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Ralph S. Phillips
Ralph Saul Phillips (23 June 1913 – 23 November 1998) was an American mathematician and academic known for his contributions to functional analysis, scattering theory, and servomechanisms. He served as a Professor of mathematics at Stanford University. He made major contributions to acoustical scattering theory in collaboration with Peter Lax, proving remarkable results on local energy decay and the connections between poles of the scattering matrix and the analytic properties of the resolvent. With Lax, he coauthored the widely referred book on scattering theory titled ''Scattering Theory for Automorphic Functions''. Phillips received the 1997 Leroy P. Steele Prize for Lifetime Achievement. Education and career Phillips was born in Oakland on 23 June 1913. He received his bachelor's degree from the University of California at Los Angeles (UCLA) in 1935 and his Ph.D. from the University of Michigan in 1939 under the direction of Theophil H. Hildebrandt. From 1939 until 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oakland, California
Oakland is the largest city and the county seat of Alameda County, California, United States. A major West Coast of the United States, West Coast port, Oakland is the largest city in the East Bay region of the San Francisco Bay Area, the third largest city overall in the Bay Area and the List of largest California cities by population, eighth most populated city in California. With a population of 440,646 in 2020, it serves as the Bay Area's trade center and economic engine: the Port of Oakland is the busiest port in Northern California, and the fifth busiest in the United States of America. An act to municipal corporation, incorporate the city was passed on May 4, 1852, and incorporation was later approved on March 25, 1854. Oakland is a charter city. Oakland's territory covers what was once a mosaic of California coastal prairie, California coastal terrace prairie, oak woodland, and north coastal scrub. In the late 18th century, it became part of a large ''rancho'' grant in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resolvent Formalism
In mathematics, the resolvent formalism is a technique for applying concepts from complex analysis to the study of the spectrum of operators on Banach spaces and more general spaces. Formal justification for the manipulations can be found in the framework of holomorphic functional calculus. The resolvent captures the spectral properties of an operator in the analytic structure of the functional. Given an operator , the resolvent may be defined as : R(z;A)= (A-zI)^~. Among other uses, the resolvent may be used to solve the inhomogeneous Fredholm integral equations; a commonly used approach is a series solution, the Liouville–Neumann series. The resolvent of can be used to directly obtain information about the spectral decomposition of . For example, suppose is an isolated eigenvalue in the spectrum of . That is, suppose there exists a simple closed curve C_\lambda in the complex plane that separates from the rest of the spectrum of . Then the residue : -\frac \oin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ''ad hoc'' solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramanujan Graphs
In the mathematical field of spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are excellent spectral expanders. AMurty's survey papernotes, Ramanujan graphs "fuse diverse branches of pure mathematics, namely, number theory, representation theory, and algebraic geometry". These graphs are indirectly named after Srinivasa Ramanujan; their name comes from the Ramanujan–Petersson conjecture, which was used in a construction of some of these graphs. Definition Let G be a connected d-regular graph with n vertices, and let \lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_n be the eigenvalues of the adjacency matrix of G (or the spectrum of G). Because G is connected and d-regular, its eigenvalues satisfy d = \lambda_1 > \lambda_2 \geq \cdots \geq \lambda_n \geq -d . Define \lambda(G) = \max_, \lambda_i, = \max(, \lambda_2, , , \lambda_n, ). A connected d-regular graph G is a ''Ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Sarnak
Peter Clive Sarnak (born 18 December 1953) is a South African-born mathematician with dual South-African and American nationalities. Sarnak has been a member of the permanent faculty of the School of Mathematics at the Institute for Advanced Study since 2007. He is also Eugene Higgins Professor of Mathematics at Princeton University since 2002, succeeding Andrew Wiles, and is an editor of the Annals of Mathematics. He is known for his work in analytic number theory. He also sits on the Board of Adjudicators and the selection committee for the Mathematics award, given under the auspices of the Shaw Prize. Education Sarnak is the grandson of one of Johannesburg's leading rabbis and lived in Israel for three years as a child. He graduated from the University of the Witwatersrand (BSc 1975, BSc(Hons) 1976) and Stanford University (PhD 1980), under the direction of Paul Cohen. Sarnak's highly cited work (with A. Lubotzky and R. Phillips) applied deep results in number theory to Ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexander Lubotzky
Alexander Lubotzky ( he, אלכסנדר לובוצקי; born 28 June 1956) is an Israeli mathematician and former politician who is currently a professor at the Weizmann Institute of Science and an adjunct professor at Yale University. He served as a member of the Knesset for Third Way (Israel), The Third Way party between 1996 and 1999. In 2018 he won the Israel Prize for his accomplishments in mathematics and computer science. Biography Alexander (Alex) Lubotzky was born in Tel Aviv to Holocaust survivors. His father, Iser Lubotzky was a Partisan (military), Partisan, Irgun officer and the legal advisor of Herut. After school, Lubotzky did his Israel Defence Forces, IDF national service as a captain officer in a special intelligence and communication unit. He studied mathematics at Bar-Ilan University during highschool, gaining a Bachelor of Arts, BA (summa cum laude) and continuing directly with studying for his PhD under the supervision of Hillel Furstenberg. Lubotzky married ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Southern California
The University of Southern California (USC, SC, or Southern Cal) is a Private university, private research university in Los Angeles, California, United States. Founded in 1880 by Robert M. Widney, it is the oldest private research university in California. The university is composed of one Liberal arts education, liberal arts school, the University of Southern California academics, Dornsife College of Letters, Arts and Sciences, and 22 Undergraduate education, undergraduate, Graduate school, graduate, and professional schools, enrolling roughly 21,000 undergraduate and 28,500 Postgraduate education, post-graduate students from all 50 U.S. states and more than 115 countries. It is also a member of the Association of American Universities, which it joined in 1969. USC is ranked as one of the top universities in the United States and admission to its programs is considered College admissions in the United States, highly selective. USC has graduated more alumni who have gone on to w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Courant Institute Of Mathematical Sciences
The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU), and is among the most prestigious mathematics schools and mathematical sciences research centers in the world. Founded in 1935, it is named after Richard Courant, one of the founders of the Courant Institute and also a mathematics professor at New York University from 1936 to 1972, and serves as a center for research and advanced training in computer science and mathematics. It is located on Gould Plaza next to the Stern School of Business and the economics department of the College of Arts and Science. NYU is ranked #1 in applied mathematics in the US (as per US News), #5 in citation impact worldwide, and #12 in citation worldwide. It is also ranked #19 worldwide in computer science and information systems. On the Faculty Scholarly Productivity Index, it is ranked #3 with an index of 1.84. It is also known for its extensive res ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Massachusetts Institute Of Technology
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the most prestigious and highly ranked academic institutions in the world. Founded in response to the increasing industrialization of the United States, MIT adopted a European polytechnic university model and stressed laboratory instruction in applied science and engineering. MIT is one of three private land grant universities in the United States, the others being Cornell University and Tuskegee University. The institute has an urban campus that extends more than a mile (1.6 km) alongside the Charles River, and encompasses a number of major off-campus facilities such as the MIT Lincoln Laboratory, the Bates Center, and the Haystack Observatory, as well as affiliated laboratories such as the Broad and Whitehead Institutes. , 98 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher learning in the United States and one of the most prestigious and highly ranked universities in the world. The university is composed of ten academic faculties plus Harvard Radcliffe Institute. The Faculty of Arts and Sciences offers study in a wide range of undergraduate and graduate academic disciplines, and other faculties offer only graduate degrees, including professional degrees. Harvard has three main campuses: the Cambridge campus centered on Harvard Yard; an adjoining campus immediately across Charles River in the Allston neighborhood of Boston; and the medical campus in Boston's Longwood Medical Area. Harvard's endowment is valued at $50.9 billion, making it the wealthiest academic institution in the world. Endowment inco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Washington
The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seattle approximately a decade after the city's founding. The university has a 703 acre main campus located in the city's University District, as well as campuses in Tacoma and Bothell. Overall, UW encompasses over 500 buildings and over 20 million gross square footage of space, including one of the largest library systems in the world with more than 26 university libraries, art centers, museums, laboratories, lecture halls, and stadiums. The university offers degrees through 140 departments, and functions on a quarter system. Washington is the flagship institution of the six public universities in Washington state. It is known for its medical, engineering, and scientific research. Washington is a member of the Association of American Universiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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