Civil Rights
Movements, leaders, victories and the continuing fight for equality.
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.
Mansa Musa was the ruler of the Mali Empire in West Africa. Details recorded here should be sourced; unknown information is left blank.
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
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden "qualitative" or topological change in its behavior. Bifurcations occur in both continuous systems (described by ordinary, delay or partial differential equations) and discrete systems (described by maps). The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior.
Biological applications of bifurcation theory provide a framework for understanding the behavior of biological networks modeled as dynamical systems. In the context of a biological system, bifurcation theory describes how small changes in an input parameter can cause a bifurcation or qualitative change in the behavior of the system. The ability to make dramatic change in system output is often essential to organism function, and bifurcations are therefore ubiquitous in biological networks such as the switches of the cell cycle.
In mathematics, particularly in dynamical systems, a bifurcation diagram shows the values visited or approached asymptotically (fixed points, periodic orbits, or chaotic attractors) of a system as a function of a bifurcation parameter in the system. It is usual to represent stable values with a solid line and unstable values with a dotted line, although often the unstable points are omitted. Bifurcation diagrams enable the visualization of bifurcation theory. In the context of discrete-time dynamical systems, the diagram is also called orbit diagram.
The elastica theory is a theory of mechanics of solid materials developed by Leonhard Euler that allows for very large scale elastic deflections of structures. Euler (1744) and Jakob Bernoulli developed the theory for elastic lines (yielding the solution known as the elastica curve) and studied buckling. Certain situations can be solved exactly by elliptic functions. Later elastica theory was generalized together by the Cosserat brothers François and Eugene into a geometric theory with intrinsic directions at each point (1907). Elastica theory is an example of bifurcation theory. For most boundary conditions several solutions exist simultaneously. When small deflections of a structure are to be analyzed, elastica theory is not required and an approximate solution may be found using the simpler linear elasticity theory or (for 1-dimensional components) beam theory. A modern treatise of the planar elastica with full account of bifurcation and instability has been recently presented by Bigoni.
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 →The Greenwood District.