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1.
Let C = (C, ) be a linear ordering, E a subset of {(x, y):x< y in C} whose transitive closure is the linear orderingC, and let :E G be a map from E to a finite group G = (G, ).We showed with M. Pouzet that, when C is countable, there isF E whose transitive closure is still C, and such that (p) = (xo, x1)(x1, x2)....(xn– 1, xn) G depends only upon the extremities x0, xn ofp, where p = (xo, x1...,xn) (with 1 n < ) is a finite sequencefor which (xi, xi + 1) F for all i < n. Here, we show thatthis property does not hold if C is the real line, but is stilltrue if C does not embed an 1-dense linear ordering, or evena 2-dense linear ordering when Martin's Axiom holds (it followsin particular that it is independent of ZFC for linear orderingsof size ). On the other hand, we prove that this property isalways valid if E = {(x,y):x < y in C}, regardless of anyother condition on C. 相似文献
2.
A. Brochet und R. Cambier 《Fresenius' Journal of Analytical Chemistry》1895,34(1):623-624
Ohne Zusammenfassung 相似文献
3.
Universal attractor and inertial sets for the phase field model 总被引:1,自引:0,他引:1
We consider the phase field equations in dimensions 1, 2 and 3. We show that it is well-posed when assuming that the initial data is square integrable and prove the existence of a universal attractor and of inertial sets. 相似文献
4.
We prove the following results which are related to Menger's theorem for (infinite) ordered sets. (i) If the space of maximal chains of an ordered set is compact, then the maximum number of pairwise disjoint maximal chains is finite and is equal to the minimum size of a cutset, (i.e. a set which meets all maximal chains). (ii) If the maximal chains pairwise intersect, then the intersection of finitely many is never empty. One corollary of (ii) is that, if the maximal chains pairwise intersect and if one of the maximal chains is complete, then there is an element common to all maximal chains. 相似文献
5.
J-M. Brochet 《Order》1991,8(1):63-75
We say that an ordered set P is spanned by a family C of chains if P=(P, ) is the transitive closure of {(C, | C) C C. It is shown that there is a function h: such that if P is spanned by k< chains, then P has a finite cutset-number h(k) (i.e. for any xP, there is a finite set F of size |F|h(k)–1, such that the elements of F are incomparable with x and {x}F meets every maximal chain of P). The function h is exponentially bounded but eventually dominates any polynomial function, even if it is only required that there are at most h(k) pairwise disjoint maximal chains in P, whenever P is spanned by k< chains. 相似文献
6.
Johan Floriot Xavier Levecq Samuel Bucourt Muriel Thomasset François Polack Mourad Idir Pascal Mercère Thierry Moreno Sylvain Brochet 《Journal of synchrotron radiation》2008,15(2):134-139
The recent development of short‐wavelength optics (X/EUV, synchrotrons) requires improved metrology techniques in terms of accuracy and curvature dynamic range. In this article a stitching Shack–Hartmann head dedicated to be mounted on translation stages for the characterization of X‐ray mirrors is presented. The principle of the instrument is described and experimental results for an X‐ray toroidal mirror are presented. Submicroradian performances can be achieved and systematic comparison with a classical long‐trace profiler is presented. The accuracy and wide dynamic range of the Shack–Hartmann long‐trace‐profiler head allow two‐dimensional characterizations of surface figure and curvature with a submillimeter spatial resolution. 相似文献
7.
The homologation of furfural 1a and methyl 3-(5-formyl-2-furyl) propenoate 1b or ethyl 3-(5-formyl-2-furyl) propenoate 1c to the corresponding furylacetaldehydes was carried out in two stages: i) preparation of the furan epoxides from 1a, 1b, 1c ii) cleavage and rearrangement of the epoxides on sepiolite. Sepiolite is a convenient catalyst for this last stage involving substrates as labile as the furan epoxides. 相似文献
8.
M. Delépine Brochet und Cambier J. Weiss 《Fresenius' Journal of Analytical Chemistry》1897,36(1):322-325
Ohne Zusammenfassung 相似文献
9.
J.-M. Brochet 《Mathematical Logic Quarterly》1993,39(1):158-164
A cutset of H is a subset of ∪ H which meets every element of H. H has the finite cutset property if every cutset of H contains a finite one. We study this notion, and in particular how it is related to the compactness of H for the natural topology. MSC: 04A20, 54D30. 相似文献
10.
It is shown that, if an ordered set P contains at most k pairwise disjoint maximal chains, where k is finite, then every finite family of maximal chains in P has a cutset of size at most k. As a corollary of this, we obtain the following Menger-type result that, if in addition, P contains k pairwise disjoint complete maximal chains, then the whole family, M
(P), of maximal chains in P has a cutset of size k. We also give a direct proof of this result. We give an example of an ordered set P in which every maximal chain is complete, P does not contain infinitely many pairwise disjoint maximal chains (but arbitrarily large finite families of pairwise disjoint maximal chains), and yet M
(P) does not have a cutset of size <x, where x is any given (infinite) cardinal. This shows that the finiteness of k in the above corollary is essential and disproves a conjecture of Zaguia. 相似文献