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Dmitry Gudkov (mathematician)
Dmitrii Andreevich Gudkov (1918–1992; alternative spelling Dmitry) was a Soviet mathematician famous for his work on Hilbert's sixteenth problem and the related Gudkov's conjecture in algebraic geometry. He was a student of Aleksandr Andronov.Jeremy Gray – ''The Hilbert Challenge'', p. 147 Selected papers *D. A. Gudkov, "The topology of real projective algebraic varieties", ''Russian Mathematical Surveys'', 1974, 29 (4), pp. 1–79 (translated from the Russian original). *D. A. Gudkov "Periodicity of the Euler characteristic of real algebraic (M—1)-manifolds", ''Functional Analysis and Its Applications'', April–June, 1973, Volume 7, Issue 2, pp. 98–102 (translated from the Russian original). *D.A Gudkov. "Ovals of sixth order curves". in the book ''Nine Papers on Hilbert's 16th Problem'' ''American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert's Sixteenth Problem
Hilbert's 16th problem was posed by David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900, as part of his list of 23 problems in mathematics. The original problem was posed as the ''Problem of the topology of algebraic curves and surfaces'' (''Problem der Topologie algebraischer Kurven und Flächen''). Actually the problem consists of two similar problems in different branches of mathematics: * An investigation of the relative positions of the branches of real algebraic curves of degree ''n'' (and similarly for algebraic surfaces). * The determination of the upper bound for the number of limit cycles in two-dimensional polynomial vector fields of degree ''n'' and an investigation of their relative positions. The first problem is yet unsolved for ''n'' = 8. Therefore, this problem is what usually is meant when talking about Hilbert's sixteenth problem in real algebraic geometry. The second problem also remains unsolved: no up ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gudkov's Conjecture
In real algebraic geometry, Gudkov's conjecture, also called Gudkov’s congruence, (named after Dmitry Gudkov) was a conjecture, and is now a theorem, which states that an M-curve of even degree 2d obeys the congruence : p - n \equiv d^2\, (\!\bmod 8), where p is the number of positive ovals and n the number of negative ovals of the M-curve. (Here, the term M-curve stands for "maximal curve"; it means a smooth algebraic curve over the reals whose genus is k-1, where k is the number of maximal components of the curve.) The theorem was proved by the combined works of Vladimir Arnold and Vladimir Rokhlin. See also *Hilbert's sixteenth problem *Tropical geometry In mathematics, tropical geometry is the study of polynomials and their geometric properties when addition is replaced with minimization and multiplication is replaced with ordinary addition: : x \oplus y = \min\, : x \otimes y = x + y. So fo ... References {{reflist Conjectures that have been proved Theorems in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of the points of special interest like the singular points, the inflection points and the points at infinity. More advanced questions involve the topo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aleksandr Andronov
Aleksandr Aleksandrovich Andronov (russian: Алекса́ндр Алекса́ндрович Андро́нов; , Moscow – October 31, 1952, Gorky) was a Soviet physicist and member of the Soviet Academy of Sciences (1946). He worked extensively on the theory of stability of dynamical systems, introducing (together with Lev Pontryagin) the notion of structural stability. In that context, he also contributed to the mathematical theory of self-oscillation (a term that he coined) by establishing a link between the generation of oscillations and the theory of Lyapunov stability. He developed the comprehensive theory of self-oscillations by linking it with the qualitative theory of differential equations, topology, and with the general theory of stability of motion. The crater Andronov on the Moon is named after him. References External links * Author profilein the database zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Arnold
Vladimir Igorevich Arnold (alternative spelling Arnol'd, russian: link=no, Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, he made important contributions in several areas including dynamical systems theory, algebra, catastrophe theory, topology, algebraic geometry, symplectic geometry, differential equations, classical mechanics, hydrodynamics and singularity theory, including posing the ADE classification problem, since his first main result—the solution of Hilbert's thirteenth problem in 1957 at the age of 19. He co-founded two new branches of mathematics—KAM theory, and topological Galois theory (this, with his student Askold Khovanskii). Arnold was also known as a popularizer of mathematics. Through his lectures, seminars, and as the author of several textbooks (such as the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the '' Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soviet Mathematicians
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national republics; in practice, both its government and its economy were highly centralized until its final years. It was a one-party state governed by the Communist Party of the Soviet Union, with the city of Moscow serving as its capital as well as that of its largest and most populous republic: the Russian SFSR. Other major cities included Leningrad (Russian SFSR), Kiev (Ukrainian SSR), Minsk (Byelorussian SSR), Tashkent (Uzbek SSR), Alma-Ata (Kazakh SSR), and Novosibirsk (Russian SFSR). It was the largest country in the world, covering over and spanning eleven time zones. The country's roots lay in the October Revolution of 1917, when the Bolsheviks, under the leadership of Vladimir Lenin, overthrew the Russian Provisional Government that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1918 Births
This year is noted for the end of the First World War, on the eleventh hour of the eleventh day of the eleventh month, as well as for the Spanish flu pandemic that killed 50–100 million people worldwide. Events Below, the events of World War I have the "WWI" prefix. January * January – 1918 flu pandemic: The "Spanish flu" (influenza) is first observed in Haskell County, Kansas. * January 4 – The Finnish Declaration of Independence is recognized by Soviet Russia, Sweden, Germany and France. * January 9 – Battle of Bear Valley: U.S. troops engage Yaqui Native American warriors in a minor skirmish in Arizona, and one of the last battles of the American Indian Wars between the United States and Native Americans. * January 15 ** The keel of is laid in Britain, the first purpose-designed aircraft carrier to be laid down. ** The Red Army (The Workers and Peasants Red Army) is formed in the Russian SFSR and Soviet Union. * January 18 - The Historic Concert for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1992 Deaths
Year 199 ( CXCIX) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was sometimes known as year 952 ''Ab urbe condita''. The denomination 199 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Mesopotamia is partitioned into two Roman provinces divided by the Euphrates, Mesopotamia and Osroene. * Emperor Septimius Severus lays siege to the city-state Hatra in Central-Mesopotamia, but fails to capture the city despite breaching the walls. * Two new legions, I Parthica and III Parthica, are formed as a permanent garrison. China * Battle of Yijing: Chinese warlord Yuan Shao defeats Gongsun Zan. Korea * Geodeung succeeds Suro of Geumgwan Gaya, as king of the Korean kingdom of Gaya (traditional date). By topic Religion * Pope Zephyrinus succeeds Pope Vic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
