Generic Regular Decompositions for Parametric Polynomial Systems

This paper presents a generalization of our earlier work in [19]. In this paper, the two concepts, generic regular decomposition (GRD) and regular-decomposition-unstable (RDU) variety introduced in [19] for generic zero-dimensional systems, are extended to the case where the parametric systems are not necessarily zero-dimensional. An algorithm is provided to compute GRDs and the associated RDU varieties of parametric systems simultaneously on the basis of the algorithm for generic zero-dimensional systems proposed in [19]. Then the solutions of any parametric system can be represented by the solutions of finitely many regular systems and the decomposition is stable at any parameter value in the complement of the associated RDU variety of the parameter space. The related definitions and the results presented in [19] are also generalized and a further discussion on RDU varieties is given from an experimental point of view. The new algorithm has been implemented on the basis of DISCOVERER with Maple 16 and experimented with a number of benchmarks from the literature.Comment: It is the latest version. arXiv admin note: text overlap with arXiv:1208.611

Special Algorithm for Stability Analysis of Multistable Biological Regulatory Systems

We consider the problem of counting (stable) equilibriums of an important family of algebraic differential equations modeling multistable biological regulatory systems. The problem can be solved, in principle, using real quantifier elimination algorithms, in particular real root classification algorithms. However, it is well known that they can handle only very small cases due to the enormous computing time requirements. In this paper, we present a special algorithm which is much more efficient than the general methods. Its efficiency comes from the exploitation of certain interesting structures of the family of differential equations.Comment: 24 pages, 5 algorithms, 10 figure

A PDE-based Method for Optimizing Solar Cell Performance

In this paper, we address the optimal design problem for organic solar cells (OSC). In particular, our focus is to enhance short-curcuit photocurrent by optimizing the donor-acceptor interface. To that end, we propose two drift-diffusion models for organic solar cells, both of which account for the physics of OSC\u27s that charge carriers are mostly generated in the region near the donor-acceptor interface. For the first drift-diffusion model, the generation of charge carriers is translated into a boundary condition across the donor-acceptor interface. We apply the theory of shape optimization to compute the shape gradient functional of the photocurrent. In particular, shape differential calculus is extensively applied in the computation. For the second drfit-diffusion model, we parameterize the donor-acceptor interface as a leve set of a function, i.e. the phase field function . The dependence of the second drift-diffusion model on the geometry is therefore transformed into its dependence on the phase field function. Such transformation greatly simplifies the sensitivity analysis and leads to an easy-to-implement numerical optimization algorithm. In numerical examples, it is shown that the maximum output power of the optimized solar cell can be increased by a factor of 3. Our analysis and examples in this paper are in two dimensions, but the generelization of both the analysis and numerical optimization to three dimensions is straightforward

Breastfeeding in China: a review

This review aims to describe changes in breastfeeding and summarise the breastfeeding rates, duration and reasons of discontinuing 'any breastfeeding' or 'exclusive breastfeeding' in P.R. China. Breastfeeding rates in China fell during the 1970s when the use of breast milk substitutes became widespread, and reached the lowest point in the 1980s. As a result many efforts were introduced to promote breastfeeding. The breastfeeding rate in China started to increase in the 1990s, and since the mid-1990s 'any breastfeeding' rates in the majority of cities and provinces, including minority areas, have been above 80% at four months. But most cities and provinces did not reach the national target of 'exclusive breastfeeding' of 80%. The 'exclusive breastfeeding' rates in minority areas were relatively lower than comparable inland provinces. The mean duration of 'any breastfeeding' in the majority of cities or provinces was between seven and nine months. The common reasons for ceasing breastfeeding, or introducing water or other infant food before four months, were perceived breast milk insufficiency, mother going to work, maternal and child illness and breast problems. Incorrect traditional perceptions have a strong adverse influence on 'exclusive breastfeeding' in less developed areas or rural areas. China is a huge country, geographically and in population size, and there is considerable ethnic diversity. Therefore breastfeeding rates in different parts of China can vary considerably