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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.

This paper generalises the GM(1,1) direct modeling method with a step by step majorizing grey derivative's whiten values to unequal time interval sequence modeling, and proves that the new method still has linear transformation consistency of the old method. The example indicates that the new method still has gradual approaching white exponential law coincidence property. With this new method, we then model the high precision soft foundation settlement.

Studies an analytic solution and a reliable numerical approximation of linear and non‐linear wave equations by using the Adomian decomposition method. The solution is calculated in the form of a series with easily computable components. The non‐homogeneous problem is quickly solved by observing the self‐cancelling “noise terms” where the sum of the components vanishes in the limit. Several linear or non‐linear partial differential equations are considered and their numerical approximate solutions are compared with its numerical analytic solutions by applying the Adomian decomposition method and using a computer algebraic system (MATLAB). The numerical results show the effectiveness of the method for these types of equations.

The purpose of this paper is to critically review the latest approaches for capturing and explaining heterogeneity in partial least squares (PLS) path modelling and to classify these into a methodological taxonomy. Furthermore, several areas for future research effort are introduced in order to stimulate ongoing development in this important research field.

Different approaches to treat heterogeneity in PLS path models are introduced, critically evaluated and classified into a methodological taxonomy. Future research directions are derived from a comparison of benefits and limitations of the procedures.

The review reveals that finite mixture‐PLS can be regarded as the most comprehensive and commonly used procedure for capturing heterogeneity within a PLS path modelling framework. However, further research is necessary to explore the capabilities and limitations of the approach.

Directions for additional research, common to most latent class detection procedures include the verification and comparison of available approaches, the handling of large data sets, the allowance of varying structures of path models, the profiling of segments and the problem of model selection.

Whereas modelling heterogeneity in covariance structure analysis has been studied for several years, research interest has only recently been devoted to the question of clustering in PLS path modelling. This is the first contribution which critically consolidates available approaches, discloses problematic aspects and addresses significant areas for future research.

To provide several comparisons between linear and nonlinear approaches in denoising applications.

The comparison is based on the peak signal noise ratio (PSNR) image quality measure. Which one of the algorithms gives higher PSNR and then denoises more the original picture is studied.

Nonlinear reconstruction operators can improve the accuracy of the prediction in the vicinity of isolated singularities. A better treatment of the singularities corresponding to the image edges and, therefore, an improvement on the sparsity of the multiresolution representation of images are then expected.

In this paper the point‐value framework is considered. Other frameworks, as the cell‐average discretization, are more suitable for image processing where noise and texture appear. But, the point value schemes can be adapted to the cell‐average discretization using primitive function.

People can use the new denoising algorithm presented in the paper.

In this paper nonlinear schemes in the Harten's multiresolution framework that improve the results of the classical linear schemes are presented.

The purpose of this paper is to prove that under sufficient conditions the linearization method used for identifying a nonlinear bicompartmental system is stable.

The problem of identifying a nonlinear compartmental system appears as badly stated a priori. In fact the problem is not to identify the general behavior law of exchange between compartments, but to assume these laws known such as in Michaelis‐Menten systems or in polynomial compartmental systems with coefficients that need to be identified. It has been proved previously that with a linearization method an approximation can be obtained to the identification of these nonlinear systems. To validate this method, a stability study is necessary.

Sufficient conditions are established for the evolution law of a nonlinear bicompartmental system under which the linearization method is stable, and an upper bound is given on the approximation error – with an application, in the last section to the case of an open Michaelis‐Menten system.

The paper is of value in establishing sufficient conditions about the evolution law of a nonlinear system in order to show that this method is stable and to give an upper bound on the approximation error.

Considers the Adomian decomposition method to be a powerful technique that can solve efficiently a large class of linear and nonlinear differential equations. Describes a general method for approximating the solution of the Laplace equation with Dirichlet‐boundary conditions and which can be applied to a large class of problems.

The paper examines the convergence characteristics of the “minimized residual method based on the MRTR (three‐term recurrence formula of CG‐type) method” for solving large linear simultaneous equations.

The paper uses an example of magnetic field analysis of permanent magnet type of MRI taking account of the minor loop and eddy current.

It is shown that the preconditioned MRTR method can get a stable and quick convergence for such a relatively ill‐conditioned problem.

Illustrates that the convergence of the Incomplete Cholesky Conjugate Gradient method is one of the important issues in the practical 3D magnetic field analysis.

This paper seeks to explore how moderation can and should be modeled in cross‐national/cultural contexts. A multi‐national study of consumer involvement is utilized to demonstrate proper methods for modeling the different types of moderation.

Using data from a consumer survey regarding wine purchasing preferences conducted in Australia, New Zealand and the USA, the paper demonstrates how to identify moderators of form and of strength. A form moderator is modeled using multiplicative interactions while a strength moderator is modeled using multi‐group analyses in structural equation modeling (SEM). Differences in consumers across the three countries are examined from the results.

This study suggests that search behavior is positively influenced by involvement in New Zealand and the USA but not in Australia. It also shows that perceived risk of occasion decreases involvement in all three countries, while partial support for the positive effects of importance of tradition on involvement is found. Furthermore, “perceived risk of occasion,” identified as a moderator of form, is found to significantly moderate the relationship between importance of tradition and involvement in the US sample only. Finally, the results demonstrate significant differences across the three samples in relationships among importance of tradition, perceived risk of occasion, involvement, and search behavior, indicating that the country variable has significant moderator effects.

Understanding form vs strength moderation is important when evaluating multi‐national/cultural differences so that proper methodology can be utilized. This paper provides international marketing researchers with guidelines on how to model interactions and multi‐group comparisons using SEM.

This study was designed to extend knowledge of cognitive processing of country of origin cues by refining the concept of country image and investigating its role in product evaluations.

Data were collected from residents of a large North American metropolitan. A total of 436 usable questionnaires were returned. Data analysis was conducted using the EQS structural equation modeling software

We found that country image is a three‐dimensional concept consisting of cognitive, affective, and conative components. We modeled the relationships among country image, product beliefs, and product evaluations, and found that country image and product beliefs affect product evaluations simultaneously regardless of consumers' level of familiarity with a country's products. Findings also indicated that the structure of country image influences product evaluations both directly and indirectly through product beliefs. Consistent with affect transfer theory, the results showed that when a country's image has a strong affective component, its direct influence on product evaluations is stronger than its influence on product beliefs. Alternatively, when a country's image has a strong cognitive component, its direct influence on product evaluations was smaller than its influence on product beliefs.

One limitation pertains to the relatively poor psychometric properties of some items. Future research will benefit from further improvements in the measures of country image that tap into the various facets of the construct.

The major contributions of the study consist of the full operationalization of country image as a three‐dimensional concept, and the findings on the impact of country image structure on consumers' evaluation processes.