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Roger Penrose
Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics in the University of Oxford, an emeritus fellow of Wadham College, Oxford, and an honorary fellow of St John's College, Cambridge and University College London. Penrose has contributed to the mathematical physics of general relativity and cosmology. He has received several prizes and awards, including the 1988 Wolf Prize in Physics, which he shared with Stephen Hawking for the Penrose–Hawking singularity theorems, and one half of the 2020 Nobel Prize in Physics "for the discovery that black hole formation is a robust prediction of the general theory of relativity". He is regarded as one of the greatest living physicists, mathematicians and scientists, and is particularly noted for the breadth and depth of his work in both natural and formal sciences. Early life and education Bor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birkbeck, University Of London
, mottoeng = Advice comes over nightTranslation used by Birkbeck. , established = , type = Public research university , endowment = £4.3 m (2014) , budget = £109 million (2015) , parent = University of London , staff = , president = Baroness Bakewell , chancellor = The Princess Royal (University of London) , vice_chancellor = Wendy Thomson (University of London) , head_label = Master , head = David S Latchman , students = () , undergrad = () , postgrad = () , location = London, England, United Kingdom , coordinates = , colours = , mascot = , nickname = , affiliations = ACU European University AssociationRoyal Academy of Dramatic ArtUniversiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Colchester
Colchester ( ) is a city in Essex, in the East of England. It had a population of 122,000 in 2011. The demonym is Colcestrian. Colchester occupies the site of Camulodunum, the first major city in Roman Britain and its first capital. Colchester therefore claims to be Britain's first city. It has been an important military base since the Roman era, with Colchester Garrison currently housing the 16th Air Assault Brigade. Situated on the River Colne, Colchester is northeast of London. The city is connected to London by the A12 road and the Great Eastern Main Line railway. Colchester is less than from London Stansted Airport and from the port of Harwich. Attractions in and around the city include Colchester United Football Club, Colchester Zoo, and several art galleries. Colchester Castle was constructed in the eleventh century on earlier Roman foundations; it now contains a museum. The main campus of the University of Essex is located just outside the city. Local governme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tristan Needham
Tristan Needham is a British mathematician and professor of mathematics at the University of San Francisco. Education, career and publications Tristan is the son of social anthropologist Rodney Needham of Oxford, England. He attended the Dragon School. Later Needham attended the University of Oxford and studied physics at Merton College, and then transferred to the Mathematical Institute where he studied under Roger Penrose. He obtained his D.Phil. in 1987 and in 1989 took up his post at University of San Francisco. In 1993 he published ''A Visual Explanation of Jensen's inequality''. The following year he published ''The Geometry of Harmonic Functions'', which won the Carl B. Allendoerfer Award for 1995. Needham wrote the book ''Visual Complex Analysis'', which has received positive reviews. Though it is described as a "radical first course in complex analysis aimed at undergraduates", writing in ''Mathematical Reviews'' D.H. Armitage said that "the book will be appreciated mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive differently where and when events occur. Until the 20th century, it was assumed that the three-dimensional geometry of the universe (its spatial expression in terms of coordinates, distances, and directions) was independent of one-dimensional time. The physicist Albert Einstein helped develop the idea of spacetime as part of his theory of relativity. Prior to his pioneering work, scientists had two separate theories to explain physical phenomena: Isaac Newton's laws of physics described the motion of massive objects, while James Clerk Maxwell's electromagnetic models explained the properties of light. However, in 1905, Einstein based a work on special relativity on two postulates: * The laws of physics are invariant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black Hole Bomb
A black hole bomb is the name given to a physical effect utilizing how a bosonic field impinging on a rotating black hole can be amplified through superradiant scattering. If the amplified field is reflected back towards the black hole, the amplification can be repeated, leading to a run-away growth of the field, i.e. an explosion. One way this reflection could be realized in nature is if the bosonic field has mass. The mass of the field can then cause the amplified modes to be trapped around the black hole, leading to an endless cycle of self-amplification. The mechanism by which the black hole bomb functions is called superradiant instability. It can also refer to one such method of creating such a runaway effect, a Penrose sphere with no means for energy to passively escape. History The idea that angular momentum and energy may be transferred from a rotating black hole to a particle being scattered by it was proposed by Roger Penrose in 1971. The first discussion of a runaway e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Index Notation
Abstract index notation (also referred to as slot-naming index notation) is a mathematical notation for tensors and spinors that uses indices to indicate their types, rather than their components in a particular basis. The indices are mere placeholders, not related to any basis and, in particular, are non-numerical. Thus it should not be confused with the Ricci calculus. The notation was introduced by Roger Penrose as a way to use the formal aspects of the Einstein summation convention to compensate for the difficulty in describing contractions and covariant differentiation in modern abstract tensor notation, while preserving the explicit covariance of the expressions involved. Let V be a vector space, and V^* its dual space. Consider, for example, an order-2 covariant tensor h \in V^*\otimes V^*. Then h can be identified with a bilinear form on V. In other words, it is a function of two arguments in V which can be represented as a pair of ''slots'': : h = h(-,-). Abstract in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin Network
In physics, a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics. From a mathematical perspective, the diagrams are a concise way to represent multilinear functions and functions between representations of matrix groups. The diagrammatic notation can thus greatly simplify calculations. Roger Penrose described spin networks in 1971. Spin networks have since been applied to the theory of quantum gravity by Carlo Rovelli, Lee Smolin, Jorge Pullin, Rodolfo Gambini and others. Spin networks can also be used to construct a particular functional on the space of connections which is invariant under local gauge transformations. Definition Penrose's definition A spin network, as described in Penrose (1971),R. Penrose (1971a), "Angular momentum: an approach to combinatorial spacetime," in T. Bastin (ed.), ''Quantum Theory and Beyond'', Cambridge University Press (this paper can be found onli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Twistor Theory
In theoretical physics, twistor theory was proposed by Roger Penrose in 1967 as a possible path to quantum gravity and has evolved into a branch of theoretical and mathematical physics. Penrose proposed that twistor space should be the basic arena for physics from which space-time itself should emerge. It leads to a powerful set of mathematical tools that have applications to differential and integral geometry, nonlinear differential equations and representation theory and in physics to general relativity and quantum field theory, in particular to scattering amplitudes. Development seems to be indirectly influenced by Einstein–Cartan–Sciama–Kibble theory. Overview Mathematically, projective twistor space \mathbb is a 3-dimensional complex manifold, complex projective 3-space \mathbb^3. It has the physical interpretation of the space of massless particles with spin. It is the projectivisation of a 4-dimensional complex vector space, non-projective twistor space \mathbb w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moore–Penrose Inverse
In mathematics, and in particular linear algebra, the Moore–Penrose inverse of a matrix is the most widely known generalization of the inverse matrix. It was independently described by E. H. Moore in 1920, Arne Bjerhammar in 1951, and Roger Penrose in 1955. Earlier, Erik Ivar Fredholm had introduced the concept of a pseudoinverse of integral operators in 1903. When referring to a matrix, the term pseudoinverse, without further specification, is often used to indicate the Moore–Penrose inverse. The term generalized inverse is sometimes used as a synonym for pseudoinverse. A common use of the pseudoinverse is to compute a "best fit" ( least squares) solution to a system of linear equations that lacks a solution (see below under § Applications). Another use is to find the minimum ( Euclidean) norm solution to a system of linear equations with multiple solutions. The pseudoinverse facilitates the statement and proof of results in linear algebra. The pseudoinverse is defined a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tim Poston
Timothy Poston (19 June 1945 – 22 August 2017) was an English mathematician and polymath best known for his work on catastrophe theory. His early childhood was in Moscow where his father served in the British Embassy for 18 months. When his father moved back to the UK to work for the BBC, Tim went to Datchworth primary school. Later his father ran The Near East Broadcasting Station Sharq al-Adna; his mother taught her children by PNEU until Tim went to The Junior School in Nicosia as a boarder. After the Suez débâcle, his father returned to the UK to train as a parson, and the family lived in Oxfordshire, Wiltshire and Dorset. Tim boarded at the Perse school to age 15 and then to Dauntsey's. From 1964 to 1967 he was an undergraduate at the University of Hull, obtaining a 1st Class BSc. (Special Honours) in Mathematics. In 1967-1969 he began graduate work at Hull, taking a sabbatical year as Student Union president. He then moved to the University of Warwick to take a PhD ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lane P
In road transport, a lane is part of a roadway that is designated to be used by a single line of vehicles to control and guide drivers and reduce traffic conflicts. Most public roads (highways) have at least two lanes, one for traffic in each direction, separated by lane markings. On multilane roadways and busier two-lane roads, lanes are designated with road surface markings. Major highways often have two multi-lane roadways separated by a median. Some roads and bridges that carry very low volumes of traffic are less than wide, and are only a single lane wide. Vehicles travelling in opposite directions must slow or stop to pass each other. In rural areas, these are often called country lanes. In urban areas, alleys are often only one lane wide. Urban and suburban one lane roads are often designated for one-way traffic. History For much of human history, roads did not need lane markings because most people walked or rode horses at relatively slow speeds. However, when auto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John McNamara (mathematical Biologist)
John M. McNamara is an English mathematical biologist and Emeritus Professor of Mathematics and Biology in the School of Mathematics at the University of Bristol. He was elected a fellow of the Royal Society in 2012. In 2013, he and Alasdair Houston jointly received the ASAB Medal, and in 2014, he received the Weldon Memorial Prize. In 2018, he was awarded the Sewall Wright Award from the American Society of Naturalists The American Society of Naturalists was founded in 1883 and is one of the oldest professional societies dedicated to the biological sciences in North America. The purpose of the Society is "to advance and diffuse knowledge of organic evolution and o .... References External linksFaculty page* 20th-century English mathematicians 21st-century English mathematicians English biologists Living people Academics of the University of Bristol Alumni of the University of Oxford Alumni of the University of Sussex English ecologists Fellows of the Royal Socie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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