A fourth-order accurate, three-point compact approximation of the boundary gradient, for electrochemical kinetic simulations by the extended Numerov method

The fourth-order accurate, three-point compact (extended Numerov) finite-difference scheme of Chawla [J. Inst. Math. Appl. 22 (1978) 89] has been recently found superior (in terms of accuracy and efficiency) to the conventional second-order accurate spatial discretisation commonly used in electrochemical kinetic simulations. However, the two-point compact boundary gradient approximation, accompanying the scheme, is difficult to apply in the case of time-dependent kinetic partial differential equations, because it introduces unwanted second temporal derivatives into calculations. The conventional five-point gradient formula is free from this drawback, but it is also not very convenient, owing to the locally increased bandwidth of the matrix of linear equations arising from the spatio-temporal discretisation. A new three-point compact boundary gradient approximation derived in this work, avoids the above inconveniences and economically re-uses expressions utilised by the extended Numerov discretisation. The fourth-order accuracy of the new approximation is proven theoretically and verified in computational experiments performed for examples of kinetic models.     

China's energy situation in the new millennium

Many are interested in China's energy situation, however, many energy related issues in China still remain unanswered, for example, what are the potential forces driving energy demand and supply? Previous reviews focused only on fossil fuel based energy and ignored other important elements including renewable and ‘clean’ energy sources. The work presented here is intended to fill this gap by bringing the research on fossil-based and renewable energy economic studies together and identifying the potential drivers behind both energy demand and supply to provide a complete picture of China's energy situation in the new millennium. This will be of interest to anyone concerned with the development of China's economy in general and the energy economy, in particular.     

Representations of the group-as-a whole: Personality, situational, and dynamic determinants.

This article reports on a preliminary empirical investigation designed to operationalize the construct of the representation of the group-as-a-whole and to assess its validity by examining its relationships to personality as well as to content and dynamic aspects of the group. In the context of a group-relations conference, 291 participants in 29 self-study groups rated their views of their own group. Exploratory factor analysis of these adjective ratings yielded a meaningful 4-factor solution: Rejecting, Incomprehensible, Threatening Versus Benign, and Unelaborated. These constellations were found to be associated with leader gender, group culture, participants' characteristic style of regulating personal boundaries, and defensive group processes, in keeping with theoretical expectation. Findings were discussed in terms of the deployment of fusion fantasies and associated anxieties in the early stages of group life. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Automatic simulation of cyclic voltammograms by the adaptive Huber method for weakly singular second kind Volterra integral equations

Considering modern trends of laboratory automation in electroanalysis, the development of adaptive methods for automatic simulation of electrochemical transient techniques such as cyclic voltammetry is a topical issue. One of the classical simulation approaches relies on formulating, and solving numerically, relevant integral equations. In former work of the present author an adaptive variant of the popular Huber method serving for this purpose has been proposed, and successfully tested on electrochemical examples of first kind Abel integral equations (IEs). The method has been recently extended to second kind Volterra integral equations with weakly singular kernels and linear and non-linear dependences between the unknowns and their integrals. In the present work the validity of the extended method, for electrochemical simulations, is tested on representative examples of such equations, occurring in the theory of cyclic voltammetry. The performance of the method is found satisfactory, although errors of the simulated transients may deviate from the prescribed error tolerance parameter, so that achieving a given target accuracy is less straightforward than it was for the voltammograms described by the first kind Abel equations.     

Shape understanding system: Visual intelligence tests

Understanding is based on a large number of highly varied abilities called intelligence that can be measured. In this paper understanding abilities of the shape understanding system (SUS) are tested based on the methods used in intelligence tests. These tests are formulated as tasks given to the system and performance is compared with the human performance of these tasks. The main novelty of the presented method is that the process of understanding is related to the visual concept represented as a symbolic name of the possible class of shapes. The visual concept is one of the ingredients of the concept of the visual object (the phantom concept) that makes it possible to perform different tasks that are characteristic for visual understanding. The presented results are part of the research aimed at developing the shape understanding method that would be able to perform complex visual tasks connected with visual thinking. The shape understanding method is implemented as the shape understanding system. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 799–826, 2005.     

Filling n-sided regions with NURBS patches

n -sided region with G ^ɛ continuous NURBS patches that interpolate boundary curves and approximate given cross-boundary derivatives. The NURBS surfaces joining along inner or boundary curves have normal vectors that do not deviate more than the user-specified angular tolerance ɛ. The method is general in that there are no restrictions on the number of boundary curves, and the cross-boundary derivatives can be specified independently. To satisfy all conditions, only one degree elevation is needed.     

An adaptive Huber method for weakly singular second kind Volterra integral equations with non-linear dependencies between unknowns and their integrals

Numerical methods for weakly singular Volterra integral equations with non-linear dependencies between unknowns and their integrals, are almost non-existent in the literature. In the present work an adaptive Huber method for such equations is proposed, by extending the method previously formulated for the first kind Abel equations. The method is tested on example integral equations involving integrals with kernels K(t, τ) = (t ? τ)^?1/2, K(t, τ) = exp[?λ(t ? τ)](t ? τ)^?1/2 (where λ > 0), and K(t, τ) = 1. By controlling estimated local discretisation errors, the integral equation can be solved adaptively on a discrete grid of nodes in the independent variable domain, in a step-by-step fashion. The practical accuracy order is close to 2. The accuracy can be varied by varying the prescribed local error tolerance parameter tol, although the actual errors tend to be larger than tol. Approximations to off-nodal solution values can also be computed, with a comparable accuracy. The method appears numerically stable when partial derivatives, of the non-linear function representing the equation, with respect to the unknown and its integral(s), are of the same sign. The stability of the method in the opposite case may be debated.     

ERP in the Internet Economy

This paper discusses the future of Enterprise Resource Planning and (ERP) in the Internet Economy. In the Internet Economy, ERP as a distinct entity is giving way to a much broader value proposition that effectively fuses different forms of business applications and services. Back-office and front-office applications within an enterprise will come together, along with applications and services for value-chain collaboration between business partners.