The Tetrad, with its fourfold M�bius topological structure of enhancement, reversal, retrieval and obsolescence, is mobilized by McLuhan and Powers to illuminate the media or technological inventions of cash money, the compass, the computer, the database, the satellite, and the global media network.
32.
In this coordinatization, which has a distorted geometry from the standard diamond cubic structure but has the same topological structure, the vertices of the diamond cubic are represented by all possible 3d grid points and the edges of the diamond cubic are represented by a subset of the 3d grid edges.
33.
In physics, a "'spinfoam "'or "'spin foam "'is a topological structure made out of two-dimensional faces that represents one of the configurations that must be summed by functional integration to obtain a Feynman's path integral description of quantum gravity.
34.
Indeed, several classic results in random graph theory show that even networks with no real topological structure exhibit the small-world phenomenon, which mathematically is expressed as the diameter of the network growing with the logarithm of the number of nodes ( rather than proportional to the number of nodes, as in the case for a lattice ).
35.
Let ( \ Omega, \ mathcal F, \ mathfrak P ) be a probability space, and let the random variables " X ", " Y ", and " Z " each be defined as a Borel-measurable function from \ Omega to some state space endowed with a topological structure.
36.
However, contrary to the topological structure which is unique ( topologically, there is only one way to make the real line " longer " at either end ), the differentiable structure is not unique : in fact, for each natural number " k " there exist infinitely many " C k + 1 " or " C & infin; " structures on the long line or ray inducing any given " C k " structure on it.
37.
Traditional envelope theorem derivations use the first-order condition for ( 1 ), which requires that the choice set X have the convex and topological structure, and the objective function f be differentiable in the variable x . ( The argument is that changes in the maximizer have only a " second-order effect " at the optimum and so can be ignored . ) However, in many applications such as the analysis of incentive constraints in contract theory and game theory, nonconvex production problems, and " monotone " or " robust " comparative statics, the choice sets and objective functions generally lack the topological and convexity properties required by the traditional envelope theorems.
