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Lyapunov Fractal Segment
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] |
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] |
Lyapunov Vector
In applied mathematics and dynamical system theory, Lyapunov vectors, named after Aleksandr Lyapunov, describe characteristic expanding and contracting directions of a dynamical system. They have been used in predictability analysis and as initial perturbations for ensemble forecasting in numerical weather prediction. In modern practice they are often replaced by bred vectors for this purpose. Mathematical description Lyapunov vectors are defined along the trajectories of a dynamical system. If the system can be described by a d-dimensional state vector x\in\mathbb^d the Lyapunov vectors v^(x), (k=1\dots d) point in the directions in which an infinitesimal perturbation will grow asymptotically, exponentially at an average rate given by the Lyapunov exponent In mathematics, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories. Quantitatively, two trajectories i ... [...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] |
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 Russ ... [...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 1610 by ... [...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 ... [...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 and 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 fath .... 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 ... [...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 toge ...al rat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lyapunov Time
In mathematics, the Lyapunov time is the characteristic timescale on which a dynamical system is chaotic. It is named after the Russian mathematician Aleksandr Lyapunov. It is defined as the inverse of a system's largest Lyapunov exponent. Use The Lyapunov time mirrors the limits of the predictability of the system. By convention, it is defined as the time for the distance between nearby trajectories of the system to increase by a factor of '' e''. However, measures in terms of 2-foldings and 10-foldings are sometimes found, since they correspond to the loss of one bit of information or one digit of precision respectively. While it is used in many applications of dynamical systems theory, it has been particularly used in celestial mechanics where it is important for the problem of the stability of the Solar System. However, empirical estimation of the Lyapunov time is often associated with computational or inherent uncertainties. Examples Typical values are:Pierre Gaspard, ''Cha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexey Lyapunov
Alexey Andreevich Lyapunov (russian: Алексе́й Андре́евич Ляпуно́в; 25 September 1911 – 23 June 1973) was a Soviet mathematician and an early pioneer of computer science. One of the founders of Soviet cybernetics, Lyapunov was member of the Soviet Academy of Sciences and a specialist in the fields of real function theory, mathematical problems of cybernetics, set theory, programming theory, mathematical linguistics, and mathematical biology. Biography Composer Sergei Lyapunov, mathematician Aleksandr Lyapunov, and philologist Boris Lyapunov were close relatives of Alexey Lyapunov. In 1928, Lyapunov enrolled at Moscow State University to study mathematics, and in 1932 he became a student of Nikolai Luzin. Under his mentorship, Lyapunov began his research in descriptive set theory. He became world-wide known for his theorem on the range of an atomless vector-measure in finite dimensions, now called the Lyapunov Convexity Theorem. From 1934 un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lyapunov's Central Limit Theorem
In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. This theorem has seen many changes during the formal development of probability theory. Previous versions of the theorem date back to 1811, but in its modern general form, this fundamental result in probability theory was precisely stated as late as 1920, thereby serving as a bridge between classical and modern probability theory. If X_1, X_2, \dots, X_n, \dots are random samples drawn from a population with overall mean \mu and finite variance and if \bar_n is the sample mean of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
