Sentence examples for a generalized section from inspiring English sources

Chang et al. [6] obtained a Ky Fan minimax inequality for vector-valued mappings on W-spaces by applying a generalized section theorem and a generalized fixed point theorem.

Figure 5 shows a generalized stratigraphic section of the sedimentary sequence.

Theorem 3.5 generalizes [4, Theorem  2.3] in several aspects: Section 1(1) from -convex space to -space without linear structure; Section 1(2) from a -majorized mapping to a generalized -majorized mapping; Section 1(3) condition (ii) of Theorem 3.5 is weaker than condition (ii) of [4, Theorem  2.3].

In [5], Chen proved a Ky Fan minimax inequality for vector-valued mappings on H-spaces by using a generalized Fan's section theorem and a generalized Browder's fixed point theorem.

To this end, we present an acceptance-rejection method for simulating random vectors (X i,j,Y i,j ) T in Section 6.2, and a generalized polar method in Section 6.3.

2. As an application of these methods in theory of Fourier series, we will consider the degree of approximation in accordance with generalized deferred Cesáro means in a generalized Hölder metric in Section 2 and present some applications of the approach concerned with some sequence classes in Section 3.

In the next section, a generalized analog of the Heisenberg uncertainty inequality for the Euclidean motion group (M n)) is proved.

Figure 3 shows a simplified generalized stratigraphic section of the study area.

This section also includes the description of an exemplary problem (Section 3.1), and a generalized and simplified exhibition of Valiant's algorithm and its running time analysis (Section 3.3).

This section provides a generalized OPF problem description.

Equation (2.1) is a generalized difference equation (see [3, Section 21] and [11]).