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In this paper, the formulation and analytic solutions for fractional continuously variable order dynamic models, namely, fractional continuously mass-spring damper (continuously variable fractional order) systems, have been presented. The authors will demonstrate via two cases where the frictional damping given by fractional derivative, the order of which varies continuously – while the mass moves in a guide. Here, the continuously changing nature of the fractional-order derivative for dynamic systems has been studied for the first time. The solutions of the fractional continuously variable order mass-spring damper systems have been presented here by using a successive recursive method, and the closed form of the solutions has been obtained. By using graphical plots, the nature of the solutions has been discussed for the different cases of continuously variable fractional order of damping force for oscillator. The purpose of the paper is to formulate the continuously variable order mass-spring damper systems and find their analytical solutions by successive recursion method.

The authors have used the viscoelastic and viscous – viscoelastic dampers for describing the damping nature of the oscillating systems, where the order of the fractional derivative varies continuously.

By using the successive recursive method, here, the authors find the solution of the fractional continuously variable order mass-spring damper systems, and then obtain close-form solutions. The authors then present and discuss the solutions obtained in the cases with the continuously variable order of damping for an oscillator through graphical plots.

Formulation of fractional continuously variable order dynamic models has been described. Fractional continuous variable order mass-spring damper systems have been analysed. A new approach to find solutions of the aforementioned dynamic models has been established. Viscoelastic and viscous – viscoelastic dampers are described. The discussed damping nature of the oscillating systems has not been studied yet.

In the Taguchi’s experimentations, orthogonal arrays, interaction tables, and linear graphs are provided for planning experiments, but they become quite unwieldy when the number of runs is large. The purpose of this article is to propose a quick and easy method for obtaining two‐factor interaction columns in two‐level orthogonal arrays. Geometrical designs proposed by Plackett and Burman are two‐level orthogonal arrays and can be obtained very easily by a successive doubling method. Based on the property of doubling, a NR method using a number representation system whose base is a power of 2 is derived in this article for obtaining two‐factor interaction columns in geometrical designs. Furthermore, since Taguchi’s two‐level orthogonal arrays are obtainable by successive doubling with some column permutations, it is shown that their two‐factor interaction columns can be obtained directly by using the NR method without looking up tables.

The purpose of this paper is to propose successive-over-relaxation (SOR) based recursive Bayesian approach (RBA) for the configuration identification of a Power System. Moreover, to present a comparison between the proposed method and existing RBA approaches regarding convergence speed and robustness.

Swift power network configuration identification is important for adopting the smart grid features like power system automation. In this work, a new SOR-based numerical approach is adopted to increase the convergence speed of the existing RBA algorithm and at the same time maintaining robustness against noise. Existing RBA and SOR-RBA are tested on IEEE 6 bus, IEEE 14 bus networks and 48 bus Danish Medium Voltage distribution network in the MATLAB R2014b environment and a comparative analysis is presented.

The comparison of existing RBA and proposed SOR-RBA is performed, which reveals that the latter has good convergence speed compared to the former RBA algorithms. Moreover, it is robust against bad data and noise.

Existing RBA techniques have slow convergence and are also prone to measurement noise. Their convergence speed is effected by noisy measurements. In this paper, an attempt has been made to enhance convergence speed of the new identification algorithm while keeping its numerical stability and robustness during noisy measurement conditions. This work is novel and has drastic improvement in the convergence speed and robustness of the former RBA algorithms.

The purpose of this paper is to provide a comparison of the Adomian decomposition method (ADM) with the variational iteration method (VIM) for solving the Lane‐Emden equations of the first and second kinds.

The paper examines the theoretical framework of the Adomian decomposition method and compares it with the variational iteration method. The paper seeks to determine the relative merits and computational benefits of both the Adomian decomposition method and the variational iteration method in the context of the important physical models of the Lane‐Emden equations of the first and second kinds.

The Adomian decomposition method is shown to readily solve the Lane‐Emden equations of both the first and second kinds for all positive real values of the system coefficient α and for all positive real values of the nonlinear exponent m. The decomposition series solution of these nonlinear differential equations requires the calculation of the Adomian polynomials appropriate to the particular system nonlinearity. The paper shows that the variational iteration method works effectively to solve the Lane‐Emden equation of the first kind for system coefficient values α=1, 2, 3, 4 but only for positive integer values of the nonlinear exponent m. The successive approximations of the solution of these nonlinear differential equations require the determination of the appropriate Lagrange multipliers, which are established in this paper. These two methodologies overcome the singular behavior at the origin x=0. The paper shows that the variational iteration method is impractical for solving either the Lane‐Emden equation of the first kind for non‐integer values of the system exponent m or the Lane‐Emden equations of the second kind. Indeed the Adomian decomposition method is shown to solve even the generalized Lane‐Emden equation for any analytic nonlinearity and all positive values of the system coefficient α in a practical and straightforward manner. The conclusions are supported by several numerical examples.

This paper presents an accurate comparison of the Adomian decomposition method with the variational iteration method for solving the Lane‐Emden equations of the first and second kinds. The paper presents a new solution algorithm for the generalized Lane‐Emden equation for any analytic system nonlinearity and for any model geometry as characterized by all possible positive real values of the system coefficient α.

The philosophical foundations determine how an academic discipline identifies, understands and analyzes phenomena. The choice of philosophical perspective is vital for both marketing and service research. This paper aims to propose a social and systemic perspective that addresses current challenges in service and marketing research by revisiting the philosophy of science debate.

The paper revisits the philosophy of science debate to address the implications of an emergent, complex and adaptive view of marketing and service research. It draws on critical realism by combining structuration and systemic perspectives.

A recursive perspective, drawing on structures and action, is suggested as it includes multiple actors’ intentions and captures underlying drivers of market exchange as a basis for developing marketing and service strategies in practice. This is aligned with other scholars arguing for a more systemic, adaptive and complex view of markets in light of emerging streams in academic marketing and service research, ranging from value cocreation, effectuation, emergence and open source to empirical phenomena such as digitalization, robotization and the growth of international networks.

The reciprocal dynamic between individuals and the overarching system provides a reflexivity approach intrinsic to the service ecosystem. This creates new avenues for research on marketing and service phenomena.

This paper discusses critics, conflicts and conceptualization in service research. It suggests a possible approach for service research and marketing scholars capable of responding to current complexities and turbulence in economic and societal contexts.

A recursive scheme for the ALIENOR method is proposed as a remedy for the difficulties induced by the method. A progressive focusing on the most promising region, in combination with a variation of the density of the alpha-dense curve, is proposed.

ALIENOR method is aimed at reducing the space dimensions of an optimization problem by spanning it by using a single alpha-dense curve: the curvilinear abscissa along the curve becomes the only design parameter for any design space. As a counterpart, the transformation of the objective function in the projected space is much more difficult to tackle.

A fine tuning of the procedure has been performed in order to identity the correct balance between the different elements of the procedure. The proposed approach has been tested by using a set of algebraic functions with up to 1,024 design variables, demonstrating the ability of the method in solving large scale optimization problem. Also an industrial application is presented.

In the knowledge of the author there is not a similar paper in the current literature.

To determine and/or examine overall behaviour of simulation models with large input using as few parameters as possible. To introduce a methodology describing stability of the partitioning of simulation results and the corresponding parameter space.

Partitionings of the parameter space are performed using real‐valued mappings called measures of merit. Tools for examining evolution of partitionings and correlations between different partitionings are developed. These tools are applied in two case studies within the field of electrical engineering.

The presented approach provides tools for systematic analysis of parametrised models. Since the classification of results is based on measures of merit, a good choice both simplifies the analysis and improves the stability of partitioning. Included case studies highlight these conclusions.

The present form of the methodology is targeted at recursive simulations. Use of more complex partitioning procedures could be the topic of further research.

Solid framework for handling and analysing complex parametrised simulations.

An improvement transformation is a transformation which has the following two properties, namely, (1) after applying it, all the already achieved subgoals are still being accomplished and (2) additional new subgoals or partial new subgoals may be accomplished. By using improvement transformations, an intelligent problem‐solving method is presented with illustrative examples. This method consists of three parts: (1) goal decomposition and subgoal ordering; (2) successive improvement transformations; and (3) backtrack algorithms. The intelligent problem‐solving method using successive improvement transformations may have useful applications in goal decomposition, goal regression, genetic algorithms, robotics, and future expert system design.

The purpose of this paper is to revisit the recursive computation of closed-form expressions for the topological derivative of shape functionals in the context of time-harmonic acoustic waves scattering by sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions).

The elliptic boundary value problems in the singularly perturbed domains are equivalently reduced to couples of boundary integral equations with unknown densities given by boundary traces. In the case of circular or spherical holes, the spectral Fourier and Mie series expansions of the potential operators are used to derive the first-order term in the asymptotic expansion of the boundary traces for the solution to the two- and three-dimensional perturbed problems.

As the shape gradients of shape functionals are expressed in terms of boundary integrals involving the boundary traces of the state and the associated adjoint field, then the topological gradient formulae follow readily.

The authors exhibit singular perturbation asymptotics that can be reused in the derivation of the topological gradient function in the iterated numerical solution of any shape optimization or imaging problem relying on time-harmonic acoustic waves propagation. When coupled with converging Gauss−Newton iterations for the search of optimal boundary parametrizations, it generates fully automatic algorithms.

The purpose of this paper is to devise an experimental lab like infrastructure in the higher education connecting social innovation with sustainable tourism.

In order to model a laboratory of social innovation and sustainable tourism lab (SISTOUR-LAB), the method of agile research was employed. This method involves the creation of successive and accumulative prototypes of four kinds: conceptual, relational, functional and transferable. Thus, agile research enables the integration of different social perspectives into the same prototype in a recursive manner.

The SISTOUR-LAB is a work-based learning strategy that allows for the development of a mapping process on tourism vulnerabilities (linked to opportunities for social innovation); the development of experimental training in prototyping social innovations on sustainable tourism; the design of hybrid social innovation business models linked to sustainable tourism; and the development of a relational model of evaluation linking together social innovation competencies with processes of transition toward sustainable tourism.

The SISTOUR-LAB is a prototypical lab that combines social innovation and sustainable tourism in an experimental setting. The SISTOUR-LAB has been modeled based on the agile research method, but it will be necessary to test it empirically to stabilize the model. Once stabilized, the model shall lead to a better understanding of the relationship between work-based learning, social innovation and sustainable tourism in the area of higher education.

The SISTOUR-LAB has four implications: teachers: the SISTOUR-LAB provides teachers with a setting for the development of experimental education models that connect the problems of conventional tourism with social innovation in order to foster new learning environments oriented toward sustainable tourism; students: the SISTOUR-LAB enhances the employability of students since it connects them with agents and demands of touristic transition, while also fostering entrepreneurial development by means of improving the acquisition of social entrepreneurship competences for sustainable tourism; organizations: the SISTOUR-LAB provides an experimental setting for the prototyping of social innovations so as to assist organizations in the formulation of models, prototypes and evaluations that facilitate the transition toward sustainable tourism; policymaking: the SISTOUR-LAB promotes the design of evidence-based public policies, which fosters inclusive models of innovation and the regional monitoring of transitions toward sustainable tourism.

There exist little reference to the link between social innovation and sustainable tourism in the academic and institutional literature. The SISTOUR-LAB is a work-based learning strategy that fosters the structuring of experimental relations between social innovation and sustainable tourism by integrating touristic organizations to the development of competencies in higher education. The SISTOUR-LAB has programmatic and prospective value. It can be considered as a guide for the development of generative competencies, i.e. competencies that generate social innovations that impact chain triggers transitions toward sustainable tourism.