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1.
Istvá n Juhá sz Zoltá n Szentmikló ssy 《Proceedings of the American Mathematical Society》2008,136(8):2979-2984
All spaces below are Tychonov. We define the projective - character of a space as the supremum of the values where ranges over all (Tychonov) continuous images of . Our main result says that every space has a -base whose order is ; that is, every point in is contained in at most -many members of the -base. Since for compact , this is a significant generalization of a celebrated result of Shapirovskii.
2.
Rui Miguel Saramago 《Proceedings of the American Mathematical Society》2008,136(8):2699-2709
We use Dieudonné theory for periodically graded Hopf rings to determine the Dieudonné ring structure of the -graded Morava -theory , with an odd prime, when applied to the -spectrum (and to ). We also expand these results in order to accomodate the case of the full Morava -theory .
3.
Stefano Meda Peter Sjö gren Maria Vallarino 《Proceedings of the American Mathematical Society》2008,136(8):2921-2931
We prove that if is in , is a Banach space, and is a linear operator defined on the space of finite linear combinations of -atoms in with the property that then admits a (unique) continuous extension to a bounded linear operator from to . We show that the same is true if we replace -atoms by continuous -atoms. This is known to be false for -atoms.
4.
Lucian Badescu 《Proceedings of the American Mathematical Society》2008,136(5):1505-1513
Let be a submanifold of dimension of the complex projective space . We prove results of the following type.i) If is irregular and , then the normal bundle is indecomposable. ii) If is irregular, and , then is not the direct sum of two vector bundles of rank . iii) If , and is decomposable, then the natural restriction map is an isomorphism (and, in particular, if is embedded Segre in , then is indecomposable). iv) Let and , and assume that is a direct sum of line bundles; if assume furthermore that is simply connected and is not divisible in . Then is a complete intersection. These results follow from Theorem 2.1 below together with Le Potier's vanishing theorem. The last statement also uses a criterion of Faltings for complete intersection. In the case when this fact was proved by M. Schneider in 1990 in a completely different way.
5.
Let , , be the sequence of Hecke eigenvalues of a cuspidal Siegel eigenform of degree . It is proved that if is not in the Maaß space, then there exist infinitely many primes for which the sequence , , has infinitely many sign changes.
6.
Tomoaki Ono 《Proceedings of the American Mathematical Society》2008,136(9):3079-3087
Let be a tower of commutative rings where is a regular affine domain over an algebraically closed field of prime characteristic and is a regular domain. Suppose has a -basis over and . For a subset of whose elements satisfy a certain condition on linear independence, let be a set of maximal ideals of such that is a -basis of over . We shall characterize this set in a geometrical aspect.
7.
Jack Sonn 《Proceedings of the American Mathematical Society》2008,136(6):1955-1960
Let be a monic polynomial in with no rational roots but with roots in for all , or equivalently, with roots mod for all . It is known that cannot be irreducible but can be a product of two or more irreducible polynomials, and that if is a product of irreducible polynomials, then its Galois group must be a union of conjugates of proper subgroups. We prove that for any , every finite solvable group that is a union of conjugates of proper subgroups (where all these conjugates have trivial intersection) occurs as the Galois group of such a polynomial, and that the same result (with ) holds for all Frobenius groups. It is also observed that every nonsolvable Frobenius group is realizable as the Galois group of a geometric, i.e. regular, extension of .
8.
For all previous constructions of lattice space-time codes with a positive diversity product, the rank was at most . In this paper, we give an example of a lattice space-time code of rank with a positive diversity product.
9.
Let be the set of all positive integers , where are primes and possibly two, but not all three of them are equal. For any , define a function by where is the largest prime factor of . It is clear that if , then . For any , define , for . An element is semi-periodic if there exists a nonnegative integer and a positive integer such that . We use ind to denote the least such nonnegative integer . Wushi Goldring [Dynamics of the function and primes, J. Number Theory 119(2006), 86-98] proved that any element is semi-periodic. He showed that there exists such that , ind, and conjectured that ind can be arbitrarily large.
In this paper, it is proved that for any we have ind , and the Green-Tao Theorem on arithmetic progressions in the primes is employed to confirm Goldring's above conjecture.
10.
Andrew G. Bakan 《Proceedings of the American Mathematical Society》2008,136(10):3579-3589
It has been proved that algebraic polynomials are dense in the space , , iff the measure is representable as with a finite non-negative Borel measure and an upper semi-continuous function such that is a dense subset of the space as equipped with the seminorm . The similar representation ( ) with the same and ( , and is also a dense
subset of ) corresponds to all those measures (supported by ) that are uniquely determined by their moments on ( ). The proof is based on de Branges' theorem (1959) on weighted polynomial approximation. A more general question on polynomial denseness in a separable Fréchet space in the sense of Banach has also been examined.
11.
Srdjan Petrovic 《Proceedings of the American Mathematical Society》2008,136(12):4283-4288
We consider the spectral radius algebras associated to contractions. If is such an operator we show that the spectral radius algebra always properly contains the commutant of .
12.
Edward M. Fan 《Proceedings of the American Mathematical Society》2008,136(9):3255-3261
Consider an -dimensional smooth Riemannian manifold with a given smooth measure on it. We call such a triple a Riemannian measure space. Perelman introduced a variant of scalar curvature in his recent work on solving Poincaré's conjecture , where and is the scalar curvature of . In this note, we study the topological obstruction for the -stable minimal submanifold with positive -scalar curvature in dimension three under the setting of manifolds with density.
13.
It is an observation due to J. J. Kohn that for a smooth bounded pseudoconvex domain in there exists such that the -Neumann operator on maps (the space of -forms with coefficient functions in -Sobolev space of order ) into itself continuously. We show that this conclusion does not hold without the smoothness assumption by constructing a bounded pseudoconvex domain in , smooth except at one point, whose -Neumann operator is not bounded on for any .
14.
Stuart Zoble 《Proceedings of the American Mathematical Society》2008,136(5):1807-1814
There is a well-known global equivalence between sets having the universal Baire property, two-step generic absoluteness, and the closure of the universe under the sharp operation. In this note, we determine the exact consistency strength of sets being -cc-universally Baire, which is below . In a model obtained, there is a set which is weakly -universally Baire but not -universally Baire.
15.
Kathleen L. Petersen 《Proceedings of the American Mathematical Society》2008,136(7):2387-2393
Let be a number field with real places and complex places, and let be the ring of integers of . The quotient has cusps, where is the class number of . We show that under the assumption of the generalized Riemann hypothesis that if is not or an imaginary quadratic field and if , then has infinitely many maximal subgroups with cusps. A key element in the proof is a connection to Artin's Primitive Root Conjecture.
16.
We refine our earlier work on the existence and uniqueness of structures on -theoretic spectra to show that the connective versions of real and complex -theory as well as the connective Adams summand at each prime have unique structures as commutative -algebras. For the -completion we show that the McClure-Staffeldt model for is equivalent as an ring spectrum to the connective cover of the periodic Adams summand . We establish a Bousfield equivalence between the connective cover of the Lubin-Tate spectrum and .
17.
Rosa Maria Miró -Roig Helena Soares 《Proceedings of the American Mathematical Society》2008,136(11):3751-3757
A very long-standing problem in Algebraic Geometry is to determine the stability of exceptional vector bundles on smooth projective varieties. In this paper we address this problem and we prove that any exceptional vector bundle on a smooth complete intersection -fold of type with and is stable.
18.
Sam Lichtenstein 《Proceedings of the American Mathematical Society》2008,136(10):3419-3428
Suppose that (resp. ) is a modular form of integral (resp. half-integral) weight with coefficients in the ring of integers of a number field . For any ideal , we bound the first prime for which (resp. ) is zero ( ). Applications include the solution to a question of Ono (2001) concerning partitions.
19.
Xian-Jin Li 《Proceedings of the American Mathematical Society》2008,136(6):1945-1953
An explicit Dirichlet series is obtained, which represents an analytic function of in the half-plane except for having simple poles at points that correspond to exceptional eigenvalues of the non-Euclidean Laplacian for Hecke congruence subgroups by the relation for . Coefficients of the Dirichlet series involve all class numbers of real quadratic number fields. But, only the terms with for sufficiently large discriminants contribute to the residues of the Dirichlet series at the poles , where is the multiplicity of the eigenvalue for . This may indicate (I'm not able to prove yet) that the multiplicity of exceptional eigenvalues can be arbitrarily large. On the other hand, by density theorem the multiplicity of exceptional eigenvalues is bounded above by a constant depending only on .
20.
Serguei V. Astashkin Guillermo P. Curbera 《Proceedings of the American Mathematical Society》2008,136(10):3493-3501
Let be a rearrangement invariant function space on [0,1]. We consider the Rademacher multiplicator space of measurable functions such that for every a.e. converging series , where are the Rademacher functions. We characterize the situation when . We also discuss the behaviour of partial sums and tails of Rademacher series in function spaces.