Sentence examples for existence of a singular from inspiring English sources

Property 3 follows from the first two properties: The compactness of H ij, established in Property 1, implies the existence of a singular system, since there exists a singular system for any compact operator (see Section 16.1 of [32]).

Detailed testing also revealed the existence of a singular time step at which the instability level is minimized, independently of numerical dispersion.

The existence of a singular region as well as the nature of the state feedback law (static or dynamic) is completely characterized in terms of the system dynamics.

In fact, we do not exclude the possibility of existence of a singular component along the line L={x 1=x 2≥0}, i.e. it may happen that P(X 1=X 2)>0.

We give a necessary and sufficient condition on a positive compact operatorTfor the existence of a singular trace (i.e. a trace vanishing on the finite rank operators) which takes a finite non-zero value onT.

The existence of a singular region as well as the nature of the feedback law (static or dynamic) are completely characterized in terms of the Lie bracket structure of the system dynamics.

In the sixth paper entitled, "Existence of positive solutions of a singular nonlinear boundary value problem," R. Ma and J. Li have showed the existence for a singular ordinary differential equation by using topological degree and global bifurcation theorem due to Rabinowitz.

Motivated by the existence of a universal singular stress field at bimaterial interface corners, a fair amount of work has been performed to support the use of the corresponding critical stress intensities to correlate fracture initiation.

We propose an approach to correlate fracture initiation at three-dimensional bimaterial interface corners based on the existence of a universal singular stress field in the context of linear elasticity.

Among women, special mention must be made of the existence of a strikingly singular pattern, not in evidence for any other tumors and marked by excess risk in towns situated in the Salamanca area and Extremaduran Autonomous Region.

However, there are few papers to deal with the existence of a high-order singular differential equation system boundary value problem, especially with Riemann-Stieltjes integral boundary condition.