Sentence examples for depend smoothly from inspiring English sources

where (3.15).,, are smooth functions in variables at least of the third order, and the coefficients depend smoothly on and.

The torque inputs depend smoothly on time, as our design of the minimized evaluation function of the QP formulation intended.

where (3.19). is smooth function in variables at least of order three, and all the coefficients depend smoothly on and.

We assume that the coefficients of the operator depend smoothly on u and satisfy (1.6), and (1.7) for some fixed (Lambda >0).

If the solution does not depend "smoothly" on the problem data, small variations on the data could create huge variations on the solutions, resulting in strong instability which is not acceptable.

Remark 1 Observe that, when ν < 0, ν ∉ ℤ, the right inverse even though is not unique and can be chosen to depend smoothly on the points x1,..., x m, at least locally.

However, when the solution depends smoothly on the random data, the WLe scheme exhibits superior convergence.

We consider a family of short range, quantum spin Hamiltonians H s) depending smoothly on a parameter s in [0, 1].

Combined with the fact that the model depends smoothly on all parameters, all these bifurcations are structural.

As in the previous section, observe that the function being obtained as a fixed point for contraction mapping, depends smoothly on the parameters and the points.

A is a linear strongly elliptic self-adjoint partial differential operator of second order with coefficients depending smoothly on the spatial variables, and C ( t, τ ) is an arbitrary second-order linear partial differential operator, with coefficients depending smoothly on both time and spatial variables in the closure of their respective domains; B is a suitable continuous operator.