This paper is concerned with tight closure in a commutative Noetherian ring of prime characteristic , and is motivated by an argument of K. E. Smith and I. Swanson that shows that, if the sequence of Frobenius powers of a proper ideal of has linear growth of primary decompositions, then tight closure (of ) `commutes with localization at the powers of a single element'. It is shown in this paper that, provided has a weak test element, linear growth of primary decompositions for other sequences of ideals of that approximate, in a certain sense, the sequence of Frobenius powers of would not only be just as good in this context, but, in the presence of a certain additional finiteness property, would actually imply that tight closure (of ) commutes with localization at an arbitrary multiplicatively closed subset of .
Work of M. Katzman on the localization problem for tight closure raised the question as to whether the union of the associated primes of the tight closures of the Frobenius powers of has only finitely many maximal members. This paper develops, through a careful analysis of the ideal theory of the perfect closure of , strategies for showing that tight closure (of a specified ideal of ) commutes with localization at an arbitrary multiplicatively closed subset of and for showing that the union of the associated primes of the tight closures of the Frobenius powers of is actually a finite set. Several applications of the strategies are presented; in most of them it was already known that tight closure commutes with localization, but the resulting affirmative answers to Katzman's question in the various situations considered are believed to be new.
The difference absorption spectra of different grades of gasoline (A-76, AI-92, and AI-95) with octane numbers lying within 76–85 have been investigated experimentally in comparison with hydrocarbons: isooctane, benzene, and n-heptane. The spectra obtained contain absorption bands of the CH3, CH2, and CH groups and supposedly of the olefin double bond. The possibility of determining the octane number of an unknown grade of gasoline by using the absorption of a measured difference spectrum at one selected wavelength is shown. 相似文献
We consider the stochastic differential equation: dXt=(|Xt|)dBt, where B is a Brownian motion and is a non-Hölder Borel function. A sufficient condition of pathwise uniqueness is given. 相似文献
In this paper, we generalize the exitence result for pure strategy Nash equilibria in anonymous nonatomic games. By working directly on integrals of pure strategies, we also generalize, for the same class of games, the existence result for undominated pure strategy Nash equilibria even though, in general, the set of pure strategy Nash equilibria may fail to be weakly compact.
Received August 2001 相似文献
The values of the gas-chromatographic indicator reflecting the capacity of analytes for self-association in pure liquids,
δTb.p., were estimated for C1–C9 and C11n-alkanols by capillary gas chromatography on a nonpolar stationary phase under isothermal conditions. The δTb.p. values ofn-alkanols, found as the difference between the boiling points measured directly and those calculated from GC data, are correlated
with thermodynamic characteristics of the formation ofn-alkanol associates in pure liquids. Usingn-alkanols as analytes with insignificant temperature increments of the retention indices, it was shown that the δTb.p. values can be determined under conditions used in gas chromatography with temperature programming. In this way a single chromatographic
run can be used to compare the capacities for self-association of analytes boiling over a wide temperature range. The C2–C9n-alkanethiols, which are not associated in neat liquids, have negative δTb.p. values. An interpretation of this finding is proposed.
Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 2, pp. 315–318 February, 2000. 相似文献
In this paper, we investigate the problems of convergence of experience-based ratemakings regarding the Esscher principle. In addition to the Bayes and the classical credibility premiums, we suggest a new credibility formula for the Esscher premium. Then we show the convergence of the Bayes and the newly defined credibility premiums towards the individual premium and point out that the classical credibility premium does not generally converge to the individual premium by presenting a sufficient and necessary condition under which the classical credibility Esscher premium converges to the individual premium. A simulation study is carried out to illustrate the theoretical conclusions. 相似文献