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Roger Penrose
Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, Philosophy of science, philosopher of science and Nobel Prize in Physics, 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 physical cosmology, 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 the 2020 Nobel Prize in Physics "for the discovery that black hole formation is a robust prediction of the general theory of relativity". He won the Royal Society Prizes for Science Books, Royal Society Science Books Prize for ''The Emperor's New Mind'' (1989), which outlines his views on physics and con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Colchester
Colchester ( ) is a city in northeastern Essex, England. It is the second-largest settlement in the county, with a population of 130,245 at the 2021 United Kingdom census, 2021 Census. The demonym is ''Colcestrian''. Colchester occupies the site of Camulodunum, the first Colonia (Roman), 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 Empire, Roman era, with Colchester Garrison currently housing the 16th Air Assault Brigade (United Kingdom), 16th Air Assault Brigade. On the River Colne, Essex, River Colne, Colchester is northeast of London. It is connected to London by the A12 road (England), 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 St Botolph's Priory, Colchester Zoo, and several art galleries. Colchester Castle was constructe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claude LeBrun
Claude R. LeBrun (born 1956) is an American mathematician who holds the position of Distinguished Professor of Mathematics at Stony Brook University. Much of his research concerns the Riemannian geometry of 4-manifolds, or related topics in complex and differential geometry. After enrolling as an undergraduate at Rice University at age 16, LeBrun received his Master of Arts in mathematics from Rice in 1977. He then went on to earn his D.Phil. (Oxford equivalent of a Ph.D.) from the University of Oxford in 1980, for a thesis on complex differential geometry written under the supervision of Roger Penrose. That same year, he then accepted his first faculty position at Stony Brook.Math Department and Institute Faculty - by Rank Stony Brook University, retrieved 2013-01-30. Although he would eventu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Illumination Problem
Illumination problems are a class of mathematical problems that study the illumination of rooms with mirrored walls by point light sources. Original formulation The original formulation was attributed to Ernst Straus in the 1950s and has been resolved. Straus asked whether a room with mirrored walls can always be illuminated by a single point light source, allowing for repeated reflection of light off the mirrored walls. Alternatively, the question can be stated as asking that if a billiard table can be constructed in any required shape, is there a shape possible such that there is a point where it is impossible to hit the billiard ball at another point, assuming the ball is point-like and continues infinitely rather than stopping due to friction. Penrose unilluminable room The original problem was first solved in 1958 by Roger Penrose using ellipses to form the Penrose unilluminable room. He showed that there exists a room with curved walls that must always have dark region ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cosmic Censorship Hypothesis
The weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of gravitational singularities arising in general relativity. Singularities that arise in the solutions of Einstein's equations are typically hidden within event horizons, and therefore cannot be observed from the rest of spacetime. Singularities that are not so hidden are called ''naked''. The weak cosmic censorship hypothesis was conceived by Roger Penrose in 1969 and posits that no naked singularities exist in the universe. Basics Since the physical behavior of singularities is unknown, if singularities can be observed from the rest of spacetime, causality may break down, and physics may lose its predictive power. The issue cannot be avoided, since according to the Penrose–Hawking singularity theorems, singularities are inevitable in physically reasonable situations. Still, in the absence of naked singularities, the universe, as described by the general theory of rela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spacetime
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive ''where'' and ''when'' events occur. Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its description in terms of locations, shapes, distances, and directions) was distinct from time (the measurement of when events occur within the universe). However, space and time took on new meanings with the Lorentz transformation and special theory of relativity. In 1908, Hermann Minkowski presented a geometric interpretation of special relativity that fused time and the three spatial dimensions into a single four-dimensional continuum now known as Minkowski space. This interpretation proved vital t ... [...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. This explosion can be as powerful as a supernova. 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 ... [...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 tensor contraction, contractions and covariant derivative, covariant differentiation in modern abstract tensor notation, while preserving the explicit Covariance and contravariance of vectors, covariance of the expressions involved. Let V be a vector space, and V^* its dual space. Consider, for example, an order-2 Covariance and contravariance of vectors, covariant tensor h \in V^*\otimes V^*. Then h can be identified with a bilinear form on V. In ot ... [...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 ... [...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 widely studied branch of theoretical and mathematical physics. Penrose's idea was that twistor space should be the basic arena for physics from which space-time itself should emerge. It has led to powerful mathematical tools that have applications to differential and integral geometry, nonlinear differential equations and representation theory, and in physics to general relativity, quantum field theory, and the theory of scattering amplitudes. Twistor theory arose in the context of the rapidly expanding mathematical developments in Einstein's theory of general relativity in the late 1950s and in the 1960s and carries a number of influences from that period. In particular, Roger Penrose has credited Ivor Robinson as an important early influence in the development of twistor theory, through his construction of so-called ''Robinson congruences ... [...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 , often called the pseudoinverse, 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. The terms ''pseudoinverse'' and ''generalized inverse'' are sometimes used as synonyms for the Moore–Penrose inverse of a matrix, but sometimes applied to other elements of algebraic structures which share some but not all properties expected for an inverse element. A common use of the pseudoinverse is to compute a "best fit" ( least squares) approximate solution to a system of linear equations that lacks an exact 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 pseu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard S
Richard is a male given name. It originates, via Old French, from Old Frankish and is a compound of the words descending from Proto-Germanic language">Proto-Germanic ''*rīk-'' 'ruler, leader, king' and ''*hardu-'' 'strong, brave, hardy', and it therefore means 'strong in rule'. Nicknames include " Richie", " Dick", " Dickon", " Dickie", " Rich", " Rick", "Rico (name), Rico", " Ricky", and more. Richard is a common English (the name was introduced into England by the Normans), German and French male name. It's also used in many more languages, particularly Germanic, such as Norwegian, Danish, Swedish, Icelandic, and Dutch, as well as other languages including Irish, Scottish, Welsh and Finnish. Richard is cognate with variants of the name in other European languages, such as the Swedish "Rickard", the Portuguese and Spanish "Ricardo" and the Italian "Riccardo" (see comprehensive variant list below). People named Richard Multiple people with the same name * Richard Ander ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asghar Qadir
Asghar Qadir ( born 23 July 1946) ''HI'', ''SI'', ''FPAS'', is a Pakistani mathematician and a prominent cosmologist, specialised in mathematical physics and physical cosmology. Nowadays, he is widely considered one of the top mathematicians in Pakistan. Asghar has played a prominent role in promoting Relativity in Pakistan. To this day, Qadir has made important and significant contributions to the fields of differential equations, theoretical cosmology and mathematical physics. He is noted for his work in mathematics and mathematical physics, in particular his contributions to general relativity and cosmology. He has mentored several graduate students throughout his career and also held important administrative positions, including being the Chairman of the Mathematics Department at Quaid-i-Azam University, Islamabad, and later the Dean of Faculty of Natural Sciences at the same university. Professor Qadir founded the Center for Advanced Mathematics & Physics at the Na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
