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This article proposes a relaxed gradient iterative (RGI) algorithm to solve coupled Sylvester-conjugate transpose matrix equations (CSCTME) with two unknowns.

This article proposes a RGI algorithm to solve CSCTME with two unknowns.

The introduced (RGI) algorithm is more efficient than the gradient iterative (GI) algorithm presented in Bayoumi (2014), where the author's method exhibits quick convergence behavior.

The introduced (RGI) algorithm is more efficient than the GI algorithm presented in Bayoumi (2014), where the author's method exhibits quick convergence behavior.

In systems and control, Lyapunov matrix equations, Sylvester matrix equations and other matrix equations are commonly encountered.

In systems and control, Lyapunov matrix equations, Sylvester matrix equations and other matrix equations are commonly encountered.

This article proposes a relaxed gradient iterative (RGI) algorithm to solve coupled Sylvester conjugate transpose matrix equations (CSCTME) with two unknowns. For any initial matrices, a sufficient condition is derived to determine whether the proposed algorithm converges to the exact solution. To demonstrate the effectiveness of the suggested method and to compare it with the gradient-based iterative algorithm proposed in [6] numerical examples are provided.

This study aims to construct a mathematical model to study the dispersion analysis of magneto-electro elastic plate of arbitrary cross sections immersed in fluid by using the Fourier expansion collocation method (FECM).

The analytical formulation of the problem is designed and developed using three-dimensional linear elasticity theories. As the inner and outer boundaries of the arbitrary cross-sectional plate are irregular, the frequency equations are obtained from the arbitrary cross-sectional boundary conditions by using FECM. The roots of the frequency equation are obtained using the secant method, which is applicable for complex solutions.

The computed physical quantities such as radial stress, hoop strain, non-dimensional frequency, magnetic potential and electric potential are plotted in the form of dispersion curves, and their characteristics are discussed. To study the convergence, the non-dimensional wave numbers of longitudinal modes of arbitrary (elliptic and cardioid) cross-sectional plates are obtained using FECM and finite element method and are presented in a tabular form. This result can be applied for optimum design of composite plates with arbitrary cross sections.

This paper contributes the analytical model for the role of arbitrary cross-sectional boundary conditions and impact of fluid loading on the dispersion analysis of magneto-electro elastic plate. From the graphical patterns of the structure, the effects of stress, strain, magnetic, electric potential and the surrounding fluid on the various considered wave characteristics are more significant and dominant in the cardioid cross sections. Also, the aspect ratio (a/b) and the geometry parameters of elliptic and cardioids cross sections are significant to the industry or other fields that require more flexibility in design of materials with arbitrary cross sections.

The authors propose a semiparametric approach for testing independence between two infinite-order cointegrated vector autoregressive series (IVAR(∞)). The procedures considered can be viewed as extensions of classical methods proposed by Haugh (1976, JASA) and Hong (1996b, Biometrika) for testing independence between stationary univariate time series. The tests are based on the residuals of long autoregressions, hence allowing for computational simplicity, weak assumptions on the form of the underlying process, and a direct interpretation of the results in terms of innovations (or shocks). The test statistics are standardized versions of the sum of weighted squares of residual cross-correlation matrices. The weights depend on a kernel function and a truncation parameter. Multivariate portmanteau statistics can be viewed as a special case of our procedure based on the truncated uniform kernel. The asymptotic distributions of the test statistics under the null hypothesis are derived, and consistency is established against fixed alternatives of serial cross-correlation of unknown form. A simulation study is presented which indicates that the proposed tests have good size and power properties in finite samples.

The issues of development of decisions are very important during formation of the system of management of modern business systems in the conditions of turbulence of external conditions. The ideas of rational structuring of information flows, which are used for decision making, are related to the necessity for development of communicative culture of companies. Quality of interaction between persons that participate in decision making should be assessed by analyzing the ratio of probabilities that characterize quality of information and correctness of decisions and development of a special model.

Compiled by K.G.B. Bakewell covering the following journals published by Emerald: Facilities Volumes 8‐19; Journal of Property Investment & Finance Volumes 8‐19; Property Management Volumes 8‐19; Structural Survey Volumes 8‐19.

Compiled by Indexing Specialists (UK) Ltd covering the following journals published by Emerald: Facilities Volumes 8‐20; Journal of Property Investment & Finance Volumes 8‐20; Property Management Volumes 8‐20; Structural Survey Volumes 8‐20.

Compiled by K.G.B. Bakewell covering the following journals published by Emerald: Facilities Volumes 8‐19; Journal of Property Investment & Finance Volumes 8‐19; Property Management Volumes 8‐19; Structural Survey Volumes 8‐19.

Compiled by Indexing Specialists (UK)Ltd covering the following journals published by Emerald: Facilities Volumes 8‐20; Journal of Property Investment & Finance Volumes 8‐20; Property Management Volumes 8‐20; Structural Survey Volumes 8‐20.

The purpose of this paper is to make multivariable gray model to be available for the application on interval gray number sequences directly, the matrix form of interval multivariable gray model (IMGM(1,m,k) model) is constructed to simulate and forecast original interval gray number sequences in this paper.

Firstly, the interval gray number is regarded as a three-dimensional column vector, and the parameters of multivariable gray model are expressed in matrix form. Based on the dynamic gray action and optimized background value, the interval multivariable gray model is constructed. Finally, two examples and comparisons are carried out to verify the effectiveness of IMGM(1,m,k) model.

The model is applied to simulate and predict expert value, foreign direct investment, automobile sales and steel output, respectively. The results show that the proposed model has better simulation and prediction performance than another two models.

Due to the uncertainty information and continuous changing of reality, the interval gray numbers are used to characterize full information of original data. And the IMGM(1,m,k) model not only considers the characteristics of parameters changing with time but also takes into account information on lower, middle and upper bounds of interval gray numbers simultaneously to make better suitable for practical application.

The main contribution of this paper is to propose a new interval multivariable gray model, which considers the interaction between the lower, middle and upper bounds of interval numbers and need not to transform interval gray number sequences into real sequences. According to combining different characteristics of each bound of interval gray numbers, the matrix form of interval multivariable gray model is established to simulate and forecast interval gray numbers. In addition, the model introduces dynamic gray action to reflect the changes of parameters over time. Instead of white equation of classic MGM(1,m), the difference equation is directly used to solve the simulated and predicted values.

The Equal Pay Act 1970 (which came into operation on 29 December 1975) provides for an “equality clause” to be written into all contracts of employment. S.1(2) (a) of the 1970 Act (which has been amended by the Sex Discrimination Act 1975) provides: