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Fichera's Existence Principle
In mathematics, and particularly in functional analysis, Fichera's existence principle is an existence and uniqueness theorem for solution of functional equations, proved by Gaetano Fichera in 1954. More precisely, given a general vector space and two linear maps from it onto two Banach spaces, the principle states necessary and sufficient conditions for a linear transformation between the two dual Banach spaces to be invertible for every vector in .See , , , . See also * * * * * Notes References *. A survey of Gaetano Fichera's contributions to the theory of partial differential equations, written by two of his pupils. *. *. *: for a review of the book, see . *. The paper ''Some recent developments of the theory of boundary value problems for linear partial differential equations'' describes Fichera's approach to a general theory of boundary value problems for linear partial differential equations through a theorem similar in spirit to the Lax–Milgram theorem. *. A mo ... [...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] |
Lax–Milgram Theorem
Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. In a weak formulation, equations or conditions are no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". In a strong formulation, the solution space is constructed such that these equations or conditions are already fulfilled. The Lax–Milgram theorem, named after Peter Lax and Arthur Milgram who proved it in 1954, provides weak formulations for certain systems on Hilbert spaces. General concept Let V be a Banach space, V' its dual space, A\colon V \to V', and f \in V'. Finding the solution u \in V of the equation Au = f is equivalent to finding u\in V such that, for all v \in V, uv) = f(v). Here, v is called a test vector or test function. To bring this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Operator
In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and returns another function (in the style of a higher-order function in computer science). This article considers mainly linear differential operators, which are the most common type. However, non-linear differential operators also exist, such as the Schwarzian derivative. Definition An order-m linear differential operator is a map A from a function space \mathcal_1 to another function space \mathcal_2 that can be written as: A = \sum_a_\alpha(x) D^\alpha\ , where \alpha = (\alpha_1,\alpha_2,\cdots,\alpha_n) is a multi-index of non-negative integers, , \alpha, = \alpha_1 + \alpha_2 + \cdots + \alpha_n, and for each \alpha, a_\alpha(x) is a function on some open domain in ''n''-dimensional space. The operator D^\alpha is interpreted as D^\alp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenvalue
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by \lambda, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated. Formal definition If is a linear transformation from a vector space over a field into itself and is a nonzero vector in , then is an eigenvector of if is a scalar multiple of . This can be written as T(\mathbf) = \lambda \mathbf, where is a scalar in , known as the eigenvalue, characteristic value, or characteristic root ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Accademia Nazionale Dei Lincei
The Accademia dei Lincei (; literally the "Academy of the Lynx-Eyed", but anglicised as the Lincean Academy) is one of the oldest and most prestigious European scientific institutions, located at the Palazzo Corsini on the Via della Lungara in Rome, Italy. Founded in the Papal States in 1603 by Federico Cesi, the academy was named after the lynx, an animal whose sharp vision symbolizes the observational prowess that science requires. Galileo Galilei was the intellectual centre of the academy and adopted "Galileo Galilei Linceo" as his signature. "The Lincei did not long survive the death in 1630 of Cesi, its founder and patron", and "disappeared in 1651". During the nineteenth century, it was revived, first in the Vatican and later in the nation of Italy. Thus the Pontifical Academy of Science, founded in 1847, claims this heritage as the ''Accademia Pontificia dei Nuovi Lincei ("Pontifical Academy of the New Lynxes")'', descending from the first two incarnations of the Academy. S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rome
, established_title = Founded , established_date = 753 BC , founder = King Romulus (legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption = The territory of the ''comune'' (''Roma Capitale'', in red) inside the Metropolitan City of Rome (''Città Metropolitana di Roma'', in yellow). The white spot in the centre is Vatican City. , pushpin_map = Italy#Europe , pushpin_map_caption = Location within Italy##Location within Europe , pushpin_relief = yes , coordinates = , coor_pinpoint = , subdivision_type = Country , subdivision_name = Italy , subdivision_type2 = Region , subdivision_name2 = Lazio , subdivision_type3 = Metropolitan city , subdivision_name3 = Rome Capital , government_footnotes= , government_type = Strong Mayor–Council , leader_title2 = Legislature , leader_name2 = Capitoline Assemb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ergebnisse Der Mathematik Und Ihrer Grenzgebiete
''Ergebnisse der Mathematik und ihrer Grenzgebiete''/''A Series of Modern Surveys in Mathematics'' is a series of scholarly monographs published by Springer Science+Business Media. The title literally means "Results in mathematics and related areas". Most of the books were published in German or English, but there were a few in French and Italian. There have been several sequences, or ''Folge'': the original series, neue Folge, and 3.Folge. Some of the most significant mathematical monographs of 20th century appeared in this series. Original series The series started in 1932 with publication of ''Knotentheorie'' by Kurt Reidemeister as "Band 1" (English: volume 1). There seems to have been double numeration in this sequence. Neue Folge This sequence started in 1950 with the publication of ''Transfinite Zahlen'' by Heinz Bachmann. The volumes are consecutively numbered, designated as either "Band" or "Heft". A total of 100 volumes was published, often in multiple editions, but pre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SIAM Review
Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific society devoted to applied mathematics, and roughly two-thirds of its membership resides within the United States. Founded in 1951, the organization began holding annual national meetings in 1954, and now hosts conferences, publishes books and scholarly journals, and engages in advocacy in issues of interest to its membership. Members include engineers, scientists, and mathematicians, both those employed in academia and those working in industry. The society supports educational institutions promoting applied mathematics. SIAM is one of the four member organizations of the Joint Policy Board for Mathematics. Membership Membership is open to both individuals and organizations. By the end of its first full year of operation, SIAM had 130 memb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Press
Academic Press (AP) is an academic book publisher founded in 1941. It was acquired by Harcourt, Brace & World in 1969. Reed Elsevier bought Harcourt in 2000, and Academic Press is now an imprint of Elsevier. Academic Press publishes reference books, serials and online products in the subject areas of: * Communications engineering * Economics * Environmental science * Finance * Food science and nutrition * Geophysics * Life sciences * Mathematics and statistics * Neuroscience * Physical sciences * Psychology Well-known products include the ''Methods in Enzymology'' series and encyclopedias such as ''The International Encyclopedia of Public Health'' and the ''Encyclopedia of Neuroscience''. See also * Akademische Verlagsgesellschaft (AVG) — the German predecessor, founded in 1906 by Leo Jolowicz (1868–1940), the father of Walter Jolowicz Walter may refer to: People * Walter (name), both a surname and a given name * Little Walter, American blues harmonica player Marion Wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
INdAM
The Istituto Nazionale di Alta Matematica Francesco Severi, abbreviated as INdAM, is a government created non-profit research institution whose main purpose is to promote research in the field of mathematics and its applications and the diffusion of higher mathematical education in Italy.See the Italian law and its later amendment . Its founder and first president, later nominated life president, was Francesco Severi, who exerted also a major influence on the creation of the institute. History The institute was established on 13 July 1939 as the ''Royal National Institute of High Mathematics'', with a law signed by Vittorio Emanuele III, Benito Mussolini, Paolo Thaon di Revel and Giuseppe Bottai. Its foundation is largely due to the action of Francesco Severi, possibly starting from an idea by Luigi Fantappié. The first Scientific Council was made up of Francesco Severi (president), Luigi Fantappiè, Giulio Krall, Enrico Bompiani and Mauro Picone. In 1946, following the It ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
