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Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The purpose of this paper is to report the implementation of an alternative time integration procedure for the dynamic non-linear analysis of structures.

The time integration algorithm discussed in this work corresponds to a spectral decomposition technique implemented in the time domain. As in the case of the modal decomposition in space, the numerical efficiency of the resulting integration scheme depends on the possibility of uncoupling the equations of motion. This is achieved by solving an eigenvalue problem in the time domain that only depends on the approximation basis being implemented. Complete sets of orthogonal Legendre polynomials are used to define the time approximation basis required by the model.

A classical example with known analytical solution is presented to validate the model, in linear and non-linear analysis. The efficiency of the numerical technique is assessed. Comparisons are made with the classical Newmark method applied to the solution of both linear and non-linear dynamics. The mixed time integration technique presents some interesting features making very attractive its application to the analysis of non-linear dynamic systems. It corresponds in essence to a modal decomposition technique implemented in the time domain. As in the case of the modal decomposition in space, the numerical efficiency of the resulting integration scheme depends on the possibility of uncoupling the equations of motion.

One of the main advantages of this technique is the possibility of considering relatively large time step increments which enhances the computational efficiency of the numerical procedure. Due to its characteristics, this method is well suited to parallel processing, one of the features that have to be conveniently explored in the near future.

This paper deals with theory and computation of fluid flow in fractured rock. Non‐Darcian flow behavior was observed in pumping tests at the geothermal research site at Soultz‐sous‐Forêts (France). Examples are examined to demonstrate the influence of fracture roughness and pressure‐gradient dependent permeability on pressure build‐up. A number of test examples based on classical models are investigated, which may be suited as benchmarks for non‐linear flow. This is a prelude of application of the non‐linear flow model to real pumping test data. Frequently, conceptual models based on simplified geometric approaches are used. Here, a realistic fracture network model based on borehole data is applied for the numerical simulations. The obtained data fit of the pumping test shows the capability of fracture network models to explain observed hydraulic behavior of fractured rock systems.

Modeling helps to determine how structural parameters of fabric affect the surface of a fabric and also identify the way they influence fabric properties. Moreover, it helps to estimate and evaluate without the complexity and time-consuming experimental procedures. The purpose of this study is to develop and select the best regression model equations for the prediction and evaluation of surface roughness of plain-woven fabrics.

In this study, a linear and quadratic regression model was developed for the prediction and evaluation of surface roughness of plain-woven fabrics, and the capability in accuracy and reliability of the two-model equation was determined by the root mean square error (RMSE). The Design-Expert AE11 software was used for developing the two model equations and analysis of variance “ANOVA.” The count and density were used for developing linear model equation one “SMD1” as well as for quadratic model equation two “SMD2.”

From results and findings, the effects of count and density and their interactions on the roughness of plain-woven fabric were found statistically significant for both linear and quadratic models at a confidence interval of 95%. The count has a positive correlation with surface roughness, while density has a negative correlation. The correlations revealed that models were strongly correlated at a confidence interval of 95% with adjusted R² of 0.8483 and R² of 0.9079, respectively. The RMSE values of the quadratic model equation and linear model equation were 0.1596 and 0.0747, respectively.

Thus, the quadratic model equation has better capability accuracy and reliability in predictions and evaluations of surface roughness than a linear model. These models can be used to select a suitable fabric for various end applications, and it was also used for tests and predicts surface roughness of plain-woven fabrics. The regression model helps to reduce the gap between the subjective and objective surface roughness measurement methods.

To prove two results. Namely that if in a linear homogeneous bicompartmental system one compartment is measured then it is indefinable. The second one is related to the identification of non‐linear compartmental models by mean of a linear method.

The first result is generalized to linear non‐homogeneous bicompartmental systems of Michaelis‐Menten (M‐M systems). The second one is related to the identification of a non‐linear compartmental model. The obtained linear system is not homogeneous and must be generalized to nonhomogeneous systems. Then the Jacobian matrix associated to the M‐M systems is identified and the M‐M parameters are deduced by continuity from the Cauchy problem's solution.

Both stated results were proved and any open linear bicompartmental system whether homogeneous or not, of the type I is identifiable.

In compartmental analysis the exchange hypothesis allows us to represent a model of any phenomenon depending on time. Many phenomena require “the enzyme reactions” leading to the M‐M laws. These laws assert that the quantity of matter going from compartment can be defined and M‐M constants prescribed. This research considers both homogeneous and nonhomogeneous systems cases.

Contributes to the identification of linear and non‐linear bicompartmental systems which are of biocybernetical significance.

The two proven results are new and applicable.

In this paper, the exact solutions of the Schlömilch’s integral equation and its linear and non-linear generalized formulas with application are solved by using two efficient iterative methods. The Schlömilch’s integral equations have many applications in atmospheric, terrestrial physics and ionospheric problems. They describe the density profile of electrons from the ionospheric for awry occurrence of the quasi-transverse approximations. The paper aims to discuss these issues.

First, the authors apply a regularization method combined with the standard homotopy analysis method to find the exact solutions for all forms of the Schlömilch’s integral equation. Second, the authors implement the regularization method with the variational iteration method for the same purpose. The effectiveness of the regularization-Homotopy method and the regularization-variational method is shown by using them for several illustrative examples, which have been solved by other authors using the so-called regularization-Adomian method.

The implementation of the two methods demonstrates the usefulness in finding exact solutions.

The authors have applied the developed methodology to the solution of the Rayleigh equation, which is an important equation in fluid dynamics and has a variety of applications in different fields of science and engineering. These include the analysis of batch distillation in chemistry, scattering of electromagnetic waves in physics, isotopic data in contaminant hydrogeology and others.

In this paper, two reliable methods have been implemented to solve several examples, where those examples represent the main types of the Schlömilch’s integral models. Each method has been accompanied with the use of the regularization method. This process constructs an efficient dealing to get the exact solutions of the linear and non-linear Schlömilch’s integral equation which is easy to implement. In addition to that, the accompanied regularization method with each of the two used methods proved its efficiency in handling many problems especially ill-posed problems, such as the Fredholm integral equation of the first kind.

The purpose of this paper is to present a comparison of nonlinear and linear simulations of aircraft dynamics to determine the divergence of the linear solution from the nonlinear solution.

The general equations of motion of a transport aircraft are presented both in nonlinear and linear form. The nonlinear equations are solved by using the Runge Kutta method. Linear equations are solved numerically by using the Runge Kutta method and they are also solved exactly by using the Laplace transformation method. All of these solutions are obtained by using the body axis system. The results of the simulations are plotted for different control deflections.

Solution of linear equations by both methods gave the same results as expected. There are important differences in amplitude and frequency of oscillations which are obtained by using nonlinear and linear equations. These differences increase with growing input control deflection. Therefore, it is appropriate to prefer nonlinear approach to obtain more satisfactory results.

Accurate determination of the aerodynamic derivatives is important for the accuracy of the nonlinear solutions.

Many classical approaches use stability axis system for the solution of linear equations. However, in this paper transfer functions of the aircraft are redefined in the body axis system, because stability axes change with angle of attack and some of the stability derivatives need to be re‐evaluated for each angle of attack. Moreover, in addition to classical text book, linear equations are also solved by using the 4th order Runge Kutta medhod.

The linear matrix equations have wide applications in engineering, physics, economics and statistics. The purpose of this paper is to introduce iterative methods for solving the systems of linear matrix equations.

According to the hierarchical identification principle, the authors construct alternating direction gradient-based iterative (ADGI) methods to solve systems of linear matrix equations.

The authors propose efficient ADGI methods to solve the systems of linear matrix equations. It is proven that the ADGI methods consistently converge to the solution for any initial matrix. Moreover, the constructed methods are extended for finding the reflexive solution to the systems of linear matrix equations.

This paper proposes efficient iterative methods without computing any matrix inverses, vec operator and Kronecker product for finding the solution of the systems of linear matrix equations.

This paper attempts to establish the conceptional and computational systems of grey determinant and apply it to solve n grey equations with n grey linear equations, which can be viewed as the important parts of grey mathematics.

Starting from the fact that missing information often appears in complex systems, the true values of elements when constructing a determinant and of coefficients when solving n equations with n linear equations cannot be obtained, so they are uncertain. However, their ranges can be obtained by using correct investigation methods. The uncertain elements and coefficients are grey and their ranges are number‐covered sets. On the basis of the results of Li and Wang, the paper systematically proposes the definition system of grey determinant and n grey linear equations, and utilizes the computational rules of grey determinant to solve the n grey equations with n grey linear equations. Some numerical examples are computed to illustrate the results in this paper.

The results show that the ranges of grey value of grey determinant and grey solutions of grey equations with n grey linear equations can be obtained by using computational rules proposed.

Because the determinant and the linear equations have been widely used in many fields such as system controlling, economic analysis and social management, and the missing information is a general phenomenon for complex systems, grey determinant and grey linear equations may have great potential application in the real world. The method realizes the feasibility of system analysis under uncertain situations.

The paper succeeds in providing systematic results of computation of uncertain determinant and n linear equations by using grey systems theory and enriches the contents of grey mathematics.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.