非全局Lipschitz条件下跳适应向后Euler方法的强收敛性分析

本文研究跳适应向后Euler方法求解跳扩散随机微分方程在非全局Lipschitz条件下的强收敛性.通过克服方程非全局Lipschitz系数给收敛性分析带来的主要困难,我们成功地建立了跳适应后向Euler方法的强收敛性结果并得到相应的收敛率.最后,我们通过数值试验对前文所得理论结果做进一步的验证.     

Some Properties of Solutions to the Novikov Equation with Weak Dissipation Terms

In this paper, we investigate the Novikov equation with weak dissipation terms. First, we give the local well-posedness and the blow-up scenario. Then, we discuss the global existence of the solutions under certain conditions. After that, on condition that the compactly supported initial data keeps its sign, we prove the infinite propagation speed of our solutions, and establish the large time behavior. Finally, we also elaborate the persistence property of our solutions in weighted Sobolev space.     

The relative canonical algebra for genus 4 fibrations

In this paper, we prove that for the genus 4 fibration, the relative canonical algebra is generated in degrees 3.     

Simultaneous determination of uric acid, xanthine and hypoxanthine with an electrochemically pretreated carbon paste electrode

A simple method is presented for the simultaneous differential pulse voltammetric determination of uric acid, xanthine and hypoxanthine. It is based on the improved current responses of the three analytes at carbon paste electrodes polarized in a dilute alkaline medium (0.002 mol/l NaOH, 0.1 mol/l NaClO₄) at 1.3 V vs. SCE for a short time. Compared with the methods reported in the literature, this procedure has a much wider linear range (2 to 3 orders of magnitude in concentration), lower detection limits (5 to 10 g l^–1) and less interference by ascorbic acid. The electrochemical responses were found to be dependent on the pre-anodization potential and the time imposed on the electrodes as well as on the alkalinity of the supporting electrolyte. The proposed procedure was used to determine uric acid, xanthine and hypoxanthine in human urine without any preliminary treatment.     

Highly Efficient and Practical Syntheses of Lavendamycin Methyl Ester and Related Novel Quinolindiones

The novel 7-(N-formyl-, 7-(N-acetyl-, and 7-(N-isobutyrylamino)-2-methylquinoline-5,8-diones were synthesized in excellent overall yields in three steps via the nitration of the commercially available 8-hydroxy-2-methylquinoline followed by a reduction-acylation step and then oxidation. Acid hydrolysis of 7-(N-acetylamino)-2-methylquinoline-5,8-dione (14a) afforded the novel 7-aminoquinoline-5,8-dione 7 in excellent yields. Due to our efficient preparation of dione 14a, we now report a short and practical method for the total synthesis of the potent antitumor agent lavendamycin methyl ester (1b) with an excellent overall yield.