We approximate the solution in the form u N ( x ) = ∑ j = 0 N a j L t, j ( x ), then, making use of formula (13) enables us to express explicitly the derivatives D ν u ( x ), D δ 1 u ( x ), …, D δ k u ( x ) in terms of the expansion coefficients a j and the shifted Legendre polynomials.
To avoid dealing with singular matrix C1 in (2), which does not enable us to express explicitly x(T), it is useful to carry out the following parametrization x 2 ( T ) = λ, (4).
It can be seen from the above derivation that the separation of structure recovery from noise amplification in the VanCittert expression is the key that enables us to express noise amplification factor in the kth iteration to be F k /F k−1, which is always between 1 and 2 for all k.
This paper enables us to express various behavior of the compression wave by using analytical solutions with the phase velocity and the spatial absorption coefficient.
In other words, like its predecessor, "Moral Clarity" is a sustained defense of a particular set of values, and of a moral vocabulary that enables us to express them.
This enables us to express the distribution of the received power by (6).
This enables us to express important distinctions concerning the logic of time and existence.
