Sentence examples for in the generalizations from inspiring English sources

The interest in the generalizations of a random fixed point theorem from self-maps to nonself-mappings has been revived after the papers by Sehgal and Waters [6], Sehgal and Singh [7], Papageorgiou [8, 9], Lin [10, 11], Xu [5], Tan and Yuan [12] and Beg and Shahzad [13] and has received much attention in recent years (see, e.g., [14 24]).

This study resulted in the generalizations that GTA ratings are not impacted by undergraduate student major and gender of the GTA, yet they are influenced by degree held (higher degrees result in higher ratings), teaching experience, and GTA age (those in their late twenties are rated higher than those in their early twenties; Bos et al., 1980).

"Precious Mirror" corresponds to the final stage in the generalization of the northern Chinese technique of tian yuan ("method of the celestial unknown"), a kind of algebraic computation performed with counting rods to solve problems.

This will help in the generalization of piezo-actuator usage for smart applications.

This is the technical insight in the generalization of Theorem 4 in Sect. 4.

Verifiable hypotheses employ conventional elements in the generalization process and may presuppose the (empirical) principle of induction.

The primary goal of this paper does not consist in the generalization of these results.

Different kinds of Variables: Invariance theories distinguish two kinds of variables: (1) Explicit variables, that figure explicitly in a generalization and (2) background variables, that describe background conditions which are not mentioned in the generalization in question.

Hua and Sun [12] have proved that the Gaussian kernel provide superior performance in the generalization ability and convergence speed.

In stability/invariance accounts, generalizations which are qualified by a cp-clause are considered to be non-strict in the sense that they do not quantify over all possible values of the variables occurring in the generalization.

In the generalization presented in the following sections the magnetic field will be represented by a dipole moment m̱ and a quadrupole moment Q͇.