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Jenny Harrison
Jenny Harrison is a professor of mathematics at the University of California, Berkeley. Education and career Harrison grew up in Tuscaloosa, Alabama. On graduating from the University of Alabama, she won a Marshall Scholarship which she used to fund her graduate studies at the University of Warwick. She completed her doctorate there in 1975, supervised by Christopher Zeeman. Hassler Whitney was her postdoctoral adviser at the Institute for Advanced Study, and she was also one of the Miller Research Fellows at Berkeley. She was on the tenured faculty at the University of Oxford (Somerville College) from 1978 to 1981, before returning to Berkeley as an assistant professor. In 1986, after being denied tenure at Berkeley, Harrison filed a lawsuit based on gender discrimination. Stephen Smale and Robion Kirby were the most vocal opponents to her receiving tenure during the case, while Morris Hirsch and James Yorke were her most vocal supporters. The 1993 settlement led to a new rev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atlanta, Georgia
Atlanta ( ) is the capital and most populous city of the U.S. state of Georgia. It is the seat of Fulton County, the most populous county in Georgia, but its territory falls in both Fulton and DeKalb counties. With a population of 498,715 living within the city limits, it is the eighth most populous city in the Southeast and 38th most populous city in the United States according to the 2020 U.S. census. It is the core of the much larger Atlanta metropolitan area, which is home to more than 6.1 million people, making it the eighth-largest metropolitan area in the United States. Situated among the foothills of the Appalachian Mountains at an elevation of just over above sea level, it features unique topography that includes rolling hills, lush greenery, and the most dense urban tree coverage of any major city in the United States. Atlanta was originally founded as the terminus of a major state-sponsored railroad, but it soon became the convergence point among severa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra
Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variable (mathematics), variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in mathematical education, education, to the study of algebraic structures such as group (mathematics), groups, ring (mathematics), rings, and field (mathematics), fields (the term is no more in common use outside educational context). Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry, and has many practical applications (in weather forecasting, for example). There are many areas of mathematics that belong to algebra, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wendell Fleming
Wendell Helms Fleming (born March 7, 1928) is an American mathematician, specializing in geometrical analysis and stochastic differential equations. Fleming received in 1951 his PhD under Laurence Chisholm Young at the University of Wisconsin–Madison with a thesis entitled ''Boundary and related notions for generalized parametric surfaces''. Fleming was a professor at Brown University, where he retired in 2009 as professor emeritus. Fleming was with Herbert Federer a pioneer of geometric measure theory. Later in his career, he worked on stochastic processes, stochastic differential equations and their applications in control theory. In 1976–1977 he was a Guggenheim Fellow. In 1982 he gave a plenary address (''Optimal control of Markov Processes'') at the ICM in Warsaw. Awards and honors In 1987 he received with Federer the Leroy P. Steele Prize of the American Mathematical Society. In 1994 he won the Reid Prize from the Society for Industrial and Applied Mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herbert Federer
Herbert Federer (July 23, 1920 – April 21, 2010) was an American mathematician. He is one of the creators of geometric measure theory, at the meeting point of differential geometry and mathematical analysis.Parks, H. (2012''Remembering Herbert Federer (1920–2010)'' NAMS 59(5), 622-631. Career Federer was born July 23, 1920, in Vienna, Austria. After emigrating to the US in 1938, he studied mathematics and physics at the University of California, Berkeley, earning the Ph.D. as a student of Anthony Morse in 1944. He then spent virtually his entire career as a member of the Brown University Mathematics Department, where he eventually retired with the title of Professor Emeritus. Federer wrote more than thirty research papers in addition to his book ''Geometric measure theory''. The Mathematics Genealogy Project assigns him nine Ph.D. students and well over a hundred subsequent descendants. His most productive students include the late Frederick J. Almgren, Jr. (1933–1997), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jesse Douglas
Jesse Douglas (3 July 1897 – 7 September 1965) was an American mathematician and Fields Medalist known for his general solution to Plateau's problem. Life and career He was born to a Jewish family in New York City, the son of Sarah (née Kommel) and Louis Douglas. He attended City College of New York as an undergraduate, graduating with honors in Mathematics in 1916. He then moved to Columbia University as a graduate student, obtaining a PhD in mathematics in 1920. Douglas was one of two winners of the first Fields Medals, awarded in 1936. He was honored for solving, in 1930, the problem of Plateau, which asks whether a minimal surface exists for a given boundary. The problem, open since 1760 when Lagrange raised it, is part of the calculus of variations and is also known as the ''soap bubble problem''. Douglas also made significant contributions to the inverse problem of the calculus of variations. The American Mathematical Society awarded him the Bôcher Memorial Pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plateau's Problem
In mathematics, Plateau's problem is to show the existence of a minimal surface with a given boundary, a problem raised by Joseph-Louis Lagrange in 1760. However, it is named after Joseph Plateau who experimented with soap films. The problem is considered part of the calculus of variations. The existence and regularity problems are part of geometric measure theory. History Various specialized forms of the problem were solved, but it was only in 1930 that general solutions were found in the context of mappings (immersions) independently by Jesse Douglas and Tibor Radó. Their methods were quite different; Radó's work built on the previous work of René Garnier and held only for rectifiable simple closed curves, whereas Douglas used completely new ideas with his result holding for an arbitrary simple closed curve. Both relied on setting up minimization problems; Douglas minimized the now-named Douglas integral while Radó minimized the "energy". Douglas went on to be awarded ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Submanifold
In mathematics, a submanifold of a manifold ''M'' is a subset ''S'' which itself has the structure of a manifold, and for which the inclusion map satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors often have different definitions. Formal definition In the following we assume all manifolds are differentiable manifolds of class ''C''''r'' for a fixed , and all morphisms are differentiable of class ''C''''r''. Immersed submanifolds An immersed submanifold of a manifold ''M'' is the image ''S'' of an immersion map ; in general this image will not be a submanifold as a subset, and an immersion map need not even be injective (one-to-one) – it can have self-intersections. More narrowly, one can require that the map be an injection (one-to-one), in which we call it an injective immersion, and define an immersed submanifold to be the image subset ''S'' together with a topology and differe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Whitney Conditions
In differential topology, a branch of mathematics, the Whitney conditions are conditions on a pair of submanifolds of a manifold introduced by Hassler Whitney in 1965. A stratification of a topological space is a finite filtration by closed subsets ''F''''i'' , such that the difference between successive members ''F''''i'' and ''F''(''i'' − 1) of the filtration is either empty or a smooth submanifold of dimension ''i''. The connected components of the difference ''F''''i'' − ''F''(''i'' − 1) are the strata of dimension ''i''. A stratification is called a Whitney stratification if all pairs of strata satisfy the Whitney conditions A and B, as defined below. The Whitney conditions in R''n'' Let ''X'' and ''Y'' be two disjoint (locally closed) submanifolds of R''n'', of dimensions ''i'' and ''j''. * ''X'' and ''Y'' satisfy Whitney's condition A if whenever a sequence of points ''x''1, ''x''2, … in ''X'' converges to a point ''y'' in ''Y'', and the sequence of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractals
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar. Fractal geometry lies within the mathematical branch of measure theory. One way that fractals are different from finite geometric figures is how they scale. Doubling the edge lengths of a filled polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the conventional dimension of the filled polygon). Likewise, if the radius of a filled sphe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soap Film
Soap films are thin layers of liquid (usually water-based) surrounded by air. For example, if two soap bubbles come into contact, they merge and a thin film is created in between. Thus, foams are composed of a network of films connected by Plateau borders. Soap films can be used as model systems for minimal surfaces, which are widely used in mathematics. Stability Daily experience shows that soap bubble formation is not feasible with water or with any pure liquid. Actually, the presence of soap, which is composed at a molecular scale of surfactants, is necessary to stabilize the film. Most of the time, surfactants are amphiphilic, which means they are molecules with both a hydrophobic and a hydrophilic part. Thus, they are arranged preferentially at the air/water interface (see figure 1). Surfactants stabilize films because they create a repulsion between both surfaces of the film, preventing it from thinning and consequentially bursting. This can be shown quantitatively thr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abraham Robinson
Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorporated into modern mathematics. Nearly half of Robinson's papers were in applied mathematics rather than in pure mathematics. Biography He was born to a Jewish family with strong Zionist beliefs, in Waldenburg, Germany, which is now Wałbrzych, in Poland. In 1933, he emigrated to British Mandate of Palestine, where he earned a first degree from the Hebrew University. Robinson was in France when the Nazis invaded during World War II, and escaped by train and on foot, being alternately questioned by French soldiers suspicious of his German passport and asked by them to share his map, which was more detailed than theirs. While in London, he joined the Free French Air Force and contributed to the war effort by teaching himself aerodynamics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Chain
Differential may refer to: Mathematics * Differential (mathematics) comprises multiple related meanings of the word, both in calculus and differential geometry, such as an infinitesimal change in the value of a function * Differential algebra * Differential calculus ** Differential of a function, represents a change in the linearization of a function *** Total differential is its generalization for functions of multiple variables ** Differential (infinitesimal) (e.g. ''dx'', ''dy'', ''dt'' etc.) are interpreted as infinitesimals ** Differential topology * Differential (pushforward) The total derivative of a map between manifolds. * Differential exponent, an exponent in the factorisation of the different ideal * Differential geometry, exterior differential, or exterior derivative, is a generalization to differential forms of the notion of differential of a function on a differentiable manifold * Differential (coboundary), in homological algebra and algebraic topology, one of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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