共查询到20条相似文献,搜索用时 78 毫秒
1.
Open covers and partition relations 总被引:1,自引:0,他引:1
Marion Scheepers 《Proceedings of the American Mathematical Society》1999,127(2):577-581
An open cover of a topological space is said to be an -cover if there is for each finite subset of the space a member of the cover which contains the finite set, but the space itself is not a member of the cover. We prove theorems which imply that a set of real numbers has Rothberger's property if, and only if, for each positive integer , for each -cover of , and for each function from the two-element subsets of , there is a subset of such that is constant on , and each element of belongs to infinitely many elements of (Theorem 1). A similar characterization is given of Menger's property for sets of real numbers (Theorem 6).
2.
Erkki Laitinen Krzysztof Pawalowski 《Proceedings of the American Mathematical Society》1999,127(1):297-307
Using smooth one-fixed-point actions on spheres and a result due to Bob Oliver on the tangent representations at fixed points for smooth group actions on disks, we obtain a similar result for perfect group actions on spheres. For a finite group , we compute a certain subgroup of the representation ring . This allows us to prove that a finite perfect group has a smooth -proper action on a sphere with isolated fixed points at which the tangent representations of are mutually nonisomorphic if and only if contains two or more real conjugacy classes of elements not of prime power order. Moreover, by reducing group theoretical computations to number theory, for an integer and primes , we prove similar results for the group , , or . In particular, has Smith equivalent representations that are not isomorphic if and only if , , .
3.
Nobuhiko Fujii Akihiro Nakamura Ray Redheffer 《Proceedings of the American Mathematical Society》1999,127(6):1815-1818
For let be complex numbers such that is bounded. For define , where . Then the excesses in the sense of Paley and Wiener satisfy .
4.
Y. Bahturin A. Giambruno M. Zaicev 《Proceedings of the American Mathematical Society》1999,127(1):63-69
Let be an algebra over a field and a finite group of automorphisms and anti-automorphisms of . We prove that if satisfies an essential -polynomial identity of degree , then the -codimensions of are exponentially bounded and satisfies a polynomial identity whose degree is bounded by an explicit function of . As a consequence we show that if is an algebra with involution satisfying a -polynomial identity of degree , then the -codimensions of are exponentially bounded; this gives a new proof of a theorem of Amitsur stating that in this case must satisfy a polynomial identity and we can now give an upper bound on the degree of this identity.
5.
Konrad J. Swanepoel 《Proceedings of the American Mathematical Society》1999,127(7):2155-2162
A hollow axis-aligned box is the boundary of the cartesian product of compact intervals in . We show that for , if any of a collection of hollow axis-aligned boxes have non-empty intersection, then the whole collection has non-empty intersection; and if any of a collection of hollow axis-aligned rectangles in have non-empty intersection, then the whole collection has non-empty intersection. The values for and for are the best possible in general. We also characterize the collections of hollow boxes which would be counterexamples if were lowered to , and to , respectively.
6.
Kohji Yanagawa 《Proceedings of the American Mathematical Society》1999,127(2):377-383
Let be a monomial ideal of . Bayer-Peeva-Sturmfels studied a subcomplex of the Taylor resolution, defined by a simplicial complex . They proved that if is generic (i.e., no variable appears with the same non-zero exponent in two distinct monomials which are minimal generators), then is the minimal free resolution of , where is the Scarf complex of . In this paper, we prove the following: for a generic (in the above sense) monomial ideal and each integer , there is an embedded prime of . Thus a generic monomial ideal with no embedded primes is Cohen-Macaulay (in this case, is shellable). We also study a non-generic monomial ideal whose minimal free resolution is for some . In particular, we prove that if all associated primes of have the same height, then is Cohen-Macaulay and is pure and strongly connected.
7.
Greg Hjorth 《Proceedings of the American Mathematical Society》1999,127(1):271-278
Let be a Polish group, a Polish topology on a space , acting continuously on , with -invariant and in the Borel algebra generated by . Then there is a larger Polish topology on so that is open with respect to , still acts continuously on , and has a basis consisting of sets that are of the same Borel rank as relative to .
8.
Sy D. Friedman 《Proceedings of the American Mathematical Society》1999,127(12):3707-3709
We use ``iterated square sequences' to show that there is an -definable partition such that if is an inner model not containing :
- (a)
- For some is stationary.
- (b)
- For each there is a generic extension of in which does not exist and is non-stationary.
9.
The main theorem says that any module-finite (but not necessarily commutative) algebra over a commutative Noetherian universally catenary ring is catenary. Hence the ring is catenary if is Cohen-Macaulay. When is local and is a Cohen-Macaulay -module, we have that is a catenary ring, for any , and the equality holds true for any pair of prime ideals in and for any saturated chain of prime ideals between and .
10.
Michael Levin 《Proceedings of the American Mathematical Society》2000,128(2):623-624
In this note we simplify the proof of some properties of Kulesza's metric space with ind and Ind.
11.
Yuan-chung Sheu 《Proceedings of the American Mathematical Society》1999,127(12):3721-3728
Consider an -superdiffusion on , where is an uniformly elliptic differential operator in , and . The -polar sets for are subsets of which have no intersection with the graph of , and they are related to the removable singularities for a corresponding nonlinear parabolic partial differential equation. Dynkin characterized the -polarity of a general analytic set in term of the Bessel capacity of , and Sheu in term of the restricted Hausdorff dimension. In this paper we study in particular the -polarity of sets of the form , where and are two Borel subsets of and respectively. We establish a relationship between the restricted Hausdorff dimension of and the usual Hausdorff dimensions of and . As an application, we obtain a criterion for -polarity of in terms of the Hausdorff dimensions of and , which also gives an answer to a problem proposed by Dynkin in the 1991 Wald Memorial Lectures.
12.
Vladimir G. Troitsky 《Proceedings of the American Mathematical Society》2000,128(2):521-525
We show that the celebrated Lomonosov theorem cannot be improved by increasing the number of commuting operators. Specifically, we prove that if is the operator without a non-trivial closed invariant subspace constructed by C. J. Read, then there are three operators , and (non-multiples of the identity) such that commutes with , commutes with , commutes with , and is compact. It is also shown that the commutant of contains only series of .
13.
Zhi-Wei Sun 《Proceedings of the American Mathematical Society》1999,127(5):1293-1300
Let be a system of arithmetic sequences which forms an -cover of (i.e. every integer belongs at least to members of ). In this paper we show the following surprising properties of : (a) For each there exist at least subsets of with such that . (b) If forms a minimal -cover of , then for any there is an such that for every there exists an for which and
14.
Piotr Pawlowski 《Proceedings of the American Mathematical Society》1999,127(5):1493-1497
Let be a complex polynomial of degree having zeros in a disk . We deal with the problem of finding the smallest concentric disk containing zeros of . We obtain some estimates on the radius of this disk in general as well as in the special case, where zeros in are isolated from the other zeros of . We indicate an application to the root-finding algorithms.
15.
Toshihiro Okuyama Keiichi Watanabe 《Proceedings of the American Mathematical Society》1998,126(9):2631-2634
Let and be bounded linear operators, and let be a partial isometry on a Hilbert space. Suppose that (1) , (2) , (3) and (4) . Then we have .
16.
Yong-Gao Chen 《Proceedings of the American Mathematical Society》1999,127(7):1927-1933
Erdös and Szemerédi proved that if is a set of positive integers, then there must be at least integers that can be written as the sum or product of two elements of , where is a constant and . Nathanson proved that the result holds for . In this paper it is proved that the result holds for and .
17.
Harold Donnelly 《Proceedings of the American Mathematical Society》1999,127(4):1231-1241
Every rank one symmetric space , of noncompact type, admits a compactification by attaching a sphere at infinity. If does not have constant sectional curvature, then admits a natural contact structure. This paper presents a number of harmonic maps , from to , which extend continuously to , and have noncontact boundary values. If the boundary values are assumed continuously differentiable, then the contact structure must be preserved.
18.
Victor Tan 《Proceedings of the American Mathematical Society》1999,127(10):2811-2820
Let and be the pair of unitary groups over a global field and an irreducible cuspidal representation of which satisfies a certain -function condition. By using a regularized Siegel-Weil formula, we can show that the global theta lifting of in is non-trivial if every local factor of has a local theta lifting (Howe lifting) in .
19.
Nikolai A. Volodin 《Proceedings of the American Mathematical Society》1999,127(2):349-353
We say that the multinomial coefficient (m.c.) has order and power . Let be the number of m.c. that are not divisible by and have order with powers which are not larger than . If and
then for any integer
20.
For a nowhere constant continuous function on a real interval and for a Borel measure on , we give simple necessary and sufficient conditions guaranteeing, for any Borel function on , the existence of a continuous function on such that the derivative of with respect to is, almost everywhere, equal to .