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Hawkins–Simon Condition
The Hawkins–Simon condition refers to a result in mathematical economics, attributed to David Hawkins and Herbert A. Simon, that guarantees the existence of a non-negative output vector that solves the equilibrium relation in the input–output model where demand equals supply. More precisely, it states a condition for mathbf - \mathbf/math> under which the input–output system : mathbf - \mathbf\cdot \mathbf = \mathbf has a solution \mathbf \geq 0 for any \mathbf \geq 0. Here \mathbf is the identity matrix and \mathbf is called the ''input–output matrix'' or ''Leontief matrix'' after Wassily Leontief, who empirically estimated it in the 1940s. Together, they describe a system in which :\sum_^ a_ x_ + d_ = x_ \quad i = 1, 2, \ldots, n where a_ is the amount of the ''i''th good used to produce one unit of the ''j''th good, x_ is the amount of the ''j''th good produced, and d_ is the amount of final demand for good ''i''. Rearranged and written in vector notation, this gives ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Economics
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity. Mathematics allows economists to form meaningful, testable propositions about wide-ranging and complex subjects which could less easily be expressed informally. Further, the language of mathematics allows economists to make specific, positive claims about controversial or contentious subjects that would be impossible without mathematics. Much of economic theory is currently presented in terms of mathematical economic models, a set of stylized and simplified mathematical relationships asserted to clarify ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michio Morishima
was a Japanese heterodox economist and public intellectual who was the Sir John Hicks Professor of Economics at the London School of Economics from 1970–88. He was also professor at Osaka University and member of the British Academy. In 1976 he won the Order of Culture (文化勲章, Bunka-kunshō). Career Originally desiring a career as a historical novelist, at the university Morishima pursued social science, studying both economics and sociology under Yasuma Takada. At Kyoto University, Morishima was rigorously trained in both mainstream neoclassical economic theory and Marxian economics. Mathematically gifted, in 1946, he graduated from Kyoto University and taught there in addition to Osaka University. He starteInstitute of Social and Economic Research(ISER) of Osaka University with Yasuma Takada. In 1960 he established with Nobel-laureate Lawrence R. Klein from the Economics Department of the University of Pennsylvania the International Economic Review (today publishe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diagonally Dominant Matrix
In mathematics, a square matrix is said to be diagonally dominant if, for every row of the matrix, the magnitude of the diagonal entry in a row is larger than or equal to the sum of the magnitudes of all the other (non-diagonal) entries in that row. More precisely, the matrix ''A'' is diagonally dominant if :, a_, \geq \sum_ , a_, \quad\text i \, where ''a''''ij'' denotes the entry in the ''i''th row and ''j''th column. Note that this definition uses a weak inequality, and is therefore sometimes called ''weak diagonal dominance''. If a strict inequality (>) is used, this is called ''strict diagonal dominance''. The unqualified term ''diagonal dominance'' can mean both strict and weak diagonal dominance, depending on the context. Variations The definition in the first paragraph sums entries across each row. It is therefore sometimes called ''row diagonal dominance''. If one changes the definition to sum down each column, this is called ''column diagonal dominance''. Any stric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Felix Gantmacher
Felix Ruvimovich Gantmacher (russian: Феликс Рувимович Гантмахер) (23 February 1908 – 16 May 1964) was a Soviet mathematician, professor at Moscow Institute of Physics and Technology, well known for his contributions in mechanics, linear algebra and Lie group theory. In 1925–1926 he participated in seminar guided by Nikolai Chebotaryov in Odessa and wrote his first research paper in 1926. His book ''Theory of Matrices'' (1953) is a standard reference of linear algebra. It has been translated into various languages including a two-volume version in English prepared by Joel Lee Brenner, Donald W. Bushaw, and S. Evanusa. George Herbert Weiss noted that "this book cannot be recommended too highly as it contains material otherwise unavailable in book form". Gantmacher collaborated with Mark Krein on ''Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems''. In 1939 he contributed to the classification problem of the real Lie algebras ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matematicheskii Sbornik
''Matematicheskii Sbornik'' (russian: Математический сборник, abbreviated ''Mat. Sb.'') is a peer reviewed Russian mathematical journal founded by the Moscow Mathematical Society in 1866. It is the oldest successful Russian mathematical journal. The English translation is ''Sbornik: Mathematics''. It is also sometimes cited under the alternative name ''Izdavaemyi Moskovskim Matematicheskim Obshchestvom'' or its French translation ''Recueil mathématique de la Société mathématique de Moscou'', but the name ''Recueil mathématique'' is also used for an unrelated journal, '' Mathesis''. Yet another name, ''Sovetskii Matematiceskii Sbornik'', was listed in a statement in the journal in 1931 apologizing for the former editorship of Dmitri Egorov, who had been recently discredited for his religious views; however, this name was never actually used by the journal. The first editor of the journal was Nikolai Brashman, who died before its first issue (dedicated to hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Kotelyanskiĭ
David (; , "beloved one") (traditional spelling), , ''Dāwūd''; grc-koi, Δαυΐδ, Dauíd; la, Davidus, David; gez , ዳዊት, ''Dawit''; xcl, Դաւիթ, ''Dawitʿ''; cu, Давíдъ, ''Davidŭ''; possibly meaning "beloved one". was, according to the Hebrew Bible, the third king of the United Kingdom of Israel. In the Books of Samuel, he is described as a young shepherd and harpist who gains fame by slaying Goliath, a champion of the Philistines, in southern Canaan. David becomes a favourite of Saul, the first king of Israel; he also forges a notably close friendship with Jonathan, a son of Saul. However, under the paranoia that David is seeking to usurp the throne, Saul attempts to kill David, forcing the latter to go into hiding and effectively operate as a fugitive for several years. After Saul and Jonathan are both killed in battle against the Philistines, a 30-year-old David is anointed king over all of Israel and Judah. Following his rise to power, Davi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiple Discovery
Multiple may refer to: Economics *Multiple finance, a method used to analyze stock prices *Multiples of the P/E, price-to-earnings ratio *Chain stores, are also referred to as 'Multiples' *Box office multiple, the ratio of a film's total gross to that of its opening weekend Sociology *Multiples (sociology), a theory in sociology of science by Robert K. Merton, see Science *Multiple (mathematics), multiples of numbers *List of multiple discoveries, instances of scientists, working independently of each other, reaching similar findings *Multiple birth, because having twins is sometimes called having "multiples" *Multiple sclerosis, an inflammatory disease *Parlance for people with multiple identities, sometimes called "multiples"; often theorized as having dissociative identity disorder Printing *Printmaking, where ''multiple'' is often used as a term for a print, especially in the US *Artist's multiple, series of identical prints, collages or objects by an artist, subverting the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hukukane Nikaido
was a Japanese economist. Career He received a B.S. in mathematics from the University of Tokyo and a D.Sc. in mathematics from the University of Tokyo in 1961. honors * 1962, Fellow, Econometric Society The Econometric Society is an international society of academic economists interested in applying statistical tools to their field. It is an independent organization with no connections to societies of professional mathematicians or statisticians. .... * 2000, Order of the Rising Sun, 3rd class. Published works Books * * * * Journal articles * * * * * * * * * References External links {{DEFAULTSORT:Nikaido, Hukukane 1923 births 2001 deaths 20th-century Japanese economists General equilibrium theorists University of Tokyo alumni Academic staff of Tokyo University of Science Academic staff of Hitotsubashi University University of Minnesota faculty University of California, Berkeley faculty University of Southern California faculty Academic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minor (linear Algebra)
In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix, cut down from A by removing one or more of its rows and columns. Minors obtained by removing just one row and one column from square matrices (first minors) are required for calculating matrix cofactors, which in turn are useful for computing both the determinant and inverse of square matrices. Definition and illustration First minors If A is a square matrix, then the ''minor'' of the entry in the ''i''th row and ''j''th column (also called the (''i'', ''j'') ''minor'', or a ''first minor'') is the determinant of the submatrix formed by deleting the ''i''th row and ''j''th column. This number is often denoted ''M''''i,j''. The (''i'', ''j'') ''cofactor'' is obtained by multiplying the minor by (-1)^. To illustrate these definitions, consider the following 3 by 3 matrix, :\begin 1 & 4 & 7 \\ 3 & 0 & 5 \\ -1 & 9 & 11 \\ \end To compute the minor ''M''2,3 and the cofactor ''C''2,3, we fin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Hawkins (philosopher)
David Hawkins (February 28, 1913 – February 24, 2002) was a professor whose interests included the philosophy of science, mathematics, economics, childhood science education, and ethics. He was also an administrative assistant at the Manhattan Project's Los Alamos Laboratory and later one of its official historians. Together with Herbert A. Simon, he discovered and proved the Hawkins–Simon theorem. Early life David Hawkins was born in El Paso, Texas, the youngest of seven children of William Ashton Hawkins, and his wife Clara ' Gardiner. His father was a prominent lawyer noted for his work on water law, who worked for the El Paso and Northeastern Railway, and was one of the founders of the city of Alamogordo, New Mexico. He grew up in La Luz, New Mexico. Hawkins attended Hotchkiss School in Lakeville, Connecticut, but left after his junior year to enter Stanford University. He initially studied chemistry, but then switched to physics before finally majoring in philosophy. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wassily Leontief
Wassily Wassilyevich Leontief (russian: Васи́лий Васи́льевич Лео́нтьев; August 5, 1905 – February 5, 1999), was a Soviet-American economist known for his research on input–output analysis and how changes in one economic sector may affect other sectors. Leontief won the Nobel Memorial Prize in Economic Sciences in 1973, and four of his doctoral students have also been awarded the prize (Paul Samuelson 1970, Robert Solow 1987, Vernon L. Smith 2002, Thomas Schelling 2005). Biography Early life Wassily Leontief was born on August 5, 1905, in Munich, Germany, the son of Wassily W. Leontief (professor of Economics) and Zlata (German spelling ''Slata''; later Evgenia) Leontief (née Becker). Wassily Leontief Sr. belonged to a family of Russian old-believer merchants living in St. Petersburg since 1741. Evgenia (Genya) Becker belonged to a wealthy Jewish family from Odessa. At 15 in 1921, Wassily Jr. entered University of Leningrad in present-day St. P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identity Matrix
In linear algebra, the identity matrix of size n is the n\times n square matrix with ones on the main diagonal and zeros elsewhere. Terminology and notation The identity matrix is often denoted by I_n, or simply by I if the size is immaterial or can be trivially determined by the context. I_1 = \begin 1 \end ,\ I_2 = \begin 1 & 0 \\ 0 & 1 \end ,\ I_3 = \begin 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end ,\ \dots ,\ I_n = \begin 1 & 0 & 0 & \cdots & 0 \\ 0 & 1 & 0 & \cdots & 0 \\ 0 & 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & 1 \end. The term unit matrix has also been widely used, but the term ''identity matrix'' is now standard. The term ''unit matrix'' is ambiguous, because it is also used for a matrix of ones and for any unit of the ring of all n\times n matrices. In some fields, such as group theory or quantum mechanics, the identity matrix is sometimes denoted by a boldface one, \mathbf, or called "id" (short for identity). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
