The KED model universe incorporates an additive, [p.sub.2] = -[[rho].sub.2][c.sup.2]/3, to the equation of state that describes the total energy integral, often treated as a special case of 'quintessence'.
In the paper (Sapar, 1964) a number of analytical formulae, including for the universe with matter, radiation, and the kinetic energy integral in the flat space, were derived.
Summing up, in our model universe dark matter and dark energy have been replaced by a single and well understood physical parameter--the total energy integral in the space.
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the energy integral of the Brownian particle and dx = 1/N [[PI].sub.t] dx(t) is symbolically a product of Lebesgue measures dx(t) and N is a normalized constant.
Similar to (1.1) we consider the following energy integral:
Then we see that the above one-loop energy integral of the photon gives the mass-energy parameter [omega] of electron which gives the mass m of electron.
In this article, a higher-order system of dispersive evolution equations and the associated energy integral are used to study the energy balance across an undular bore.
The energy contained in a control volume of unit width above the interval [[x.sub.1], [x.sub.2]] is given by the energy integral E(h, u) associated with the shallow-water system (2).
In the next section we will derive a dispersive system of partial differential equations along with the corresponding energy integral. In Section 3, a finite difference method for solving the dispersive system is put forward.
If we prescribe a point charge (3D delta-function) then the energy integral
will be infinite.
The importance of null Lagrangians is highlighted by of recent research in the calculus of variations (polyconvex energy integrals
), nonlinear PDEs (compensated compactness), geometric function theory (quasiconformal deformations) and some areas of applied mathematics: nonlinear elasticity, material science and crystals (rank-one connections).
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