Global asymptotic stability in a rational recursive sequence

In this paper, we study the global stability of the difference equation x(n) = a + bx(n-1) + cx(n-1)(2)/d - x(n-2), n = 1,2,....., where a, b greater than or equal to 0 and c, d > 0. We show that one nonnegative equilibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive Solution of the equation in the basin exponentially converges to the attractor. (C) 2003 Elsevier Inc. All rights reserved.

On the recursive sequence Xn = axn-1+bxn-2/c+dxn-1xn-2

In this Paper, we study the invariant intervals, the global attractivity of the equilibrium points, and the asymptotic behavior of the solutions of the difference equation x(n) = ax(n-1) + bx(n-2) / c + dx(n-1)x(n-2), n =1, 2, ..., where a greater than or equal to 0, b, c, d > 0. (C) 2004 Elsevier Inc. All rights reserved.

Simplified recursive identifier for ARMA processes

Symmetrical behaviour of the covariance matrix and the positive-definite criterion are used to simplify identification of single-input/single-output systems using recursive least squares. Simulation results are obtained and these are compared with ordinary recursive least squares. The adaptive nature of the identifier is verified by varying the system parameters on convergence.

Managing multiple markets: big firms and PFI contracts

The Private Finance Initiative (PFI) is frequently portrayed as a vehicle for change for the UK construction sector. Significant change in the working practices of construction companies is predicted as new business models based on whole-life value creation emerge. This paper shifts the focus of discussion from projected ideals and possible developments to the current situation. More specifically, it focuses on the challenges that large firms participating in both PFI and traditional markets face. The analysis focuses on the relations between business units and on day-to-day challenges to greater long-term commitment, through life-service provision and increased integration between construction and service provision. The paper offers insights into the effects of PFI on construction practice and their implications for theorizing on organizational and strategic change. It suggests abandoning a simplistic model of the centralized, homogenous firm and instead capturing the dynamics of decentralized, large firms working in multiple markets on a variety of projects. This would assist in the provision of more realistic and fruitful models of how to realize the PFI vision.

Contracts and incentives in the construction sector

The aim of this chapter is to examine what the construction sector brings to our understanding of the procurement of complex performance. The chapter is divided into the following parts: fi rst, an overview of the various matters that contribute to the complexity of construction procurement is provided. Second, the most important contractual incentive schemes found in construction contracts are discussed, and this is followed by, third, an examination of the changes associated with the shift towards procuring complex performance (PCP) (service provision). Fourth, the main findings of the authors’ recent research on PCP contracts are summarised, followed by the conclusion. It should be noted that the procurement of services is referred to as ‘PCP’ in this chapter.

Adaptive recursive control of a soil testing load frame

Recursive Learning Control (RLC) has the potential to significantly reduce the tracking error in many repetitive trajectory applications. This paper presents an application of RLC to a soil testing load frame where non-adaptive techniques struggle with the highly nonlinear nature of soil. The main purpose of the controller is to apply a sinusoidal force reference trajectory on a soil sample with a high degree of accuracy and repeatability. The controller uses a feedforward control structure, recursive least squares adaptation algorithm and RLC to compensate for periodic errors. Tracking error is reduced and stability is maintained across various soil sample responses.

Entrepreneurial opportunities, implicit contracts and market making for complex consumer goods

This article extends the theory of entrepreneurial opportunity exploitation, outlining how under certain conditions, opportunity exploitation is dependent on market making innovations. Where adverse selection and moral hazard characterize markets, consumers are likely to withdraw regardless of product quality. In order to overcome consumer resistance, entrepreneurs must signal credible commitments. But because consumers purchase without fully specifying requirements, entrepreneurs' commitments take the partial form of implicit contracts, creating strong mutual commitments to repeated transactions. These commitments enable novel markets to function, but introduce additional costs. This article illustrates the theory with the historic case of Singer in sewing machines

Transfers, contracts and regulation: a new institutional economics perspective on the changing provision of social housing in Britain

Social housing policy in the UK mirrors wider processes Associated with shifts in broad welfare regimes. Social housing has moved from dominance by state housing provision to the funding of new investment through voluntary sector housing associations to what is now a greater focus on the regulation and private financing of these not-for-profit bodies. If these trends run their course, we are likely to see a range of not-for-profit bodies providing non-market housing in a highly regulated quasi-market. This paper examines these issues through the lens of new institutional economics, which it is believed can provide important insights into the fundamental contractual and regulatory relationships that are coming to dominate social housing from the perspective of the key actors in the sector (not-for-profit housing organisations, their tenants, private lenders and the regulatory state). The paper draws on evidence recently collected from a study evaluating more than 100 stock transfer organisations that inherited ex-public housing in Scotland, including 12 detailed case studies. The paper concludes that social housing stakeholders need to be aware of the risks (and their management) faced across the sector and that the state needs to have clear objectives for social housing and coherent policy instruments to achieve those ends.

Construction contracts: law and management. 4th edition

This is a fully revised edition of the UK’s leading textbook on the law governing construction contracts and the management and administration of those contracts. Although the legal principles involved are an aspect of general contract law, the practical and commercial complexities of the construction industry have increasingly made this a specialist area. This new edition has been brought up to date with recent cases and developments in the law as it stands at March 2007. The basic approach of the book has been retained. Rather than provide a commentary on standard-form contracts, our approach is to introduce the general principles that underlie contracts in construction, illustrating them by reference to the most important standard forms currently in use. Some of the common standard-form contracts have been revised since the previous edition, and the text has been revised to take account of these changes. Practitioners (consultants, builders, clients and lawyers) will find this an extremely useful source of reference, providing in-depth explanations for all of the features found in contemporary construction contracts, with reasons. A unique feature of this book is the way that it brings together the relevant principles of law with the practical issues arising in construction cases. It is a key text for construction undergraduates and postgraduates as well as for those taking the RIBA Part III and CIOB Part II examinations.

Finite sample weighting of recursive forecast errors

This paper proposes and tests a new framework for weighting recursive out-of-sample prediction errors according to their corresponding levels of in-sample estimation uncertainty. In essence, we show how to use the maximum possible amount of information from the sample in the evaluation of the prediction accuracy, by commencing the forecasts at the earliest opportunity and weighting the prediction errors. Via a Monte Carlo study, we demonstrate that the proposed framework selects the correct model from a set of candidate models considerably more often than the existing standard approach when only a small sample is available. We also show that the proposed weighting approaches result in tests of equal predictive accuracy that have much better sizes than the standard approach. An application to an exchange rate dataset highlights relevant differences in the results of tests of predictive accuracy based on the standard approach versus the framework proposed in this paper.