Sentence examples for some assumptions for from inspiring English sources

Here we list some assumptions for convenience.

Here are some assumptions for our model.

Some assumptions for this routing algorithm are as follows.

First, we give some assumptions for the kernel functions K ( x ).

First, under some assumptions for drive system, a kind of full-order observer-based synchronization method is summarized.

In this subsection, we recall that some notions of fractional calculus and give some assumptions for the stochastic system (1.1).

Under some assumption for the nonlinear terms and a priori estimates in Section 3, we prove that the initial value problem (2.8) of the nonlinear ordinary differential equations has global solutions in the interval ([0,T]).

As a matter of fact, it is known that if ∇f fails to be strongly monotone, and is only 1 L -ism, namely, there is a constant L > 0 such that 〈 x − y, ∇ f ( x ) − ∇ f ( y ) 〉 ≥ 1 L ∥ ∇ f ( x ) − ∇ f ( y ) ∥ 2, x, y ∈ C, under some assumption for γ or γ n, then algorithms (5) and (6) can still converge in the weak topology.

It has been found that some assumptions of Ramey are unsuitable for carbon dioxide injection.

The generalized Morrey spaces are defined with (r^{lambda}) replaced by a general non-negative function (varphi x,r)) satisfying some assumptions (see, for example, [5 8]).

The generalized Morrey spaces are defined with (r^{lambda}) replaced by a general nonnegative function (varphi x,r)) satisfying some assumptions (see, for example, [15, 23, 25, 30]).