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The purpose of this paper is to provide a comprehensive analysis of different material models when observing the magnetisation dynamics and power losses in non-oriented soft magnetic steel sheets (SMSSs).

During the analysis four different magnetic material models were used for describing the static material characteristics, which characterised the materials’ magnetisation behaviour with increasing accuracies: linear material model, piecewise linear material model, non-linear H(B) characteristic and the static hysteresis material model proposed by Tellinen. The described material models were implemented within a parametric magneto-dynamic model (PMD) of SMSSs, where the dynamic responses as well as power loss calculations from the obtained models were analysed.

The momentous influences of various levels of detail on the calculation of dynamic variables and power losses inside SMSS with non-uniform magnetic fields were elaborated, where various static material characteristic models were evaluated, ranging from linear to hysteretic constitutive relationships.

The resulting PMD model using different static models was analysed over a frequency range from quasi-static to f=1,000 Hz for different levels of magnetic flux density up to B _max=1.5 T.

The presented analysis provides fundamental insight when calculating dynamic electromagnetic variables and power losses inside non-linear SMSSs, which is instrumental when selecting an adequate model for a specific application.

This paper provides closer insight on the way non-linearity, magnetic saturation and hysteresis affect the energy loss and magnetisation dynamics in SMSSs through the level of detail in the used material model. The strongly coupled model addresses both induced eddy currents and the ferromagnetic materials’ magnetisation behaviour simultaneously using varying levels of detail so that the interplay between skin effect (i.e. eddy currents) across laminations and hysteresis can be resolved accurately. Therewith, adequate models for specific applications can be selected.

In the optimisation of electrical drives, the required degree of detail in the simulation increases constantly. Especially, the industrial demand on multi‐objective optimisation craves for highly efficient models. The purpose of this paper is to propose a hybrid model for the computation of the air‐gap field of a permanent magnet synchronous motor (PMSM) combining analytic and numeric methods.

The classic conformal mapping (CM) approach is improved by the numeric approximation of the required ansatz‐functions. This approach allows to consider the non‐linear permeability of the applied materials and complex geometries. The non‐linear permeance‐function is described by a one‐dimensional wave varying in time and space.

The permeance‐function has to be derived for different load cases at the actual stage.

A physical motivated modelling allowing for an appropriate interpolation between different load cases is planned in further research.

The proposed approach is applied to a surface mounted PMSM. It is validated by means of a non‐linear finite element analysis.

The hybrid model offers to consider rotors with buried magnets using the CM approach. It is possible to either use analytic or numeric modelling of rotor ansatz‐function, stator current ansatz‐function and permeance‐function with the proposed approach. Non‐linear permeability of iron is modelled by means of a wave representation of the permeance‐function. This can significantly reduce the computational cost in the design and optimisation stage of electrical machines.

This study seeks to explore the nature of a data‐generating process for four dollar exchange rates.

Using a discrete parametric modeling approach, an efficient test statistic was computed for nonlinearity in terms of variance of the residuals of the linear and nonlinear autoregressive models by Akaike Information Criterion, and a surrogate data analysis was conducted.

It shows that a nonlinear autoregressive model outperforms a linear stochastic model in certain subsamples of baht, pound, ringgit, and yen dollar exchange rates. However, when the test statistics using different model orders and the data for the entire samples are estimated, it appears that the nonlinear model has a better performance than the linear model in fitting Thai and Malaysian currencies. The nonlinear model performs better than the linear model in the case of the UK pound in two thirds of the models, but the linear models completely outperform the nonlinear models for the yen data.

More financial and economic time series will be explored to employ the methodology used in the study, and tests for possible presence of nonlinear deterministic dynamics (chaos) in the exchange rates series will be conducted based on the present findings in further study.

These findings suggest that the assumption of linear stochastic process as the underlying dynamics for all currencies examined in this study may not be justifiable.

To the best of the authors' knowledge, this study is the first attempt to use the test statistic based on the information‐theoretical method in testing nonlinearity in financial and economic time series.

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.

This study examines the use of linear regressions that include interaction terms, finding frequent interpretation errors in published accounting research. We provide insights on how to estimate, interpret, and present interactive regression models, and explain seldom-used but easily-implemented methods to report conditional marginal effects. We also examine the use of interaction terms in tax and financial reporting trade-off studies, evaluating the conceptual fit between a regression model with interactions and alternative definitions of trade-off. Although we advocate the use of interactive models, noise levels common in accounting research greatly reduce the ability to detect interaction effects.

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.

This paper attempts to establish the general formula for computing the inverse of grey matrix, and the results are applied to solve grey linear programming. The inverse of a grey matrix and grey linear programming plays an important role in establishing a grey computational system.

Starting from the fact that missing information often appears in complex systems, and therefore that true values of elements are uncertain when the authors construct a matrix, as well as calculate its inverse. However, the authors can get their ranges, which are called the number-covered sets, by using grey computational rules. How to get the matrix-covered set of inverse grey matrix became a typical approach. In this paper, grey linear programming was explained in detail, for the point of grey meaning and the methodology to calculate the inverse grey matrix can successfully solve grey linear programming.

The results show that the ranges of grey value of inverse grey matrix and grey linear programming can be obtained by using the computational rules.

Because the matrix and the linear programming 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 matrix and grey linear programming may have great potential application in real world. The methodology realizes the feasibility to control the complex system under uncertain situations.

The paper successfully obtained the ranges of uncertain inverse matrix and linear programming by using grey system theory, when the elements of matrix and the coefficients of linear programming are intervals and the results enrich the contents of grey mathematics.

This chapter presents the survey of selected linear and mixed integer programming multi-objective portfolio optimization. The definitions of selected percentile risk measures are presented. Some contrasts and similarities of the different types of portfolio formulations are drawn out. The survey of multi-criteria methods devoted to portfolio optimization such as weighting approach, lexicographic approach, and reference point method is also presented. This survey presents the nature of the multi-objective portfolio problems focuses on a compromise between the construction of objectives, constraints, and decision variables in a portfolio and the problem complexity of the implemented mathematical models. There is always a trade-off between computational time and the size of an input data, as well as the type of mathematical programming formulation with linear and/or mixed integer variables.

Even though most previous research studies suggest that the relationship between common financial ratios and stock returns is linear, recent studies by Mramor and Mramor‐Kosta (1997), and Mramor and Pahor (1998) show that such a linear relationship might not generally exist. In this study, we model the relationships between common financial ratios and stock returns from 1996 to 2000 using linear and non‐linear forms for a sample of 46 Egyptian firms. Our empirical findings suggest that non‐linear relationships exist and are more descriptive of the behavior of stock returns.

Baltagi and Li (2001) derived Lagrangian multiplier tests to jointly test for functional form and spatial error correlation. This companion paper derives Lagrangian multiplier tests to jointly test for functional form and spatial lag dependence. In particular, this paper tests for linear or log-linear models with no spatial lag dependence against a more general Box-Cox model with spatial lag dependence. Conditional LM tests are also derived which test for (i) zero spatial lag dependence conditional on an unknown Box-Cox functional form, as well as, (ii) linear or log-linear functional form given spatial lag dependence. In addition, modified Rao-Score tests are also derived that guard against local misspecification. The performance of these tests are investigated using Monte Carlo experiments.