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1.
2.
There are 2
n-1 ways in which a tree on n vertices can be oriented. Each of these can be regarded as the (Hasse) diagram of a partially ordered set. The maximal and minimal widths of these posets are determined. The maximal width depends on the bipartition of the tree as a bipartite graph and it can be determined in time O(n). The minimal width is one of [/2] or [/2]+1, where is the number of leaves of the tree. An algorithm of execution time O(n + 2 log ) to construct the minimal width orientation is given.This research was partially funded by the National Science and Engineering Research Council of Canada under Grant Number A4219. 相似文献
3.
The hydroxy- and methoxyphthalimidoacetic acids and the methyl methoxyphthalimidoacetates have been synthesized. The ultraviolet absorption spectra of these compounds in 95% ethanol, aqueous acid, and aqueous base are discussed. Structures are suggested for the hydroxy- and methoxyphthalamate ions which are formed in basic solution. The Gabriel-Colman rearrangements of methyl 3- and 4 - methoxyphthalimidoacetate give, respectively, 8-methoxy-4-hydroxy-3 - carbomethoxy-1(2H)-isoquinolone (VII) and 6-methoxy-4-hydroxy-3-carbomethoxy-1(2H)-isoquinolone (VIII). 相似文献
4.
A priority queue transforms an input permutation of some set of sizen into an output permutation. It is shown that the number of such pairs (, ) is (n + 1)
n–1. Some related enumerative and algorithmic questions are also considered.Supported by the National Science and Engineering Research Council of Canada under Grant A4219. 相似文献
5.
Atkinson CE Aliev AE Motherwell WB 《Chemistry (Weinheim an der Bergstrasse, Germany)》2003,9(8):1714-1723
A binding site optimisation protocol for the design of artificial enzymes based on "small molecule-small molecule" binding studies by diffusion NMR is presented. Since the reaction chosen was the hydrolysis of ester 1 ([4-(4-carboxy-1-oxobutyl)-aminobenzyl]-phenethyl ester), an analogous phosphonate ester 2 ([4-(4-carboxy-1-oxobutyl)-aminobenzyl]-phosphonic phenethyl ester) was selected as a suitable transition state analogue (TSA). The key objective of the NMR studies was to find a unit with functional groups capable of binding to the acidic sites of the TSA. Nine dipeptides, mainly with basic and hydroxyl groups, were used and their affinity to the TSA was studied by measuring the change in the diffusion coefficient, D(pep), upon binding by pulse field gradient NMR. The value of D(pep) at 298 K in D(2)O at pD 5, 7 and 10 was measured both in free solution, and mixtures containing one dipeptide and the TSA. As both components are low molecular weight species with M < 500, a TSA-to-dipeptide ratio of 10:1 was used to detect significant changes in D(pep). The results revealed that dipeptides with basic residues show higher affinity to the TSA than those with hydroxyl or aliphatic side chains in aqueous solutions. The dipeptide showing the most significant relative change in D(pep) was H-Arg-Arg-OH, and the binding constant was estimated to be 86 L M(-1) by measuring D(pep) at varying concentrations of the TSA. In addition, binding of the TSA to a new water-soluble polymer with a polyallylamine backbone and randomly distributed Arg-Arg binding sites was examined, and the binding constant was estimated to be > or =1500 L M(-1). As confirmed by further catalytic activity tests, polymers containing Arg-Arg as a binding site are capable of significant rate accelerations in the hydrolysis of ester 1. 相似文献
6.
Hyperfine structures of transitions in the a 3Πu ← X1Σg system of Na2 have been accurately measured by Doppler-free laser excitation spectroscopy in a collimated molecular beam. The hyperfine patterns are quantitatively explained and the reduced matrix elements of the magnetic dipole hf interaction determined from a least-squares fit to the measured line positions. 相似文献
7.
The ν1(CN) band of SCN? in acetonitrile solvent has been observed, surface enhanced, at a silver electrode. Adsorption through the S of SCN? is suggested. The changes of frequency and intensity with the change of electrode potential are reported. The υ(CN) band of the solvent is also probably enhanced. 相似文献
8.
Bromophenol blue indicator was used in UV-visible spectrophotometric measurements to study ion association constants of alkali metal fluorides. The equilibrium constants for the ion pair formation of the alkali metal fluorides were determined as a function of ionic strength at one atmosphere pressure and 25°C. The effect of pressure on these association constants was measured at a constant total ionic strength of 1.0 mol-kg–1 over a pressure range of 1 to 2000 atmospheres at 25°C. The pressure dependences of the stoichiometric association constants of the alkali metal fluorides are given by: lnK
LiF
*
=0.77–2.47×10–4P–2.12×10–8P2; lnK
NaF
*
=0.53–1.08×10–4P–1.66×10–8P2; lnK
KF
*
=0.24–4.41×10–5P–7.15×10–8P2; lnK
RbF
*
=–0.17–8.65×10–5P–4.51×10–8P2; and lnK
CsF
*
= –0.37–1.14×10–4P–6.82×10–8P2, where P is the pressure in atmospheres. The stoichiometric molar volume and compressibility changes for ion pair formation of the alkali metal fluorides were evaluated from the pressure dependence of K
MF
*
data. The thermodynamic association constants were also calculated making use of activity coefficient data from the Pitzer equations. The partial molal volume and compressibility changes for ion pair formation of each alkali metal fluoride are reported. 相似文献
9.
10.
R. J. Apsimon M. Atkinson M. Baake L. S. Bagdasarian D. Barberis T. J. Brodbeck N. Brook T. Charity A. B. Clegg P. Coyle et al. 《Zeitschrift fur Physik C Particles and Fields》1992,56(2):185-192
Measurements are reported of inclusive production of -mesons in the beam fragmentation region in p, p andKp collisions. Results include a small but significant departure from VMD, and a pronounced rise in the/
0 ratio with increasingp
T
. 相似文献