In this paper, the special attention is given to the  product of two  modular operators, and when at least one of them is EP, some interesting results is made, so the equivalent conditions are presented  that imply  the product of operators is EP. Also, some conditions are provided, for which the reverse order law is hold. Furthermore, it is proved  that $P(RPQ)$ is idempotent, if $RPQ$†</...

A bounded linear operator on a Hilbert space $${\mathcal {H}}$$ is said to be an EP (hypo-EP) if ranges of and $$A^*$$ are equal (range contained in range ) has closed range. In this paper, we define hypo-EP operators for densely defined spaces extend results from settings (possibly unbounded) settings.

Abstract Genetic programming (GP) automatically designs programs. Evolutionary (EP) is a real-valued global optimisation method. EP uses probability distribution as mutation operator, such Gaussian, Cauchy, or Lévy distribution. This study proposes hyper-heuristic approach that employs GP to design different operators for EP. At each generation, the algorithm can adaptively explore search space...

We focus on two problems relating to the question of when product posinormal operators is posinormal, giving (1) necessary conditions and sufficient for have closed range, (2) commuting closed-range be with range. also discuss relationship between EP (as well as hypo-EP operators), concluding a new proof Hartwig–Katz Theorem, which characterizes Cn posinormal.

Evolutionary artiicial neural networks (EANNs) refer to a special class of artiicial neural networks (ANNs) in which evolution is another fundamental form of adaptation in addition to learning. The evolution in EANNs is often simulated by genetic algorithms (GAs), evolutionary programming (EP), or other evolutionary algorithms. This paper describes an EP-based EANNs which learn both their weigh...

In the Evidential Probability (EP) (Kyburg and Teng 2001) framework, interval-valued probabilities are assigned to events given a knowledge base containing statements about logical relationships of classes of objects as well as statements about relative frequencies pertaining to some of those classes. We are interested in the robustness of this inference with respect to perturbations in the giv...