इवान – बोगोमोलोव (Ivan – Bogomolov Marathi/Hindi)

Posted on May 8, 2022 by The Mitr

In this post, we will see the Marathi book Ivan by V.  Bogolomov

इवान  व्लादिमीर बोगोमोलोव

About the book

A Soviet Novel in Marathi for children. Set during the Second World War. A nice summary is given here. The book was also adapted into a movie Ivan’s Childhood which was directed by great Russian director Andrei Tarkovsky.

The book was translated from Russian by Anil Havaldar and designed by S. A. Barabash. The illustrations are by Orest Veryesky. The book was published in 1987 by Lokwangmay Gruh, orginally Raduga 1987.

 

PS: There is a Hindi version too. Do post in the comments if you know of any other translations.

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Fun With Numbers – Stepnova

Posted on May 7, 2022 by The Mitr

In this post, we will see the book Fun With Numbers by I. Stepnova.

About the book

This is a small book to teach children numbers and arithmetic operations on them. The book uses variety of contexts and situations to present exercises in numbers.

The book was translated from Russian by was published in 198? by Raduga Publishers. The illustrations are by B Rytman. The present scan is a reprint from Visalaandhra Publishing House in 2005. Unfortunately the illustrations are in black and white in VPH copy, so they are in the scan. If anyone has the original Raduga copy, please consider scanning it.

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Commutative Normed Rings – Gelfand, Raikov, Shilov

Posted on May 6, 2022 by The Mitr

In this post, we will see the book Commutative Normed Rings by I. Gelfand; D. Raikov; G. Shilov.

About the book

The present book gives an account of the theory of commu­tative normed rings with applications to analysis and topology. The paper by I. N. Gelfand and M. A. Naimark Normed Rings with an Involution and their Representations, which is presented here as Chapter VIII, may serve as an intro­duction to the theory of non-commutative normed rings with an involution.
The book is addressed to mathematicians—students in ad­vanced courses, research students, and scholars—who are interested in functional analysis and its applications.

The book was translated from Russian and  was published in 1964.

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Contents

PART ONE

I. THE GENERAL THEORY OF COMMUTATIVE NORMED RINGS 15

§ 1. The Concept of a Normed Ring 15
§ 2. Maxiimal Ideals 20
§ 3. Abstract Analytic Functions 27
§ 4. Functions on Maximal Ideals. The Radical of a Ring 30
§ 5. The Space of Maximal Ideals 37
§ 6. Analytic Functions of an Element of a Ring 46
§ 7. The Ring R of Functions x(M) 51
§ 8. Rings with an Involution 56

 

II. THE GENERAL THEORY OF COMMUTATIVE NORMED RINGS (cont’d)66

§ 9. The Connection between Algebraic and Topological Isomorphisms 66
§ 10. Generalized Divisors of Zero 69
§ 11. The Boundary of the Space of Maximal Ideals 73
§ 12. Extension of Maximal Ideals 78
§ 13. Locally Analytic Operations on Certain Elements of a Ring 80
§ 14. Decomposition of a Normed Ring into a Direct Sum of Ideals 94
§ 15. The Normed Space Adjoint toa Normed Ring 97

PART TWO

III. THE RING OF ABSOLUTELY INTEGRABLE FUNCTIONS AND
THEIR DISCRETE ANALOGUES 100

§ 16. The Ring V of Absolutely Integrable Functions on the Line 100
§ 17. Maximal Ideals of the Rings V and V+ 106
§ 18. The Ring of Absolutely Integrable Functions With a Weight 113
§ 19. Discrete Analogues to the Rings of Absolutely Integrable
Functions 116

IV. HARMONIC ANALYSIS ON COMMUTATIVE LOCALLY COMPACT GROUPS 121

§ 20. The Group Ring of a Commutative Locally Compact Group 123
§ 21. Maximal Ideals of the Group Ring and the Characters of
a Group 129
§ 22. The Uniqueness Theorem for the Fourier Transform and the Abundance of the Set of Characters 135
$ 23. The Group of Characters 141
§ 24. The Invariant Integral on the Group of Characters 144
§ 25. Inversion Formulas for the Fourier Transform 151
§ 26. The Pontrjagin Duality Law 156
§ 27. Positive-Definite Functions 159

V. THE RING OF FUNCTIONS OF BOUNDED VARIATION ON A LINE 165

§ 28. Functions of Bounded Variation on a Line 165
§ 29. The Ring of Jump Functions 167
§ 30. Absolutely Continuous and Discrete Maximal Ideals of the Ring) 176
§ 31. Singular Maximal Ideals of the Ring V^(b) 180
§ 32. Perfect Sets with Linearly Independent Points. The Asymmetry of the Ring V^(b) 187
§ 33. The General Form of Maximal Ideals of the Ring V^(b) 192

PART THREE

VI. REGULAR RINGS 197

§ 34. Definitions, Examples, and Simplest Properties 197
§ 35: The Local Theorem 200
§ 36. Minimal Ideals 204
§ 37. Primary Ideals 205
§ 38. Locally Isomorphic Rings 207
§ 39. Connection between the Residue-Class Rings of Two Rings of Functions, One Embedded in the Other 210
§ 40. Wiener’s Tauberian Theorem 213
§ 41. Primary Ideals in Homogeneous Rings of Functions 214
§ 42. Remarks on Arbitrary Closed Ideals. An Example of L. Schwartz 219

VII. RINGS WITH UNIFORM CONVERGENCE 223

§ 43. Symmetric Subrings of C(S) and Compact Extensions of Space S 223
§ 44. The Problem of Arbitrary Closed Subrings of the Ring C(S) 227
§ 45. Ideals in Rings with Uniform Convergence 234

VII. NORMED RINGS WITH AN INVOLUTION AND THEIR REPRESENTATIONS 240

§ 46. Rings with an Involution and their Representations 241
§ 47. Positive Functionals and their Connection with Representations Of Rings 244
§ 48. Embedding of a Ring with an Involution in a Ring of Operators 251
§ 49. Indecomposable Functionals and Irreducible Representations 255
§ 50. The Case of Commutative Rings 259
§ 51. Group Rings 263
§ 52. Example of an Unsymmetric Group Ring 268

IX. THE DECOMPOSITION OF A COMMUTATIVE NORMED RING INTO A DIRECT SUM OF IDEALS 275

§ 53. Introduction 275
§ 54. Characterization of the Space of Maximal Ideals of a Commutative Normed Ring 277
§ 55. A Problem on Analytic Functions in a Finitely Generated Ring 278
§ 56. Construction of a Special Finitely Generated Subring 282
§ 57. Proof of the Theorem on the Decomposition of a Ring
into a Direct Sum of Ideals 285
S56. Some Corollaries 285

HISTORICO-BIBLIOGRAPHICAL NOTES 291
BIBLIOGRAPHY 295
INDEX 303

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Mathematical Analysis – Differentiation and Integration – Aramanovich et al

Posted on May 5, 2022 by The Mitr

In this post, we will see the book Mathematical Analysis – Differentiation And Integration
by I. G. Aramanovich; R.S.Guter; L.A.Lyusternik; I.L. Raukhvarger; M. I. Skanavi; A. R.Yanpol’skii.

 

About the book

The present volume of the series in Pure and Applied Mathe­matics is devoted to two basic operations of mathematical analysis — differentiation and integration. It discusses the complex of problems directly connected with the operations of differentiation and integration of functions of one or several variables, in the classical sense, and also elementary generalizations of these operations. Further generalizations will be given in subsequent volumes of the series, volumes devoted to the theory of functions of real variables and to functional analysis.
Together with an earlier volume in the series, volume 69, L. A. Lyusternik and A. R. Yanpol’skii, Mathematical Analysis (Functions, Limits, Series, Continued Fractions), the present one includes material for a course of mathematical analysis, which is treated in a logically connected manner, briefly and without proofs, but with many examples worked in detail.

The book was translated from Russian by H. Moss and edited by I. N. Sneddon and was published in 1965.

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Contents

CHAPTER I. DIFFERENTIATION OF FUNCTIONS OF ONE VARIABLE 1

CHAPTER II. DIFFERENTIATION OF FUNCTIONS OF n VARIABLES 46

CHAPTER III. COMPOSITE AND IMPLICIT FUNCTIONS OF n VARIABLES 76

CHAPTER IV. SYSTEMS OF FUNCTIONS AND CURVILINEAR COORDINATES IN A PLANE AND IN SPACE 99

CHAPTER V. INTEGRATION OF FUNCTIONS 135

CHAPTER VI. IMPROPER INTEGRALS. INTEGRALS DEPENDENT ON A PARAMETER. STIELTJES’ INTEGRAL 135

CHAPTER VII. THE TRANSFORMATION OF DIFFERENTIAL AND INTEGRAL EXPRESSIONS 226

APPENDICES 257

REFERENCES 309

INDEX 311

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Mathematical Analysis – A Brief Course For Engineering Students – Bermant, Aramanovich

Posted on May 4, 2022 by The Mitr

In this post, we will see the book Mathematical Analysis – A Brief Course For Engineering Students by A.F . Bermant; I. G. Aramanovich.

About the book

This course is designed as a textbook for engineering students. It embraces the topics in mathematical analysis usually included into curricula of technical colleges. The course also contains some optional material which may be omitted in a first reading of the book; the corresponding items are marked with the asterisk.
There are a number of courses dealing with special divisions of mathematical analysis, such as equations of mathematical physics, functions of a complex argument and the like, and therefore, although these divisions are important for mathematical education of an engineer, they are not treated in this book. We also draw attention to the fact that only a few questions related to approximate calculations and programming (e.g. the applica­tion of the differential to approximate calculations, methods of approximate solution of equations, numerical integration and solution of differential equations, etc.) are discussed in this course. For a thorough study of this subject some other textbooks should be used.
In this course many examples are given which demonstrate the application of mathematical analysis to various divisions of mechanics and physics. The study of these examples is very impor­tant since the main interest of an engineer lies in solving concrete applied problems. At the end of each chapter we give a number of questions aimed at checking the understanding of the theore­tical material. In the presentation of the material the main emphasis has been laid upon practical aspects, and some purely mathematical facts are given without proof. On the other hand, in some cases detailed proofs of theorems are given, especially when this elucidates the meaning of the theorem and shows in which way it can be applied. Besides, the study of the proofs helps the student to acquire practice in logical argument and provides prerequisites for further mathematical self-education.

The book was translated from Russian by was published in 1986  by Mir Publishers.

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Contents

(The starred items indicate the sections that may
be omitted in a first reading of the book)

Preface 5
Introduction 15

1. The Subject of Mathematical Analysis 15
2. Variables and Functions 15
3. The Role of Mathematics and Mathematical Analysis in Natural Sciences and Engineering 16

CHAPTER I. FUNCTION 19

§ 1. Real Numbers 19
§ 2. The Concept of Function 26
§ 3. Characteristics of Behaviour of Functions. Some Important Examples 38
§ 4. Inverse Function. Power, Exponential and Logarithmic Function 51
§ 5. Trigonometric, Inverse Trigonometric, Hyperbolic and Inverse
Hyperbolic Functions. 60

CHAPTER II. LIMIT. CONTINUITY 72

§ 1. Limit. Infinitely Large Magnitudes 72
§ 2. Continuous Functions 98
Oo. CONUIAUIN ai ads Sa aca & ee Ss ae ee eee ee :
§ 3. Comparison of Infinitesimals. Comparison of Infinitely Large
Magnitudes 109

CHAPTER III. DERIVATIVE AND DIFFERENTIAL. DIFFERENTIAL CALCULUS 118

§ 1. Derivative 118
§ 2. Differentiating Functions 126
§ 3. Some Geometrical Problems. Graphical Differentiation 148
§ 4. Differential 155
§ 5. Derivatives and Differentials of Higher Orders 167

CHAPTER IV. APPLICATION OF DIFFERENTIAL CALCULUS TO INVESTIGATION OF BEHAVIOUR OF FUNCTIONS 175

§ 1. Theorems of Fermat, Rolle, Lagrange and Cauchy 175
§ 2. Investigating Functions wita the Aid of First and Second Derivatives 181
§ 3. L’Hospital’s Rule. General Scheme for Investigating Functions 204
§ 4. Curvature 219
§ 5. Space Curves. Vector Function of a Scalar Argument 225
§ 6. Complex Functions of a Real Argument 237
§ 7. Solution of Equations 245
QUESTIONS 255

CHAPTER V. INTEGRAL CALCULUS 258

§ 1. Indefinite Integral 258
§ 2. Definite Integral 291
§ 3. Methods of Evaluating Definite Integrals. 318
§ 4. Improper Integrals 331

CHAPTER VI. APPLICATION OF INTEGRAL CALCULUS 345

§ 1. Some Problems of Geometry and Statics 345
§ 2. General Scheme of the Application of the Integral 358

CHAPTER VII. FUNCTIONS OF SEVERAL VARIABLES AND THEIR DIFFERENTIATION 365

§ 1. Functions of Several Variables 365
§ 2. Derivatives and Differentials. Differential Calculus 376
§ 3. Applications of Differential Calculus to Geometry 409
§ 4. Extrema of Functions of Two Variables 414
§ 5. Scalar Field 427

CHAPTER VIII. DOUBLE AND TRIPLE INTEGRAL 437

§ 1. Double Integrals 437
§ 2. Triple Integrals 459
§ 3. Integrals Dependent on Parameters 471

CHAPTER IX. LINE INTEGRALS AND SURFACE INTEGRALS. FIELD THEORY 482

§ 1. Line Integrals 482
§ 2. Surface Integrals 515
§ 3. Field Theory 533
Questions 561

CHAPTER X. DIFFERENTIAL EQUATIONS 564

§ 1. Differential Equations of the First Order 564
§ 2. Differential Equations of the Second and Higher Orders 592
§ 3. Linear Differential Equations 603
§ 4. Systems of Differential Equations 635
QUESTIONS 656

CHAPTER XI. SERIES 659

§ 1. Numerical Series 659
§ 2. Functional Series 678
§ 3. Power Series 684
§ 4. Expanding Functions into Power Series 691
§ 5. Some Applications of Taylor’s Series 706
§ 6*. Some Further Topics in the Theory of Power Series 716
Questions 721

CHAPTER XII. FOURIER SERIES AND FOURIER INTEGRAL. 724

§ 1. Fourier Series 724
§ 2. Some Further Topics in the Theory of Fourier Series 746
§ 3. Fourier-Integral 753
Questions 761

Table of Integrals 762

Bibliography 768

Name Index 770

Subject Index 772

 

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An Introduction To The Theory Of Plasma Turbulence – Tsytovich

Posted on May 3, 2022 by The Mitr

In this post, we will see the book An Introduction To The Theory Of Plasma Turbulence
by V. N. Tsytovich.

About the book

This book is based upon lectures given by Professor Tsytovich at Culham Laboratory. The preceding text can only represent the present state of the development of the theory of plasma turbulence. The author has tried to follow the logic, but not the history of this field and, therefore, the references are very fragmented and not by any means complete. The essential physical statements that the author wants to emphasise finally are:

  1. The plasma properties in the turbulent region are mostly non-linear. This raises the possibility of universal plasma properties like a universal spectrum that can be independent of the type of instability.

  2. Nevertheless, the turbulence is often weak: W/nT << 1, and when describing the properties of the turbulent oscillation interactions it is not possible to expand the non-linear interactions in terms of the turbulent energy. The elementary excitations such as plasmons and “dressed” particles have thus a finite lifetime which is connected with their non­-linear interactions.

  3. The small low-frequency perturbations in a turbulent plasma have quite a different nature because of the frequent turbulent collisions, and the dielectric constant that describes such perturbations cannot be expanded in terms of the turbulent energy.

  4. The development of a turbulent state is very probable for a plasma as a result of the fact that the energy applied has a tendency to disperse to the greatest possible degree of freedom. Innumerable numbers of different plasma instabilities can bring the plasma to a turbulent state. The plasmas in astrophysical conditions must, therefore, often be turbulent. This can lead to a way of explaining cosmic-ray origins with a universal power-type spectrum.

  5. The development of plasma turbulence can occur as a result of development, firstly, of one or a small number of collective modes, with a subsequent spread of the energy to other modes by non-linear inter­actions as well as by the excitation of many modes at the first stage. For the case of the excitation of one mode, the first stage is not turbulent and the turbulence develops as the energy is spread, if the system is ergodic. The plasma collective motions seem to be the best test for an investigation of the general problems of the development of the random­isation process, as well as of the general problems of the possibility of a statistical description of a system.

The book was translated from Russian and was published in  1972.

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Contents

 

1. Comparison of plasma and liquid turbulence 1
2. General Problems of the Theory of Plasma Turbulence 14
3. The Balance Equation for a Turbulent Plasma 27
4. Turbulent Collisions and Resonance Broadening 44
5. The Spectrum and Correlation Functions of Ion-sound Turbulence 62
6. The Spectrum and Correlation Functions of Langmuir Turbulence 74
7. Electromagnetic Properties of a Turbulent Plasma 93
8. The Cosmic-ray Spectrum 105

Conclusions 128

References 130

Index 133

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Method Of Edge Waves In The Physical Theory Of Diffraction – Ufimtsev

Posted on May 2, 2022 by The Mitr

In this post, we will see the book Method Of Edge Waves In The Physical Theory Of Diffraction by P. Ya. Ufimtsev.

About the book

The book is a monograph written as a result of research by the author. The diffraction of plane electromagnetic waves by ideally conducting bodies, the surface of which have discontinuities, is investigated in the book. The linear dimensions of the bodies are assumed to be large in comparison with the wavelength. The method developed in the book takes into account the perturbation of the field in the vicinity of the surface discontinuity and allows one to substantially refine the approximations of geometric and physical optics. Expressions are found for the fringing field in the distant zone. A numerical calculation is performed of the scattering characteristics, and a comparison is made with the results of rigorous theory and with experiments. The book is intended for physicists and radio engineers who are interested in diffraction phenomena, and also for students of advanced courses and aspirants who are specializing in antennas and the propagation of radio waves.

The book was translated from Russian and was published in 1962  by Foreign Technology Division of USA.

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Contents

FOREWORD

INTRODUCTION

CHAPTER I. DIFFRACTION BY A WEDGE 1

§ 1. The Rigorous Solution 1
§ 2. Asymptotic Expressions 12
§ 3. The Physical Optics Approach 18
§ 4. The Field Radiated by the Nonuniform part of the Current 26
§ 5. The Oblique Incidence of a Plane Wave on a Wedge 32
§ 6. Diffraction by a Strip 35

CHAPTER II. DIFFRACTION BY A DISK 43

§ 7. The Physical Optics Approach 43
§ 8. The Field from the Uniform Part of the Current 48
§ 9. The Total Field Being Scattered by a Disk with Normal Irradiation 52
§ 10. The Physical Optics Approach 54
§ 11. The Field Radiated the Nonuniform Part of the Current 57
§ 12. The Scattering Characteristics: with an Arbitrary Irradiation66

CHAPTER III. DIFFRACTION BY A FINITE LENGTH CYLINDER 73

§ 13. The Physical Optics Approach 74
§ 14. The Field Created by the Nonuniform Part of the Current 80
§ 15. The Total Fringing Field 83

CHAPTER IV. DIFFRACTION OF A PLANE WAVE INCIDENT ALONG THE SYMMETRY AXIS OF FINITE BODIES OF ROTATION 90

§ 16. The Field Created by the Nonuniform Part of the Current 90
§ 17. A Cone 95
§ 18. A Paraboloid of Rotation 103
§ 19. A Spherical Surface 108

CHAPTER V. SECONDARY DIFFRACTION 114

§ 20. Secondary Diffraction by a Strip. Formulation of the Problem 115
§ 21. Secondary Diffraction by a Strip (H-Polarization) 118
§ 22. Secondary Diffraction by a Strip (E-Polarization) 126
§ 23. The Scattering Characteristics of a Plane Wave by a Strip 129
§ 24. Secondary Diffraction by a Disk 138
§ 25. A Brief Review of the Literature 154

CHAPTER VI. CERTAIN PHENOMENA CONNECTED WITH THE NONUNIFORM PART OF THE SURFACE CURRENT 163

§ 26. Measurement of the Field Radiated by the Nonuniform part of the Current 163
§ 27. Reflected Wave Depolarization 170

CHAPTER VII. DIFFRACTION BY A THIN CYLINDRICAL CONDUCTOR 175

§ 28. Current Waves in an Ideally Conducting Vibrator 176
§ 29. Radiation of a Transmitting Vibrator 183
§ 30. Primary and Secondary Diffraction by a Passive Vibrator 185
§ 31. Multiple Diffraction of Edge Waves 193
§ 32. Total Fringing Field 196
§ 33. A Vibrator Which is Short in Comparison with the Wavelength (a Passive Dipole) 204
§ 34. The Results of Numerical Calculations 208

CONCLUSION 217
REFERENCES 221

 

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Diseases Of The Ear, Nose And Throat – Likhachev

Posted on May 1, 2022 by The Mitr

In this post, we will see the book Diseases Of The Ear, Nose And Throat by A. Likhachev.

About the book

The present text-book of otorhinolaryngology is intended for secondary medical schools and gives the most essential theoretical and practical information needed by the junior medical personnel engaged in independent practice.
It is calculated to enable the junior medical personnel, employed as assistant physicians in medic”al institutions or working on their own, to diagnose typical diseases of the ear, nose and throat, prescribe and give correct treatment, and if need he, render first aid to the patient.
Before discussing the clinical aspects of diseases of the ear, nose and throat, we deem it necessary to give a concise description of the anatomy and physiology of these organs, which should considerably facilitate the clinical study.
Special attention is devoted to early diagnosis of ear, nose and throat diseases, which is very important for both treatment and prophylaxis.

The book was translated from Russian (translators name is not given) was published in 1955 by Foreign Languages Publishing House.

Original scan from Digital Library of India.

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Contents

Preface 7

DISEASES OF THE EAR 11

Anatomy of the Ear 11
Physiology of the Ear 22
Examination of the Ear 27
General Methods of Nursing and Treatment of Ear diseases 37
Diseases of the External Ear 42
Inflammations of the Middle Ear
Intracranial Complications of Suppurative Otitis 83
Nonsuppurative Diseases of the Middle and Internal Ear 88
Deaf-Mutism 97
Traumatic Lesions of the Ear 99
Occupational Diseases of the Ear 102

DISEASES OF THE NOSE, PHARYNX AND LARYNX 106

Diseases of the Nose and Paranasal Sinuses 106

Anatomy of the Nose 106
Physiology of the Nose 111
General Methods of Treatment in Nasal Diseases 116
Diseases of the External Nose 120
Acute Inflammations of the Nose 133
Chronic Inflammations of the Nose (Chronic Rhinitis) 138
Vasomotor or Allergic Rhinitis 145
Disturbances of the Sense of Smell 147
Neoplasms in the Nose 148
Acute and Chronic Diseases of Paranasal Sinuses 150

Diseases of the Pharynx 161

Anatomy of the Pharynx 161
Physiology of the Pharynx 163
Methods of Examining the Pharynx 164
Acute Inflammations of the Pharynx 172
Chronic Inflammations of the Pharynx 194
Benign Tumours of the Pharynx 198
Malignant Tumours of the Pharynx 200

Diseases of the Larynx 202

Anatomy of the Larynx 202
Methods of Examining of the Larynx 205
General Methods of Treatment in Laryngeal Diseases 207
General Symptoms of Laryngeal Diseases 210
Acute Laryngitis 211
Chronic Laryngitis 213
Laryngeal Perichondritis 215
Benign Tumours of the Larynx 215
Malignant Tumours of the Larynx 217
Acute and Chronic Stenoses of the Larynx 218
Motor Disorders of the Larynx 221
Tuberculosis of the Upper Respiratory Tract 223
Syphilis of the Upper Respiratory Tract 227
Scleroma 232

Diseases of the Trachea 234

Anatomy of the Trachea 234
Tracheobronchoscopy 234
Intubation 237
Tracheotomy 238
Foreign Bodies in the Larynx, Trachea and Bronchi 245
Traumatic Lesions of the Upper Respiratory Tract 247
Occupational Diseases of the Upper Respiratory Tract 255

Diseases of the Esophagus 260

Anatomy of the Esophagus 260
Methods of Examining the Esophagus 260
Burns and Strictures of the Esophagus 261
Foreign Bodies of the Esophagus 262
Cancer of the Esophagus 263

Supplement: Health Education 265

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Ten Decimal Tables – Lyusternik (Ed.)

Posted on April 30, 2022 by The Mitr

In this post, we will see the book Ten Decimal Tables Of The Logarithms Of Complex Numbers And For The Transformation From Cartesian To Polar Coordinates
edited by L. A. Lyusternik.

About the book

The present tables were compiled in the Department for Approximate Computations of the Institute of Exact Mechanics and Computational Methods of the U.S.S.R. Academy of Sciences. The computations were carried out by this department in conjunction with the Computational- Experimental Laboratory of the Institute.

The book was translated from Russian by D. E. Brown and was published in 1965.

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Qualitative Methods In The Many Body Problem – Khilmi

Posted on April 29, 2022 by The Mitr

In this post, we will see the book Qualitative Methods In The Many Body Problem by G. F. Khilmi.

About the book

The n-body problem is the name usually given to the problem of the motion of a system of many particles attracting each other according to Newton’s law of gravitation. This is the classical problem of mathematical natural science, the significance of which goes far beyond the limits of its astronomical applications.

The n-body problem has been the main topic of celestial mechanics from the time of its inception as a science. Now that many of the problems of celestial mechanics have become part of geophysics, the central position of the w-body problem has been further strengthened.

The fundamental dynamical problem for a system of n gravitating bodies is the investigation and predetermina­tion of the changes in position and velocity that the particles undergo as the time varies. However, this is a very complex non-linear problem whose solution has not been possible under the present-day status of mathematical analysis.

In the first chapter, we give the equations and general integrals of the n-body problem, and we study the simplest theorems on the final motion due to Jacobi.

In the second chapter, we consider means of applying the method of dimensional analysis to the n-body problem. As far as we know, dimensional analysis has not been used before in the investigation of the final motion; though it does not yield definitive results in this area, it is very use­ ful in carrying out a preliminary analysis of the problem.

In the third chapter, we present our “method of continuous induction” and we consider some applications of it in which the final motion in the n-body problem is analyzed. This method allows us to obtain effective qualitative results, namely, it allows us to formulate suffi­cient conditions for the occurrence of certain types of final motions in the form of conditions on the initial state of the dynamical system.

The fourth chapter is devoted to the method of invariant measure. The application of this method to the many-body problem has necessitated working out a number of theorems on the measure theory of dynamical systems. These are presented at the beginning of the chapter. At the end of the chapter, we prove some very general theorems on the motion of a system of gravitating bodies using the method of invariant measure.

In the fifth chapter, an attempt is made to analyze some cases of the evolution of a system of n gravitating bodies on the basis of celestial mechanics. Here, we shall be concerned with the processes which are of cosmogonical interest, and which are accompanied by the conversion of mechanical energy into non-mechanical forms.

The book was translated from Russian by B. D. Seckler and was published in 1961.

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Contents

CHAPTER 1. Equations and general integrals of the n-body problem. Simplest theorems on the final motion 1

CHAPTER 2. Method of dimensional analysis 15

CHAPTER 3. Method of continuous induction 27

CHAPTER 4. Method of invariant measure 61

CHAPTER 5. Analysis of some cases of the evolution of a system of gravitating bodies 97

Bibliography 113
Index 117

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