Sentence examples for conditions to the case of from inspiring English sources

We give a generalization of the two previous options of finding of the stabilization conditions to the case of the system (1), (2).

Two variants of this new method are developed by adapting two existing algorithms, suitable for prescribed velocity boundary conditions, to the case of prescribed normal and tangential stresses at the free boundary.

This relationship, which is a generalization of equilibrium conditions to the case of a chemical process occurring in a nonequilibrium steady state in dilute solution, provides a novel equivalent definition for chemical reaction free energy.

Journal 51, 3028 3038]] and extends the bifurcations condition to the case of moving fronts.

Basically it took four decades to extend the contractive condition to the case of mappings with Lipschitz constant (k =1).

When we relax the contraction condition to the case of the Lipschitz constant equal to 1, i.e., nonexpansive mapping, the completeness of the distance will not be enough as it was in the original case.

The main result of this paper is a complete and rigorous derivation of the generalisation of the classical Courant–Friedrichs Lewy stability condition to the case of dynamic piezoelectricity for variational difference schemes.

Using classical fixed point theory one needs strong conditions to establish the case of FDEs and therefore restrict the applicability to certain classes of FDEs and their systems.

In the modeling, we used data from [16] for temperature dependence of silver ions diffusion coefficient and the approach and numerical data presented in [4, 20] to formulate initial conditions corresponding to the case of hydrogen processing of the poled glass.

Of course, if, then ; so the conditions (2.1)–(2.4) reduce to the case of conjugate parameters.

More recently, some boundary value problems with eigenparameter in boundary and transmission conditions were extended to the case of two, more than two or a finite number of transmissions in [43 47] and the references therein.