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281.
Summary Free boundary value problems, too complicated for formulation as a variational inequality, are broken up into two problems on overlapping regions. On one region the problem is treated as an ordinary boundary value problem; on the second region, the free boundary part of the problem is reduced to a variational inequality. By solving the two problems successively it is shown that under certain conditions the successive solutions converge to a single function that gives a solution of the original problem. Application to a filtration problem is given. 相似文献
282.
283.
Summary Most boundary element methods for two-dimensional boundary value problems are based on point collocation on the boundary and the use of splines as trial functions. Here we present a unified asymptotic error analysis for even as well as for odd degree splines subordinate to uniform or smoothly graded meshes and prove asymptotic convergence of optimal order. The equations are collocated at the breakpoints for odd degree and the internodal midpoints for even degree splines. The crucial assumption for the generalized boundary integral and integro-differential operators is strong ellipticity. Our analysis is based on simple Fourier expansions. In particular, we extend results by J. Saranen and W.L. Wendland from constant to variable coefficient equations. Our results include the first convergence proof of midpoint collocation with piecewise constant functions, i.e., the panel method for solving systems of Cauchy singular integral equations.Dedicated to Prof. Dr. Dr. h.c. mult. Lothar Collatz on the occasion of his 75th birthdayThis work was begun at the Technische Hochschule Darmstadt where Professor Arnold was supported by a North Atlantic Treaty Organization Postdoctoral Fellowship. The work of Professor Arnold is supported by NSF grant BMS-8313247. The work of Professor Wendland was supported by the Stiftung Volkswagenwerk 相似文献
284.
Melvin Hausner 《Combinatorica》1985,5(3):215-225
Ifμ is a positive measure, andA
2, ...,A
n
are measurable sets, the sequencesS
0, ...,S
n
andP
[0], ...,P
[n] are related by the inclusion-exclusion equalities. Inequalities among theS
i
are based on the obviousP
[k]≧0. Letting
=the average average measure of the intersection ofk of the setsA
i
, it is shown that (−1)
k
Δ
k
M
i
≧0 fori+k≦n. The casek=1 yields Fréchet’s inequalities, andk=2 yields Gumbel’s and K. L. Chung’s inequalities. Generalizations are given involvingk-th order divided differences. Using convexity arguments, it is shown that forS
0=1,
whenS
1≧N−1, and
for 1≦k<N≦n andv=0, 1, .... Asymptotic results asn → ∞ are obtained. In particular it is shown that for fixedN,
for all sequencesM
0, ...,M
n
of sufficiently large length if and only if
for 0<t<1. 相似文献
285.
A topological graph is a graph G=(V, E) on a topological space V such that the edge set E is a closed subset of the product space V x V. If the graph contains no infinite independent set then, by a well-known theorem of Erdös, Dushnik and Miller, for any infinite set LV, there is a subset LL of the same oardinality |L| = |L| such that the restriction G L is a complete graph. We investigate the question of whether the same conclusion holds if we weaken the hypothesis and assume only that some dense subset AV does not contain an infinite independent set. If the cofinality cf (|L|)>|A|, then there is an L as before, but if cf (|L|)<-|A|, then some additional hypothesis seems to be required. We prove that, if the graph GA is a comparability graph and A is a dense subset, then for any set LV such that cf (|L|)>, there is a subset LL of size |L|=|L| such that GL is complete. The condition cf (|L|)> is needed.Research supported by NSERC grant #A5198. 相似文献
286.
Joseph P. S. Kung 《Order》1985,2(2):105-112
An element in a lattice is join-irreducible if x=ab implies x=a or x=b. A meet-irreducible is a join-irreducible in the order dual. A lattice is consistent if for every element x and every join-irreducible j, the element xj is a join-irreducible in the upper interval [x, î]. We prove that in a finite consistent lattice, the incidence matrix of meet-irreducibles versus join-irreducibles has rank the number of join-irreducibles. Since modular lattices and their order duals are consistent, this settles a conjecture of Rival on matchings in modular lattices. 相似文献
287.
Anna B. DenisovaVyacheslav Ya. Sosnovskikh Wim Dehaen Suzanne ToppetLuc Van Meervelt Vasiliy A. Bakulev 《Journal of fluorine chemistry》2002,115(2):183-192
Reaction of 2-hydrazinothiazoles 1 with 1-thienyl- and 1-furyl-1,3-butanediones 2a,b in methanol in the presence of hydrochloric acid mainly leads to a mixture of pyrazoles 3 and pyrazolines 4 or pyrazoles 3 and 5 in strong acidic conditions. Isomeric hydrazones 6 and pyrazolines 4 were formed and isolated in these reactions in the absence of hydrochloric acid. It has been shown that the regioselectivity in the reaction of diketones 2 with hydrazine 1 is governed by both the concentration of acid and the nature of substituents in the 1,3-diketones 2. Cyclization of hydrazones 6 is shown to occur under milder conditions than dehydration for pyrazolines 4. The new heterocyclic compounds were prepared and fully characterized by NMR spectra and by X-ray analysis for 3c. 相似文献
288.
289.
290.
V. E. Schneider E. E. Tornau A. A. Vlasova A. A. Gurskas 《Journal of inclusion phenomena and macrocyclic chemistry》1985,3(3):235-242
Clathrate thermodynamic stability conditions and the phase transitions associated with either the orientational ordering of the guest molecules or with the condensation of the guest molecules in the host lattice are investigated by means of the common microscopic model. The theory proposed describes the thermodynamic properties of -hydroquinone (Q
) clathrates. The dielectric constant (T) was measured experimentally inQ
·CH3OH andQ
·SO2 in the temperature range from 4.2 to 300 K and the phase transitions were found. It is shown that the theory qualitatively explains the experimental data obtained.Dedicated to Professor H. M. Powell. 相似文献