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11.
As is well known, Lovász Local Lemma implies that everyd-uniformd-regular hypergraph is 2-colorable, providedd 9. We present a different proof of a slightly stronger result; everyd-uniformd-regular hypergraph is 2-colorable, providedd 8.Research supported in part by Allon Fellowship and by a grant from the United States Israel Binational Science Foundation. 相似文献
12.
Forr2 letp(n, r) denote the maximum cardinality of a subsetA ofN={1, 2,...,n} such that there are noBA and an integery with
b=y
r. It is shown that for any>0 andn>n(), (1+o(1))21/(r+1)
n
(r–1)/(r+1)p(n, r)n
+2/3 for allr5, and that for every fixedr6,p(n, r)=(1+o(1))·21/(r+1)
n
(r–1)/(r+1) asn. Letf(n, m) denote the maximum cardinality of a subsetA ofN such that there is noBA the sum of whose elements ism. It is proved that for 3n
6/3+mn
2/20 log2
n andn>n(), f(n, m)=[n/s]+s–2, wheres is the smallest integer that does not dividem. A special case of this result establishes a conjecture of Erds and Graham.Research supported in part by Allon Fellowship, by a Bat-Sheva de Rothschild Grant and by the Fund for Basic Research administered by the Israel Academy of Sciences. 相似文献
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16.
R. Hoelzl Christian Hoelzl Ludwig Kotz Lazlo Fabry 《Accreditation and quality assurance》1998,3(5):185-188
Inductively coupled plasma mass spectrometry (ICP-MS) and high resolution inductively coupled plasma mass spectrometry (HR-ICP-MS)
are powerful methods of determining metallic impurities in the low- and sub-ppt level in process media such as ultra-pure
water used in semiconductor and wafer manufacturing. By using mass spectrometers for analysis, an isotope dilution analysis
(IDMS) is possible. The reproducibility of an IDMS is unmatched. For concentration levels near the instrument detection limit
a novel method is reported to find the optimal amount of isotopic spike solution. This optimal value can be derived by the
law of propagation of uncertainty combined with the Poisson statistics of the measured number of counts. Generally, an excess
of isotopic spike solution should be used to provide results of lowest possible uncertainty. The results are presented in
a diagram for easy practical use.
Received: 14 October 1997 · Accepted: 13 February 1998 相似文献
17.
The hydrogen-deuterium exchange of H-2 in 4-pyrimidone, a number of 1- and 3-alkyl-4-pyrimidones and several of their thione analogs in deuterium oxide at moderate temperatures is reported. This reaction is apparently not susceptible to acid or base catalysis. Cations of the 4-pyrimidones were found not to exchange H-2 at all in acid media. Catalytic amounts of bases do not alter the exchange rates whereas more concentrated alkali decompose the pyrimidone. However, 1,4(3,4)-dihydro-1,3-dimethyl-4-oxopyrimidinium iodide (and its 6-methyl analog) exchange H-2 quite rapidly in neutral deuterium oxide, almost instantly when triethylamine is added as a catalyst, and very slowly in dilute solutions of deuterium chloride in deuterium oxide. Mechanisms are proposed to account for these phenomena. 相似文献
18.
Summary The optimized Wittig reaction of selectively functionalized 3-acylindoles yield new, and for Diels-Alder reactions highly reactive donor- and acceptor substituted 3-vinylindoles, respectively. 相似文献
19.
Bernard A. Mikrut Krishan K. Khullar Pamela Y. P. Chan John M. Kokosa Ludwig Bauer Richard S. Egan 《Journal of heterocyclic chemistry》1974,11(5):713-718
The reaction of pyridine 1-oxide with 1-adamantanethiol in acetic anhydride produced a mixture of 2- and 3-(1-adamantanethio)pyridines, 1-aeetyl-2-(1-adamantanethio)-3-hydroxy-4-acetoxy-1,2,3,4-telrahydropyridine and the corresponding 3-acetoxyderivative. Pure substances were separated by means of column chromatography on alumina. The tetrahydropyridines were identified by means of their proton magnetic and mass spectra. 4-(1-Adamantanethio)pyridine was synthesized from 4-chloropyridinc and 1-adamantanethiol. The three isomeric (1-adamantanethio)-pyridines were, each, cleaved by concentrated hydrochloric acid to give 1-chloroadamantane and the corresponding pyridinethiol. 相似文献
20.
A regressive function (also called a regression or contractive mapping) on a partial order P is a function mapping P to itself such that (x)x. A monotone k-chain for is a k-chain on which is order-preserving; i.e., a chain x
1<...ksuch that (x
1)...(xk). Let P
nbe the poset of integer intervals {i, i+1, ..., m} contained in {1, 2, ..., n}, ordered by inclusion. Let f(k) be the least value of n such that every regression on P
nhas a monotone k+1-chain, let t(x,j) be defined by t(x, 0)=1 and t(x,j)=x
t(x,j–1). Then f(k) exists for all k (originally proved by D. White), and t(2,k) < f(K) <t( + k, k) , where k 0 as k. Alternatively, the largest k such that every regression on P
nis guaranteed to have a monotone k-chain lies between lg*(n) and lg*(n)–2, inclusive, where lg*(n) is the number of appliations of logarithm base 2 required to reduce n to a negative number. Analogous results hold for choice functions, which are regressions in which every element is mapped to a minimal element. 相似文献