The verification of the conditions of Theorem 12 is also pretty much similar to the latter case.
Since this theorem eases difficulties in verification of the coercivity condition but requires conditions of a form similar to Lyapunov-type theorems for stochastic lumped-parameter systems, it has a potential application to other stochastic distributed-parameter systems.
The relationship between continuous variables will be analyzed with the Pearson correlation coefficient, and the relationship between two categorical variables will be analyzed with the chi-square test (after verification of the test conditions; if conditions are not met, Fisher's exact test will be used).
The safety standard presently set by the German Reaktor-Sicherheitskommission (Reactor Safety Commission) requires that the expected number of unfailed rods in the core during one cycle is at least N − 1, i.e., E(∑i≤N Xi) = ∑i≤N pi ≥ N − 1, whereby a confidence level of 0.95 for the verification of this condition is demanded.
The paper focuses on the issues of the application of the tools of technical diagnostics in verification of the technical condition of two-stage bevel-spur gearbox operating in difficult conditions of paper industry.
By application of the model to nanoscale grain growth in Ni P, Pb Zr, Fe Zr and Ru Al alloys, the validity of the present model was confirmed, in combination with verification of the initial condition of GB segregation.
If the overvaluing matrix (M ( A (cdot ) )) has its non-constant elements isolated in only one row, the verification of the Kotelyanski condition enables one to conclude to the stability of the initial system.
It is interesting to note that verification of the optimality condition (25) at any two neighboring points θ, (theta_{1}) is more convenient but not sufficient for its complete application (see Example 3).
The set Q should satisfy the transversality condition (v), i.e., it should have a fixed-point free boundary with respect to the solution mapping T. Since the direct verification of the transversality condition is usually a difficult task, we will devote this section to a bound sets technique which can be used for guaranteeing such a condition.
