The Schwarz inequality and Jensen’s one are fundamental in a Hilbert space. Regarding a sesquilinear map B(X, Y ) = Y*X as an operatorvalued inner product, we discuss operator versions for the above inequalities and give simple conditions that the equalities hold.

In this investigation, using Opoola differential operator ($D^{m}(\mu,\beta,t)f(z)$), a new integral operator: $I_{t,\beta,\mu}^{m,\sigma}(f_{1},...,f_{n})(z): A^{n}\rightarrow A$  is defined in the unit disk, $U=\left\lbrace z\in C:\left|z\right|<1\right\rbrace$; and we investigated the Univalence conditions of this generalized operator. Finally, a number of corollaries and remarks which show the extension of our results are presented.

Introduction: Continuous monitoring of operator functional State is one of the most important topics and data mining methods are considered as a suitable tool for providing performance evaluation models. However, there has been no comprehensive study on the use of data mining methods in this field so far, and in so doing, the aim of the present article was to systematically review the role and importance of data mining methods to monitor the operator functional State in human-machine systems. Methods and Materials: A total of 86 published articles evaluated operator functional State were reviewed in five databases. All articles were analyzed in four groups related to operator functional State, three critical safety systems, and three types of data mining techniques. The operator functional State was also assessed through methods of physical measurement, psychophysiological measurement, task-performance indicators, and subjective judgment. Results: Most of the data mining models were related to the field of road and air transportation, which are mainly focused on fatigue and task-performance indicators. Support vector machine and neural network models were the most frequently used data mining methods. The results showed that most studies were performed on fatigue models, among the functional States where mainly physical measurements were used; however, to psychophysiological measurements were the most frequently measurement method applied to mental workload models and task performance indicators. Conclusion: A comprehensive evaluation of data mining methods and the parameters used in these models to assess the operator functional State will identify research gaps in this area and conduct more extensive studies to improve human performance.

Application of regulators in production of pot plants have been increasing due to lowering growth, improving branching and the number of flowering branches. In order to study the effect of levels and application method of trinexapac-ethyl regulator on height control and morphophysiological characteristics and flowering of Zinnia elegans, a factorial experiment based on completely randomized design with three replications was performed. Zinnias seedlings were planted in polyethylene pots and subjected to trinexapac-ethyl with levels of zero, 2×10-3, 1×10-3, 0.5×10-3 and 4.5×10-4 g when the first bud emerged. Trinexapac-ethyl was applied in both foliar spray and soil application. According to the results, 1×10-3 and 2×10-3g trinexapac-ethyl caused significant reduction in plant height. As trinexapac-ethyl level increased, number of branches and flowers were increased accordingly most of which was under the latter treatment. Branch length and leaf number was not affected. The concentrations 1×10-3 and 2×10-3g increased chlorophyll and shoots sugars, but not on root. Similarly, soil application of Trinexapac-ethyl did not showed positive effects. In light of obtained results, foliar spray application of Trinexapac-ethyl may serve as a suitable way to produce dwarf and pot Zinnia elegans  ‘State fair mix’. Based on the obtained results, application of Trinexapac-ethyl as foliar application can control and reduce the height of the Zinnia elegans ‘State fair mix’.

A generalized integral operator of order $\alpha$ of a real function $f$  including a parameter set $P$, namely $K_P^\alpha f(t)$ has been introduced by O. P.  Agrawal  (Computers and Mathematics with Applications, 59 (2010) 1852--1864), which is a generalization of some important fractional integrals such as the Riemann-Liouville fractional integral. Using pseudo-analysis, this paper introduces a pseudo-operator integral of order $\alpha$ including a parameter set $P$  in a semiring $([a, b], \oplus, \odot)$, which is  a generalization of  $K_P^\alpha f(t)$. We also discuss some particular cases and we obtain the well-known H\"{o}lder's and Minkowski's  inequalities  for this kind of pseudo-operator integral. The results given in this paper provide a generalization of several inequalities obtained in earlier studies.