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Educational change and improvement are constant processes. Practically every country in the world today is attempting to improve, reform, transform or change its educational system. The results of these development efforts have generally been disappointing. A general consensus seems to be that the gap between societal expectations and educational achievements is wide and becoming greater. The perceived failures of education are particularly difficult for political and educational leaders to understand given the massive influx of resources invested in educational systems in recent years. This is a result of a linear expectation wherein output is proportional to the input. Non‐linear theory, proposed in this paper as a more valid way of conceptualizing educational development efforts, does not assume this proportional relationship. This paper addresses non‐linear theory by using it to examine educational development efforts in Western and Eastern European nations.

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.

This paper aims to present an approach for calibrating the numerical models of dynamical systems that have spatially localized nonlinear components. The approach implements the extended constitutive relation error (ECRE) method using multi-harmonic coefficients and is conceived to separate the errors in the representation of the global, linear and local, nonlinear components of the dynamical system through a two-step process.

The first step focuses on the system’s predominantly linear dynamic response under a low magnitude periodic excitation. In this step, the discrepancy between measured and predicted multi-harmonic coefficients is calculated in terms of residual energy. This residual energy is in turn used to spatially locate errors in the model, through which one can identify the erroneous model inputs which govern the linear behavior that need to be calibrated. The second step involves measuring the system’s nonlinear dynamic response under a high magnitude periodic excitation. In this step, the response measurements under both low and high magnitude excitation are used to iteratively calibrate the identified linear and nonlinear input parameters.

When model error is present in both linear and nonlinear components, the proposed iterative combined multi-harmonic balance method (MHB)-ECRE calibration approach has shown superiority to the conventional MHB-ECRE method, while providing more reliable calibration results of the nonlinear parameter with less dependency on a priori knowledge of the associated linear system.

This two-step process is advantageous as it reduces the confounding effects of the uncertain model parameters associated with the linear and locally nonlinear components of the system.

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.

The non‐linear damping mechanisms are expressed in two general forms: velocity dependent and displacement dependent. The non‐linear damping phenomena are expressed by an array of ‘local constants’, whose value depends upon excitation frequency, excitation amplitude, and type of non‐linearity. Thus, the non‐linear system is replaced by several localized linear systems corresponding to every discrete frequency and amplitude of excitation. Each of the localized linear systems, thus formulated, characterizes the response behaviour of the original non‐linear system, quite accurately in the vicinity of the specific frequency and amplitude of excitation. An algorithm is developed, which expresses the non‐linear damping by an array of ‘local constants’. The algorithm then employs the usual linear design tools to generate the response characteristics almost identical to the response behaviour of the non‐linear system.

The analysis of certain structures must be performed with due consideration to non‐linear behavior, such as material and geometric non‐linearities. The existing methods for treating non‐linear structural behavior generally make use of repeated linearization, such as load increment methods. This paper demonstrates that there is an alternative type of linearization that appears to have significant advantages when applied to the analysis of non‐linear structural systems. Briefly stated, this alternative linearization can be thought of as a “monomialization”. This monomial (single‐termed power function) approximation more faithfully models the power function behavior inherent in typical structural systems. Conveniently, it becomes a linear form when transformed into log space. Thus, computational tools based on linear algebra remain useful and effective. Preliminary results indicate that the monomial approximation provides a higher quality approximation to non‐linear phenomena exhibited in structural applications. Consequently, incremental and iterative methods become more effective because larger steps can be taken. The net result is an increase in reliability of the solution process and a significant reduction in computational effort. Two examples are presented to demonstrate the method.

A simple numerical algorithm is developed for the implementation of the harmonic balance method to analyse periodic responses of a general dynamic system having geometrical non‐linearities of the quadratic and cubic types. The resulting non‐linear algebraic equations which are not explicitly determined are solved by non‐linear equation routines available in most mathematical libraries. Various non‐linear responses, such as the combinational resonances of a hinged‐clamped beam, the non‐linear effect on degenerate vibration modes of a square plate and the non‐linear oscillation of thin rings, are presented to demonstrate the versatility of the algorithm.

This paper presents several methods for enhancing computational efficiency in both static and dynamic analysis of structural systems with localized non‐linear behaviour. A significant reduction of computational effort with respect to brute‐force non‐linear analysis is achieved in all cases at the insignificant (or no) loss of accuracy. The presented methodologies are easily incorporated into a standard computer program for linear analysis.

The traditional network scheduling methods such as the Critical Path Method (CPM), Programme Evaluation Review Technique (PERT), and bar charting are typically not effective for the planning of linear construction projects. Linear scheduling methods, on the other hand, model the progress of repetitive activities in sloping lines and are more effective for linear modelling and analysis. Nonetheless, their use in the construction industry has so far been very limited. Among other reasons for this is the unfamiliarity of construction personnel with these techniques, which plays a major role in hampering their application. This paper introduces a graphically based approach to assist in the linear programming (LP) modelling of linear scheduling analysis. The Planning & Optimization for Linear Operations (POLO) system provides a graphic LP modelling environment in which model formulation can be easily accomplished in a graphic and interactive fashion. Thus, the application of linear scheduling methods can be facilitated. The Isle of Palms Connector Bridge project in Mount Pleasant, South Carolina is used to demonstrate the use of the system.

Addresses the lack of success in educational reform efforts by utilizing a metacognitive analysis of the base assumption of most, if not all, current reform efforts. Suggests a different theoretical orientation and perspective for understanding education and attempts to improve it. By contrasting the common orientation of today and the one proposed, the paper applies this new perspective to two examples. Examines educational reform in light of the orientation proposed.