We consider second order hyperbolic equations with unbounded Operator’s coefficients possessing time dependent domain of definition in a Hilbert space. Existence and uniqueness of the strong generalized solution are studied. The proofs rely on a generalization of the well known energy integral method. First, we derive a priori estimates for the strong generalized solutions with the help of Yosida Operator approximation. Then, using previous results, we show that the range of the Operators generated by the posed problem is dense.

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.

functional MRI is a noninvasive method in brain imaging. Localization, classification, prediction and connectivity are the most common issues. functional connectivity is a branch of fMRI that focuses on connectivity between voxels and ROIs. There are several methods for investigating functional connectivity such as correlation analysis. In any field, it is very important that results of any research have reliability according to the experiment. Any methods and measurement instruments need to be reliable. Without reliability, results are meaningless and our research is not trustworthy. Brain imaging can be used as a valuable tool for pre-surgical planning, so the results should be highly reproducible. Test-retest reliability can be explored using the intra-class correlation coefficient (ICC). I2C2 is an extent of ICC to verify the reliability in high-dimensional data as imaging studies. 13 subjects of testretest resting-state fMRI are used to investigate reliability. I2C2 of four ROIs are also computed (Caudate, Cingulate, Cuneus and Precentral regions). functional connectivity is found to have moderate reliability ranging 0. 6244 to 0. 6941. 95% confidence interval of I2C2 is calculated by nonparametric bootstrap in which CI of Caudate region I2C2 has the shortest length.

Introduction: This study aimed to assess the effect of controlled mouth breathing during the resting state using functional magnetic resonance imaging (fMRI). Methods: Eleven subjects participated in this experiment in which the controlled “, Nose”,and “, Mouth”,breathings of 6 s respiratory cycle were performed with a visual cue at 3T MRI. Voxel-wise seed-to-voxel maps and whole-brain region of interest (ROI)-to-ROI connectome maps were analyzed in both “, Nose>Mouth”,and “, Mouth>Nose”,contrasts. Results: As a result, there were more connection pairs in the “, Mouth”,breathing condition, i. e., 14 seeds and 14 connecting pairs in the “, Mouth>Nose”,contrast, compared to 7 seeds and 4 connecting pairs in the “, Nose>Mouth”,contrast (false discovery rate [FDR] of P<0. 05). Conclusion: The present study demonstrated that mouth breathing with controlled respiratory cycles could significantly induce alterations in functional connectivity in the resting-state network, suggesting that it can differently affect resting brain function,in particular, the brain can hardly rest during mouth breathing, as opposed to conventional nasal breathing.

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.

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