Civil Rights
Movements, leaders, victories and the continuing fight for equality.
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Explore the people, places, events, achievements, struggles and stories that shaped our journey.
Movements, leaders, victories and the continuing fight for equality.
Innovation, patents, science, technology and world-changing contributions.
Pioneers, champions, Negro Leagues, records, activism and excellence.
Meet the people whose lives, choices and achievements shaped the journey.
Black towns, communities, institutions and places where history happened.
Moments that changed communities, movements, institutions and the nation.
Wilmington, North Carolina once had a thriving Black middle class and an elected interracial government. In 1898 white supremacists used violence to overthrow that government, kill Black residents and drive many others from the city.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
In physics, the S-matrix or scattering matrix is a matrix that relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT). More formally, in the context of QFT, the S-matrix is defined as the unitary matrix connecting sets of asymptotically free particle states (the in-states and the out-states) in the Hilbert space of physical states: a multi-particle state is said to be free (or non-interacting) if it transforms under Lorentz transformations as a tensor product, or direct product in physics parlance, of one-particle states as prescribed by equation (1) below. Asymptotically free then means that the state has this appearance in either the distant past or the distant future. While the S-matrix may be defined for any background (spacetime) that is asymptotically solvable and has no event horizons, it has a simple form in the case of the Minkowski space. In this special case, the Hilbert space is a space of irreducible unitary representations of the inhomogeneous Lorentz group (the Poincaré group); the S-matrix is the evolution operator between t = − ∞ {\displaystyle t=-\infty } (the distant past), and t = + ∞ {\displaystyle t=+\infty } (the distant future). It is defined only in the limit of zero energy density (or infinite particle separation distance). It can be shown that if a quantum field theory in Minkowski space has a mass gap, the state in the asymptotic past and in the asymptotic future are both described by Fock spaces.
S-matrix theory was a proposal for replacing local quantum field theory as the basic principle of elementary particle physics. It avoided the notion of space and time by replacing it with abstract mathematical properties of the S-matrix. In S-matrix theory, the S-matrix relates the infinite past to the infinite future in one step, without being decomposable into intermediate steps corresponding to time-slices. This program was very influential in the 1960s, because it was a plausible substitute for quantum field theory, which was plagued with the zero interaction phenomenon at strong coupling. Applied to the strong interaction, it led to the development of string theory. S-matrix theory was largely abandoned by physicists in the 1970s, as quantum chromodynamics was recognized to solve the problems of strong interactions within the framework of field theory. But in the guise of string theory, S-matrix theory is still a popular approach to the problem of quantum gravity. The S-matrix theory is related to the holographic principle and the AdS/CFT correspondence by a flat space limit. The analog of the S-matrix relations in AdS space is the boundary conformal theory. The most lasting legacy of the theory is string theory. Other notable achievements are the Froissart bound, and the prediction of the pomeron.
In linear algebra, a completely-S matrix is a square matrix such that for every principal submatrix R there exists a positive vector u such that Ru > 0.
The term R-matrix has several meanings, depending on the field of study. Its original use has been to mathematically describe nuclear reactions. In particular the general problem of nuclear reactions is to relate the values of the scattering or collision matrix elements (which in principle can be obtained from measurements) to the (slow) dynamics of nuclear structure. The R-matrix formalism describes the effects of the interaction of the nucleus with the outside world. Its interior is not specified, i.e. it is considered a "black box". The original formulations of the theory came from nuclear scientists Wigner, Eisenbud, Breit, Blatt, Weisskopf, and others. Related theories are U-matrix, S-matrix, by M-matrix, or T-matrix.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Mae Jemison, aboard Space Shuttle Endeavour in 1992.
