Sentence examples for in the case of function from inspiring English sources
However, the R 2 test in the case of function (7) has provided a result equal to 0.81.
The explicit formulation of relations in Eq. (5), or equivalently in Eq. (6), can be expressed in closed form in the case of function (vartheta left( cdot right)) (whose details are provided in Sect. 3) and function (gamma left( cdot right)) (whose formulation is provided in Eq. 3).
Since then, many studies have been done to prove the ASCLT in different situations, for example, in the case of function-typed almost sure central limit theorem (FASCLT) (see Berkes et al. [3], Ibragimov and Lifshits [4]).
This is unfortunately not true in the case of functions.
In this paper we prove this conjecture in the case of functions with one singularity.
For the sake of notational simplicity, these generalizations are described in the case of functions of two variables.
This was established in the case of functions of positive integers by Church and Kleene (Church 1936a, Kleene 1936).
In the case of functions derived from natural selection, he views a "virtuous" consequence as an adaptive consequence.
We already have the result of Hölder continuity for functions by Morrey lemma in the case of functions.
end{aligned}The following result proved in [47] plays the same role as fundamental inequality (1.4.2) in the case of functions of one self-adjoint operator.
Our starting point here is the following analogue of Theorem 3.1, where the novelty is that in the case of functions in (X^infty ), their samples are used for approximation.
