Green matrix expression

If the matrix C is not singular, which requires the number of basis functions to match the number of solid harmonics used to expand the Green function, a local r-matrix is defined by t = —SC l. The consistency condition expressed above in terms of C and S matrices then reduces to the simple matrix expression... 

The Green matrix of this system can be given, by analogy with expression (4.37), as... 

Vayalil PK, Mittal A, Kara Y, Elmets CA, Katiyar SK (2004) Green tea polyphenols prevent ultraviolet light-induced oxidative damage and matrix metal-loproteinases expression in mouse skin. J Invest Dermatol 122 1480-1487... 

The matrix current Ib through the tunnel barrier can be expressed in terms of Green functions G and G+ at the left and right sides of the barrier by using the boundary condition [29],... 

Ahmed, S. et al. Green tea polyphenol epigallocatechin-3-gallate (EGCG) differentially inhibits interleukin-1 beta-induced expression of matrix metalloproteinase-1 and -13 in human chondrocytes. J Pharmacol Exp Ther. 308, 767, 2004. 

Now we can use these expressions to obtain some general properties of Green functions without explicit calculation of the matrix elements. Exchanging indices n and m in the expression (248) and taking into account that Em = En — e because of delta-function, we see that... 

This problem can be avoided by expressing the MST equations in terms of the square matrix S C = CVS, Hermitian in consequence of the surface-matching theorem. This matrix has full rank because it is contracted over the larger index lg. From the definitions of the C and S matrices, the matrix product S C is a specific integral involving the Helmholtz Green function [281],... 

The retarded and advanced Green functions can be expressed in terms of the electron propagator matrix that is supposed to be known from numerical calculations [55, 56]. Usually, it can be found, for example, from GAUSSIAN program [22] whose output provides all necessary information for the... 

In these expressions the Liouville space Green function matrix elements representing one-exciton coherence are... 

In terms of the familiar correlation functions, G and G<, the matrix equation for the super -Green function, is exactly the same as the following expression... 

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