Computing greatest common divisor of several parametric univariate polynomials via generalized subresultant polynomials

In this paper, we tackle the following problem: compute the gcd for several univariate polynomials with parametric coefficients. It amounts to partitioning the parameter space into ``cells'' so that the gcd has a uniform expression over each cell and constructing a uniform expression of gcd in each cell. We tackle the problem as follows. We begin by making a natural and obvious extension of subresultant polynomials of two polynomials to several polynomials. Then we develop the following structural theories about them. 1. We generalize Sylvester's theory to several polynomials, in order to obtain an elegant relationship between generalized subresultant polynomials and the gcd of several polynomials, yielding an elegant algorithm. 2. We generalize Habicht's theory to several polynomials, in order to obtain a systematic relationship between generalized subresultant polynomials and pseudo-remainders, yielding an efficient algorithm. Using the generalized theories, we present a simple (structurally elegant) algorithm which is significantly more efficient (both in the output size and computing time) than algorithms based on previous approaches

Parametric "Non-nested" Discriminants for Multiplicities of Univariate Polynomials

We consider the problem of complex root classification, i.e., finding the conditions on the coefficients of a univariate polynomial for all possible multiplicity structures on its complex roots. It is well known that such conditions can be written as conjunctions of several polynomial equations and one inequation in the coefficients. Those polynomials in the coefficients are called discriminants for multiplicities. It is well known that discriminants can be obtained by using repeated parametric gcd's. The resulting discriminants are usually nested determinants, that is, determinants of matrices whose entries are determinants, and so son. In this paper, we give a new type of discriminants which are not based on repeated gcd's. The new discriminants are simpler in that they are non-nested determinants and have smaller maximum degrees

Arbitrary Shape Electromagnetic Transparent Device Based on Laplace’s Equation

Transparent device is deliberately-designed electromagnetic structure that is transparent to electromagnetic wave. It can be used as a radome structure which is capable of protection antenna inside without sacrificing its performance. In this paper, two-dimensional (2D) arbitrary shape electromagnetic transparent device is designed based on transformation optics. Laplace’s equation is adopted to construct the coordinate mapping between the original space and the transformed space. The design method is flexibly extended to three-dimensional (3D) case, which greatly enhances the applicability of transparent device. The protection of a horn antenna is taken as an example to show the effectiveness of the transparent device. Since the performance of the transparent device is independent on the inner antenna, it can be designed separately. Full-wave simulations are made to validate the results

Ecological model to predict potential habitats of Oncomelania hupensis, the intermediate host of Schistosoma japonicum in the mountainous regions, China

Schistosomiasis japonica is a parasitic disease that remains endemic in seven provinces in the People's Republic of China (P.R. China). One of the most important measures in the process of schistosomiasis elimination in P.R. China is control of Oncomelania hupensis, the unique intermediate host snail of Schistosoma japonicum. Compared with plains/swamp and lake regions, the hilly/mountainous regions of schistosomiasis endemic areas are more complicated, which makes the snail survey difficult to conduct precisely and efficiently. There is a pressing call to identify the snail habitats of mountainous regions in an efficient and cost-effective manner.; Twelve out of 56 administrative villages distributed with O. hupensis in Eryuan, Yunnan Province, were randomly selected to set up the ecological model. Thirty out of the rest of 78 villages (villages selected for building model were excluded from the villages for validation) in Eryuan and 30 out of 89 villages in Midu, Yunnan Province were selected via a chessboard method for model validation, respectively. Nine-year-average Normalized Difference Vegetation Index (NDVI) and Land Surface Temperature (LST) as well as Digital Elevation Model (DEM) covering Eryuan and Midu were extracted from MODIS and ASTER satellite images, respectively. Slope, elevation and the distance from every village to its nearest stream were derived from DEM. Suitable survival environment conditions for snails were defined by comparing historical snail presence data and remote sensing derived images. According to the suitable conditions for snails, environment factors, i.e. NDVI, LST, elevation, slope and the distance from every village to its nearest stream, were integrated into an ecological niche model to predict O. hupensis potential habitats in Eryuan and Midu. The evaluation of the model was assessed by comparing the model prediction and field investigation. Then, the consistency rate of model validation was calculated in Eryuan and Midu Counties, respectively. The final ecological niche model for potential O. hupensis habitats prediction comprised the following environmental factors, namely: NDVI (≥ 0.446), LST (≥ 22.70°C), elevation (≤ 2,300 m), slope (≤ 11°) and the distance to nearest stream (≤ 1,000 m). The potential O. hupensis habitats in Eryuan distributed in the Lancang River basin and O. hupensis in Midu shows a trend of clustering in the north and spotty distribution in the south. The consistency rates of the ecological niche model in Eryuan and Midu were 76.67% and 83.33%, respectively.; The ecological niche model integrated with NDVI, LST, elevation, slope and distance from every village to its nearest stream adequately predicted the snail habitats in the mountainous regions

Solution-processed small-molecule solar cells: breaking the 10% power conversion efficiency.

A two-dimensional conjugated small molecule (SMPV1) was designed and synthesized for high performance solution-processed organic solar cells. This study explores the photovoltaic properties of this molecule as a donor, with a fullerene derivative as an acceptor, using solution processing in single junction and double junction tandem solar cells. The single junction solar cells based on SMPV1 exhibited a certified power conversion efficiency of 8.02% under AM 1.5 G irradiation (100 mW cm(-2)). A homo-tandem solar cell based on SMPV1 was constructed with a novel interlayer (or tunnel junction) consisting of bilayer conjugated polyelectrolyte, demonstrating an unprecedented PCE of 10.1%. These results strongly suggest solution-processed small molecular materials are excellent candidates for organic solar cells