Sentence examples for composition of operators from inspiring English sources

In this paper we propose a general framework which formalizes a KD process as an algebraic expression, that is, as a composition of operators representing elementary operations on two worlds: the data and the model worlds.

The solvability criterion for the problem (4.29) has the form (in computations below we need a composition of operators and the order of operations is following the inner operator which acts to matrices and vector function having an argument denoted by and the outer operator which acts to matrices having an argument denoted by (4.30).

The operation in the algebra is the usual composition of operators; we will omit the composition sign.

Thus, as pointed out by Hailperin (1986), it seems likely that this established notation convention handed Boole his definition of multiplication of elective symbols as composition of operators.

Applications to the Hardy Littlewood maximal operator, the Hilbert transform and composition of operators are also given.

For example, (ii Mutation removes a branch of a function and replaces it with another composition of operators of the same type.

In many cases, we need to study or to use the compositions of operators.

There are recommended compositions of operators; for example, it is useful to apply a windowing function to each frame after a Split: Note that this heuristics can be generalized to any operator which does not alter the type of its input (usually a signal, "t:a").

As an application, we develop some estimates for homotopy operator T, Green's operator G and the composition of the operators T ∘ G. Inequalities for the other class operators and composition operators can be obtained similarly.

The composition formula of operators are given by [156].

As stated in the following two theorems, the composition of fractional operators behaves well if the inner operator is a fractional difference.