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Showing papers by "Polytechnic University of Turin published in 2003"


01 Jan 2003
TL;DR: In this article, a monolithic terahertz injection laser that is based on interminiband transitions in the conduction band of a semiconductor (GaAs/AlGaAs) heterostructure is presented.
Abstract: Semiconductor devices have become indispensable for generating electromagnetic radiation in everyday applications. Visible and infrared diode lasers are at the core of information technology, and at the other end of the spectrum, microwave and radio-frequency emitters enable wireless communications. But the terahertz region (1-10 THz; 1 THz = 10(12) Hz) between these ranges has remained largely underdeveloped, despite the identification of various possible applications--for example, chemical detection, astronomy and medical imaging. Progress in this area has been hampered by the lack of compact, low-consumption, solid-state terahertz sources. Here we report a monolithic terahertz injection laser that is based on interminiband transitions in the conduction band of a semiconductor (GaAs/AlGaAs) heterostructure. The prototype demonstrated emits a single mode at 4.4 THz, and already shows high output powers of more than 2 mW with low threshold current densities of about a few hundred A cm(-2) up to 50 K. These results are very promising for extending the present laser concept to continuous-wave and high-temperature operation, which would lead to implementation in practical photonic systems.

2,132 citations


Journal ArticleDOI
TL;DR: A review of the Zig-Zag theories for multilayered structures can be found in this article, where the authors refer to these three theories by using the following three names: Lekhnitskii Multi-layered Theory, ~LMT!, Ambartsumian Multi-Layered Theory ~AMT!, and Reissner Multilayed Theory ~RMT.
Abstract: This paper gives a historical review of the theories that have been developed for the analysis of multilayered structures. Attention has been restricted to the so-called Zig-Zag theories, which describe a piecewise continuous displacement field in the plate thickness direction and fulfill interlaminar continuity of transverse stresses at each layer interface. Basically, plate and shell geometries are addressed, even though beams are also considered in some cases. Models in which the number of displacement variables is kept independent of the number of constitutive layers are discussed to the greatest extent. Attention has been restricted to those plate and shell theories which are based on the so-called method of hypotheses or axiomatic approach in which assumptions are introduced for displacements and/or transverse stresses. Mostly, the work published in the English language is reviewed. However, an account of a few articles originally written in Russian is also given. The historical review conducted has led to the following main conclusions. 1! Lekhnitskii ~1935! was the first to propose a Zig-Zag theory, which was obtained by solving an elasticity problem involving a layered beam. 2! Two other different and independent Zig-Zag theories have been singled out. One was developed by Ambartsumian ~1958!, who extended the well-known Reissner-Mindlin theory to layered, anisotropic plates and shells; the other approach was introduced by Reissner ~1984!, who proposed a variational theorem that permits both displacements and transverse stress assumptions. 3 ! On the basis of historical considerations, which are detailed in the paper, it is proposed to refer to these three theories by using the following three names: Lekhnitskii Multilayered Theory, ~LMT!, Ambartsumian Multilayered Theory ~AMT!, and Reissner Multilayered Theory ~RMT!. As far as subsequent contributions to these three theories are concerned, it can be remarked that: 4! LMT although very promising, has almost been ignored in the open literature. 5! Dozens of papers have instead been presented which consist of direct applications or particular cases of the original AMT. The contents of the original works have very often been ignored, not recognized, or not mentioned in the large number of articles that were published in journals written in the English language. Such historical unfairness is detailed in Section 3.2. 6! RMT seems to be the most natural and powerful method to analyze multilayered structures. Compared to other theories, the RMT approach has allowed from the beginning development of models which retain the fundamental effect related to transverse normal stresses and strains. This review article cites 138 references. @DOI: 10.1115/1.1557614#

972 citations


Proceedings ArticleDOI
09 Jul 2003
TL;DR: This paper proposes a distributed and scalable acceptance algorithm called generous tit-for-tat (GTFT), which is used by the nodes to decide whether to accept or reject a relay request, and shows that GTFT results in a Nash equilibrium and proves that the system converges to the rational and optimal operating point.
Abstract: In wireless ad hoc networks, nodes communicate with far off destinations using intermediate nodes as relays. Since wireless nodes are energy constrained, it may not be in the best interest of a node to always accept relay requests. On the other hand, if all nodes decide not to expend energy in relaying, then network throughput will drop dramatically. Both these extreme scenarios (complete cooperation and complete noncooperation) are inimical to the interests of a user. In this paper we address the issue of user cooperation in ad hoc networks. We assume that nodes are rational, i.e., their actions are strictly determined by self interest, and that each node is associated with a minimum lifetime constraint. Given these lifetime constraints and the assumption of rational behavior, we are able to determine the optimal throughput that each node should receive. We define this to be the rational Pareto optimal operating point. We then propose a distributed and scalable acceptance algorithm called generous tit-for-tat (GTFT). The acceptance algorithm is used by the nodes to decide whether to accept or reject a relay request. We show that GTFT results in a Nash equilibrium and prove that the system converges to the rational and optimal operating point.

641 citations


Journal ArticleDOI
TL;DR: Variation of parameters such as the maximum cell proliferation rate and the rate of natural cell death yield results which are consistent with analyses performed on simpler tumour growth models and indicate that the two-phase formulation is a natural extension of the earlier models.
Abstract: In this paper the theory of mixtures is used to develop a two-phase model of an avascular tumour, which comprises a solid, cellular, phase and a liquid phase. Mass and momentum balances which are used to derive the governing equations are supplemented by constitutive laws that distinguish the two phases and enable the stresses within the tumour to be calculated. Novel features of the model include the dependence of the cell proliferation rate on the cellular stress and the incorporation of mass exchange between the two phases. A combination of numerical and analytical techniques is used to investigate the sensitivity of equilibrium tumour configurations to changes in the model parameters. Variation of parameters such as the maximum cell proliferation rate and the rate of natural cell death yield results which are consistent with analyses performed on simpler tumour growth models and indicate that the two-phase formulation is a natural extension of the earlier models. New predictions relate to the impact of mechanical effects on the tumour's equilibrium size which decreases under increasing stress and/or external loading. In particular, as a parameter which measures the reduction in cell proliferation due to cell stress is increased a critical value is reached, above which the tumour is eliminated.

444 citations


Journal ArticleDOI
TL;DR: In this work the quadrature method of moments (QMOM) is tested for size-dependent growth and aggregation and is validated by comparison with both Monte Carlo simulations and analytical solutions using several functional forms for the aggregation kernel.
Abstract: Although use of computational fluid dynamics (CFD) for simulating precipitation (and particulate systems in general) is becoming a standard approach, a number of issues still need to be addressed. One major problem is the computational expense of coupling a standard discretized population balance (DPB) with a CFD code, as this approach requires the solution of an intractably large number of transport equations. In this work the quadrature method of moments (QMOM) is tested for size-dependent growth and aggregation. The QMOM is validated by comparison with both Monte Carlo simulations and analytical solutions using several functional forms for the aggregation kernel. Moreover, model predictions are compared with a DPB to compare accuracy, computational time, and the number of scalars involved. Analysis of the relative performance of various methods for treating aggregation provides readers with useful information about the range of application and possible limitations.

414 citations


Reference BookDOI
18 Jun 2003
TL;DR: Cancer Modelling and Simulation demonstrates how mathematical modelling and computer simulation techniques are used to gain insight into the dynamics of tumour development and growth.
Abstract: Understanding how cancer tumours develop and spread is vital for finding treatments and cures Cancer Modelling and Simulation demonstrates how mathematical modelling and computer simulation techniques are used to gain insight into the dynamics of tumour development and growth It highlights the benefits of tumour modelling, such as discovering optimal tumour therapy schedules, identifying the most promising candidates for further clinical investigation, and reducing the number of animal experiments By examining the analytical, mathematical, and biological aspects of tumour growth and modelling, the book provides a common language and knowledge for professionals in several disciplines

348 citations


Journal ArticleDOI
TL;DR: In this article, the authors proposed a new approach for predicting iron losses in soft magnetic materials with any voltage supply, starting from the knowledge of the iron losses with a sinusoidal or pulsewidth modulation supply.
Abstract: We propose a new approach for predicting iron losses in soft magnetic materials with any voltage supply, starting from the knowledge of the iron losses with a sinusoidal or pulsewidth modulation supply. The model is based on the separation of the loss contributions due to hysteresis, eddy currents, and excess losses with the two supplies. Since any contribution depends on the voltage supply characteristics, it is possible to find a direct mathematical relationship between the iron loss contribution and the voltage supply characteristics. As a consequence, an iron loss prediction can be obtained with any voltage supply if it does not produce a hysteresis minor loop. The energetic model is based on coefficients that depend on the magnetic material characteristic. We performed an accurate analysis of the model on eight magnetic materials used for electrical machine construction, of different thicknesses and alloy compositions. In this way, we found the main coefficients for a large spread of magnetic materials. As a consequence, our approach can be a useful support for electrical machine designers when the energetic performance of a magnetic material has to be predicted for a voltage supply different from the sinusoidal one.

282 citations


Journal ArticleDOI
TL;DR: The main features of the power line communication channel are illustrated, and some of the solutions advocated for modem design are illustrated.
Abstract: Designing a system able to cope with a hostile channel is a typical challenge for data communication engineers. High-data-rate communication over power lines is an exemplar case: while power lines are a potentially convenient and inexpensive "no new wire" medium for data transmission, their features make it very difficult to design a simple modem. In this article we illustrate the main features of the power line communication channel, and some of the solutions advocated for modem design.

275 citations


Journal ArticleDOI
TL;DR: In this review, the basic principles of operation of linear electrode arrays for the detection of surface EMG signals are described, together with their most relevant current applications.

274 citations


Journal ArticleDOI
TL;DR: A simple model is proposed which reproduces many features of the biological system and shows that both the model and the real system exhibit a fractal behavior at small scales, followed at large scale by a random percolation behavior due to the coalescence of aggregates.
Abstract: Experiments of in vitro formation of blood vessels show that cells randomly spread on a gel matrix autonomously organize to form a connected vascular network. We propose a simple model which reproduces many features of the biological system. We show that both the model and the real system exhibit a fractal behavior at small scales, due to the process of migration and dynamical aggregation, followed at large scale by a random percolation behavior due to the coalescence of aggregates. The results are in good agreement with the analysis performed on the experimental data.

274 citations


Journal ArticleDOI
TL;DR: In this article, the authors show that the chromite catalyst contributes actively to soot combustion by spillover in the temperature range 300-500°C, but negligibly to methane combustion.

Journal ArticleDOI
TL;DR: The estimation of on-off timing of human skeletal muscles during movement is an important issue in surface electromyography (EMG) signal processing with relevant clinical applications and a novel approach to address this issue is proposed.
Abstract: The estimation of on-off timing of human skeletal muscles during movement is an important issue in surface electromyography (EMG) signal processing with relevant clinical applications. In this paper, a novel approach to address this issue is proposed. The method is based on the identification of single motor unit action potentials from the surface EMG signal with the use of the continuous wavelet transform. A manifestation variable is computed as the maximum of the outputs of a bank of matched filters at different scales. A threshold is applied to the manifestation variable to detect EMG activity. A model, based on the physical structure of the muscle, is used to test the proposed technique on synthetic signals with known features. The resultant bias of the onset estimate is lower than 40 ms and the standard deviation lower than 30 ms in case of additive colored Gaussian noise with signal-to-noise ratio as low as 2 dB. Comparison with previously developed methods was performed, and representative applications to experimental signals are presented. The method is designed for a complete real-time implementation and, thus, may be applied in clinical routine activity.

Journal ArticleDOI
TL;DR: In this paper, the influence of soil moisture dynamics on soil carbon and nitrogen cycles is analyzed by coupling an existing stochastic soil moisture model [Adv. Water Resour. 24 (7) (2001) 707; Proc. R. Soc. A 455 (1999) 3789] to a system of eight nonlinear differential equations that describe the temporal evolution of the organic matter and the mineral nitrogen in the soil at the daily to seasonal time scales.

Proceedings ArticleDOI
03 Nov 2003
TL;DR: Experimental results show that the proposed approach is far more effective than the other considered techniques in terms of fault detection capability, at the cost of a limited increase in memory requirements and in performance overhead.
Abstract: Over the last few years, an increasing number of safety-critical tasks have been demanded of computer systems. In this paper, a software-based approach for developing safety-critical applications is analyzed. The technique is based on the introduction of additional executable assertions to check the correct execution of the program control flow. By applying the proposed technique, several benchmark applications have been hardened against transient errors. Fault injection campaigns have been performed to evaluate the fault detection capability of the proposed technique in comparison with state-of-the-art alternative assertion-based methods. Experimental results show that the proposed approach is far more effective than the other considered techniques in terms of fault detection capability, at the cost of a limited increase in memory requirements and in performance overhead.

Journal ArticleDOI
TL;DR: In this article, NH 4 NO 3 was used as an additive to boost the specific surface area of the catalysts, and the results showed that the resulting materials behave practically as the perovskites obtained by the “citrates” method.

Journal ArticleDOI
TL;DR: In this paper, a general model for the ontogenetic growth of living organisms has been recently proposed and the extension of this model to the growth of solid malignant tumors is investigated.

Journal ArticleDOI
TL;DR: The overall network concept is presented and the major choices are highlighted and compared with alternative solutions, as well as both the wide-area network and multiple-area networks parts of the network.
Abstract: In this paper, promising technologies and a network architecture are presented for future optical packet switched networks. The overall network concept is presented and the major choices are highlighted and compared with alternative solutions. Both long and shorter term approaches are considered, as well as both the wide-area network and multiple-area networks parts of the network. The results presented in this paper were developed in the frame of the research project DAVID (Data And Voice Integration over DWDM) project, funded by the European Commission through the IST-framework.

Proceedings ArticleDOI
09 Jul 2003
TL;DR: Analytical techniques that can be used to better understand the behavior of malware, a generic term that refers to all kinds of malicious software programs propagating on the Internet, such as e-mail viruses and worms are presented.
Abstract: In this paper we present analytical techniques that can be used to better understand the behavior of malware, a generic term that refers to all kinds of malicious software programs propagating on the Internet, such as e-mail viruses and worms. We develop a modeling methodology based on Interactive Markov Chains that is able to capture many aspects of the problem, especially the impact of the underlying topology on the spreading characteristics of malware. We propose numerical methods to obtain useful bounds and approximations in the case of very large systems, validating our results through simulation. An analytic methodology represents a fundamentally important step in the development of effective countermeasures for future malware activity. Furthermore, we believe our approach can help to understand a wide range of "dynamic interactions on networks", such as routing protocols and peer-to-peer applications.

Journal ArticleDOI
TL;DR: In this article, an alternative two-phase theory is developed to describe solid tumour growth, which represents a more general, and natural, modelling framework for studying solid tumor growth than existing theories.

Journal ArticleDOI
TL;DR: Bahri and Coron as mentioned in this paper showed that if q = N+2 N−2 and if some homology group of Ω with coefficients in Z2 is nontrivial, then problem (1.2) has a solution.
Abstract: has at least one solution when q < N+2 N−2 for any smooth bounded domain Ω. On the contrary, when q is critical or supercritical the existence of solutions to problem (1.2) depends strongly on the shape of the domainΩ. Indeed, if q ≥ N+2 N−2 Pohozaev’s identity [18] gives that problem (1.2) has no solution ifΩ is star-shaped. On the other hand, if q = N+2 N−2 , problem (1.2) has at least one solution when Ω is a symmetric annulus, see Kazdan-Warner [15], or when Ω has a “small hole”, see Coron [9]. In a remarkable work [3], Bahri and Coron generalize the previous results, by proving that if q = N+2 N−2 and if some homology group of Ω with coefficients in Z2 is nontrivial, then problem (1.2) has a solution.

Proceedings ArticleDOI
14 Dec 2003
TL;DR: Simulation results are exhibited, showing that only a relatively small percentage of the transmitted frame need be allocated to pilot symbols in order to experience an acceptable degradation of error probability due to imperfect channel knowledge.
Abstract: Under the assumption of a frequency-flat slow Rayleigh fading channel with multiple transmit and receive antennas, we examine the effects on system performance of imperfect estimation of the channel parameters when the receiver either assumes that the estimate is perfect or uses a proper maximum-likelihood decision metric. An algorithm for the recursive calculation of the maximum-likelihood decision metric is developed for application to trellis space-time codes.

Journal ArticleDOI
TL;DR: This letter presents a new method for the evaluation of the bit error probability of a time hopping binary pulse position ultra-wideband modulation scheme, in the presence of multiuser interference, and a comparison with the Gaussian approximation is presented.
Abstract: This letter presents a new method for the evaluation of the bit error probability of a time hopping binary pulse position ultra-wideband modulation scheme, in the presence of multiuser interference. The technique permits to predict the system performance with high accuracy and reasonable complexity. A perfect agreement with simulation results is shown, and a comparison with the Gaussian approximation is presented.

Journal ArticleDOI
TL;DR: This approach for obtaining a direct measure of the DCF muscles, which differs from those previously used, may be useful for the examination of these muscles in future electromyographic applications.
Abstract: Background and Purpose. This study evaluated an electromyographic technique for the measurement of muscle activity of the deep cervical flexor (DCF) muscles. Electromyographic signals were detected from the DCF, sternocleidomastoid (SCM), and anterior scalene (AS) muscles during performance of the craniocervical flexion (CCF) test, which involves performing 5 stages of increasing craniocervical flexion range of motion-the anatomical action of the DCF muscles. Subjects. Ten volunteers without known pathology or impairment participated in this study. Methods. Root-mean-square (RMS) values were calculated for the DCF, SCM, and AS muscles during performance of the CCF test. Myoelectric signals were recorded from the DCF muscles using bipolar electrodes placed over the posterior oropharyngeal wall. Reliability estimates of normalized RMS values were obtained by evaluating intraclass correlation coefficients and the normalized standard error of the mean (SEM). Results. A linear relationship was evident between the amplitude of DCF muscle activity and the incremental stages of the CCF test (F=239.04, df=36, P<.0001). Normalized SEMs in the range 6.7% to 10.3% were obtained for the normalized RMS values for the DCF muscles, providing evidence of reliability for these variables. Discussion and Conclusion. This approach for obtaining a direct measure of the DCF muscles, which differs from those previously used, may be useful for the examination of these muscles in future electromyographic applications.

Journal ArticleDOI
TL;DR: In this paper, the thermal and combustion behavior of an intumescent fire retardant system based on polyamide 6 and ammonium polyphosphate (APP), used to improve flame retardant properties of poly(ethylene-co-vinyl acetate) (EVA), loaded with Mg(OH) 2 (MH) was examined.

Journal ArticleDOI
TL;DR: A general framework based on a sort of Lyapunov approach encompassing known stabilization techniques is proposed, and an alternative stabilization method, based on the chaotic behavior of piecewise affine maps is proposed.
Abstract: It is well known that a linear system controlled by a quantized feedback may exhibit the wild dynamic behavior which is typical of a nonlinear system. In the classical literature devoted to control with quantized feedback, the flow of information in the feedback was not considered as a critical parameter. Consequently, in that case, it was natural in the control synthesis to simply choose the quantized feedback approximating the one provided by the classical methods, and to model the quantization error as an additive white noise. On the other hand, if the flow of information has to be limited, for instance, because of the use of a transmission channel with limited capacity, some specific considerations are in order. The aim of this paper is to obtain a detailed analysis of linear scalar systems with a stabilizing quantized feedback control. First, a general framework based on a sort of Lyapunov approach encompassing known stabilization techniques is proposed. In this case, a rather complete analysis can be obtained through a nice geometric characterization of asymptotically stable closed-loop maps. In particular, a general tradeoff relation between the number of quantization intervals, quantifying the information flow, and the convergence time is established. Then, an alternative stabilization method, based on the chaotic behavior of piecewise affine maps is proposed. Finally, the performances of all these methods are compared.

Journal ArticleDOI
TL;DR: In this paper, a new approach for managing outsourcing processes is presented, which can be easily adapted to different application fields, with the main aim of managing strategic decisions, economic factors and human resources.
Abstract: Outsourcing is a management approach by which an organization delegates some non‐core functions to specialized and efficient service providers. In the era of “global market” and “e‐economy”, outsourcing is one of the main pillars of the new way to conceive the relationships among companies. Despite outsourcing large diffusion, huge business cases and big deals of documentation available on network or press, there is no structured procedure able to support the govern of the evolution of a generic outsourcing process. In accordance with the principles of total quality management, this paper describes a proposal of a new approach for managing outsourcing processes. The model, which can be easily adapted to different application fields, has been conceived with the main aim of managing strategic decisions, economic factors and human resources. The approach is supported by different decision and analysis tools, such as benchmarking techniques, multiple criteria decision aiding (MCDA) methods, cost analysis, and other process‐planning methodologies. An application of the method to a real case is also provided.

Journal ArticleDOI
TL;DR: In this article, the authors proposed a model to explain how a gamma-ray burst can take place days or years after a supernova explosion, based on the conversion of a pure hadronic star (neutron star) into a star made at least in part of deconfined quark matter.
Abstract: We propose a model to explain how a gamma-ray burst can take place days or years after a supernova explosion. Our model is based on the conversion of a pure hadronic star (neutron star) into a star made at least in part of deconfined quark matter. The conversion process can be delayed if the surface tension at the interface between hadronic and deconfined quark matter phases is taken into account. The nucleation time (i.e., the time to form a critical-size drop of quark matter) can be extremely long if the mass of the star is small. Via mass accretion the nucleation time can be dramatically reduced and the star is finally converted into the stable configuration. A huge amount of energy, on the order of 1052-1053 ergs, is released during the conversion process and can produce a powerful gamma-ray burst. The delay between the supernova explosion generating the metastable neutron star and the new collapse can explain the delay inferred in GRB 990705 and in GRB 011211.

Journal ArticleDOI
TL;DR: In this article, a new level set method is developed for describing surfaces that are frozen behind a moving front, such as cracks, which combines very naturally with the extended finite element method (XFEM) where the discontinuous enrichment for cracks is best described in terms of level set functions.
Abstract: A new level set method is developed for describing surfaces that are frozen behind a moving front, such as cracks. In this formulation, the level set is described in two dimensions by a three-tuple: the sign of the level set function and the components of the closest point projection to the surface. The update of the level set is constructed by geometric formulas, which are easily implemented. Results are given for growth of lines in two dimensions that show the method is very accurate. The method combines very naturally with the extended finite element method (XFEM) where the discontinuous enrichment for cracks is best described in terms of level set functions. Examples of crack growth simulations obtained by combining this level set method with the extended finite element method are given. Copyright © 2003 John Wiley & Sons, Ltd.

Journal ArticleDOI
TL;DR: In this article, a unified framework for the mathematical representation of the market dispatch and redispatch problems that the IGO must solve in congestion management (CM) in these various jurisdictions is presented.
Abstract: The restructuring of the electricity industry has spawned the introduction of new independent grid operators (IGOs), typically called transmission system operators (TSOs); independent system operator (ISOs); or regional transmission organizations (RTOs), in various parts of the world. An important task of an IGO is congestion management (CM) and pricing. This activity has significant economic implications on every market participant in the IGO's region. The paper briefly reviews the CM schemes and the associated pricing mechanism used by the IGOs in five representative schemes. These were selected to illustrate the various CM approaches in use: England and Wales, Norway, Sweden, PJM, and California. The authors develop a unified framework for the mathematical representation of the market dispatch and redispatch problems that the IGO must solve in CM in these various jurisdictions. They use this unified framework to develop meaningful metrics to compare the various CM approaches so as to assess their efficiency and the effectiveness of the market signals provided to the market participants. They compare, using a small test system, side by side, the performance of these schemes.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the mechanism of fire retardancy induced by expandable graphite in a polyurethane coating and demonstrated that the crystalline structure of the graphite is maintained during the intumescent process.
Abstract: The study investigates the mechanism of fire retardancy induced by expandable graphite in a polyurethane coating. A complementary investigation to the spectroscopic study performed previously confirms that little interaction occurs between the matrix and the additive. X-ray diffraction study demonstrates that the crystalline structure of the graphite is maintained during the intumescent process. The presence of free radicals in the protective shield is then demonstrated but at low concentration compared with classical intumescent systems, such as for example polyurethane/ammonium polyphosphate. Finally, the physical properties of the char are then investigated. Blowing measurement demonstrates the high degree of expansion of the layer which may partially explain the fire retardant performance of expandable graphite in polyurethane. Surface analyses by optical microscopy and optical profilometry also enable a better understanding of the efficiency of expandable graphite. In the absence of a fire retardant additive the coating displays cracks and holes, providing a pathway for oxygen diffusion as well as heat and mass transfer between the flame and the virgin polymer. Both phenomena are limited when expandable graphite is added to polyurethane. Consequently, fire retardancy of expandable graphite results more from a physical than from a chemical action. Copyright © 2003 John Wiley & Sons, Ltd.