Mild Solutions for Impulsive Integro-Differential Equations Involving Hilfer Fractional Derivative with almost Sectorial Operators

In this manuscript, we establish the mild solutions for Hilfer fractional derivative integro-differential equations involving jump conditions and almost sectorial operator. For this purpose, we identify the suitable definition of a mild solution for this evolution equations and obtain the existence results. In addition, an application is also considered.

Prefrontal Cortex Definitions and Their Use in Distinguishing Pornography Addicted Juveniles

Background and aims: Increasing popularity of Internet has exposed our children pornography addiction. As in other types of addiction, it affects a brain region known as prefrontal cortex (PFC), which is important in executive functions and inhibitory control. However, this region was loosely defined, and there was no consensus for that definition. We aimed to use volumetric MRI in finding the defining region of PFC which would be suitable in distinguishing pornography addicted juveniles. Methods: We enrolled 30 juveniles (12-16 y.o.) consisting of 15 pornography addiction and 15 non-addiction subjects. We proposed several models of PFC definition from mix-and-matched subregions, consisting of orbitofrontal (OFC), inferior frontal gyrus (IFG; pars orbitalis, opercularis, and triangularis), dorsolateral PFC (DLPFC), and anterior cingulate (ACC). Suitable PFC definition was defined as models which volume statistically different between both groups. Brain volumetric was measured using 3D-T1 3T MRI images and analyzed using FreeSurfer for automatic cortical reconstruction and brain segmentation (recon-all command). Results: We found significant differences between groups in 6 models, which mainly included OFC, ACC, and DLPFC, with models devoid of DLPFC had lowest mean differences. Conclusion: The most suitable definition of PFC for pornography addiction study should consist of OFC, ACC, and especially DLPFC. Inferior frontal gyrus pars orbitalis was not necessary for this purpose, but may increase effect size if it is included. Keywords: Addiction, Juvenile, Pornography, Functional Brain Imaging, Defining Area.

Speaking of Fake News

This chapter shows why defining “fake news” is worthwhile and what a suitable definition of “fake news” might look like. It begins by introducing the authors’ definition of “fake news” (§2) and employs it to set fake news apart from related phenomena that are often conflated with it (§3). It then extracts seven potential dimensions of the concept of fake news from the literature (§4) and compares the most representative definitions that have been proposed so far along those dimensions (§5). The chapter’s primary aims are (i) to enable a systematic evaluation of prevalent definitions with respect to their extensional scope, practical utility, and conceptual transparency, (ii) to demonstrate that there is more widespread agreement than one would think at the outset, and (iii) to show (in §6) that defining “fake news” is not only far from futile, but of vital importance to confront the epistemic threats posed by fake news.

Factor structure of intelligence and divergent thinking subtests: A registered report

Psychologists have investigated creativity for 70 years, and it is now seen as being an important construct, both scientifically and because of its practical value to society. However, several fundamental unresolved problems persist, including a suitable definition of creativity and the ability of psychometric tests to measure divergent thinking—an important component of creativity—in a way that aligns with theory. It is this latter point that this registered report is designed to address. We propose to administer two divergent thinking tests (the verbal and figural versions of the Torrance Tests of Creative Thinking; TTCT) with an intelligence test (the International Cognitive Ability Resource test; ICAR). We will then subject the subscores from these tests to confirmatory factor analysis to test which of nine theoretically plausible models best fits the data. When this study is completed, we hope to better understand whether the degree to which the TTCT and ICAR measure distinct constructs. This study will be conducted in accordance with all open science practices, including pre-registration, open data and syntax, and open materials (with the exception of copyrighted and confidential test stimuli).

Fuzzy Inner Product Space: Literature Review and a New Approach

The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Due to the emergence of various studies on fuzzy inner product spaces, it is necessary to make a comprehensive overview of the published papers on the aforementioned subject in order to facilitate subsequent research. Then we considered another approach to the notion of fuzzy inner product starting from P. Majundar and S.K. Samanta’s definition. In fact, we changed their definition and we proved some new properties of the fuzzy inner product function. We also proved that this fuzzy inner product generates a fuzzy norm of the type Nădăban-Dzitac. Finally, some challenges are given.

Some Remarks on Fuzzy Hilbert Spaces

The aim of this paper is to determine a suitable definition for the concept of fuzzy Hilbert space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Then we considered another approach to the notion of fuzzy inner product and analysed its properties.

A Simplified Fractional Order PID Controller’s Optimal Tuning: A Case Study on a PMSM Speed Servo

A simplified fractional order PID (FOPID) controller is proposed by the suitable definition of the parameter relation with the optimized changeable coefficient. The number of the pending controller parameters is reduced, but all the proportional, integral, and derivative components are kept. The estimation model of the optimal relation coefficient between the controller parameters is established, according to which the optimal FOPID controller parameters can be calculated analytically. A case study is provided, focusing on the practical application of the simplified FOPID controller to a permanent magnet synchronous motor (PMSM) speed servo. The dynamic performance of the simplified FOPID control system is tested by motor speed control simulation and experiments. Comparisons are performed between the control systems using the proposed method and those using some other existing methods. According to the simulation and experimental results, the simplified FOPID control system achieves the optimal dynamic performance. Therefore, the validity of the proposed controller structure and tuning method is demonstrated.

Analysis and Trends of Global Research on Nautical, Maritime and Marine Tourism

Tourism related to the sea and boating activities is becoming increasingly popular and revolves around a range of leisure, water sports, nautical or other maritime activities. This article studies the main scientific contributions in this area, bearing in mind the complexity of finding a suitable definition of this concept. Hence, the aim of this paper is to analyze the scientific production from 1986 to 2020 in impact journals of the terms “nautical tourism”, “maritime tourism” and “marine tourism” considering the following variables: number of documents, number of articles, period being studied, Hirsch citations and index. The results show an increasing trend in terms of both the number of published articles and citations publications from 2007 onwards and the review of the literature raises the need to define a new concept: “blue tourism”. Future trends in research include terms such as tourist ports, quality of websites and blue economy.

Extended conditional G-expectations and related stopping times

<p style='text-indent:20px;'>In this paper, we extend the definition of conditional <inline-formula> <tex-math id="M2">\begin{document}$ G{\text{-}}{\rm{expectation}} $\end{document}</tex-math> </inline-formula> to a larger space on which the dynamical consistency still holds. We can consistently define, by taking the limit, the conditional <inline-formula> <tex-math id="M3">\begin{document}$ G{\text{-}}{\rm{expectation}} $\end{document}</tex-math> </inline-formula> for each random variable <inline-formula> <tex-math id="M4">\begin{document}$ X $\end{document}</tex-math> </inline-formula>, which is the downward limit (respectively, upward limit) of a monotone sequence <inline-formula> <tex-math id="M5">\begin{document}$ \{X_{i}\} $\end{document}</tex-math> </inline-formula> in <inline-formula> <tex-math id="M6">\begin{document}$ L_{G}^{1}(\Omega) $\end{document}</tex-math> </inline-formula>. To accomplish this procedure, some careful analysis is needed. Moreover, we present a suitable definition of stopping times and obtain the optional stopping theorem. We also provide some basic and interesting properties for the extended conditional <inline-formula> <tex-math id="M7">\begin{document}$ G{\text{-}}{\rm{expectation}} $\end{document}</tex-math> </inline-formula>. </p>

Half-space Gaussian symmetrization: applications to semilinear elliptic problems

We consider a class of semilinear equations with an absorption nonlinear zero order term of power type, where elliptic condition is given in terms of Gauss measure. In the case of the superlinear equation we introduce a suitable definition of solutions in order to prove the existence and uniqueness of a solution in ℝ N without growth restrictions at infinity. A comparison result in terms of the half-space Gaussian symmetrized problem is also proved. As an application, we give some estimates in measure of the growth of the solution near the boundary of its support for sublinear equations. Finally we generalize our results to problems with a nonlinear zero order term not necessary of power type.