPUTATIONAL WORK 15

CHAPTER 1 APPROXIMATE NUMBERS 19

1.1 Absolute and relative errors 19
1.2 Basic sources of errors 22
1.3 Scientific notation. Significant digits. The number of correct digits 23
1.4 Rounding of numbers 26
1.5 Relationship between the relative error of an approximate number and the number of correct digits 27
1.6 Tables for determining the limiting relative error from the number of correct digits and vice versa 30
1.7 The error of a sum 33
1.8 The error of a difference 35
1.9 The error of a product 37
1.10 The number of correct digits in a product 29
1.11 The error of a quotient 40
1.12 The number of correct digits in a quotient 41
1.13 The relative error of a power 41
1.14 The relative error of a root 41
1.15 Computations in which errors are not taken into exact account 42
1.16 General formula for errors 42
1.17 The inverse problem of the theory of errors 44
1.18 Accuracy in the determination of arguments from a tabulated function 48
1.19 The method of bounds 50
1.20 The notion of a probability error estimate 52

References for Chapter 1 54

CHAPTER 2 SOME FACTS FROM THE THEORY OF CONTINUED FRACTIONS 55

2.1 The definition of a continued fraction 55
2.2 Converting a continued fraction to a simple fraction and vice versa 56
2.3 Convergents 58
2.4 Nonterminating continued fractions 66
2.6 Expanding functions into continued fractions 72

References for Chapter 2 76

CHAPTER 3 COMPUTING THE VALUES OF FUNCTIONS 77

3.1 Computing the values of a polynomial. Horner’s scheme 77
3.2 The generalized Horner scheme 80
3.3 Computing the values of rational fractions 82
3.4 Approximating the sums of numerical series 83
3.5 Computing the values of an analytic function 89
3.6 Computing the values of exponential functions 91
3.7 Computing the values of a logarithmic function 95
3.8 Computing the values of trigonometric functions 98
3.9 Computing the values of hyperbolic functions 101
3.10 Using the method of iteration for approximating the values of a function 103
3.11 Computing reciprocals 104
3.12 Computing square roots 107
3.13 Computing the reciprocal of a square root 111
3.14 Computing cube roots 112
References for Chapter 3 114

CHAPTER 4 APPROXIMATE SOLUTIONS OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS 115

4.1 Isolation of roots 115
4,2 Graphical solution of equations 119
4.3 The halving method 121
4.4 The method of proportional parts (method of chords) 122
4.5 Newton’s method (method of tangents) 127
4.6 Modified Newton method 135
4,7 Combination method 136
4.8 The method of iteration 138
4.9 The method of iteration for a system of two equations 152
4.10 Newton’s method for a system of two equations 156
4.11 Newton’s method for the case of complex roots 157

References for Chapter 4 161

CHAPTER 5 SPECIAL TECHNIQUES FOR APPROXIMATE SOLUTION OF ALGEBRAIC EQUATIONS 162

5.1 General properties of algebraic equations 162
5.2 The bounds of real roots of algebraic equations 167
5.3 The method of alternating sums 169
5,4 Newton’s method 171
5.5 The number of real roots of a polynomial 173
5.6 The theorem of Budan-Fourier 175
5.7 The underlying principle of the method of Lobachevsky-Graeffe 179
5.8 The root-squaring process 182
5.9 The Lobachevsky-Graeffe method for the case of real and distinct roots 184
5.10 The Lobachevsky-Graeffe method for the case of complex foots 187
5.11 The case of a pair of complex roots 190
5.12 The case of two pairs of complex roots 194
5.13 Bernoulli’s method 198
References for Chapter 5 202

CHAPTER 6 ACCELERATING THE CONVERGENCE OF SERIES 203

6.1 Accelerating the convergence of numerical series 203
6.2 Aecelerating the convergence of power series by the Euler-Abel methods 209
6.3 Estimates of Fourier coefficients 213
6.4 Accelerating the convergence of Fourier trigonometric series by the method of A. N. Krylov 217
6.5 Trigonometric approximation 225

References for Chapter 6 228

CHAPTER 7 MATRIX ALGEBRA 229

7.1 Basic definitions 229
7.2 Operations involving matrices 230
7.3 The transpose of a matrix 234
7.4 The.inverse matrix 236
7.5 Powers of a matrix 240
7.6 Rational functions of a matrix 241
7.7 The absolute value and norm of a matrix 242
7.8 The rank of a matrix 248
7.9 The limit of a matrix 249
7.10 Series of matrices 251
7.11 Partitioned matrices 256
7.12 Matrix inversion by partitioning 260
7.13 Triangular matrices 265
7.14 Elementary transformations of matrices 268
7.15 Computation of determinants 269

References for Chapter 7 272

CHAPTER 8 SOLVING SYSTEMS OF LINEAR EQUATIONS 273

8.1 A general description of methods of solving systems of linear equations 273
8.2 Solution by inversion of matrices, Cramer’s rule 273
8.3 The Gaussian method 277
8.4 Improving roots 284 287 288 290 293 296 300 307 309 311 313 316 321 322 322 324 327
8.5 The method of principal elements 287
8.6 Use of the Gaussian method in computing determinants 288
8.7 Inversion of matrices by the Gaussian method 290
8.8 Square-root method 293
8.9 The scheme of Khaletsky 296
8.10 The method of iteration 300
8.11 Reducing a linear system to a form convenient for iteration 307
8.12 The Seidel method 309
8.13 The case of a normal system 311
8.14 The method of relaxation 313
8.15 Correcting elements of an approximate inverse matrix 316

References for Chapter 8 321

CHAPTER 9 THE CONVERGENCE OF ITERATION PROCESSES FOR SYSTEMS OF LINEAR EQUATIONS 322

9.1 Sufficient conditions for the convergence of the iteration process 322
9.2 An estimate of the error of approximations in the iteration process 324
9.3 First sufficient condition for convergence of the Seidel process 327
9.4 Estimating the error of approximations in the Seidel process by the m-norm 330
9.5 Second sufficient condition for convergence of the Seidel process 330
9.6 Estimating the error of approximations in the Seidel process by the i-norm 332
9.7 Third sufficient condition for convergence of the Seidel proces 333

References for Chapter 9 335

CHAPTER 10 ESSENTIALS OF THE THEORY OF LINEAR VECTOR SPACES 336

10.1 The concept of a linear vector space 336
10.2 The linear dependence of vectors 337
10.3 The scalar product of vectors 343
10,4 Orthogonal systems of vectors 345
10.5 Transformations of the coordinates of a vector under changes in the basis 348
10.6 Orthogonal matrices 350
10.7 Orthogonalization of matrices 351
10.8 Applying orthogonalization methods to the solution of systems of linear equations 358
10.9 The solution space of a homogeneous system 364
10.10 Linear transformations of variables 367
10.11 Inverse transformation 373
10.12 Eigenvectors and eigenvalues of a matrix 375
10.13 Similar matrices 380
10.14 Bilinear form of a matrix 384
10.15 Properties of symmetric matrices 384
10.16 Properties of matrices with real elements 389

References for Chapter 19 393

CHAPTER 11 ADDITIONAL FACTS ABOUT THE CONVERGENCE OF ITERATION PROCESSES FOR SYSTEMS OF LINEAR EQUATIONS 394

11.1 The convergence of matrix power series 394
11.2 The Cayley-Hamilton theorem 397
11.3 Necessary and sufficient conditions for the convergence of the process of iteration for a system of linear equations 398
11.4 Necessary and sufficient conditions for the convergence of the Seidel process for a system of linear equations 400
11.5 Convergence of the Seidel process for a normal system 403
11.6 Methods for effectively checking the conditions of convergence 405

References for Chapter 11 409

CHAPTER 12 FINDING THE EIGENVALUES AND EIGENVECTORS OF A MATRIX 410

12.1 Introductory remarks 410
12.2 Expansion of secular determinants 410
12,3 The method of Danilevsky 412
12.4 Exceptional cases in the Danilevsky method 418
12.5 Computation of eigenvectors by the Danilevsky method 420
12.6 The method of Krylov 421
12.7 Computation of eigenvectors by the Krylov method 424
12.8 Leverrier’s method 426
12.9 On the method of undetermined coefficients 428
12.10 A comparison of different methods of expanding a secular determinant 429
12.11 Finding the numerically largesi eigenvalue of a matrix and the corresponding eigenvector 430
12.12 The method of ‘scalar products for finding the first eigenvalue of a real matrix 436
12.13 Finding the second eigenvalue of a matrix and the second eigenvector 439
12.14 The method of exhaustion 443
12.15 Finding the EES and eigenvectors of a positive definite symmetric matrix 445
12.16 Using the coefficients of the characteristic polynomial of a matrix for matrix inversion 450
12.17 The method of Lyusternik for accelerating the convergence of the iteration process in the solution of a system of linear equations 453

References for Chapter 12 458

CHAPTER 13 APPROXIMATE SOLUTION OF SYSTEMS OF NONLINEAR EQUATIONS 459

13.1 Newton’s method 459
13.2 General remarks on the convergence of the Newton process 465
13.3 The existence of roots of a system and the convergence of the Newton process 469
13.4 The rapidity of convergence of the Newton process 474
13.5 Uniqueness of solution 475
13.6 Stability of convergence of the Newton process under variations of the initial approximation 478
13.7 The modified Newton method 481
13.8 The method of iteration 484
13.9 The notion of a contraction mapping 487
13.10 First sufficient condition for the convergence of the process of iteration 491
13.11 Second sufficient condition for the convergence of the process of iterations 493
13.12 The method of steepest descent (gradient method) 496
13.13 The method of steepest descent for the case of a system of linear equations 501
13.14 The method of power series 504

References for Chapter 13 506

CHAPTER 14 THE INTERPOLATION OF FUNCTIONS 507

14.1 Finite differences of various orders 507
14.2 Difference table 510
14.3 Generalized power 517
14.4 Statement of the problem of interpolation 518
14.5 Newton’s first interpolation formula 519
14,6 Newton’s second interpolation formula 526
14.7 Table of central differences 530
14.8 Gaussian interpolation formulas 531
14.9 Stirling’s interpolation formula 533
14.10 Bessel’s interpolation formula 534
14.11 General description of interpolation formulas with constant interval 536
14.12 Lagrange’s interpolation formula 539
14.13 Computing Lagrangian coefficients 543
14.14 Error estimate of Lagrange’s interpolation formula 547
14.15 Error estimates of Newton’s interpolation formulas 550
14.16 Error estimates of the centrai interpolation formulas 552
14.17 On the best choice of interpolation points 553
14.18 Divided differences 554
14.19 Newton’s interpolation formula for unequally spaced values of the argument 556
14.20 Inverse interpolation for the case of equally spaced points 559
14.21 Inverse interpolation for the case of unequally spaced points 562
14.22 Finding the roots of an equation by inverse interpolation 564
14.23 The interpolation method for expanding a secular determinant 565
14.24 Interpolation of functions of two variables 567
14.25 Double differences of higher order 570
14.26 Newton’s interpolation formula for a function of two variables 571

References for Chapter 14 573

CHAPTER 15 APPROXIMATE DIFFERENTIATION 574

15.1 Statement of the problem 574
15.2 Formulas of approximate differentiation based on Newton’s first interpolation formula 575
15.3 Formulas of approximate differentiation based on Stirling’s formula 580
15.4 Formulas of numerical differentiation for equally spaced points 583
15.5 Graphical differentiation 586
15.6 On the approximate calculation of partial derivatives 588

References for Chapter 15 FBO

CHAPTER 16 APPROXIMATE INTEGRATION OF FUNCTIONS 590

16.1 General remarks 590
16.3 The trapezoidal formula and its remainder term 595
16.4 Simpson’s formula and its remainder term 596
16.5 Newton-Cotes formulas of higher orders 599
16.6 General trapezoidal formula (trapezoidal rule) 601
16.7 Simpson’s general formula (parabolic rule) 603
16.8 On Chebyshev’s quadrature formula 607
16.10 Some remarks on the accuracy of quadrature formulas 618
16.11 Richardson extrapolation 622
16.12 Bernoulli numbers 625
16.13 Euler-Maclaurin formula 628
16.14 Approximation of improper integrals 633
16.15 The method of Kantorovich for isolating singularities 635
16.16 Graphical integration 639
16.17 On cubature formulas 641
16.18 A cubature formula of Simpson type 644

References for Chapter 16 648

CHAPTER 17 THE MONTE CARLO METHOD 649

17.1 The idea of the Monte Carlo method 649
17.2 Random numbers 650
17.3 Ways of generating random numbers 653
17.4 Monte Carlo evaluation of multiple integrals 656
17.5 Solving systems of linear algebraic equations by the Monte Carlo method 666

References for Chapter 17 674

Complet list of references 675

INDEX 679

## Lectures on Nuclear Theory – Landau, Smorodinsky

In this post, we will see the book Lectures On Nuclear Theory by L. D. Landau; Ya. Smorodinsky.

This book is based on a series of lectures delivered to experimental physicists by one of the authors (L. Landau) in Moscow in 1954.

In maintaining the lecture form in the printed edition we are emphasizing the fact that the presentation makes no pretense at completeness and that the choice of subject matter is purely arbitrary.

Since there is, at the present time, no rational theory of nuclear forces, we have limited our conclusions concerning nuclear structure to those which can be reached from an analysis of the available experimental data, using only general quantum-mechanical relations.

No attempt has been made to give a bibliography of the literature; rather we have indicated only new experimental results.

The book was translated from Russian and was published in 1959.

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Contents

Foreword V

LECTURE ONE: Nuclear Forces 1

LECTURE TWO: Nuclear Forces (Scattering of Nucleons by Nucleons) 13

LECTURE THREE: Nuclear Forces (Scattering of Nucleons at High Energies) 23

LECTURE FOUR: Nuclear Structure (Independent Particle Model) 33

LECTURE FIVE: Structure of the Nucleus (Light Nuclei) 43

LECTURE SIX: Structure of the Nucleus (Heavy Nuclei) 53

LECTURE SEVEN: Nuclear Reactions (Statistical Theory) 69

LECTURE EIGHT: Nuclear Reactions (Optical Model. Deuteron Reactions) 77

LECTURE NINE: 𝜋-Mesons 87

LECTURE TEN: Interaction of 𝜋-Mesons with Nucleons 99

## Space and Time in the Microworld – Blokhintsev

In this post, we will see the book Space and Time in the Microworld by D. I. Blokhintsev  .

In comprehending the physical content of dynamic variables which have geometric meaning, for example, the space-time particle coordinates x, y, z, t it is often necessary to have recourse to gedanken experiments which, although not feasible in practice, can nevertheless be compatible with the basic principles of geometry and quantum mechanics. In a desert sea of abstract constructions there is a still larger distance between macroscopic concepts of space-time and the way of employing the coordinates x, y, z and t in relativistic quantum field theory.

It is shown in this monograph that if elementary particles have a structure it is doubtful whether the coordinates of elementary particles, x, y, z, t, can even be defined exactly, let alone the coordinates of the elements which make up these particles (if they do not exist only in our imagination). This important fact is revealed in even the most favourable gedanken experiments.

From this fact, doubt arises about the logical validity of using the symbols x, y, z, t as the space-time coordinates to describe phenomena inside elementary particles. This allows theoreticians a certain freedom of choice of space-time and causal relationships within elementary particles; in other words, an arbitrariness of choice of the geometry in
the small.

The last chapters of this book describe some models used to illustrate the situation described above. In concluding, experimental data and experimental possibilities relating to geometric and causal problems in the microworld are discussed.

The book was translated from Russian by Zdenka Smith and was published in 1970.

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Contents

INTRODUCTION

I. GEOMETRICAL MEASUREMENTS IN THE MACROWORLD 1

1. The Arithmetization of Space-Time 1
2. The Physical Methods of Arithmetization of Space-Time 3
3. On Dividing the Manifold of Events into Space and Time 10
4. The Affine Manifold 19
5. The Riemann Manifold 23
6. The Physics of Arithmetization of the Space-Time Manifold 28
7. Arithmetization of Events in the Case of the Non-Linear Theory of Fields 33
8. The General Theory of Relativity and the Arithmetization of Space-Time 37
9. Chronogeometry 42

II. GEOMETRICAL MEASUREMENTS IN THE MICROWORLD 44

10. Some Remarks on Measurements in the Microworld 44
11. The Measurement of Coordinates of the Microparticles 46
12. The Mechanics of Measuring Coordinates of Microparticles 52
13. Indirect Measurement of a Microparticle Coordinates at a Given Instant in Time 64

III. GEOMETRICAL MEASUREMENTS IN THE MICROWORLD IN THE RELATIVISTIC CASE 69

14. The Fermion Field 69
15. The Uncertainty Relation for Fermions 74
16. The Boson Field 77
17. The Localization of Photons 82
18. The Diffusion of Relativistic Packets 86
19. The Coordinates of Newton and Wigner 89
20. The Measurement of a Microparticle’s Coordinates in the Relativistic Case

IV. THE ROLE OF FINITE DIMENSIONS OF ELEMENTARY PARTICLES 95

21. The Polarization of Vacuum. The Dimensions of an Electron 95
22. The Electromagnetic Structure of Nucleons 99
23. The Meson Structure of Nucleons 108
24. The Structure of Particles in Quantized Field Theory 114

V. CAUSALITY IN QUANTUM THEORY 124

25. A Few Remarks on Causality in the Classical Theory of Fields 124
26. Causality in Quantum Field Theory 132
27. The Propagation of a Signal “Inside” a Microparticle 141
28. Microcausality in the Quantum Field Theory 147
29. Microcausality in the Theory of Scattering Matrices 153
30. Causality and the Analytical Properties of the Scattering Matrix 159

VI. MACROSCOPIC CAUSALITY 173

31. Formal S-matrix Theory 173
32. Space-Time Descriptions Using the S-matrix 182
33. The Scale for the Asymptotic Time T 187
34. Unstable Particles (Resonances) 191
35. Conditions of Macroscopic Causality for the S-matrix 200
36. Examples of Acausal Influence Functions 207
37. An Example of Constructing an Acausal Scattering Matrix 211
38. The Dispersion Relation for the Acausal S_{a},-Matrix 219

VII. A GENERALIZATION OF CAUSAL RELATIONSHIPS AND GEOMETRY 226

39. Two Possible Generalizations 226
40. Euclidean Geometry in the Microworld 232
41. Stochastic Geometry 237
42. Discrete Space-Time 243
43. Quasi-Particles in Quantized Space 250
44. Fluctuations of the Metric 255
45. Nonlinear Fields and the Quantization of Space-Time 261

VIII. EXPERIMENTAL QUESTIONS 269

46. Concluding Remarks on the Theory 269
47. Experimental Consequences of Local Acausality 270
48. Experimental Results of Models with the “External” Vector 278

APPENDICES 282

BIBLIOGRAPHY 326