Hilbert’s Fourth Problem by A. V. Pogorelov

Hilbert’s fourth problem, which involves finding all geometries where “ordinary lines” are “geodesics,” is both accessible and profound. While the problem can be appreciated by beginning graduate students, its solution requires tools from various branches of mathematics, including geometry, analysis, and the calculus of variations.

A partial solution was provided by Georg Hamel in 1901. Later, A. V. Pogorelov, inspired by Herbert Busemann’s idea presented at the 1966 International Congress of Mathematicians in Moscow, offered an elegant and comprehensive solution. Pogorelov’s approach, which slightly reformulates Hilbert’s problem, is celebrated for its clarity and mathematical depth.

The book is well-written, introducing necessary mathematical concepts as needed, making it accessible to readers with a foundation in advanced calculus. The English translation, reviewed by Eugene Zaustinsky, includes helpful notes guiding readers to further literature.

Pogorelov’s work is a valuable contribution to the mathematical literature, particularly for those interested in geometry and its foundations.

You can get the book here and here.

INTRODUCTION 5

SECTIONS

1. Projective Space 9

2. Projective Transformations 13

3. Desarguesian Metrizations of Projective Space 19

4. Regular Desarguesian Metrics in the Two-Dimensional Case 24

5. Averaging Desarguesian Metrics 31

6. The Regular Approximation of Desarguesian Metrics 38

7. General Desarguesian Metrics in the Two-Dimensional Case 46

8. Funk’s Problem 54

9. Desarguesian Metrics in the Three-Dimensional Case 61

10. Axioms for the Classical Geometries 68

11. Statement of Hilbert’s Problem 75

12. Solution of Hilbert’s Problem 82

NOTES 88

BIBLIOGRAPHY 93

INDEX 95

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Measure And Derivative A Unified Approach by G.E. Shilov; B.L. Gurevich

This volume is intended as a textbook for students of
mathematics and physics, at the graduate or advanced
undergraduate level. It should also be intelligible to
readers with a good background in advanced calculus
and sufficient “mathematical maturity.”
The phrase “unified approach” in the title of the book
refers to the consistent use of the Daniell scheme, which
starts from the concept of an elementary integral defined
(axiomatically) on a family of elementary functions. In
the Introduction we explain in detail why we prefer
this approach to others, in particular to the Lebesgue-
Radon-Frechet approach, which starts from axiomatic
measure theory.

Revised English Edition
Translated and Edited by Richard A. Silverman

You can get the book here and here.

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Dunno’s Adventures How Dunno Became A Poet by Nikolai Nosov

A picture story book for children.

Dunno’s adventures in creating poetry

Drawings by Boris Kalaushin
Translated from the Russian by Margaret Wettlin

You can get the book here and here.

 

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Dunno’s Adventures Up In The Clouds by Nikolai Nosov

A picture story book for children.

Dunno’s adventures with a hot air balloon

Drawings by Boris Kalaushin
Translated from the Russian by Margaret Wettlin

You can get the book here and here.

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Soviet Foreign Policy 1945-1975 by B. Ponomaryov (Ed.); A. Gromyko (Ed.); V. Khvostov (Ed.)

 

Part two of a collection of Soviet Foreign policies with regard to various political events and nations.

Translated from the Russian by David Skvirsky

Compiled by A. Alexandrov, A. Blatov, V. Grubyakov, A. Dobrynin,
I. Zemskov, V. Israelyan, M. Kapitsa, I. Koblyakov, L. Kutakov,
A. Roshchin, S. Sanakoyev, V. Falin, V. Khvostov

 

You can get the book here and here.

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Dunno’s Adventures – An Accident by Nikolai Nosov

A picture story book for children.

Dunno’s adventures with a hot air balloon and its accident

Drawings by Boris Kalaushin
Translated from the Russian by Margaret Wettlin

You can get the book here and here.

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Global Ecology by M. I. Budyko

Following the rapid development of anthropogenic changes in the environment in recent years there emerged a heightened interest in problems of global ecology. This is why it was important to write a book devoted entirely to the problems of that science, even though this has presented some difficulties.

Global ecology as a distinct scientific discipline is still in a state of development,rand its boundaries are not yet clearly defined. While not seeking to encompass all branches of that science, the author has found it appropriate to emphasize the central problem of world ecology, namely, the [circulation of energy and of different types of matter within the biosphere. Wide use has been made of the author’s own earlier studies, including relevant sections of Thermal Balance of the Earth’s Surface (1956), Climate and Life (1971), and Climatic Changes (1974).

These studies are fneeded to solve current problems of global ecology, as well as to explain the patterns of the biosphere’s evolution in the past and to forecast its possible changes in the future.

Particular emphasis has been given to the geophysical aspects of global ecology, since the author possessed more data on that subject than on other aspects of that science.

Translated from the Russian
Designed by Mikhail Shevtsov

You can get the book here and here.

Preface 5
The Biosphere 6
1. The Problems and Tasks of Global Ecology 6
2. The Structure of the Biosphere 17
The Transformations of Solar Radiation 36
1. Components of the Biosphere’s Energy Balance 36
2. The Geographical Distribution of Energy Balance Components 50
III Climate 72
1. Climate and Life 72
2. The Theory of Climate 81
3. Changes in Climate 99
IV The Hydrological Cycle 114
1. The Water Balance 114
2. Relations Between Energy and Water Balances on Land 120
3. The Water Exchange in the Atmosphere 128
V Geographical Zones 136
1. Climatic Factors Determining Geographical Zonality 136
2. A Periodic Law of Geographical Zonality 142
VI The Circulation of Organic Matter 154
1. Activities of Autotrophic Plants 154
2. The Global Biological Cycle 175
VII The Ecological Mechanism of the Evolution of Organisms 191
1. The Stability of Ecological Systems 191
2. Critical Ages in the History of the Biosphere 202
VIII The Ecological Mechanism of the Evolution of Man 222
1. The Origin of Man 222
2. The Ecological Crisis of the Upper Paleolithic 233
IX Man and the Biosphere 249
1. The Current Ecological Situation 249
2. Man’s Influence on Global Processes 259
X The Future of the Biosphere 276
1. The Evolution of the Biosphere 276
2. The Biosphere in the Near Future 293
Conclusion 310
Bibliography 313

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Gaseous Composition Of The Atmosphere And Its Analysis by B. A. Mirtov

The problem of the gaseous composition of the atmosphere is one of the central questions of modern atmospheric physics. We need not consider in detail the fact that the gaseous composition, which varies considerably with height, has a vital influence on most phenomena occurring in the Earth’s atmosphere. In the upper layers of the atmosphere, there is no single problem (with the possible exception of the wind conditions) that can be solved accurately without a knowledge of the chemical nature of these layers.

As far as I know, this is the first book to appear in either Russian or foreign literature which attempts to collect and systematize the large amount of work devoted to the investigation of the composition of the Earth’s air cover. Hundreds of papers, not connected by any unifying idea—some of them old and undeservedly forgotten, others scattered throughout various journals—cannot give a complete impression of the gaseous composition of the atmosphere. The scattered nature of the material makes it necessary to spend a large amount of time and trouble just to become acquainted with the work that has been done.

The absence of a critical appraisal of the often somewhat contradictory results of various experiments has led to the inclusion of incorrect information in modern courses on atmospheric physics and in most reference books. This has happened even when dealing with the lower atmosphere, which has been most thoroughly investigated.

The recent use of rockets and artificial satellites has led to rapid progress in our exploration of the upper atmosphere. The large amount of very interesting material, which has accumulated within the short space of the last decade, needs analysis and detailed commentary. All these considerations have led me to write this monograph, in which I have tried to collect and critically discuss the existing experimental material on the chemical composition of the atmosphere.

This book deals with a series of problems connected with the investigation of the composition of the atmosphere, but it is by no means my intention to try to describe all sides of this subject. In order to avoid giving the reader a false impression of the volume of work discussed, I shall now clearly define the range covered.

You can get the book here and here.

PREFACE 1
CHAPTER I. INVESTIGATIONS OF THE LOWER ATMOSPHERE
Introduction

Early geophysical investigations 9
The discovery of new gases in air the present state of knowledge of the gaseous composition of the lower atmosphere 18
Conclusion 26
CHAPTER II. INVESTIGATIONS OF THE COMPOSITION OF THE MIDDLE ATMOSPHERE (up to a height of 30 km)
Introduction 27

Balloon ascents 28
Discovery of the stratosphere and the problem of the gravitational separation of gases 30
Early investigations of the composition of the atmosphere at high altitudes by indirect methods 32
Direct investigations in the stratosphere 33
Balloon ascents into the stratosphere 36
Sounding-balloon investigations with automatic equipment 41
Conclusion 49
CHAPTER III. INVESTIGATIONS OF THE COMPOSITION OF THE UPPER ATMOSPHERE USING ROCKETS (sampling method)
Introduction 51

Gaseous composition one of the central problems of the physics of the upper atmosphere 56
Sounding rockets 57
Characteristics of rocket investigations 63
Methods and results of investigations of gaseous composition 64
Conclusion 78
CHAPTER IV. SOVIET INVESTIGATIONS OF THE UPPER ATMOSPHERE USING ROCKETS (sampling method)
Introduction 80

Sampling 81
Storing the samples 91
Analysis of the samples 93
Spectroscopic microanalysis of gases 95
The vacuum apparatus 101
Experimental results 106
CHAPTER V. INVESTIGATIONS OF THE COMPOSITION OF THE UPPER ATMOSPHERE USING ROCKET-BORNE RADIO-FREQUENCY MASS SPECTROMETERS
Introduction 110

Characteristics of the composition of the upper atmosphere 110
The use of the radio-frequency mass spectrometer for investigating the upper atmosphere 113
American investigations on the neutral composition of the atmosphere 117
Investigations of the neutral composition of the atmosphere carried out in the Soviet Union 128
Discussion of results 133
Investigations of the ionic composition of the atmosphere carried out in the USA 136
Investigations of the ionic composition of the atmosphere carried out in the USSR 142
Conclusion 144
CHAPTER VI. INVESTIGATIONS OF THE IONIC COMPOSITION OF THE UPPER ATMOSPHERE USING RADIO-FREQUENCY MASS SPECTROMETERS MOUNTED IN ARTIFICIAL SATELLITES (SPUTNIKS)

The use of artificial satellites for the investigation of the Earth’s upper and outer atmosphere 146
Characteristics of the method of investigation 147
Investigations of the ionic composition of the upper atmosphere 157
Discussion of the results 163
Conclusion 165
BIBLIOGRAPHY 172

APPENDIX THE CONCENTRATION OF OZONE IN THE ATMOSPHERE
Introduction 179
The variation of the overall ozone content and the study of ozone in the lower atmosphere 180
Investigations on the vertical distribution of ozone at high altitudes 187
Photochemical theory 193
Conclusion 196
Bibliography 198

LIST OF ABBREVIATIONS 209

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Russian Fairy Tales

A collection of Russian fairy tales for children.

Compiled by A. Afanasiev
Illustrations by I. Bilibin
Translated from Russian by A. Zamchuk

Sister Alionushka and brother Ivanushka 1
Tale of Ivan-Tsarevich, the firebird and the grey wolf 9
Vasilisa the Beautiful 23
Tale of the Frog Tsarevna 35
Tale of the feather of Finist, the bright Falcon 43
Maria Morevna 53
Tale of the White Duck 66

You can get the book here and here.

 

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फूलनगर के बौने (The Mites Of Flower Town Dunno’s Adventures in Hindi) by निकोलाई नोसोव (Nikolai Nosov)

नजानू की अस्पताल की फुलनगर की सैर

अनुवादक सरस्वती हैदर

चित्रकार बोरीस कलऊशिन

You can get the book here and here.

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