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]. . . - .

---

---

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

Isomorphism of two realizations of quantum affine algebraU_q (\widehat{\mathfrak{g}\mathfrak{l}{\text{(}}n{\text{)}}})

We establish an explicit isomorphism between two realizations of the quantum affine algebra given previously by Drinfeld and Reshetikhin-Semenov-Tian-Shansky. Our result can be considered as an affine version of the isomorphism between the Drinfield/Jimbo and the Faddeev-Reshetikhin-Takhtajan constructions of the quantum algebra .     

Synthesis of 4-halophosphaisocoumarins via halocyclization of 2-(1-alkynyl)phenylphosphonates

A series of 4-halophosphaisocoumarins were prepared with high regioselectivity in good to excellent yields under mild conditions by the reaction of 2-(1-alkynyl)phenylphosphonic acid diesters with I₂ in CHCl₃ or ICl in CH₂Cl₂, or by the reaction of 2-(1-alkynyl)phenylphosphonic acid monoesters with NBS or NCS in DMF. Whether the alkynylphosphonates could cyclize or not was affected by the substituents, reaction solvents and electrophiles. A rationale for this reaction is discussed.