Sentence examples for then under certain from inspiring English sources

Under certain circumstances, after the sampling part of that process is taken, if it's taken, in the county canvassing board's discretion, then under certain circumstances it is supposed to go forward with a more fulsome process.

Then, under certain limitations, specifications and performances of conventional interior permanent magnet synchronous (IPMS) motor, the preliminary performances of the recommended DESF motor are evaluated based on two-dimensional Finite Element Analysis (FEA).

In many cases there is a faithful conditional expectation E: Φ(A, η)→A; if A is tracial, then under certain assumptions on η, Φ(A, η) also has a trace.

Then, under certain differen control conditions, we establish strong convergence theorems on the composite iterative schemes.

Then, under certain assumptions, we show the exponential stability of the mild solution for the considered system in the mean square moment.

We also show (Theorem 6.1) that if (lambda> frac{mu}{K}) and (alpha>frac{deltalambda}{mutheta}), then, under certain conditions, the equilibrium (E_{3}) of system (1.2) is stochastically asymptotically stable.

The proposed models are first formulated as multi-level programming problems and then recast, under certain assumptions, as single-level mixed-integer linear or non-linear optimization problems using duality theory.

Then (maybe under certain additional conditions), for any given, there exist a solution of (6.6) and an such.

Xin and Zhang [20] established the global existence of the weak solution for the Camassa-Holm equation in the energy space H 1 ( R ) without imposing any sign conditions on the initial value, and the uniqueness of the weak solution was then obtained under certain conditions on the solution [21].

So only a woman's husband was permitted in his wife's marriage bed, and then only under certain circumstances.

Then, under some certain assumptions, the existence of fixed points for the given systems is proved and a free-type control sequence is designed to guarantee the best strategy profile reachable globally.