Sentence examples for a system of functions from inspiring English sources

Given a natural number valued function m and a system of functions encoded in a matrix H satisfying certain conditions, a construction procedure is described that produces an abstract GMRA with multiplicity function m and filter system H.

A system of functions is the basis of the, and the above-mentioned equality is equivalent to the condition below (2.12).

The completeness of a system of functions on a compact interval can be straightforwardly proved, while the difficult cases are dealing with the system of functions on unbounded intervals.

Accordingly, L 2 α is an F α -Hilbert space, which will also be denoted by H α. A system of functions { f n ( x ) } in H α is said to be an orthogonal system if ∫ a b f n ( x ) f m ( x ) d F α x = δ n, m. (29).

The system of trigonometrical functions, (3.4). is a system of orthonormal functions in.

This, its inverse f′: Y→X, and the two identity functions on respectively X and Y, form a system of four functions closed under composition.

Its applicability is performed via Theorem 4, where an important role is played by a system of initial functions (see Definition 3).

We developed a system of trigonometric functions of time in days that incorporated significant frequencies estimated by the multifrequential periodogram.

Proof Let { ω j ( x ) } be a system of base functions of W 0 1, p.

Proper choice of such a system of initial functions together with the application of Theorem 4 form the mainstay of the proof of Theorem 5.

Then for every there exists a unique system of functions such that (2.7).