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Minkowski space is a four-dimensional space possessing a Minkowski metric, i.e., a metric tensor having the form dtau^2=-(dx^0)^2+(dx^1)^2+(dx^2)^2+(dx^3)^2. Alternatively ...

The motivating force of topology, consisting of the study of smooth (differentiable) manifolds. Differential topology deals with nonmetrical notions of manifolds, while ...

Dual pairs of linear programs are in "strong duality" if both are possible. The theorem was first conceived by John von Neumann. The first written proof was an Air Force ...

For discrete problems in which no efficient solution method is known, it might be necessary to test each possibility sequentially in order to determine if it is the solution. ...

Given two circles, draw the tangents from the center of each circle to the sides of the other. Then the line segments AB and CD are of equal length. The theorem can be proved ...

Let the elements in a payoff matrix be denoted a_(ij), where the is are player A's strategies and the js are player B's strategies. Player A can get at least min_(j<=n)a_(ij) ...

The hazard function (also known as the failure rate, hazard rate, or force of mortality) h(x) is the ratio of the probability density function P(x) to the survival function ...

Find the tunnel between two points A and B on a gravitating sphere which gives the shortest transit time under the force of gravity. Assume the sphere to be nonrotating, of ...

The standard Lorentzian inner product on R^4 is given by -dx_0^2+dx_1^2+dx_2^2+dx_3^2, (1) i.e., for vectors v=(v_0,v_1,v_2,v_3) and w=(w_0,w_1,w_2,w_3), ...

Generally speaking, a Green's function is an integral kernel that can be used to solve differential equations from a large number of families including simpler examples such ...