Presentation "Contribution of scientists S. Popov and V.A

ST. PETERSBURG BRANCH

MATHEMATICAL INSTITUTE

THEM. V.A.STEKLOVA

Abstract on the history of science by a graduate student

Lifshits Yuri Mikhailovich

Scientific supervisor ………………../ Yu.V. Matiyasevich

Doctor of Physical and Mathematical Sciences, corresponding member. RAS

Principles of development of the theory of algorithms

Yuri Lifshits

1. 
   Introduction
2. 
   Timeline of algorithm theory
3. 
   Current state theory of algorithms
   1. 
      Using other sciences in algorithms
   2. 
      The most significant applications of algorithms

   3. Ideas and techniques in the theory of algorithms

4. 
   Formation of popular areas of research
5. 
   Research styles
6. 
   Conclusion and conclusions
7. 
   List of sources

1. Introduction

In this work we want to systematize the factors influencing the formation of an active research plan in the theory of algorithms. How do specific areas of research become popular, enter the spotlight, and then gradually lose their leading role? What factors determine the popularity of research tasks? On what principles is the assessment of scientists' achievements based? What work styles exist to obtain the most important (in the future) results. To answer these questions, we begin by introducing the chronology of the main achievements in theoretical computer science. In the next section we describe the current state of research in theoretical computer science. Next we list the main factors that influence the assessment of the “importance” of theorems and theories. The next issue examined was research styles. In conclusion, we will formulate themes that may become central in the very near future.

2. Chronology

• 
  IV-III centuries BC The appearance of the first algorithms: Euclid's algorithm for the greatest common divisor, the sieve of Eratosthenes.

• 
  1822 - Charles Babbage began to create a "difference engine"

• 
  1926 – Boruvka - the first algorithm for finding a spanning tree (hereinafter Jarnik, Prim and Kruskal).

• 
  1936 - In Germany, Konrad Zuse comes to the conclusion that programs consisting of bit combinations can be remembered; he is applying to patent a method for automatically performing calculations using a "combination memory"

• 
  1936 – Alan Turing, the strict concept of an algorithm (Turing machine). Church's thesis: any algorithm can be represented as a Turing machine.

• 
  1939 – Leonid Kantorovich – formulation of the problem linear programming, the first algorithm to solve it.

• 
  1945 - John von Neumann, in his report on the design of the EDVAC (Electronic Discrete Variable Automatic Computer), introduced the concept of stored programs

• 
  1947 – Georg Danzig creates the simplex method

• 
  1948 – Alfred Tarski – an algorithm for testing the truth of any statement about real numbers in first-order logic.

• 
  1948 - Claude Shannon published "The Mathematical Theory of Communication", thus laying the foundation for the modern understanding of communication processes

• 
  1948 - Richard Hamming formulated a method for detecting and correcting errors in data blocks

• 
  1952 – Huffman archiving algorithm

• 
  1954 – Seward - counting sort (linear time average)

• 
  1959 - John McCarthy developed LISP (list processing), a language for use in problem-solving artificial intelligence

• 
  1962 – Davis, Lodgeman, Loveland – DLL algorithm for SAT and other NP-complete problems.

• 
  1962 - Ford and Fulkerson - polynomial algorithm for finding maximum flow.

• 
  1962 – Hoare – Quicksort (quick sorting algorithm)

• 
  1962 – Adelson-Velsky and Landis – AVL trees (balanced trees)

• 
  1964 – J. Williams – Heapsort (sorting using a heap)

• 
  1965 – Alan Robinson – founding of logic programming.

• 
  1965 – Hartmanis and Stearns: definition of the concept of “computational complexity”, the birth of complexity theory. The concept of a mass task?

• 
  1965 – Vladimir Levenshtein - Introduction of editorial distance

• 
  1969 – Strassen – fast matrix multiplication algorithm

• 
  1970 – Yuri Matiyasevich – computational undecidability of the solution of Diophantine equations (Hilbert’s 10th problem was solved).

• 
  1971 – Vapnik and Chervonenkis – support vector machines (support vector machines and VC dimension).

• 
  1971-1972 - Cook, Levin, Karp - foundation of the theory of NP-completeness.

• 
  1975 – John Holland – development of genetic algorithms

• 
  1976 – Diffie and Hellman – establishing a direct connection between cryptography and complexity theory.

• 
  1977 – Lempel and Ziv – an algorithm for archiving texts.

• 
  1976 – Knuth, Morris and Pratt – linear substring search algorithm

• 
  1977 – Boyer-Moore algorithm for searching substrings

• 
  1978 – Rivest, Shamir, Adleman – development of the RSA cryptosystem.

• 
  1979 – Gary and Johnson – systematization of the theory of NP-completeness.

• 
  1979 – Leonid Khachiyan – polynomial algorithm for solving a linear programming problem

• 
  1981 – Karl Pomerantz – quadratic sieve method for factoring numbers

• 
  1982 – Andrew Yao – definition of a function with a secret.

• 
  1982 – Teivo Kohonen – self-organizing maps

• 
  1984 – Karmarkar – interior point method for linear programming problem

• 
  1985 – Alexander Razborov – Razborov’s theorem (lower exponential bound on the complexity of solving the clique problem with monotone schemes).

• 
  1986 – Pseudo-random generator by Blum, Blum and Shuba

• 
  1989 - Tim Berners-Lee proposed the World Wide Web project to CERN (European Council for Nuclear Research)

• 
  1989 – Goldwasser, Micali and Rakov – Definition of zero-knowledge proof.

• 
  1991 – Corman, Leiserson and Rivest – “Introduction to Algorithms” - the main book on algorithms worldwide.

• 
  1992 – Adi Shamir - IP = PSPACE ( important result in complexity theory, explaining that two different understandings of task complexity actually coincide).

• 
  1992 – Arora, Safra and Arora, Lund, Motwani, Sudan, Shegedi – Probabilistic Verifiable Proof Theorem (PCP-theorem).

• 
  1993 – MacMillan – Symbolic algorithm for program verification

• 
  1994 – Peter Shore - Quantum algorithm for factoring numbers.

• 
  1994 - At the University of Southern California, Leonard Adleman demonstrated that DNA could be used as a computational tool.

• 
  1994 – Burroughs-Wheeler transformation

• 
  1996 – Grover's algorithm for searching on a quantum computer

• 
  2002 – Agrawal, Kayal, Saxena, polynomial algorithm for checking a number for primality.

• 
  2004 – Williams’ algorithm – breaking through the 2^n barrier for the maximum cut problem.

3. Current state of the theory of algorithms.

3.1. Using other sciences in algorithms
Computer science and its central field, the theory of algorithms, are recent developments. And naturally, it takes a lot from its older neighboring sciences.
Physics. The influence of physics in computer science has only emerged in recent years and has caused a veritable explosion of new research. The central direction uniting these sciences is the study of non-standard models of calculations. As physicist Richard Feynman showed, physical phenomena such as electron spin can be used for calculations. Modern research have shown that quantum algorithms apparently cannot be reduced to the conventional (bit-based) model of computation. Consequently, the space of effectively solved problems is expanding. We will also mention here such topics as calculations with real numbers(Real RAM), optical computer and even (!) billiard calculations.
Probability theory. One of the most used mathematical theories in computer science. Two key areas: estimating the running time of an algorithm “on average”, and probabilistic algorithms. Research in complexity theory shows that deterministic algorithms do not always give best solution. Moreover, in practice, probabilistic algorithms can work noticeably faster even in the presence of an alternative deterministic algorithm (for example, a primality test problem).
Biology. To solve the most difficult tasks In his activities, man turns to nature for help. What if we want to find a solution to such difficult and unformalizable problems as classification and pattern recognition? See how this problem is solved in nature - that is, human brain! This is how the idea of ​​simulating and simulating the computational abilities of neurons arose. The proposed model was named neural networks. Then the next step was taken. It is important not only how a person solves a specific problem (babies are quite poorly adapted to life), it is important at what phenomenal speed a person learns throughout his life. This is how the theory arose machine learning(machine learning).
Graph theory and combinatorics. Modern computers work with discrete data. The simplest objects of this kind are natural numbers, sequences, finite sets and graphs. Therefore, their basic properties, studied in the relevant branches of mathematics, are used incredibly often in the theory of algorithms. When algorithm specialists grow to work with more complex objects, perhaps the following levels of mathematics will find their application.
Mathematical logic. Actually, the theory of algorithms grew out of it. The dream of mathematicians at the beginning of the 20th century was to create a unified (computational) method for solving mathematical problems. Unfortunately, as Turing already showed, there are computationally intractable problems. Nevertheless, logic has provided a powerful apparatus for expressing various properties of mathematical objects and formal rules for working with these properties. In modern theoretical computer science, logic is used to develop new programming languages, problems of automatic verification of programs, and to study the complexity of computational problems (proof complexity).
Functional analysis. It turns out that continuous mathematics is also necessary in the development of algorithms. This happens mainly during computer processing of phenomena of a continuous nature. This, of course, is digital processing of audio and video recordings. Widely used standards such as MPEG and JPG contain ideas taken from the properties of the Fourier transform and make extensive use of the discrete analogue of the convolution operation.
3.2. The most significant applications of algorithms
The first applied direction, which essentially separated the theory of computing into a separate direction, was the numerical solution of equations from physics, calculations in the atomic sphere, and control of spacecraft and satellites.
The next source of many computational problems was the optimization of problems in economics. The main achievements include the formulation of the linear programming problem (Kantorovich), the simplex method, Karmarkar algorithms and the Khachiyan algorithm.
Advances in mathematical statistics and the development of measuring instruments and X-rays have created the need for algorithms for automatic diagnostics and processing of tomography data. Nowadays, computer technology is being introduced at great speed in a variety of areas of medicine.
With the growth of information volumes, the need arose for effective mechanisms for storing and using it. database query processing algorithms are among the most widely applicable.
As is known, a person perceives the largest amount of information through vision. Therefore, it is not surprising that there is great interest in image processing algorithms, modeling landscapes and movement through imaginary terrain (virtual reality). Huge efforts are spent on developing new compression algorithms raster images, audio and video streams (MPEG4, JPEG).
The main direction of development of information technology over the past two decades has been the Internet and distributed computing. The theory of algorithms here finds its application in packet routing problems (TCP/IP and DNS) and search engines. The unprecedented success of Google's system was perhaps the most memorable case in which a simple mathematical idea (the PageRank algorithm) led to phenomenal commercial success.
Of particular importance is the solution of problems in which success cannot be strictly formulated - the so-called problems of artificial intelligence. Let's list just a few: automatic recognition of speech, fingerprints, people's faces, friend-foe recognition systems, automatic classification, automatic quality control.
Ultimately, the theory of algorithms came to the point that algorithms themselves became the objects of processing. The main objectives are automatic verification and optimization of programs and systems for parallelizing program execution on multiprocessor computing systems.
The next area is linguistic algorithms: spell checking, automatic translation, “talking” programs. The next step was working with grammar.
Finally, computers began to be trusted more and more important tasks. Machine learning methods are used in the development of robots (creating a robot soccer team that can beat the world champions of 2050 sounds especially tempting). It is natural to expect that the time of proliferation of devices equipped with sensors and capable of independently making the optimal decision will come very soon.
The most popular applied direction in the most lately began research in bioinformatics: calculation (reconstruction) of genomes and construction of the most probable chain of mutations that transforms one genotype into another.

3.3. Ideas and techniques in the theory of algorithms

Simultaneously with the solution of certain computational problems, the theory of algorithms accumulates and systematizes fundamental ideas and techniques for effective computing. Below we list the main research areas of this kind.

1. 
   Collect a collection of initial data with known answers
2. 
   Divide this collection into two groups: training and test
3. 
   Choose general view decisive rule
4. 
   Select coefficients and characteristics of the decision rule on the training collection that give maximum agreement with the correct answers
5. 
   Check the quality of the resulting algorithm on a test collection
6. 
   If the results are unsatisfactory, return to step 3.

4. Factors determining the “importance” of tasks and results.

Based on these signs, you can determine current popular topics:

• 
  Subjects of works for which scientific prizes are awarded
• 
  Subjects of monographs published in major publishing houses
• 
  Topics most widely represented at general conferences
• 
  Topics of specialized conferences and schools

Choice of destinations scientific activity the following factors influence:

• 
  Opportunity to find government funding
• 
  Availability of large companies interested in this area
• 
  The topic is one of the most popular at the moment
• 
  The age of the topic. Scope of research already carried out
• 
  Scale of current research: number of scientists, laboratories, conferences, journals involved in this area
• 
  Connections of this area with other topics and sciences
• 
  “Price of entry”: the required amount of prior knowledge to begin original research

When choosing a research problem, the following are usually taken into account:

• 
  Own intrinsic interest in the task
• 
  Interest of the research community in the problem
• 
  Applied interest in solving the problem
• 
  Background of research on the problem
• 
  Author of the task. Participants from previous studies
• 
  Connections of this task with other tasks and areas
• 
  Scale of the task. Estimated task difficulty.
• 
  Fitting the problem into a broader research question
• 
  Possibility of expanding and generalizing the solution to this problem
• 
  The problem belongs to several scientific directions at once
• 
  The ability to present the essence of the task (and especially the result) in the simplest and most accessible language

Mechanisms used to disseminate problems in the scientific community:

• 
  Review scientific articles
• 
  Bulletins scientific associations(eg EATCS)
• 
  Open questions in monographs
• 
  “Diagonal reading” of the proceedings of the largest conferences and most important journals
• 
  Co-authored work
• 
  Work schools-seminars (workshops, for example seminars in Dagstuhl).
• 
  Sections “directions for further work” in scientific articles
• 
  (Rarely) publishing individual lists of open issues

6. Styles of conducting scientific research.
Perhaps there is no single most effective method for selecting research tasks and directions. On the contrary, several styles can be distinguished.
Problem solver. In this method, research consists of choosing a strictly formulated problem with a known value and technically attacking the problem. After a certain period of time (say two weeks), either the result is achieved, or the effort stops and the search begins new task. For this approach, the following factors influence success:

• 
  Well-established mechanism for finding tasks
• 
  Selecting tasks with a relatively low “entry cost”
• 
  Powerful evidence technique

Theory developer. Here the main goal is to accumulate, systematize and generalize maximum number facts united by a common concept or research question. Success factors here will be:

• 
  Choosing an important, meaningful and recognized topic
• 
  Work towards external goals: applied results or related topics
• 
  Aesthetic attractiveness (harmoniousness) of the theory being developed
• 
  Naturalness of the questions being studied

Creator of the concept. Perhaps the rarest and most difficult type of research. Exploring informal phenomena, information relations and applied problems, highlight an abstract model that reflects the essence of these phenomena, but at the same time is as simple as possible. Here we are not talking about solving a scientific problem; it is much more difficult to expand the language of science. Factors allowing you to achieve success in this direction:

• 
  The choice of a scientific direction in chaos and uncertainty
• 
  Practical importance of real phenomena
• 
  A clear understanding of the purpose for which the scientific language being created will be used
• 
  Thorough knowledge of a variety of formal descriptive devices
• 
  Intuition that allows you to highlight the important and discard the unimportant
• 
  Belief in your model and ability to popularize a new approach

Bridge builder. For a number of reasons, the scientific community especially values ​​the results obtained at the interface different areas or even science. Such discoveries often bring new understanding of phenomena that would not be possible within individual fields. These kinds of results cannot be obtained without:

• 
  Wide erudition
• 
  Scientific interests and research work in fundamentally different areas
• 
  Desires to build analogies between different topics

Question generator. The entire scientific industry is aimed at solving certain problems. But before you start solving them, you need to formulate goals, which, as you know, is half the work. There is an art to generating truly important questions. The important things here are:

• 
  Constant and insatiable curiosity
• 
  Vision of global goals
• 
  Developed sense of taste
• 
  Authority in the scientific community
• 
  Understanding the application needs and goals of the scientific movement

7. Conclusion

Let us try once again to formulate the distinctive features of outstanding results. Each of the following factors contributes to the widespread acceptance of the result:

• 
  Solving a strictly formulated and long-standing unresolved problem
• 
  Introduction of a new definition, which turned out to be convenient for describing many phenomena and concepts
• 
  First suggested method for a problem
• 
  First work in a certain direction
• 
  Systematization of accumulated facts into a unified theory.
• 
  Simplifying proofs of important theorems, finding alternative proofs
• 
  Refutation/proof of hypotheses

Having studied the list of the most significant results of the theory of algorithms, and looking at the time when these discoveries were made, an interesting conclusion can be drawn. In almost every case, these concepts and algorithms were proposed before the corresponding section theoretical computer science reached the peak of its popularity. That is, to conduct the most important research, it is worth focusing not on those areas that are currently of greatest interest, but on those that can yet become the focus of theory development.

1. 
   Algorithms that process objects of the “second level of complexity”. For computational problems that work with basic mathematical objects, such as strings, elements of ordered sets, natural numbers, (weighted) graphs, finite state machines, and matrices, many effective algorithms have been built. On the contrary, the automatic processing of more complex objects that cannot be directly represented by these elementary concepts is yet to become a subject of study. Now we are trying to pick efficient algorithms handling concepts such as a program (automatic optimization, parallelization and verification), the Internet (searching and sorting sites by importance), texts in natural languages ​​(automatic translation and literacy testing) or the human genome.

1. 
   Algorithms using knowledge bases. Technologies of the present make it possible to collect a lot of interesting information about humanity: the structure of relationships (social networks), complete purchase statistics, music, book and movie preferences, the list and dynamics of each person’s search queries. All these huge volumes of data remain relatively useless. However, it seems that in the very near future it will be possible to automatically extract some general patterns and patterns from such data, and use them to predict future events in various fields.

1. 
   Progress towards understanding questions in natural language. Now all programs are capable of processing input data only strictly defined mathematical type. While the absolute ideal would be a machine capable of answering any human question. The first step on this path should be to identify some kind of intermediate query language, which, if not the same as the natural one, is at least significantly more expressive than the query language that we use in Internet search engines.

Let us note that for the third direction, close cooperation with linguistic specialists can play an important role. It is quite possible that linguistics will become the next strategic partner of the theory of algorithms, and now it is worth thinking about the closest cooperation with representatives of this science.

List of sources

1. 
   Theory of Computation: Goals and Perspective

1. 
   Papers in Computer Science

1. 
   ACM/IEEE Computing Curriculum 2001

1. Most cited articles in Computer Science

1. 
   Nevanlinna Prize

1. Rivest R., Cormen T., Leiserson Ch. “Algorithms: construction and analysis”

2. 
   Michael Nielsen: Principles of Effective Research

1. A. Razborov. Theoretical Computer Science: a mathematician's view.

1. 
   Lance Fortnow. My favorite theorems.

1. 
   Multimedia product "History of Computer Science"

1. 
   Computer Sciences - milestones ("Timeline of Computing History", Computer, Vol. 29, No.10 Translated from the original English version and reprinted with permission (IEEE))

1. 
   History of Algorithms

1. 
   Timeline of algorithms

Name: Agrippina Steklova

Age: 46 years old

Activity: Theater and film actress

Agrippina Steklova: biography

Agrippina Steklova is a red-haired beauty who was remembered by the audience for her roles in the films “Once Upon a Time There Was a Woman,” “Wapit Hunting” and “The Geographer Drank the Globe Away,” the TV series “Mother under Contract” and “Ship,” as well as numerous productions in the theater “ Satyricon."

Childhood and youth

Agrippina was born into an acting family. Her father, a famous Russian theater and film actor, is known to a wide audience thanks to his enormous track record, which houses dozens of films and theater performances.

In the family, the father’s word was law; Vladimir Alexandrovich enjoyed enormous authority. The girl's mother was also an actress. Lyudmila Moshchenskaya met her future husband in Astrakhan. Together, the young people attended a theater club, then entered the local theater school.

The girl received her unusual name in honor of her grandmother and at first she was embarrassed by it: when asked what her name was, little Granya tried to answer as quietly as possible so that the interlocutor could hear “Anya.” Also, in childhood, fiery hair caused a lot of trouble, but the lazy one did not sing the girl a song about the red-freckled one.

However, with age, Agrippina realized that all her “shortcomings” were advantages and even advantages that set her apart from the crowd. And this was important, given that Steklova decided to follow in the footsteps of her parents and after graduation school studies entered GITIS. At a theater university, the girl took a course at.

Contrary to popular belief that the children of actors who chose the same path work after university with their parents, the red-haired beauty in her youth decided to do it her own way. Instead of getting a job at the Lenkom Theater, on whose stage her father had played for many years, the girl got a job working under the supervision of the Satyricon Theater a year before graduation.

The theater director himself spoke favorably of the young actress, noting both her professionalism, emphasized by her unusual appearance, and her surprisingly gentle and cheerful character. Thus, the actress’s career growth was ensured by her talent, and not by her family connections.

Films and theater

Being the daughter of an actor, little Granya was familiar with theatrical life since childhood. Her first appearance on the big stage took place in tandem with, where the master played, and Steklova played his little daughter.

The artist's film debut took place when she was 16 years old. Then she starred in the children's film "Tranti-Vanti". Then there were several episodic roles, and for some time the actress devoted herself to the theater.

At the Satyricon Theater, the actress made her debut in the production of “Kyojin Skirmishes,” where Madonna Libera became her character. Steklova appeared in several of William Shakespeare's classic plays: starting with a small role as a townswoman in Romeo and Juliet, she subsequently played Lady Macbeth, Regan in King Lear, and Queen Elizabeth in Richard III.

Agrippina often plays in tandem with another famous actor from Satyricon. They appeared together in the plays “Others”, “It All Starts with Love”, “Portrait” and others. Together with Averin, Steklova recorded a song called “The Ballad of a Smoky Car.”

Also on the stage of “Satyricon,” Steklova poignantly revealed the character of Nina Zarechnaya, the famous Chekhov’s “The Seagull.” Among the age roles, it is worth noting the image of Mrs. Higgins from the sparkling comedy Pygmalion.

In addition, the artist quite often appears in enterprise performances. Creative biography Agrippina Steklova includes roles in the productions “It’s not all Maslenitsa for the cat” and “I.O.”

Since the beginning of the 2000s, Steklova has again appeared on wide screens: both in the comedy “True Incidents” based on sparkling stories, and in the critically acclaimed drama “Koktebel” directed by the director tandem of Popogrebsky and.

From more later works The actress is worth noting the role of the sister-in-law Panka-Polenka, a woman with a difficult character, in the difficult military-retrospective film “Once Upon a Time There Was a Woman,” as well as the character of the head teacher of the school in the drama “The Geographer Drank the Globe Away” by Alexander Veledinsky.

However, Agrippina Steklova first gained fame as a serial actress. The first serial film in which she starred was the detective telenovela “Citizen Chief”. The actress presented the main characters in the detective story “Tango with an Angel” and the melodrama “Frozen”.

Then there were roles in “The Hunt for the Red Deer,” “The Law” and a dozen other TV series, the most notable of which can be called the popular Russian adaptation of the Spanish telenovela “Ark,” which was released in Russian theaters under the name “Ship.” In “The Ship,” Steklova’s character is the ship’s cook Nadezhda Solomatina, who is the focus of care and integrity.

Among the actress’s works is a role in the TV series “Contract Mom.” According to the plot of the film, Steklova’s heroine becomes the adoptive mother of the character’s child when she is on a long business trip related to work. Upon arrival, a real drama unfolds between the women.

The actress successfully combined numerous filming in TV series with acting in the theater and in 2012 she won the prestigious Theater Star award for best supporting actress. Agrippina received the award from Dorina from the play Tartuffe.

In 2015, Steklova played nurse Nadezhda in Insight. Agrippina’s acting was celebrated at several film festivals: “Vivat, Russian Cinema!”, “Amur Autumn” and the international “Golden Linden”. In the melodrama, the actress’s heroine helps the character Pavel Zuev (), a patient who lost his sight due to an accident, find the meaning of life.

At the same time, Steklova’s repertoire was replenished with a cameo role in the comedy “Election Day 2,” where she played the wife of the chairman of the election commission. The artist also appeared in the drama “The Heirs” and in the film adaptation of “Paradise” by Alexander Proshkin.

In 2016, Agrippina starred in the series "". The 8-episode film tells the story of the Grand Duchess, a wife who made an invaluable contribution to the culture and politics of the time, but remains an unknown figure to modern viewers. The project is primarily artistic and focuses not so much on historical events, how much on the love story and relationship of Sofia and Ivan.

In the same year, the actress surprised viewers with a new facet of her talent, again appearing on screen in a character role. Agrippina Steklova starred in the comedy of the STS TV channel “Fugitive Relatives”, where she performed in the acting ensemble together with, and.

In addition to working in the now-familiar Satyricon, Agrippina appears on the stages of other metropolitan theater groups. At the theater. Ermolova she appeared on stage in the production of “Hamlet”, and at the Theater of Nations - in “Yvonne, Princess of Burgundy”.

Personal life

The actress had an affair in her 2nd year at the institute. When Agrippina found out about the pregnancy, she did not insist on the wedding, but, on the contrary, decided not to connect her personal life with the child’s father and broke up with her chosen one. She registered her son under her last name and does not advertise the identity of his father. When the boy was 5 years old, he got a new dad.

The actress has been living in a happy marriage with a theater colleague for more than 20 years. The artists play in the same theater. They didn’t notice each other for a year, but as soon as they just started talking, they both realized that they had found their person. They lived in a civil marriage for 10 years, after which they got married.

Despite the age difference of 15 years and the presence of children from previous relationships (Bolshov has a daughter, Maria, from his first marriage, Steklova is raising a son, Danil), the family of artists is friendly and often gives joint interviews. They play together in the plays “All Shades of Blue” and “Jacques and His Master” and help each other in the acting field. Agrippina Steklova and her husband are considered the brightest and most cheerful couple in the capital's theater world.

The family also has no problems in everyday life. Bolshov does not mind sharing housekeeping responsibilities with his wife and, in addition, is a good cook. Steklova and her husband love to travel: when the children were little, they traveled with the whole family, and now they are increasingly going on trips with friends.

Despite her popularity, Agrippina does not use social networks. The actors leave photos from their trips for family use only. But on Instagram, fans of the actress registered a group dedicated to the work of their favorite.

The grown-up children also chose the acting path for themselves. Danil after graduation theater university at one time he served in Satyricon, then became an actor at the Moscow Art Theater. , the young man also acts in films. Maria graduated from GITIS and joined the “Workshop” troupe.

Filmography

• 1989 – “Tranti-Vanti”
• 2003 – “Koktebel”
• 2005 – “Hunting for the Red Deer”
• 2007 – “The personal life of Doctor Selivanova”
• 2009 – “Frozen”
• 2009 – “Tango with an angel”
• 2009 – “Once upon a time there was a woman”
• 2010 – “Mom under contract”
• 2012 – “Poor Relatives”
• 2013 – “The geographer drank the globe away”
• 2014 – “Ship”
• 2015 – “Insight”
• 2015 – “Paradise”
• 2016 – “Fugitive Relatives”
• 2017 – “Big Money”
• 2018 – “Without Me”

Committee on Science and Higher Education

St. Petersburg State Budgetary Professional Educational Institution "Nevsky Mechanical Engineering College"

(SPb GBPOU "NMT")

Scientists' contribution

A.S. Popov and V.A. Steklova

in development national science

Completed

student gr. 2315 Grabovoi V.

Supervisor

Sushchenko T.A.

Goals and objectives

• To attract the attention of a wide audience to the life and scientific activities of two outstanding scientists who have a close connection with St. Petersburg.
• Reveal the significance of their inventions in the life of modern society

Alexander Stepanovich Popov

• Russian physicist and electrical engineer, professor, inventor, state councilor (1901),
• Honorary Electrical Engineer (1899).
• Inventor of radio.

Biography

• Alexander Stepanovich Popov was born on March 4, 1859 (March 16, 1859) in the Urals in the village of Turinskie Rudniki, Verkhoturye district, Perm province (now Krasnoturinsk, Sverdlovsk region).
• In the family of his father, local priest Stepan Petrovich Popov (1827-1897), besides Alexander there were 6 more children, among them sister Augusta, a future famous artist. They lived more than modestly. Cousin the future inventor Pavel Popov held a professorship at Kiev University, and his son Igor Popov (1913-2001) was engaged in seismology in the USA

Education

• The first education in the biography of Alexander Popov was received at a theological school. Then he began to study at the Perm Theological Seminary. He received his higher education at the University of St. Petersburg.
• Having become interested in physics, after graduating from university he began teaching in Kronstadt. Then he began to read physics at a technical school.
• Since 1901, he was a professor at the Electrical Engineering Institute of St. Petersburg, and after that its rector.
• But the true passion in the biography of A.S. Popov was experiments. Free time he devoted himself to the study of electromagnetic oscillations.

Connection with St. Petersburg

Alexander Stepanovich Popov since 1901 worked at the St. Petersburg State Electrotechnical University "LETI" named after V. I. Ulyanov (Lenin)

Research

• Alexander Stepanovich Popov managed to generalize and find a reasonable technical implementation scientific ideas about the possibilities of using electromagnetic waves for wireless communications, creating the first radio receiver and putting it at the service of humanity.

• Order of St. Anne, 2nd class (1902)
• Order of St. Stanislaus, 2nd class (1897)
• Order of St. Anne, 3rd class (1895)
• Medal "In memory of the reign of Emperor Alexander III"
• According to the Highest Decree, he received a reward of 33 thousand rubles for continuous work on the introduction of wireless telegraphy to navy(April 1900)
• IRTS Prize “for a receiver for electrical oscillations and devices for telegraphing at a distance without wires” (1898).

The influence of A.S.’s discoveries Popov for the development of science and technology

A. S. Popov ended with the words: “In conclusion, I can express the hope that my device, with further improvement, can be used to transmit signals over a distance using fast electrical oscillations, as soon as a source of such oscillations with sufficient energy is found.” Thus, A.S. Popov was the first to point out the possibility of using Hertz waves for communication and confirmed this possibility with extremely convincing experiments.

1. During the study, we learned that the discovery of radio by A. Popov marked the beginning of the development of radio engineering and radio electronics, how far they have come over the years. The scope of radio has long gone beyond communications. The development of all modern science, technology and economy is largely associated with radio electronics.

2. From large-sized electronic devices, electronics have moved to microminiature ones, from simple radio communications to Internet communications, to a vast, worldwide network formed by hundreds of millions of computers.

3. New branches of science and new applications of radio engineering have been created.

4. One of the main areas of modern electronic technology is integrated microelectronics. Nanotechnology is ahead, which is a promising area of ​​research.

5. The country’s universities have faculties that train specialists for new promising areas, for example: physics of nanostructures and nanotechnologies; ultra-fast electronics; quantum computers; quantum radiophysics etc.

Mathematician at the junction of two eras

It rarely happens that a mathematical scientist combines the desire for precision and generalization in order to use his work to develop another branch of science. These scientists include Soviet mathematician and mechanic V.A. Steklov.

Tadeusz Swiantkowski

Vladimir Andreevich Steklov

• Russian mathematician and mechanic.
• Full member of the St. Petersburg Academy of Sciences (1912), vice-president of the USSR Academy of Sciences (1919-1926). Organizer and first director of the Institute of Physics and Mathematics of the Russian Academy of Sciences, named after the death of V. A. Steklov after him. After the division of the Institute of Physics and Mathematics into the Institute of Mathematics and the Institute of Physics (in 1934), the name of V. A. Steklov was given to the Institute of Mathematics (MIAN).

Biography

• Vladimir Andreevich Steklov was born on January 9, 1864 (December 28, 1863) in Nizhny Novgorod in the family of a priest. Already during his studies at the Nizhny Novgorod Noble Institute (1874-1882; graduated from silver medal) showed an aptitude for mathematics and physics. In 1882, he entered the Faculty of Physics and Mathematics of Moscow University, but his studies were unsuccessful in this first year of university life, and in 1883 he transferred to Kharkov University. From this time begins the long Kharkov period of V. A. Steklov’s life. When he was in his third year, the outstanding mathematician A. M. Lyapunov, then still a young scientist, came to Kharkov. With his excellent lectures, he instilled in many university students a love of mathematics. Thanks to A.M. Lyapunov, Steklov found his calling in mathematics and began his scientific career.

Biography

• In 1887, V. A. Steklov graduated from Kharkov University and in 1889 was appointed assistant at the Department of Mechanics. In 1891 he was confirmed with the rank of privatdozent, in 1893 he received a master's degree in applied mathematics, and in 1901 - a doctorate in applied mathematics. By this time, V. A. Steklov was already known for his scientific works (45 works) in the field of mechanics and mathematical physics. From 1894 he also taught mechanics at the Kharkov Institute of Technology.
• From 1902 to 1906 V. A. Steklov was the chairman of the Kharkov Mathematical Society. In 1904 - dean Faculty of Mathematics Kharkov University.
• Since 1906, V. A. Steklov has been a professor at the Department of Mathematics at St. Petersburg University. In 1910 he was elected an adjunct of the St. Petersburg Academy of Sciences, in March 1912 - an extraordinary academician and in July of the same year - an ordinary academician.

Research

• The main works of V. A. Steklov (there are more than 150 of them) relate to mathematical physics, mechanics, quadrature formulas of approximation theory, asymptotic methods, closedness theory, and orthogonal polynomials. His work on partial differential equations relates to electrostatics, vibrations of elastic (or quasi-elastic) bodies, and problems of heat propagation. He gave a complete theoretical justification for solutions to the problem of heat propagation in an inhomogeneous rod for a given initial condition and boundary conditions at the ends of rods, as well as problems about the vibration of an inhomogeneous string or rod under certain initial and boundary conditions. The problem of heat propagation was also studied by him in the case three-dimensional body. He obtained significant results in solving Dirichlet and Neumann problems. These problems were previously solved using spherical functions. The great merit of V. A. Steklov in creating the theory of closure orthogonal systems functions.

Research

• He owns the idea of ​​smoothing functions. Steklov devotes many works to questions of decomposability in own functions the Sturm-Liouville problem, while improving and developing the Schwartz-Poincaré method. In the field of hydrodynamics, he studied the motion of a solid body in a liquid, the theory of vortices, the motion of an ellipsoid, the motion of a solid body with an ellipsoidal cavity filled with liquid. V. A. Steklov was the organizer and first director of the Institute of Physics and Mathematics, which was subsequently divided into two institutes - the Institute of Mathematics and the Institute of Physics. On the basis of the Institute of Mathematics, over time, independent institutes were also organized, two of which are the Mathematical Institute named after. V. A. Steklova and the St. Petersburg Department of the Mathematical Institute named after. V. A. Steklova - now bear his name. The Steklov crater is also named in his honor. back side Moons.

Research results

The following mathematical objects are named after Steklov:

• fundamental Steklov functions
• Steklov function
• Steklov's closed theory
• Steklov transformation
• Steklov's theorem
• Liouville–Steklov method.

Connection with St. Petersburg

• V.A. lived in this house from 1907 to 1917. Steklov

St. Petersburg State University

• Since 1906, V. A. Steklov was a professor in the department of mathematics at this university.

St. Petersburg Academy of Sciences

• In 1910 he was elected adjunct of the St. Petersburg Academy of Sciences.

Connection with St. Petersburg

• Vladimir Andreevich Steklov worked at St. Petersburg State University since 1906.
• V.A. Steklov was buried on the Literatorskie Mostki in St. Petersburg.

Vladimir Andreevich Steklov (1864-1926)

Vladimir Andreevich Steklov is one of the brilliant representatives of the St. Petersburg mathematics school, created in mid-19th V. the brilliant Russian mathematician P. L. Chebyshev. Its main feature was the desire to closely connect the issues mathematical science with fundamental questions of natural science and technology, mechanics, physics, astronomy and other sciences. One of the greatest Russian mathematicians, a student of P. L. Chebyshev, A. M. Lyapunov characterizes the St. Petersburg mathematical school as follows: “... P. L. Chebyshev and his followers remain constantly on the basis of reality, guided by the view that only those researches have prices that arise from applications (scientific or practical), and only those theories are truly useful that arise from the consideration of particular cases. Detailed development of questions that are especially important from the point of view of applications and at the same time present special theoretical difficulties requiring the invention of new methods and. ascending to the principles of science, then generalizing the conclusions obtained and thereby creating more or less general theory- this is the direction of most of the works of P. L. Chebyshev and the scientists who adopted his views." Being direct student A. M. Lyapunova, V. A. Steklov took these views from him.

Vladimir Andreevich Steklov was born on January 9, 1864 in Nizhny Novgorod, in the family of a priest and teacher at the Nizhny Novgorod Seminary. He was the nephew of the famous Russian critic N.A. Dobrolyubov. Already from his student days, V. A. Steklov discovered a desire to study mathematics and physics. In 1883, he entered the Faculty of Physics and Mathematics of Kharkov University, where in 1885 he studied under the guidance of A. M. Lyapunov. The leadership of such outstanding mathematician What A. M. Lyapunov was was of great importance for the further scientific activity of V. A. Steklov. After graduating from the university, he was left there for scientific work. After defending his dissertation on the topic “On the Motion of a Rigid Body in a Liquid” in 1894, he received a master’s degree in applied mathematics, and in 1902 he defended his dissertation “General methods for solving problems of mathematical physics” and received a doctorate in applied mathematics. In 1906, V. A. Steklov accepted an offer to occupy the department of mathematics at St. Petersburg University. The appearance of V. A. Steklov at the university immediately brought great excitement to the entire educational and scientific life of the Faculty of Physics and Mathematics. A large number of students and young scientists working under his leadership grouped around V. A. Steklov. Since 1910, V. A. Steklov has been an adjunct of the Academy of Sciences, and since 1912 - an ordinary academician. Soon after this, he concentrated all his work at the Academy. From 1919 until his death he was vice-president of the Academy of Sciences. His activities at the Academy, both organizational and scientific, and administrative and economic, were enormous. It was a difficult time. But he managed to organize the printing of scientific works and the acquisition of books and instruments from abroad. He worked a lot on restoring the seismic network and organizing the Institute of Physics and Mathematics, which was later divided into three institutes. The Mathematical Institute of the Academy of Sciences is currently named after V. A. Steklov. Along with this, Vladimir Andreevich was the director of the Institute of Physics and Mathematics and a member of the commissions: library, publishing, construction, commission for the study of the country's productive forces under the State Planning Committee, a member of the Science Committee under the Council of People's Commissars and chairman of the Permanent Seismic Commission. And his active and full of initiative character was evident everywhere. But still, the most important thing in his life was scientific work. He led it continuously until the end of his life. Vladimir Andreevich Steklov died on May 30, 1926 in Gaspra. It is difficult for a non-mathematician to find out the meaning and results of the work of V. A. Steklov. All of them are associated with a large mathematical apparatus, and the essential meaning of most of them is to analyze with complete rigor in reasoning the corresponding mathematical problems usually associated with any of the problems of natural science.

In his works on the theory of elasticity and hydromechanics, V. A. Steklov considered a number of specific problems that had remained unsolved until then. In the theory of elasticity, he develops the question of the equilibrium of elastic cylinders, continuing the work of the famous scientists Clebsch and Saint-Venant. IN master's thesis he gave one new case of the motion of a rigid body in a liquid, when the problem receives a complete solution in a simple form. This was the third case of this kind. The first two were discovered by Clebsch. The fourth case was discovered by A. M. Lyapunov.

In 1908, a large memoir by V. A. Steklov appeared, “The problem of the motion of a liquid incompressible mass of an ellipsoidal shape, the particles of which are attracted according to Newton’s law.” The purpose of the work is to consider all possible cases of motion of a liquid ellipsoid under some simple assumption about the velocities of points of the liquid. Also related to hydromechanics is the work of V. A. Steklov “On the motion of a rigid body having an ellipsoidal cavity filled with an incompressible fluid, and on changes in latitudes.” The results of this work are attached by V. A. Steklov to the study of one of critical issues astronomy and celestial mechanics- the question of changes in latitudes caused by movements of the earth's axis. Among other interesting conclusions, V. A. Steklov found that the thickness dura shell The Earth is located within 800-1100 kilometers, the density of its shell is approximately 6, and the density of the liquid filling is between 5, 6 and 5.

The most important in the scientific heritage of V. A. Steklov are his works on mathematical physics - the field mathematical analysis, which is related to problems of physics. The years when V. A. Steklov’s scientific work began were turning points in the history of mathematical physics. The brilliant flourishing of this branch of mathematics in the first half of the 19th century. gave way to comparative calm in the second. At that time, the focus was on the following three main problems of mathematical physics: the main electrostatic problem of determining surface density electricity in equilibrium on a given conducting surface; common task electrostatics, which consists in determining electrostatic potential inside a certain surface by its value on the surface itself, if it is known that there are no charges inside the surface; a problem in hydromechanics devoted to the study of steady-state, i.e., time-independent, motion of a fluid flowing around a given solid body, for some additional conditions about the properties of liquid and the nature of its movement. This last problem in its mathematical apparatus is related to the above problems of electrostatics. The solutions to these problems proposed before the work of V. A. Steklov were suitable only for surfaces of a special class. In addition, the mathematical analysis of the study of these problems in some points did not have sufficient accuracy, which is required when solving a mathematically posed problem. V. A. Steklov connected the solution of all three problems with the solution of the main electrostatic problem of finding the equilibrium density of electricity on a given surface. For the first time they were given strict solution this problem for a fairly wide class of surfaces. Using the mathematical apparatus used to solve it, V. A. Steklov then gives a rigorous and general solution to two other problems - the general electrostatic problem and the problem in hydromechanics. In his works, he then gave another original method for solving the last two problems. This method consists in constructing for a given surface a special family of functions with the help of which these solutions are constructed. Such functions and their basic meaning were previously known only for surfaces of a special type, for example, for a sphere and an ellipsoid. V. A. Steklov was the first to construct a theory of such functions and gave a rigorous proof of their existence for a wide class of surfaces.

A characteristic feature of all V. A. Steklov’s works on mathematical physics is the desire for impeccable accuracy of mathematical analysis and for solving problems in the widest possible class of cases. In this regard, Vladimir Andreevich was faithful to the traditions of the St. Petersburg mathematical school and, in particular, to his teacher A. M. Lyapunov, who wrote in one of his works: “It is impermissible to use dubious judgments as long as we are solving a certain problem, be it a problem of mechanics or physics - it doesn’t matter, which is posed quite definitely from the point of view of mathematics. It then becomes a problem. pure analysis and should be treated as such."

V. A. Steklov’s work in mathematical physics was not limited to only the three problems mentioned above. In a number of works, he gave a deep analysis and complete solution to problems relating to the distribution of heat in a given body under various external conditions in which this body is placed. In addition to these external conditions, when solving the problem, it is also necessary to take into account the thermal regime that took place in the body at the initial moment of time, after which the phenomenon occurs according to the law of thermal conductivity, already known from physics. The French mathematicians Fourier and Poisson put forward the idea: to look for some basic - elementary solutions to the problem, taking into account only the law of heat conduction, which is expressed by the corresponding heat equation, and the external regime in which the body is located, but not yet worrying about the initial condition, i.e. that at the initial moment of time the body is at a given thermal mode. Research shows that such elementary solutions There are countless numbers of them that are different from each other. The main difficulty of the entire Fourier-Poisson method was to construct a new solution to the problem from elementary solutions that would satisfy not only the law of heat conduction and limit conditions, but also the initial condition, i.e., it is necessary to compose a solution to the problem that would at the initial moment in time gave a given thermal regime. This leads to one of the difficult problems of mathematical analysis and mathematical physics - to the representation of a function expressing the initial temperature distribution as a sum of an infinite number of terms. The terms of this sum are the values ​​of elementary solutions at the initial moment of time, multiplied by various constants. This problem is usually called in mathematics the problem of expanding a given function into a series. It was this point in all previous works containing the use of the Fourier-Poisson method that caused the greatest objections. A rigorous consideration of this issue is the main merit of V. A. Steklov in mathematical analysis and mathematical physics. He considers this problem in connection with questions of mathematical physics and as an independent problem of mathematical analysis. V.A. Steklov found out under what conditions the function expressing the initial distribution of temperature in the body can be represented in the form of such a series. In these works of V. A. Steklov, not only the specific results that they contain are interesting, but also the original research methods, for which the name of V. A. Steklov is attached to science.

Most often he uses the method of isolation, which is associated in science with his name. In order for any given function could be decomposed according to the functions of a given system, it is necessary that this system be in some sense sufficiently complete, that is, it should contain a sufficiently diverse set of functions. As a mathematical formulation of such completeness, V. A. Steklov took a formula that generalizes the well-known Pythagorean theorem to the case of functions. V. A. Steklov pursued this idea in most of his works devoted to the above problem, and the fundamental significance and fruitfulness of this idea were confirmed both in the works of V. A. Steklov and in later works.

In the works of the same cycle, V. A. Steklov puts forward another fundamentally important idea. In many questions of mathematical physics, the usual mathematical apparatus often turns out to be poorly adapted to express the essence physical phenomenon with the usual method of describing this phenomenon. For example, the concept of temperature at a given point is an idealized concept. In real experience, we always deal with the average temperature in a certain area of ​​the body. Therefore in mathematical research problem, it is advisable to consider from the very beginning not the temperature at a given point, but average temperature in some small volume containing a point. This approach requires modification of the mathematical apparatus: it should be rebuilt, adapting it to the calculation of average values. In the works of V. A. Steklov we find clear indications of these unique ideas in mathematical physics. In contemporary mathematical physics, these ideas have been widely developed and led to a radical revision of the basic concepts of mathematical science and the creation of a new mathematical apparatus - the theory of functions of domains, more adapted to the description of real phenomena.

As we said earlier, many problems of mathematical physics associated with stationary modes (electrostatic problem, the indicated problem of hydromechanics) and with the Fourier-Poisson method first found their rigorous solution in the works of V. A. Steklov. But these works, as we have just indicated, also contain completely new ideas that were widely developed in subsequent works.

In the life of Vladimir Andreevich exact sciences played a completely exceptional role. He saw them as not office work individuals, but a powerful creative force in the life of humanity. He was an integral and strong man and devoted all his strength and his whole life to science.

Vladimir Andreevich was not interested in abstract theories, and in his works we did not encounter any abstract constructions. All his scientific activities are characterized by the words of our “Copernicus of Geometry” N. I. Lobachevsky, which Vladimir Andreevich loved to quote: “Stop working in vain, trying to extract all the wisdom from one mind, ask nature, it keeps all the secrets and will answer your questions certainly and to your satisfaction."

One should not imagine V. A. Steklov as a narrow specialist who has no interests outside of mathematics. Previously, according to V. A. Steklov himself, he had a big voice, and he was thinking about a career as a singer. His life path turned out to be different, but intense scientific studies did not drown out his love for music. Until recently, he often talked with love and inspiration about music, recalled various works of Russian music, and even sang excerpts from his favorite operas. The love for Russian music, the habit of citing the sayings of Peter the Great, Lomonosov, Lobachevsky - all this was in V. A. Steklov not just a love for Russian style, but an expression of his genuine, blood connection with Russian culture, and V. A. Steklov himself was one of the largest representatives of this culture.

The most important works of V. A. Steklov: a) in hydrodynamics: On the motion of a solid body in a liquid. Thesis for the master's degree in applied mathematics, "Scientific Notes of Kharkov University", 1893; Probleme du mouvement d"une masse fluide incompressible de la forme ellipsoïdale dont les parties s"attirent suivant la loi de Newton (2 parts), "Ann. de l"Ec. Norm. Sup.", 1908-1909, tt. 25 and 26; b) in mathematical physics: General methods for solving basic problems of mathematical physics. Thesis for the degree of Doctor of Applied Mathematics, Kharkov, 1901; Sur les problemes fondamentaux de la physique mathernatique, "Ann . de l"Ec. Norm. Sup.", 1902, t. 19; Basic problems of mathematical physics, Pg., 1922 (part I), 1923 (part II); c) varia: M. V. Lomonosov, Gosizdat, 1921; Galileo Galilei, Gosizdat, 1923; Mathematics and its significance for humanity, Gosizdat, 1923.

About V. A. Steklov: In memory of V. A. Steklov, ed. Academy of Sciences of the USSR, Leningrad, 1928; Uspensky Ya. V., V. A. Steklov, L., 1926.