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Lesley Sibner
Lesley Millman Sibner (August 13, 1934 – September 11, 2013) was an American mathematician and professor of mathematics at Polytechnic Institute of New York University. She earned her Bachelors at City College CUNY in Mathematics. She completed her doctorate at Courant Institute NYU in 1964 under the joint supervision of Lipman Bers and Cathleen Morawetz. Her thesis concerned partial differential equations of mixed-type. Research career In 1964, Lesley Sibner became an instructor at Stanford University for two years. She was a Fulbright Scholar at the Institut Henri Poincaré in Paris the following year. At this time, in addition to solo work on the Tricomi equation and compressible flows, she began working with her husband Robert Sibner on a problem suggested by Lipman Bers: do there exists compressible flows on a Riemann surface? As part of her work in this direction, she studied differential geometry and Hodge theory eventually proving a nonlinear Hodge–DeRham ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York City
New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the List of United States cities by population density, most densely populated major city in the United States, and is more than twice as populous as second-place Los Angeles. New York City lies at the southern tip of New York (state), New York State, and constitutes the geographical and demographic center of both the Northeast megalopolis and the New York metropolitan area, the largest metropolitan area in the world by urban area, urban landmass. With over 20.1 million people in its metropolitan statistical area and 23.5 million in its combined statistical area as of 2020, New York is one of the world's most populous Megacity, megacities, and over 58 million people live within of the city. New York City is a global city, global Culture of New ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tricomi Equation
Tricomi may refer to: *31189 Tricomi (1997 YZ7) Tricomi (asteroid 31189), Main-belt Asteroid *Bartolommeo Tricomi (first half of 17th century), Italian painter of the Baroque period *Euler-Tricomi equation, linear partial differential equation useful in the study of transonic flow *Francesco Tricomi (1897–1978), Italian mathematician famous for his studies on mixed type partial differential equations {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Atiyah
Sir Michael Francis Atiyah (; 22 April 1929 – 11 January 2019) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004. Life Atiyah grew up in Sudan and Egypt but spent most of his academic life in the United Kingdom at the University of Oxford and the University of Cambridge and in the United States at the Institute for Advanced Study. He was the President of the Royal Society (1990–1995), founding director of the Isaac Newton Institute (1990–1996), master of Trinity College, Cambridge (1990–1997), chancellor of the University of Leicester (1995–2005), and the President of the Royal Society of Edinburgh (2005–2008). From 1997 until his death, he was an honorary professor in the University of Edinburgh. Atiyah's mathematical collaborators included Raoul Bott, Friedrich Hirzebruch and Isadore Sin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute For Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholars, including J. Robert Oppenheimer, Albert Einstein, Hermann Weyl, John von Neumann, and Kurt Gödel, many of whom had emigrated from Europe to the United States. It was founded in 1930 by American educator Abraham Flexner, together with philanthropists Louis Bamberger and Caroline Bamberger Fuld. Despite collaborative ties and neighboring geographic location, the institute, being independent, has "no formal links" with Princeton University. The institute does not charge tuition or fees. Flexner's guiding principle in founding the institute was the pursuit of knowledge for its own sake.Jogalekar. The faculty have no classes to teach. There are no degree programs or experimental facilities at the institute. Research is never contracted or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sturm–Liouville Theory
In mathematics and its applications, classical Sturm–Liouville theory is the theory of ''real'' second-order ''linear'' ordinary differential equations of the form: for given coefficient functions , , and , an unknown function ''y = y''(''x'') of the free variable , and an unknown constant λ. All homogeneous (i.e. with the right-hand side equal to zero) second-order linear ordinary differential equations can be reduced to this form. In addition, the solution is typically required to satisfy some boundary conditions at extreme values of ''x''. Each such equation () together with its boundary conditions constitutes a Sturm–Liouville problem. In the simplest case where all coefficients are continuous on the finite closed interval and has continuous derivative, a function ''y = y''(''x'') is called a ''solution'' if it is continuously differentiable and satisfies the equation () at every x\in (a,b). In the case of more general , , , the solutions must be understood in a weak ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Operator
In the theory of partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined by the condition that the coefficients of the highest-order derivatives be positive, which implies the key property that the principal symbol is invertible, or equivalently that there are no real characteristic directions. Elliptic operators are typical of potential theory, and they appear frequently in electrostatics and continuum mechanics. Elliptic regularity implies that their solutions tend to be smooth functions (if the coefficients in the operator are smooth). Steady-state solutions to hyperbolic and parabolic equations generally solve elliptic equations. Definitions Let L be linear differential operator of order ''m'' on a domain \Omega in R''n'' given by Lu = \sum_ a_\alpha(x)\partial^\alpha u where \alpha = (\alpha_1, \dots, \alpha_n) denotes a multi-index, and \partial^\alpha u = \partial^_1 \cdots \partial_n^ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Morse Index Theorem
Morse may refer to: People * Morse (surname) * Morse Goodman (1917-1993), Anglican Bishop of Calgary, Canada * Morse Robb (1902–1992), Canadian inventor and entrepreneur Geography Antarctica * Cape Morse, Wilkes Land * Mount Morse, Churchill Mountains * Morse Nunataks * Morse Spur, Victoria Land Canada * Rural Municipality of Morse No. 165, Saskatchewan ** Morse, Saskatchewan, a town * Morse (provincial electoral district), Saskatchewan China * Morse Park, Hong Kong New Zealand * Morse River, New Zealand South Georgia Island * Morse Point, South Georgia Island United States * Morse, Illinois, an unincorporated community * Morse, Iowa, an unincorporated community * Morse, Louisiana, a village * Morse River (Maine) * Morse Township, Itasca County, Minnesota * Morse Township, St. Louis County, Minnesota * Morse, Texas, an unincorporated community and census-designated place * Morse, Wisconsin, a town * Morse (community), Wisconsin, an unincorporated community Outer space * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brooklyn, New York
Brooklyn () is a borough of New York City, coextensive with Kings County, in the U.S. state of New York. Kings County is the most populous county in the State of New York, and the second-most densely populated county in the United States, behind New York County (Manhattan). Brooklyn is also New York City's most populous borough,2010 Gazetteer for New York State . Retrieved September 18, 2016. with 2,736,074 residents in 2020. Named after the Dutch village of Breukelen, Brooklyn is located on the w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Form
In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold ''M'' using partial differential equations. The key observation is that, given a Riemannian metric on ''M'', every cohomology class has a canonical representative, a differential form that vanishes under the Laplacian operator of the metric. Such forms are called harmonic. The theory was developed by Hodge in the 1930s to study algebraic geometry, and it built on the work of Georges de Rham on de Rham cohomology. It has major applications in two settings: Riemannian manifolds and Kähler manifolds. Hodge's primary motivation, the study of complex projective varieties, is encompassed by the latter case. Hodge theory has become an important tool in algebraic geometry, particularly through its connection to the study of algebraic cycles. While Hodge theory is intrinsically dependent upon the real and complex numbers, it can be applied to questions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hodge Theory
In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold ''M'' using partial differential equations. The key observation is that, given a Riemannian metric on ''M'', every cohomology class has a canonical representative, a differential form that vanishes under the Laplacian operator of the metric. Such forms are called harmonic. The theory was developed by Hodge in the 1930s to study algebraic geometry, and it built on the work of Georges de Rham on de Rham cohomology. It has major applications in two settings: Riemannian manifolds and Kähler manifolds. Hodge's primary motivation, the study of complex projective varieties, is encompassed by the latter case. Hodge theory has become an important tool in algebraic geometry, particularly through its connection to the study of algebraic cycles. While Hodge theory is intrinsically dependent upon the real and complex numbers, it can be applied to questions in nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of size, distance, shape, volume, or other rigidifying structu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
