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Alexander Bruno
Alexander Dmitrievich Bruno (russian: Александр Дмитриевич Брюно) (26 June 1940, Moscow) is a Russian people, Russian mathematician who has made contributions to the Normal form (bifurcation theory), normal forms theory. Bruno developed a new level of mathematical analysis and called it "power geometry". He also applied it to the solution of several problems in mathematics, mechanics, celestial mechanics, and hydrodynamics. The Brjuno numbers were introduced by him in 1971, and are named after him. Bruno won third prize at the Moscow Mathematical Olympiade in 1956 and first prize in 1957. He studied at Moscow State University, where he won second prizes for student papers in 1960 and 1961, and earned a master's degree there in 1962.Bio Keldysh Institute of Applied Mathematics, Retrieved 2015-05-04. He completed a doct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bruno 2
Bruno may refer to: People and fictional characters *Bruno (name), including lists of people and fictional characters with either the given name or surname * Bruno, Duke of Saxony (died 880) * Bruno the Great (925–965), Archbishop of Cologne, Duke of Lotharingia and saint * Bruno (bishop of Verden) (920–976), German Roman Catholic bishop * Pope Gregory V (c. 972–999), born Bruno of Carinthia * Bruno of Querfurt (c. 974–1009), Christian missionary bishop, martyr and saint * Bruno of Augsburg (c. 992–1029), Bishop of Augsburg * Bruno (bishop of Würzburg) (1005–1045), German Roman Catholic bishop * Pope Leo IX (1002–1054), born Bruno of Egisheim-Dagsburg * Bruno II (1024–1057), Frisian count or margrave * Bruno the Saxon (fl. 2nd half of the 11th century), historian * Saint Bruno of Cologne (d. 1101), founder of the Carthusians * Bruno (bishop of Segni) (c. 1045–1123), Italian Roman Catholic bishop and saint * Bruno (archbishop of Trier) (died 1124), German Roman ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russian People
, native_name_lang = ru , image = , caption = , population = , popplace = 118 million Russians in the Russian Federation (2002 ''Winkler Prins'' estimate) , region1 = , pop1 = approx. 7,500,000 (including Russian Jews and Russian Germans) , ref1 = , region2 = , pop2 = 7,170,000 (2018) ''including Crimea'' , ref2 = , region3 = , pop3 = 3,512,925 (2020) , ref3 = , region4 = , pop4 = 3,072,756 (2009)(including Russian Jews and Russian Germans) , ref4 = , region5 = , pop5 = 1,800,000 (2010)(Russian ancestry and Russian Germans and Jews) , ref5 = 35,000 (2018)(born in Russia) , region6 = , pop6 = 938,500 (2011)(including Russian Jews) , ref6 = , region7 = , pop7 = 809,530 (2019) , ref7 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Form (bifurcation Theory)
In mathematics, the normal form of a dynamical system is a simplified form that can be useful in determining the system's behavior. Normal forms are often used for determining local bifurcations in a system. All systems exhibiting a certain type of bifurcation are locally (around the equilibrium) topologically equivalent to the normal form of the bifurcation. For example, the normal form of a saddle-node bifurcation is : \frac = \mu + x^2 where \mu is the bifurcation parameter. The transcritical bifurcation : \frac = r \ln x + x - 1 near x=1 can be converted to the normal form : \frac = \mu u - u^2 + O(u^3) with the transformation u = x -1, \mu = r + 1 .Strogatz, Steven. "Nonlinear Dynamics and Chaos". Westview Press, 2001. p. 52. See also canonical form In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. Often, it is one which provid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanics
Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects result in displacements, or changes of an object's position relative to its environment. Theoretical expositions of this branch of physics has its origins in Ancient Greece, for instance, in the writings of Aristotle and Archimedes (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo, Kepler, Huygens, and Newton laid the foundation for what is now known as classical mechanics. As a branch of classical physics, mechanics deals with bodies that are either at rest or are moving with velocities significantly less than the speed of light. It can also be defined as the physical science that deals with the motion of and forces on bodies not in the quantum realm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Celestial Mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to produce ephemeris data. History Modern analytic celestial mechanics started with Isaac Newton's Principia of 1687. The name "celestial mechanics" is more recent than that. Newton wrote that the field should be called "rational mechanics." The term "dynamics" came in a little later with Gottfried Leibniz, and over a century after Newton, Pierre-Simon Laplace introduced the term "celestial mechanics." Prior to Kepler there was little connection between exact, quantitative prediction of planetary positions, using geometrical or arithmetical techniques, and contemporary discussions of the physical causes of the planets' motion. Johannes Kepler Johannes Kepler (1571–1630) was the first to closely integrate the predictive geom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrodynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time. Bef ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brjuno Number
In mathematics, a Brjuno number (sometimes spelled Bruno or Bryuno) is a special type of irrational number named for Russian mathematician Alexander Bruno, who introduced them in . Formal definition An irrational number \alpha is called a Brjuno number when the infinite sum :B(\alpha) = \sum_^\infty \frac converges to a finite number. Here: * q_n is the denominator of the th convergent \tfrac of the continued fraction expansion of \alpha. * B is a Brjuno function Importance The Brjuno numbers are important in the one–dimensional analytic small divisors problems. Bruno improved the diophantine condition in Siegel's Theorem, showed that germs of holomorphic functions with linear part e^ are linearizable if \alpha is a Brjuno number. showed in 1987 that this condition is also necessary, and for quadratic polynomials is necessary and sufficient. Properties Intuitively, these numbers do not have many large "jumps" in the sequence of convergents, in which the denominat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow State University
M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious university in the country. The university includes 15 research institutes, 43 faculties, more than 300 departments, and six branches (including five foreign ones in the Commonwealth of Independent States countries). Alumni of the university include past leaders of the Soviet Union and other governments. As of 2019, 13 List of Nobel laureates, Nobel laureates, six Fields Medal winners, and one Turing Award winner had been affiliated with the university. The university was ranked 18th by ''The Three University Missions Ranking'' in 2022, and 76th by the ''QS World University Rankings'' in 2022, #293 in the world by the global ''Times Higher World University Rankings'', and #326 by ''U.S. News & World Report'' in 2022. It was the highest-ran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Keldysh Institute Of Applied Mathematics
The Keldysh Institute of Applied Mathematics (russian: Институт прикладной математики им. М.В.Келдыша) is a research institute specializing in computational mathematics. It was established to solve computational tasks related to government programs of nuclear and fusion energy, space research and missile technology. The Institute is a part of the Department of Mathematical Sciences of the Russian Academy of Sciences. The main direction of activity of the institute is the use of computer technology to solve complex scientific and technical issues of practical importance. Since 2016, development of mathematical and computational methods for biological research, as well as a direct solution to the problems of computational biology with the use of such methods, has also been included in the circle of scientific activities of the institute. Scientific activity Nuclear physics Prominent theoretical physicist Yakov Borisovich Zel'dovich headed one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moldova State University
The Moldova State University (Romanian: ''Universitatea de Stat din Moldova'') is a university located in Chișinău, Moldova. History The university was founded on 1 October 1946. Initially, it had 320 students enrolled in 5 faculties, Physics and Mathematics, Geology and Pedology, History and Philology, Biology, Chemistry. Within the 12 departments there were 35 teachers. Among the initiators of the founding of the university were Macarie Radu and Mihail Pavlov. In 1969, the State University of Moldova joined the International Association of Universities as a plenipotentiary member. The prestige of the State University of Moldova on the international arena has been strengthened by the 14 scientists and cultures of 9 countries of the world who have been awarded the title of Doctor Honoris Causa of the State University of Moldova. The State University of Moldova has concluded more than 60 cooperation agreements in the field of education and science with university centers in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
