Sentence examples for functions under consideration from inspiring English sources

The functions under consideration are defined on an open subset of and take values in the Clifford algebra.

The functions under consideration are defined on (open subsets of) and take values in the Clifford algebra.

The functions under consideration are addition and multiplication because they form an algebraic commutative ring which contains a multiplicative inverse for every non-zero element.

We study the classical limit of these so-called Bohmian measures, in dependence on the scale of oscillations and concentrations of the sequence of wave functions under consideration.

Such estimates mainly depend on two facts: the set of functions under consideration (parts (a -(c) in Theorem 5.3), and the kind of estimate we are interested in, namely, pointwise estimate or uniform estimate (see equations (48) and (49), respectively).

Therefore the quantitative versions of (6.12) available require either a control on the size of the set where (|nabla f|) is small, see [40, 42], or further assumptions on the class of functions under consideration, see [12, Th. 1.3].

K0 is the least sensitive model parameter, and no objective function under consideration identified K0.

Open image in new window Fig. 10 Value of the objective function under consideration versus iteration number (single diode model).

Open image in new window Fig. 17 Value of the objective function under consideration versus iteration number (double-diode model).

We prove that the objective function under consideration is supermodular and monotonic, which guarantees near-optimal solutions for the greedy method.

We will obtain the first term of the asymptotics under assumptions that the function under consideration attains its minimum at a unique point and that the Hessian at the point is non-degenerate.