|
Norman Levinson
Norman Levinson (August 11, 1912 in Lynn, Massachusetts – October 10, 1975 in Boston) was an American mathematician. Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing. He worked closely with Norbert Wiener in his early career. He joined the faculty of the Massachusetts Institute of Technology in 1937. In 1954, he was awarded the Bôcher Memorial Prize of the American Mathematical Society and in 1971 the Chauvenet Prize (after winning in 1970 the Lester R. Ford Award) of the Mathematical Association of America for his paper ''A Motivated Account of an Elementary Proof of the Prime Number Theorem''. In 1974 he published a paper proving that more than a third of the zeros of the Riemann zeta function lie on the critical line, a result later improved to two fifths by Conrey. He received both his bachelor's degree and his master's degree in electrical engineering from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lynn, Massachusetts
Lynn is the eighth-largest municipality in Massachusetts and the largest city in Essex County. Situated on the Atlantic Ocean, north of the Boston city line at Suffolk Downs, Lynn is part of Greater Boston's urban inner core. Settled by Europeans in 1629, Lynn is the 5th oldest colonial settlement in the Commonwealth. An early industrial center, Lynn was long colloquially referred to as the "City of Sin", owing to its historical reputation for crime and vice. Today, however, the city is known for its contemporary public art, immigrant population, historic architecture, downtown cultural district, loft-style apartments, and public parks and open spaces, which include the oceanfront Lynn Shore Reservation; the 2,200-acre, Frederick Law Olmsted-designed Lynn Woods Reservation; and the High Rock Tower Reservation, High Rock Reservation and Park designed by Olmsted Brothers, Olmsted's sons. Lynn also is home to Lynn Heritage State Park, the southernmost portion of the Essex Co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal Processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, Data storage, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. History According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the Bell System Technical Journal. The paper laid the groundwork for later development of information c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levinson's Theorem
Levinson's theorem is an important theorem in non-relativistic quantum scattering theory. It relates the number of bound states of a potential to the difference in phase of a scattered wave at zero and infinite energies. It was published by Norman Levinson Norman Levinson (August 11, 1912 in Lynn, Massachusetts – October 10, 1975 in Boston) was an American mathematician. Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, ... in 1949. Statement of theorem The difference in the \ell-wave phase shift of a scattered wave at zero energy, \varphi_\ell(0), and infinite energy, \varphi_\ell(\infty), for a spherically symmetric potential V(r) is related to the number of bound states n_\ell by: : \varphi_\ell(0) - \varphi_\ell(\infty) = ( n_\ell + \fracN )\pi \ where N = 0 or 1. The case N = 1 is exceptional and it can only happen in s-wave scattering. The following conditions are sufficient to guarantee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
