Sentence examples for singular functions of the from inspiring English sources

We also prove that the order of the error is doubled if we consider separately the regular part and the two first singular functions of the velocity and the pressure.

The SFM is a variant of the finite element method (FEM), where the space of trial and test functions is enriched by the singular functions of the SPP. We proved in the above mentioned work that the SFM is ε-uniformly convergent of optimal order in appropriate norms.

Accordingly, the exact role(s) the singular functions of CD4+CD28null could directly contribute to tissue injuries of IPF (or other chronic immunologic diseases [19] [34]) in situ cannot be deduced from highly reductionist in vitro studies of single isolated cell types.

Since the singular functions of elliptic problem of fourth order (bilaplacian with homogeneous boundary conditions) are explicitly known (see [1, 2]), we deduce the singularities of the velocity and the pressure [3].

This paper presents a framework for the dynamic identification of singular functions of an unknown DPS.

To improve the order of the convergence in the case of the crack, we need to add the two first singular functions to the discrete space of the velocity.

In particular, we complement famous Connes Trace Theorem by describing the asymptotics of the singular function of order −n classical pseudo-differential operators on an n-dimensional compact Riemannian manifold.

Recall that the set of left-singular functions of H 11, (left {U_{11}^{(l)} right }_{l=1}^{text {dim} mathcal {R}_{11}},) form an orthonormal basis for (mathcal {R}_{11}).

We handle the Strang and Fix algorithm [9] that permits one to add the first singular function to the discrete space of the velocity.

That is, we avoid numerical integration by making use of the explicit form of the singular functions in the computations of the stiffness matrix and the load vector.

The boundary element method uses singular functions to reduce the dimension of the domain by transforming the domain variables to boundary variables.