Sentence examples for a singular coefficient from inspiring English sources

Such a singular coefficient matrix does not occur for j = 2, so this will be our choice.

The consideration of using off-step nodal points for discretization is motivated by the polar form of one space Laplacian operator (nabla ^{2}equivpartial^{2}/partial r^{2}+(alpartial/partialpartial r)), which has a singular coefficient associated with the first-order derivative term.

The interest of this algorithm is the approximation of the solution and the leading singular coefficient which has a physical significance in the propagation of cracks.

(5) The regular part of the solution ({tilde{varphi}}_{R}) is in the space (H^{s+2}(Omega)) such that Vert {tilde{varphi}}_{R} Vert _{H^{s+2}(Omega)}+ vert lambda_{1} vert + vert lambda_{2} vert le C Vert f Vert _{H^{s-2}(Omega)}, where C is a positive constant and (lambda_{2}) is the second singular coefficient.

The solution of problem (1) is decomposed into the form (varphi=varphi_{R}+lambda S_{1}) such that (varphi_{R}in H^{s+2}(Omega ), s< 1+eta omega)) and Vert varphi_{R} Vert _{H^{s+2}(Omega)}+ vert lambda_{1} vert le C Vert f Vert _{H^{s-2}(Omega)}, where C is a positive constant, (lambda_{1}) is the first singular coefficient and S_{1}(r,theta)=r^{1+eta omega)} phi(theta).

We study the limit of the solution of linear and semilinear second order PDEs of parabolic type, with rapidly oscillating periodic coefficients, singular drift, and singular coefficient of the zeroth order term.

We do not impose any restrictions on the growth or the sign of the singular coefficient.

We also discuss the application of the proposed method to a wave equation with singular coefficients.

Using the non-smooth critical point theory we investigate the existence and multiplicity of solutions for a differential inclusion problem with singular coefficients involving the p(x -Laplacian.

Note the latest work [15] on this topic, where the Dirichlet problem for a three-dimensional elliptic equation with singular coefficients was investigated.

In order to use the truncation method for evaluating the singular coefficients, we consider a very small parameter eps > 0 to reduce the domain of integration by eliminating the singularity.