X = ⋃ i = 1 m A i is a cyclic representation of X with respect to f; for any x ∈ A i, y ∈ A i + 1, i = 1, 2, …, m, φ ( d ( f x, f y ) ) ≤ ϕ ( φ ( d ( x, y ) ) ), where A m + 1 = A 1. By using the above concept, Chen established the following fixed point theorem.
Now, we use the above concept to derive the numerical method for quasi-linear equation (1.1).
Using the above introduced concepts the formal definition of clustering coefficient is given by Formula 3.
Using the above introduced concepts and definitions, we now state our main theorem.
Using the above described concepts of separability, reducibility, and lifting, the CS with muting INLP formulation in (15) can be reformulated as an ILP, which can be efficiently solved by commercial solvers.
In this scheme, Kûkai is adamant in using the above-discussed concepts to distinguish esoteric from exoteric Buddhism.
As proof-of-concept, deposition of layered, composite and functionally graded coatings using the above system is also demonstrated using appropriate case studies.
Using the above method: 10x/2 = 5x.
Although emotional reactivity and anxiety are not synonymous, because they consist of a number of components that appear to be genetically independent [ 7], it is not possible to distinguish between the two concepts using the above-mentioned test paradigms and so we use the term "emotional reactivity" throughout this manuscript.
