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1.
Gé rard Letac Dhafer Malouche Stefan Maurer 《Proceedings of the American Mathematical Society》2002,130(7):2107-2114
For 0,$"> this note computes essentially the set of in such that the entire series in defined by has all its coefficients non-negative. If and are independent random variables which have respectively Bernoulli and negative binomial distributions, denote by the distribution of . The above problem is equivalent to finding the set of 0$"> such that exists; this set is a finite union of intervals and may be the first example of this type in the literature. This gives the final touch to the classification of the natural exponential families with variance functions of Babel type, i.e. of the form , where is a polynomial with degree
2.
Alejandro Illanes 《Proceedings of the American Mathematical Society》2002,130(7):2179-2182
A topological space is said to be -contractible provided that there exists a continuous onto function such that is homotopic to a constant function. Answering a question by Sam B. Nadler, Jr., in this paper we construct a metric continuum such that its hyperspace of subcontinua is not -contractible.
3.
Let denote the (upper) unitriangular group of degree over the finite field with elements. In this paper we consider the basic (complex) characters of and we prove that every irreducible (complex) character of is a constituent of a unique basic character. This result extends a previous result which was proved by the author under the assumption , where is the characteristic of the field .
4.
Roman Dwilewicz Joë l Merker 《Proceedings of the American Mathematical Society》2002,130(7):1975-1980
Let be a compact, connected, -smooth and globally minimal hypersurface in which divides the projective space into two connected parts and . We prove that there exists a side, or , such that every continuous CR function on extends holomorphically to this side. Our proof of this theorem is a simplification of a result originally due to F. Sarkis.
5.
Bryan Clair Shahriar Mokhtari-Sharghi 《Proceedings of the American Mathematical Society》2002,130(7):1881-1886
The -zeta function of an infinite graph (defined previously in a ball around zero) has an analytic extension. For a tower of finite graphs covered by , the normalized zeta functions of the finite graphs converge to the -zeta function of .
6.
H. F. Kreimer 《Proceedings of the American Mathematical Society》2002,130(10):2853-2856
Let be a Hopf algebra over a commutative ring such that is a finitely generated, projective module over , let be a right -comodule algebra, and let be the subalgebra of -coinvariant elements of . If is a Galois extension of and is a local subalgebra of the center of , then is a cleft right -comodule algebra or, equivalently, there is a normal basis for over .
7.
Let be a complete local domain containing the integers with maximal ideal such that is at least the cardinality of the real numbers. Let be a nonmaximal prime ideal of such that is a regular local ring. We construct an excellent local ring such that the completion of is , the generic formal fiber of is local with maximal ideal and if is a nonzero ideal of , then is complete.
8.
The f-depth of an ideal on a module 总被引:2,自引:0,他引:2
Rencai Lü Zhongming Tang 《Proceedings of the American Mathematical Society》2002,130(7):1905-1912
Let be an ideal of a Noetherian local ring and a finitely generated -module. The f-depth of on is the least integer such that the local cohomology module is not Artinian. This paper presents some part of the theory of f-depth including characterizations of f-depth and a relation between f-depth and f-modules.
9.
10.
Akira Koyama Manuel A. Moron 《Proceedings of the American Mathematical Society》2002,130(10):3091-3096
We shall prove the following: Let be a refinable map between paracompact spaces. Then is finitistic if and only if is finitistic. Let be a hereditary shape equivalence between metric spaces. Then if is finitistic, is finitistic.
11.
Ikumitsu Nagasaki 《Proceedings of the American Mathematical Society》2002,130(6):1843-1850
In this paper, we show that the dimension function of every semilinear -sphere is equal to that of a linear -sphere for finite nilpotent groups of order , where , are primes. We also show that there exists a semilinear -sphere whose dimension function is not virtually linear for an arbitrary nonsolvable compact Lie group .
12.
Kohzo Yamada 《Proceedings of the American Mathematical Society》2002,130(8):2461-2469
Let and be respectively the free topological group and the free Abelian topological group on a Tychonoff space . For every natural number we denote by () the subset of () consisting of all words of reduced length . It is well known that if a space is not discrete, then neither nor is Fréchet-Urysohn, and hence first countable. On the other hand, it is seen that both and are Fréchet-Urysohn for a paracompact Fréchet-Urysohn space . In this paper, we prove first that for a metrizable space , () is Fréchet-Urysohn if and only if the set of all non-isolated points of is compact and is Fréchet-Urysohn if and only if is compact or discrete. As applications, we characterize the metrizable space such that is Fréchet-Urysohn for each and is Fréchet-Urysohn for each except for . In addition, however, there is a first countable, and hence Fréchet-Urysohn subspace of () which is not contained in any (). We shall show that if such a space is first countable, then it has a special form in (). On the other hand, we give an example showing that if the space is Fréchet-Urysohn, then it need not have the form.
13.
Nilson C. Bernardes Jr. 《Proceedings of the American Mathematical Society》2002,130(7):1983-1992
Let be a metric space. A function is said to be non-sensitive at a point if for every 0$"> there is a 0$"> such that for any choice of points , , , we have that for every . Let be the set of all homeomorphisms from onto endowed with the topology of uniform convergence. The main goal of the present paper is to prove that for certain spaces , ``most' functions in are non-sensitive at ``most' points of .
14.
Stefan Geschke Menachem Kojman 《Proceedings of the American Mathematical Society》2002,130(10):2871-2881
For 2$"> let be the -ideal in generated by all sets which do not contain equidistant points in the usual metric on . For each 2$"> a set is constructed in so that the -ideal which is generated by the convex subsets of restricted to the convexity radical is isomorphic to . Thus is equal to the least number of convex subsets required to cover -- the convexity number of .
For every non-increasing function \aleph_0\}$"> we construct a model of set theory in which for each . When is strictly decreasing up to , uncountable cardinals are simultaneously realized as convexity numbers of closed subsets of . It is conjectured that , but never more than , different uncountable cardinals can occur simultaneously as convexity numbers of closed subsets of . This conjecture is true for and . 相似文献
15.
Manuel Gonzá lez Antonio Martí nez-Abejó n 《Proceedings of the American Mathematical Society》2002,130(11):3255-3258
We show that is a local dual of , and is a local dual of , where is a Banach space. A local dual space of a Banach space is a subspace of so that we have a local representation of in satisfying the properties of the representation of in provided by the principle of local reflexivity.
16.
Dimitris Gatzouras 《Proceedings of the American Mathematical Society》2002,130(9):2687-2699
Let and be metric spaces. We show that the tight images of a (fixed) tight Borel probability measure on , under all Borel mappings , form a closed set in the space of tight Borel probability measures on with the weak-topology. In contrast, the set of images of under all continuous mappings from to may not be closed. We also characterize completely the set of tight images of under Borel mappings. For example, if is non-atomic, then all tight Borel probability measures on can be obtained as images of , and as a matter of fact, one can always choose the corresponding Borel mapping to be of Baire class 2.
17.
Daciberg L. Gonç alves Jan Jaworowski Pedro L. Q. Pergher 《Proceedings of the American Mathematical Society》2002,130(10):3111-3115
Let be a finite group acting freely in a CW-complex which is a homotopy -dimensional sphere and let be a map of to a finite -dimensional CW-complex . We show that if , then has an -coincidence for some nontrivial subgroup of .
18.
Alireza Abdollahi Gunnar Traustason 《Proceedings of the American Mathematical Society》2002,130(10):2827-2836
For a given positive integer and a given prime number , let be the integer satisfying . We show that every locally finite -group, satisfying the -Engel identity, is (nilpotent of -bounded class)-by-(finite exponent) where the best upper bound for the exponent is either or if is odd. When the best upper bound is or . In the second part of the paper we focus our attention on -Engel groups. With the aid of the results of the first part we show that every -Engel -group is soluble and the derived length is bounded by some constant.
19.
Ryszard Rudnicki 《Proceedings of the American Mathematical Society》2002,130(7):1981-1982
We prove that the local lower and upper pointwise dimensions of a probability measure are bounded from below by the lower generalized dimension for 1$">and from above by the upper generalized dimension for .
20.
Let be a polynomial whose Julia set is locally connected. Then a non-preperiodic non-precritical vertex of must have the limit set which coincides with the limit set of an appropriately chosen recurrent critical point of . In particular, if all critical points of are non-recurrent then all vertices of are preperiodic or precritical.