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This paper aims to study fractional Brownian motion and its applications to nonlinear stochastic integral equations. Bernstein polynomials have been applied to obtain the numerical results of the nonlinear fractional stochastic integral equations.

Bernstein polynomials have been used to obtain the numerical solutions of nonlinear fractional stochastic integral equations. The fractional stochastic operational matrix based on Bernstein polynomial has been used to discretize the nonlinear fractional stochastic integral equation. Convergence and error analysis of the proposed method have been discussed.

Two illustrated examples have been presented to justify the efficiency and applicability of the proposed method. The corresponding obtained numerical results have been compared with the exact solutions to establish the accuracy and efficiency of the proposed method.

To the best of the authors’ knowledge, nonlinear stochastic Itô–Volterra integral equation driven by fractional Brownian motion has been for the first time solved by using Bernstein polynomials. The obtained numerical results well establish the accuracy and efficiency of the proposed method.

The collection of chapters in this 30th volume of Advances in Econometrics provides a well-deserved tribute to Thomas B. Fomby and R. Carter Hill, who have served as editors of the Advances in Econometrics series for 25 and 21 years, respectively. Volume 30 contains a more varied collection of chapters than previous volumes, in essence mirroring the wide variety of econometric topics covered by the series over 30 years. Volume 30 starts with a chapter discussing the history of this series over the last 30 years. The next five chapters can be broadly categorized as focusing on model specification and testing. Following this section are three contributions that examine instrumental variables models in quite different settings. The next four chapters focus on applied macroeconomics topics. The final chapter offers a practical guide to conducting Monte Carlo simulations.

In this chapter we demonstrate the construction of inverse test confidence intervals for the turning-points in estimated nonlinear relationships by the use of the marginal or first derivative function. First, we outline the inverse test confidence interval approach. Then we examine the relationship between the traditional confidence intervals based on the Wald test for the turning-points for a cubic, a quartic, and fractional polynomials estimated via regression analysis and the inverse test intervals. We show that the confidence interval plots of the marginal function can be used to estimate confidence intervals for the turning-points that are equivalent to the inverse test. We also provide a method for the interpretation of the confidence intervals for the second derivative function to draw inferences for the characteristics of the turning-point.

This method is applied to the examination of the turning-points found when estimating a quartic and a fractional polynomial from data used for the estimation of an Environmental Kuznets Curve. The Stata do files used to generate these examples are listed in Appendix A along with the data.

The purpose of this paper is to obtain a numerical scheme for finding numerical solutions of linear and nonlinear fractional differential equations involving ψ-Caputo derivative.

An operational matrix to find numerical approximation of ψ-fractional differential equations (FDEs) is derived. This study extends the method to nonlinear FDEs by using quasi linearization technique to linearize the nonlinear problems.

The error analysis of the proposed method is discussed in-depth. Accuracy and efficiency of the method are verified through numerical examples.

The method is simple and a good mathematical tool for finding solutions of nonlinear ψ-FDEs. The operational matrix approach offers less computational complexity.

Engineers and applied scientists may use the present method for solving fractional models appearing in applications.

The purpose of this paper is to introduce a new class of fractional positive continuous‐time and discrete‐time linear systems.

Solutions to the state equations of the fractional systems are given.

Necessary and sufficient conditions are established for the internal and external positivity and of the reachability and controllability to zero of the fractional systems.

A method for analysis of the fractional positive linear systems is proposed.

This paper aims to present a special transformation that is applied to univariable polynomials of an arbitrary order, resulting in the generation of the proposed offset eliminated polynomial. This transform-based approach is used in the analysis and synthesis of temporal arc functions, which are time domain polynomial functions possessing two or more values simultaneously. Using the proposed transform, the submerged values of temporal arcs can also be extracted in measurements.

The methodology involves a two-step mathematical procedure in which the proposed transform of the weighted modified derivative of the polynomial is generated, followed by multiplication with a linear or ramp function. The transform introduces a stretching in the temporal or spatial domain depending on the type of variable under consideration, resulting in modifications for parameters such as time derivative and relative velocity.

Detailed analysis of various parameters in this modified time domain is performed and results are presented. Additionally, using the proposed methodology, the submerged value of any temporal arc function can also be extracted in measurements, thereby unraveling the temporal arc.

A typical implementation study with results is also presented for an operational amplifier-based temporal arc-producing square rooting circuit for the extraction of the submerged value of the function.

The proposed transform-based approach has major applications in extracting the values of temporal arc functions that are submerged in conventional experimental measurements, thereby providing a novel method in unraveling that class of special functions.

Recent evidence on the impact of the crisis on developed countries shows that changes in income inequality and poverty have been relatively small in spite of the macroeconomic heterogeneity of the recession across different economies. However, when evaluating individual perceptions linked to the crisis any changes in the chances to scale up or lose ground in the income ladder are also crucial. Our aim in this paper is to analyze to what extent the recession has had an impact on individual equivalent incomes and, in particular, on the prevalence of downward mobility in two developed countries where job losses have been large. We find that income losses have increased, particularly in Spain, and while age and education are key determinants of the probability of experiencing an income loss in both countries, the presence of children only increases the probability of an income loss in Spain.

Recently, a new formulation has been introduced for non-local mechanics in terms of fractional calculus. Fractional calculus is a branch of mathematical analysis that studies the differential operators of an arbitrary (real or complex) order and is used successfully in various fields such as mathematics, science and engineering. The purpose of this paper is to introduce a new fractional non-local theory which may be applicable in various simple or complex mechanical problems.

In this paper (by using fractional calculus), a fractional non-local theory based on the conformable fractional derivative (CFD) definition is presented, which is a generalized form of the Eringen non-local theory (ENT). The theory contains two free parameters: the fractional parameter which controls the stress gradient order in the constitutive relation and could be an integer and a non-integer and the non-local parameter to consider the small-scale effect in the micron and the sub-micron scales. The non-linear governing equation is solved by the Galerkin and the parameter expansion methods. The non-linearity of the governing equation is due to the presence of von-Kármán non-linearity and CFD definition.

The theory has been used to study linear and non-linear free vibration of the simply-supported (S-S) and the clamped-free (C-F) nano beams and then the influence of the fractional and the non-local parameters has been shown on the linear and non-linear frequency ratio.

A new parameter of the theory (the fractional parameter) makes the modeling more fixable – this model can conclude all of integer and non-integer operators and is not limited to special operators such as ENT. In other words, it allows us to use more sophisticated mathematics to model physical phenomena. On the other hand, in the comparison of classic fractional non-local theory, the theory applicable in various simple or complex mechanical problems may be used because of simpler forms of the governing equation owing to the use of CFD definition.

The authors performed a systematic review and meta-analysis of all published randomized controlled trials with the aim to determine and quantify the anti-hyperglycemic effects of glutamine (Gln) in acute and chronic clinical settings.

The authors conducted a comprehensive search of all randomized clinical trials performed up to December 2018, to identify those investigating the impact of Gln supplementation on fasting blood sugar (FBS), insulin levels and homeostatic model assessment-insulin resistance (HOMA-IR) via ISI Web of Science, Cochrane library PubMed and SCOPUS databases. A meta-analysis of eligible studies was conducted using random effects model to estimate the pooled effect size. Fractional polynomial modeling was used to explore the dose–response relationships between Gln supplementation and diabetic indices.

The results of the present meta-analysis suggest that of Gln supplementation had a significant effect on FBS (weighted mean difference (WMD): –2.868 mg/dl, 95 per cent CI: –5.467, –0.269, p = 0.031). However, the authors failed to observe that Gln supplementation affected insulin levels (WMD: 1.06 units, 95 per cent CI: –1.13, 3.26, p = 0.34) and HOMA-IR (WMD: 0.001 units, 95 per cent CI: –2.031, 2.029, p = 0.999). Subgroup analyses showed that the highest decrease in FBS levels was observed when the duration of intervention was less than two weeks (WMD: –4.064 mg/dl, 95 per cent CI: –7.428, –0.700, p = 0.01) and when Gln was applied via infusion (WMD: –5.334 mg/dl, 95 per cent CI: –10.48, 0.17, p = 0.04).

The results from this meta-analysis show that Gln supplementation did not have a significant effect on insulin levels and HOMA-IR. However, it did significantly reduce the levels of FBS, obtaining a higher effect when the duration of the intervention period was less than two weeks.

A three‐axes synchronous torque motor with permanent magnet excitation and solid stator and rotor yoke is used to adjust an air borne telescope and to eliminate oscillations. Hence the motor is part of a complex mechanical system and has to be included in the structural analysis. For this reason the attempt is made to simulate the nonlinear behavior of the motor by a dynamic model considering the eddy current fields and the magnetization characteristic of the iron.