Beta-Gamma函数对余元公式的推导与实现

对构造的公式①,在复数域将其被积函数分解得2n个复根.在实数域将其实虚部积分取极限获证.对构造的公式②,由①将其被积函数的连续性、收敛性及一致收敛性与构造的有理数列用变量替换代入取极限获证.再由①与②应用Gamma-Beta函数的另一形式及(3),得到了余元公式的实现.     

活用参数思想巧解数学问题

数学问题中条件和结论间存在着众多的联系,有些联系比较明显,有些比较隐蔽.为了将那些隐蔽的关系凸现出来,人们常借助于辅助元素--参数为桥梁,通过设参,沟通问题条件和结论间的联系,达到解题的目的.这就是参数思想.     

谈谈迭加法的延伸运用

1　迭加法的背景若数列 {an}为等差数列 ,则有 an+1 - an= d( n∈ N* ,d为常数 ) .于是 ,an- an- 1 =d,an- 1 - an- 2 =d,… ,a3- a2 =d,a2 - a1 =d,将这 n- 1个式子迭加 ,有 an- a1 =( n- 1 ) d,即得等差数列通项公式 an=a1 + ( n- 1 ) d.考虑到这 n- 1个式子中的被减项是 a2 ,a3,… ,an,而减项是 a1 ,a2 ,… ,an- 1 ,故在被减项和减项中同时出现的项为 a2 ,a3,… ,an- 1 ,于是 ,迭加后这些项被消去 ,得 an- a1 =( n-1 ) d.这种将一系列等式相加的方法叫迭加法 .2　迭加法的延伸点迭加法在求数列通项时的运用 ,是基于数列相邻项的差的特点…     

Synthetic and biological studies on a cyclopolypeptide of plant origin

Objective: A natural cyclic peptide previously isolated from Citrus medica was synthesized by coupling oftetrapep-tide units Boc-Leu-Pro-Trp-Leu-Ome and Boc-Ile-Ala-Ala-Gly-Ome after proper deprotection at carboxyl and amino terminals followed by cyclization of linear octapeptide segment.Methods: Solution phase technique was adopted for the synthesis of cyclooctapeptide--sarcodactylamide.Required tetrapeptide units were prepared by coupling of Boc-protected dipeptides viz.Boc-Leu-Pro-OH and Boc-Ile-Ala-OH with respective dipeptide methyl esters Trp-Leu-Ome and Ala-Gly-Ome.Cyclization of linear octapeptide unit was done by p-nitrophenyl ester method.The structure of synthesized cyclopolypeptide was elucidated by FTIR,1H NMR,13C NMR,FABMS spectral data and elemental analysis.The newly synthesized peptide was evaluated for dif-ferent pharmacological activities including antimicrobial,anthelmintic and cytotoxic activities.Results: Synthesis of sarcodac-tylamide was accomplished with >78% yield utilizing dicyclohexylcarbodiimide (DCC) as coupling agent.Newly synthesized peptide possessed potent cytotoxic activity against Dalton's lymphoma ascites (DLA) and Ehrlich's ascites carcinoma (EAC) cell lines,in addition to moderate anthelmintic activity against earthworms Megascoplex konkanensis,Pontoscotex corethruses and Eudrilus sp.Moreover,cyclopolypeptide displayed good antimicrobial activity against pathogenic fungi Candida albicans and Gram-negative bacteria Pseudomonas aeruginosa,in comparison to standard drugs griseofulvin and ciprofloxacin.Conclusion: Solution phase technique employing DCC and triethylamine (TEA) as base proved to be effective for the synthesis of natural cyclooctapeptide.N-methyl morpholine (NMM) was found to be a better base for the cyclization of linear octapeptide unit in comparison to TEA and pyridine.     

二元函数局部一致收敛的条件

给出了当x→a时二元函数f(x,y)在y0局部一致收敛的充要条件,并且建立了实用的判别方法.     

用递推法探求几个概率问题

概率是高中数学教材中的新增内容,由于它与实际生活有密切的关系,这就使概率成为近年来高考的热点内容.本文拟用递推思想方法探求几个有趣的概率问题,体现了数列与概率知识的交汇性,对提高学生学习概率的兴趣、解题能力和创新思维能力都有一定的帮助.     

丙氨酸尾式卟啉及其锌配合物的电化学性质

本文采用循环伏安法研究了 5 -邻 [N - (L -丙氨酸 ) -乙氧基 ]苯基 - 10 ,15 ,2 0 -三苯基卟啉及其锌配合物在CH2 Cl2 为溶剂和TBPA为电解质条件下的电化学性质 .在循环伏安图中 ,两种物质都呈现 4对可逆的氧化还原峰 ,其氧化还原过程仅发生在卟啉的π电子体系上 .同时对其电化学反应机理作了推测     

高中数学基础训练题（2）

数　列1.下列四个数中 ,哪一个是数列 { n(n+ 1) }中的一项(　 )(A) 380　 (B) 39　 (C) 35　 (D) 2 32 .在等比数列 { an}中 ,首项 a1<0 ,则 { an}是递增数列的充要条件是公比 (　 )(A) q>1　 (B) q<1　 (C) 0 相似文献   

宏编程技术探析及其在数控中工中的应用

探析了宏编程技术及其扩展数控系统功能的使用。通过例子阐述了数控加工中采用宏编程技术的重要作用,为解决一些特殊及复杂零件的加工程序编制问题提供了思路。     

“信息迁移型试题”在高考复习中应重视——由2006年北京市一道高考题目引发的思考

（2006年北京高考第20题）在数列{an}中．若a1,a2是正整数．且an=｜an-1-an-2｜,n=3．4．5．…．则称{an}为“绝对差数列”．[第一段]