On weighted means and their inequalities

In (Pal et al. in Linear Multilinear Algebra 64(12):2463–2473, 2016), Pal et al. introduced some weighted means and gave some related inequalities by using an approach for operator monotone functions. This paper discusses the construction of these weighted means in a simple and nice setting that immediately leads to the inequalities established there. The related operator version is here immediately deduced as well. According to our constructions of the means, we study all cases of the weighted means from three weighted arithmetic/geometric/harmonic means by the use of the concept such as stable and stabilizable means. Finally, the power symmetric means are studied and new weighted power means are given.

Geometric properties of some applications of the Tremblay operator

By this research notes, the well-known Tremblay operator and certain core knowledge therewith are firstly introduced and an extensive result containing numerous (analytic and) geometric properties (of possible applications of the related operator) along with a number of special implications are then constituted. As method for proving, the well-known assertion proposed by [8] is also considered there.

Some results concerning the Tremblay operator and some of its applications to certain analytic functions

The aim of this scientific note is first to present certain information associated with the Tremblay operator in the complex plane and then to determine several results constituted by the related operator for certain analytic functions and also to point some implications of them out.

FUNCTIONAL VERSIONS OF SOME REFINED AND REVERSED OPERATOR MEAN INEQUALITIES

We present refined and reversed inequalities for the weighted arithmetic mean–harmonic mean functional inequality. Our approach immediately yields the related operator versions in a simple and fast way. We also give some operator and functional inequalities for three or more arguments. As an application, we obtain a refined upper bound for the relative entropy involving functional arguments.

The Automation-by-Expertise-by-Training Interaction

Objective: I introduce the automation-by-expertise-by-training interaction in automated systems and discuss its influence on operator performance. Background: Transportation accidents that, across a 30-year interval demonstrated identical automation-related operator errors, suggest a need to reexamine traditional views of automation. Method: I review accident investigation reports, regulator studies, and literature on human computer interaction, expertise, and training and discuss how failing to attend to the interaction of automation, expertise level, and training has enabled operators to commit identical automation-related errors. Results: Automated systems continue to provide capabilities exceeding operators’ need for effective system operation and provide interfaces that can hinder, rather than enhance, operator automation-related situation awareness. Because of limitations in time and resources, training programs do not provide operators the expertise needed to effectively operate these automated systems, requiring them to obtain the expertise ad hoc during system operations. As a result, many do not acquire necessary automation-related system expertise. Conclusion: Integrating automation with expected operator expertise levels, and within training programs that provide operators the necessary automation expertise, can reduce opportunities for automation-related operator errors. Application: Research to address the automation-by-expertise-by-training interaction is needed. However, such research must meet challenges inherent to examining realistic sociotechnical system automation features with representative samples of operators, perhaps by using observational and ethnographic research. Research in this domain should improve the integration of design and training and, it is hoped, enhance operator performance.