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991.
Stefania Gabelli Evan Houston Thomas G. Lucas 《Journal of Pure and Applied Algebra》2004,194(3):281-298
Generalizing work of Gilmer and Heinzer, we define a t#-domain to be a domain R in which for any two distinct subsets and of the set of maximal t-ideals of R. We provide characterizations of these domains, and we show that polynomial rings over t#-domains are again t#-domains. Finally, we study overrings of t#-domains. 相似文献
992.
Let X be a locally compact Hausdorff space and C
0(X) the Banach space of continuous functions on X vanishing at infinity. In this paper, we shall study unbounded disjointness preserving linear functionals on C
0(X). They arise from prime ideals of C
0(X), and we translate it into the cozero set ideal setting. In particular, every unbounded disjointness preserving linear functional of c
0 can be constructed explicitly through an ultrafilter on complementary to a cozero set ideal. This ultrafilter method can be extended to produce many, but in general not all, such functionals on C
0(X) for arbitrary X. We also make some remarks where C
0(X) is replaced by a non-commutative C*-algebra. 相似文献
993.
N. Watt 《Monatshefte für Mathematik》2004,141(1):45-81
For X,Y,>0, let and define I
8(X,Y,) to be the cardinality of the set. In this paper it is shown that, for >0, Y
2/X
3=O(), =O(Y
3/X
3) and X=O (Y
2), one has I
8(X,Y,)=O(X
2
Y
2+X
min (X
{3/2}
Y
3, X
{11/2}
Y
{–1})+X
min ({1/3}
X
2
Y
3, X
{14/3}
Y
{1/3})), with the implicit constant depending only on . There is a brief report on an application of this that leads, by way of the Bombieri-Iwaniec method for exponential sums, to some improvement of results on the mean squared modulus of a Dirichlet L-function along a short interval of its critical line. 相似文献
994.
In earlier papers the authors studied finite pseudorandom binary sequences, and they constructed sequences with strong pseudorandom properties. In these earlier constructions multiplicative characters were used. In this paper a new construction is presented which utilizes properties of additive characters. These new sequences can be computed fast, they are well-distributed relative to arithmetic progressions and their correlations of small order are small, but the price paid for the fast computation is that the correlations of large order can be large. 相似文献
995.
Projective metrics were first introduced by A. Cayley and F. Klein who constructed analytical models over the field of complex numbers. The aim of this paper is to give for the first time a purely synthetic definition of all projective spaces with Cayley-Klein metrics and to develop the synthetic foundation of projective-metric geometry to a level of generality including metrics over arbitrary fields of characteristic 2. 相似文献
996.
An explicit coloring of the edges of Kn is constructed such that every copy of K4 has at least four colors on its edges. As n , the number of colors used is n1/2+o(1). This improves upon the previous bound of O(n2/3) due to Erds and Gyárfás obtained by probabilistic methods. The exponent 1/2 is optimal, since it is known that at least (n1/2) colors are required in such a coloring.The coloring is related to constructions giving lower bounds for the multicolor Ramsey number rk(C4). It is more complicated however, because of restrictions imposed on interactions between color classes.* Research supported in part by NSF Grant No. DMS–9970325. 相似文献
997.
Béla?BollobásEmail author David?Gamarnik Oliver?Riordan Benny?Sudakov? 《Combinatorica》2004,24(2):187-207
Consider a complete graph on n vertices with edge weights chosen randomly and independently from an exponential distribution with parameter 1. Fix k vertices and consider the minimum weight Steiner tree which contains these vertices. We prove that with high probability the weight of this tree is (1+o(1))(k-1)(log n-log k)/n when k =o(n) and n.* Research supported in part by NSF grant DSM9971788 Research supported in part by NSF grants DMS-0106589, CCR-9987845 and by the State of New Jersey. Part of this research was done while visiting IBM T. J. Watson Research Center. 相似文献
998.
A graph G is
inexhaustible if whenever a vertex of G is deleted the remaining graph is
isomorphic to G. We address a
question of Cameron [6], who asked which countable graphs are
inexhaustible. In particular, we prove that there are continuum
many countable inexhaustible graphs with properties in common
with the infinite random graph, including adjacency properties
and universality. Locally finite inexhaustible graphs and
forests are investigated, as is a semigroup structure on the
class of inexhaustible graphs. We extend a result of [7] on
homogeneous inexhaustible graphs to pseudo-homogeneous
inexhaustible graphs.The authors gratefully acknowledge support from the
Natural Science and Engineering Research Council of Canada
(NSERC). 相似文献
999.
We consider the poset SO(n) of all words over an n-element alphabet ordered by the subword relation. It is known that SO(2) falls into the class of Macaulay posets, i. e. there is a theorem of Kruskal–Katona type for SO(2). As the corresponding linear ordering of the elements of SO(2) the vip-order can be chosen.Daykin introduced the V-order which generalizes the vip-order to the n2 case. He conjectured that the V-order gives a Kruskal–Katona type theorem for SO(n).We show that this conjecture fails for all n3 by explicitly giving a counterexample. Based on this, we prove that for no n3 the subword order SO(n) is a Macaulay poset. 相似文献
1000.
The Diameter of a Scale-Free Random
Graph 总被引:1,自引:0,他引:1
We consider a random graph process in which vertices are
added to the graph one at a time and joined to a fixed number
m of earlier vertices, where
each earlier vertex is chosen with probability proportional to
its degree. This process was introduced by Barabási and Albert
[3], as a simple model of the growth of real-world graphs such
as the world-wide web. Computer experiments presented by
Barabási, Albert and Jeong [1,5] and heuristic arguments given
by Newman, Strogatz and Watts [23] suggest that after
n steps the resulting graph
should have diameter approximately logn. We show that while this holds for
m=1, for
m2 the diameter is
asymptotically log n/log
logn.* Research supported in part by NSF grant no.
DSM9971788 相似文献