A Short Handbook of Heat Treatment – Kamenichny

Posted on January 24, 2022 by The Mitr

In this post, we will see A Short Handbook Of Heat Treatment by I. Kamenichny .

About the book

The present hand book aims at giving the operating personnel of heat-treatment shops a reference book which would serve to overcome difficulties arising in everyday practice.

The handbook describes heat-treatment charts, heat-treatment procedures for tools, parts of lathes, automobiles, and agricultural machinery.

In addition the handbook deals briefly with the following subjects: quality control of metals before and after heat-treatment; heat-treatment and case-hardening of steel; heat-treatment of cast iron, non-ferrous metals, and alloys. The book also contains some practical hints on safety engineering.

The book was translated from Russian by I. Savin and designed V. Novoselova. The book was published in 1969 by Peace Publishers.

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Preface 5

Chapter I. Physical Characteristics 7

1. Mechanical Characteristics 7
2. Thermal Characteristics 8
3. Electrical Characteristics 9
4. Some Properties of Elements and Materials Dealt with in Heat-treatment of Metals 10

Chapter II. Quality Control of Metals 13

1. Hardness 13
2. Detection of Cracks in Metals 22
3. Approximate Determination of Steel Composition 94

Chapter III. Steel 26

1. Constituents of Steel 26
2. Structure of Iron and Steel. Equilibrium Diagram of Iron-carbon Alloys 26
3. Alloying Elements and Their Effect on the Properties of Steel 31
4. Chemical Composition and. ‘Hardness of Market Steels 31
5. Common Uses of Various Grades of Steels and Alloys 61

Chapter IV. Heat-treatment of Steel 74

1. Heating of Steel 74
2. Oxidation and Decarburisation on Heating 76
3. Annealing 78
4. Normalising 81
5. Hardening 81
6. Tempering 93

Chapter V. Case-hardening 104

1. Carburising 104
2. Nitriding 113
3. Cyaniding 116
4. Calorising 122
5. Sulphiding (sulphating) 122
6. Cleaning and Pickling of Articles after Heat-treatment 128
7. Anticorrosion Protection for Articles after Heat-treatment 129

Chapter VI. Heat-treatment Technology 130

1. Approximate Heat-treatment Schedules and Mechanical Properties of Various Grades of Steels 130
2. Practical Hints on Heat-treatment of Articles 161

Chapter VII. Heat-treatment of Cast Iron 197

Chapter VIII. Heat-treatment of Non-ferrous Metals 201

Chapter IX. Forging of Ferrous and Non-ferrous Metals 203

1. Forging of Steel 223
2. Forging of Non-ferrous Metals 230

Chapter: X. Manufacture of Built-up Cutting Tools 234

Chapter: XI. Equipment, Fuel and Accessory Materials for Heat-treatment 243

1. Furnaces 243
2. Refractories 252
3. Fuel 252
4. Temperature Control Instruments 254

Chapter: XII. Safety Engineering 268

INDEX 272

Posted in books, engineering, metals, soviet, technology | Tagged alloys, cast iron, cutting tools, engineering, equipments, forging, hardening, heat, metal working, metallurgy, metals, non-ferrous metals, peace publishers, quality control, safety, smelting, soviet, steel, technique, technology, tools | 1 Comment

Sons of the Blue Planet – Lebedev, Luk’yanov, Romanov

Posted on January 23, 2022 by The Mitr

In this post, we will see the book Sons Of The Blue Planet by L. Lebedev; B. Lyk’yanov; A. Romanov.

About the book

The daring wish of mankind was, and still is, to look at the earth from a sufficient height to be able to encompass the whole of it at a glance, and to find out what lies in the depths beyond the blue dome of the sky. This interest, this desire to apprehend what surrounds the world, is a mighty and unquenchable thirst, which leads humanity from one step in its development to another, higher one.

Today when much arm-chair talk is going on about the Apollo Moon missions, the first exciting events toward mastering outer space seem to have lost their glamor. Indeed the beginning of the space era is to be traced to the launching of the first artificial earth satellite into the orbit. Manned flights in spacecraft started with the historic flight of Yurii Gagarin. Since then tremendous advances have been made, many records broken, and new records established in the space race between the world’s two great space giants.

This book is devoted to the decade since the day of the historic flight by Yurii Gagarin. The book tells about all the Soviet astronauts, their lives, aspirations and exploits. The matter has been presented in a very lucid narrative style and the authors of the book have established intimate rapport with the astronauts. It also presents short biographical sketches of Russian astronauts.

The presence of Gagarin is felt throughout the book because he started the starry hour of humanity’s venture into space. His space comrades strive to multiply our successes in understanding and conquering the universe with their efforts and knowledge.

The book was translated from Russian by Prema Pande and edited by V. S. Kothekar and was published for the National Aeronautics and Space Administration in 1973.

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THE SHORE OF THE UNIVERSE, BY B.N. PETROV 1

IN OUR HEARTS 7
TUE “VOSTOK” DESIGN 26
MIGHTY WINGS 39
HOW THE ASTRONAUTS WERE TRAINED 49
MAN OR IRON TENACITY 59
THE JOY OF A COMMUNIST 67
TUE FIRST GROUP FLIGHT 75
A YOUNA COMMUNIST LEAGUER’S HEART 83
SEA GULL 95
“HAWK” AND “SEA GULL” IN “OUTER SPACE 102
OUTER SPACE CREW 111
THE NEW ROCKET-SPACE 128
STEPS OVER THE PLANET 141
MAN IN THE OPEN IN OUTER SPACE 157
“I SEE A TESTER IN HIM…” 163
NEW AIMS — NEW CRAFT 169
MASTER 177
AUTOMATIC DEVICES DOCK IN OUTER SPACE 177
A DREAM COMES TRUE 193
‘ZARYA’, THIS IS ‘BAIKAL’ 205
ALEKSEI ELISEEV’S MAIDEN TRIP 212
AN ASTRONAUT RECRUITED ALONG WITH GAGARIN 218
EXPERIMENTAL SPACE STATION 224
TOWARD THE CHERISHED GOAL 233
FLIGHT ENGINEER OF “SOYUZ-6” 240
THE CHUGUEV TEMPERING 253
THE WAY TO START 260
SON OR KUBAN’ 267
THEE LENIN SHIFT 277
“TO FLY CONTINUOUSLY” 283
THE RESEARCH PROGRAM 288
“KNOWLEDGE, AND AGAIN MORE KNOWLEDGE” 299
THE DEAREST THING 307
424 HOURS IN ORBIT AROUND THE EARTH 314
A PEEP INTO THE FUTURE 318
IN THE NAME OF MAN 325

Posted in books, history, NASA Technical Translations, soviet, space, technology | Tagged astronauts, biographies, cosmonauts, history, russian, soviet, soyuz, space, space ship, space station, space technology, space travel, yuri gargarin | Leave a comment

Some Basic Problems of The Mathematical Theory of Elasticity – Muskhelishvili

Posted on January 22, 2022 by The Mitr

In this post, we will see the book Some Basic Problems of The Mathematical Theory of Elasticity by N. I. Muskhelishvili.

About the book

This book reproduces, in a considerably revised and enlarged form, the contents of a course of lectures, delivered by the author in Spring 1931 at the invitation of the Seismological Institute of the Academy of Sciences of the U.S.S.R. before the scientific workers of the Institute, and of lectures delivered in 1932 before post-graduate students of the Physico- Mathematical Institute of Mathematics and Mechanics at the University of Leningrad. The lectures were intended for persons acquainted with the principles of the theory of elasticity and were to be devoted to separate fundamental questions the choice of which was largely left to me; author naturally dwelt on subject matter in which author had been working myself.

Thus, this book deals only with a few chapters of the theory of elasticity each of which receives fairly complete treatment.

The book was translated from Russian by JRM Radok and was published in 1948.

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Part I – Fundamental equations of the mechanics of an elastic body. 1

CHAPTER 1. ANALYSIS OF STRESS. 5

CHAPTER 2. ANALYSIS OF STRAIN 28

CHAPTER 3. THE FUNDAMENTAL LAW OF THE THEORY OF ELASTICITY; THE BASIC EQUATIONS. 52

Part II – General formulae of the plane theory of elasticity 85

CHAPTER 4. BASIC EQUATIONS OF THE PLANE THEORY OF ELASTICITY. 89

CHAPTER 5. STRESS FUNCTION. COMPLEX REPRESENTATION OF THE GENERAL SOLUTION OF THE EQUATIONS OF THE PLANE THEORY OF ELASTICITY. 104

CHAPTER 6. MULTI-VALUED DISPLACEMENTS. THERMAL STRESSES. 157

CHAPTER 7. TRANSFORMATION OF THE BASIC FORMULAE FOR CON-
FORMAL MAPPING. 166

PART III – Solution of several problems of the plane theory of Aran by means of power series 187

CHAPTER 8. ON FOURIER SERIES. 189

CHAPTER 9. SOLUTION FOR REGIONS, BOUNDED BY A CIRCLE. 194

CHAPTER 10. THE CIRCULAR RING. 218

CHAPTER 11. APPLICATION OF CONFORMAL MAPPING. 237

Part IV – On Cauchy Integrals 251

CHAPTER 12, FUNDAMENTAL PROPERTIES OF CAUCHY INTEGRALS 253

CHAPTER 13. BOUNDARY VALUES OF HOLOMORPHIC FUNCTIONS. 283

Part V – Application of Cauchy integrals to the solution of boundary problems of plane elasticity

CHAPTER 14, GENERAL SOLUTION OF THE FUNDAMENTAL PROBLEMS FOR REGIONS BOUNDED BY ONE CONTOUR. 303

CHAPTER 15. SOLUTION OF THE FUNDAMENTAL PROBLEMS FOR
REGIONS MAPPED ON TO A CIRCLE BY RATIONAL FUNCTIONS. EXTENSION TO APPROXIMATE SOLUTION FOR REGIONS OF GENERAL SHAPE

CHAPTER 16. SOLUTION OF THE FUNDAMENTAL PROBLEMS FOR THE HALF-PLANE AND FOR SEMI-INFINITE REGIONS 373

CHAPTER 17. SOME GENERAL METHODS OF SOLUTION OF BOUNDARY VALUE PROBLEMS. GENERALIZATIONS. 395

Part VI – Solution of the boundary of the plane theory of elasticity
by reduction to the problem of linear relationship 425

CHAPTER 18. THE PROBLEM OF LINEAR RELATIONSHIP 427

CHAPTER 19. SOLUTION OF THE FUNDAMENTAL PROBLEMS FOR THE HALF-PLANE AND FOR THE PLANE WITH STRAIGHT CUTS. 451

CHAPTER 20. SOLUTION OF BOUNDARY PROBLEMS FOR REGIONS, BOUNDED BY CIRCLES, AND FOR THE INFINITE PLANE, CUT ALONG CIRCULAR ARCS. 504

CHAPTER 21. SOLUTION OF THE BOUNDARY PROBLEMS FOR REGIONS, MAPPED ON TO THE CIRCLE BY RATIONAL FUNCTIONS 525

Part VII –
Extension, torsion and bending of homogeneous and compound bars 557

CHAPTER 22, TORSION AND BENDING OF HOMOGENEOUS BARS (PROBLEM OF SAINT-VENANT). 561

CHAPTER 23. TORSION OF BARS CONSISTING OF DIFFERENT
MATERIALS. 597

CHAPTER 24. EXTENSION AND BENDING OF BARS, CONSISTING OF DIFFERENT MATERIALS WITH UNIFORM POISSON’S RATIO 614

CHAPTER 25. EXTENSION AND BENDING FOR DIFFERENT POISSON’S RATIOS 624

APPENDIX l. On the concept of a tensor 656
APPENDIX 2. On the determination of functions from their differentials in multiply connected regions 671
APPENDIX 3. Determination of a function of a complex variable from its real part. Indefinite integrals of holomorphic functions 682

Author Index 687
Subject Index 701

Posted in books, engineering, mathematics, soviet | Tagged bars, bending, boundary value problems, cauchy integral, conformal mappings, elasticity, equations, extensions, fourier series, fundamental law, generalization, holomorphic functions, linear relationships, mathematics, solutions, strain, stress, stress function, theory, thermal stress, torsion | 1 Comment

Our Atmospheric Ocean – Kolobkov

Posted on January 21, 2022 by The Mitr

In this post, we will see the book Our Atmospheric Ocean by N. Kolobkov.

About the book

A book about various atmospheric phenomena.

The importance of the atmosphere in the life of our planet cannot be overestimated. The earth is surrounded on all sides by air, with the surface like the floor of an enormous ocean of gas.

The atmosphere is like a mantle preserving the heat that comes from the sun. It is like the glass of a hot-house, for it lets in the solar rays but prevents the heat from dissipating into space. That is why the alternation of day and night on our planet does not give rise to sharp contrasts of heat and cold. The atmosphere is the planet’s invisible shield. It protects all living beings on earth from the scorching rays of the sun. It gives birth to the clouds, to the winds, and to the rains. It scatters the sunshine and makes gradual the change from light to darkness; it brings light to hidden parts of the globe; and it is a medium for the propagation of sound. Through the air, liners fly to all parts of the world. And through the air, man’s first interplanetary ships will hurtle.

This is why we must study the atmosphere, its composition, its properties, and its structure. The history of atmospheric studies is the story of how man learned about the clouds and beyond, of how he made light, sound, and radio serve as his scouts into this ocean of air. It is the history of numerous inventions, bold surmises, and wonderful discoveries. The achievements of investigators of the atmosphere are added proof of the prowess of science disclosing the innermost secrets of nature.

The book was translated from Russian by George Yankovsky and was published in 1960 by Foreign Languages Publishing House.

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Introduction 5

Part One
THE ATMOSPHERE

Chapter One. The Atmospheric Ocean and Methods of Studying It 15
Chapter Two. Atmospheric Electricity 95
Chapter Three, Lightning and Thunder 106

Part Two
STORMS

Chapter One. Thunderstorms 143
Chapter Two. Rainstorms 167
Chapter Three. Windstorms 200
Chapter Four. The Effects of Large Cities on the Microclimate 258

Part Three
EXTRAORDINARY PHENOMENA IN THE EARTH’S ATMOSPHERE

Chapter One. Phenomena in the Upper Layers of the Atmosphere 301
Chapter Two. Optical Phenomena іп the Atmosphere 312

Posted in books, foreign languages publishing, meteorology, physics, popular science, science, soviet | Tagged atmosphere, atmospheric phenomena, climate, clouds, foreign languages publishing house, geology, lightning, meteorology, observatories, optical phenomena, rain, sky, snow, soviet, thunder, thunderstorms, weather, winds, windstorms | 1 Comment

Generalized Analytic Functions – Vekua

Posted on January 20, 2022 by The Mitr

In this post, we will see the book Generalized Analytic Functions by I. Vekua.

About the book

THIS book is concerned with foundations of the general theory of generalized analytic functions and some applications to problems of differential geometry and theory of shells.

The book is intended for students of advanced courses of the mechanico-mathematical faculties, postgraduates, and likewise for research workers.

The book was translated from Russian by Ian N. Sneddon and was published in 1962.

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PART ONE

FOUNDATIONS OF THE GENERAL THEORY
OF GENERALIZED ANALYTIC FUNCTIONS
AND BOUNDARY VALUE PROBLEMS 1

Chapter 1. Some classes of functions and operators 5
Chapter 2. Reduction of a positive differential quadratic form to the canonical form. Beltrami’s equation. Geometric applications 76
Chapter 3. Foundations of General Theory of Generalized Analytic Functions 132
Chapter 4. Boundary Value Problems 221

Appendix to Chapter 4 366

PART TWO

SOME APPLICATIONS TO PROBLEMS OF THE THEORY OF SURFACES AND THE MEMBRANE THEORY OF SHELLS 390

Chapter 5. Foundations of the General Theory of Infinitesimal Bendings of Surfaces 391
Chapter 6. Problems of the membrane theory of shells 563

References 646

Subject Index 660

Posted in books, mathematics, soviet | Tagged analytic functions, applications, differential geometry, generalized functions, mathematics, mechanics, operators, quadratic forms, soviet, theory of shells | 1 Comment

From Spaceships to Orbiting Stations – Dmitriyev et al

Posted on January 19, 2022 by The Mitr

In this post, we will see the book From Spaceships to Orbiting Stations by A. Yu. Dmitriyev; V. P. Denisov; A. A. Yermil’ov; V. A. Polyakov; B. I. Zhelyabin; A. V. Kirsanov; I. L. Leonidov; A. A. Timonin; A. M. Tumano

About the book

Book discusses the Soviet manned space program. The main stages of development-of Soviet cosmonautics are considered, as well .as the programs for the manned spacecraft “Vostok”,”Voskhod”and “Soyuz”,

and the orbital research station “Salyut”. The construction and equipment of the spacecraft, and their use on the earth and in flight are described. A description is given of the first orbital space station of the “Soyuz” spacecraft, as well as its operation and the experiments performed when the crew changed from one spacecraft to another in open space. The development of methods for assembling a station and performing scientific studies, and also the scientific station “Salyut”, on which the Soviet cosmonauts lived for several days are described. The book also discusses the future prospects for cosmonautics.

The book was translated from Russian under NASA Technical Translation series F-812 was published by NASA in 1973.

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Annotation
Foreword vii

1. The Main Stages of Soviet Cosmonautics 1

2 Programs of the “Vostok” and “Voskhod” Manned Spacecraft 8

Preparation for Human Flight into Space 8
The “Vostok” Program 10
The “Vostok,” The World’s First Spacecraft 12
The “Voskhod” Program 15
The First Man in Open Space 17

3. The Program of the Manned “Soyuz” Spacecraft 21

The Tasks of the Program 21
Design Characteristics of the “Soyuz” Spacecraft 23
The Main Systems of the “Soyuz” Spacecraft 27
Fabrication and Ground Testing of the Spacecraft 30
Fabrication of the Spacecraft 30
Ground Testing of Systems 21
Flight Tests of the Spacecraft Systems 35
Training the Cosmonauts for Space Flights 39

4. The Main Stages of Flight of the “Soyuz” Spacecraft 44

Orbit Injection 44
Orbital Flight 47
Gyroscopic Orientation (“Warping”) of the Spacecraft toward the Sun 47
Celestial Orientation of the Spacecraft 48
Orbital Correction 49
Reentry and Descent in the Atmosphere 51

5. The World’s First Experimental Space Station 55

The Experimental Orbital Station of the “Soyuz” Complex 55
Docking of Two Spacecraft 56
Space Walk of the Cosmonauts 63
Scientific Investigations and Experiments 67

6. When There Are Three Spacecraft in Orbit 72

Maneuvering of Spacecraft 72
Scientific and Technical Experiments and Observations 75
Welding of Metals in Orbit 77

7. “Soyuz-9” Working in Orbit 78

Medical and Biological Investigations During 78
Prolonged Space Flight 83
Maneuvering and Navigation Measurements 88
Investigations of Importance to the National Economy

8. The First Orbital Station of Long Duration Is in Space 89

“Salyut” Is in Orbit 89
Call Signs are “Granit” 90
Into Space Toward the Station 92
A Tour of the “Salyut” 93
Watch in Space 96

9. The Principal Methods of Developing Orbital Stations 101

Automatic or Manned Stations? 101
Design Characteristics of Future Space Stations 105
The Problem of Servicing Space Stations 111
Space Stations in the Service of Man 114
The Bridge to the Future is Being Erected Today 118

Posted in books, NASA Technical Translations, soviet, space, technology | 3 Comments

Criteria For Divisibility (Popular Lectures in Mathematics Vol 16) – Vorob’ev

Posted on January 18, 2022 by The Mitr

In this post, we will see the book Criteria For Divisibility by N. N. Vorob’ev. This book is Volume 16 of Popular Lectures in Mathematics series.

About the book

N. N. Vorob’ev’s Criteria for Divisibility introduces the high school or early college student to a specific number-theoretic topic and explains the general mathematical structures which underlie the particular concepts discussed. Vorob’ev discusses the ideas of well-ordered sets, partial and linear orderings, equivalence relations, equivalence classes, algorithms, and the relationship between the determinability of algorithms defined on the integers and the well-ordering principle.

The book was translated from Russian by Daniel Levine and Timothy McLarnan was published in 1980.

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Preface vii

1. Divisibility of Numbers 1
2. The Divisibility of Sums and Products 17
3. Criteria for Congruence and Criteria for Divisibility 22
4. Divisibility of Powers 36
5. Proofs of Theorems 41
6. Solutions to Problems 50

Posted in books, mathematics, popular lectures in mathematics, soviet | Tagged algorithms, divisibility, equivalence classes, equivalence relations, integers, linear ordering, mathematics, number theory, numbers, partial ordering, popular lectures in mathematics, sets, soviet, well-ordered sets, well-ordering principles | 1 Comment

Stories About Sets – Vilenkin

Posted on January 17, 2022 by The Mitr

In this post, we will see the book Stories About Sets N. Ya. Vilenkin.

About the book

I want to tell the reader about the theory of sets in the same way, in which I learned it, by following the “corridor” course of study. Thus, our attention will be focused mainly on giving clear presentations of problems, discussing unexpected or surprising examples, quite often giving contradictory “naive” discussions. We shall find that the theory of functions of a real variable is richly endowed with all these. And if, after he has read this book, a high-school or college student wants to study the theory of sets or the theory of functions of a real variable more deeply, the author will feel that his book has been a success.

Professor Vilenkin has produced a small masterpiece that can be read with profit and delight by students of mathematics and laymen with an interest in mathematics. Slightly more than half the book explores the notion of cardinality of sets and the remainder traces the evolution of some of the most important concepts of m athem atics such as function, curve, surface and dimension.

The exposition combines informality with integrity of presentation and there is a wealth of unusual examples illustrating the paradoxical properties of curves and surfaces. Professor Vilenkin’s essay provides a royal road to the important concepts with which it is concerned.

…

Professor Vilenkin has produced a small masterpiece
which can be read with profit and delight by anybody,
beginning with high school juniors and seniors. Slightly
more than half of the book explores the notion of cardinality
of sets and the remainder traces the evolution of some of
the most important concepts of mathematics such as func-
tion, curve, surface, and dimension. The exposition combines
informality with integrity of presentation and there is a
wealth of unusual examples illustrating the paradoxical
properties of curves and surfaces. It is safe to say that
Professor Vilenkin’s essay provides a royal road to the
important concepts with which it is concerned.

The book was translated from Russian by Scripta Technica was published in 1968.

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Foreword v
Preface vii

1. Some Extraordinary Properties of Infinite Sets

The Extraordinary Hotel, or the Thousand and First Journey of Ion the Quiet 4
From the Author 14

2. Sets and Operations on Sets

What Do We Mean by a Set? 16
How We Specify a Set 18
To Shave or Not to Shave? 21
The Empty Set 24
The Theory of Sets and Elementary Mathematics 26
Subsets 27
The Universal Set 29
The Intersection of Sets 29
Union of Sets 31
Partitioning of Sets 35
Subtraction of Sets 37
The Algebra of Sets 39
Boolean Algebras 41

3. The Cardinality of Sets

Equality between Sets 43
On the Dance Floor 44
For Every Flow There Is an Ebb 46
Can a Part Be Equal to the Whole? 47
Countable Sets 49
Algebraic Numbers 51
Unequal Sets 53
The Countable Set—The Smallest of the Infinite Sets 56
Uncountable Sets 57
The Census That Never Took Place 58
The Uncountability of the Continuum 61
The Existence of Transcendental Numbers 63
Long and Short Line Segments Have Equally Many Points 64
Segment and Square 66
Somehow One Problem Does Not Work Out 69
Is There a Set of Largest Cardinality ? 71
The Arithmetic of the Infinite 73
Infinite Exponents 76
On the Ordering of Numbers 78
Completely Ordered Sets 80
The Enigmatic Axiom 82
Two Apples from One 84

4. Remarkable Functions and Curves, or a Stroll through a Mathematical Art Museum

How the Notion of Function Developed 86
The Genie Escapes from the Bottle 91
Wet Points 93
The Devil’s Staircase 97
A Prickly Curve 99
A Closed Curve of Infinite Length 104
A Mathematical Carpet 107
Euclid Does Not Rely on Euclid 111
Are Rigorous Definitions Needed ? 112
A Curve Is the Path of a Moving Point 114
The Theorem Is Obvious, but the Proof Is Not 118
A Curve Passing through All the Points of a Square 120
Everything Had Come Unstrung 122
How to Make a Statue 124
Continua 126
Cantor Curves 128
Can the Area of a Curve Be Different from Zero ? 129
Domains without Area 133
Some Surprising Examples 135
Domains and Boundaries 137
The Great Irrigation Project 139
A “Nondissertable’’ Subject 141
The Inductive Definition of Dimension 144
The Article Is to Be Printed, Not Reviewed! 146
Conclusion 149
Exercises and Examples 150

Posted in books, mathematics, soviet | Tagged algebra of sets, boolean algebra, cantor curves, cardinality of sets, countable sets, devil's staircase, dimensions, domains without area, enigmatic axiom, functions, intersection of sets, mathematics, operations on sets, properties of infinite sets, properties of sets, remarkable curves, set theory, sets and elementary mathematics, transcendental numbers, union of sets, universal set | Leave a comment

Some Applications Of Mechanics To Mathematics (Popular Lectures in Mathematics Vol 3) – Uspenskii

Posted on January 16, 2022 by The Mitr

In this post, we will see the book Some Applications Of Mechanics To Mathematics by V. A. Uspenskii. This book is Volume 3 of the Popular Lectures in Mathematics series.

About the book

The applications of mathematics to physics (in particular, to mechanics) are well-known. We need only open a school text-book to find examples. The higher branches of mechanics demand a complex and refined mathematical apparatus.

There are, however, mathematical problems for whose solution we can successfully use the ideas and laws of physics. A number of problems of this kind soluble by methods drawn from mechanics (namely, by using the laws of equilibrium) were given by the author in his lecture “The solving of mathematical problems by the methods of mechanics”, which

was read to pupils in their seventh year of secondary school at the Moscow State University on 19 February 1956, this lecture, with very minor additions, makes up the contents of this article.

The book was translated from Russian by Halina Moss and edited by Ian N. Sneddon. was published in 1960.

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Foreword vii

1. Problem on a tangent to a circle 1

2. Problem on a tangent to an ellipse 5

3. Problems on tangents to parabolas and hyperbolas 11

4. Principle of least potential energy 18

5. Material points and the centre of gravity 23

6. The centre of gravity and a system of two material points 28

7. Theorems about the intersection of straight lines 30

8. The centre of gravity of a rod with many loads 35

9. A problem in the theory of numbers (formulation) 39

10. A problem in the theory of numbers (solution) 43

11. The impossibility of perpetual motion 49

Conclusion 51

Posted in mathematics, physics, popular lectures in mathematics, soviet | Tagged applications. mechanics, centre of gravity, material points, mathematics, perpetual motion, popular lectures, potential energy, quadric curves, soviet, tangents, theory of numbers | 4 Comments

Electric Slag Welding – Paton

Posted on January 15, 2022 by The Mitr

In this post, we will see the book Electric Slag Welding by B. Paton.

About the book

Electric slag welding is a fundamentally new method of permanently joining metals. It has been developed and put to practical use by the Paton Electric Welding Institute of the Ukrainian Academy of Sciences in collaboration with the Engineering Works at Novo-Kramatorsk and the Krasny Kotelshchik Boiler- Making Factory at Taganrog, both of which are leading plants in the field.

As distinct from other fusion welding methods, the electric slag process depends on the lioaL generated by the passage of an electric current from the welding rod (electrode) to the workpiece through the molten pool of a high-resistance conductive flux, or slag. Hence its name—electric slag process.

Submerged arc welding has proved less efficient on thicknesses over 50 or 60 mm than on lighter sections. This is because of the difficulty and, at limes, impossibility of making well-shaped welds with strong arcs in the downhand position in a single pass. Therefore, heavy-gauge plate has to be bevelled prior to welding and welded in many passes—which is out of pace with modern heavy engineering practice.

Electric slag welding is a big step forward, as this process, coupled with weld moulding, has rendered possible the single-pass welding of plate of practically unlimited thickness.

The obvious advantages, both technical and economic, that the electric slag process possesses in comparison with other methods and processes of fusion welding of heavy sections have appealed to welding people in some Western countries. In 1959, equipment for electric slag welding went into production in Britain and West Germany.

In this book, the authors have sought to cover all the latest achievements in the science and art of electric slag welding.

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

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FOREWORD? 5

Chapter I. ELECTRIC SLAG WELDING 1

1. Definitions 7
2. Classification 12
3. Features 17
4. Applications 19

Chapter II. WELD FORMATION IN ELECTRIC SLAG WELDING 22

1. Heat Input and Distribution 22
2. Propagation of Heat in the Parent Metal 26
3. Welding Procedures and Their Effect on Weld Shape and Dimensions 29
4. Structure of Weld Metal in Electric Slag Welding 48

Chapter III. METALLURGY OF ELECTRIC SLAG WELDING 63

1. Reactions of Manganese and Silicon 64
2. Reactions of Chromium 71
3. Oxidation of Carbon 71
4. Reactions of Phosphorus and Sulphur 72
5. Effect of Welding Conditions on the Rate of Metallurgical Reactions 74
6. Effect of Type of Current aud Polarity on Metallurgical Reactions 77
7. Behaviour of Gases in Electric Slag Welding 81
8. Fluxes for Electric Slag Welding 83
9. Electrodes for Electric Slag Welding 87

Chapter IV. TECHNIQUE OF ELECTRIC SLAG WELDING AND HARDFACING 90

1. Types of Joints and Welds 90
2. Edge Preparation and Fit-up 95
3. Technique for Straight Seams 100
4. Technique for Circumferential Seams 107
5. Consumable Electrode-guide Technique 111
6. Welding Technique with Large-size Flectrodes 116
7. Hard-facing by the Electric Slag Process 118
8. Electric Slag Welding in Repair of Thick-walled Articles and Machine Parts 124
9, Defects in Electric Slag Welds 128
10. Weld Inspection and Testing 139

Chapter V. DISTORTIONS AND THE!R CONTROL IN ELECTRIC SLAG WELDING 142

1. Distortions in Flat-plate Structures Joined by Straigh Seams 142
2. Distortions in Corner Joints 146
3. Distortions in Welded Frames lens 146
4. Distortions In Slag-welded High-pressure High-temperature Boilers 148
5. Distortions in Circumferential Seams 150

Chapter VI. EQUIPMENT FOR ELECTRIC SLAG WELDING 153

1. Features of Design 153
3. Track-riding Electric Slag Welding 155
3. Trackless Electric Slag Welding Equipment 170
4. Walking Magnet Welding Sets 175
5. Sets for Electric Slag Circumferential Seams 117
6. Equipment for Electric Slag Welding with Plate and Rod Electrodes 181
7. Sets for Welding with Consumable Electrode Guides 184
8. Electric Slag Welding Outfits 185

Chapter VII. POWER SOURCES AND AUTOMATIC CONTROL IN ELECTRIC SLAG WELDING 200

1. Power Sources for Electric Slag Welding 200
2. Automatic Control of Electric Slag Welding 205

Chapter VIII. WELDING PROCEDURES FOR CARBON AND ALLOY STRUCTURAL STEELS 217

1. Killed Carbon Steels 217
2. Rimmed Low-carbon Steels 234
3. Boiler Carbon Steels 231
4. Medium-alloy Steels 247
5. Austenitic Steels and Heat-resistant Alloys 267
6. Titanium 282
T. Cast Iron 287
8. Hard Facing by the Electric Slag Process 289

Chapter IX. ELECTRIC SLAG WELDING OF HIGII-PRESSURE VESSELS 299

1. Types of Welded Vessels 299
2. Slag-welded Vessels from Roll-formed Plate 303
3. Slag-welded Vessels from Pressed Plate 307
4. Heat Treatment of Thick-walled Boiler Drums and High-pressure Vessels 313
5 Distortions of Boilers Due to Heat Treatment in Gas-fired Furnaces and Their Control 315
6. Economic Gain and Technical Advantages 317

Chapter X. TYPICAL APPLICATIONS OF ELECTRIC SLAG WELDING 320

1. Rolled-welded Structures 321
2. Cast-welded Structures 332
3. Forged-welded Structures 344
4. Composite Structures from Plate, Forgings and Castings 351
5. Electric Slag Welding of Heavy-gauge Reinforcing Bars 359

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About the book

Contents

Chapter I. Physical Characteristics 7

Chapter II. Quality Control of Metals 13

Chapter III. Steel 26

Chapter IV. Heat-treatment of Steel 74

Chapter V. Case-hardening 104

Chapter VI. Heat-treatment Technology 130

Chapter VII. Heat-treatment of Cast Iron 197

Chapter VIII. Heat-treatment of Non-ferrous Metals 201

Chapter IX. Forging of Ferrous and Non-ferrous Metals 203

Chapter: X. Manufacture of Built-up Cutting Tools 234

Chapter: XI. Equipment, Fuel and Accessory Materials for Heat-treatment 243

Chapter: XII. Safety Engineering 268

About the book

Contents

About the book

Contents

Part I – Fundamental equations of the mechanics of an elastic body. 1

CHAPTER 1. ANALYSIS OF STRESS. 5

CHAPTER 2. ANALYSIS OF STRAIN 28

CHAPTER 3. THE FUNDAMENTAL LAW OF THE THEORY OF ELASTICITY; THE BASIC EQUATIONS. 52

Part II – General formulae of the plane theory of elasticity 85

CHAPTER 4. BASIC EQUATIONS OF THE PLANE THEORY OF ELASTICITY. 89

CHAPTER 5. STRESS FUNCTION. COMPLEX REPRESENTATION OF THE GENERAL SOLUTION OF THE EQUATIONS OF THE PLANE THEORY OF ELASTICITY. 104

CHAPTER 6. MULTI-VALUED DISPLACEMENTS. THERMAL STRESSES. 157

CHAPTER 7. TRANSFORMATION OF THE BASIC FORMULAE FOR CON- FORMAL MAPPING. 166

PART III – Solution of several problems of the plane theory of Aran by means of power series 187

CHAPTER 8. ON FOURIER SERIES. 189

CHAPTER 9. SOLUTION FOR REGIONS, BOUNDED BY A CIRCLE. 194

CHAPTER 10. THE CIRCULAR RING. 218

CHAPTER 11. APPLICATION OF CONFORMAL MAPPING. 237

Part IV – On Cauchy Integrals 251

CHAPTER 12, FUNDAMENTAL PROPERTIES OF CAUCHY INTEGRALS 253

CHAPTER 13. BOUNDARY VALUES OF HOLOMORPHIC FUNCTIONS. 283

Part V – Application of Cauchy integrals to the solution of boundary problems of plane elasticity

CHAPTER 14, GENERAL SOLUTION OF THE FUNDAMENTAL PROBLEMS FOR REGIONS BOUNDED BY ONE CONTOUR. 303

CHAPTER 15. SOLUTION OF THE FUNDAMENTAL PROBLEMS FOR REGIONS MAPPED ON TO A CIRCLE BY RATIONAL FUNCTIONS. EXTENSION TO APPROXIMATE SOLUTION FOR REGIONS OF GENERAL SHAPE

CHAPTER 16. SOLUTION OF THE FUNDAMENTAL PROBLEMS FOR THE HALF-PLANE AND FOR SEMI-INFINITE REGIONS 373

CHAPTER 17. SOME GENERAL METHODS OF SOLUTION OF BOUNDARY VALUE PROBLEMS. GENERALIZATIONS. 395

Part VI – Solution of the boundary of the plane theory of elasticity by reduction to the problem of linear relationship 425

CHAPTER 18. THE PROBLEM OF LINEAR RELATIONSHIP 427

CHAPTER 19. SOLUTION OF THE FUNDAMENTAL PROBLEMS FOR THE HALF-PLANE AND FOR THE PLANE WITH STRAIGHT CUTS. 451

CHAPTER 20. SOLUTION OF BOUNDARY PROBLEMS FOR REGIONS, BOUNDED BY CIRCLES, AND FOR THE INFINITE PLANE, CUT ALONG CIRCULAR ARCS. 504

CHAPTER 21. SOLUTION OF THE BOUNDARY PROBLEMS FOR REGIONS, MAPPED ON TO THE CIRCLE BY RATIONAL FUNCTIONS 525

Part VII – Extension, torsion and bending of homogeneous and compound bars 557

CHAPTER 22, TORSION AND BENDING OF HOMOGENEOUS BARS (PROBLEM OF SAINT-VENANT). 561

CHAPTER 23. TORSION OF BARS CONSISTING OF DIFFERENT MATERIALS. 597

CHAPTER 24. EXTENSION AND BENDING OF BARS, CONSISTING OF DIFFERENT MATERIALS WITH UNIFORM POISSON’S RATIO 614

CHAPTER 25. EXTENSION AND BENDING FOR DIFFERENT POISSON’S RATIOS 624

About the book

Contents

About the book

Contents

PART ONE

FOUNDATIONS OF THE GENERAL THEORY OF GENERALIZED ANALYTIC FUNCTIONS AND BOUNDARY VALUE PROBLEMS 1

PART TWO

SOME APPLICATIONS TO PROBLEMS OF THE THEORY OF SURFACES AND THE MEMBRANE THEORY OF SHELLS 390

About the book

Contents

1. The Main Stages of Soviet Cosmonautics 1

2 Programs of the “Vostok” and “Voskhod” Manned Spacecraft 8

3. The Program of the Manned “Soyuz” Spacecraft 21

4. The Main Stages of Flight of the “Soyuz” Spacecraft 44

5. The World’s First Experimental Space Station 55

6. When There Are Three Spacecraft in Orbit 72

7. “Soyuz-9” Working in Orbit 78

8. The First Orbital Station of Long Duration Is in Space 89

9. The Principal Methods of Developing Orbital Stations 101

About the book

Contents

About the book

Contents

1. Some Extraordinary Properties of Infinite Sets

2. Sets and Operations on Sets

3. The Cardinality of Sets

4. Remarkable Functions and Curves, or a Stroll through a Mathematical Art Museum

About the book

Contents

About the book

CHAPTER 7. TRANSFORMATION OF THE BASIC FORMULAE FOR CON-
FORMAL MAPPING. 166

CHAPTER 15. SOLUTION OF THE FUNDAMENTAL PROBLEMS FOR
REGIONS MAPPED ON TO A CIRCLE BY RATIONAL FUNCTIONS. EXTENSION TO APPROXIMATE SOLUTION FOR REGIONS OF GENERAL SHAPE

Part VI – Solution of the boundary of the plane theory of elasticity
by reduction to the problem of linear relationship 425

Part VII –
Extension, torsion and bending of homogeneous and compound bars 557

CHAPTER 23. TORSION OF BARS CONSISTING OF DIFFERENT
MATERIALS. 597

FOUNDATIONS OF THE GENERAL THEORY
OF GENERALIZED ANALYTIC FUNCTIONS
AND BOUNDARY VALUE PROBLEMS 1