Sentence examples for for continuous cases from inspiring English sources

For continuous cases, there are also many related results.

For example, see [1 12] for continuous cases, and [13 20] for discrete cases.

Among them, Kangas et al. (2015) consider the stochastic multi-criteria acceptability analysis (SMAA) as a tool fit for discrete cases and stochastic goal programming for continuous cases including uncertainty.

Now we recall the invexity for continuous case as follows.

Yao [16] studied the existence and stability of almost periodic solutions for continuous case of equation (1.2).

ChaoWang and Zhongfu Ye [11] propose the brightness preserving histogram equalization with maximum entropy (BPHEME), which provides acceptable results for continuous case, but fails for discrete ones.

For example, Agarwal et al. [4] have established the existence of positive solutions for continuous case of the semipositone Sturm-Liouville BVPs.

This article introduces a new method for continuous case-based reasoning, and discusses its application to the dynamic selection, modification, and acquisition of robot behaviors in an autonomous navigation system, SINS (self-improving navigation system).

As a result, the importance of this paper is that we can enlarge conditions for the existence of the positive periodic solutions of predator-prey dynamic systems with Beddington-DeAngelis functional response for continuous case and for a general time-scale case.

Recently, existence theory for positive solutions of second-order boundary value problems on time scales has received much attention (see, e.g., [3 6] for general case, [7] for the continuous case, and [8] for the discrete case).

In a particular case when the matrix of linear terms is constant, a representation of the fundamental matrix given by a special matrix function (so-called delayed matrix exponential, etc)., for example, in [10, 11] (for a continuous case) and in [12, 13] (for a discrete case), can give concrete formulas expressing solution of the considered problem in analytical form.