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Mikhail Samuilovich Livsic
Mikhail Samuilovich Livsic (4 July 1917 – 30 March 2007) was a Ukrainian-born Israeli mathematician who specialized in functional analysis. Biography Born in Pokotilova, Uman district on 4 July 1917, Livsic moved to Odessa with his family when he was four years old. His father was an associate professor of mathematics who frequented leading Soviet mathematicians in Odessa like Nikolai Chebotaryov, Veniamin Fedorovich Kagan, Mark Krein and Samuil O. Shatunovsky. In 1931 Livsic graduated from school was a close friend of the mathematician Israel Markowitsch Glasman (1916–1968) at the school. Both were very interested in philosophy and therefore decided to study natural science and mathematics. After graduation, Livsic attended first a school for radio engineers and from 1933 the newly created Departmenr of Physics and Mathematics of the Odessa State University, with Mark Krein, Mark Naimark and Boris Yakovlevich Lewin as teachers. Kerin was one of the major figures of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Definition, norm, Topological space#Definition, topology, etc.) and the linear transformation, linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of function space, spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous function, continuous, unitary operator, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential equations, differential and integral equations. The usage of the word ''functional (mathematics), functional'' as a noun goes back to the calculus of variati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Odessa State 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 million ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Naftali Kravitsky
According to the Book of Genesis, Naphtali (; ) was the last of the two sons of Jacob and Bilhah (Jacob's sixth son). He was the founder of the Israelite Tribe of Naphtali. Some biblical commentators have suggested that the name ''Naphtali'' may refer to the struggle between Rachel and Leah for the favours of Jacob. Bilhah was the handmaid of Rachel, who was infertile at the time, and had persuaded Jacob to have a child with Bilhah as a proxy for having one with herself. Biblical references According to the Targum Pseudo-Jonathan, Naphtali was a swift runner, though this appears to have been inferred from the Blessing of Jacob, which equates Naphtali to a hind. However, Biblical scholars believe this to actually be a description of the tribe of Naphtali. Naphtali is listed in Deuteronomy 34.2 when God takes Moses up to the mountain of Nebo and shows him the extent of the land which he had promised to Abraham, Isaac and Jacob. See article on Tribe of Simeon for a map o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ben-Gurion University Of The Negev
Ben-Gurion University of the Negev (BGU) ( he, אוניברסיטת בן-גוריון בנגב, ''Universitat Ben-Guriyon baNegev'') is a public research university in Beersheba, Israel. Ben-Gurion University of the Negev has five campuses: the Marcus Family Campus, Beer Sheva; the David Bergmann Campus, Beer Sheva; the David Tuviyahu Campus, Beer Sheva; the Sede Boqer Campus, and Eilat Campus. Ben-Gurion University has about 20,000 students. Some of its research institutes include the National Institute for Biotechnology in the Negev, the Ilse Katz Institute for Nanoscale Science and Technology, the Jacob Blaustein Institutes for Desert Research with the Albert Katz International School for Desert Studies, and the Ben-Gurion Research Institute for the Study of Israel and Zionism. History Ben-Gurion University was established in 1969 as the University of the Negev with the aim of promoting the development of the Negev desert that comprises more than sixty percent of Israel. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beersheba
Beersheba or Beer Sheva, officially Be'er-Sheva ( he, בְּאֵר שֶׁבַע, ''Bəʾēr Ševaʿ'', ; ar, بئر السبع, Biʾr as-Sabʿ, Well of the Oath or Well of the Seven), is the largest city in the Negev desert of southern Israel. Often referred to as the "Capital of the Negev", it is the centre of the fourth-most populous metropolitan area in Israel, the eighth-most populous Israeli city with a population of , and the second-largest city in area (after Jerusalem), with a total area of 117,500 dunams. The Biblical site of Beersheba is Tel Be'er Sheva, lying some 4 km distant from the modern city, which was established at the start of the 20th century by the Ottoman Turks. The city was captured by the British-led Australian Light Horse in the Battle of Beersheba during World War I. The population of the town was completely changed in 1948–49. ''Bir Seb'a'' ( ar, بئر السبع), as it was then known, had been almost entirely Muslim and Christian, and wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cayley–Hamilton Theorem
In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix over a commutative ring (such as the real or complex numbers or the integers) satisfies its own characteristic equation. If is a given matrix and is the identity matrix, then the characteristic polynomial of is defined as p_A(\lambda)=\det(\lambda I_n-A), where is the determinant operation and is a variable for a scalar element of the base ring. Since the entries of the matrix (\lambda I_n-A) are (linear or constant) polynomials in , the determinant is also a degree- monic polynomial in , p_A(\lambda) = \lambda^n + c_\lambda^ + \cdots + c_1\lambda + c_0~. One can create an analogous polynomial p_A(A) in the matrix instead of the scalar variable , defined as p_A(A) = A^n + c_A^ + \cdots + c_1A + c_0I_n~. The Cayley–Hamilton theorem states that this polynomial expression is equal to the zero matrix, which is to say tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National University Of Kharkiv
The Kharkiv University or Karazin University ( uk, Каразінський університет), or officially V. N. Karazin Kharkiv National University ( uk, Харківський національний університет імені В. Н. Каразіна), is one of the major universities in Ukraine, and earlier in the Russian Empire and Soviet Union. It was founded in 1804 through the efforts of Vasily Karazin becoming the second oldest university in modern-day Ukraine. History Russian Empire On , the Decree on the Opening of the Imperial University in Kharkiv came into force. The university became the second university in the south of the Russian Empire. It was founded on the initiative of the local community with Vasily Karazin at the fore, whose idea was supported by the nobility and the local authorities. Count Seweryn Potocki was appointed the first supervisor of the university, the first rector being the philologist and philosopher Ivan Rizhsky. In 1811 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kharkiv
Kharkiv ( uk, wikt:Харків, Ха́рків, ), also known as Kharkov (russian: Харькoв, ), is the second-largest List of cities in Ukraine, city and List of hromadas of Ukraine, municipality in Ukraine.Kharkiv "never had eastern-western conflicts" ''Euronews'' (23 October 2014) Located in the northeast of the country, it is the largest city of the historic Sloboda Ukraine, Slobozhanshchyna region. Kharkiv is the administrative centre of Kharkiv Oblast and of the surrounding Kharkiv Raion. The latest population is Kharkiv was founded in 1654 as Kharkiv fortress, and after these humble beginnings, it grew to be a major centre of industry, trade and Ukrainian culture in the Russian Empire. At the beginning of the 20th century, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steklov Institute Of Mathematics
Steklov Institute of Mathematics or Steklov Mathematical Institute (russian: Математический институт имени В.А.Стеклова) is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Steklov, who in 1919 founded the Institute of Physics and Mathematics in Leningrad. In 1934, this institute was split into separate parts for physics and mathematics, and the mathematical part became the Steklov Institute. At the same time, it was moved to Moscow. The first director of the Steklov Institute was Ivan Matveyevich Vinogradov. From 19611964, the institute's director was the notable mathematician Sergei Chernikov. The old building of the Institute in Leningrad became its Department in Leningrad. Today, that department has become a separate institute, called the ''St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Israel Gelfand
Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand ( yi, ישראל געלפֿאַנד, russian: Изра́иль Моисе́евич Гельфа́нд, uk, Ізраїль Мойсейович Гельфанд; – 5 October 2009) was a prominent Soviet-American mathematician. He made significant contributions to many branches of mathematics, including group theory, representation theory and functional analysis. The recipient of many awards, including the Order of Lenin and the first Wolf Prize, he was a Foreign Fellow of the Royal Society and professor at Moscow State University and, after immigrating to the United States shortly before his 76th birthday, at Rutgers University. Gelfand is also a 1994 MacArthur Fellow. His legacy continues through his students, who include Endre Szemerédi, Alexandre Kirillov, Edward Frenkel, Joseph Bernstein, David Kazhdan, as well as his own son, Sergei Gelfand. Early years A native of Kherson Go ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stefan Banach
Stefan Banach ( ; 30 March 1892 – 31 August 1945) was a Polish mathematician who is generally considered one of the 20th century's most important and influential mathematicians. He was the founder of modern functional analysis, and an original member of the Lwów School of Mathematics. His major work was the 1932 book, ''Théorie des opérations linéaires'' (Theory of Linear Operations), the first monograph on the general theory of functional analysis. Born in Kraków to a family of Goral descent, Banach showed a keen interest in mathematics and engaged in solving mathematical problems during school recess. After completing his secondary education, he befriended Hugo Steinhaus, with whom he established the Polish Mathematical Society in 1919 and later published the scientific journal '' Studia Mathematica''. In 1920, he received an assistantship at the Lwów Polytechnic, subsequently becoming a professor in 1922 and a member of the Polish Academy of Learning in 1924. Banach ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensions Of Symmetric Operators
In functional analysis, one is interested in extensions of symmetric operators acting on a Hilbert space. Of particular importance is the existence, and sometimes explicit constructions, of self-adjoint extensions. This problem arises, for example, when one needs to specify domains of self-adjointness for formal expressions of observables in quantum mechanics. Other applications of solutions to this problem can be seen in various moment problems. This article discusses a few related problems of this type. The unifying theme is that each problem has an operator-theoretic characterization which gives a corresponding parametrization of solutions. More specifically, finding self-adjoint extensions, with various requirements, of symmetric operators is equivalent to finding unitary extensions of suitable partial isometry, partial isometries. Symmetric operators Let ''H'' be a Hilbert space. A linear operator ''A'' acting on ''H'' with dense domain Dom(''A'') is symmetric if :\langle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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