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11.
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
12.
A family of of open subsets of the real line is called an ω-cover of a set X iff every finite subset of X is contained in an element of . A set of reals X is a γ-set iff for every ω-cover of X there exists such that In this paper we show that assuming Martin's axiom there is a γ-set X of cardinality the continuum. 相似文献
13.
Norbert Brunner 《Archive for Mathematical Logic》1984,24(1):119-135
A set is amorphous, if it is not a union of two disjoint infinite subsets. The following variants of the Tychonoff product theorem are investigated in the hierarchy of weak choice principles. TA1: An amorphous power of a compactT
2 space is compact. TA2: An amorphous power of a compactT
2 space which as a set is wellorderable is compact. In ZF0TA1 is equivalent to the assertion, that amorphous sets are finite. RT is Ramsey's theorem, that every finite colouring of the set ofn-element subsets of an infinite set has an infinite homogeneous subset and PW is Rubin's axiom, that the power set of an ordinal is wellorderable. In ZF0RT+PW implies TA2. Since RT+PW is compatible with the existence of infinite amorphous sets, TA2 does not imply TA1 in ZF0. But TA2 cannot be proved in ZF0 alone. As an application, we prove a theorem of Stone, using a weak wellordering axiomD
3 (a set is wellorderable, if each of its infinite subsets is structured) together with RT.
Diese Arbeit ist Teil der Habilitationsschrift des Verfassers im Fachgebiet Mathematische Analysis an der Technischen Universität Wien. 相似文献
14.
Ab initio SCF computations on the intrinsic preferences of the H+, CH
3
+
and C2H
5
+
cations towards the two principal sites of protonation or alkylation on cytosine, N3 or O2, show that this preference undergoes a continuous modification with the increase in size and complexity of the cation. N3 is the preferred site of fixation of H+, O2 the preferred site of C2H
5
+
, while CH
3
+
has no marked preference. The exchange repulsion term of the binding energy appears responsible for the preference of C2H
5
+
for O2.This work was supported by the Ligue Francaise contre le Cancer and the National Foundation for Cancer Research (USA) 相似文献
15.
A family of Hermite interpolants by bisection algorithms 总被引:9,自引:0,他引:9
J. L. Merrien 《Numerical Algorithms》1992,2(2):187-200
A two point subdivision scheme with two parameters is proposed to draw curves corresponding to functions that satisfy Hermite conditions on [a, b]. We build two functionsf andf
1 on dyadic numbers and for some values of the parameters,f is in 04741gj7g2/xxlarge8467.gif" alt="ell" align="BASELINE" BORDER="0">1 withf
1=f04741gj7g2/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">. Examples are provided which show how different the curves can be. 相似文献
16.
17.
The paper deals with second order nonlinear evolution inclusions and their applications. We study evolution inclusions involving a Volterra-type integral operator, which are considered within the framework of an evolution triple of spaces. First, we deliver a result on the unique solvability of the Cauchy problem for the inclusion by combining a surjectivity result for multivalued pseudomonotone operators and the Banach contraction principle. Next, we provide a theorem on the continuous dependence of the solution to the inclusion with respect to the operators involved in the problem. Finally, we consider a dynamic frictional contact problem of viscoelasticity for materials with long memory and indicate how the result on evolution inclusion is applicable to the model of the contact problem. 相似文献
18.
George Victor McIlvaine 《Expositiones Mathematicae》2019,37(3):333-346
This paper reports on findings relating to catenaries since the publication in Expositiones Mathematicae of Denzler and Hinz’s pioneering 1999 paper, Catenaria Vera – the True Catenary. New governing differential equations and explicit solutions are derived for the catenary in positive and negative radial potentials with physical constants incorporated in the derivations. In keeping with precedent by Denzler and Hinz, a measure of historical perspective is offered as homage to Gottfried Wilhelm Leibniz, Christiaan Huygens and Johann Bernoulli, the original first-solvers of the catenary. 相似文献
19.
This paper will deal with an anisotropic area-preserving flow which keeps the convexity of the evolving curve and the limiting curve converges to a homothety of a symmetric smooth strictly convex plane curve. 相似文献
20.
Miller's 1937 splitting theorem was proved for every finite n>0 for all ρ-uniform families of sets in which ρ is infinite. A simple method for proving Miller-type splitting theorems is presented here and an extension of Miller's theorem is proved in ZFC for every cardinal ν for all ρ -uniform families in which ρ≥?ω(ν). The main ingredient in the method is an asymptotic infinitary Löwenheim–Skolem theorem for anti-monotone set functions. 相似文献