|
Robert Phelps
Robert Ralph Phelps (March 22, 1926 – January 4, 2013) was an American mathematician who was known for his contributions to analysis, particularly to functional analysis and measure theory. He was a professor of mathematics at the University of Washington from 1962 until his death. Biography Phelps wrote his dissertation on subreflexive Banach spaces under the supervision of Victor Klee in 1958 at the University of Washington. Phelps was appointed to a position at Washington in 1962. In 2012 he became a fellow of the American Mathematical Society. He was a convinced atheist. Research With Errett Bishop, Phelps proved the Bishop–Phelps theorem, one of the most important results in functional analysis, with applications to operator theory, to harmonic analysis, to Choquet theory, and to variational analysis. In one field of its application, optimization theory, Ivar Ekeland began his survey of variational principles with this tribute: ''The central result''. The gran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
California
California is a U.S. state, state in the Western United States, located along the West Coast of the United States, Pacific Coast. With nearly 39.2million residents across a total area of approximately , it is the List of states and territories of the United States by population, most populous U.S. state and the List of U.S. states and territories by area, 3rd largest by area. It is also the most populated Administrative division, subnational entity in North America and the 34th most populous in the world. The Greater Los Angeles area and the San Francisco Bay Area are the nation's second and fifth most populous Statistical area (United States), urban regions respectively, with the former having more than 18.7million residents and the latter having over 9.6million. Sacramento, California, Sacramento is the state's capital, while Los Angeles is the List of largest California cities by population, most populous city in the state and the List of United States cities by population, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator Theory
In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators or closed operators, and consideration may be given to nonlinear operators. The study, which depends heavily on the topology of function spaces, is a branch of functional analysis. If a collection of operators forms an algebra over a field, then it is an operator algebra. The description of operator algebras is part of operator theory. Single operator theory Single operator theory deals with the properties and classification of operators, considered one at a time. For example, the classification of normal operators in terms of their spectra falls into this category. Spectrum of operators The spectral theorem is any of a number of results about linear operators or about matrices. In broad terms the spectral theorem provides cond ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joram Lindenstrauss
Joram Lindenstrauss ( he, יורם לינדנשטראוס) (October 28, 1936 – April 29, 2012) was an Israeli mathematician working in functional analysis. He was a professor of mathematics at the Einstein Institute of Mathematics. Biography Joram Lindenstrauss was born in Tel Aviv. He was the only child of a pair of lawyers who immigrated to Israel from Berlin. He began to study mathematics at the Hebrew University of Jerusalem in 1954 while serving in the army. He became a full-time student in 1956 and received his master's degree in 1959. In 1962 Lindenstrauss earned his Ph.D. from the Hebrew University (dissertation: ''Extension of Compact Operators'', advisors: Aryeh Dvoretzky, Branko Grünbaum). He worked as a postdoc at Yale University and the University of Washington in Seattle from 1962 - 1965. He was appointed senior lecturer at the Hebrew University in 1965, associate professor on 1967 and full professor in 1969. He became the Leon H. and Ada G. Miller Memorial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University College, London
, mottoeng = Let all come who by merit deserve the most reward , established = , type = Public research university , endowment = £143 million (2020) , budget = £1.544 billion (2019/20) , chancellor = Anne, Princess Royal(as Chancellor of the University of London) , provost = Michael Spence , head_label = Chair of the council , head = Victor L. L. Chu , free_label = Visitor , free = Sir Geoffrey Vos , academic_staff = 9,100 (2020/21) , administrative_staff = 5,855 (2020/21) , students = () , undergrad = () , postgrad = () , coordinates = , campus = Urban , city = London, England , affiliations = , colours = Purple and blue celeste , nickname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shangri-La
Shangri-La is a fictional place in Asia's Kunlun Mountains (昆仑山), Uses the spelling 'Kuen-Lun'. described in the 1933 novel ''Lost Horizon'' by English author James Hilton. Hilton portrays Shangri-La as a mystical, harmonious valley, gently guided from a lamasery, enclosed in the western end of the Kunlun Mountains. Shangri-La has become synonymous with any earthly paradise, particularly a mythical Himalayan utopia – an enduringly happy land, isolated from the world. In the novel, the people who live at Shangri-La are almost immortal, living hundreds of years beyond the normal lifespan and only very slowly aging in appearance. Ancient Tibetan scriptures mention the existence of seven such places as ''Nghe-Beyul Khembalung''. Khembalung is one of several Utopia ''beyuls'' (hidden lands similar to Shangri-La) which Tibetan Buddhists believe that Padmasambhava established in the 9th century CE as idyllic, sacred places of refuge for Buddhists during times of str ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Locally Convex Topological Vector Space
In functional analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. They can be defined as topological vector spaces whose topology is generated by translations of balanced, absorbent, convex sets. Alternatively they can be defined as a vector space with a family of seminorms, and a topology can be defined in terms of that family. Although in general such spaces are not necessarily normable, the existence of a convex local base for the zero vector is strong enough for the Hahn–Banach theorem to hold, yielding a sufficiently rich theory of continuous linear functionals. Fréchet spaces are locally convex spaces that are completely metrizable (with a choice of complete metric). They are generalizations of Banach spaces, which are complete vector spaces with respect to a metric generated by a norm. History Metrizable topologies on vecto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Top Roping
Top rope climbing (or top roping) is a style in climbing in which the climber is securely attached to a rope which then passes up, through an anchor system at the top of the climb, and down to a belayer at the foot of the climb. The belayer takes in slack rope throughout the climb, so that if at any point the climber were to lose their hold, they would not fall more than a short distance. Description Top-roping is often done on routes that cannot be lead climbed for one reason or another. Most top-rope anchors can be reached through non-technical means, such as by hiking or scrambling to the top of the cliff. It is the most common style used at indoor climbing walls and is also used in situations where other methods would be unsafe or environmentally damaging. For example, in Kent and Sussex in south-east England, the sandstone rock is soft and prone to erosion, so placing protection into the rock would be both damaging and unreliable. There, top-roping from permanent anchors a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carabiner
A carabiner or karabiner () is a specialized type of shackle, a metal loop with a spring-loaded gate used to quickly and reversibly connect components, most notably in safety-critical systems. The word is a shortened form of ''Karabinerhaken'' (or also short ''Karabiner''), a German phrase for a "spring hook" used by a carbine rifleman, or carabinier, to attach his carabin to a belt or bandolier. Use Carabiners are widely used in rope-intensive activities such as climbing, fall arrest systems, arboriculture, caving, sailing, hot air ballooning, rope rescue, construction, industrial rope work, window cleaning, whitewater rescue, and acrobatics. They are predominantly made from both steel and aluminium. Those used in sports tend to be of a lighter weight than those used in commercial applications and rope rescue. Often referred to as carabiner-style or as mini-biners, carabiner keyrings and other light-use clips of similar style and design have also become popular. Most ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Piton
A piton (; also called ''pin'' or ''peg'') in climbing is a metal spike (usually steel) that is driven into a crack or seam in the climbing surface using a climbing hammer, and which acts as an anchor for protecting the climber against the consequences of falling or to assist progress in aid climbing. Pitons are equipped with an eye hole or a ring to which a carabiner is attached; the carabiner can then be directly or indirectly connected to a climbing rope. Pitons were the original form of protection and are still used where there is no alternative. Repeated hammering and extraction of pitons damage the rock, and climbers who subscribe to the clean climbing ethic avoid their use as much as possible. With the popularization of clean climbing in the 1970s, pitons were largely replaced by faster and easier-to-use clean protection, such as nuts and camming devices. Pitons are still found in place (as "fixed" pitons) on some established free climbing routes, as fixed bela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edgar Asplund
Edgar is a commonly used English given name, from an Anglo-Saxon name ''Eadgar'' (composed of '' ead'' "rich, prosperous" and ''gar'' "spear"). Like most Anglo-Saxon names, it fell out of use by the later medieval period; it was, however, revived in the 18th century, and was popularised by its use for a character in Sir Walter Scott's ''The Bride of Lammermoor'' (1819). People with the given name * Edgar the Peaceful (942–975), king of England * Edgar the Ætheling (c. 1051 – c. 1126), last member of the Anglo-Saxon royal house of England * Edgar of Scotland (1074–1107), king of Scotland * Edgar Angara, Filipino lawyer * Edgar Barrier, American actor * Edgar Baumann, Paraguayan javelin thrower * Edgar Bergen, American actor, radio performer, ventriloquist * Edgar Berlanga, American boxer * Edgar H. Brown, American mathematician * Edgar Buchanan, American actor * Edgar Rice Burroughs, American author, creator of ''Tarzan'' * Edgar Cantero, Spanish author in Catalan, Spa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variational Principle
In science and especially in mathematical studies, a variational principle is one that enables a problem to be solved using calculus of variations, which concerns finding functions that optimize the values of quantities that depend on those functions. For example, the problem of determining the shape of a hanging chain suspended at both ends—a catenary—can be solved using variational calculus, and in this case, the variational principle is the following: The solution is a function that minimizes the gravitational potential energy of the chain. Overview Any physical law which can be expressed as a variational principle describes a self-adjoint operator. These expressions are also called Hermitian. Such an expression describes an invariant under a Hermitian transformation. History Felix Klein's Erlangen program attempted to identify such invariants under a group of transformations. In what is referred to in physics as Noether's theorem, the Poincaré group of transformations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ivar Ekeland
Ivar I. Ekeland (born 2 July 1944, Paris) is a French mathematician of Norwegian descent. Ekeland has written influential monographs and textbooks on nonlinear functional analysis, the calculus of variations, and mathematical economics, as well as popular books on mathematics, which have been published in French, English, and other languages. Ekeland is known as the author of Ekeland's variational principle and for his use of the Shapley–Folkman lemma in optimization theory. He has contributed to the periodic solutions of Hamiltonian systems and particularly to the theory of Kreĭn indices for linear systems (Floquet theory).According to D. Pascali, writing for ''Mathematical Reviews'' () Ekeland helped to inspire the discussion of chaos theory in Michael Crichton's 1990 novel '' Jurassic Park''. Biography Ekeland studied at the École Normale Supérieure (1963–1967). He is a senior research fellow at the French National Centre for Scientific Research (C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
