Thus, the columns of the matrices (e x, 0)) and (z(x)) form a fundamental system of solutions for equation (1) for (lambda = 0).
For (rhoinmathbb{R} backslash{ 0}) the columns of the matrix functions (e x, rho)) and (e x, -rho)) form a fundamental system of solutions for equation (1).
(i4): For (rhoinmathbb{R} backslash{ 0}) the columns of the matrix functions (e x, rho)) and (e x, -rho)) form a fundamental system of solutions for equation (1).
Therefore, these functions form a fundamental system of solutions of equation (3) for (lambda=lambda_{sjn}).
According to (10 - 13 10 - 13ll the discrete function (G^{g}) a generalized discrete Green's function and the system of functions (v^{g,1}), (v^{g,2}) a generalized fundamental system for the problem (5)-(6).
The implications of climate change and the end of the fossil fuel era suggest that we are entering a period of major, transformative, change requiring the restructure of the most fundamental systems for urban living.
So what is often a fundamental support system for others experiencing discrimination (racial, religious or otherwise) is that they can rely on family or larger cultural institutions to shore up their inner core to face the challenges presented to them in the face of discrimination, because the family understands, and has experienced, the discrimination.
The OPG/RANKL/RANK signaling pathway is a fundamental regulatory system for osteoclastogenesis.
The very analogous properties of a generalized Green's function and a biorthogonal fundamental system can be obtained for mth order discrete boundary value problems with m nonlocal conditions as well.
