Lenin Prizes 1970

Kvant 1970, No. 8 p. 58-64 Tag 6T0H

Rough automatic draft, low quality: expect mistakes and awkward wording. It will be replaced by a better translation. Original →

1970 is the year of the Great Jubilee, the 100th anniversary of the birth of V.I. Lenin, whose name is given to awards for the most outstanding research and achievements in the field of science and technology. It is gratifying to note that the majority of the anniversary year prizes went to physiomathematical research. This is convincing evidence of the successful development of modern physics and mathematics, which occupy the forefront of world science. Next, a short story about the works awarded the Lenin Prize will, of necessity, take up several pages in our magazine.

A team of employees from four leading scientific institutes - the Institute of Experimental and Theoretical Physics, the Radio Engineering Institute, the Institute of High Energy Physics and the Research Institute of Electrophysical Equipment - includes Corresponding Member of the USSR Academy of Sciences V.V. Vladimirsky, D.G. Koshkarev, A.A. Kuzmin, Corresponding Member of the USSR Academy of Sciences A.A. Logunov, R.M. Sulyaev, I.F. Malysheva was awarded the Lenin Prize for the development and commissioning of the promon synchropron of the Institute of High Energy Physics for an energy of 70 GeV.

The main experimental tool for studying the wonderful world of elementary particles is the loaded particle accelerator. By accelerating particles to gigantic energies, it makes it possible to study the interaction of accelerated particles with matter, from the various features of which one can judge the nature of the forces acting between particles. With such interactions, new elementary particles are born that do not exist under normal conditions.

The largest accelerator in the world is the Soviet proton synchrotron, recently built in the young science city of Protvino near Serpukhov. It accelerates the atomic nuclei of hydrogen - protons - to an energy of 70 billion electron volts (70 GeV; 1 electron volt equals energy

gini, which acquires an electron by passing through an electron potential difference of one volt). Left behind are the recent record holders—the proton intensifier of the European Atomic Center in Geneva at 28 Gsv and a similar American accelerator at Brookhaven National Laboratory at 33 Gsv. It should be noted that in a number of experiments, the energy of protons achieved in Protvino turned out to be higher than the design one and amounted to 76 Gsv.

The main part of the accelerator is the pressing chamber - a giant underground ring 1480 m long. The chamber is located in a magnetic field formed by 120 magnetic sections weighing 200 tons, between which 54 accelerating devices (resonance) are placed. The creator of the accelerator had to offer enormous difficulties associated with unusually strict requirements for the characteristics of the magnetic field and the arrangement of the blocks. It is enough to indicate that the deviation of any block from the specified position by more than 0.1 mm disrupts the operation of the accelerator!

The accelerated particles make about 400,000 revolutions in 2.6 seconds and reach speeds very close to the speed of light in vacuum. When they hit targets, they generate streams of secondary particles (mesons, antiprotons, neutrinos, etc.), which are sorted by special separators into different channels for further research.

During the short period of operation of the accelerator in Protvino, a number of unique experiments have already been performed on it. One of them was devoted to the Japanese so-called “quarks” (hypothetical elemental particles with fractional values of electron charges), the other ended with the creation of atomic nuclei of the anti-helement - antihelium with a mass of 3. They will consist of two antiprotons and one antineutron. There is no doubt that the new record-breaking Soviet accelerator can wrest more secrets of the microworld from nature.

A team of employees of the Evvan Physical Institute, the Institute of Physics of the Academy of Sciences of the Georgian SSR and the Moscow Engineering Physics Institute - corresponding member of the USSR Academy of Sciences A. I. Alikhanyan, T. L. Asatini, G. E. Chikovani, V. N. Roinishvili, B. A. Dolgoshen, B. I. Luchkov - received a premio for the creation of a new means of observing elementary particles - preque art cameras.

Research on elementary particles requires not only accelerators capable of creating such particles, but also special methods for recording traces of these particles. There are few such methods, and each of them brings fundamental discoveries to science. A track spark chamber is one of the best modern methods for recording elementary particles. It consists of several electrodes (plates or wires) connected to a high voltage source and placed in a vessel filled with a neutral gas. Passing through the gas gaps between the electrodes, a rapidly charged particle destroys gas atoms. A track appears - a visible trace of a particle formed by a chain of bright sparks. The design of the cameras is such that they are capable of recording particles for very short periods of time, amounting to millionths of a second. This allows experimenters to target the camera to record specific types of particle elements and their characteristic interactions. Track spark chambers have helped make important discoveries, for example, the discovery of the existence of two types of special particle elements - neutrinos, one of which is associated with the birth of electrons,

and the other - we will generate mesons.

Professor of the Faculty of Physics of Moscow University A. A. Vlasov was awarded the Lenin Prize for a series of works on the theory of plasma, containing a fundamental method for studying its properties.

Plasma is an inoculated gas consisting of a huge number of loaded particles. We will encounter it in various electronic devices. It forms the upper layers of the earth’s atmosphere and fills outer space. The behavior of plasma is very different from the behavior of an ordinary gas consisting of neutral particles. In an ordinary gas, the main role is played by direct collisions of its particles. The behavior of such a gas is described by the Boltzmann equation. A. A. Vlasov was the first to show that in plasma such collisions play practically no role, since the electrostatic response does not allow the particles to come close to each other. Therefore, in his equation for plasma, Vlasov excluded the classical term that takes into account the direct abundances of particles, and introduced a term that takes into account the collective influence of loaded neighbors on the behavior of individual particles. This is how the famous “Vlasov equation” was obtained, which formed the basis of plasma theory.

The method of plasma research developed by A. A. Vlasov is used in work on the creation of controlled thermonuclear reactions, in the study of the propagation of radio waves in the atmosphere and outer space, as well as in a vast new field of physics, the so-called magnetic hydrodynamics, associated in part with methods of direct conversion of thermal energy into electrical energy.

Corresponding Member of the USSR Academy of Sciences R.V. Khokhlov and Professor S.A. Akhmanov, working at the Faculty of Physics of Moscow University, were awarded a prize for the study of nonlinear co-ferential interactions in optics.

Object optics deals with processes in which the intensity of light is insufficient to change the physical properties of the medium through which the light passes. The emergence of powerful sources of light beams - lasers - makes it possible to create new optics, so-called nonlinear. She studies the numerous changes in the physical characteristics of the environment under the influence of the passage of light. The foundations of this area of physics were laid by R.V. Khokhlov and S.A. Akhmanov. However, one of the most important achievements of these scientists was the creation of lasers with varying wavelengths of radiation. Typically, each laser has its own strictly fixed wavelength of emitted radiation, its own color. It is determined by natural radiatingweise. The range of possible wavelengths for different lasers is quite poor; it does not contain many tricks needed for physics, chemistry and biological sciences. R.V. Khokhlov and S.A. Akhmanov developed new principles that allowed less colorization of the laser in a very wide range of wavelengths. For example, using their methods, a laser operating on invisible infrared waves can be made to emit ultraviolet rays. Such lasers have many important practical applications. They greatly expanded the possibilities of studying the nature of substances.

The fifth Lenin Prize in Physics was awarded to Yu. N. Denisyuk, an employee of the State Optical Institute, for a series of works “Holeraphy with recording in a three-dimensional environment.”

Objects give us a flat image of the objects imprinted on them. And in the mirror we see a three-dimensional image - the object appears to be located in the depths of the mirror. Of course, what we see behind the mirror is not really there. The image is created by light waves incident on the mirror and reflected from it. Is it not possible

make sure that the three-dimensional picture that we see in the mirror does not disappear even after removing the mirror?
In other words, is it possible to capture a three-dimensional image of opaque objects in the same way that regular photographic film does with a flat image? This problem was solved by Yu. N. Denisok (before him, a similar problem of obtaining a volumetric image of solid bodies was solved by the English physicist Gabor). It turns out that for this it is necessary to record in a special transparent fine-grained emulsion the distribution of light waves near the object under consideration (as they say, to obtain a hologram of the object). If you develop the resulting “photograph,” it will be completely different from the object depicted. However, having illuminated the developed plate with white light, we will see close to it a magnificent three-dimensional image of the object photographed in this way.

If you insert a mirror and take a photo in the usual way, you will get a circle with light reflections. If you get a hologram of such a mirror, then the image created with its help will be so real that it can focus the light falling on it like a real mirror.

A new method for obtaining three-dimensional images, created by Yu. N. Denisok, opens up the possibility of creating color three-dimensional cinema and television, improving radar and sonar.

In the field of mathematics, the Lenin Prize was awarded to a team of Leningrad scientists - academician Yu. V. Linnik, corresponding member of the USSR Academy of Sciences Yu. V. Prozhorov, professor I. A. Ibragimov and Yu. A. Rozanov for a series of works on limit methods of probability techniques. In these works, the most important patterns of a number of complex random processes that play a major role in many areas of science and technology were found. The patterns found greatly facilitate the study of random processes that are widespread in nature and society.

The Central Committee of the CPSU and the Council of Ministers of the USSR also decided to award the 1970 Lenin Prizes in the field of science and technology to a large group of scientists, designers and industrial workers for the following works:

— a set of scientific and technical work carried out with the aim of creating an experimental orbital station and implementing it during launches of the Soyuz rocket and space system;

— creation of automatic mechanical stations “Venera-4”, “Venera-5”, “Venera-6” and a complex of scientific research to determine the physical parameters and chemical composition of the atmosphere of the planet Venus;

the creation of a meteorological system that, with the help of artificial Earth satellites “Meteor”, provides the receipt and prompt processing of global meteorological information for those in need of addressing these complex scientific and technical problems, a great contribution was made by Soviet mathematicians and physicists.

To the article “Non-hanging polyhedra”

Let us show that from each face of an arbitrary convex polyhedron one can go to any other, moving from funny face to funny face. To do this, take two arbitrary faces and select a point in them that does not lie on the boundary. Let’s connect the selected points with a segment. This segment does not intersect the planes of the faces of the polyhedron, or the polyhedron is convex. Let us draw a plane through this segment that does not contain the vertices of the polyhedron: this is possible, since the polyhedron has only a finite number of vertices. The drawn plane carves two broken lines on the surface of the polyhedron. They do not pass through the vertices of the polyhedron, i.e., moving along them, we will move from one adjacent face to another and pass from the vertex face to the second. Telerfficium some face of a polyhedron, say $\Gamma_1$ , and two points $O_1$ and $O_2$ , distant $r_h$ from all its vertices. Let us assume for simplicity that three faces converge at all vertices of the polyhedron; In general, the essence of the matter remains unchanged. the vertices of any face adjacent to $\Gamma_1$ are removed by $r_h$ either from $O_1$ or from $O_2$ , but not from both, or all points equidistant from $O_1$ and $O_2$ lie in the plane of face $\Gamma_1$ . Let us assume that there are also faces $\Gamma_2$ and $\Gamma_3$ , that the vertices of the first lie at a distance $r_h$ from $O_1$ , and the vertices of the second lie at a distance $O_2$ . It is clear that then there are two such faces that converge at one vertex, and therefore, by virtue of an additional assumption, are adjacent. Then the second end of their common edge is equal to $O_2$ and $O_1$ , which contradicts the convexity of the polyhedron.

So, the vertices of all faces adjacent to $\Gamma_1$ are equal to the same point, for example, $O_1$ . This is also true for the vertices of faces adjacent to $\Gamma_2$ or $\Gamma_3$ , etc., i.e., for all vertices of the polyhedron. The opposite statement is obvious.

Let us show that if all arc boundaries and angles of the constructed polyhedron are less than l, then it is convex. Let us take a plane polyhedron of its faces. All faces adjacent to it lie on one side of this plane, which means that on the same side lies the entire triangular paramid containing the extended face, and three other paramids that have a common edge with the first. Consequently, on the same side lie two faces of the octahedron, containing one of the edges of the vertex, and therefore the octahedron itself and the remaining paramides. To complete the proof, it is enough to calculate the arc boundary angle of the octahedron.
Proceeding as in the proof of Steinitz’s theorem, it is easy to see that the sum in the first part is strictly greater than 0 (and not greater than 0).
In the example based on Steinitz’s theorem, it is necessary to glue only part of the amdd.
The proof coincides exactly with the proof that if $k$ faces converge at each vertex of a polyhedron, then it does not completely satisfy Steinitz’s theorem.
Let us show that any closed broken line composed of edges of a polyhedron is even-linked. It is clear that it is sufficient to prove this for broken lines without self-intersection.

Let us consider some broken line that does not contain self-intersection and cut the polyhedron along this broken line. Let there be $K$ faces in one part, and $L$ and $L \leq K$ in the other. The integer $L$ is called the girth of the broken line. If the girth is equal to 1, then the statement we prove follows from the conditions of the problem. Let us apply induction, let the problem be solved for broken girths less than $L$ . Let us choose a face $\Gamma$ whose edge belongs to the broken line and which lies in that part of the polyhedron where there are fewer faces. Let $P_1, P_2, \dots, P_k$ be the edges of the polyline that are the edges of the face $\Gamma$ and $P_{k+1}, \dots, P_s$ the remaining edges of the face $\Gamma$ . Let’s move on to a new broken line, which is obtained from the original by replacing the edges $P_1, \dots, P_k$ with $P_{k+1}, \dots, P_s$ . It is possible that the new broken line has self-intersections and even consists of several unconnected pieces, but the girth of each of its non-self-intersecting parts is certainly less than $L$ , which means that the new broken line is even-linked. Let’s assume that it has $2N$ ringing. The face chosen at the beginning of the proof has $2Q = s$ lines, then the number of links in the original broken line is $2N+2Q-2K$ —an even number (Fig. 1).

We will present the solution to Problem 8, from which Problem 7 follows easily. Consider a $k$ -faceted angle whose vertex does not lie on the sphere. Let us draw a ray $l$ , entirely contained by the rutri (but not on the boundary) of the angle. Let the vertex initially lie outside the ball. Each circle divides the sphere into two “hats”. Let’s consider the circles - the intersections of the edges of the angle with the sphere and choose for each of them the cap that does not contain the point $A$ and $B$ - the points of intersection of the ray $l$ with the sphere. Consider a step-afficient projection onto a plane with the center of the projection at point $A$ . The fixed $k$ caps do not intersect at one point, which means that the projection will produce a picture similar to figure 2.

Fig. 2.
$B'$ is the image of point $B$ under projection. The sum of the angles of a polygon $A_1, \dots, A_k$ is strictly greater than the sum of the relative angles. We do not know whether it is convex, but it is clear that the straight segments connecting the point $B'$ with the points $A_i$ belong entirely to it. This follows from the definition of ray $l$ . Due to this, $A_1 + \dots + A_k = \pi(k-2)$ and the sum of relative angles is less than $\pi(k-2)$ .

If the vertex lies inside the ball, then we prove in exactly the same way that the sum of the relative angles is greater than $\pi(k-2)$ .

Let’s move directly to solving the problem. Let $B_1$ be a vertex whose position is undefined. Let’s divide the vertices, as described in task 6, into black and white. Let $B_1$ be white. It is easy to see that if the vertex of a $k$ -faceted angle lies on the sphere and all its edges intersect the sphere except one edge tangent to the sphere, then the sum of the relative angles is equal to $\pi(k-2)$ .

Now let’s move on to the external relative angles and calculate their sums at each vertex. For all vertices except $B_1$ , these sums are obviously equal to 2π. If $B_1$ does not lie on the sphere, then the sum under it is not equal to 2π. Let’s add the equalities for white vertices, subtract from them the equalities for black and

As a result, we get that $0 \neq 0$ . Thus, $B_1$ lies on the sphere.

Let’s assume the opposite. Let us connect the point of contact of each face with the vertices of the face by segments and consider the angle between two segments, which rests on some edge of the polygon (Fig. 3). The magnitude of this angle does not depend on the choice of one of the faces containing the edge. $\Delta O'B_1B_2 = \Delta O''B_1B_2$ (according to the sides), which means $<B_1O'B_2 = <B_1O''B_2$ .

We assign to each edge the value of the angle resting on it. Let us denote the angle assigned to the edge $P_k$ by $\beta_k$ . The sum of the angles assigned by the edge of each face is 2π.

Further proof comes from

Fig. 3.
proof of Steinitz’s theorem by replacing the word vertex with the words edge.

$\frac{a}{b} = [1; 1, 2, 1, 2, \dots]$ .
$[1; 1, 1, \dots] = \frac{\sqrt{5}+1}{2}$ ;
$a_{10} = R \frac{\sqrt{5}-1}{2}; \sin 18^\circ = \frac{\sqrt{5}-1}{4}$ .
$[0; 1, 1, \dots] = \frac{\sqrt{5}-1}{2}$ ;
$a_{10} = R \frac{\sqrt{5}-1}{2}; \sin 18^\circ = \frac{\sqrt{5}-1}{4}$ .
If $a_0 \neq 0$ , then move the entire “comb” one step to the right, and put a zero in place of the integers. If $a_0 = 0$ , then move the entire comb one step to the right. For example:
$\alpha = [3; 1, 2, 5], \frac{1}{\alpha} = [0; 3, 1, 2, 5]$ ,
$\beta = [0; 2, 2, \dots], \frac{1}{\beta} = [2; 2, 2, \dots].$

Yes, with the only difference that the ≤ sign will be one step to the right, i.e.

$p_0 < p_1 \leq p_2 < p_3 < \dots$

To the article “Alice through the Looking Glass”

4 fum.
2 fum; 6 inch
60 fum; 3 inch; 3 inch; 4.
2.6 inch; 6 inch
0,25; $1/4 = (1/2)^2$ .
A truncated paramid measuring about $1/2 \times 1/2 \times 1/4$ inch.
3 inches wide; $3/8$ inch thick.
She will be too thin.
a) ordinary; 6) oval dial; when expressed, the arrows lengthen and shorten.
The same as with the clock in Exercise 11, 6.
In the direction $63^\circ 50'$ northeast.
No.

To the article “On one inductive method for proving inequalities”

a) $f(x) = x^p$ ; to prove the inequality for $n - 2$ it is convenient to introduce the notations $x = \frac{x_1 + x_2}{2}$ and $d = \frac{x_2 - x_1}{2}$ and replace that if $(x + d)^p = C_p^0 x^p + C_p^1 x^{p-1} d + C_p^2 x^{p-2} d^2 + C_p^3 x^{p-3} d^3 + \dots + C_p^p d^p$ , where $C_p^0, C_p^1, C_p^2, \dots$ are the coefficients of the polynomial $(x + d)^p$ , then $(x - d)^p = C_p^0 x^p - C_p^1 x^{p-1} d + C_p^2 x^{p-2} d^2 - C_p^3 x^{p-3} d^3 + \dots + (-1)^p C_p^p$

c) $f(\alpha) = \lg \sin \alpha; \quad 0 < \alpha < \frac{\pi}{2}$ .

e) $f(x) = \lg (1 + 10^x), -\infty < x < \infty$ ; in the resulting inequality put $x_h = \lg \frac{b_h}{a_h}$ ,

To the article “An endless work”

First, let’s make sure that we get a geometric progression:

$(1 + x + x^2 + \dots + x^9) \times (1 + x^{10} + x^{20} + \dots + x^{90}) \times (1 + x^{100} + x^{200} + \dots + x^{900}) \dots = 1 + x + x^2 + x^3 + x^4 + \dots$

Indeed, $x^{a_n a_{n-1} \dots a_0}$ (where $a_n a_{n-1} \dots a_0 = a_0 + 10a_1 + \dots + 10^n a_n$ is the decimal notation of any non-negative integer) must necessarily appear in the process of multiplying parentheses and, moreover,