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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.

Accurate numerical differentiation of approximate data by methods based on Green's second identity often involves singular or nearly singular integrals over domains or their boundaries. This paper applies the finite part integration concept to evaluate such integrals and to generate suitable quadrature formulae. The weak singularity involved in first derivatives is removable; the strong singularities encountered in computing higher derivatives can be reduced. To find derivatives on or near the edge of the integration region, special treatment of boundary integrals is required. Values of normal derivative at points on the edge are obtainable by the method described. Example results are given for derivatives of analytically known functions, as well as results from finite element analysis.

The purpose of this paper is to present some modifications in the spline‐based differential quadrature method (DQM), in order to accelerate the convergence of the method. The improvements are explained and examined by the examples of the free vibration of conical shells. The composite laminated shell, as well as isotropic one, are taken under consideration.

To determine weighting coefficients for the DQM, the spline interpolation with non‐standard definitions of the end conditions is used. One of these definitions combines natural and not‐a‐knot end conditions, while the other one uses the boundary conditions for considered problem as the end conditions. The weighting coefficients can be determined by solving set of equations arising from spline interpolation.

It is shown that the proposed modifications significantly improve the convergence of the method, especially when the boundary conditions are introduced at the stage of the computation of the weighting coefficients. Unfortunately, the use of this approach is limited to some types of boundary conditions.

The paper describes development of the modified spline interpolation dedicated to DQM and examines the possibility of building boundary conditions into the weighting coefficients at the stage of the computation of these coefficients.

The purpose of this paper is to analyze previous models of the concept of ranking accuracy within the weighted aggregated sum product assessment (WASPAS) method and make necessary refinements.

This paper presents a correct combination of the weighted sum model (WSM) and weighted product model (WPM), which is usually performed on an ad hoc basis in the literature.

One of the reasons of rarely conducting ranking accuracy analysis might be that some of the reported equations in the literature are confusing, and hence, accurate partial derivatives cannot be calculated. In this study, all of the necessary formulations are re-derived and necessary modifications are proposed.

A corrected WASPAS equation for optimal combination parameters is derived. Two examples are used to validate the formulations, and software implementation is provided. Because multiple attribute decision-making (MADM) has gained widespread attention from both the academia and industry, the findings of this paper help decision makers fully capitalize the concept of ranking accuracy and avoid possible confusions regarding the equations reported in the literature.

WASPAS is a relatively new MADM method and has enjoyed a visible position in the MADM literature. In addition to its simplicity, the WASPAS method utilizes the concept of ranking accuracy by combining the well-known WSM and WPM. This combination realized via an optimization criterion brings unique opportunities for decision makers such as evaluating confidence intervals for relative significance of alternatives and reducing estimated variance of ranking results. Despite its crucial importance, the combination of WSM and WPM is usually performed on an ad hoc basis in the literature. In this study, all of the necessary formulations are re-derived and necessary modifications are proposed along with clarifying examples.

The purpose of the paper is to extend the differential quadrature method (DQM) for solving time and space fractional non-linear partial differential equations on a semi-infinite domain.

The proposed method is the combination of the Legendre polynomials and differential quadrature method. The authors derived and constructed the new operational matrices for the fractional derivatives, which are used for the solutions of non-linear time and space fractional partial differential equations.

The fractional derivative of Lagrange polynomial is a big hurdle in classical DQM. To overcome this problem, the authors represent the Lagrange polynomial in terms of shifted Legendre polynomial. They construct a transformation matrix which transforms the Lagrange polynomial into shifted Legendre polynomial of arbitrary order. Then, they obtain the new weighting coefficients matrices for space fractional derivatives by shifted Legendre polynomials and use these in conversion of a non-linear fractional partial differential equation into a system of fractional ordinary differential equations. Convergence analysis for the proposed method is also discussed.

Many engineers can use the presented method for solving their time and space fractional non-linear partial differential equation models. To the best of the authors’ knowledge, the differential quadrature method has never been extended or implemented for non-linear time and space fractional partial differential equations.

Body forces are always applied to structures in the form of the weight of materials. In some cases, they can be neglected in comparison with other applied forces. Nevertheless, there is a wide range of structures in civil and mechanical engineering in which weight or other types of body forces are the main portions of the applied loads. The optimal topology of these structures is investigated in this study.

Topology optimization plays an increasingly important role in structural design. In this study, the topological derivative under body forces is used in a level-set-based topology optimization method. Instability during the optimization process is addressed, and a heuristic solution is proposed to overcome the challenge. Moreover, body forces in combination with thermal loading are investigated in this study.

Body forces are design-dependent loads that usually add complexity to the optimization process. Some problems have already been addressed in density-based topology optimization methods. In the present study, the body forces in a topological level-set approach are investigated. This paper finds that the used topological derivative is a flat field that causes some instabilities in the optimization process. The main novelty of this study is a technique used to overcome this challenge by using a weighted combination.

There is a lack of studies on level-set approaches that account for design-dependent body forces and the proposed method helps to understand the challenges posed in such methods. A powerful level-set-based approach is used for this purpose. Several examples are provided to illustrate the efficiency of this method. Moreover, the results show the effect of body forces and thermal loading on the optimal layout of the structures.

In this chapter we consider the “Regularization of Derivative Expectation Operator” (Rodeo) of Lafferty and Wasserman (2008) and propose a modified Rodeo algorithm for semiparametric single index models (SIMs) in big data environment with many regressors. The method assumes sparsity that many of the regressors are irrelevant. It uses a greedy algorithm, in that, to estimate the semiparametric SIM of Ichimura (1993), all coefficients of the regressors are initially set to start from near zero, then we test iteratively if the derivative of the regression function estimator with respect to each coefficient is significantly different from zero. The basic idea of the modified Rodeo algorithm for SIM (to be called SIM-Rodeo) is to view the local bandwidth selection as a variable selection scheme which amplifies the coefficients for relevant variables while keeping the coefficients of irrelevant variables relatively small or at the initial starting values near zero. For sparse semiparametric SIM, the SIM-Rodeo algorithm is shown to attain consistency in variable selection. In addition, the algorithm is fast to finish the greedy steps. We compare SIM-Rodeo with SIM-Lasso method in Zeng et al. (2012). Our simulation results demonstrate that the proposed SIM-Rodeo method is consistent for variable selection and show that it has smaller integrated mean squared errors (IMSE) than SIM-Lasso.

This paper proposes an interpolating approach of the element‐free Galerkin method (EFGM) coupled with a modified truncation scheme for solving Poisson's boundary value problems in domains involving material non‐homogeneities. The suitability and efficiency of the proposed implementation are evaluated for a given set of test cases of electrostatic field in domains involving different material interfaces.

The authors combined an interpolating approximation with a modified domain truncation scheme, which avoids additional techniques for enforcing the Dirichlet boundary conditions and for dealing with material interfaces usually employed in meshfree formulations.

The local electric potential and field distributions were correctly described as well as the global quantities like the total potency and resistance. Since, the treatment of the material interfaces becomes practically the same for both the finite element method (FEM) and the proposed EFGM, FEM‐oriented programs can, thus, be easily extended to provide EFGM approximations.

The robustness of the proposed formulation became evident from the error analyses of the local and global variables, including in the case of high‐material discontinuity.

The proposed approach has shown to be as robust as linear FEM. Thus, it becomes an attractive alternative, also because it avoids the use of additional techniques to deal with boundary/interface conditions commonly employed in meshfree formulations.

This paper reintroduces the domain truncation in the EFGM context, but by using a set of interpolating shape functions the authors avoided the use of Lagrange multipliers as well as of a penalty strategy. The resulting formulation provided accurate results including in the case of high‐material discontinuity.