Good afternoon, dear Colleagues!
I call you Colleagues, because you are now students of the University and I am connected to the Universites for a long time: more than 30 years. We are also Colleagues, because you entered the Department related to Mechanical Engineering, and I work in the Institute for Problems of Mechanical Engineering.

The title of my lecture is pretty long:


First of all I would like to tell you about St.Petersburg. It is my native city, my favorite city, my beloved city, and I would like to share with you my love. It is a very beautiful city and I would like you to taste its beauty now.

Second, I would like to use this unique opportunity to talk to such a large audience of young Japanese students. I am 50, and you are less then 20. I would like to share with you some important information which a person of my generation need to share with people of your generation. That is why I would like to speak about "Virtual Age" or "Information Age", as the next, XXI century is sometimes called.

Third, since we are Colleagues, I would like to share with you the most interesting and exciting information about our profession and to tell you what I am interested in now. I would like to give you an idea of new results in my field by simple example. My field is Control Theory and currently I am interested in control of oscillatory systems. I believe you agree that the pendulum is perhaps the simplest oscillatory system of Mechanical Engineering and you understand why the third part of my lecture is devoted to pendulum and control.

Now let us start.


- Virtual Look

I arrived to Kumamoto from St.Petersburg. It is at the Far West of Russia (far, if you are looking from Japan!)
And you will NOT find it on the World Map, if you click here:
because World is too large. However you will find it on the Map of Europe, if you click here:
It is even better seen on the map of Finland:
because it is very close to the border of Finland - less than 200 kilometers or half an hour of flight.
My flight took 20 hours, with two stops: in Copenhagen and in Tokyo. Its last part (from Tokyo to Kumamoto) took only 1.5 hours. Now I know that Kumamoto is near Tokyo!

St.Petersburg is second biggest city in Russia, after Moscow. The population of St.Petersburg is about 5 millions, while the population of Moscow is about 13 millions. Of course these are "small" cities compared with Tokyo (34 millions). By the way, you may find more up-to-date information about these and other big cities in the World on the WEB:
As you know, Moscow is Russian Capital city. But St. Petersburg is former capital of Russia! It used to be the Russian capital for 200 years, almost from its foundation in 1703 till 1918 when the capital was moved to Moscow because of the Wars (World War I and Russian Civil War). Thanks to being the capital in the past, St.Petersburg has many attractions: beautiful buildings, churches and cathedrals, palaces and museums. Perhaps it can be compared with Kyoto, which also is former capital city.

St.Petersburg is almost 300 years old. It was founded in 1703 by the Russian Emperor Peter the First (or Peter the Great) and called in honor of St. Peter, guardian of the gates of Heaven.. Peter was at war with Sweden and after a few victories his troops reached the mouth of a big river (Neva) that falled into a gulf of the Baltic Sea. And he began building the fortress on the small Zayachij island in the mouth of Neva. You may see Zayachij island at
He has built the fortress and called it the Peter and Paul fortress:
and he invited the italian architect Domenico Tresini who built this beautiful shrine - the Peter and Paul cathedral:
It reaches 122.5 meters height and there is an angel on the top of its spire:
Peter the Great himself is buried in this cathedral and other Russian Tsars and Tsaritsas (Kings and Queens) are also buried in this cathedral. In 1998 a very important event took place here: the last Russian Emperor Nikolas II, who was killed by communists in 1918 was finally buried in this cathedral too.

One of the first buildings in St.Petersburg was Admiralty - the shipyard (verf) where different ships used to be built:
Another big and very beautiful building is St.Isaac's Cathedral
Its height is 101 meter. It was erected by french architect Monferrant.

You may also want to take its winter look:
Speaking about Tsar Peter, we should not miss the chance to take a look at the monument dedicated to his memory:
It is a favorite attraction for many tourists. It was created by French architect Falconet. It is beautiful even in winter, under the snow, just look:
The horse of this monument is oppressing the snake which symbolizes the victory of Russia over Sweden.

There are many beautiful churches and shrines in St.Petersburg. Among the most beautiful ones is the Church of Resurrection:
It was erected just over the place where the Emperor Alexander II was killed in 1881 by a terrorist. That is why the church is called: Savoir on the Blood. Other magnificent churches are Cathedral of Smolny monastery:
and Kazan Cathedral:
You can enjoy the views of other St.Petersburg churches on the WEB:

Unfortunately, many beautiful churches were destroyed during the communists rule in the 1930s. However - again thanks to the WEB - you can take a look of some of them if you visit the site "Lost St.Petersburg" with collection of views of nonexisting buildings:
For example, you will find there views of nice Borisoglebskaya church:
or Savoir on the Water shrine
which was erected as a memorial to Russian seamen who died in the Russian-Japanese war in 1904-1905. Both of them were destroyed in 1932.

- Hermitage

Now let us talk about museums. There are more than 110 museums in St.Petersburg. The list of them can be found at:

However the most famous of them and the largest one is The Hermitage. The museum is located in 4 buildings. One of them is Winter Palace - the former residence of Russian Emperors. You may enjoy its view from the riverside:
or from the side of Palace Square:
By the way you can see here the column which is also very famous - the Alexandrovsky column. It is amazing that the column is made from single piece of the stone (granite). A very big stone for the monument was found and mined in Finland and it was a big problem to transport it to St.Petersburg. The column is 47.5 meters high, it weights 600 tons. Look as big it is:
The Hermitage is the second largest museum in the world after the Louvre in Paris. Since it is located in the former Palace of the Emperors, you can find reachly decorated interiors there. There are some former gala and private Emperors' rooms on display:

The Hermitage houses huge collections of Western European Art, Oriental Art, Applied Art, Ancient Roman, Greek and Egyptian Art. However, the main fame of The Hermitage is due to its collections of paintings and sculptures, especially those of Western European Art. There are collections of Italian, Spanish, Flamish, Dutch, French, English and German paintings dated from 13th to 20th centuries. Just small celection already looks very impressive: Madonna Litta by Leonardo da Vinci:
The Apostles Peter and Paul by El Greco:
One more Madonna - this one with flower, also by Leonardo da Vinci:
Danae by Titian:
Another Madonna with Joseph by Rafael:
"Venus and Cupid" by Lucas Cranach:
The famous "Return of the Prodigal Son" by Rembrandt:"

The Hermitage has huge collection of Impressionists.
Pierre-Auguste Renoir:
Paul Cezanne:
Vincent van Gogh:
Paul Gauguin:

Also Postimpressionists like Henri Matisse:
and Pablo Picasso:

You can know more about The Hermitage if you click at:

- Petergof

There are masterpieces of architecture not only in the center of the city. As you can imadgine tsars needed palaces not only for winter but also for summer. That is why we have a few brilliant architectural ensembles in the suburbs. The most famous one is of course Petergof, where the Summer Palace of Peter the Great was created:
Its style is similar to that of the Palace of Versailles, the residence of the french Kings . It is very rich and well decorated:
And the most famous attraction of the Petergof are its fountains look here:
or, better here:
There are more than 200 fountains in the Petergof. But the key figure among them is the famous Samson:
who is still fighting with the lion. It also symbolises the victory of Peter the Great over Swedish King...
You can see even more fountains at

And you can find more fascinating views of St.Petersburg on the WEB, for example here:
You can make a virtual tour of St.Petersburg here:
know more about its history and architecture here:
and even get a visitor's guide here:
You do not need to know Russian, just English. However, you would be able to learn much more interesting if you would know Russian. So, why not to start virtual learning Russian language here:

Let us take a general view of St.Petersburg center:
In the left corner of this picture you can see the main building of the St.Petersburg State University. It means that it is high time now to speak about universities and students.

- University

There are 43 state universities, 22 more military universities and some number of private universities in St.Petersburg. The most well known of them is St.Petersburg State Univerity which is classical university with many different Faculties and Departments. It was founded 275 years ago, in 1724 by special decision of Tsar Peter the Great, together with Russian Academy of Sciences and the special school: Academic Gimnasia. Therefore 1999 is a kind of jubillee year and we have a lot of different special events dedicated to this jubillee. Among them are special ceremony of fountains opening in Petergof, and the chess match between University alumni: grossmeister Viktor Korchnoy and World ex-champion Boris Spassky. (By the way the match was won by Korchnoy with the score 6:4). You can know more about the St.Petersburg University at:

Among first professors of the St.Petersburg University were great mathematicians: Leonhard Euler and Daniel Bernoulli. By the way Euler worked for 30 years in St.Petersburg, and his best papers were written there. Later great physicist and chemist Mikhail Lomonosov was rektor of the University, great chemist Dmitry Mendeleev, author of the periodic system of chemical elements also was professor of our University. In XIX-XX centuries the famous Russian mathematician P.L.Chebyshev and his successors A.A.Markov, A.M.Lyapunov, V.A.Steklov created tradition of St.Petersburg mathematical school. And many famous Russian writers, poets, composers, musicians, painters graduated from St.Petersburg University. Among its alumni and professors are 7 Nobel prize winners, namely, I.P.Pavlov (1904), I.I.Mechnikov (1908), N.N.Semenov (1956), L.D.Landau (1962), A.M.Prokhorov (1964), V.V.Leontjev (1973), L.V.Kantorovich (1975). Now there are 20 Faculties in the University with about 20000 students. Among them is the Faculty of Mathematics and Mechanics which I proudly graduated from in 1971. Now it is situated in the new campus of the University in Petergof, not far from the famous Petergof Fountains. You may visit its home page and take a look of its building:

A disadvantage of the Petergof campus is that it is rather far from the center of the city: it takes 1.5 hours to get there by train. Frankly speaking, the life of students in Russia is rather difficult during recent years, especially after the financial crisis that happened in Russia on August 17, 1998. The student's scolarship is about US$10-US$15, while before August 17, 1998 it was about US$40-US$60. And professors' salary is about US$40-US$50, while before August 17, 1998 it was some US$150-US$200. Therefore both students and teachers need to find some extra jobs in order to survive. And it is very difficult to maintain traditions of Euler, Lomonosov and Mendeleev novadays. Nevertheless, we are trying and we are happy that we have many talanted students.

I give you only one example. May be some of you know about the International Collegiate Programming Contest. The teams of young software programmers from different universities worldwide are competing there in solving tasks from Computer Science. This Contest is organized by ACM (Association of Computing Machinery), sponsored by IBM Corporation and it is very prestigeous. In 1998 the Contest took place in Atlanta, USA. And in 1998 the team of young programmers from St.Petersburg University was second in this prestigeous competition among 54 teams advanced to the Finals from 1250 teams. You may take a look of the Final Standings of 1998:

In 1999 the Contest took place on April 11 in Eindhoven, The Netherlands. This year the competition was still more strong: 62 teams from 1457 were selected for participation in the Finals. This year our team was not so lucky: it was only 9th. However, another team from St.Petersburg was the 3rd! It was the team of St.Petersburg Institute of Fine Mechanics and Optics. So now two student teams from St.Petersburg are among top ten in this Contest. You may take a look of the Final Standings of 1999:

You may also look at the team of St.Petersburg University:

or at the Champions of Asia - the team of National Taiwan University:

You may know more about the ACM Contest at:

Why not to download the tasks set and try to solve them! And may be next year the team of the Kumamoto University will be the Champions of Asia!

After discussing such real things as St.Petersburg and St.Petersburg University let us pass to the second part of the lecture and talk about some virtual things.


- Paradoxes of the Virtual World

During the first part of my lecture you could learn some information about St.Petersburg and university life and also could enjoy some interesting and beautiful pictures. An important and impressive thing for me was that all this information, pictures and much more about St.Petersburg one can find in the Internet (terms "on the WEB" or "in the Net" are also of use). It means that there exists not only real city St.Petersburg, but also a kind of "virtual St.Petersburg" which is, perhaps, not so large and diverse as the real one but is very interesting nevertheless. Same is valid for other cities of the World. Therefore we can say that there exists a kind of "VIRTUAL WORLD". It was created very recently, in fact in the late 90s. It was generated by the real world, but now it has already its own independent life. Not only the cities with their business, travel, shopping information are objects of this Virtual World. There exist virtual literature, virtual music, virtual video, virtual games, entertainments, so on. Just imagine: the Virtual World did not exist some 10 years ago. Some 5 years ago it was in its very beginning. And now many people of the Real World spend a few hours per day in the Virtual World! So what can we expect for new century?

Let me tell you about one of my observations here in Kumamoto. I saw big aquariums with fish in some public places like banks and department stores in Kumamoto. And I was very surprised when learning that these fishes were virtual ones! They were very nice small things: they were floating and looking at me, but they were virtual. They were floating in the virtual water, eating virtual sea plants and even making virtual fights! And I began thinking that may be soon the Virtual World will become as rich, interesting and important as the Real one...

That is why I decided to share with you my thoughts about some features of this Virtual World in order to better understand its virtual life.

Important thing is that the Virtual World deals with neither substance or matter, nor with energy. It deals with information and the laws in it are quite different from the laws of the physical world. I think that some of these laws are stil to be discovered. In XXI century people will make new efforts to understand the laws of the Virtual World. May be some of you will discover these laws in future. And now I would like to draw you attention to some paradoxes which may give rise to new discoveries.

EXAMPLE 1. Suppose I give some money to one of you. In this case I will have less money, won't I? Similarly, if the moving ball strikes another ball and transfers its energy to another ball it will have less energy. In the contrary, if I have some information and give it to one of you or, even to all of you I will not have less information! Instead, you will have more information and the total amount of information will increase. Moreover, the value of my information for myself will also grow, because more people know about my information. And if you pass this information to other people, saying "It is information from Mr. Fradkov from St.Petersburg, Russia", the value of my information will grow further and I will be pleased still more! It is surprising, but it is true. So, please, pass the information from my lecture to everybody and do not forget to mention that "It is information from Professor Fradkov from St.Petersburg, Russia"

Sometimes people do not want information to grow and to be distributed freely. They introduce restrictions of access, passwords and so on, because they want to get money for their information. But information has its own laws: it may go through even very small holes. You can find a lot of free information on the WEB: free books, free software, free news, etc. You can hardly imagine how much can be found!

EXAMPLE 2. There are no distances on the WEB.
Internet has some geography, but it is topic-oriented rather than space-oriented. During my staying in Kumamoto I discussed many things with my friends and colleagues. One of them is in USA now, another one is in Holland, the third one is in Norway, and of course many of them are in St.Petersburg. Looks like far from each other. However I never noticed this spatial difference just because we had same language and culture and the things we were discussing were important for all of us. We were close in the cyberspace because we understood each other very well. Summarizing: Cyberspace has no distances.
The difference between points is determined by language and culture rather than by geographical location.

EXAMPLE 3. Information and ideas in the Virtual World can be created and freely distributed as texts, images and sounds independently of the Real World. The things (texts, images and sounds) which do not exist or are not allowed in the Real World are possible in the Virtual World. For example, look at this fork.

How many teeth does it have?

Another puzzle: How many legs does this elephant have?

Many images which are impossible in the Real World were created by the famous Dutch graphic artist Maurits Cornelis Escher. For example, look at one of his so called "impossible buildings" (lithograph "Ascending and Descending", 1960):

Or, look at this lithograph ("Drawing hands", 1948):

You can learn more about M.C.Escher and enjoy other his images and other optical illusions at:

M.C.Escher was born in 1898 and died in 1970. It is amazing that he created his images before the Computer Age and long before creation of the Virtual World. In 1998 the 100th anniversary of his birth was celebrated and the big exhibition of his works was organized in Rotterdam, in his native country Holland. I was lucky to visit this exhibition. You can learn more about this celebration at:

Perhaps, Maurits Escher was the first WEB-designer in the history. I believe, profession of WEB-designer will be very popular in the XXI century.

- Virtual Watches Real

Although the Virtual World looks exactly like a free world, it is not the case. In fact it is driven by the Real World. It means that the Virtual World is watching and copying the images of the Real World. An interesting thing is that live copying is possible. Perhaps you know that there are live cameras in many places of the Real World that are connected to Internet. Images are renewed every few minutes or even seconds. You can check what is going on in New York, Paris or Tokyo RIGHT NOW. There are live cameras in St.Petersburg too. One of them watches St.Isaac Cathedral which you are already familiar with:

The view is beautiful and it is listed among Top Ten live cameras of the World. You can look at the other of Top Ten and also to browse other live cameras at:;file:TOP10

By the way, there is Japanese site in Moscow with live view of Kremlin:

One nice thing about live cameras is that you can make pictures of your friends or relatives. For example from Kumamoto I have made the picture of my wife Olga in St.Petersburg with the help of another live camera located near beautiful small river Mojka:
It was not so difficult. I just asked my wife to come near this camera and copied the image when I saw her in the picture. Then I sent it to my wife by E-mail. She was very happy to receive her picture "Made in Japan".

There are also other projects related to watching the Real World. I would like to tell you a few words about space flights. Perhaps you know about the project of International Space Station (ISS), carried out by 16 nations, including Russia, USA and Japan. This project evolved from program of International flights on the Russian space station "Mir". You can see the photo of real "Mir" station:
or here:

Station "Mir" works already for 13 years in the space, much more than was initially planned. It is an absolute World record. Soon it will go down and finish its life. And the ISS station is now under development. Its first two parts were launched in December, 1998 by Russians and Americans and connected in the space as follows:

You can see the Russian made module "Zarya" and US made module "Unity". The next module is to be launched and connected in May, 1999. The first mission will start in 2000, while the whole station will be ready in 2004. So how is this story related to the Virtual World? Let me explain. You can watch current location of already existing part of ISS if you visit the WEB-site with realtime data:

The picture is changing every 5 seconds. And when you find out that ISS is near Kumamoto NOW, why not to go out and to check it in the sky?!

Similarly, you can watch current location of Russian station "Mir" at:

And you can learn more about space flights, if you visit WEB sites of US space agency NASA:

Russian Space Agency:
or National Space Development Agency of Japan:

You can also visit the page of Russian Space Agency at NASA site:

but information is different there.
Among different historical photo you will find there Russian shuttle "Buran" flying on the huge Russian-Ukrainian aircraft "AN-225":
Or, you will see "Buran" prototype staying in the Park in the center of Moscow and open for visitors: everybody can touch the spacecfaft, enter it and walk in it:
And this is photo of Mir-Shuttle joint station (from NASA):

More pictures and stories are available from Russian Aerospace Guide:

I would like to say that it is a very good example of international cooperation. You know that US and Soviet Union were competing in the space flights for many years. E.g. SU launched the first artifucial satellite ("sputnik" in Russian) in 1957, then SU first launched a man (his name was Yuri Gagarin) into the space in 1961. US first performed the manned moon landing (Apollo-11)in 1969. And now you can see US and Russian modules together in the sky. Isn't it better than bombing each other?!

Also it is very good that Japan participates in the project. May be some of you will take part in this project in future and watch the Real World from the sky!.


- What is Control?

During the previous part of my lecture we were discussing about the Virtual World and how it can watch the Real World. But the Virtual World can not only watch, it can influence the Real World and even control it. Therefore let us talk about Control. Such a back influence is called "feedback" It is studied by Control Theory and in a more general context, by Cybernetics (this term was introduced in 1948 by American mathematician Norbert Wiener for the science studying communication and control in the animal and machine, but now its meaning is even more wide). The Control Theory is very much related to your future field: Mechanical Engineering and Material Science. And it is also my field where I am doing research for about 30 years. During recent years I am interested in Control of Oscillations and Chaos. Now I would like to take a simple example of real mechanical oscillatory system and demonstrate how you can change its physical properties by means of Cybernetics.

I believe you agree that pendulum is the simplest mechanical oscillatory system. Let me create an experimental pendulum device right now. I take simple wooden ruler which I brought from Russia, having a small hole near its end. Then I take a metal pin borrowed in the University of Kumamoto and put it into the hole - it will be the rotation axis of our pendulum. The device is ready. Isn't it a real "Russian-Japanese made" device!

Now I should explain what is control system. In general control system consists of 4 parts: controlled plant (in our case it is the pendulum itself); actuator (in our case it is just my hand), sensor (in our case it is my eye which can measure the angle of the pendulum and, possibly, its angular velocity) and, finally, controller acting according to some rule or algorithm (in our case the controller is is in my mind, while its rule or algorithm, I suppose, belongs to the Virtual World). Thus, controlling the pendulum requires some influence from the Virtual World.

Look at the two possible schemes of the control system. The simplest case is when controller does not use the measurements (so called open loop systems, see Fig.1) while more advanced controllers use online measurements and that is why they may achieve better quality (such systems are called "feedback" or "closed loop" control systems, see Fig.2).

In our case moving the pin horisontally back and forth will be input or control action. Angle of the pendulum will be output variable. Now let us perform some experiments.

- Feedback Resonance

First let the pendulum be affected by small periodic control action without any feedback. Then it will perform some periodic oscillatory motions - swings - with the same frequency. If the input frequency is changing, the amplitude of the swings will also be changing and reach its maximum at the so called resonance frequency that is just natural frequency of small oscillations of the pendulum. This phenomenon is called resonance and it is well known in physics since Galileo Galilei first mentioned it in 1638. Resonance has many applications in science and engineering, e.g. it provides base for spectroscopic investigations, telecommunications, etc.

Then let us increase input amplitude. The motion of the pendulum is becoming more complicated and even nonperiodic. This phenomenon is caused by nonlinear dynamics of the large oscillations of the pendulum. It is called nonlinear resonance. It is well studied by physicists during last two decades.

And now we come to the culmination, key point of the lecture. Is it possible to swing the pendulum more than the physical intuition predicts? Look: I am moving the pin slightly, but following the swings of the angle, And I can make the swings larger! Why it is possible? Because I was using the feedback! Our control system is the closed loop system. It can provide a physical system with new properties, and one of them we were observing right now. This property can be called "FEEDBACK RESONANCE". The concept of "Feedback Resonance" is a new one. The paper describing it was published in the scientific journal "Physica D" in April,1999 (see references below). So, you have got acquainted with very recent scientific result. I believe, it will have applications in many fields, including Mechanical Engineering and Material Science.

The question arises naturally: how to design the algorithm, which provides the system with new properties? To answer it we need to jump into the Virtual World and to write down the mathematical model of the pendulum. In fact it is just the Newton's law applied to the mechanical system:

m y''+ ry'+mg sin(y)=(cos y)u(t),

where u(t) is input acceleration, y=y(t) is angle of the pendulum, y' is angular velocity, y'' is angular acceleration, m is mass, r is friction coefficient. After applying the theory that was developed in our Lab (see references) different control algorithms can be obtain. For example, the following one:

u(t)= - K[E(t)-Ed](cos y)y',

where E(t) is the current energy of the pendulum, Ed is the desired value of energy, K is proportionality coefficient called "feedback gain". Our algorithms confirm existence of the Feedback Resonance and allow to reach the desired energy level from almost all initial conditions.

If you get interested and want to play with the controlled pendulum yourself - why not to play with the Virtual Controlled Pendulum which you can find on the WEB here (requires Internet Explorer)

The pendulum system is very simple and nicely demonstrates the feedback resonance phenomenon. If you get more interested and would like to know how to solve more complicated problems you may find the theory and examples in our recent books and papers:


1. Fradkov A.L., Pogromsky A.Yu., ``Introduction to control of oscillations and chaos", World Scientific Pub. Co, Singapore, (1998).

2. Fradkov A.L., Miroshnik I.V., Nikiforov V.O. ``Nonlinear and adaptive control of complex systems'' Kluwer , Dordrecht, (1999).

3.Fradkov A.L., ``Exploring nonlinearity by feedback'', Physica D, vol. 128/2-4 pp. 159-168, (1999).

4.Fradkov A.L., ``Investigation of physical systems by means of feedback", Automation and Remote Control, vol. 60(3), (1999).

5.Fradkov A.L. ``Feedback resonance of nonlinear oscillators'' Proc. 5th European Control Conference, Karlsruhe, Aug.31-Sept.3, (1999).

6.Andrievsky B.R., Fradkov A.L. ``Feedback resonance in single and coupled 1-DOF oscillators'', International J. of Bifurcations and Chaos, vol 9(10),(1999) (to appear).

7.Fradkov A.L., ``Speed-gradient scheme in adaptive control'', Automation and Remote Control, vol. 40(9), 1333--1342, (1979).

8.Fradkov A.L., ``Swinging control of nonlinear oscillations'', International J. of Control, vol. 64(6), 1189--1202, (1996).

Also I invite you to visit the home page of our Lab:
where you can find more information and publications, including the ongoing conferences on control and nonlinear dynamics.

Particularly you may get interested in the 2nd International Conference "Control of Oscillations and Chaos" (COC'2000), see its WEB-site here:
It will take place in St.Petersburg, on July 5-7, 2000. This time of the year is especially pleasant: it is so called "White Nights" period. During this period the dark time of the night is very short and light. It makes the sights of St.Petersburg still more fascinating and attracts still more tourists from all over the World during this season.

Why not to take chance to visit our beautiful city during the "White Nights" and to visit this Conference?! !


I would like to thank Japan Society for Promotion of Science (JSPS) for support of my staying in Japan which made this lecture possible. I am also grateful to Prof.Z.Iwai for his kindest invitation and for arrangements which made my visit to Kumamoto not only possible but also very pleasant. I would like to thank other professors, students and staff of the Department of Mechanical Engineering and Material Science for their kind assistance during my staying in Kumamoto. Finally I am grateful to member of our Lab Dmitry Tomchin for WEB-design.