Sentence examples for approximation upon from inspiring English sources
We further show that with two different typical kernel functions the SPH approximation, upon satisfying the partition of unity property, is able to achieve very high-order of the integration error, which previously could be shown only with particles on a uniform grid.
The resulting equations, which are expressible in any system of coordinates and may be used through simultaneous approximation upon all the field variables in a direct method of solutions, pave the way to the study of important dislocation, fracture and interface problems of both elasticity and piezoelasticity of quasicrystal materials.
Spedding et al. [27] showed that predictions based upon fixed wing data agree well with quantitative observations of flapping flight in birds and that this approach "shows the simplest tenable baseline approximation, upon which more complex and realistic theories might be constructed".
Under the null hypothesis of homogeneity of risk over the 12-week period, the expected numbers of such deaths in weeks 1 + 2 would be so small that the large sample approximation, upon which the χ distribution is based, breaks down.
The treatment of bond polarizabilities use cluster approximation based upon special point.
Guinea et al. (1994) proposed the bilinear approximation based upon the cohesive crack model.
This happens because a truncation error in a finite-difference approximation depends upon the derivative of the variable as well as mesh spacing.
This happens because the truncation error in a finite-difference approximation depends upon the derivative of the variable as well as mesh spacing.
Our space deformation technique based on moving least squares approximation improves upon existing approaches in crucial aspects: It offers the same level of modeling flexibility as surface-based deformations, but it is independent of the underlying geometry representation and therefore highly robust against defects in the input data.
In this section, we derive a numerical approximation based upon the definition of newly proposed derivative of fractional order [4], _{0}^{CF} D_{t}^{alpha} bigl( f ( t ) bigr) = frac{M alpha)}{1-alpha} int_{0}^{t} f ' ( x ) exp biggl[ - alpha frac{t-x}{1-alpha} biggr],dx.
The latter is implied within the Thomas-Fermi approximation based upon the assumption that a local internal chemical potential of electrons (read the electrochemical potential or consequently the redox potential of an electrode) can be defined as a function of the electron concentration at that point.
