Pyotr Novikov and Yuri Manin, both worked as which occupation, for the Soviets?
mathematician
Pyotr Novikov Yuri Manin
In mathematics, the Manin conjecture describes the conjectural distribution of rational points on an algebraic variety relative to a suitable height function.  It was proposed by Yuri I. Manin and his collaborators in 1989 when they initiated a program with the aim of describing the distribution of rational points on suitable algebraic varieties.
In mathematics, a quadratic algebra is a filtered algebra generated by degree one elements, with defining relations of degree 2.  It was pointed out by Yuri Manin that such algebras play an important role in the theory of quantum groups.  The most important class of graded quadratic algebras is Koszul algebras.
Yuri Ivanovitch Manin (Russian: Ю́рий Ива́нович Ма́нин ; born 1937) is a Soviet/Russian/German mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.  Moreover, Manin was one of the first to propose the idea of a quantum computer in 1980 with his book "Computable and Uncomputable".
Pyotr Kirichek (Russian: Пётр Тихонович Киричек ; 1902 — 1968) was a Soviet singer, a bass-baritone.  After graduating from the Moscow Conservatory, he worked as a soloist at the Bolshoi Theater (1934–1944) and then mostly toured with programs devoted to romances and contemporary Soviet songs.  He was awarded the title of Meritorious Artist of the RSFSR in 1960.  Kirichek performed or recorded such songs as "March of the Soviet Tankmen" ("Марш советских танкистов"), "Anthem of the International Union of Students" ("Гимн международного союза студентов"), "Goodbye, Rocky Mountains" ("Прощайте, скалистые горы").  Composer Anatoly Novikov praised him as a real tribune and a real fighter who didn't care about the conditions under which he had to sing, who performed in factories, at field camps and on ships and gave about 1,500 concerts on the front line during the Great Patriotic War.
Pyotr Velikiy (Russian: "Пётр Великий") is the fourth "Kirov"-class battlecruiser of the Russian Navy.  Initially named Yuri Andropov (Russian: "Юрий Андропов") for Yuri Andropov, the former General Secretary of the Communist Party, the ship's name was changed after the fall of the Soviet Union.  The Russian designation for the type is "heavy missile cruiser", but Western defense commentators re-invented the term "battlecruiser" to describe these as they are the largest surface combatant warships in the world.  "Pyotr Velikiy" is the flagship of the Northern Fleet.
Pyotr Sergeyevich Novikov (Russian: Пётр Серге́евич Но́виков ; 15 August 1901, Moscow, Russian Empire – 9 January 1975, Moscow, Soviet Union) was a Soviet mathematician.
In mathematics, Manin matrices, named after Yuri Manin who introduced them around 1987–88, are a class of matrices with elements in a not-necessarily commutative ring, which in a certain sense behave like matrices whose elements commute.  In particular there is natural definition of the determinant for them and most linear algebra theorems like Cramer's rule, Cayley–Hamilton theorem, etc. hold true for them.  Any matrix with commuting elements is a Manin matrix.  These matrices have applications in representation theory in particular to Capelli's identity, Yangian and quantum integrable systems.
Pyotr Georgyevich Novikov (Russian: Пётр Георгиевич Новиков ; 18 December 1907 – August 1944) was a Red Army major general.  Novikov fought in the Spanish Civil War as a battalion commander.  After returning to the Soviet Union he fought in the Winter War.  After the end of the Winter War Novikov became commander of the 2nd Cavalry Division.  He led the division in battles on the Southern Front.  The division became the 109th Rifle Division and fought in the Siege of Sevastopol.  After the evacuation of Filipp Oktyabrsky and Ivan Yefimovich Petrov, Novikov became commander of the Sevastopol defense.  Novikov attempted to evacuate the city on a patrol boat and was intercepted and captured by German forces.  He was sent to concentration camps in Germany and died at Flossenbürg concentration camp in August 1944.
Quantum computing studies computation systems (quantum computers) that make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data.  Quantum computers are different from binary digital electronic computers based on transistors. Whereas common digital computing requires that the data be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits, which can be in superpositions of states.  A quantum Turing machine is a theoretical model of such a computer, and is also known as the universal quantum computer.  The field of quantum computing was initiated by the work of Paul Benioff and Yuri Manin in 1980, Richard Feynman in 1982, and David Deutsch in 1985.  A quantum computer with spins as quantum bits was also formulated for use as a quantum spacetime in 1968.
In mathematics, in the field of arithmetic algebraic geometry, the Manin obstruction (named after Yuri Manin) is attached to a variety "X" over a global field, which measures the failure of the Hasse principle for "X".  If the value of the obstruction is non-trivial, then "X" may have points over all local fields but not over the global field.
Manin conjecture Quadratic algebra Yuri Manin Pyotr Kirichek Russian battlecruiser Pyotr Velikiy Pyotr Novikov Manin matrix Pyotr Georgyevich Novikov Quantum computing Manin obstruction
In mathematics, the Manin conjecture describes the conjectural distribution of rational points on an algebraic variety relative to a suitable height function.  It was proposed by Yuri I. Manin and his collaborators in 1989 when they initiated a program with the aim of describing the distribution of rational points on suitable algebraic varieties.
Manin conjecture
In mathematics, a quadratic algebra is a filtered algebra generated by degree one elements, with defining relations of degree 2.  It was pointed out by Yuri Manin that such algebras play an important role in the theory of quantum groups.  The most important class of graded quadratic algebras is Koszul algebras.
Quadratic algebra
Yuri Ivanovitch Manin (Russian: Ю́рий Ива́нович Ма́нин ; born 1937) is a Soviet/Russian/German mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.  Moreover, Manin was one of the first to propose the idea of a quantum computer in 1980 with his book "Computable and Uncomputable".
Yuri Manin
Pyotr Kirichek (Russian: Пётр Тихонович Киричек ; 1902 — 1968) was a Soviet singer, a bass-baritone.  After graduating from the Moscow Conservatory, he worked as a soloist at the Bolshoi Theater (1934–1944) and then mostly toured with programs devoted to romances and contemporary Soviet songs.  He was awarded the title of Meritorious Artist of the RSFSR in 1960.  Kirichek performed or recorded such songs as "March of the Soviet Tankmen" ("Марш советских танкистов"), "Anthem of the International Union of Students" ("Гимн международного союза студентов"), "Goodbye, Rocky Mountains" ("Прощайте, скалистые горы").  Composer Anatoly Novikov praised him as a real tribune and a real fighter who didn't care about the conditions under which he had to sing, who performed in factories, at field camps and on ships and gave about 1,500 concerts on the front line during the Great Patriotic War.
Pyotr Kirichek
Pyotr Velikiy (Russian: "Пётр Великий") is the fourth "Kirov"-class battlecruiser of the Russian Navy.  Initially named Yuri Andropov (Russian: "Юрий Андропов") for Yuri Andropov, the former General Secretary of the Communist Party, the ship's name was changed after the fall of the Soviet Union.  The Russian designation for the type is "heavy missile cruiser", but Western defense commentators re-invented the term "battlecruiser" to describe these as they are the largest surface combatant warships in the world.  "Pyotr Velikiy" is the flagship of the Northern Fleet.
Russian battlecruiser Pyotr Velikiy
Pyotr Sergeyevich Novikov (Russian: Пётр Серге́евич Но́виков ; 15 August 1901, Moscow, Russian Empire – 9 January 1975, Moscow, Soviet Union) was a Soviet mathematician.
Pyotr Novikov
In mathematics, Manin matrices, named after Yuri Manin who introduced them around 1987–88, are a class of matrices with elements in a not-necessarily commutative ring, which in a certain sense behave like matrices whose elements commute.  In particular there is natural definition of the determinant for them and most linear algebra theorems like Cramer's rule, Cayley–Hamilton theorem, etc. hold true for them.  Any matrix with commuting elements is a Manin matrix.  These matrices have applications in representation theory in particular to Capelli's identity, Yangian and quantum integrable systems.
Manin matrix
Pyotr Georgyevich Novikov (Russian: Пётр Георгиевич Новиков ; 18 December 1907 – August 1944) was a Red Army major general.  Novikov fought in the Spanish Civil War as a battalion commander.  After returning to the Soviet Union he fought in the Winter War.  After the end of the Winter War Novikov became commander of the 2nd Cavalry Division.  He led the division in battles on the Southern Front.  The division became the 109th Rifle Division and fought in the Siege of Sevastopol.  After the evacuation of Filipp Oktyabrsky and Ivan Yefimovich Petrov, Novikov became commander of the Sevastopol defense.  Novikov attempted to evacuate the city on a patrol boat and was intercepted and captured by German forces.  He was sent to concentration camps in Germany and died at Flossenbürg concentration camp in August 1944.
Pyotr Georgyevich Novikov
Quantum computing studies computation systems (quantum computers) that make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data.  Quantum computers are different from binary digital electronic computers based on transistors. Whereas common digital computing requires that the data be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits, which can be in superpositions of states.  A quantum Turing machine is a theoretical model of such a computer, and is also known as the universal quantum computer.  The field of quantum computing was initiated by the work of Paul Benioff and Yuri Manin in 1980, Richard Feynman in 1982, and David Deutsch in 1985.  A quantum computer with spins as quantum bits was also formulated for use as a quantum spacetime in 1968.
Quantum computing
In mathematics, in the field of arithmetic algebraic geometry, the Manin obstruction (named after Yuri Manin) is attached to a variety "X" over a global field, which measures the failure of the Hasse principle for "X".  If the value of the obstruction is non-trivial, then "X" may have points over all local fields but not over the global field.
Manin obstruction
Pyotr Novikov and Yuri Manin, both worked as which occupation, for the Soviets?
Pyotr Novikov and Yuri Manin, both worked as which occupation, for the Soviets?