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171.
Summary A critical issue in drug discovery utilizing combinatorial chemistry as part of the discovery process is the choice of scaffolds to be used for a proper presentation, in a three-dimensional space, of the critical elements of structure necessary for molecular recognition (binding) and information transfer (agonist/ antagonist). In the case of polypeptide ligands, considerations related to the properties of various backbone structures (-helix, -sheets, etc.; , space) and those related to three-dimensional presentation of side-chain moieties (topography; (chi) space) must be addressed, although they often present quite different elements in the molecular recognition puzzle. We have addressed aspects of this problem by examining the three-dimensional structures of chemically different scaffolds at various distances from the scaffold to evaluate their putative diversity. We find that chemically diverse scaffolds can readily become topographically similar. We suggest a topographical approach involving design in chi space to deal with these problems. 相似文献
172.
Cécile Huybrechts 《Journal of Algebraic Combinatorics》1996,5(4):329-335
Let be a rank three incidence geometry of points, lines and planes whose planes are linear spaces and whose point residues are dual linear spaces (notice that we do not require anything on the line residues). We assume that the residual linear spaces of belong to a natural class of finite linear spaces, namely those linear spaces whose full automorphism group acts flag-transitively and whose orders are polynomial functions of some prime number. This class consists of six families of linear spaces. In the amalgamation of two such linear spaces imposes an equality on their orders leading, in particular, to a series of diophantine equations, the solutions of which provide a reduction theorem on the possible amalgams of linear spaces that can occur in .We prove that one of the following holds (up to a permutation of the words point and plane):A) the planes of and the dual of the point residues belong to the same family and have the same orders,B) the diagram of is in one of six families,C) the diagram of belongs to a list of seven sporadic cases.Finally, we consider the particular case where the line residues of are generalized digons. 相似文献
173.
D. H. Fremlin R. A. Johnson E. Wajch 《Proceedings of the American Mathematical Society》1996,124(9):2897-2903
A space Borel multiplies with a space if each Borel set of is a member of the -algebra in generated by Borel rectangles. We show that a regular space Borel multiplies with every regular space if and only if has a countable network. We give an example of a Hausdorff space with a countable network which fails to Borel multiply with any non-separable metric space. In passing, we obtain a characterization of those spaces which Borel multiply with the space of countable ordinals, and an internal necessary and sufficient condition for to Borel multiply with every metric space.
174.
J. Ignacio Extremiana Aldana L. Javier Herná ndez Paricio M. Teresa Rivas Rodrí guez 《Proceedings of the American Mathematical Society》1996,124(11):3545-3553
For each integer , we give a distinct closed model category structure to the category of pointed spaces such that the corresponding localized category is equivalent to the standard homotopy category of -connected CW-complexes. The structure of closed model category given by Quillen to is based on maps which induce isomorphisms on all homotopy group functors and for any choice of base point. For each , the closed model category structure given here takes as weak equivalences those maps that for the given base point induce isomorphisms on for .
175.
Carleson measure characterization of Bloch functions 总被引:1,自引:0,他引:1
Lou Zengjian 《数学学报(英文版)》1996,12(2):175-184
We give several equivalences of Bloch functions and little Bloch functions. Using these results we obtain the generalized Carleson measure characterization of Bloch functions and the generalized vanishing Carleson measure characterization of little Bloch functions, that is,f B if and only if |D
f(z)|
p
(1-|z|2)p-1
dm(z) is a generalized Carleson measure;f B
0 if and only if |D
f(z)|
p
(1-|z|2)p-1
dm(z) is a generalized vanishing Carleson measure, whereD
f( > 0) is the fractional derivative of analytic functionf of order, m denotes the normalised Lebesgue measure.Supported partly by the Young Teacher Natural Science Foundation of Shandong Province. 相似文献
176.
Shigeru Arimoto 《Journal of mathematical chemistry》2007,41(3):231-269
The present article is the first part of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes
and related molecular networks. Four key problems are formulated whose affirmative solutions imply the formation of the initial
investigative bridge between the research field of nanotubes and that of the additivity and other network problems studied
and solved by using the RST. All of these four problems are solved affirmatively by using tools from the RST. The Piecewise
Monotone Lemmas (PMLs) are cornerstones of the proof of the Fukui conjecture concerning the additivity problems of hydrocarbons.
The solution of the fourth problem gives a generalized analytical formula of the pi-electron energy band curves of nanotube
(a, b), with two new complex parameters c and d. These two parameters bring forth a broad class of analytic curves to which the PMLs and associated theoretical devices apply.
Based on the above affirmative solutions of the problems, a central theorem in the RST, called the asymptotic linearity theorem
(ALT) has been applied to nanotubes and monocyclic polyenes. Analytical formulae derived in this application of the ALT illuminate
in a new global context (i) the conductivity of nanotubes and (ii) the aromaticity of monocyclic polyenes; moreover an analytical
formula obtained by using the ALT provides a fresh insight into Hückel’s (4n+2) rule. The present article forms a foundation of the forthcoming articles in this series.
The present series of articles is closely associated with the series of articles entitled ‘Proof of the Fukui conjecture via
resolution of singularities and related methods’ published in the JOMC. 相似文献
177.
178.
The crystal structure of Zr3N4 is shown to crystallize in the centrosymmetric space group Pnam rather than in the noncentrosymmetric space group Pna21. 相似文献
179.
For 357 subshells of the 53 neutral atoms He through Xe in their ground states, the two-electron intracule (relative motion)
<u
k
>
nl
and extracule (center-of-mass motion) <R
k
>
nl
subshell moments in position space are examined as well as their counterparts <v
k
>
nl
and <P
k
>
nl
in momentum space, where n and l are the principal and azimuthal quantum numbers of the atomic subshell, respectively. It is clarified that between the intracule
and extracule moments the “2
k
-rule” is strictly valid, which means <u
k
>
nl
= 2
k
<R
k
>
nl
and <v
k
>
nl
= 2
k
<P
k
>
nl
for any nl subshell. Theoretical analysis also proves that for a particular case of k = +2, two relations <u
2>
nl
= (N
nl
−1)<r
2>
nl
and <v
2>
nl
= (N
nl
−1)<p
2>
nl
hold exactly, where N
nl
(≥2) is the number of electrons in the subshell nl, and <r
k
>
nl
and <p
k
>
nl
are the familiar one-electron subshell moments in position and momentum spaces, respectively. The latter equality establishes
a new and rigorous relation between the second electron-pair moments in momentum space and the total energy of an atom through
the virial theorem. For k=+1, −1, and −2, the numerical Hartree-Fock results for the 357 subshells show that there are approximate but accurate linear
relations between <u
k
>
nl
and <r
k
>
nl
and between <v
k
>
nl
and <p
k
>
nl
, in which the proportionality constant in each space depends on n,l, and k.
Received: 27 April 1998 / Accepted: 29 May 1998 / Published online: 28 August 1998 相似文献
180.
Shigeru?ArimotoEmail author Mark?Spivakovsky Keith?F.?Taylor Paul?G.?Mezey 《Journal of mathematical chemistry》2005,37(2):171-189
The present article is a direct continuation of the first part of this series. We reduce a proof of the Fukui conjecture (concerning the additivity problem of the zero-point vibrational energies of hydrocarbons) to that of a proposition related to the theory of algebraic curves, so that we can focus on the key mechanism of the additivity phenomena. Namely, by establishing what is called the Basic Piecewise Monotone Theorem (BPMT), we reduce a proof of the Fukui conjecture to that of a proposition, called the Local Analyticity Proposition, Version 1 (LAP1), which admits a proof via resolution of singularities. By LAP1, the essential part of the mechanism of the asymptotic linearity phenomena is extracted and is elucidated by using tools from the mathematical theory of algebraic curves, whose language is of vital importance in analyzing the crux of the additivity mechanism.
Dedicated to the memory of Prof. Kenichi Fukui (1918–1998). 相似文献