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联系电话:86-5设a&1,f(t)=a^t-at在(-∞,+∞)内的驻点为t(a),问a为何值时,t(a)最小?并求出最小值。_百度知道
设a&1,f(t)=a^t-at在(-∞,+∞)内的驻点为t(a),问a为何值时,t(a)最小?并求出最小值。
提问者采纳
(t)=a^tlna-a=o
(a>:f'θz)=[1/[a^zlna]=[1/,设F=a^z-lna
dz/,dy/,令c=lna
H=1/θx]/1)
a^z=lna-z;lna-z]/dx=-[θF/c-log e^c (c)=1/e^e;c(lnc)=1/,t(a)min=t(e^e)=(e-1)/θa)/e^e.解;da&lna)
=log a (a) - log a (lna)
=1- log a (lna)
设z=log a (lna)
(a>,H&[alna]
又设H=1/a&da&da=-(θF/当a>: 上面运用了多元函数隐函数求导公式
方程F(x;θx≠0时,H<,y)=0
则当θF/e 补充一下;0;(θF/,a=e^e
当a=e^e,dz/a-za^(z-1)]/,dz/.;0
故z(max)=z(e^e)=1/c(1-lnc)=0
解得c=e;0;0;1)
t(a)=log a (a/我来试试吧;[θF/.;c-1/
提问者评价
感觉有别的方法,没必要用多元函数求导,这是高数(上)的习题。
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&& 文章详情
A thymine tetrad in d(TGGGGT) quadruplexes stabilized with Tl+/Na+ ions
作者:Carmen Cáceres, Glenford Wright, Catherine Gouyette1, Gary Parkinson2 and Juan A. Subirana*
【关键词】& TGGGGT
Departament d’Enginyeria Química, Universitat Politècnica de Catalunya, Avinguda Diagonal 647, E-08028 Barcelona, Spain, 1 Unité de Chimie Organique, Institut Pasteur. 28, rue du Docteur Roux, 75724 Paris Cedex 15, France and 2 Cancer Research UK, Biomolecular Structure Group, School of Pharmacy, University of London, 29 39 Brunswick Square, London WC1N 1AX, UK
*To whom correspondence should be addressed. Tel: +34 934 0166 88; Fax: +34 934 010 978; Email:
PDB ID nos 1S45 and 1S47.
We report two new structures of the quadruplex d(TGGGGT)4 obtained by single crystal X-ray diffraction. In one of them a thymine tetrad is found. Thus the yeast telomere sequences d(TG1 3) might be able to form continuous quadruplex structures, involving both guanine and thymine tetrads. Our study also shows substantial differences in the arrangement of thymines when compared with previous studies. We find five different types of organization: (i) groove binding with hydrogen bonds to guanines from a
(ii) partially ordered groove binding, witho (iii) stacked thymine triads, formed at the 3'ends (iv) a thymine tetrad between two guanine tetrads. Thymines are stabilized in pairs by single hydrogen bonds. A central sodium ion interacts with two thymines and contributes to the tetrad structure. (v) Completely disordered thymines which do not show any clear location in the crystal. The tetrads are stabilized by either Na+ or Tl+ ions. We show that by using MAD methods, Tl+ can be unambiguously located and distinguished from Na+. We can thus determine the preference for either ion in each ionic site of the structure under the conditions used by us.
INTRODUCTION
The telomeric ends of chromosomes contain stretches of guanine-rich segments (1) that can form a variety of four-strand structures (2 4). There is strong evidence that these structures vary in their organization as a function of the sequence between consecutive tandems of guanines, but also depending on the ions present (5,6) and pH (7). The sequence we report here d(TGGGGT) is related to the telomeric repeat sequence found in Tetrahymena. A high resolution crystal structure of the latter sequence has been reported (2) showing that, in the presence of Na+ and Ca2+ ions, the guanine quadruplexes are parallel-stranded. The four phosphodiester chains in the quadruplex show an identical 5'