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.

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Theory of Shock Waves and Introduction to Gas Dynamics – Zeldovich

In this post, we will see the book Theory of Shock Waves and Introduction to Gas Dynamics Ya. B. Zeldovich.

About the book

Gas dynamics is defined as the science of motion at great pressure differentials and high velocities, velocity being measured in terms of the speed of sound. The book confines itself to specific phenomena of gas dynamics, i.e., those which have nc analogies in the mechanics of an incompressible liquid. Emphasis is placed on careful definition of the fundamentals of gas dynamics, fundamental laws, and methods of solving simplest problems, rather than an the computational methods
of gas dynamics or methods of numerical integration of complex two- and three-dimensional flows, etc. Attention is devoted to problems of flow around bodies moving at great speeds, motion of a gas in ducts such as nozzles and pipes, aid compressibility of the moving medium. The second main topic is shock waves considered under the theory of shock waves, shock wave laws, and the problem of the destructive effect of explosions and propagation of the explosion on the explosive substance (capable of chemical reaction). The author intends the text to also serve as an introduction to the theory of explosions.

The book was translated from Russian and was published in 1946.

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Introduction 1

Chapter 1
Gas Dynamics Equations 6
Appendix 10

Chapter 2
Principles of Acoustics. The Speed of Sound 16

Chapter 3
Gas Flow Through Nozzles 36

Chapter 4
Properties of Supersonic Jets 47

Chapter 5
Gas Flow in a Long Cylindrical Pipe 53

Chapter 6
Motion that Depends or the Relation Between Coordinates and Time 62

Chapter 7
Theory of Shock Waves. Introduction 74

Chapter 8
Hugoniot’s Adiabatic Curve. Its Derivation From the Equations of
Conservation 76

Chapter 9
Properties of Hugoniot’s Adiabatic Curve. Shock Waves in Air and
Water 82

Chapter 10
The History of the Shock Wave Problem 90

Chapter 11.
Graphical Methods of Shock Wave Theory. Waves Near a
Critical Point 95

Chapter 12
Structure of Shock Wave Front 107

Chapter 13
Propagation of Shock Waves in a Gas with Delayed Excitation of
internal Degree of Freedom 114

Chapter 14
Formation of Shock Waves 119

Chapter 15
Shock Waves in the Case of Oscillations of Large Amplitude 127

Chapter 16
Propagation of an Arbitrary Discontinuity 131

Chapter 17 .
Supersonic Flow Around a Body 144

Chapter 18
Theory of Jet Propulsion 153

Chapter 19
Reflection of a Shock Wave 166

Chapter 20
The Effect of Explosives. Introduction 171

Chapter 21
Simulation of an Explosion area of the Propagation of Blast Waves 176

Chapter 22
Simulation and Similarity of Destructions Caused by Shock Waves 184

Chapter 23
Phenomena Occurring in the Immediate Vicinity of the Charge 189

Chapter 24
Laws Governing the Propagation of a Shock Wave at a Great Distance from the Charge 200



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Thermal Engineering

In this post, we will see the book Thermal Engineering by Ivan Shvets, M. Kondak, N Kirakovsky, I Neduzhy, D Shevtsov, I Sheludko.

About the book

The book has been written by a group of scientists working
for many years at Higher Educational Institutions of the Soviet
Union and is a textbook for students both of Higher and of
Secondary Schools.

The book contains the theoretical fundamentals of thermal
engineering (engineering thermodynamics and heat transfer), contains
characteristics of fuels, describes combustion processes, boiler
units and heat engines, such as steam engines, internal-combustion
engines, steam and gas turbines and steam power plants.
Besides being a textbook for students, the book will also be of
interest to specialists in the field of thermal engineering.

The book was translated from Russian by G. Leib and was published in 1960 by Peace Publishers.

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Foreword 11


Chapter I. Basic Concepts of Thermodynamics 13

1. Parameters of Gases and Relation between Them. The Equation of State for Gases 13
2. Mixtures of Gases 19
3. Thermodynamic Processes bn hake wave 28
4. Work and Heat of a Process. Heat Capacity 204
5. Internal Energy of a Gas 33
6. Enthalpy of a Gas 35
7. Entropy 36

Chapter II. The First Law of Thermodynamics and Investigation of Thermodynamic Processes 37

1. The Law of Conservation and Conversion of Energy 37
2. The First Law of Thermodynamics 38
3. Investigation of the Basic Thermodynamic Processes for Ideal Gases

Chapter III. Water Vapour and Steam 55

1. Process of Vaporization in p-v and T-s Diagrams 55
2. Determining the Parameters of Steam of Different States 58
3. The i-s (Mollier) Diagram for Steam 61
4. Thermodynamic Processes of Water Vapour (Steam) 62
5. Humid Air Sad Bice 65
6. Flow and Throttling of Gases and Vapours. 68

Chapter IV. The Second Law of Thermodynamics 76

1. Cyclic Processes and the Carnot Cycle 76
2. The Second Law of Thermodynamics 82
3. Mathematical Expression of the Second Law of Thermodynamics and Change in the Entropy of an Isolated System 83

Chapter V. Ideal Cycles of Heat Engines 89

1. Cycles of Internal-combustion Engines View 89
2. Gas Turbine Cycles 93
3. Compressor Processes 95
4. Basic Cycle of a Steam Power Plant 98
5. Methods of Improving the Efficiency of the Basic Cycle 101
6. Heating and Power Systems 103
7. Regenerative Cycle 105
8. Steam-gas Cycle 107
9. Refrigeration Cycles 108


Chapter I. Kinds of Heat Transfer 111

1. Conduction 111
2. Convection 112
3. Heat Transfer upon Change in Aggregate State 126
4. Radiation 130

Chapter II. Heat-exchange Equipment 140

1. Combined Heat Transfer 140
2. Calculation of Heat-exchange Equipment 145


Chapter I. Properties of Fuel 150

1. General Information 150
2. Composition 151
3. Basic Specifications of Fuel 152

Chapter II. Kinds of Fuels and Processing Thereof 159

1. Fuels 159
2. Liquid Fuels 164
3. Gaseous Fuels 167
4. Processing of Solid Fuels 173


Chapter I. General Information on Boiler Installations 179

1. Classification of Boiler Installations 179
2. General Information on Boiler Units 180

Chapter II. Combustion Processes 182.

1. Combustion of Fuels and Ignition Temperature 182
2. Air Required for Combustion 184
3. Excess-air Coefficient 184
4. Volumes of Combustion Products Calculated from the Elementary Composition of Fuel 184
5. Volumes of Dry Combustion Products Determined by Flue
Gas Analysis 188
6. Volumes of Combustion Products oi siens Fuels 189
7. Enthalpy of Fuel Combustion Products 190

Chapter III. Heat Balance of a Boiler Unit 192

1. General Equation 192
2. Available Heat 192
3. Heat Utilized in Boiler Unit 192
4. Heat Losses with Flue Gases 193
5. Heat Losses due to Chemically Incomplete Combustion 194
6. Heat Losses due to Mechanically Incomplete Combustion 195
7. Heat Losses due to External Cooling of Boiler Unit 195
8. Heat Losses due to Physical Heat of Slags and for Cooling of Beams and Panels not Included into Boiler Circulation Systems 196
9. Boiler Unit Efficiency 196
10. Fuel Consumption 196
11. Evaporative Capacity of Fuel 197

Chapter IV. Temperatures and Heat Transfer in Furnace 198

1. Temperatures in Furnace 198
2. Heat Transfer in Furnace 199

Chapter V. Furnaces 201

1. Classification. of Furnaces 201
2. Thermal Characteristics of Furnaces 205
3. Waterwalls 206
4. Gas-fired Furnaces 206
5. Furnaces for Fuel Oil 211
6. Pulverized-coal Furnaces 216
7. Grate-fired Furnaces for Solid Fuel 225

Chapter VI. Boiler Units 241

1. General Information and Parameters 241
2. Development of Natural Circulation Boilers 252
3. Forced Circulation Boilers 260

Chapter VII. Superheaters, Water Economizers, Air Heaters 263

1. Superheaters 268
2. Water Economizers 266
3. Air Heaters 268

Chapter VIII. Heat Transfer in Convective Passes of Boiler Units 270

Chapter IX. Auxiliary Equipment, Settings and Frame 272

1. Draught Production Equipment 272
2. Equipment for Flue Gas Purification 275
3. Boiler Unit Settings and Frames 279
4. Feedwater Pumps and Piping 280

Chapter X Conditions in Boiler Units and Feedwater Treatment 281

1. Boiler Water Conditions 281
2. Characteristics of Initial Water 282
3. Methods of Feedwater Treatment апа Equipment Used 282


Chapter I. Steam Engines 286

1. Classification of Steam 288
2. Working Cycle 289
3. Determination of Engine Power 290
4. Steam Engine Efficiencies 294
5. Steam Consumption 297
6. Valve Gear 297
7. Methods of Governing Engine Power 303
8. Types of Engines 305

Chapter II. Reciprocating Compressors 309

Chapter III. Internal-combustion Engines 314

1. Operating Principles and Classification of Engines 314
2. Working Cycles of Engines 316
3. Utilization of Heat in Engines 322
4. Indicated Efficiency (were ag the cus 323
5. Mechanical Efficiency 329
6. Brake Thermal Efficiency and Parameters of Working Cycle 330
7. Comparison of Theoretical and Actual Indicator Diagrams 335
8. Determination of Principal Dimensions of Engines 336
9. Heat Balance of Engine 338
10. Mixture Formation 340
11. Fuel Supply Equipment 343
12. Flywheel and Unbalanced Forces of Inertia 349
13. Governing Systems and Governors 350
14. Timing 354
15. Fuel System 356
16. Lubrication 359
17. Cooling Systems 361
18. Electric Ignition 364
19. Starting Devices 367
20. Types of Engines 368
21. Further Development of Internal combustion Engines 374


Chapter I. Steam Turbines 36

1. General Information oe 976
2. Processes in Turbine Nozzles and Moving Blades 378
3. Heat Losses and Stage Efficiency 388
4. Turbine Heat Calculations 392
5. Turbine Governing 402
6. Steam Turbine Design 405
7. Condenser Units 413

Chapter II. Gas Turbines 419

1. Development of Gas Turbines A19
2. Fundamentals of Theory of Heat Processes. in 1 Gas Turbines 423
3. Heat. Cycles 428
4. Efficiencies of Gas Turbine Installations 435
5. Constant-volume Combustion Gas Turbines 436
6. Closed-cycle Gas Turbine Installations 438
7. Cycle Diagram Calculations 44l
8. Compressors 446
9. Gas Turbine Design 448
10. Materials for and Cooling of Turbine Blades and Disks 452
I]. Regenerators 454
12. Fuel and Combustion Chambers 455


Chapter I. Heat Electric Generating Plants 458

1. Types of Plants 458
2. Layout and Equipment of Steam Turbine Plants 463
3. Fuel Facilities 469
4. Power Plant Economy 476

Chapter II. Automation in Power Plants 480



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Complex Numbers in Geometry – Yaglom

In this post, we will see the book Complex Numbers in Geometry by I. M. Yaglom.

About the book

This book is intended for pupils in the top classes in high schools and for students in mathematics departments of universities and teachers’ colleges. It may also be useful in the work of mathematical societies and may be of interest to teachers of mathematics in junior high and high schools.
The subject matter is concerned with both algebra and geometry. There are many useful connections between these two disciplines. Many applications of algebra to geometry and of geometry to algebra were known in antiquity; nearer to our time there appeared the important subject of analytical geometry, which led to algebraic geometry, a vast and rapidly developing science, concerned equally with algebra and geometry. Algebraic methods are now used in projective geometry, so that it is uncertain whether projective geometry should be called a branch of geometry or algebra. In the same way the study of complex numbers, which arises primarily within the bounds of algebra, proved to be very closely connected with geometry; this can be
seen if only from the fact that geometers, perhaps, made a greater contribution to the development of the theory than algebraists.

The book is intended for quite a wide circle of readers. The early sections of each chapter may be used in mathematical classes in secondary schools, and the later sections are obviously intended for more advanced students (this has necessitated a rather complicated system of notation to distinguish the various parts of the book).

The book was translated from Russian by Eric Primrose and was published in 1968 from a 1963 Russian edition.

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Translator’s Note v

Preface vii

Chapter I: Three Types of Complex Numbers

1. Ordinary Complex Numbers 1
2. Generalized Complex Numbers 7
3. The Most General Complex Numbers 10
5. Dual Numbers 14
5. **Double Numbers 18
6. **Hypercomplex Numbers 22

Chapter II: Geometrical Interpretation of Complex Numbers

7. Ordinary Complex Numbers as Points of a Plane 26
8. *Applications and Examples 34
9. Dual Numbers as Oriented Lines of a Plane 80
10. *Applications and Examples 95
11. **Interpretation of Ordinary Complex Numbers in the Lobachevskii Plane 108
12. **Double Numbers as Oriented Lines of the Lobachevskii Plane 118

Chapter III: Circular Transformations and Circular Geometry

13. Ordinary Circular Transformations (Mobius Transformations) 130
14. *Applications and Examples 145
15. Axial Circular Transformations (Laguerre Transformations) 157
16. *Applications and Examples 161
17. **Circular Transformations of the Lobachevskii Plane 179
18. **Axial Circular Transformations of the Lobachevskii Plane 188

Appendix: Non-Euclidean Geometries in the Plane and Complex Numbers

A1. Non-Euclidean Geometries in the Plane 195
A2. Complex Coordinates of Points and Lines of the plane Non-Euclidean Geometries 205
A3. Cycles and Circular Transformations 212

Addenda 220

Index 241

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Updates: Printing books, some new acquisitions and titles we will see soon

Some updates!

Sorry for being erratic in the posts in the last few months.


Thank you for the fantastic response on the reprinting idea. We have 400+ people who have shown interest in buying the entire set. We will soon start the pre-order on books, hopefully start shipping sometime at end of October. Sorry for all the delays in the printing, most of it my procrastination and some of it the pandemic.

Keep the fingers crossed!!

New Haul

Recently got a nice haul of books. Many thanks to @desperadomar and @imsmam for making this possible.

New Scans

In coming couple of months we will see a lot of new titles being added. The first batch will be from this set:

There are few titles already on the Internet Archive which I not posted on the blog so far. You can check them at

Plus we will see some children’s books in Indic languages as well: Marathi, Bengali and Hindi

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Theory of Elasticity – Amenzade

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

About the book

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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Notation 9
Introduction 13


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


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


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


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


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


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


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


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


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


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


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



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Fundamentals of Radio – Izyumov, Linde

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

About the book

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.

All this increases the interest in radio engineering knowledge on the part of an ever growing number of people. The study of radio is, however, made more difficult for the majority of readers as it is usually explained with the use of higher mathematics. On the other hand, when higher mathematics is not used, many important problems are often oversimplified and treated without sufficient explanation and demonstration. Moreover radio engineering is a coherent science in which everything is interrelated and interdependent; therefore lack of understanding of fundamental phenomena and laws prevents the reader from fully understanding further problems. It is far from clear what one should understand under the name of “radio engineering,’ and its fundamentals since this branch has been extended, diversified and become interwoven with many other branches of science and technology. Under “radio engineering” proper one usually understands the use of electromagnetic radiation for the obtaining of information from a distant source. This is effected through the use of a transmitting (radiating) device and a receiving device provided conditions for propagation of radio waves are favourable. In accordance with this, the book describes the operating principles of radio transmitters, radio receivers and radiating devices, as well as radio wave propagation. It goes without saying that one book cannot exhaustively deal with all the varieties of existing radio circuits and devices; therefore, we concentrate our attention only on the most important and representative types.


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

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Foreword 9


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


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


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


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

6-1. Radiating Systems 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


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


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


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


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


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

Chapter XII. RECEIVERS 579

12-1. Purpose and Basic Characteristics 579
12-2. Receiver Input Circuits 587
12-3. High-Frequency Amplifiers 595
12-4. Intermediate-Frequency Amplifiers 607
12-5. Radio Interference 611
12-6. Frequency Converters 618
12-7. Receiver Detector Stages 633
12-8. Controls and Adjustments in Receivers 647
12-9. Examples of Receiver Circuitry 653

Reference Data 659
Index 664

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The Remarkable Sine Functions – Markushevich

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

About the book

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.

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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




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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.

About the book

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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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



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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.

About the book

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.

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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


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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

About the book

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


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




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


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


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


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.

Unsteady Flow in Tubes 266

Explanatory List of Abbreviations 274

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