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K/L capture; Isomeric. ... These equations need to be refined such that the notation is defined as has been done for the previous sets of equations. Name Equations
In fact computability can itself be defined via the lambda calculus: a function F: N → N of natural numbers is a computable function if and only if there exists a lambda expression f such that for every pair of x, y in N, F(x)=y if and only if f x = β y, where x and y are the Church numerals corresponding to x and y, respectively and = β ...
The cosmological constant was originally introduced in Einstein's 1917 paper entitled “The cosmological considerations in the General Theory of Reality”. [2] Einstein included the cosmological constant as a term in his field equations for general relativity because he was dissatisfied that otherwise his equations did not allow for a static universe: gravity would cause a universe that was ...
With sufficiently clever assumptions of this sort, it is often possible to reduce the Einstein field equation to a much simpler system of equations, even a single partial differential equation (as happens in the case of stationary axisymmetric vacuum solutions, which are characterized by the Ernst equation) or a system of ordinary differential ...
The equations are a set of differential equations – over time – of the probabilities that the system occupies each of the different states. The name was proposed in 1940: [ 1 ] [ 2 ] When the probabilities of the elementary processes are known, one can write down a continuity equation for W, from which all other equations can be derived and ...
This reflects the fact that the system is gauge invariant (in general, absent some symmetry, any choice of a curvilinear coordinate net on the same system would correspond to a numerically different solution.) A "gauge fixing" is needed, i.e. we need to impose 4 (arbitrary) constraints on the coordinate system in order to obtain unequivocal ...
In previous equations, a, ρ, and p are functions of time. k / a 2 is the spatial curvature in any time-slice of the universe; it is equal to one-sixth of the spatial Ricci curvature scalar R since = (¨ + ˙ +) in the Friedmann model.
The best-known example is the ADM formalism. [174] These decompositions show that the spacetime evolution equations of general relativity are well-behaved: solutions always exist, and are uniquely defined, once suitable initial conditions have been specified. [175] Such formulations of Einstein's field equations are the basis of numerical ...