On a problem of D.H. Lehmer over short intervals

Let p be an odd prime and a be an integer coprime to p. Denote by N(a,p) the number of pairs of integers b,c with bc≡a (mod p), and with b,c having different parity. The main purpose of this paper is to study the sum , and obtain a sharp asymptotic formula.     

Chemoenzymatic syntheses of iGb3 and Gb3

[STRUCTURE: SEE TEXT] Efficient chemoenzymatic syntheses of iGb3 and Gb3 have been developed. Isoglobotrihexose and globotrihexose were enzymatically synthesized by a three-enzyme system in both solid and solution phases. Then iGb3 and Gb3 were chemically synthesized by coupling of the corresponding trisaccharides with lipid.     

关于广义Kloosterman和的高次均值的一个注记

本文的主要目的是利用三次特征的性质,以及W.Duke,H.Iwaniec,B.J Birch等人的重要工作来研究广义Kloosterman和的高次均值,并给出一些有趣的计算公式.     

Synthesis of 3-Amino-2,2-dimethyl-8-thia-1-azaspiro[4.5]decane

The synthesis of 3-amino-2,2-dimethyl-8-thia-1-azaspiro[4.5]decane is described. Key steps include the addition of prenyl magnesium bromide to a 4-methoxybenzylimine without reversal of stereochemistry and the iodine-initiated aminocyclization to form the azaspirocycle.     

响应面法优化磺丁基醚-β-环糊精合成工艺

以碱性电解水为介质,β-CD和1,4-丁磺内酯为原料,分别采用水浴法和微波法合成了取代度为3的SBE-β-CD。考察了两种不同工艺条件下反应温度、反应时间和碱性电解水pH对产物收率的影响。以产物收率为响应值,采用Box-Behnken响应曲面设计探究了微波法中各变量及其交互作用对产物收率的影响,并建立回归方程预测模型。结果表明,相较于水浴法,微波法反应时间缩短了十几个小时,产物收率提高约10~20%;最佳合成工艺参数为：反应温度为77 ℃,反应时间为2.75 h,碱性电解水pH=12.7,产物收率达到70.4%,且与模型的理论预测值较为接近。     

The First Power Mean of the Inversion of L-Functions and General Kloostermann Sums

 The main purpose of this paper is using the estimate for classical Kloostermann sums and E. Bombieri–A. I. Vinogradov’s important work to study the first power mean of the inversion of Dirichlet L-functions with the weight of general Kloostermann sums, and give an interesting asymptotic formula. Received 30 March 2001; in revised form 12 November 2001     

关于Hurwitz zeta—函数的四次均值

对ｓ＝σ＋ｉｔ，ζ（ｓ，ａ）是Ｈｕｒｗｉｔｚｚｅｔａ－函数，ζ１（ｓ，ａ）＝ζ（ｓａ）－ａ＾－ｓ，。本文的主要目的是用解析的方法给出了Ｈｕｒｗｉｔｚｚｅｔａ－函数四次均值较强的渐近公式。     

Synthetic oligodeoxynucleotide purification by polymerization of failure sequences

Synthetic oligodeoxynucleotide is purified by capping failure sequences with an acrylated phosphoramidite followed by polymerization and product extraction. The method is suitable for large scale oligonucleotide drug purification.     

Isolation and characterization of a new benzofuran from the fungus Alternaria sp. (HS-3) associated with a sea cucumber

A new compound, 4-acetyl-5-hydroxy-3, 6, 7-trimethylbenzofuran-2(3H)-one (1), together with two known compounds, 2-carboxy-3-(2-hydroxypropanyl) phenol (2) and 5-methyl- 6-hydroxy-8-methyoxy-3-methylisochroman (3) were isolated from the fungus Alternaria sp. (HS-3) associated with a sea cucumber from the Yellow Sea in China. Their structures were elucidated by spectral methods.     

A hybrid mean value related to certain hardy sums and Kloosterman sums

The main purpose of this paper is using the mean value formula of Dirichlet L-functions and the analytic methods to study a hybrid mean value problem related to certain Hardy sums and Kloosterman sums, and give some interesting mean value formulae and identities for it.