Sentence examples for considerably more general from inspiring English sources

Note that in [6] the above results were generalized to the case of considerably more general operator ideals.

Later Krein [42] generalized the trace formula to a considerably more general situation when A is an arbitrary self-adjoint operator and B is a trace class perturbation of A. Let A be a self-adjoint operator on Hilbert space and let B be a perturbed self-adjoint operator with (A-Bin {varvec{S}}_1).

Note that Theorem 2.4.1 was used in [10] to obtain considerably more general trace formulae.

The analysis of this section can be extended to Markov chains on considerably more general spaces than ℝ along the lines of [12, 13, 16].

The power of the operator-theoretic approach lies in the fact that the conclusions of this paper are valid for considerably more general models than those actually used herein.

In the special case when (k = 1), equation (1.1) reduces to a quasilinear Poisson equation, as the matrix A can then be absorbed in the scalar B and considerably more general results for arbitrary smooth domains (Omega ) follow from the classical Schauder theory [7].

Topic 8 sounds considerably more generic and is consistent with burglary in general.

We do not discuss these works further, except to make the observation that things can change considerably in these more general scenarios.

Single world justification models were developed considerably before the more general possible world justification models we have been discussing, (Mkrtychev 1997).

First, there was considerably more variation in general in the all-cause mortality effects by region.

But lawyers said it would be considerably more difficult now for General Vides to avoid such an order.