Mathematician and mechanic of Austrian origin; worked in fluid mechanics, aerodynamics, aeronautics, statistics and probability theory; in the theory of probability proposed and defended the frequency concept of the concept of probability, introduced into common usage Stieltes integrals and was the first to explain the role of the theory of Markov chains in physics; was incredible dynamic person and at the same time surprisingly versatile, especially well versed in the field of technology; recognized expert in the poetry of Rainer Maria Rilke. Brother of Ludwig von Mises.

Born in Lemberg, Austria-Hungary (now Lvov, Ukraine) in the family of Arthur Edler von Mises, Dr. technical sciences, who worked as an expert in the Austrian state railways, and Adele von Landau. Richard's elder brother was one of the largest representatives of the Austrian school in economics, Ludwig von Mises.

In 1901 he graduated Academic Gymnasium in Vienna with honors Latin and mathematics. In 1905 he graduated from the Vienna University of Technology with a degree in mathematics, physics and engineering. After graduation, he worked as an assistant to the German mathematician Georg Hamel in Brunn (now Brno, Czech Republic). In 1908 he received doctoral degree in Vienna with a dissertation "Determining the mass of a flywheel in a crank mechanism." In 1909, at the age of 26, he became a professor applied mathematics in Strasbourg (then part German Empire, now - France) and receives Prussian citizenship. His attempt to get a teaching position in Technological University Brno was interrupted by the First World War.

With experience in flying and lecturing on aircraft design and being the first to give a university course in active flight in 1913 in Strasbourg, Mises joins the Austro-Hungarian army as a test pilot and instructor. In 1915, under his leadership, an aircraft with an 600 hp engine was created. (450 kW), so-called. Mises plane, for Austrian army. The aircraft was completed in 1916, but never took part in hostilities.

After the war, Mises became head of the department of hydrodynamics and aerodynamics in Dresden technical university. In 1919, he became director of the newly created Institute of Applied Mathematics at Berlin University(where he also holds the title of professor). In 1921 he founded the journal Zeitschrift für Angewandte Mathematik und Mechanik and became its editor.

With the coming to power of the Nazis in 1933, Mises, who has Jewish roots, does not feel safe and emigrates to Turkey, where he heads the newly created Department of Pure and Applied Mathematics at Istanbul University.

In 1939, after the death Turkish President Kemal Atatürk and the uncertain aftermath political situation, Mises emigrates to the USA, where in 1944 he becomes a professor of aerodynamics and applied mathematics in Harvard University.

In 1950, Mises refused an honorary membership in the Academy of Sciences of the GDR.

Richard Edler von Mises(April 19, 1883, Lemberg, Austria-Hungary (now Lviv, Ukraine) - July 14, 1953, Boston, USA) - mathematician and mechanic of Austrian origin; works are devoted to aerodynamics, applied mechanics, fluid mechanics, aeronautics, statistics and probability theory. In the theory of probability, he proposed and defended the frequency concept of the concept of probability, introduced the Stieltjes integrals into general use and was the first to explain the role of the theory of Markov chains in physics; was an incredibly dynamic person and at the same time surprisingly versatile, especially well versed in the field of technology; recognized expert in the poetry of Rainer Maria Rilke. Brother of Ludwig von Mises.

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Biography

Born in Lemberg, Austria-Hungary (now Lviv, Ukraine) in the family of Arthur Edler von Mises, Doctor of Technical Sciences, who worked as an expert in the Austrian State Railways, and Adele von Landau. Richard's elder brother was one of the largest representatives of the Austrian school in economics, Ludwig von Mises.

In 1901 he graduated from the Academic Gymnasium in Vienna with honors in Latin and mathematics. In 1905 he graduated from the Vienna University of Technology with a degree in mathematics, physics and engineering. After graduation, he worked as an assistant to the German mathematician Georg Hamel in Brunn (now Brno, Czech Republic). In 1908 he received his doctorate in Vienna with the thesis "Determination of the mass of a flywheel in a crank mechanism". In Brunn he passed the procedure of "habilitation" (for the work "Theory of the water wheel") for lecturing on engineering. In 1909, at the age of 26, he became a professor of applied mathematics in Strasbourg (then part of the German Empire, now France) and received Prussian citizenship. His attempt to secure a teaching position at the Brno University of Technology was interrupted by the First World War.

With experience in flying and lecturing on aircraft design and being the first to give a university course in active flight in 1913 in Strasbourg, Mises joins the Austro-Hungarian army as a test pilot and instructor. In 1915, under his leadership, an aircraft with an 600 hp engine was created. (450 kW), so-called. "Mises plane", for the Austrian army. The aircraft was completed in 1916, but never took part in hostilities. During the First World War, he studied the conditions of elastic stability of cylindrical shells under the combined action of axial and transverse pressure.

After the war, Mises became the head of the department of hydrodynamics and aerodynamics at the Dresden University technical school. In 1919 he became director of the new Institute for Applied Mathematics at the University of Berlin (where he also held the title of professor). Founder and Chief Editor(1921-1933) of the Zeitschrift für Angewandte Mathematik und Mechanik magazine.

With the coming to power of the Nazis in 1933, Mises was forced by virtue of his Jewish origin emigrate to Turkey, where he headed the newly established Department of Pure and Applied Mathematics at Istanbul University.

In 1939, after the death of Turkish President Kemal Atatürk and the resulting uncertain political situation after that, Mises emigrated to the United States, where in 1944 he became a professor of aerodynamics and applied mathematics at Harvard University. In 1945 he gave an enhanced formulation of the Saint-Venant principle.

In 1943, he married Hilde Geiringer, a mathematician who was Mises's assistant during his time at the University of Berlin, who, due to her Jewish origin, was also forced to leave the university and the country in 1933. Accompanied Mises during his emigration to Turkey and later to the USA.

In 1950, Mises refused an honorary membership in the Academy of Sciences of the GDR.

Circle of interests

According to him own words, said shortly before his death, the range of his interests:

« practical analysis, integral and differential equations, mechanics, hydrodynamics and aerodynamics, constructive geometry, probability calculus, statistics and philosophy (in the spirit of Ernst Mach's neopositivism)."

Plasticity criterion

In 1913, in the field of continuum mechanics, together with Huber, he proposed a criterion for plasticity, obtained on the basis of the condition of constancy of the energy of shape change:

$\backslash sigma\_i\; =\; \backslash sigma\_y$,

where $\backslash sigma\_y$- yield strength, $\backslash sigma\_i$- stress intensity, the square of which is proportional to the second invariant of the stress deviator:

$\backslash sigma\_i\; =\; \backslash sqrt(3J\_2)\; =\; \backslash sqrt(\backslash frac((\backslash sigma\_(11)\; -\; \backslash sigma\_(22))^2\; +\; (\backslash sigma\_(22)\; -\; \backslash sigma\_(33))^2\; +\; (\backslash sigma\_\; (33)\; -\; \backslash sigma\_(11))^2\; +\; 6(\backslash sigma\_(12)^2\; +\; \backslash sigma\_(23)^2\; +\; \backslash sigma\_(31)^2))(2))$

The Mises criterion is “macroscopic”: “A polycrystal with randomly oriented grains will have noticeable plasticity if the deformation in it proceeds according to at least, five independent systems slip."

This is one of the two main plasticity criteria used today. Second important criterion owned by Henri Tresca.

Mises and Kolmogorov

Mises' views on probability theory were criticized by A. N. Kolmogorov, B. V. Gnedenko, A. Ya. Khinchin.

A. N. Kolmogorov, whose competing axiomatics of probability theory is more widely accepted, noted:

"Basis for applicability of results mathematical theory probabilities to real random events must depend on some form of frequency conception of the notion of probability, the inevitable nature of which was very enthusiastically established by von Mises.

Bibliography

• Richard von Mises, Mathematical Theory of Probability and Statistics, New York, Academic Press, 1964.
• Selected papers, v. 1-2, Providence, 1963-1964.
• Wahrscheinlichkeitsrechnung und ihre Anwendung in der Statistik und theoretischen Physik, Lpz. - W. 1931.
• Probability and statistics, M.-L., 1930.
• Differential and integral equations mathematical physics , L.-M., 1937 (co-author F. Frank).
• flight theory, M., 1949.
• Mathematical theory of compressible fluid flows, M., 1961.

) in the family of Arthur Edler von Mises, Doctor of Technical Sciences, who worked as an expert in the Austrian State Railways, and Adele von Landau. Richard's elder brother was one of the largest representatives of the Austrian school in economics, Ludwig von Mises.

In 1901 he graduated from the Academic Gymnasium in Vienna with honors in Latin and mathematics. In 1905 he graduated from the Vienna University of Technology with a degree in mathematics, physics and engineering. After graduation, he worked as an assistant to the German mathematician Georg Hamel in Brunn (now Brno, Czech Republic). In 1908 he received his doctorate in Vienna with the thesis "Determination of the mass of a flywheel in a crank mechanism". In Brunn he passed the procedure of "habilitation" (for the work "Theory of the water wheel") for lecturing on engineering. In 1909, at the age of 26, he became a professor of applied mathematics in Strasbourg (then part of the German Empire, now France) and received Prussian citizenship. His attempt to secure a teaching position at the Brno University of Technology was interrupted by the First World War.

With experience in flying and lecturing on aircraft design and being the first to give a university course in active flight in 1913 in Strasbourg, Mises joins the Austro-Hungarian army as a test pilot and instructor. In 1915, under his leadership, an aircraft with an 600 hp engine was created. (450 kW), so-called. "Mises plane", for the Austrian army. The aircraft was completed in 1916, but never took part in hostilities. During the First World War, he studied the conditions of elastic stability of cylindrical shells under the combined action of axial and transverse pressure.

After the war, Mises became the head of the department of hydrodynamics and aerodynamics at the Dresden Higher Technical School. In 1919 he became director of the new Institute for Applied Mathematics at the University of Berlin (where he also held the title of professor). Founder and editor-in-chief (1921-1933) of the Zeitschrift f?r Angewandte Mathematik und Mechanik magazine.

When the Nazis came to power in 1933, Mises was forced by virtue of his Jewish origin to emigrate to Turkey, where he headed the newly created Department of Pure and Applied Mathematics at Istanbul University.

In 1939, after the death of Turkish President Kemal Atatürk and the resulting uncertain political situation after that, Mises emigrated to the United States, where in 1944 he became a professor of aerodynamics and applied mathematics at Harvard University. In 1945 he gave an enhanced formulation of the Saint-Venant principle.

In 1943, he married Hilde Geiringer (German), a mathematician who was Mises's assistant during his work at the University of Berlin, who, due to her Jewish origin, was also forced to leave the university and the country in 1933. Accompanied Mises during his emigration to Turkey and later to the USA.

Biography

With experience in flying and lecturing on aircraft design and being the first to give a university course in active flight in 1913 in Strasbourg, Mises joins the Austro-Hungarian army as a test pilot and instructor. In 1915, under his leadership, an aircraft with an 600 hp engine was created. (450 kW), so-called. "Mises plane", for the Austrian army. The aircraft was completed in 1916, but never took part in hostilities. During the First World War, he studied the conditions of elastic stability of cylindrical shells under the combined action of axial and transverse pressure.

After the war, Mises becomes head of the department of hydrodynamics and aerodynamics at the Dresden Technische Hochschule. In 1919 he became director of the new Institute for Applied Mathematics at the University of Berlin (where he also held the title of professor). Founder and editor-in-chief (1921-1933) of the Zeitschrift für Angewandte Mathematik und Mechanik magazine ( "ZAMM").

Circle of interests

In his own words, spoken shortly before his death, the range of his interests:

"practical analysis, integral and differential equations, mechanics, hydrodynamics and aerodynamics, constructive geometry, probability calculus, statistics and philosophy (in the spirit of Ernst Mach's neopositivism)".

Plasticity criterion

This is one of the two main plasticity criteria used today. The second important criterion belongs to Henri Tresca.

Maximum principle in plasticity

In 1913 he formulated the maximum principle: “For a given plastic flow of a material, stresses are distributed in such a way that the power of plastic deformation takes a stationary value”. From this principle follows the associated law of plastic flow:

$\backslash varepsilon\_(ij)=\backslash lambda\backslash frac(\backslash partial\; f)(\backslash partial\backslash sigma\_(ij))$,

where $\backslash varepsilon\_(ij)$ are the strain rate tensor components, $\backslash sigma\_(ij)$ are the stress tensor components, $f(\backslash sigma\_1,\backslash sigma\_2,\backslash sigma\_3)=0$- condition of plasticity.

Mises and Kolmogorov

Mises' views on probability theory were criticized by A. N. Kolmogorov, B. V. Gnedenko, A. Ya. Khinchin.

A. N. Kolmogorov, whose competing axiomatics of probability theory is more widely accepted, noted:

"The basis for the applicability of the results of the mathematical theory of probability to real random events must depend on some form of frequency conception of the notion of probability, the inevitable nature of which was very enthusiastically established by von Mises.

Bibliography

• Richard von Mises. Mathematical Theory of Probability and Statistics. - New York: Academic Press, 1964.
• Selected papers, v. 1-2. Providence, 1963-1964.
• Wahrscheinlichkeitsrechnung und ihre Anwendung in der Statistik und theoretischen Physik. Lpz. - W., 1931.
• Probability and statistics. M.-L., 1930.
• Differential and integral equations of mathematical physics. L.-M., 1937 (co-author F. Frank).
• flight theory. M., 1949.
• Mathematical theory of compressible fluid flows. M., 1961.
• Mises R. Mechanic der plastischen Formandenderung von Kristallen // ZAMM. - 1928. - Bd. 8, H. 3. - S. 161-184.

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- They didn’t know how to take Murat alive in the morning and arrive on time at the place: now there’s nothing to do! he replied to another.
When Kutuzov was informed that in the rear of the French, where, according to the reports of the Cossacks, there had been no one before, there were now two battalions of Poles, he glanced back at Yermolov (he had not spoken to him since yesterday).
- Here they ask for an offensive, they offer various projects, but as soon as you get down to business, nothing is ready, and the warned enemy takes his measures.
Yermolov screwed up his eyes and smiled slightly when he heard these words. He realized that the storm had passed for him and that Kutuzov would confine himself to this hint.
“He’s amused at my expense,” Yermolov said quietly, pushing Raevsky, who was standing beside him, with his knee.
Shortly thereafter, Yermolov moved forward to Kutuzov and respectfully reported:
“Time has not been lost, Your Grace, the enemy has not left. If you order to attack? And then the guards will not see the smoke.
Kutuzov did not say anything, but when he was informed that Murat's troops were retreating, he ordered an offensive; but every hundred steps he stopped for three-quarters of an hour.
The whole battle consisted only in what the Cossacks of Orlov Denisov did; the rest of the troops only lost a few hundred people in vain.
As a result of this battle, Kutuzov received a diamond badge, Bennigsen also received diamonds and a hundred thousand rubles, others, according to their ranks, also received a lot of pleasant things, and after this battle, new changes were made in the headquarters.
“This is how we always do it, everything is upside down!” - Russian officers and generals said after the Tarutino battle, - just like they say now, making it feel that someone stupid is doing it upside down, but we wouldn’t have done it that way. But people who say this either do not know the business they are talking about, or deliberately deceive themselves. Every battle - Tarutino, Borodino, Austerlitz - everything is not carried out in the way that its stewards intended. This is an essential condition.
Countless free forces(for nowhere is a man freer than in a battle, where life and death are at stake) affects the direction of the battle, and this direction can never be known in advance and never coincides with the direction of any one force.
If many, simultaneously and differently directed forces act on some body, then the direction of movement of this body cannot coincide with any of the forces; but there will always be an average, shortest direction, that which in mechanics is expressed by the diagonal of the parallelogram of forces.
If in the descriptions of historians, especially French ones, we find that their wars and battles are carried out according to a predetermined plan, then the only conclusion that we can draw from this is that these descriptions are not correct.
The Tarutino battle, obviously, did not achieve the goal that Tol had in mind: to bring troops into action in order, according to the disposition, and the one that Count Orlov could have had; capture Murat, or the goal of instantly exterminating the entire corps, which Benigsen and other persons could have, or the goals of an officer who wanted to get into business and distinguish himself, or a Cossack who wanted to get more booty than he got, etc. But , if the goal was what actually happened, and what was then a common desire for all Russian people (the expulsion of the French from Russia and the extermination of their army), then it will be completely clear that the Battle of Tarutino, precisely because of its incongruities, was the very , which was needed during that period of the campaign. It is difficult and impossible to think of any outcome of this battle more expedient than the one that it had. With the least exertion, with the greatest confusion and with the most insignificant loss, the greatest results in the entire campaign were obtained, the transition from retreat to attack was made, the weakness of the French was exposed, and that impetus was given, which was only expected by the Napoleonic army to start the flight.

Napoleon enters Moscow after a brilliant victory de la Moskowa; there can be no doubt about victory, since the battlefield remains with the French. The Russians retreat and give up the capital. Moscow, filled with provisions, weapons, shells and untold riches, is in the hands of Napoleon. Russian army, twice as weak as the French, for a month does not make a single attempt to attack. Napoleon's position is the most brilliant. In order to fall on the remnants of the Russian army with double strength and exterminate it, in order to negotiate a favorable peace or, in case of refusal, to make a threatening movement on Petersburg, in order even, in case of failure, to return to Smolensk or Vilna , or stay in Moscow - in order, in a word, to keep the brilliant position in which it was at that time French army, it would seem that no special genius is needed. To do this, it was necessary to do the simplest and easiest thing: to prevent the troops from plundering, to prepare winter clothes, which would be enough in Moscow for the entire army, and to correctly collect provisions for the entire army that were in Moscow for more than six months (according to French historians). Napoleon, the most brilliant of geniuses and having the power to direct the army, historians say, did nothing of the sort.
Not only did he not do any of this, but, on the contrary, he used his power to choose from all the paths of activity presented to him that which was most stupid and pernicious of all. Of all that Napoleon could do: spend the winter in Moscow, go to Petersburg, go to Nizhny Novgorod, go back, north or south, the way that Kutuzov later went - well, no matter what you think up, it’s more stupid and more pernicious than what Napoleon did, that is, stay in Moscow until October, leaving the troops to rob the city, then, hesitating, leave or not to leave the garrison, leave Moscow, approach Kutuzov, do not start the battle, go to the right, reach Maly Yaroslavets, again without experiencing chance to break through, go not along the road along which Kutuzov went, but go back to Mozhaisk and along the devastated Smolensk road - it was impossible to think of anything more stupid than this, more detrimental to the army, as the consequences showed. Let the most skillful strategists come up with, imagining that Napoleon's goal was to destroy his army, come up with another series of actions that would, with the same certainty and independence from everything that the Russian troops undertake, would completely destroy the whole French army like what Napoleon did.
The brilliant Napoleon did it. But to say that Napoleon destroyed his army because he wanted it, or because he was very stupid, would be just as unfair as to say that Napoleon brought his troops to Moscow because he wanted it, and because that he was very smart and brilliant.
In both cases, his personal activity, which had no more power than the personal activity of each soldier, only coincided with the laws according to which the phenomenon took place.
Quite falsely (only because the consequences did not justify the activities of Napoleon) historians present to us the strength of Napoleon weakened in Moscow. He, just as before, as after, in the 13th year, used all his skill and strength to do the best for himself and his army. Napoleon's activity during this time is no less amazing than in Egypt, in Italy, in Austria and in Prussia. We do not know correctly about the extent to which the genius of Napoleon was real in Egypt, where forty centuries looked at his greatness, because all these great feats are described to us only by the French. We cannot correctly judge his genius in Austria and Prussia, since information about his activities there must be drawn from French and German sources; and the incomprehensible surrender of corps without battles and fortresses without siege should incline the Germans to recognize genius as the only explanation for the war that was waged in Germany. But there is no reason for us to recognize his genius in order to hide our shame, thank God. We have paid to have the right to simply and directly look at the matter, and we will not cede this right.
His activity in Moscow is as amazing and ingenious as elsewhere. Orders after orders and plans after plans come from him from the moment he enters Moscow until he leaves it. The absence of residents and deputations, and the fire of Moscow itself, do not bother him. He does not lose sight of either the good of his army, or the actions of the enemy, or the good of the peoples of Russia, or the administration of the valleys of Paris, or diplomatic considerations about the forthcoming conditions of peace.

In military terms, immediately upon entering Moscow, Napoleon strictly orders General Sebastiani to monitor the movements of the Russian army, sends corps to different roads and Murat orders to find Kutuzov. Then he diligently orders the strengthening of the Kremlin; then he makes an ingenious plan for a future campaign across the entire map of Russia. In terms of diplomacy, Napoleon calls to himself the robbed and ragged captain Yakovlev, who does not know how to get out of Moscow, sets out to him in detail all his policy and his generosity and, writing a letter to Emperor Alexander, in which he considers it his duty to inform his friend and brother that Rostopchin badly ordered in Moscow, he sends Yakovlev to Petersburg. Having set out in the same detail his views and generosity before Tutolmin, he sends this old man to St. Petersburg for negotiations.