Sentence examples for provided that the equation from inspiring English sources

provided that the equation defines a fuzzy.

If (f:[0,+infty)rightarrow E^{n}), then the Riemann-Liouville fractional derivative of order (0

If the fuzzy function t ↦ ∫ 0 t ( t − s ) − q y ( s ) d s is Hukuhara differentiable on [ 0, a ], then we define the fractional derivative of order q ∈ ( 0, 1 ) of y by D q y ( t ) = 1 Γ ( 1 − q ) d d t ∫ 0 t ( t − s ) − q y ( s ) d s, provided that the equation defines a fuzzy number D q y ( t ) ∈ E n.

The proposed model addresses a network of routers supporting any Active Queue Management AQMM) techniques, provided that the equations describing the AQM rules implemented in the routers are introduced in the fluid framework.

By the techniques of impulsive analysis, we obtain the existence of stable invariant manifolds for the impulsive perturbed equation provided that the linear equation admits a ρ-nonuniform exponential dichotomy and f, g are sufficiently small Lipschitz perturbation.

provided that equation defines a fuzzy.

Regarding that z i has n states, then u 0 can be considered with n terms provided that equation (22) would be established as follows: u 0 = ∑ i = 1 n u i. (22).

A self-similar solution for comminuted particles is shown to be a useful representation for the solution of the population balance equation provided that this equation is solved over a sufficiently long time interval.

But we can choose any order of moment β provided that the integral in Equation (9) exists.

The scheme conserves both momentum and kinetic energy for inviscid flow with the exception of the time marching error, provided that the discrete continuity equation is satisfied.

As a result, provided that the conditions for Equation 5 are met, for the given offset frequency Δ f, transmitter power, and modulation pulse shape, the average interference power is proportional to the symbol rate raised to the power of 2n.