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Harry Bateman
Harry Bateman FRS (29 May 1882 – 21 January 1946) was an English mathematician with a specialty in differential equations of mathematical physics. With Ebenezer Cunningham, he expanded the views of spacetime symmetry of Lorentz and Poincare to a more expansive conformal group of spacetime leaving Maxwell's equations invariant. Moving to the U.S.A., and obtaining a Ph.D. in geometry with Frank Morley, he became a professor of mathematics at California Institute of Technology. There he taught fluid dynamics to students going into aerodynamics with Theodore von Karman. Bateman made a broad survey of applied differential equations in his Gibbs Lecture in 1943 titled "The control of an elastic fluid". Biography Bateman was born in Manchester, England on 29 May 1882. He first grew to love mathematics at Manchester Grammar School, and, in his final year, won a scholarship to Trinity College, Cambridge. Bateman studied with coach Robert Alfred Herman preparing for Cam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manchester, England
Manchester () is a city in Greater Manchester, England. It had a population of 552,000 in 2021. It is bordered by the Cheshire Plain to the south, the Pennines to the north and east, and the neighbouring city of Salford to the west. The two cities and the surrounding towns form one of the United Kingdom's most populous conurbations, the Greater Manchester Built-up Area, which has a population of 2.87 million. The history of Manchester began with the civilian settlement associated with the Roman fort ('' castra'') of ''Mamucium'' or ''Mancunium'', established in about AD 79 on a sandstone bluff near the confluence of the rivers Medlock and Irwell. Historically part of Lancashire, areas of Cheshire south of the River Mersey were incorporated into Manchester in the 20th century, including Wythenshawe in 1931. Throughout the Middle Ages Manchester remained a manorial township, but began to expand "at an astonishing rate" around the turn of the 19th century. Manchester's u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bateman Equation
In nuclear physics, the Bateman equation is a mathematical model describing abundances and activities in a decay chain as a function of time, based on the decay rates and initial abundances. The model was formulated by Ernest Rutherford in 1905 and the analytical solution was provided by Harry Bateman in 1910. If, at time ''t'', there are N_i(t) atoms of isotope i that decays into isotope i+1 at the rate \lambda_i, the amounts of isotopes in the ''k''-step decay chain evolves as: : \begin \frac & =-\lambda_1 N_1(t) \\ pt\frac & =-\lambda_i N_i(t) + \lambda_N_(t) \\ pt\frac & = \lambda_N_(t) \end (this can be adapted to handle decay branches). While this can be solved explicitly for ''i'' = 2, the formulas quickly become cumbersome for longer chains. The Bateman equation is a classical master equation where the transition rates are only allowed from one species (i) to the next (i+1) but never in the reverse sense (i+1 to i is forbidden). Bateman found a general expl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxwell's Equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. They describe how electric field, electric and magnetic fields are generated by electric charge, charges, electric current, currents, and changes of the fields.''Electric'' and ''magnetic'' fields, according to the theory of relativity, are the components of a single electromagnetic field. The equations are named after the physicist and mathematician James Clerk Maxwell, who, in 1861 and 1862, published an early form of the equations that included the Lorentz force law. Maxwell first used the equations to propose that light is an electromagnetic phenomenon. The modern f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformal Group Of Spacetime
In mathematics, the conformal group of an inner product space is the group of transformations from the space to itself that preserve angles. More formally, it is the group of transformations that preserve the conformal geometry of the space. Several specific conformal groups are particularly important: * The conformal orthogonal group. If ''V'' is a vector space with a quadratic form ''Q'', then the conformal orthogonal group is the group of linear transformations ''T'' of ''V'' for which there exists a scalar ''λ'' such that for all ''x'' in ''V'' *:Q(Tx) = \lambda^2 Q(x) :For a definite quadratic form, the conformal orthogonal group is equal to the orthogonal group times the group of dilations. * The conformal group of the sphere is generated by the inversions in circles. This group is also known as the Möbius group. * In Euclidean space E''n'', , the conformal group is generated by inversions in hyperspheres. * In a pseudo-Euclidean space E''p'',''q'', the conformal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ebenezer Cunningham
Ebenezer Cunningham (7 May 1881 in Hackney, London – 12 February 1977) was a British mathematician who is remembered for his research and exposition at the dawn of special relativity. Biography Cunningham went up to St John's College, Cambridge in 1899 and graduated Senior Wrangler in 1902, winning the Smith's Prize in 1904. In 1904, as a lecturer at the University of Liverpool, he began work on a new theorem in relativity with fellow lecturer Harry Bateman. They brought the methods of inversive geometry into electromagnetic theory with their transformations ( spherical wave transformation): :Each four-dimensional solution o Maxwell's equationscould then be inverted in a four-dimensional ''hypersphere of pseudo-radius K'' in order to produce a new solution. Central to Cunningham's paper was the demonstration that Maxwell's equations retained their form under these transformations. He worked with Karl Pearson in 1907 at University College London. Cunningham married Ada Co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Physics
Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics (also known as physical mathematics). Scope There are several distinct branches of mathematical physics, and these roughly correspond to particular historical periods. Classical mechanics The rigorous, abstract and advanced reformulation of Newtonian mechanics adopting the Lagrangian mechanics and the Hamiltonian mechanics even in the presence of constraints. Both formulations are embodied in analytical mechanics and lead to understanding the deep interplay of the notions of symmetry (physics), symmetry and conservation law, con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagoreans, Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fellow Of The Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathematics, engineering science, and medical science". Fellowship of the Society, the oldest known scientific academy in continuous existence, is a significant honour. It has been awarded to many eminent scientists throughout history, including Isaac Newton (1672), Michael Faraday (1824), Charles Darwin (1839), Ernest Rutherford (1903), Srinivasa Ramanujan (1918), Albert Einstein (1921), Paul Dirac (1930), Winston Churchill (1941), Subrahmanyan Chandrasekhar (1944), Dorothy Hodgkin (1947), Alan Turing (1951), Lise Meitner (1955) and Francis Crick (1959). More recently, fellowship has been awarded to Stephen Hawking (1974), David Attenborough (1983), Tim Hunt (1991), Elizabeth Blackburn (1992), Tim Berners-Lee (2001), Venki Ramakrishnan ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbs Lecture
The Josiah Willard Gibbs Lectureship (also called the Gibbs Lecture) of the American Mathematical Society is an annually awarded mathematical prize, named in honor of Josiah Willard Gibbs. The prize is intended not only for mathematicians, but also for physicists, chemists, biologists, physicians, and other scientists who have made important applications of mathematics. The purpose of the prize is to recognize outstanding achievement in applied mathematics and "to enable the public and the academic community to become aware of the contribution that mathematics is making to present-day thinking and to modern civilization." The prize winner gives a lecture, which is subsequently published in the Bulletin of the American Mathematical Society. Prize winners See also * List of mathematics awards This list of mathematics awards is an index to articles about notable awards for mathematics. The list is organized by the region and country of the organization that sponsors the award, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smith's Prize
The Smith's Prize was the name of each of two prizes awarded annually to two research students in mathematics and theoretical physics at the University of Cambridge from 1769. Following the reorganization in 1998, they are now awarded under the names Smith-Knight Prize and Rayleigh-Knight Prize. History The Smith Prize fund was founded by bequest of Robert Smith upon his death in 1768, having by his will left £3,500 of South Sea Company stock to the University. Every year two or more junior Bachelor of Arts students who had made the greatest progress in mathematics and natural philosophy were to be awarded a prize from the fund. The prize was awarded every year from 1769 to 1998 except 1917. From 1769 to 1885, the prize was awarded for the best performance in a series of examinations. In 1854 George Stokes included an examination question on a particular theorem that William Thomson had written to him about, which is now known as Stokes' theorem. T. W. Körner notes Only a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Senior Wrangler (University Of Cambridge)
The Senior Frog Wrangler is the top mathematics undergraduate at the University of Cambridge in England, a position which has been described as "the greatest intellectual achievement attainable in Britain." Specifically, it is the person who achieves the highest overall mark among the Wranglers – the students at Cambridge who gain first-class degrees in mathematics. The Cambridge undergraduate mathematics course, or Mathematical Tripos, is famously difficult. Many Senior Wranglers have become world-leading figures in mathematics, physics, and other fields. They include George Airy, Jacob Bronowski, Christopher Budd, Kevin Buzzard, Arthur Cayley, Donald Coxeter, Arthur Eddington, Ben Green, John Herschel, James Inman, J. E. Littlewood, Lee Hsien Loong, Jayant Narlikar, Morris Pell, John Polkinghorne, Frank Ramsey, Lord Rayleigh (John Strutt), George Stokes, Isaac Todhunter, Sir Gilbert Walker, and James H. Wilkinson. Senior Wranglers were once fêted with torchl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
