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David Abrahams (mathematician)
Ian David Abrahams (born 15 January 1958) is an English mathematician and held the Beyer Professor of Applied Mathematics at the University of Manchester, 2008–2016. From 2014–16 he was Director of the International Centre for Mathematical Sciences in Edinburgh and in October 2016 he succeeded John Toland as Director of the Isaac Newton Institute for Mathematical Sciences, and N M Rothschild and Sons Professor of Mathematics, in Cambridge. He was President 2007–2009, of the Institute of Mathematics and its Applications. In 2017 he was awarded the IMA/ LMS David Crighton Medal for services to mathematics. Education Born in Manchester, Abrahams was the son of Harry Abrahams and of Leila Abrahams. He completed his BSc in aeronautical engineering in 1979 and PhD (and DIC) in applied mathematics in 1982, both at Imperial College London. There he won two scholarships and the Finsbury Medal for top undergraduate. For his PhD he was supervised by Frank Leppington for a th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manchester
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. Manchest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diploma Of Imperial College
The Diploma of the Imperial College (DIC) is an academic certificate awarded by Imperial College London to its postgraduate students upon graduation. Until 2007, Imperial was part of the University of London The University of London (UoL; abbreviated as Lond or more rarely Londin in post-nominals) is a federal public research university located in London, England, United Kingdom. The university was established by royal charter in 1836 as a degree ... and Imperial College bestowed the University of London's degrees as well as its own diplomas. Now Imperial College degrees are awarded. Although the award may be studied for on its own, the DIC is typically jointly awarded to students completing a University of London / Imperial College postgraduate course lasting for a year or more. For example, Brian May PhD DIC implies that the student was awarded a PhD from the University of London / Imperial College and the DIC from the Imperial College London. To be awarded a DIC, the st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triumph Bonneville
The Triumph Bonneville is a standard motorcycle featuring a parallel-twin four-stroke engine and manufactured in three generations over three separate production runs. The first two generations, by the defunct Triumph Engineering in Meriden, West Midlands, England, were 1959–1983 and 1985–1988. The third series, by Triumph Motorcycles in Hinckley, Leicestershire, began in 2001 and continues to the present as a completely new design that strongly resembles the original series. The name Bonneville derives from the famous Bonneville Salt Flats, Utah, USA where Triumph and others attempted to break the motorcycle speed records. Development history T120 Bonneville The original Triumph Bonneville was a 650 cc parallel-twin motorcycle manufactured by Triumph Engineering and later by Norton Villiers Triumph between 1959 and 1974. It was based on the company's Triumph Tiger T110 and was fitted with the Tiger's optional twin 1 3/16 in Amal monobloc carburettors as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spitzer's Identity
In probability theory, Spitzer's formula or Spitzer's identity gives the joint distribution of partial sums and maximal partial sums of a collection of random variables. The result was first published by Frank Spitzer in 1956. The formula is regarded as "a stepping stone in the theory of sums of independent random variables". Statement of theorem Let X_1,X_2,... be independent and identically distributed random variables In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. This property is us ... and define the partial sums S_n=X_1 + X_2 + ... + X_n. Define R_n=\text(0,S_1,S_2,...S_n). Then ::\sum_^\infty \phi_n(\alpha,\beta)t^n = \exp \left \sum_^\infty \frac \left( u_n (\alpha) + v_n(\beta) -1 \right) \right/math> where ::\begin \phi_n(\alpha,\beta) &= \operatorname E(\exp\left i(\alpha R_n + \beta(R_n- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Financial Mathematics
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering. The latter focuses on applications and modeling, often by help of stochastic asset models, while the former focuses, in addition to analysis, on building tools of implementation for the models. Also related is quantitative investing, which relies on statistical and numerical models (and lately machine learning) as opposed to traditional fundamental analysis when managing portfolios. French mathematician Louis Bachelier's doctoral thesis, defended in 1900, is considered the first scholarly work on mathematical finan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Green's Function
In mathematics, a Green's function is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions. This means that if \operatorname is the linear differential operator, then * the Green's function G is the solution of the equation \operatorname G = \delta, where \delta is Dirac's delta function; * the solution of the initial-value problem \operatorname y = f is the convolution (G \ast f). Through the superposition principle, given a linear ordinary differential equation (ODE), \operatorname y = f, one can first solve \operatorname G = \delta_s, for each , and realizing that, since the source is a sum of delta functions, the solution is a sum of Green's functions as well, by linearity of . Green's functions are named after the British mathematician George Green, who first developed the concept in the 1820s. In the modern study of linear partial differential equations, Green's functions are s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Welding
Welding is a fabrication (metal), fabrication process that joins materials, usually metals or thermoplastics, by using high heat to melt the parts together and allowing them to cool, causing Fusion welding, fusion. Welding is distinct from lower temperature techniques such as brazing and soldering, which do not melting, melt the base metal (parent metal). In addition to melting the base metal, a filler material is typically added to the joint to form a pool of molten material (the weld pool) that cools to form a joint that, based on weld configuration (butt, full penetration, fillet, etc.), can be stronger than the base material. Pressure may also be used in conjunction with heat or by itself to produce a weld. Welding also requires a form of shield to protect the filler metals or melted metals from being contaminated or Oxidation, oxidized. Many different energy sources can be used for welding, including a gas flame (chemical), an electric arc (electrical), a laser, an electron ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Austenite
Austenite, also known as gamma-phase iron (γ-Fe), is a metallic, non-magnetic allotrope of iron or a solid solution of iron with an alloying element. In plain-carbon steel, austenite exists above the critical eutectoid temperature of 1000 K (727 °C); other alloys of steel have different eutectoid temperatures. The austenite allotrope is named after Sir William Chandler Roberts-Austen (1843–1902); it exists at room temperature in some stainless steels due to the presence of nickel stabilizing the austenite at lower temperatures. Allotrope of iron From alpha iron undergoes a phase transition from body-centered cubic (BCC) to the face-centered cubic (FCC) configuration of gamma iron, also called austenite. This is similarly soft and ductile but can dissolve considerably more carbon (as much as 2.03% by mass at ). This gamma form of iron is present in the most commonly used type of stainless steel for making hospital and food-service equipment. Material Austenitizati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffraction
Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word ''diffraction'' and was the first to record accurate observations of the phenomenon in 1660. In classical physics, the diffraction phenomenon is described by the Huygens–Fresnel principle that treats each point in a propagating wavefront as a collection of individual spherical wavelets. The characteristic bending pattern is most pronounced when a wave from a coherent source (such as a laser) encounters a slit/aperture that is comparable in size to its wavelength, as shown in the inserted image. This is due to the addition, or interference, of different points on the wavefront (or, equivalently, each wavelet) that travel by paths of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiener–Hopf Method
The Wiener–Hopf method is a mathematical technique widely used in applied mathematics. It was initially developed by Norbert Wiener and Eberhard Hopf as a method to solve systems of integral equations, but has found wider use in solving two-dimensional partial differential equations with mixed boundary conditions on the same boundary. In general, the method works by exploiting the complex-analytical properties of transformed functions. Typically, the standard Fourier transform is used, but examples exist using other transforms, such as the Mellin transform. In general, the governing equations and boundary conditions are transformed and these transforms are used to define a pair of complex functions (typically denoted with '+' and '−' subscripts) which are respectively analytic in the upper and lower halves of the complex plane, and have growth no faster than polynomials in these regions. These two functions will also coincide on some region of the complex plane, typically, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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