Derivatives of multidimensional Bernstein operators and smoothness

We characterize the directional derivatives of multidimensional Bernstein operators by a new measure of smoothness. This task is carried out by means of establishing the relation between the asymptotic behavior of the derivatives and the smoothness of the functions they approximate. The obtained results generalize the corresponding ones for univariate Bernstein operators.     

槲皮素酯类衍生物研究进展

健康生活方式特别强调食物质量,多酚在这方面发挥了关键作用。槲皮素是一种天然多酚,是多种植物性食品中发现最丰富的类黄酮类化合物之一。槲皮素是天然的抗氧化剂,可以保护细胞免受自由基造成的损害。槲皮素是一种亲脂性化合物,能够穿过细胞膜,可调节众多与疾病进展、化学预防有关的细胞内和细胞外信号通路。槲皮素具有广泛的药理活性,抗炎、抗菌、抗癌和预防心脑血管疾病,但是它低溶解度和生物利用度限制了在临床上的应用。对槲皮素的结构进行优化修饰获得了溶解性能好、生物利用度高、活性明显改善、抗癌活性增强的槲皮素衍生物。综述了近年来槲皮素酯衍生物的研究进展,为槲皮素衍生物的进一步开发提供参考。     

Dynamic NMR of low‐sensitivity fast‐relaxing nuclei: 17O NMR and DFT study of acetoxysilanes

¹⁷O NMR is not routinely used for structure characterization, and kinetic studies of fluxional organic compounds are seldom undertaken because poor sensitivity and fast quadrupole relaxation are frequently regarded as intractable issues. This work shows how, nowadays, quantitative ¹⁷O dynamic NMR studies on small organic molecules are feasible without enrichment being needed. It reports on acetoxysilanes, a class of fluxional compounds whose structure and dynamics were to be clarified. Natural abundance ¹⁷O NMR spectra were recorded over a wide range of temperatures using standard instrumentation. The analysis relies on simple linewidth measurements and directly provides the activation parameters. The activation enthalpy is found to decrease with increasing number of acetoxy groups bound to silicon. Density functional theory calculations properly predict this trend and show that a single oxygen atom of the acetoxy group is bound to silicon, excluding chelation as binding mode, and that the dynamic process involves the shift of the silicon atom between the two oxygen atoms of the acetoxy group. Copyright © 2012 John Wiley & Sons, Ltd.     

The proof of hermann''s conjecture

This note proves Thomas Hermann's conjecture on the comparison between twoboundaries of the derivatives of rational cubic Bezier curves. The result is valuable for computer aided geometric design.     

松香胺类衍生物在非表面活性剂方面的应用研究

综述了近年来国内外松香胺类衍生物在非表面活性剂方面的应用研究进展,主要包括催化特定氧化反应、手性反应及手性拆分、Maillard反应、抗菌活性、离子识别、施胶、废水处理、缓释、缓蚀、助焊剂等方面。     

Novel NO-releasing derivatives of betulinic acid with antitumor activity

Thirteen novel NO-releasing derivatives of betulinic acid (BA) bearing two types of NO-donors (nitrates and furoxans) were synthesized and evaluated for their antitumor activity. The results showed that furoxan-based derivatives exhibited higher antitumor activity than nitrate-based derivatives, with compounds 11a and 11b displaying promising potency against B16 cell lines and HepG2 cell lines (IC50 < 1 μmol/L). Wesupposed that NO-releasing amount of these derivatives which can be detected by Griess method may contribute more to their antitumor activity. As a result, furoxan-based derivatives released larger amount of NO than that of nitrate-based derivatives, which partially explained the higher anti-tumor activity of the former.     

Decoquinate derivatives: A new class of potent antischistosomal agents against Schistosoma japonicum

Decoquinate (1), an old and inexpensive coccidiostat, exhibited potent antimalarial activity, however, its antischistosomal activity against Schistosoma japonicum has not yet been evaluated. Based on decoquinate, a series of decoquinate derivatives was designed, synthesized, evaluated as a new class of antischistosomal agents against S. japonicum adult worms in vitro. Among them, compound 15 killed 100% of adult S. japonicum in 72 h at the concentration of 10 μmol/L in vitro, exhibited stronger wormkilling activity than PZQ in vitro and could serve as a promising lead compound to develop new antischistosomal agents.     

The convergence of Krylov subspace methods for large unsymmetric linear systems

The convergence problem of many Krylov subspace methods,e.g., FOM, GCR, GMRES and QMR, for solving large unsymmetric (non-Hermitian) linear systems is considered in a unified way when the coefficient matrixA is defective and its spectrum lies in the open right (left) half plane. Related theoretical error bounds are established and some intrinsic relationships between the convergence speed and the spectrum ofA are exposed. It is shown that these methods are likely to converge slowly once one of the three cases occurs:A is defective, the distribution of its spectrum is not favorable, or the Jordan basis ofA is ill conditioned. In the proof, some properties on the higher order derivatives of Chebyshev polynomials in an ellipse in the complex plane are derived, one of which corrects a result that has been used extensively in the literature. Supported by the China State Major Key Project for Basic Researches, the National Natural Science Foundation of China, the Doctoral Program of the Chinese National Educational Commission, the Foundation of Returned Scholars of China and Liaoning Province Natural Science Foundation.     

~1H NMR确证6-氟-5(或7)-氯-3-苯基-4-(1H)-喹啉酮衍生物的结构

作者合成了６氟３（取代）苯基４（１Ｈ）喹啉酮的５氯衍生物与７氯衍生物，二者极性差异小，难于分离，以混合物形式存在．所合成的化合物均未见文献报道，本文通过１ＨＮＭＲ上的化学位移、积分面积以及偶合常数确证了混合物中两组份的结构．