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Article
Publication date: 8 February 2021

Ouadie Koubaiti, Said EL Fakkoussi, Jaouad El-Mekkaoui, Hassan Moustachir, Ahmed Elkhalfi and Catalin I. Pruncu

This paper aims to propose a new boundary condition and a web-spline basis of finite element space approximation to remedy the problems of constraints due to homogeneous…

Abstract

Purpose

This paper aims to propose a new boundary condition and a web-spline basis of finite element space approximation to remedy the problems of constraints due to homogeneous and non-homogeneous; Dirichlet boundary conditions. This paper considered the two-dimensional linear elasticity equation of Navier–Lamé with the condition CAB. The latter allows to have a total insertion of the essential boundary condition in the linear system obtained; without using a numerical method as Lagrange multiplier. This study have developed mixed finite element; method using the B-splines Web-spline space. These provide an exact implementation of the homogeneous; Dirichlet boundary conditions, which removes the constraints caused by the standard; conditions. This paper showed the existence and the uniqueness of the weak solution, as well as the convergence of the numerical solution for the quadratic case are proved. The weighted extended B-spline; approach have become a much more workmanlike solution.

Design/methodology/approach

In this paper, this study used the implementation of weighted finite element methods to solve the Navier–Lamé system with a new boundary condition CA, B (Koubaiti et al., 2020), that generalises the well-known basis, especially the Dirichlet and the Neumann conditions. The novel proposed boundary condition permits to use a single Matlab code, which summarises all kind of boundary conditions encountered in the system. By using this model is possible to save time and programming recourses while reap several programs in a single directory.

Findings

The results have shown that the Web-spline-based quadratic-linear finite elements satisfy the inf–sup condition, which is necessary for existence and uniqueness of the solution. It was demonstrated by the existence of the discrete solution. A full convergence was established using the numerical solution for the quadratic case. Due to limited regularity of the Navier–Lamé problem, it will not change by increasing the degree of the Web-spline. The computed relative errors and their rates indicate that they are of order 1/H. Thus, it was provided their theoretical validity for the numerical solution stability. The advantage of this problem that uses the CA, B boundary condition is associated to reduce Matlab programming complexity.

Originality/value

The mixed finite element method is a robust technique to solve difficult challenges from engineering and physical sciences using the partial differential equations. Some of the important applications include structural mechanics, fluid flow, thermodynamics and electromagnetic fields (Zienkiewicz and Taylor, 2000) that are mainly based on the approximation of Lagrange. However, this type of approximation has experienced a great restriction in the level of domain modelling, especially in the case of complicated boundaries such as that in the form of curvilinear graphs. Recently, the research community tried to develop a new way of approximation based on the so-called B-spline that seems to have superior results in solving the engineering problems.

Details

Engineering Computations, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0264-4401

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Book part
Publication date: 30 August 2019

Bai Huang, Tae-Hwy Lee and Aman Ullah

This chapter examines the asymptotic properties of the Stein-type shrinkage combined (averaging) estimation of panel data models. We introduce a combined estimation when…

Abstract

This chapter examines the asymptotic properties of the Stein-type shrinkage combined (averaging) estimation of panel data models. We introduce a combined estimation when the fixed effects (FE) estimator is inconsistent due to endogeneity arising from the correlated common effects in the regression error and regressors. In this case, the FE estimator and the CCEP estimator of Pesaran (2006) are combined. This can be viewed as the panel data model version of the shrinkage to combine the OLS and 2SLS estimators as the CCEP estimator is a 2SLS or control function estimator that controls for the endogeneity arising from the correlated common effects. The asymptotic theory, Monte Carlo simulation, and empirical applications are presented. According to our calculation of the asymptotic risk, the Stein-like shrinkage estimator is more efficient estimation than the CCEP estimator.

Details

Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part A
Type: Book
ISBN: 978-1-78973-241-2

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Book part
Publication date: 26 November 2020

Marek Kosny, Jacques Silber and Gaston Yalonetzky

We propose a framework for the measurement of income mobility over several time periods, based on the notion that multi-period mobility amounts to measuring the degree of…

Abstract

We propose a framework for the measurement of income mobility over several time periods, based on the notion that multi-period mobility amounts to measuring the degree of association between the individuals and the time periods. More precisely we compare the actual income share of individuals at a given time in the total income of all individuals over the whole period analyzed, with their “expected” share, assumed to be equal to the hypothetical income share in the total income of society over the whole accounting period that an individual would have had at a given time, had there been complete independence between the individuals and the time periods. We then show that an appropriate way of consistently measuring multi-period mobility should focus on the absolute rather than the traditional (relative) Lorenz curve and that the relevant variable to be accumulated should be the difference between the “a priori” and “a posteriori” shares previously defined. Moving from an ordinal to a cardinal approach to measuring multi-period mobility, we then propose classes of mobility indices based on absolute inequality indices. We illustrate our approach with an empirical application using the EU-SILC rotating panel dataset. Our empirical analysis seems to vindicate our approach because it clearly shows that income mobility was higher in the new EU countries (those that joined the EU in 2004 and later). We also observe that income mobility after 2008 was higher in three countries that were particularly affected by the financial crisis: Greece, Portugal, and Spain.

Details

Inequality, Redistribution and Mobility
Type: Book
ISBN: 978-1-80043-040-2

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Abstract

Details

Messy Data
Type: Book
ISBN: 978-0-76230-303-8

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Abstract

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Applying Maximum Entropy to Econometric Problems
Type: Book
ISBN: 978-0-76230-187-4

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Abstract

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Mathematical and Economic Theory of Road Pricing
Type: Book
ISBN: 978-0-08-045671-3

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Book part
Publication date: 1 January 2005

Hai Yang and Hai-Jun Huang

Abstract

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Mathematical and Economic Theory of Road Pricing
Type: Book
ISBN: 978-0-08-045671-3

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Book part
Publication date: 15 April 2020

Alexander Chudik, M. Hashem Pesaran and Kamiar Mohaddes

This chapter contributes to the growing global VAR (GVAR) literature by showing how global and national shocks can be identified within a GVAR framework. The usefulness of…

Abstract

This chapter contributes to the growing global VAR (GVAR) literature by showing how global and national shocks can be identified within a GVAR framework. The usefulness of the proposed approach is illustrated in an application to the analysis of the interactions between public debt and real output growth in a multicountry setting, and the results are compared to those obtained from standard single country VAR analysis. We find that on average (across countries) global shocks explain about one-third of the long-horizon forecast error variance of output growth, and about one-fifth of the long-run variance of the rate of change of debt-to-GDP. Evidence on the degree of cross-sectional dependence in these variables and their innovations are exploited to identify the global shocks, and priors are used to identify the national shocks within a Bayesian framework. It is found that posterior median debt elasticity with respect to output is much larger when the rise in output is due to a fiscal policy shock, as compared to when the rise in output is due to a positive technology shock. The cross-country average of the median debt elasticity is 1.45 when the rise in output is due to a fiscal expansion as compared to 0.76 when the rise in output follows from a favorable output shock.

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Article
Publication date: 8 April 2020

Gaoxiang Lou, Zhixuan Lai, Haicheng Ma and Tijun Fan

The purpose of this paper is to find the optimal power structure that drives green practices in the supply chain and coordinate the costs and benefits of green practices…

Abstract

Purpose

The purpose of this paper is to find the optimal power structure that drives green practices in the supply chain and coordinate the costs and benefits of green practices in supply chain under different power structures.

Design/methodology/approach

This paper developed a supply chain of one supplier and one manufacturer, in which the supplier and the manufacturer are responsible for the “greening” of products. Then, the game theory modeling method is used to explore the influence of different power structures on green practices in the supply chain. Finally, the authors developed a green cost-sharing contract made by the leader; regarding optimal supply chain profits and green performance, the proposed contracts and the non-coordination situation are compared and tested by a numerical simulation.

Findings

The increase of the green practice difficulty of any member in the supply chain will not only reduce the greenness of products at that stage but will also reduce the green investment of the supply chain partner. Becoming a channel leader does not necessarily mean being more profitable than being a follower, and when the green practice difficulty of the leader is less than a certain threshold, ceding dominant power to the follower may benefit both sides. A green cost-sharing contract made by the leader is not necessarily beneficial to all enterprises.

Originality/value

This paper helps to better understand the role of the power relation in realizing the industry's green goals and helps decision-makers to achieve win-win cooperation by adjusting power relations and optimizing green cost-sharing contracts.

Details

Industrial Management & Data Systems, vol. 120 no. 6
Type: Research Article
ISSN: 0263-5577

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Article
Publication date: 11 May 2020

Mehdi Dehghan and Vahid Mohammadi

This study aims to apply a numerical meshless method, namely, the boundary knot method (BKM) combined with the meshless analog equation method (MAEM) in space and use a…

Abstract

Purpose

This study aims to apply a numerical meshless method, namely, the boundary knot method (BKM) combined with the meshless analog equation method (MAEM) in space and use a semi-implicit scheme in time for finding a new numerical solution of the advection–reaction–diffusion and reaction–diffusion systems in two-dimensional spaces, which arise in biology.

Design/methodology/approach

First, the BKM is applied to approximate the spatial variables of the studied mathematical models. Then, this study derives fully discrete scheme of the studied models using a semi-implicit scheme based on Crank–Nicolson idea, which gives a linear system of algebraic equations with a non-square matrix per time step that is solved by the singular value decomposition. The proposed approach approximates the solution of a given partial differential equation using particular and homogeneous solutions and without considering the fundamental solutions of the proposed equations.

Findings

This study reports some numerical simulations for showing the ability of the presented technique in solving the studied mathematical models arising in biology. The obtained results by the developed numerical scheme are in good agreement with the results reported in the literature. Besides, a simulation of the proposed model is done on buttery shape domain in two-dimensional space.

Originality/value

This study develops the BKM combined with MAEM for solving the coupled systems of (advection) reaction–diffusion equations in two-dimensional spaces. Besides, it does not need the fundamental solution of the mathematical models studied here, which omits any difficulties.

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