The basic idea is to use a local analytic representation valid near the particle and to match it to an external field calculated by a standard finite-difference (or finite-element) method.
The basic idea is to use a local analytic representation valid near the particle to "transfer" the no-slip condition from the particle surface to the adjacent grid nodes.
An important assumption underlying the use of both photographic and computer rendered visualizations is that human viewers' responses to these representations provide valid indications of perceptions and judgments made in response to direct experience with the landscape conditions nominally represented.
We did, however, obtain consistent information from the different respondents, in addition to document analyses that corroborated information from key informant interviews, suggesting that respondents' representations were valid.
That belief, along with its architectural representation, remains valid in the case of government institutions.
This representation is valid when α is not a negative integer and p is not an integer.
This spectral representation is valid provided there exists M > 0 such that ∥∑i = 1NPi ∥ ⩽ M, N = 1, 2, …, and generalizes results that apply to self-adjoint, normal, and spectral operators.
Thus, the proposed invariant representation is valid for both dielectric and metal objects, and is much more robust under a variety of illumination effects than the observed reflectance data.
We first show that the following representation is valid for each (f in W^{-1,p(x)}(Omega, mathrm{C}ell_{n})): TQ_{a}Bwidetilde{T}f= u + TQ_{a}Bpi.
Lemma 1 Assume that the function q ( x, y ) solves the modified Helmholtz equation (1.1) in the upper half z-plane Ω, and that it satisfies the Dirichlet boundary conditions (1.2), then the integral representation is valid: q = β 2 π ∫ 0 ∞ e i β ( k z − z ¯ k ) ( k + 1 k ) D ( k ) d k k, (2.1).
