Padé approximants for the acoustical characteristics of rigid frame porous media

In this paper it is shown that a number of theoretical models of the acoustical properties of rigid frame porous media, especially those involving ratios of Bessel functions of complex argument, can be accurately approximated and greatly simplified by the use of Padé approximation techniques. In the case of the model of Attenborough [J. Acoust. Soc. Am. 81, 93–102 (1987)] rational approximations are produced for the characteristic impedance, propagation constant, dynamic compressibility, and dynamic density, as a function of frequency and the material parameters. The model proposed by Stinson and Champoux

Model-based vehicle detection and classification using orthographic approximations

This paper reports the current state of work to simplify our previous model-based methods for visual tracking of vehicles for use in a real-time system intended to provide continuous monitoring and classification of traffic from a fixed camera on a busy multi-lane motorway. The main constraints of the system design were: (i) all low level processing to be carried out by low-cost auxiliary hardware, (ii) all 3-D reasoning to be carried out automatically off-line, at set-up time. The system developed uses three main stages: (i) pose and model hypothesis using 1-D templates, (ii) hypothesis tracking, and (iii) hypothesis verification, using 2-D templates. Stages (i) & (iii) have radically different computing performance and computational costs, and need to be carefully balanced for efficiency. Together, they provide an effective way to locate, track and classify vehicles.

Rational modification of the hierarchy of intermolecular interactions in molecular crystal structures by using tunable halogen bonds

A family of 16 isomolecular salts (3-XpyH)(2)[MX'(4)] (3-XpyH=3-halopyridinium; M=Co, Zn; X=(F), Cl, Br, (I); X'=Cl, Br, I) each containing rigid organic cations and tetrahedral halometallate anions has been prepared and characterized by X-ray single crystal and/or powder diffraction. Their crystal structures reflect the competition and cooperation between non-covalent interactions: N-H center dot center dot center dot X'-M hydrogen bonds, C-X center dot center dot center dot X'-M halogen bonds and pi-pi stacking. The latter are essentially unchanged in strength across the series, but both halogen bonds and hydrogen bonds are modified in strength upon changing the halogens involved. Changing the organic halogen (X) from F to I strengthens the C-X center dot center dot center dot X'-M halogen bonds, whereas an analogous change of the inorganic halogen (X') weakens both halogen bonds and N-H center dot center dot center dot X'-M hydrogen bonds. By so tuning the strength of the putative halogen bonds from repulsive to weak to moderately strong attractive interactions, the hierarchy of the interactions has been modified rationally leading to systematic changes in crystal packing. Three classes of crystal structure are obtained. In type A (C-F center dot center dot center dot X'-M) halogen bonds are absent. The structure is directed by N-H center dot center dot center dot X'-M hydrogen bonds and pi-stacking interactions. In type B structures, involving small organic halogens (X) and large inorganic halogens (X'), long (weak) C-X center dot center dot center dot X'-M interactions are observed with type I halogen-halogen interaction geometries (C-X center dot center dot center dot X' approximate to X center dot center dot center dot X'-M approximate to 155 degrees), but hydrogen bonds still dominate. Thus, minor but quite significant perturbations from the type A structure arise. In type C, involving larger organic halogens (X) and smaller inorganic halogens (X'), stronger halogen bonds are formed with a type II halogen-halogen interaction geometry (C-X center dot center dot center dot X' approximate to 180 degrees; X center dot center dot center dot X'-M approximate to 110 degrees) that is electrostatically attractive. The halogen bonds play a major role alongside hydrogen bonds in directing the type C structures, which as a result are quite different from type A and B.

Multi-mode approximations to wave scattering by an uneven bed

Approximations to the scattering of linear surface gravity waves on water of varying quiescent depth are Investigated by means of a variational approach. Previous authors have used wave modes associated with the constant depth case to approximate the velocity potential, leading to a system of coupled differential equations. Here it is shown that a transformation of the dependent variables results in a much simplified differential equation system which in turn leads to a new multi-mode 'mild-slope' approximation. Further, the effect of adding a bed mode is examined and clarified. A systematic analytic method is presented for evaluating inner products that arise and numerical experiments for two-dimensional scattering are used to examine the performance of the new approximations.

Approximations to the scattering of water waves by steep topography

A new method is developed for approximating the scattering of linear surface gravity waves on water of varying quiescent depth in two dimensions. A conformal mapping of the fluid domain onto a uniform rectangular strip transforms steep and discontinuous bed profiles into relatively slowly varying, smooth functions in the transformed free-surface condition. By analogy with the mild-slope approach used extensively in unmapped domains, an approximate solution of the transformed problem is sought in the form of a modulated propagating wave which is determined by solving a second-order ordinary differential equation. This can be achieved numerically, but an analytic solution in the form of a rapidly convergent infinite series is also derived and provides simple explicit formulae for the scattered wave amplitudes. Small-amplitude and slow variations in the bedform that are excluded from the mapping procedure are incorporated in the approximation by a straightforward extension of the theory. The error incurred in using the method is established by means of a rigorous numerical investigation and it is found that remarkably accurate estimates of the scattered wave amplitudes are given for a wide range of bedforms and frequencies.

Rational conversion of substrate and product specificity in a Salvia monoterpene synthase: structural insights into the evolution of terpene synthase function

Terpene synthases are responsible for the biosynthesis of the complex chemical defense arsenal of plants and microorganisms. How do these enzymes, which all appear to share a common terpene synthase fold, specify the many different products made almost entirely from one of only three substrates? Elucidation of the structure of 1,8-cineole synthase from Salvia fruticosa (Sf-CinS1) combined with analysis of functional and phylogenetic relationships of enzymes within Salvia species identified active-site residues responsible for product specificity. Thus, Sf-CinS1 was successfully converted to a sabinene synthase with a minimum number of rationally predicted substitutions, while identification of the Asn side chain essential for water activation introduced 1,8-cineole and alpha-terpineol activity to Salvia pomifera sabinene synthase. A major contribution to product specificity in Sf-CinS1 appears to come from a local deformation within one of the helices forming the active site. This deformation is observed in all other mono- or sesquiterpene structures available, pointing to a conserved mechanism. Moreover, a single amino acid substitution enlarged the active-site cavity enough to accommodate the larger farnesyl pyrophosphate substrate and led to the efficient synthesis of sesquiterpenes, while alternate single substitutions of this critical amino acid yielded five additional terpene synthases.

Exploring the construction of social class in educational discourse: the rational order of the nation state versus global uncertainties

This article aims to create intellectual space in which issues of social inequality and education can be analyzed and discussed in relation to the multifaceted and multi-levelled complexities of the modern world. It is divided into three sections. Section One locates the concept of social class in the context of the modern nation state during the period after the Second World War. Focusing particularly on the impact of 'Fordism' on social organization and cultural relations, it revisits the articulation of social justice issues in the United Kingdom, and the structures put into place at the time to alleviate educational and social inequalities. Section Two problematizes the traditional concept of social class in relation to economic, technological and sociocultural changes that have taken place around the world since the mid-1980s. In particular, it charts some of the changes to the international labour market and global patterns of consumption, and their collective impact on the re-constitution of class boundaries in 'developed countries'. This is juxtaposed with some of the major social effects of neo-classical economic policies in recent years on the sociocultural base in developing countries. It discusses some of the ways these inequalities are reflected in education. Section Three explores tensions between the educational ideals of the 'knowledge economy' and the discursive range of social inequalities that are emerging within and beyond the nation state. Drawing on key motifs identified throughout, the article concludes with a reassessment of the concept of social class within the global cultural economy. This is discussed in relation to some of the major equity and human rights issues in education today.

On two rational difference equations

In this paper, we study the oscillating property of positive solutions and the global asymptotic stability of the unique equilibrium of the two rational difference equations [GRAPHICS] and [GRAPHICS] where a is a nonnegative constant. (c) 2005 Elsevier Inc. All rights reserved.

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 system of rational difference equations x(n) = A+(1)over-bar y(n-p), y(n) = A+(gamma(n-1))over-bar x(n-r)y(n-5)

In this paper, we study the behavior of the positive solutions of the system of two difference equations [GRAPHICS] where p >= 1, r >= 1, s >= 1, A >= 0, and x(1-r), x(2-r),..., x(0), y(1-max) {p.s},..., y(0) are positive real numbers. (c) 2005 Elsevier Inc. All rights reserved.