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Liapunov
Lyapunov (, in old-Russian often written Лепунов) is a Russian surname that is sometimes also romanized as Ljapunov, Liapunov or Ljapunow. Notable people with the surname include: * Alexey Lyapunov (1911–1973), Russian mathematician * Aleksandr Lyapunov (1857–1918), son of Mikhail (1820–1868), Russian mathematician and mechanician, after whom the following are named: ** Lyapunov dimension ** Lyapunov equation ** Lyapunov exponent ** Lyapunov function ** Lyapunov fractal ** Lyapunov stability ** Lyapunov's central limit theorem ** Lyapunov time ** Lyapunov vector ** Lyapunov (crater) * Boris Lyapunov (1862–1943), son of Mikhail (1820–1868), Russian expert in Slavic studies * Mikhail Lyapunov (1820–1868), Russian astronomer * Mikhail Nikolaevich Lyapunov (1848–1909), Russian military officer and lawyer * Prokopy Lyapunov (d. 1611), Russian statesman * Sergei Lyapunov (1859–1924), son of Mikhail (1820–1868), Russian composer * Zakhary Lyapunov (d. after 1612), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sergei Lyapunov
Sergei Mikhailovich Lyapunov (or Liapunov; russian: Серге́й Миха́йлович Ляпуно́в, ; 8 November 1924) was a Russian composer, pianist and conductor. Life Lyapunov was born in Yaroslavl in 1859. After the death of his father, Mikhail Lyapunov, when he was about eight, Sergei, his mother, and his two brothers (one of them was Aleksandr Lyapunov, later a notable mathematician) went to live in the larger town of Nizhny Novgorod. There he attended the grammar school along with classes of the newly formed local branch of the Russian Musical Society. On the recommendation of Nikolai Rubinstein, the Director of the Moscow Conservatory of Music, he enrolled in that institution in 1878. His main teachers were Karl Klindworth (piano; a former pupil of Franz Liszt), and Sergei Taneyev (composition; a former pupil of Pyotr Ilyich Tchaikovsky and his successor at the Conservatory). He graduated in 1883, more attracted by the nationalist elements in music of the New ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lyapunov (crater)
Lyapunov is a lunar impact crater named for Aleksandr Lyapunov that is located along the east-northeastern limb of the Moon, and is viewed from the side by observers on Earth. The eastern rim of this crater just falls into the section of the Moon called the far side, and visibility of this formation is affected by libration. This crater is attached to the south-southeastern rim of the larger walled plain Rayleigh. It is also attached to the western rim of the much larger walled plain Joliot, a formation that lies entirely on the far side of the Moon. To the south-southwest of Lyapunov is the crater Hubble. The shape of this crater's rim has been modified due to the large adjacent formations, so that it is somewhat polygon In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed '' polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two t ...al ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aleksandr Lyapunov
Aleksandr Mikhailovich Lyapunov (russian: Алекса́ндр Миха́йлович Ляпуно́в, ; – 3 November 1918) was a Russian mathematician, mechanician and physicist. His surname is variously romanized as Ljapunov, Liapunov, Liapounoff or Ljapunow. He was the son of the astronomer Mikhail Lyapunov and the brother of the pianist and composer Sergei Lyapunov. Lyapunov is known for his development of the stability theory of a dynamical system, as well as for his many contributions to mathematical physics and probability theory. Biography Early life Lyapunov was born in Yaroslavl, Russian Empire. His father Mikhail Vasilyevich Lyapunov (1820–1868) was an astronomer employed by the Demidov Lyceum. His brother, Sergei Lyapunov, was a gifted composer and pianist. In 1863, M. V. Lyapunov retired from his scientific career and relocated his family to his wife's estate at Bolobonov, in the Simbirsk province (now Ulyanovsk Oblast). After the death of his father in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lyapunov Dimension
In the mathematics of dynamical systems, the concept of Lyapunov dimension was suggested by Kaplan and Yorke for estimating the Hausdorff dimension of attractors. Further the concept has been developed and rigorously justified in a number of papers, and nowadays various different approaches to the definition of Lyapunov dimension are used. Remark that the attractors with noninteger Hausdorff dimension are called strange attractors. Since the direct numerical computation of the Hausdorff dimension of attractors is often a problem of high numerical complexity, estimations via the Lyapunov dimension became widely spread. The Lyapunov dimension was named after the Russian mathematician Aleksandr Lyapunov because of the close connection with the Lyapunov exponents. Definitions Consider a dynamical system \big(\_, (U\subseteq \mathbb^n, \, \cdot\, )\big) , where \varphi^t is the shift operator along the solutions: \varphi^t(u_0) = u(t,u_0), of ODE \dot = f(), t \leq 0, or differe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lyapunov Function
In the theory of ordinary differential equations (ODEs), Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Lyapunov functions (also called Lyapunov’s second method for stability) are important to stability theory of dynamical systems and control theory. A similar concept appears in the theory of general state space Markov chains, usually under the name Foster–Lyapunov functions. For certain classes of ODEs, the existence of Lyapunov functions is a necessary and sufficient condition for stability. Whereas there is no general technique for constructing Lyapunov functions for ODEs, in many specific cases the construction of Lyapunov functions is known. For instance, quadratic functions suffice for systems with one state; the solution of a particular linear matrix inequality provides Lyapunov functions for linear systems; and conservation laws can often be used to construct Lyapunov functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lyapunov Stability
Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point x_e stay near x_e forever, then x_e is Lyapunov stable. More strongly, if x_e is Lyapunov stable and all solutions that start out near x_e converge to x_e, then x_e is asymptotically stable. The notion of exponential stability guarantees a minimal rate of decay, i.e., an estimate of how quickly the solutions converge. The idea of Lyapunov stability can be extended to infinite-dimensional manifolds, where it is known as structural stability, which concerns the behavior of different but "nearby" solutions to differential equations. Input-to-state stability (ISS) applies Lyapunov notions to systems with inpu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Romanization Of Russian
The romanization of the Russian language (the transliteration of Russian text from the Cyrillic script into the Latin script), aside from its primary use for including Russian names and words in text written in a Latin alphabet, is also essential for computer users to input Russian text who either do not have a keyboard or word processor set up for inputting Cyrillic, or else are not capable of typing rapidly using a Keyboard layout#Russian, native Russian keyboard layout (JCUKEN). In the latter case, they would type using a system of transliteration fitted for their keyboard layout, such as for English QWERTY keyboards, and then use an automated tool to convert the text into Cyrillic. Systematic transliterations of Cyrillic to Latin There are a number of distinct and competing standards for the romanization of Russian Cyrillic, with none of them having received much popularity, and, in reality, transliteration is often carried out without any consistent standards. Scientific tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zakhary Lyapunov
Zakhary Petrovich Lyapunov () (? - after 1612) was a Russian political figure of the early 17th century, brother of Prokopy Lyapunov. Biography In 1605, Zakhary Lyapunov took the side of False Dmitri I. Upon the latter's death in 1606, he took part in the Bolotnikov Uprising in 1606–1607. In 1607, he joined the ranks of Vasily Shuisky and became a commander of a unit of the Ryazan dvoryane during the struggle against the rebellious peasants and supporters of False Dmitri II. In July 1610, Zachary Lyapunov took an active part in deposing Vasily Shuisky. In September 1610, he was included in a diplomatic mission, sent to the outskirts of Smolensk to sign a treaty with the Polish king Sigismund III Vasa regarding the accession of his son Wladislaus to the Russian throne. Then he returned to Moscow and remained in the city until its liberation from the Polish invaders by the army of Kuzma Minin and Dmitry Pozharsky Dmitry Mikhaylovich Pozharsky ( rus, Дми́трий Мих ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prokopy Lyapunov
Prokopy Petrovich Lyapunov () (Isady, Grand Duchy of Moscow; Grand Duchy of Ryazan became a part of Grand Duchy of Moscow in 1521 and Moscow shouldn't be confused as a birth place which is located to the east of Old Ryazan, in a village that survived to this day b. ? — July 22, 1611;Most sources agree that he died no later than August 1, 1611 Tsardom of Russia) was a prominent 17th century Russian nobleman ( dvoryanin), voivode (military chieftain) of, allegedly, a Rurikid origin who practically became a head of Pereyaslavl-Ryazansky lands nobility in the end 1590s; he took part in wars during power vacuum in succession crisis that happened in early 1598 as result of confusion about legitimate heir apparent following death of Feodor I, nobility infighting, war declared by Polish–Lithuanian Commonwealth (PLC) in 1605, and exhaustive Tatar raids; most famously he is remembered for organizing and leading the first unsuccessful uprising against occupation of Moscow of 161 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mikhail Nikolaevich Lyapunov
Mikhail Nikolaevich Lyapunov (russian: Михаил Николаевич Ляпунов; 1 March 1848 — 4 March 1909) was Russian statesman and military leader and a participant in the Russo-Japanese War. Biography Lyapunov was born into a family of hereditary nobles of Saint Petersburg Governorate. He received his secondary education at the Saint Petersburg military gymnasium and at the age of 16 he was enrolled as a cadet at the Pavel Military School . At the age of 20 he was promoted to the rank of lieutenant. The command noticed Lyapunov's legal abilities and he was sent to Odessa to the Military Law Academy. Lyapunov was promoted to staff-captain on 6 November 1872, captain from 21 October 1875, major on 20 February 1876, captain of the military judicial department from 1 April 1877, assistant military prosecutor and lieutenant colonel from 17 April 1879 and finally promoted to colonel on 30 August 1882. In December 1884 he received the post of military judge. From 27 J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mikhail Lyapunov
Mikhail Vasilyevich Lyapunov () was a Russian astronomer and a head of the Demidov Lyceum in Yaroslavl. He was the father of Aleksandr Alexander is a male given name. The most prominent bearer of the name is Alexander the Great, the king of the Ancient Greek kingdom of Macedonia who created one of the largest empires in ancient history. Variants listed here are Aleksandar, Al ... and Sergei Lyapunov. References 1820 births 1868 deaths Astronomers from the Russian Empire Mikhail {{Russia-scientist-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boris Lyapunov
Boris may refer to: People * Boris (given name), a male given name *:''See'': List of people with given name Boris * Boris (surname) * Boris I of Bulgaria (died 907), the first Christian ruler of the First Bulgarian Empire, canonized after his death * Boris II of Bulgaria (c. 931–977), ruler of the First Bulgarian Empire * Boris III of Bulgaria (1894–1943), ruler of the Kingdom of Bulgaria in the first half of the 20th century * Boris, Prince of Tarnovo (born 1997), Spanish-born Bulgarian royal * Boris and Gleb (died 1015), the first saints canonized in Kievan Rus * Boris (singer) (born 1965), pseudonym of French singer Philippe Dhondt Arts and media * Boris (band), a Japanese experimental rock trio * ''Boris'' (EP), by Yezda Urfa, 1975 * "Boris" (song), by the Melvins, 1991 * ''Boris'' (TV series), a 2007–2009 Italian comedy series * '' Boris: The Film'', a 2011 Italian film based on the TV series * '' Boris: The Rise of Boris Johnson'', a 2006 biography by Andrew Gim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
