The Three Bears – Tolstoy

Posted on December 29, 2021 by The Mitr

In this post, we will see the book The Three Bears by Leo Tolstoy.

About the book

In this little book a family of bears, father bear, mother bear and little bear Misha, find a little girl in their home. The little girl has drank their soup, broken their chair and sleeping in their beds. What will the bear family do?

This is Tolstoy’s version for “Goldilocks and the Three Bears”.The girl intruder is not named, and has been interpreted as a Napoleon figure, invading and wrecking the home of the good Russian bears, but ultimately being beaten back as Napoleon was in 1812. The story was also popular in Soviet times where mistrust of outsiders was encouraged. Source

The book was translated from Russian by Iyv Litvinov and was illustrated by Yuri Vasnetsov. The book was printed several times, the current scan is for the 1989 print by Raduga Publishers.

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Posted in books, children's books, children's stories, folk tales, raduga publishers, soviet | Tagged bear, children's book, children's literature, children's story, illustrated book, picture book, raduga publishers, russsian, soviet, three bears | Leave a comment

Mathematical Foundations of Information Theory – Khinchin

Posted on December 28, 2021 by The Mitr

In this post, we will see the book Mathematical foundations of Information Theory by A. I. Khinchin.

About the book

The book is a translation of two papers written by the Russian mathematician, A. I. Khinchin, for the expository journal Uspekhi. These papers present the mathematical foundations of information theory. While completely rigorous, the flavour of the engineering applications which led to the theory runs throughout and very much helps the intuition. Khinchin has here reformulated basic concepts and presents for the first time rigorous proofs of certain fundamental theorems in the subject.

The first paper discusses the concept of entropy and gives one major application to coding. The only stochastic processes used are Markov chains. This paper would serve as a valuable supplement to an introductory probability course.

The second and longer paper uses more advanced topics from probability theory, for example, stationary processes and martingales. However, the treatment is quite complete and the non specialist would not suffer thanks to Khinchin’s amazing expository ability. It is a tribute to Shannon’s theory that a rigorous treatment only enhances the elegance of the basic theorems.

The book was translated from Russian by R. A. Silverman and M. D. Friedman was published in 1957.

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The Entropy Concept in Probability Theory

# 1. Entropy of Finite Schemes 2

# 2. The Uniqueness Theorem 9

# 3. Entropy of Markov chains 13

# 4. Fundamental Theorems 16

#5. Application to Coding Theory 23

On the Fundamental Theorems of Information Theory

INTRODUCTION: 30

CHAPTER I. Elementary Inequalities 34

# 1. Two generalizations of Shannon’s inequality 34

# 2. Three inequalities of Feinstein 39

CHAPTER II. Ergodic Sources 44

# 3. Concept of a source. Stationarity. Entropy. 44

# 4. Ergodic Sources 49

#5. The E property. McMillan’s theorem. 54

# 6. The martingale concept. Doob’s theorem. 58

% 7. Auxiliary propositions 64

# 8. Proof of McMillan’s theorem 70

CHAPTER III. Channels and the sources driving them 75

# 9. Concept of channel. Noise. Stationarity. Anticipation 75

#10. Connection of the channel to the source 78

#11. The ergodic case 85

CHAPTER IV. Feinstein’s Fundamental Lemma 90

#12. Formulation of the problem 90

#13. Proof of the lemma 93

CHAPTER V. Shannon’s Theorems 102

# 14. Coding 102

# 15. The first Shannon theorem 104

#16. The second Shannon theorem 109

CONCLUSION 111

REFERENCES 120

Posted in books, engineering, mathematics, physics, statistics, technology | Tagged coding theory, concept of channel, entropy, ergodic sources, ergodic theory, feinstein fundamental lemma, feinstein inequality, information, markov chains, mathematics, noise, shanon's inequality, shanon's theorems, uniqueness theorem | 1 Comment

Mathematical Foundations of Statistical Mechanics – Khinchin

Posted on December 27, 2021 by The Mitr

In this post, we will see the book Mathematical Foundations of Statistical Mechanics by A. I. Khinchin.

About the book

The present book considers as its main task to make the reader familiar with the mathematical treatment of statistical mechanics on the basis of modern concepts of the theory of probability and a maximum utilization of its analytic apparatus. The book is written, above all, for the mathematician, and its purpose is to introduce him to the problems of statistical mechanics in an atmosphere of logical precision, outside of which he cannot assimilate and work, and which, unfortunately, is lacking in the existing physical expositions.

The only essentially new material in this book consists in the systematic use of limit theorems of the theory of probability for rigorous proofs of asymptotic formulas without any special analytic apparatus. The few existing expositions which intended to give a rigorous proof to these formulas, were forced to use for this purpose special, rather cumbersome, mathematical machinery. We hope, however, that our exposition of several other questions (the ergodic problem, properties of entropy, intramolecular correlation, etc.) can claim to be new to a certain extent, at least in some of its parts.

The book was translated from Russian by George Gamow was first published in 1949.

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Preface vii

Chapter I. Introduction

1. A brief historical sketch 1
2. Methodological characterization 7

Chapter II. Geometry and Kinematics of the Phase Space

3. The phase space of a mechanical system 13
4. Theorem of Liouville 15
5. Theorem of Birkhoff 19
6. Case of metric indecomposability 28
7. Structure functions 32
8. Components of mechanical systems 38

Chapter III. Ergodic Problem

9. Interpretation of physical quantities in statistical mechanics 44
10. Fixed and free integrals 47
11. Brief historical sketch 52
12. On metric indecomposability of reduced manifolds 55
13. The possibility of a formulation without the use of metric indecomposability 62

Chapter IV. Reduction to the Problem of the Theory of
Probability

14. Fundamental distribution law 70
15. The distribution law of a component and its energy 71
16. Generating functions 76
17. Conjugate distribution functions 79
18. Systems consisting of a large number of components 81

Chapter V. Application of the Central Limit Theorem

19. Approximate expressions of structure functions 84
20. The small component and its energy. Boltzmann’s law 88
21. Mean values of the sum functions 93
22. Energy distribution law of the large component 99
23. Example of monatomic ideal gas 100
24. The theorem of equipartition of energy 104
25. A system in thermal equilibrium. Canonical distribution of Gibbs 110

Chapter VI. Ideal Monatomic Gas

26. Velocity distribution. Maxwell’s law 115
27. The gas pressure 116
28. Physical interpretation of the parameter 121
29. Gas pressure in an arbitrary field of force 123

Chapter VII. The Foundation of Thermodynamics

30. External parameters and the mean values of external forces 129
31. The volume of the gas as an external parameter 131
32. The second law of thermodynamics 132
33. The properties of entropy 137
34. Other thermodynamical functions 145

Chapter VIII. Dispersion and the Distributions of Sum Functions

35. The inter molecular correlation 148
36. Dispersion and distribution laws of the sum functions 156

Appendix

The proof of the central limit theorem of the theory of probability 166

Notations 176

Index 178

Posted in books, mathematics, physics | Tagged birkhoff theorem, central limit theorem, distributions, ensemble, ergodic problem, foundations of thermodynamics, geometry of phase space, liouville theorem, manifolds, mathematics, monoatomic gas, physics, soviet, statistical mechanics, sum functions, theory of probability, thermodynamic functions | 1 Comment

Mining of Mineral Deposits – Shevyakov

Posted on December 26, 2021 by The Mitr

In this post, we will see the book Mining of Mineral Deposits by L. Shevyakov.

About the book

A textbook on mining technology and processes. The book is a treatise on various aspects of mining. The first part covers open mining. The chapters 2 and 3 discuss opening up of coal and ore deposits. Chapters 4-6 discusses shafts, plants and structures required for open mining. underground and open cut mines. The second part is about the underground aspects of mining. It discusses various methods and modes of extraction of coal and ores. The final part talks about open cut mining with discussions about open pits.

The book was translated from the Russian by V. Schiffer and edited by G. Ivanov-Mumjiev. The book was published Foreign Languages Publishing House in 1963.

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PART ONE
OPENING UP OF MINERAL DEPOSITS

Chapter I. Basic Concepts and Terminology 15

Chapter II. Opening Up of Coal and Other Stratified Deposit 30

Chapter III. Opening up of Ore Deposits 96

Chapter IV. Choice of site for shafts 109
Chapter V. Surface Plants and Structures of a Mine 125

Chapter VI. Shaft Stations. 136

PART II
UNDERGROUND MINING OF MINERAL DEPOSITS

Chapter VII. Basic Concepts and Terminology 155

Chapter VIII. Filling 161

Chapter IX. Choice of mining methods and modes of extraction 187

Chapter X. General Surveyor Coal Seam Mining Methods 217

Chapter XI. Stoping in a Continuous Face 223

Chapter XII. Continuous Methods of Mining 312

Chapter XIII. Pillar Methods of Alining 337

Chapter XV. Mining of Thick Seams 364

Chapter XVI Underground Gasification of Coal 426

Chapter XVII. Hydraulic Mining of Coni 430

Chapter XVIII. Methods of Mining Rock and Potash Sails 437

Chapter XIX. Choice of Methods for Mining Ore Deposits 408

Chapter XX. Mining of Thin and Medium-Thick Ore Deposits 470

Chapter XXI. Methods of Mining Thick Ore Deposits 506

Chapter XXII. Mining of Contiguous Beds 560

Chapter XXIII. Effects of Underground Excavations on the Ground Surface 572

Chapter XXIV. Classification and Choice of Mining Methods 584

PART THREE
OPEN-CUT MINING

Chapter XXV. Basic Definitions and Terminology 593

Chapter XXVI Equipment and Layouts of Open Pits 609

Subject Index 677

Posted in books, engineering, foreign languages publishing, soviet, technology | Tagged cleaning, coal, dips, engineering, equipment, exploring, layout, machines, mechanization, mining, open cut mining, ore, properties, salts, seams, surveying, techniques, technology, tools, transport, underground mining, vehicles | Leave a comment

Mathematical Foundations of Quantum Statistics – Khinchin

Posted on December 25, 2021 by The Mitr

In this post, we will see the book Mathematical Foundations of Quantum Statistics by A. I. Khinchin.

About the book

In the area of quantum statistics, I show that a rigorous and systematic mathematical basis of the computational formulas of statistical physics does not require a special unwieldy analytical apparatus (the method of Darwin-Fowler), but may be obtained from an elementary application of the well-developed limit theorems of the theory of probability. Apart from its purely scientific value, which is evident and requires no comment, the possibility of such an application is particularly satisfying to Soviet scientists, since the study of these limit theorems was founded by P. L. Chebyshev and was developed further by other Russian and Soviet mathematicians. The fact that these theorems can form the analytical basis for all the computational formulas of statistical physics once again demonstrates their value for applications.

This monograph, like my first book, is devoted entirely to the mathematical method of the theory and is in no way a complete physical treatise. In fact, no concrete physical problem is considered. The book is directed primarily towards the mathematical reader. However, I hope that the physicist who is concerned with the mathematical apparatus of his science will find something in it to interest him.

The book was translated from Russian by Irwin Shapiro and was published in 1960.

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INTRODUCTION

1. The most important characteristics of the mathematical apparatus
of quantum statistics 1
2. Contents of the book 4

CHAPTER I
PRELIMINARY CONCEPTS OF THE THEORY OF PROBABILITY

1. Integral-valued random variables 12
2. Limit theorems 16
3. The method of characteristic functions 21
4. The one-dimensional limit theorem 29
5. The two-dimensional limit theorem 35

CHAPTER II
PRELIMINARY CONCEPTS OF QUANTUM MECHANICS

1. Description of the state of a physical system in quantum mechanics 45
2. Physical quantities and self-adjoint linear operators 49
3. Possible values of physical quantities00 54
4. Evolution of the state of a system in time 61
5. Stationary states. The law of conservation of energy 65

CHAPTER III
GENERAL PRINCIPLES OF QUANTUM STATISTICS

1. Basic concepts of statistical methods in physics 71
2. Microcanonical averages 75
3. Complete, symmetric and antisymmetric statistics 80
4. Construction of the fundamental linear basis 85
5. Occupation numbers. Basic expressions for the structure functions 91
6. On the suitability of microcanonical averages 96

CHAPTER IV
THE FOUNDATIONS OF THE STATISTICS OF PHOTONS

1. Distinctive characteristics of the statistics of photons 102
2. Occupation numbers and their mean values 103
3. Reduction to a problem of the theory of probability 106
4. Application of a limit theorem of the theory of probability 110
5. The Planck formula 113
6. On the suitability of microcanonical averages 118

CHAPTER V
FOUNDATIONS OF THE STATISTICS OF MATERIAL PARTICLES

1. Review of fundamental concepts 123
2. Mean values of the occupation numbers 124
3. Reduction to a problem of the theory of probability 130
4. Choice of values for the parameters 𝛼 and 𝛽 135
5. Application of a limit theorem of the theory of probability 139
6. Mean values of sum functions 142
7. Correlation between occupation numbers 144
8. Dispersion of sum functions and the suitability of microcanonical
averages 147
9. Determination of the numbers g_{k} for structureless particles in the absence of external forces 149

CHAPTER VI
THERMODYNAMIC CONCLUSIONS

1. The problems of statistical thermodynamics 153
2. External parameters, external forces and their mean values 154
3. Determination of the entropy and the deduction of the second law of thermodynamics 158

Supplement I. The Statistics or Heterogeneous Systems 162
Supplement II. The Distribution of a Component and its Energy 168
Supplement III. The Principle of Canonical Averaging 172
Supplement IV. The Reduction to One-dimensional Problem in the Case of Complete Statistics 178
Supplement V. Some General Theorems of Statistical Physics. 180
Supplement VI. Symmetric Functions on Multi-dimensional Surfaces 198

1. Introduction 198
2. Preliminary formulas 199
3. Distribution of the energy of a particle. Gibbs’ theorem 203
4. Derivation of the fundamental formula 207
5. Distribution of the maximum and minimum energy of a particle 210
6. The basic limit theorem 215
7. Probability that the energy of a particle lies in a given interval 219
8. A functional limit theorem 221
9. Continuous symmetric functions004 224
10. Generalizations of Gibbs’ theorem. 226

References 231

Index 232

Posted in books, mathematics, physics | Tagged canonical averaging, elementary particles, linear operators, mathematics, microcanonical averages, particles, physical quantities, physics, planck formula, quantum mechanics, quantum statistics, soviet, states, stationary states, statistics of photons, theory of probability, thermodynamics | 1 Comment

The White Deer: A Latvian Folk Tale by Fainna Solasko

Posted on December 24, 2021 by The Mitr

In this post, we will see the book The White Deer: A Latvian Folk Tale by Fainna Solasko.

About the book

This little book tells us the Latvian folk tale of two brothers who are in search of an enchanted white deer. Antelopes, wolves and hares help the brothers. But will they succeed in finding the magical white deer?

The book was translated from Russian by Fainna Solasko and was illustrated by Nikolay Kochergin. The book was published in by Publishers in 1973 with a reprint in 1979.

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Posted in books, children's books, children's stories, folk tales, progress publishers, soviet | Tagged children's book, fairy tales, folk tales, illustrated book, latvian folk tale, magic, magical white deer, picture book, princess story, princesses, soviet, two brothers | Leave a comment

Radio Emission Of The Sun and Planets – Zheleznyakov

Posted on December 23, 2021 by The Mitr

In this post, we will see the book Radio Emission Of The Sun and Planets by V. V. Zheleznyakov.

About the book

The task of present-day radio astronomy is to study extraterrestrial objects by means of the nature of the radio emission coming from them. Radio astronomy research is valuable for the significance of the results which greatly supplement the data of optical astronomy. It has also become a basic source of information on regions which, whilst they play a part in the generation, reflection or scattering of radio waves, make no significant contribution to the optical part of the spectrum.

This book presents a detailed discussion and analysis of the radio emission of the Sun, the Moon and the planets, and is an attempt to fill a gap in the literature currently available. There is much contemporary interest in the observation and interpretation of the radio emissions from these bodies, and this work will be of considerable value both to radio and optical astronomers, and also to the theoretical physicists who seek greater understanding of the results obtained by the users of radio telescopes. There is an extensive bibliography which adds to the importance of this book as a work of reference.

The book was translated from Russian by H.S.H. Massey and was edited by J.S. Hey. The book was published in 1970.

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FOREWORD ix

FOREWORD TO THE ENGLISH EDITION xiii

CHAPTER I. PHYSICAL CONDITIONS OF THE SUN, MOON AND PLANETS 1

1. The Sun’s Atmosphere 1

The chromosphere (2).
The corona (3)

2. Solar Activity 8

Plages and flocculi (8).
Sunspots (9).
Flares (12).
Coronal condensations (14)

3. The Moon and Planets 15

Mercury, Venus and Mars (15).
Jupiter and Saturn (17).
The Moon (18)

CHAPTER II. BASIC CHARACTERISTICS OF EXTRATERRESTRIAL RADIO
EMISSION AND METHODS FOR STUDYING THEM 20

4. Frequency Spectrum 21

Aerial temperature and effective temperature of radio emission (23).
Studying the radio-emission frequency spectrum. Multi-channel receiving devices and radio spectrographs (27)

5. Angular Spectrum 30

Aerial system requirements in radio astronomy. Parabolic aerials (30).
The two-element interferometer (31).
Modifications of the two-element interferometer (33).
The problem of studying the radio brightness distribution over a source. Variable-baseline interferometer (36).
The multiple-element interferometer (39).
The Mills Cross (42).
Eclipse observations (44)

6. Polarization of Radio Emission 46

Polarization parameters (46).
Methods of polarization measurements in the metric waveband (51).
Polarization measurements in the centimetric band (59)

7. Effect of the Earth’s Atmosphere on the Observed Radio 63

Emission Absorption of radio waves in the troposphere (63). Absorption of radio waves in the ionosphere (64). Effects connected with refraction of radio waves in the atmosphere (65).
Polarization
change of the radio emission as it passes through the ionosphere (68)

CHAPTER III. RESULTS FROM OBSERVATIONS OF THE RADIO EMISSION OF THE “QUIET” SUN 73

8. Frequency Spectrum of the “Quiet” Sun’s Radio Emission 74

Determining the level of the “quiet” Sun’s radio emission (74).
Observed dependence of Tes on wavelength (77)

9. Distribution of Radio Brightness over the Sun’s Disk 83

Remarks on methods of investigation. Some preliminary data (83).
Features of the T. distribution over the disk of the “quiet” Sun in the radio-frequency band (86)

CHAPTER IV. RESULTS OF OBSERVATIONS OF THE SUN’S SPORADIC RADIO EMISSION 99

10. The Slowly Varying Component 101

General characteristics. Correlation of the radio-emission flux with sunspots (101).
Position, form and size of local sources (102).
Radio-emission frequency spectrum (110).
Directional properties and polarization (113).
Altitude of local sources above the photosphere. Connection with optical features of the solar corona (116)

11. Microwave Bursts 120

General characteristics. Basic types of microwave bursts (120).
Frequency spectrum of bursts (125).
Polarization of radio emission (128).
Microwave bursts and chromospheric flares (130)

12. Noise Storms (enhanced radio emission and type I bursts) 135

Time characteristics of noise storms (136).
Frequency spectrum (137).
Connection with optical features (139).
Directional features of the radio emission (143).
Size and position of radio-emission sources in the corona (144).
Polarization of noise storms (148)

13. Type II Bursts 154

General characteristics (154).
Harmonics of type II bursts (157).
Fine structure of type II bursts (165).
Frequency drift and its interpretation (167)

14. Type III Bursts 176

General characteristics (176).
Polarization of bursts (180).
Connection with optical phenomena (181).
Position and movement of an emitting region in the corona. Frequency drift of bursts (185).
U-bursts (191)

15. Types IV and V Radio Emission 194

Basic characteristics of type IV radio emission (194).
Type V bursts (201)

16. Other Forms of Burst 202

Decimetric continuum (202).
Rapidly drifting decimetric bursts (205).
Continuum storms (208).
The event of 4 November 1957 (210).
Wide-band bursts of short duration (212).
Reverse-drift pairs (212)

17. Sporadic Radio Emission and Geophysical Phenomena 215

Preliminary remarks (215).
Radio emission of the Sun and sudden ionospheric disturbances. Connection between microwave bursts and hard solar radiation (217).
Solar radio emission and magnetic storms with a sudden beginning. Properties of geoeffective corpuscular streams (223).
Radio emission of the Sun and polar blackouts. Connection between continuum-type radio emission and the appearance of energetic particles (230).
General picture of the Sun’s sporadic radio emission (237)

CHAPTER V. RESULTS OF OBSERVATIONS OF RADIO EMISSION OF THE PLANETS AND THE MOON 244

18. First Investigations into the Radio Emission of the Moon,
Planets and Comets 244

First study of the Moon and planets in the radio-frequency band (244).
Radio emission of comets (249)

19. Sporadic Radio Emission of Jupiter 250

Radio emission flux and its time dependence (250).
Frequency spectrum (253).
Polarization (257).
Local sources of sporadic radio emission, their period of rotation and position on Jupiter’s disk (258).
Directional features of radio emission and size of local sources (264).
Connection with solar activity (266)

20. Continuous Radio Emission of the Planets 269

Radio emission of Saturn (269).
Radio emission of Jupiter (270).
Radio emission of Mars (277).
Radio emission of Venus (277).
Radio emission of Mercury (283)

21. Radio Emission of the Moon 283

Preliminary remarks (283).
Frequency spectrum and phase dependence of the Moon’s radio emission (285).
Radio brightness distribution over the lunar disk (292)

CHAPTER VI. PROPAGATION OF ELECTROMAGNETIC WAVES IN THE SOLAR CORONA 297

22. Propagation of Electromagnetic Waves in an Isotropic Coronal
Plasma (approximation of geometrical optics) 298

Quasi-hydrodynamic method and approximation of geometrical optics (298).
Waves in an isotropic plasma (305)

23. Propagation of Electromagnetic Waves in a Magnetoactive
Coronal Plasma (approximation of geometrical optics) 318

Electromagnetic waves in a homogeneous plasma in the presence of a constant magnetic field (318).
Waves in a non-uniform magnetoactive plasma (325).
Faraday effect in the solar corona (329).
Depolarizing factors and the question of elliptical polarization of certain bursts of solar radio emission (334)

24. Coupling of Electromagnetic Waves in a Plasma and Polarization of Solar Radio Emission 342

Limiting polarization of emission leaving the coronal plasma (344).
Preliminary remarks on the effect of the coupling of waves in the region of a quasi-transverse magnetic field (350).
Calculations of coupling by the phase integral method (353).
Certain features of solar radio emission polarization and their interpretation on the basis of wave coupling in the region of a quasi-transverse magnetic field in the corona (365)

25. Coupling of Electromagnetic Waves and the Problem of the
Escape of Radio Emission from the Corona 373

Preliminary remarks (373).
Conversion of plasma waves into electromagnetic waves in a smoothly non-uniform isotropic plasma (376).
Wave coupling in a smoothly non-uniform magnetoactive plasma (385). Conversion of plasma waves into electromagnetic waves because of scattering on electron density fluctuations (391)

CHAPTER VII. GENERATION AND ABSORPTION OF ELECTROMAGNETIC WAVES IN THE SOLAR CORONA 408

26. Emission and Absorption of Electromagnetic Waves in an Equilibrium Plasma 408

Emission transfer equation (408).
Electromagnetic wave emission by individual particles (413). Absorption of electromagnetic waves in an isotropic plasma (430). Absorption of electromagnetic waves in a magnetoactive plasma (440). Gyro-resonance absorption in the solar corona (452)

27. Emission, Absorption and Amplification of Electromagnetic Waves in a Non-equilibrium Plasma 459

The kinetic equation method and the Einstein coefficients method. The problem of wave amplification and instability in a plasma (459)
Reabsorption and amplification of plasma waves in a non-equilibrium plasma with H, = 0 (quantum treatment) (471)
Amplification and instability of plasma waves in a non-equilibrium plasma with H, = 0 (classical treatment) (478)
Maximum amplitude and harmonics of amplified plasma waves (482)
Reabsorption and amplification of electromagnetic waves in a non-equilibrium magnetoactive plasma (487)
The appearance of plasma waves in shock wave fronts (501)

CHAPTER VIII. THEORY OF THE SUN’S THERMAL RADIO EMISSION 508

28. Theory of the “Quiet” Sun’s Radio Emission 511

Radio emission mechanism (511). Theory of the B-component
in the simplest model of the chromosphere and corona (513).
Interpretation of certain features in the distribution of the radio
brightness over the Sun’s disk on the basis of more complex
models of the corona and chromosphere (521). Construction of
a model of the solar atmosphere from radio data (531)

29. Origin of the Slowly Varying Component of the Sun’s Radio
Emission 538

Thermal nature of the S-component of the sporadic radio emission (538)
Bremsstrahlung mechanism of the local S-component sources above spots (542)
Magnetic-bremsstrahlung mechanism of slowly varying emission (551) Origin of radio emission of haloes and local sources above flocculi free of spots (563)

CHAPTER IX. THEORY OF THE SUN’S NON-THERMAL RADIO EMISSION 568

30. Generation of Continuum-type Sporadic Radio Emission 568

Origin of microwave bursts and certain phenomena accompanying them (569).
Origin of the enhanced radio emission connected with sunspots (579).
Mechanism of type IV radio emission (583)

31. Generation of Types I, II and III Bursts 589

Theory of type III bursts (590).
Mechanism of type II bursts (602)
Generation of type I bursts (606)

508 511 538 568 568 589 610

CHAPTER X. ORIGIN OF RADIO EMISSION OF THE PLANETS AND THE MOON 610

32. Hypotheses on the Mechanism of Jupiter’s Sporadic Radio Emission 610

The “thunderstorm” hypothesis (610).
Mechanism of plasma oscillations (612).
Plasma hypothesis of the origin of Jupiter’s radio emission when the planet’s magnetic field is taken into account (616)

33. Origin of the Continuous Radio Emission of Jupiter and Saturn 624

Radiation belts as the source of Jupiter’s decimetric radio emission (629).
Conditions of generation of Saturn’s radio emission (631)

34. Sources of Venus’s Radio Emission 638

The “ionospheric” model (639).
The “hot” surface model (645)

35. Theory of the Moon’s Radio Emission 651

Basic relations (651).
Interpretation of the results of observations of the Moon’s radio emission and the physical characteristics of its surface (657)

REFERENCES 669

INDEX 693

Posted in astronomy, books, electronics, engineering, physics, soviet, technology | Tagged Angular Spectrum, “Quiet” Sun’s Radio Emission, electromagnetic waves, equilibrium plasma, Frequency Spectrum, jupiter's radio emission, Microwave Burst, moon's radio emission, Noise Storms, non-equilibrium plasma, origin of radio emission, plasma, Polarization of Radio Emission, radio astronomy, radio emission, solar activity, solar flares, Sporadic Radio Emission and Geophysical Phenomena, sun spots, sun's radio emission, Sun’s Atmosphere, Type II Bursts, Type III Bursts, Types IV and V Radio Emission, Venus’s Radio Emission | 1 Comment

The Applications Of Continued Fractions And Their Generalizations To Problems In Approximation Theory – Khovanskii

Posted on December 22, 2021 by The Mitr

In this post, we will see the book

The Applications Of Continued Fractions And Their Generalizations To Problems In Approximation Theory by A. N. Khovanskii.

About the book

This book on continued fractions is devoted to certain selected topics in the analytic theory, with particular emphasis on those aspects that deal with rational approximations to functions and with numerical applications and computations. This text contains a tremendous mass of valuable formulas in continued fraction theory. Due to this fact, it can be considered as a useful reference manual for such formulas as well as a text on methods for research in analysis and in computational work.

In the first chapter of the present work a short exposition of the analytic theory of continued fractions is given. Problems in the arithmetic theory of continued fractions are not considered in this book.

The second chapter is devoted to the continued fraction expansion (by the method of Lagrange) of some well known functions. All expansions given in this chapter are special cases of a general expansion derived at the beginning of the chapter.

In the third chapter there is a short consideration of further methods for deriving rational function approximations to functions, leading to a series of approximation formulae for computing certain well known functions.

In the fourth chapter are considered the generalized continued fractions proposed by Euler. Examples are quoted showing the possibility of further generalizations of continued fractions which permit the approximate solution of algebraic equations of arbitrary degree.

The book was translated from Russian by Peter Wynn was published in 1963.

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CHAPTER I
Certain Problems in the Theory of Continued Fractions

§ 1. Convergents 1
§ 2. Transformations of Continued fractions 9
§ 3. The Transformation of Series into Continued Fractions 23
§ 4. General Considerations in the Convergence Theory of Continued Fractions 31
§ 5. Convergence Tests for Continued Fractions with Positive Coefficients 42
§ 6. Convergence Tests for Continued Fractions with Arbitrary Coefficients 46
§ 7. Convergence Tests for Continued Reactions which are Periodic in the Limit 58

CHAPTER II
Continued Fraction Expansions of Certain Functions

§ 1. A Solution of a Certain Riccati Equation with the help of Continued Fractions 76
§ 2. Continued Fraction Expansions. of Binomial Functions 100
§ 3. The Continued Fraction Expansion of $\sqrt[x]{x}$ 109
§ 4. Continued Fraction Expansions of the Natural Logarithm 110
§ 5. Continued Fraction Expansions of $e^{x}$ 112
§ 6. Continued Fraction Expansions of the Inverse trigonometric and Hyperbolic Functions 114
§ 7. Continued Fraction Expansions for $\tan x$ ind $\tanh x$ 122
§ 8. The Continued Fraction Expansion of the Integral $\int_{0}^{x}\frac{dx}{1+x^{k}}$ 125
§ 9. The Solution of the Equations of Boole and Riccati with the help of Continued Fractions 130
§ 10. Continued Fractions and the Hypergeometric Series 133
§ 11. Continued Fraction Expansions of Prym’s Function 142
§ 12. The Continued Fraction Expansion of the Incomplete Gamma-Function 148

CHAPTER III
Further Methods for Obtaining Rational Function Approximations

§ 1. Obreschkoff’s Formula 151
§ 2. The Derivation of Rational Function approximations to Certain Functions with the Help of Obreschkoff’s Formula 155
§ 3. The Solution of Certain Difference Equations with the Help of Continued Fractions 159
§ 4. The Derivation of Rational Function Approximations by means of Iteration 163
§ 5. Table of Approximate Values of $e^{x}$ 165
§ 6. Table of Approximate Values of $\ln x$ 166
§ 7. Table of Approximate Values of $\tan x$ and $\tanh x$ 167
§ 8. Rational Function Approximations for $\sinh x$ and $\sin x$ 167
§ 9. Rational Function Approximations for cosh x and cos x 171
§ 10. Rational Function Approximations to the Error Function 174
§ 11. The Continued Fraction Expansion of Stirling’: 5 Series 175
§ 12. Rational Function Approximations for $\Gamma(1 + x)$ 177

CHAPTER IV
Generalized Continued Fractions

§ 1. The Computation of Square Roots with the Help of Matrices of the Second Order 182
§ 2. The Solution of Quadratic Equations with the Help of Matrices of the Second Order 188
$ 3. The Calculation of Cube Roots with the Help of Matrices 194
§ 4. The Calculation of Fourth Roots with the Help of Matrices 196
§ 5. The Calculation of Roots of Arbitrary Rational Order with the Help of a Matrix 198
§ 6. The Solution of Cubic Equations with the Help of Matrices 199
$ 7. The Solution of Equations of Higher Order with the Help of Matrices 201

LITERATURE IN THE RUSSIAN LANGUAGE ON THE GENERAL THEORY OF CONTINUED FRACTIONS 203

REFERENCES 204

SUPPLEMENTARY REFERENCES 210

INDEX 211

Posted in books, mathematics, soviet | Tagged approximations, binomial function expansion, boole equation, calculations, calculations of roots, continued fractions, Convergence Tests for Continued Fractions, exponential approximation, gamma function, generalized continued fractions, hypergeometric Series, natural logarithm approximation, Obreschkoff's Formula, prym's function, rational function approximations, ricatti equation, series, trigonometric approximations, trigonometric series | 1 Comment

Mathematical Problems: An Anthology ( Pocket Mathematical Library Work Book 3) – Dynkin et al

Posted on December 21, 2021 by The Mitr

In this post, we will see the book Mathematical Problems: An Anthology ( Pocket Mathematical Library Work Book 3) by E. B. Dynkin; S. A. Molchanov; A. L. Rozental; A. K. Tolpygo.

About the book

Regardless of their difficulty, the problems in this collection will all yield to the methods of high school mathematics. No attempt has been made to arrange the problems in order of difficulty, and hence there is no need to solve them consecutively. Thus you can dip into the collection at any point and solve the problems in any order.

If you can’t solve a problem right away, don’t be in a hurry to look up the solution. However, if the problem continues to resist your efforts to solve it, you are then entitled to consult theHints and Answers section. The hints are often brief, but they will be enough to set you on the right track once you have grappled with the problem on your own. The solution should be studied even when you have managed to solve the problem yourself, since it may well turn out that there is an unsuspected gap in your solution. Moreover, the solutions given here often digress and point out interesting side issues.

The book was translated from Russian by Richard Silverman was published in 1969.

Credits to original uploader.

You can get the book here.

Write to us: mirtitles@gmail.com

Fork us at GitLab: https://gitlab.com/mirtitles/

Add new entries to the detailed book catalog here.

Preface vii
Problems 1
Hints and Answers 20
Supplementary Problems 65

Posted in books, mathematics, problem books, soviet | Tagged algebra, area, circles, combinatorics, geometry, high school mathematics, inequalities, mathematics, numbers, pocket mathematical library, polygons, problem book, problems and solutions, series, solid geometry, soviet, triangles | 1 Comment

Learn Limits Through Problems! ( Pocket Mathematical Library Workbook 2) – Gelfand et al.

Posted on December 20, 2021 by The Mitr

In this post, we will see the book Learn Limits Through Problems! ( Pocket Mathematical Library Workbook 2) by S. I. Gelfand; M. L. Gerver; A. A. Kirillov; N. N. Konstantinov; A.G. Kushnirenko.

About the book

This is the second workbook in the Pocket Mathematical Library. It is essentially a programmed text inviting you to learn about limits (a key concept of modern mathematics) by solving a series of 56 problems and reading a little interspersed text. The problems are for the most part equipped with hints and answers (or both), enough for you to get the hang of them (harder problems are marked with asterisks). Moreover, the problems fall into three groups. The first, called “Preliminaries,” puts you into the right frame of mind for absorbing the limit concept. The second, called “Concepts,” presents the irreducible amount of theoretical material needed to understand limits. The third, called “Calculations,” shows you how to evaluate limits once you know what they are.

The core of the book is really the section called “Solutions,” where all 56 problems are worked out in full detail. This section should be read carefully after you have tried solving the problems on your own. Please do not give up too soon, since this will only defeat the purpose of the book.

When you are satisfied that you have mastered the subject matter of the book, try solving the 11 problems in the section called “Test Problems.” These problems make up a little open- book examination, on which you should easily get a passing grade. Otherwise figure out where things went wrong and fill in the gaps in your knowledge. Don’t despair, because nobody finds the notion of a limit easy the first time around. Bon voyage!

The book was translated from Russian by Richard Silverman and was published in 1969.

Credits to original uploader.

You can get the book here.

Write to us: mirtitles@gmail.com

Fork us at GitLab: https://gitlab.com/mirtitles/

Add new entries to the detailed book catalog here.

Preface vii

Problems 1

Group 1 (Preliminaries) 1
Group 2 (Concepts) 6
Group 3 (Calculations) 14

Solutions 22
Test Problems 69

Posted in books, mathematics, problem books, soviet | Tagged analysis, bolzano-weierstrass axiom, conceptual problems, continuity, definitions, evaluating limits, high school mathematics, limits, limits examples, pocket mathematical library, problem book, problems and solutions, soviet education, travelling problems | Leave a comment

About the book

About the book

Contents

The Entropy Concept in Probability Theory

# 1. Entropy of Finite Schemes 2

# 2. The Uniqueness Theorem 9

# 3. Entropy of Markov chains 13

# 4. Fundamental Theorems 16

#5. Application to Coding Theory 23

On the Fundamental Theorems of Information Theory

INTRODUCTION: 30

CHAPTER I. Elementary Inequalities 34

# 1. Two generalizations of Shannon’s inequality 34

# 2. Three inequalities of Feinstein 39

CHAPTER II. Ergodic Sources 44

# 3. Concept of a source. Stationarity. Entropy. 44

# 4. Ergodic Sources 49

#5. The E property. McMillan’s theorem. 54

# 6. The martingale concept. Doob’s theorem. 58

% 7. Auxiliary propositions 64

# 8. Proof of McMillan’s theorem 70

CHAPTER III. Channels and the sources driving them 75

# 9. Concept of channel. Noise. Stationarity. Anticipation 75

#10. Connection of the channel to the source 78

#11. The ergodic case 85

CHAPTER IV. Feinstein’s Fundamental Lemma 90

#12. Formulation of the problem 90

#13. Proof of the lemma 93

CHAPTER V. Shannon’s Theorems 102

# 14. Coding 102

# 15. The first Shannon theorem 104

#16. The second Shannon theorem 109

About the book

Contents

Chapter I. Introduction

Chapter II. Geometry and Kinematics of the Phase Space

Chapter III. Ergodic Problem

Chapter IV. Reduction to the Problem of the Theory of Probability

Chapter V. Application of the Central Limit Theorem

Chapter VI. Ideal Monatomic Gas

Chapter VII. The Foundation of Thermodynamics

Chapter VIII. Dispersion and the Distributions of Sum Functions

About the book

Contents

PART ONE OPENING UP OF MINERAL DEPOSITS

Chapter I. Basic Concepts and Terminology 15

Chapter II. Opening Up of Coal and Other Stratified Deposit 30

Chapter III. Opening up of Ore Deposits 96

Chapter IV. Choice of site for shafts 109 Chapter V. Surface Plants and Structures of a Mine 125

Chapter VI. Shaft Stations. 136

PART II UNDERGROUND MINING OF MINERAL DEPOSITS

Chapter VII. Basic Concepts and Terminology 155

Chapter VIII. Filling 161

Chapter IX. Choice of mining methods and modes of extraction 187

Chapter X. General Surveyor Coal Seam Mining Methods 217

Chapter XI. Stoping in a Continuous Face 223

Chapter XII. Continuous Methods of Mining 312

Chapter XIII. Pillar Methods of Alining 337

Chapter XV. Mining of Thick Seams 364

Chapter XVI Underground Gasification of Coal 426

Chapter XVII. Hydraulic Mining of Coni 430

Chapter XVIII. Methods of Mining Rock and Potash Sails 437

Chapter XIX. Choice of Methods for Mining Ore Deposits 408

Chapter XX. Mining of Thin and Medium-Thick Ore Deposits 470

Chapter XXI. Methods of Mining Thick Ore Deposits 506

Chapter XXII. Mining of Contiguous Beds 560

Chapter XXIII. Effects of Underground Excavations on the Ground Surface 572

Chapter XXIV. Classification and Choice of Mining Methods 584

PART THREE OPEN-CUT MINING

Chapter XXV. Basic Definitions and Terminology 593

Chapter XXVI Equipment and Layouts of Open Pits 609

Subject Index 677

About the book

Contents

INTRODUCTION

CHAPTER I PRELIMINARY CONCEPTS OF THE THEORY OF PROBABILITY

CHAPTER II PRELIMINARY CONCEPTS OF QUANTUM MECHANICS

CHAPTER III GENERAL PRINCIPLES OF QUANTUM STATISTICS

CHAPTER IV THE FOUNDATIONS OF THE STATISTICS OF PHOTONS

CHAPTER V FOUNDATIONS OF THE STATISTICS OF MATERIAL PARTICLES

Chapter IV. Reduction to the Problem of the Theory of
Probability

PART ONE
OPENING UP OF MINERAL DEPOSITS

Chapter IV. Choice of site for shafts 109
Chapter V. Surface Plants and Structures of a Mine 125

PART II
UNDERGROUND MINING OF MINERAL DEPOSITS

PART THREE
OPEN-CUT MINING

CHAPTER I
PRELIMINARY CONCEPTS OF THE THEORY OF PROBABILITY

CHAPTER II
PRELIMINARY CONCEPTS OF QUANTUM MECHANICS

CHAPTER III
GENERAL PRINCIPLES OF QUANTUM STATISTICS

CHAPTER IV
THE FOUNDATIONS OF THE STATISTICS OF PHOTONS

CHAPTER V
FOUNDATIONS OF THE STATISTICS OF MATERIAL PARTICLES

CHAPTER VI
THERMODYNAMIC CONCLUSIONS

CHAPTER II. BASIC CHARACTERISTICS OF EXTRATERRESTRIAL RADIO
EMISSION AND METHODS FOR STUDYING THEM 20

CHAPTER I
Certain Problems in the Theory of Continued Fractions

CHAPTER II
Continued Fraction Expansions of Certain Functions

CHAPTER III
Further Methods for Obtaining Rational Function Approximations

CHAPTER IV
Generalized Continued Fractions

Preface vii
Problems 1
Hints and Answers 20
Supplementary Problems 65

Group 1 (Preliminaries) 1
Group 2 (Concepts) 6
Group 3 (Calculations) 14

Solutions 22
Test Problems 69