The projection method for computing multidimensional absolutely continuous invariant measures

We present an algorithm for numerically computing an absolutely continuous invariant measure associated with a piecewiseC ² expanding mappingS: on a bounded region R ^N. The method is based on the Galerkin projection principle for solving an operator equation in a Banach space. With the help of the modern notion of functions of bounded variation in multidimension, we prove the convergence of the algorithm.     

锌制剂“维宝康”治疗儿童缺锌综合征的临床研究

用维宝康治疗小儿缺锌综合征９８例,结果表明,服用维宝康一个疗程后,患者临床症状明显改善发锌值升高,总有效率为９６％,未见毒副作用,是较好的补锌制剂。     

Converse theorems for multidimensional Kantorovich operators

L _p [0, l]. . . - .

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Supported by National Science Foundation, Zhejiang Provincial Science Foundation of China, and Alexander von Humboldt Foundation of Germany.     

Novel reference gene, High-mobility-group protein I/Y, used in qualitative and real-time quantitative polymerase chain reaction detection of transgenic rapeseed cultivars

With the development of transgenic crops, regulations to label the genetically modified organisms (GMOs) and their derived products have been issued in many countries. Polymerase chain reaction (PCR) methods are thought to be reliable and useful techniques for qualitative and quantitative detection of GMOs. These methods are generally needed to amplify the transgene and compare the amplified results with that of a corresponding reference gene to get the reliable results. Specific primers were developed for the rapeseed (Brassica napus), high-mobility-group protein I/Y(HMG-I/Y) single-copy gene and PCR cycling conditions suitable for the use of this sequence as an endogenous reference gene in both qualitative and quantitative PCR assays. Both methods were assayed with 15 different rapeseed varieties, and identical amplified products were obtained with all of them. No amplification was observed when templates were the DNA samples from the other species of Brassica genus or other species, such as broccoli, stem mustard, cauliflower, Chinese cabbage, cabbage, sprouts, Arabidopsis thaliana, carrot, tobacco, soybean, mung bean, tomato, pepper, eggplant, plum, wheat, maize, barley, rice, lupine, and sunflower. This system was specific for rapeseed. Limits of detection and quantitation in qualitative and quantitative PCR systems were about 13 pg DNA (about 10 haploid genomes) and about 1.3 pg DNA (about 1 haploid genome), respectively. To further test the feasibility of this HMG-I/Y gene as an endogenous reference gene, samples containing transgenic rapeseed GT73 with the inserted glyphosate oxidoreductase (GOX) gene were quantitated. These demonstrated that the endogenous PCR detection systems were applicable to the qualitative and quantitative detection of transgenic rapeseed.