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The authors discover a new identity concerning differentiable mappings defined on m-invex set via fractional integrals. By using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized relative semi- m-(r;h1,h2)-preinvex mappings by involving generalized Mittag-Leffler function are presented. It is pointed out that some new special cases can be deduced from main results of the paper. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.

In this paper, the Cauchy-type problem for the Laplace equation was solved in the rectangular domain with the use of the Chebyshev polynomials. The purpose of this paper is to present an optimal choice of the regularization parameter for the inverse problem, which allows determining the stable distribution of temperature on one of the boundaries of the rectangle domain with the required accuracy.

The Cauchy-type problem is ill-posed numerically, therefore, it has been regularized with the use of the modified Tikhonov and Tikhonov–Philips regularization. The influence of the regularization parameter choice on the solution was investigated. To choose the regularization parameter, the Morozov principle, the minimum of energy integral criterion and the L-curve method were applied.

Numerical examples for the function with singularities outside the domain were solved in this paper. The values of results change significantly within the calculation domain. Next, results of the sought temperature distributions, obtained with the use of different methods of choosing the regularization parameter, were compared. Methods of choosing the regularization parameter were evaluated by the norm N_max.

Calculation model described in this paper can be applied to determine temperature distribution on the boundary of the heated wall of, for instance, a boiler or a body of the turbine, that is, everywhere the temperature measurement is impossible to be performed on a part of the boundary.

The paper presents a new method for solving the inverse Cauchy problem with the use of the Chebyshev polynomials. The choice of the regularization parameter was analyzed to obtain a solution with the lowest possible sensitivity to input data disturbances.

In this paper, the author introduces a degenerate exponential integral function and further studies some of its analytical properties. The new function is a generalization of the classical exponential integral function and the properties established are analogous to those satisfied by the classical function.

The methods adopted in establishing the results are theoretical in nature.

A degenerate exponential integral function which is a generalization of the classical exponential integral function has been introduced and its properties investigated. Upon taking some limits, the established results reduce to results involving the classical exponential integral function.

The results obtained in this paper are new and have the potential of inspiring further research on the subject.

This paper aims to solve inhomogeneous dielectric problems by matching boundary conditions at the interfaces among homogeneous subdomains. The capabilities of Hilbert transform computations are deeply investigated in the case of limited numbers of samples, and a refined model is presented by means of investigating accuracies in a case study with three subdomains.

The accuracies, refined by Richardson extrapolation to zero error, are compared to finite element (FEM) and finite difference methods. The boundary matching procedures can be easily applied to the results of a previous Schwarz–Christoffel (SC) conformal mapping stage in SC + BC procedures, to cope with field singularities or with open boundary problems.

The proposed field computations are of general interest both for electrostatic and magnetostatic field analysis and optimization. They can be useful as comparison tools for FEM results or when severe field singularities can impair the accuracies of other methods.

This static field methodology, of course, can be used to analyse transverse electro magnetic (TEM) or quasi-TEM propagation modes. It is possible that, in some case, these may make a contribution to the analysis of axis symmetrical problems.

The most relevant result is the possible introduction of SC + BC computations as a standard tool for solving inhomogeneous dielectric field problems.

The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition.

A weak convergence approach is adopted to establish the Laplace principle, which is same as the large deviation principle in a Polish space. The sufficient condition for any family of solutions to satisfy the Laplace principle formulated by Budhiraja and Dupuis is used in this work.

Freidlin–Wentzell type large deviation principle holds good for the solution processes of the stochastic functional integral equation with nonlocal condition.

The asymptotic exponential decay rate of the solution processes of the considered equation towards its deterministic counterpart can be estimated using the established results.

The purpose of this paper is to propose a semiparametric estimator for the tail index of Pareto-type random truncated data that improves the existing ones in terms of mean square error. Moreover, we establish its consistency and asymptotic normality.

To construct a root mean squared error (RMSE)-reduced estimator of the tail index, the authors used the semiparametric estimator of the underlying distribution function given by Wang (1989). This allows us to define the corresponding tail process and provide a weak approximation to this one. By means of a functional representation of the given estimator of the tail index and by using this weak approximation, the authors establish the asymptotic normality of the aforementioned RMSE-reduced estimator.

In basis on a semiparametric estimator of the underlying distribution function, the authors proposed a new estimation method to the tail index of Pareto-type distributions for randomly right-truncated data. Compared with the existing ones, this estimator behaves well both in terms of bias and RMSE. A useful weak approximation of the corresponding tail empirical process allowed us to establish both the consistency and asymptotic normality of the proposed estimator.

A new tail semiparametric (empirical) process for truncated data is introduced, a new estimator for the tail index of Pareto-type truncated data is introduced and asymptotic normality of the proposed estimator is established.

In this world of complexity, disruption, multi-layered crises and insecurity, people seek orientation, stability and meaning. This desire exists in everyday life, in working environments and even more in vacation time. Therefore, the way we see the world and how we interact with each other and with nature should also be reflected by tourist destinations. ‘Destination Conscience’ seems to be a promising conception that offers the desired contemporary design of destination realities and travel experiences. Accordingly, destinations and their products should be characterised by authenticity, meaning, sensitivity and humaneness on all levels. In this chapter, the concept of ‘integral ecology’ as a holistic worldview and new paradigm is presented. Integral ecology can be a source of perception and wisdom that enriches the ‘conscience’ of a destination and all its actors. Hence, this chapter addresses the question of how integral ecology can contribute to Destination Conscience. The essay uses the methods of literature review, application, transfer and case study.

Firstly, the concept of integral ecology will be presented. In the second part, this worldview will be applied to destinations. The enrichment of Destination Conscience by the principles of integral ecology can manifest in the destination's self-image and in the interaction in business relations and business actions. It can find expression in the operational management, organisation and development of a destination and in the design of the touristic services and products. In the third part, the case study of a Catholic monastery in the Altmühltal will be presented for further illustration.

The purpose of this paper is to introduce a numerical investigation used to calculate the J-integral of the main crack behavior emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in (TiB/Ti) functionally graded material (FGM) plate subjected to tensile mechanical load.

For this purpose the variations of the material properties are applied at the integration points and at the nodes by implementing a subroutine USDFLD in the ABAQUS software. The variation of the J-integral according to the position, the length and the angle of rotation of cracks is demonstrated. The variation of the J-integral according to the position, the length and the angle of rotation of cracks is examined; also the effect of different parameters for double notch FGM plate is investigated as well as the effect of band of FGM within the ceramic plate to reduce J-integral.

According to the numerical analysis, all parameters above played an important role in determining the J-integral.

The present study consists in investigating the simulation used to calculate the J-integral of the main crack behavior emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in (TiB/Ti) FGM plate under Mode I. The J-integral is determined for various load applied. The cracked plate is joined by bonding an FGM layer to TiB plate on its double side. The determination of the gain on J-integral by using FGM layer is highlighted. The calculation of J-integral of FGM’s involves the direction of the radius of the notch in order to reduce the J-integral.

This paper aims to introduce a non-invasive and convenient method to detect a life-threatening disease called aortic dissection. A Bayesian inference based on enhanced multi-sensors impedance cardiography (ICG) method has been applied to classify signals from healthy and sick patients.

A 3D numerical model consisting of simplified organ geometries is used to simulate the electrical impedance changes in the ICG-relevant domain of the human torso. The Bayesian probability theory is used for detecting an aortic dissection, which provides information about the probabilities for both cases, a dissected and a healthy aorta. Thus, the reliability and the uncertainty of the disease identification are found by this method and may indicate further diagnostic clarification.

The Bayesian classification shows that the enhanced multi-sensors ICG is more reliable in detecting aortic dissection than conventional ICG. Bayesian probability theory allows a rigorous quantification of all uncertainties to draw reliable conclusions for the medical treatment of aortic dissection.

This paper presents a non-invasive and reliable method based on a numerical simulation that could be beneficial for the medical management of aortic dissection patients. With this method, clinicians would be able to monitor the patient’s status and make better decisions in the treatment procedure of each patient.

This study aimed to assess the potential of the Clinical Dementia Rating (CDR) Scale in the prognosis of dementia in elderly subjects.

Dementia staging severity is clinically an essential task, so the authors used machine learning (ML) on the magnetic resonance imaging (MRI) features to locate and study the impact of various MR readings onto the classification of demented and nondemented patients. The authors used cross-sectional MRI data in this study. The designed ML approach established the role of CDR in the prognosis of inflicted and normal patients. Moreover, the pattern analysis indicated CDR as a strong cohort amongst the various attributes, with CDR to have a significant value of p < 0.01. The authors employed 20 ML classifiers.

The mean prediction accuracy varied with the various ML classifier used, with the bagging classifier (random forest as a base estimator) achieving the highest (93.67%). A series of ML analyses demonstrated that the model including the CDR score had better prediction accuracy and other related performance metrics.

The results suggest that the CDR score, a simple clinical measure, can be used in real community settings. It can be used to predict dementia progression with ML modeling.