DIFFERENTIAL EQUATIONS WITH GENERAL
... Much of the work mentioned above makes specific use of the fact that the number of points appearing in the boundary conditions is finite. In some cases, use is made of an increase in the dimensionality of the space while in other cases, the order of the differential system is raised. When it is obse ...
... Much of the work mentioned above makes specific use of the fact that the number of points appearing in the boundary conditions is finite. In some cases, use is made of an increase in the dimensionality of the space while in other cases, the order of the differential system is raised. When it is obse ...
One Step Equations review
... • Take out your TOC and Turn to your #2 and #3 assignments. Complete and problems you have not finished. Make needed corrections. • http://mccleskeyms.typepad.com/whittle/ ...
... • Take out your TOC and Turn to your #2 and #3 assignments. Complete and problems you have not finished. Make needed corrections. • http://mccleskeyms.typepad.com/whittle/ ...
BKL singularity
A BKL (Belinsky–Khalatnikov–Lifshitz) singularity is a model of the dynamic evolution of the Universe near the initial singularity, described by an anisotropic, homogeneous, chaotic solution to Einstein's field equations of gravitation. According to this model, the Universe is oscillating (expanding and contracting) around a singular point (singularity) in which time and space become equal to zero. This singularity is physically real in the sense that it is a necessary property of the solution, and will appear also in the exact solution of those equations. The singularity is not artificially created by the assumptions and simplifications made by the other well-known special solutions such as the Friedmann–Lemaître–Robertson–Walker, quasi-isotropic, and Kasner solutions.The Mixmaster universe is a solution to general relativity that exhibits properties similar to those discussed by BKL.