bluuebunny/crossref_metadata_2025 huggingface dataset:
A visual interpretation rating scale for validation of numerical models
Authors: Coleby D.E. , Duffy A.P.
Published: January 2007

Purpose

The comparison of large volumes of complex data resulting from numerical modelling in computational electromagnetics is a demanding task, especially when validating the performance of numerical models against experimental results and testing experimental repeatability. “By‐eye” comparisons can lead to inconsistencies and inherent subjectivity. This paper establishes a “visual” benchmark by which comparisons can be made and therefore used to assist in the development of an algorithmic approach to data comparison.

Design/methodology/approach

This new method presented here is based on the Cooper‐Harper Rating Scale, which is a test pilot's evaluation‐rating instrument. This has been modified through qualitative research. The assertion that the rating scale will leave the group mean response unaltered but will reduce the variance has been statistically tested.

Findings

The proposed rating scale provides a calibration technique by which to benchmark comparisons. The scale also reduces subjectivity by producing an overall quantitative measure of similarity. The paper concludes with an application of the rating scale to assessment of a candidate algorithmic approach against correlation.

Research limitations/implications

The research findings are based on small data sets, which is a limit imposed by the industrial environment in which this scale will be used.

Practical implications

This paper provides a tool to overcome some of the key substantial difficulties in communicating similarity or difference, namely that “similarity” and “difference” have no stand‐alone definition, there is a lack of a shared language for the comparisons and little commonality for a decision‐making framework.

Originality/value

This paper provides modellers and experimentalists in computational electromagnetics (particularly electromagnetic compatibility) with a structured approach to quantifying the quality of comparative results.
The application of polynomial matrix factorization in active network synthesis
Authors: Kandić Dragan B. , Reljin Branimir D.
Published: January 2007

Purpose

To investigate the general necessary condition for synthesis of square, real rational matrices of complex frequency as admittance matrices of active multiports with resistors, inductors, capacitors and possibly multiport transformers and to prove that this condition is also sufficient for synthesis of stable, square, real rational matrices of complex frequency as admittance matrices of balanced active multiports having only resistors, capacitors and voltage‐amplifiers with sufficiently large amplifications. The main aim of the paper is to provide a new and general method for stable admittance matrices synthesis and to develop strict realization algorithm by active balanced transformerless multiport networks.

Design/methodology/approach

The objectives of the paper are achieved by using factorization of regular polynomial matrices in complex frequency with certain degree as products of other regular polynomial matrices with specified degrees. A set of sufficient conditions for such a factorization is presented and derived a pertinent algorithm as the starting point for investigation and solving network synthesis problem and generation of class of equivalent realizations.

Findings

Theorem 1 states that sufficient condition for factorization of Pth order, generally regular polynomial matrix P(s) in complex frequency s with degree L, whose determinant has K distinct zeros, in form P(s)=P1(s)·P2(s), where 1≤p2=P20≤L−1 is degree of polynomial matrix P2(s), reads: K>(P−1)·L+p2−1. The coefficient‐matrices of s, s2,… in P1(s) and P2(s) are real or complex depending on whether distinct zeros of det P(s) are real or complex, respectively. Theorem 2 states that: (a) for realization of Pth order matrix of real rational functions in complex frequency s (i.e. RRF matrix) as admittance matrix of active balanced RLC P‐port network with multiport transformers, or without them, P generalized controlled‐sources and P controlling‐ports are necessary, in general; and (b) P balanced voltage‐controlled voltage‐sources (VCVSs) with real and by module greater than unity controlling coefficients (“voltage amplifications”) are sufficient for realization of stable admittance RRF matrix by active, balanced, transformerless, RC P‐port network.

Originality/value

This is a research paper with the following two main contributions (original results). First, a theorem on sufficient conditions for factorization of regular polynomial matrices in complex frequency; and second, a theorem relating to sufficient conditions for synthesis of matrices of real rational functions in complex frequency by active, balanced, transformerless networks. The results may be interesting for network theorists and researchers in the field of electric circuits and systems.
Frequency representations of one‐port networks
Authors: Walczak Janusz , Świszcz Piotr
Published: January 2007

Purpose

Analysis of harmonics propagation in power systems requires information about models of non‐linear loads which are the main source of harmonics. The purpose of the paper is to present a method of parameter determination of non‐linear loads.

Design/methodology/approach

A method of parameter determination of a model has been described in the article. This method has been developed assuming that mathematical description of a non‐linear load is known. In order to obtain a harmonic representation of this model for one‐phase loads the theory of harmonic balance method has been used.

Findings

Parameters of the current or voltage controlled sources can be expressed as a function of any number of voltage or current harmonics. In the case under consideration the network input current is a function of input voltage and its derivatives. Thus, contrary non‐linear element with inertialess characteristics, the first harmonic of the current depends not only on amplitude but also on frequency of the voltage across terminals of one‐ports.

Originality/value

The method presented in the paper enables relatively simple determination of frequency parameters of non‐linear models of one‐port networks.
Calculation of electrical field of spherical and cylindrical gas voids in dielectrics by taking surface conductivity into consideration
Authors: Alisoy G.T. , Alisoy H.Z. , Koseoglu M.
Published: January 2007

Purpose

To determine the electrical field E1(t) in spherical and cylindrical gas voids existing in an insulator by considering surface conductivity of gas voids having an electrical permittivity of ε1 and conductivity of γ1 for DC and AC situations.

Design/methodology/approach

Analytical expressions satisfying Laplace equation for inside and outside of the cylindrical and spherical gas voids in an insulator located in an external electrical field having a definite time dependent character, have been derived by considering the surface conductivity of the gas void. The coefficients included by these analytical expressions have been determined by utilizing the continuity equation of the current on the surface of the voids.

Findings

It has been demonstrated that the electrical field remains uniform in spherical and cylindrical gas voids when the surface conductivity of gas void has been considered. It has been determined that the contact charging process of different shaped particles has an exponential characteristic, and some expressions have been derived to determine the time constants of this process for practical purposes.

Practical implications

The results have been applied to the problems about contact charging of semi‐spherical and semi‐cylindrical insulated particles located at a charged surface and problems about the calculation of onset discharging voltage of ionization process in dielectric including gas voids.

Originality/value

For spherical and cylindrical gas voids, the onset discharging voltage corresponding to the ionization process occurring in gas voids has increased by increasing the surface conductivity of the void. For the limit value of the surface conductivity, the voids in the insulator behaves like metal particles distributed into the insulator, for this reason, at the outside of the void, especially in the regions where the voids are close to the electrodes and each other, the electrical field will be non‐uniform and will increase. This situation will cause the ignition of the partial discharge and destroy to the insulator.
Barkhausen instability and its implication in T(x) modelling of hysteresis
Authors: Takacs J.
Published: January 2007

Purpose

The paper sets out to formulate the intermolecular forces leading to Barkhausen instability. In the approach the known concept of effective field is used within the framework of the T(x) model. The aim is to provide a mathematical tool to theoreticians and applied scientists in magnetism that is easier to use than those of other models. At the same time to demonstrate the easy applicability of the T(x) model to hysteretic phenomena.

Design/methodology/approach

With the combination of the effective and the external field the model is applied to hysteresis loops as well as to the anhysteretic state showing in both cases the local development of unstable conditions at beyond a critical point, leading to local hysteresis loops.

Findings

The paper formulates the critical conditions for the hysteretic and the anhysteretic process and calculates the susceptibility as the functions of magnetisation and the applied field.

Research limitations/implications

Experimental verification will be required to prove the applicability to the various magnetic materials and to the accuracy of the model.

Practical implications

The paper provides an easy mathematical and visual method to show the conditions before and after the Barkhausen instability sets in during the magnetisation process.

Originality/value

The paper provides an easy mathematical tool for theoreticians and experimental scientists with a visual presentation of processes leading to Barkhausen instability and magnetic behaviour beyond that by using the T(x) model.
Analysis of photonic band‐gap structures in stratified medium
Authors: Tong Ming‐Sze , Chen Yinchao , Lu Yilong , Krozer Viktor , Kagoshima Kenichi , Kim Hyeong‐Seok , Chang Tae‐Gyu
Published: January 2007

Purpose

To demonstrate the flexibility and advantages of a non‐uniform pseudo‐spectral time domain (nu‐PSTD) method through studies of the wave propagation characteristics on photonic band‐gap (PBG) structures in stratified medium

Design/methodology/approach

A nu‐PSTD method is proposed in solving the Maxwell's equations numerically. It expands the temporal derivatives using the finite differences, while it adopts the Fourier transform (FT) properties to expand the spatial derivatives in Maxwell's equations. In addition, the method makes use of the chain‐rule property in calculus together with the transformed space technique in order to make the algorithm flexible in terms of non‐uniform spatial sampling.

Findings

Through the studies of the wave propagation characteristics on PBG structures in stratified medium, it has been found that the proposed method retains excellent accuracy in the occasions where the spatial distributions contain step of up to five times larger than the original size, while simultaneously the flexibility of non‐uniform sampling offers further savings on computational storage.

Research limitations/implications

Research has been mainly limited to the simple one‐dimensional (1D) periodic and defective cases of PBG structures. Nevertheless, the findings reveal strong implications that flexibility of sampling and memory savings can be realized in multi‐dimensional structures.

Practical implications

The proposed method can be applied to various practical structures in electromagnetic and microwave applications once the Maxwell's equations are appropriately modeled.

Originality/value

The method validates its values and properties through extensive studies on regular and defective 1D PBG structures in stratified medium, and it can be further extended to solving more complicated structures.
Frequency‐domain analytical investigation of space‐vector modulated PWM waveforms in four‐switch VSI
Authors: Klima Jiri
Published: January 2007

Purpose

To provide a new method and methodology for researches and academic members which can help them to develop scientific work.

Design/methodology/approach

The paper presents closed‐form expressions for the harmonic components of the space‐vector pulsewidth modulated (PWM) waveforms under inverter fault‐mode operations. The main method that is used is the Laplace transform and Fourier series expansion theorem.

Findings

Provides information about harmonic sources and its influence on the behavior of the induction machine.

Practical implications

The calculated harmonics show a very close agreement with measured harmonics from an experimental digital signal processor (DSP) based modulator. It provides a very useful source of theoretical and practical information for scientific and research area.

Originality/value

The method is original and has not been published before. The new and original approach is given by the use of the Laplace transform of space‐vectors in the complex plane. This will help to understand harmonics which are formed in four‐switch voltage source inverter.
Time step truncation in direct simulation Monte Carlo for semiconductors
Authors: Muscato Orazio , Wagner Wolfgang
Published: January 2007

Purpose

To provide an accurate analysis of the systematic error introduced by the constant time technique free flight mechanism, due to the choice of the time step and number particles.

Design/methodology/approach

A homogeneous (bulk) silicon semiconductor is studied by using direct simulation Monte Carlo (DSMC).

Findings

The systematic error turns out to be of the first order with respect to the time step. The efficiency of the method is tackled.

Research limitations/implications

The analysis is limited to the bulk case. Future researches will consider non homogeneous devices

Originality/value

An accurate analysis of an “old” free flight mechanism has been performed, and its limits have been stated.
Discontinuous Galerkin time‐domain solution of Maxwell's equations on locally‐refined nonconforming Cartesian grids
Authors: Canouet N. , Fezoui L. , Piperno S.
Published: January 2007

Purpose

The use of the prominent FDTD method for the time domain solution of electromagnetic wave propagation past devices with small geometrical details can require very fine grids and can lead to very important computational time and storage. The purpose is to develop a numerical method able to handle possibly non‐conforming locally refined grids, based on portions of Cartesian grids in order to use existing pre‐ and post‐processing tools.

Design/methodology/approach

A Discontinuous Galerkin method is built based on bricks and its stability, accuracy and efficiency are proved.

Findings

It is found to be possible to conserve exactly the electromagnetic energy and weakly preserves the divergence of the fields (on conforming grids). For non‐conforming grids, the local sets of basis functions are enriched at subgrid interfaces in order to get rid of possible spurious wave reflections.

Research limitations/implications

Although the dispersion analysis is incomplete, the numerical results are really encouraging it is shown the proposed numerical method makes it possible to handle devices with extremely small details. Further investigations are possible with different, higher‐order discontinuous finite elements.

Originality/value

This paper can be of great value for people wanting to migrate from FDTD methods to more up to date time‐domain methods, while conserving existing pre‐ and post‐processing tools.
Multiobjective optimal design of three‐phase induction motor using simulated annealing technique
Authors: Subramanian S. , Bhuvaneswari R.
Published: January 2007

Purpose

This paper presents a novel multiobjective optimal design of three phase induction motor using simulated annealing (SA) technique for minimizing annual material cost and annual loss cost as two objectives.

Design/methodology/approach

The design problem of a three‐phase induction motor is presented as a nonlinear multicriterion optimization problem on the basis of minimizing the annual cost of the motor. The annual cost referred is the sum of the annual interest and depreciation of motor active material costs, annual cost of active power loss of the motor and the annual energy cost required to supply such power loss. A computer package is built which generates initial values of motor parameters and gives the optimal values of these parameters with more than one objective function and nonviolated constraints. The problem is solved by giving weights which reflect the priority of objective functions. The SA technique is used as a tool to solve the problem.

Findings

To verify the validity, the proposed method is applied to a three‐phase induction motor design. From the results, it is found that the proposed method is fast and efficient and hence it is useful for multiobjective design of an induction motor.

Originality/value

This method is particularly useful in satisfying the needs of motor producer and consumer by prioritizing their needs and finally arriving at a best compromise solution.
Minimal positive realizations for discrete‐time systems with state time‐delays
Authors: Kaczorek Tadeusz
Published: January 2007

Purpose

Aims to formulate and solve the minimal positive realization problem for discrete‐time linear single‐input, single‐output systems with many state time‐delays.

Design/methodology/approach

A conceptual discussion and approach are taken.

Findings

Sufficient conditions for the existence of positive realizations of a given proper rational function are established. A procedure for computation of minimal positive realizations is presented and illustrated by an example.

Originality/value

Extends an earlier method for positive discrete‐time systems with many state time‐delays.
Steady‐state modeling of a phase‐shift PWM parallel resonant converter
Authors: İskender İres , Üçtug˘ Yıldürüm , Bülent Ertan H.
Published: January 2007

Purpose

To derive an analytical model for a dc‐ac‐dc parallel resonant converter operating in lagging power factor mode based on the steady‐state operation conditions and considering the effects of a high‐frequency transformer.

Design/methodology/approach

A range of published works relevant to dc‐ac‐dc converters and their control methods based on pulse‐width‐modulation technique are evaluated and their limitations in output measurement of higher output voltage converters are indicated. The circuit diagram of the converter is described and the general mathematical model of the system is obtained by deriving and combining the mathematical models of the different converter blocks existing in the system. The derived mathematical model is used to study the steady‐state and transient performance of the converter. The deriving procedure of the analytical model for a parallel resonant converter is extensively given and the analytical model obtained is verified by simulation results achieved using MATLAB/SIMULINK and the program written by the authors.

Findings

The paper suggests an analytical model for dc‐ac‐dc parallel resonant converters. The model can be used in the output voltage estimation of a converter in terms of its phase‐shift angle and the dc‐link voltage.

Research limitations/implications

The resources in the library of the authors' university and also the English resources relative to dc‐ac‐dc converters reachable through the internet were researched.

Practical implications

The analytical model suggested can be used in estimating the output voltage of the converters used in high‐voltage applications or where there are difficulties in employing sensors in measurement of the output voltage due to high price or implementation problems.

Originality/value

The originality of the paper is to present an analytical model for dc‐ac‐dc parallel resonant converters. Using this model makes it possible to estimate the output voltage of the converter using the dc‐link voltage and the phase‐shift angle. The proposed model provides researchers to regulate the output voltage of the converters using feed‐forward control technique.
Efficient computation of the periodic steady state solution of nonlinear electric systems applying parallel processing techniques
Authors: Medina Aurelio , Ramos‐Paz Antonio , Rubén Fuerte‐Esquivel Claudio
Published: January 2007

Purpose

To introduce an efficient methodology for the computation of the periodic steady state solution of power systems with nonlinear and time‐varying components which combines a Newton method based on a numerical differentiation procedure to obtain a fast steady state solution in the time domain and parallel process techniques.

Design/methodology/approach

Nonlinear electric systems are represented by a set of differential equations, the conventional solution in the time domain is accelerated by a Newton method based on a numerical differentiation procedure for the convergence of state variables to the limit cycle and thus to the network periodic steady state solution. The efficiency of the solution is further enhanced with the application of parallel processing technology based on parallel virtual machine (PVM) and multi‐threading (MT).

Findings

The periodic steady state solution of nonlinear electric systems, even of large‐scale, can be efficiently obtained in the time domain with the application of Newton methods for the fast converge of state variables to the limit cycle. The efficiency of the computer solution can be dramatically enhanced with the application of parallel processing technology. The potential of the PVM and MT platforms is shown in the investigation. A comparison of advantages and disadvantages associated with each parallel processing platforms is given; a quantitative comparison between PVM and MT is provided.

Practical implications

The steady state solution of nonlinear electric systems can be efficiently obtained with a combination of Newton methods for the convergence acceleration to the limit cycle and parallel processing techniques.

Originality/value

The steady state solution of nonlinear electric systems using a Newton method based on a numerical differentiation procedure for the convergence acceleration to the limit cycle and parallel processing based on the PVM and MT platforms has not, to the authors' knowledge, reported before.
Improved fast evolutionary program for optimum design of power transformer
Authors: Subramanian S. , Bhuvaneswari R.
Published: January 2007

Purpose

The power transformer is one of the most important pieces of equipment in a power system. The necessity for the optimum design of a power transformer arises because the design chosen should satisfy all the limitations and restrictions placed on it. This paper presents an improved fast evolutionary programming (IFEP) technique for the optimal design of a three‐phase power transformer.

Design/methodology/approach

The optimization of the transformer design problem is formulated as an NLP problem, expressing the objective and constraint functions in terms of the selected independent variables. Here the cost of the transformer is considered as the objective function and is the sum of material cost of stampings and copper windings, cost of cooling tube arrangements, cost of cooling medium, insulation cost and labour cost. A computer program is written from which the optimal design parameters are obtained. For optimization, the classical evolutionary programming (CEP) technique and its variant the IFEP technique are used and the results are compared.

Findings

The application of CEP and IFEP for transformer design has been demonstrated on two test cases. It has been observed that this IFEP outperforms the CEP in obtaining the optimum design of transformers of smaller as well as larger ratings in terms of execution time, convergence rate, quality and success rate.

Originality/value

The proposed method results in the economical design of a three‐phase power transformer which can significantly reduce the cost of manufacturing transformers.
New methods for applying the Adomian method to partial differential equations with boundary conditions
Authors: Benneouala Titem , Cherruault Yves , Abbaoui Karim
Published: January 2007

Purpose

To find methods for solving non‐linear partial differential equations. The decomposition method may be applied, but a difficulty arises when applied to non‐linear partial differential equations with initial and boundary conditions. In this work, two methods are described that take into account the boundary conditions.

Design/methodology/approach

The decomposition method whilst being a powerful tool for solving non‐linear functional equations encounters difficulties in finding solutions of partial differential equations with boundary conditions. In this paper, two methods are introduced which consist of setting boundary conditions to the equations so that the decomposition methods can be applied.

Findings

By using the two proposed methods the decomposition method can then be easily used. In this work the two methods taking account of the boundary conditions were found to be efficient and allows a solution to be found using the Adomian decomposition method.

Research limitations/implications

The two new methods provide solutions by the application of the decomposition method of George Adomian as extended by other researchers. Both are efficient: the first giving interesting results for linear and non‐linear problems; the second one is also efficient, but difficulties could arise from the calculations of the required series.

Practical implications

The research provides two efficient methods. The first method gives the demonstrated results for linear and non‐linear problems due to the use of symbolic software such as Mathematica or Maple.

Originality/value

Both methods illustrate the powerful use of the decomposition techniques pioneered by Adomian and as a result of their application may be applied to the solving of non‐linear functional equations of any kind. This paper tackles the problems by introducing new methods of applying the Adomian techniques to partial differential equations with boundary conditions.
A different approach for solving singular two‐point boundary value problems
Authors: Inc M. , Ergüt M. , Cherruault Y.
Published: January 2007

Purpose

Aims to solve singular two‐point boundary value problems, linear and non‐linear by using modified and standard decomposition methods, respectively.

Design/methodology/approach

The approximate solution of this problem is calculated in the form of series with easily computable components.

Findings

The accuracy of the presented numerical method was examined in comparison with others and was found to be superior.

Research limitations/implications

The decomposition method provided a reliable technique that required less work when compared with the traditional techniques. The method does not require unjustified assumptions linearisation discretizations or perturbation.

Practical implications

The Adomian decomposition method was found to be very easy to apply to both differential equations, higher‐order boundary value problems and linear or non‐differential systems.

Originality/value

The technique is both innovative and efficient and an original approach for solving singular two‐point boundary value problems.
Geometrical interpretation and approximate solution of non‐linear KdV equation
Authors: Bektas M. , Inc M. , Cherruault Y.
Published: January 2007

Purpose

The purpose is to study an analytical solution of non‐linear Korteweg‐de Vries (KdV) equation by using the Adomian decomposition method (ADM).

Design/methodology/approach

The solution is calculated in the form of a series with easily computable components. The non‐linear KdV equation has been considered and the analytic solution is compared with its numerical solution by using the ADM and Mathematica software program.

Findings

This approach to the non‐linear evolution equation was found to be valuable as a tool for scientists and applied mathematicians, because it provides immediate and visible symbolic terms of analytical solution as well as its numerical approximate solution to both linear and non‐linear problems without linearization or discretization.

Research limitations/implications

This geometrical interpretation and the produced approximate solution of the non‐linear KdV equation illustrates the use of the ADM. Research using ADM is ongoing but already the numerical results obtained in this paper justify the advantages of this methodology, even in a few terms of approximation.

Practical implications

Using the Mathematica software package the ADM was implemented for homogenous KdV equation as an illustrative example which has distinct applications for scientists and applied mathematicians.

Originality/value

This is an original study of the use of ADM for the solution of the non‐linear KdV equation. It also shows how the Mathematica software package can be used in such studies.
Direct identification of general linear compartmental systems by means of (n−2) compartments measures
Authors: Hebri B. , Cherruault Y.
Published: January 2007

Purpose

Aims to study direct identification of general linear compartmental systems by means of (n−2) compartmental measures. This is based on two main results.

Design/methodology/approach

The first result presented is related to the existence and uniqueness of identification exchange parameters in linear compartmental systems by using a direct method with less restrictive assumptions. A second result given, permits us to show that (n−2) observations are sufficient to identify the compartmental systems.

Findings

This research study describes a method which shows that in an open linear compartmental systems there exists an energy dissipation from compartmental 1 to the systems exterior. An explicit relationship between the dissipated energy and the exchange parameters was established. The results are probably perfectible and are optimal for n=3, where only an observable compartment is needed.

Practical implications

The identification of exchange parameters is easily obtained by using the matrix of the elementary masses and by solving a linear algebraic system. Among the open problems in compartmental analysis is the problem of minimizing the observable compartments which is studied in this paper.

Originality/value

The study is based on the original work of Yves Cherruault who has already presented methods for proving that a bicompartmental systems is uniquely identified. He has generalised his method for n‐compartments.
Solving inequalities by α‐dense curves. Application to global optimization
Authors: Mora G. , Cherruault Y. , Ubeda J.I.
Published: January 2007

Purpose

To introduce an algorithm to solve inequalities defined by real functions on a certain compact set D of a general metric space (E, D). The device is based on α‐dense curves.

Design/methodology/approach

The solution of inequalities using α‐dense curves and also an approach to a global optimization technique, similarly obtained to that of the inequalities.

Findings

A new method is presented. The algorithm for solving inequalities is described which is based on a proven result. Inequalities of n‐variable dependence are reduced by transformation using α‐dense curves.

Research limitations/implications

The research is a continuation of studies that resulted in a new method called Alienor for solving global optimization problems associated with multi‐variable functions.

Originality/value

Based on earlier research by the authors α‐dense curves have been used which allow the transformation of a n‐variables global optimization problem into a one‐variable global one. This paper gives a new method for quickly solving the one‐variable problem.
Adomian method for solving adaptive control problem
Authors: Manseur S. , Cherruault Y.
Published: January 2007

Purpose

Aims to propose methodology to solve adaptive control problems by the use of the Adomian decomposition method (ADM).

Design/methodology/approach

The approach to this problem is through the ADM which consists in finding a solution of nonlinear state equations as a convergent series that depends on the unknown parameters of the system.

Findings

It was shown that a first approach for solving adaptive control problems could be tackled by using the ADM. The solution of the systems was obtained in a series forms as a function of the unknown parameters. The objective function became a function that explicitly depends on parameters. This, it was shown, can be minimised by classical or nonclassical global optimization methods.

Research limitations/implications

The methods presented depends on ADM. It is proposed that future work involves the study of an adaptive control problem associated to a nonlinear compartmental systems of Michaels‐Menten type.

Originality/value

Presents an applications of the developed ADM using it, as adapted to control problems. It contributes to mathematical modelling studied concerning most biological, physical phenomena which are described by nonlinear systems: differential, partial differential in form and for which there is little hope of finding an exact solution.
Global optimization via α‐dense curves
Authors: Benabidallah A. , Cherruault Y.
Published: January 2007

Purpose

To study constrained or unconstrained global optimization problems in a cube of Rd where d is a positive integer.

Design/methodology/approach

α‐dense curves are initially used to transform this problem into a global optimization problem of a single variable. The optimization of the one variable is then treated by means of the Legendre‐Fenchel Transform. This discrete convex envelope of the one variable function obtained previously, can then be computed.

Findings

Global optimization problems of this nature have already been extensively studied by the authors. In this paper they have coupled the Alienor method with Legendre‐Fenchel Tranform to compute a discrete convex envelope of the function to minimize. A fast algorithm was successfully used to do this.

Research limitations/implications

This approach to global optimization is based on α‐dense curves and numerical tests performed on a Pentium IV (1,700 MHz) computer used with Mathematica 4 software.

Practical implications

Gives the solutions illustrated in the numerous examples provided that show the practicality of the methodology.

Originality/value

A new approach based on extensive research into global optimization via α‐dense curves.
Identification of closed Michaelis‐Menten system by a linear approach
Authors: Hebri B. , Cherruault Y.
Published: January 2007

Purpose

This paper aims at identifying the closed Michaelis‐Menten (M‐M) system. The system governs many phenomena that are based on “enzyme reactions”.

Design/methodology/approach

A linearization method is used. The system, however is not homogeneous and consequently earlier identification results obtained by the author cannot be applied. The approach is to show that the closed Michaelis‐Mentan system can be approximated by a sequence of open M‐M systems. The M‐M parameters are then obtained by continuity from the Cauchy's problem solution.

Findings

The main results – the identification of a closed M‐M system is described. The linearization of the closed M‐M compartmental system led to a linear nonhomogeneous system. Earlier classical methods could not applied but the “Reasonable Biological Hypothesis” of the author allowed further study.

Research limitations/implications

This study takes a preferred theoretical aspect. A generalization to n, n≥3 is considered to be interesting because we can consider an open compartmental system having n compartments as a closed system with n+1 compartments. Further work on this generalization is contemplated.

Practical implications

This theoretical study will further increase the use compartmental analysis to modelling any phenomena depending only on time.

Originality/value

Provides a methodology for identification of M‐M system using a linear strategy.
A new decomposition method based on infinite products
Authors: Abbasbandy S.
Published: January 2007

Purpose

The purpose is to apply a new decomposition method for solving non‐linear functional equations.

Design/methodology/approach

The method used is similar to the Adomian decomposition method (ADM). In this approach, Adomian's original solution for solving non‐linear functional equations and Cherruault's proposed new definition of ADM are replaced by a new decomposition technique.

Findings

Adomian gives the solution using his decomposition method as an infinite series usually converging to an accurate solution. Cherruault's new definition also proved the convergence under suitable conditions and a reasonable hypothesis. This paper has developed a new decomposition technique based on infinite products. It was found that it then became possible to prove the convergence under some given conditions.

Research limitations/implications

The new method has its convergence proved and a number of research examples presented. The method proved efficient but there remains many difficulties in this area. Further research is needed to see whether this method can be used for solving initial value problems.

Originality/value

Produces another tool and furthers the development of ADM by introducing a method based on infinite products.
A reliable method for obtaining approximate solutions of linear and nonlinear Volterra‐Fredholm integro‐differential equations
Authors: Inc M. , Cherruault Y.
Published: January 2007

Purpose

Based on the original methods of Adomian a decomposition method has been developed to find the analytic approximation of the linear and nonlinear Volterra‐Fredholm (V‐F) integro‐differential equations under the initial or boundary conditions.

Design/methodology/approach

Designed around the methods of Adomian and later researchers. The methodology to obtain numerical solutions of the V‐F integro‐differential equations is one whose essential features is its rapid convergence and high degree of accuracy which it approximates. This is achieved in only a few terms of its iterative scheme which is devised to avoid linearization, perturbation and any transformation in order to find solutions to given problems.

Findings

The scheme was shown to have many advantages over the traditional methods. In particular it provided discretization and provided an efficient numerical solution with high accuracy, minimal calculations as well as an avoidance of physical unrealistic assumptions.

Research limitations/implications

A reliable method for obtaining approximate solutions of linear and nonlinear V‐F integro‐differential using the decomposition method which avoids the tedious work needed by traditional techniques has been developed. Exact solutions were easily obtained.

Practical implications

The new method had most of its symbolic and numerical computations performed using the Computer Algebra Systems‐Mathematica. Numerical results from selected examples were presented.

Originality/value

A new effective and accurate methodology has been developed and demonstrated.
A global optimization method for a large number of variables (variant of Alienor method)
Authors: Konfé Balira O. , Cherruault Yves , Benneouala Titem
Published: January 2007

Purpose

To use α‐dense curves to allow the transform of a multiple function into a single variable function in order to solve global optimization problems.

Design/methodology/approach

Use is made of the established Alienor method which has already been applied to biological and industrial processes. The problems tackled have a number of variables and the chosen optimization method is a variant of the Alienor method.

Findings

A new method for solving global optimization problem, called the Alienor method is now the subject of many variants. In this paper, it was found that a new reducing transformation α‐dense in Rn was successful in solving this type of problem when associated to a functional depending on a large number of variables. The reducing transformation is very efficient and accurate.

Research limitations/implications

This is a variant of the proven Alienor Method which has improved the resolution of global optimization problems. It showed that the reducing transformation has the advantage that a small calculation time is obtained even when the relevant series are slowly increasing. Further development of the method is anticipated.

Practical implications

Proved very effective for obtaining the global optimum with good precision and very short calculation time for large numbers of variables. Can be performed on micro‐calculators.

Originality/value

New variant of proven method. Of interest in solution of concrete problems in biology and industry.
A new reducing transformation for global optimization (with Alienor method)
Authors: Cherruault Yves
Published: January 2007

Purpose

To propose a new reducing transformation that allows the calculation of the absolute minimum of a function that depends on a large number of variables to be performed quickly.

Design/methodology/approach

The methodology depends on the building of α‐dense curve in a compact of Rn that allows the approximate at any point of this compact with a desired precision. This approach allows global optimization problems that depend on a large number of variables, be tackled quickly and precisely.

Findings

It was found that this new method for densifying a space Rn (compact) by means of simple parametric curve (a space filling curve) could be used to deal with global optimization problems of some several hundreds or thousands of variables in some seconds or minutes. The technique is being based on the cosine function.

Research limitations/implications

The results depend on the use of a computer system or “micro‐calculator”.

Practical implications

This is an “economic” method and the technique which uses the cosine function allows the reduction of the calculation time and avoids calculus errors. It has the practical advantages that coupled with a transformation eliminating local minima, it permits the solution of global optimization problems of more than 1,000 variables in less than 1 min.

Originality/value

The method is innovative and shown to be accurate and fast even with a function of a large number of variables.
Alienor method for global optimization with a large number of variables
Authors: Benneouala T. , Cherruault Y.
Published: January 2007

Purpose

To show the usefulness of the Alienor method when applied to the global optimization problems that depend on large number of variables.

Design/methodology/approach

The approach is to use reducing transformations. The first is due to Cherruault and the second to Mora.

Findings

It was found that the Alienor method was very efficient and reliable in solving global optimization problems of many variables. Results produced to confirm this conclusion.

Research limitations/implications

The numerical results presented showed that the Alienor method was suitable for finding global minimum even in the case of a very large number of variables. The research provides a new methodology for solving such problems.

Practical implications

No other method, we believe, can obtain such results in so short a time for hundreds or even thousands of variables.

Originality/value

The new approach relies on the originality of both the Cherruault and the Mora transformations and their earlier invention of the Alienor method.
A new “Optimization‐Preserving‐Operator” applied to global optimization
Authors: Konfe Balira O. , Cherruault Yves , Some Blaise , Benneouala Titem
Published: January 2007

Purpose

To introduce Optimization‐Preserving‐Operators (O‐P‐Os), which are operators that are defined on classes of real functions that depend on a single variable, and allow us to eliminate local optima and to preserve global optima.

Design/methodology/approach

Outline a new method to build O‐P‐Os. These are introduced as O‐P‐O* and lead to a new approach for solving global optimization problems.

Findings

It was found that classical discretization methods for obtaining optimum of one variable function was too time‐consuming. The simple method introduced provided solutions to the test functions chosen as examples. The solutions were provided in a short time.

Research limitations/implications

Provides new tools for mathematical programming and in particular the global optimization problems. The O‐P‐O* introduced innovative technique for solving such problems.

Practical implications

O‐P‐O* produces solutions to global optimization problems in a much improved time. The algorithm derived, and the steps for its operation proved on implementation, the efficiency of the new method. This was demonstrated by numerical results for selected functions obtained using microcomputer systems.

Originality/value

Provides new way of solving global optimization problems.
Optimal control of chemotherapy of HIV model using the coupled Adomian/Alienor methods
Authors: Manseur S. , Attalah K. , Cherruault Y.
Published: January 2007

Purpose

This paper aims at applying the proven Adomian and Alienor methods to solve the problem of optimal chemotherapy of HIV model.

Design/methodology/approach

The combination of the Adomian decomposition method and the Alienor reduction method allows us to solve the control problem as if it were a classical one‐dimensional minimization problem. The methodology is applied to a HIV model and simulation results given.

Findings

A general abstract framework for the control of a non‐linear evolution system has been developed. It was shown that it is possible to control a system by using the powerful techniques of Adomian and Alienor, and produce results comparable with those obtained by classical methods where other cost functions are used.

Research limitations/implications

The benefit of this work is based on the CD4 healthy cells being maximized and the cost based on a drug dose being minimized. The new methodology could be used after further research for solving many control problems in biology and in other areas such as those involving industrial processes.

Practical implications

New methodology is cost‐effective in controlling the drug dose affecting rate of infection of cells by HIV virus.

Originality/value

New application of proven methodology will solve many control problems in biocybernetics/biomedicine/industry and other fields.
Second‐order cybernetics and enactive perception
Authors: Bishop J.M. , Nasuto J.S.
Published: January 2007

Purpose

To present an account of cognition integrating second‐order cybernetics (SOC) together with enactive perception and dynamic systems theory.

Design/methodology/approach

The paper presents a brief critique of classical models of cognition then outlines how integration of SOC, enactive perception and dynamic systems theory can overcome some weaknesses of the classical paradigm.

Findings

Presents the critique of evolutionary robotics showing how the issues of teleology and autonomy are left unresolved by this paradigm although their solution fits within the proposed framework.

Research limitations/implications

The paper highlights the importance of genuine autonomy in the development of artificial cognitive systems. It sets out a framework within which the robotic research of cognitive systems could succeed.

Practical implications

There are no immediate practical implications but see research implications.

Originality/value

It joins the discussion on the fundamental nature of cognitive systems and emphasise the importance of autonomy and embodiment.