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Mark Naimark
Mark Aronovich Naimark (russian: Марк Ароно́вич Наймарк) (5 December 1909 – 30 December 1978) was a Soviet mathematician who made important contributions to functional analysis and mathematical physics. Life Naimark was born on 5 December 1909 in Odessa, part of modern-day Ukraine, but which was then part of the Russian Empire. His family was Jewish, his father Aron Iakovlevich Naimark a professional artist, and his mother Zefir Moiseevna. He was four years old at the onset of World War I in 1914, and seven when the tumultuous Russian Revolution began in 1917. Showing an early talent for mathematics, Naimark enrolled in a technical college at the age of fifteen in 1924 soon after the Russian Civil War had ended. There he studied while working at a foundry until enrolling in the Physics and Mathematics faculty at Odessa Institute of National Education in 1929. He married his wife Larisa Petrovna Shcherbakova in 1932, with whom he had two sons. In 1933, Naim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Odessa University
Odesa I. I. Mechnykov National University ( uk, Одеський національний університет Iмені І. І. Мечникова, translit=Odeskyi natsionalnyi universytet imeni I. I. Mechnykova), located in Odesa, Ukraine, is one of the country's major universities, named after the scientist Élie Metchnikoff (who studied immunology, microbiology, and evolutionary embryology), a Nobel prizewinner in 1908. The university was founded in 1865 by an edict of Tsar Alexander II of Russia, which reorganized the Richelieu Lyceum of Odesa into the new Imperial Novorossiya University. In the Soviet era, the university was renamed Odesa I. I. Mechnykov State University (literally, "Odesa State University named after I. I. Mechnykov"). Odesa I. I. Mechnykov National University comprises four institutes, ten faculties, and seven specialized councils. The university is famous for its scientific library, the largest and oldest of any university in Ukraine (3,600,000 milli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World War I
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fighting occurring throughout Europe, the Middle East, Africa, the Pacific, and parts of Asia. An estimated 9 million soldiers were killed in combat, plus another 23 million wounded, while 5 million civilians died as a result of military action, hunger, and disease. Millions more died in genocides within the Ottoman Empire and in the 1918 influenza pandemic, which was exacerbated by the movement of combatants during the war. Prior to 1914, the European great powers were divided between the Triple Entente (comprising France, Russia, and Britain) and the Triple Alliance (containing Germany, Austria-Hungary, and Italy). Tensions in the Balkans came to a head on 28 June 1914, following the assassination of Archduke Franz Ferdin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C*-algebra
In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra ''A'' of continuous linear operators on a complex Hilbert space with two additional properties: * ''A'' is a topologically closed set in the norm topology of operators. * ''A'' is closed under the operation of taking adjoints of operators. Another important class of non-Hilbert C*-algebras includes the algebra C_0(X) of complex-valued continuous functions on ''X'' that vanish at infinity, where ''X'' is a locally compact Hausdorff space. C*-algebras were first considered primarily for their use in quantum mechanics to model algebras of physical observables. This line of research began with Werner Heisenberg's matrix mechanics and in a more mathematically developed form with Pascual Jordan around 1933. Subsequently, John von Neumann attempted to establi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Group
In mathematics, the classical groups are defined as the special linear groups over the reals , the complex numbers and the quaternions together with special automorphism groups of symmetric or skew-symmetric bilinear forms and Hermitian or skew-Hermitian sesquilinear forms defined on real, complex and quaternionic finite-dimensional vector spaces. Of these, the complex classical Lie groups are four infinite families of Lie groups that together with the exceptional groups exhaust the classification of simple Lie groups. The compact classical groups are compact real forms of the complex classical groups. The finite analogues of the classical groups are the classical groups of Lie type. The term "classical group" was coined by Hermann Weyl, it being the title of his 1939 monograph ''The Classical Groups''. The classical groups form the deepest and most useful part of the subject of linear Lie groups. Most types of classical groups find application in classical and modern physics. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decomposition Of Spectrum (functional Analysis)
The spectrum of a linear operator T that operates on a Banach space X (a fundamental concept of functional analysis) consists of all scalars \lambda such that the operator T-\lambda does not have a bounded inverse on X. The spectrum has a standard decomposition into three parts: * a point spectrum, consisting of the eigenvalues of T; * a continuous spectrum, consisting of the scalars that are not eigenvalues but make the range of T-\lambda a proper dense subset of the space; * a residual spectrum, consisting of all other scalars in the spectrum. This decomposition is relevant to the study of differential equations, and has applications to many branches of science and engineering. A well-known example from quantum mechanics is the explanation for the discrete spectral lines and the continuous band in the light emitted by excited atoms of hydrogen. Decomposition into point spectrum, continuous spectrum, and residual spectrum For bounded Banach space operators Let ''X'' be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectral Theory Of Ordinary Differential Equations
In mathematics, the spectral theory of ordinary differential equations is the part of spectral theory concerned with the determination of the spectrum and eigenfunction expansion associated with a linear ordinary differential equation. In his dissertation Hermann Weyl generalized the classical Sturm–Liouville theory on a finite closed interval to second order differential operators with singularities at the endpoints of the interval, possibly semi-infinite or infinite. Unlike the classical case, the spectrum may no longer consist of just a countable set of eigenvalues, but may also contain a continuous part. In this case the eigenfunction expansion involves an integral over the continuous part with respect to a spectral measure, given by the Titchmarsh–Kodaira formula. The theory was put in its final simplified form for singular differential equations of even degree by Kodaira and others, using von Neumann's spectral theorem. It has had important applications in quantum m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing military alliances: the Allies and the Axis powers. World War II was a total war that directly involved more than 100 million personnel from more than 30 countries. The major participants in the war threw their entire economic, industrial, and scientific capabilities behind the war effort, blurring the distinction between civilian and military resources. Aircraft played a major role in the conflict, enabling the strategic bombing of population centres and deploying the only two nuclear weapons ever used in war. World War II was by far the deadliest conflict in human history; it resulted in 70 to 85 million fatalities, mostly among civilians. Tens of millions died due to genocides (including the Holocaust), starvation, ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GNS Theorem
GNS may refer to: Places * Binaka Airport, in Gunung Sitoli, Nias Island, Indonesia * Gainesville station (Georgia), an Amtrak station in Georgia, United States Companies and organizations * Gesellschaft für Nuklear-Service, a German nuclear-waste services company * Ghana Nuclear Society, nuclear energy advocacy organization * Glenlyon Norfolk School in Victoria, British Columbia, Canada * GNS Healthcare, an American data analytics company * GNS Science, a New Zealand earth-science research institute * Gordon-North Sydney Hockey Club, based in Sydney, Australia * Government of National Salvation, in Serbia during the Second World War * Gunns, a defunct Australian timber company Other uses * Gelfand–Naimark–Segal construction, a theorem in functional analysis * General News Service, a BBC-internal news-distribution service * GEOnet Names Server, a database of place names and locations * Global Namespace, computer networking concept * GNS theory, in role-playing game d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow
Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million residents within the city limits, over 17 million residents in the urban area, and over 21.5 million residents in the metropolitan area. The city covers an area of , while the urban area covers , and the metropolitan area covers over . Moscow is among the world's largest cities; being the most populous city entirely in Europe, the largest urban and metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow grew to become a prosperous and powerful city that served as the capital of the Grand Duchy that bears its name. When the Grand Duchy of Moscow evolved into the Tsardom of Russia, Moscow remained the political and economic center for most of the Tsardom's history. When th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kuntsevo Cemetery
The Kuntsevo Cemetery (russian: Ку́нцевское кла́дбище, kúntsevkoye kládbishche) is a cemetery servicing Kuntsevo, Moscow. It is located on the bank of the Setun River, to the south of the Mozhaisk Highway (the continuation of the Kutuzovsky Prospekt). The local five-domed church was commissioned in 1673 by Artamon Matveyev. The cemetery is administered as part of the Novodevichy Cemetery complex. Interred * Vsevolod Bobrov, * Andrei Chabanenko, Soviet naval officer * Lona Cohen, wife of Morris Cohen, spy * Morris Cohen, spy * Leonid GaidaiList of interred at '''' * Fedor Gusev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tashkent
Tashkent (, uz, Toshkent, Тошкент/, ) (from russian: Ташкент), or Toshkent (; ), also historically known as Chach is the capital and largest city of Uzbekistan. It is the most populous city in Central Asia, with a population of 2,909,500 (2022). It is in northeastern Uzbekistan, near the border with Kazakhstan. Tashkent comes from the Turkic ''tash'' and ''kent'', literally translated as "Stone City" or "City of Stones". Before Islamic influence started in the mid-8th century AD, Tashkent was influenced by the Sogdian and Turkic cultures. After Genghis Khan destroyed it in 1219, it was rebuilt and profited from the Silk Road. From the 18th to the 19th century, the city became an independent city-state, before being re-conquered by the Khanate of Kokand. In 1865, Tashkent fell to the Russian Empire; it became the capital of Russian Turkestan. In Soviet times, it witnessed major growth and demographic changes due to forced deportations from throughout the Sov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
