共查询到20条相似文献,搜索用时 125 毫秒
1.
Albin L. Jones 《Proceedings of the American Mathematical Society》2008,136(4):1445-1449
We prove that if and , then for all . This polarized partition relation holds if for every partition either there are and with or there are and with .
2.
Donatella Danielli Nicola Garofalo Duy-Minh Nhieu 《Proceedings of the American Mathematical Society》2003,131(11):3487-3498
Let be a group of Heisenberg type with homogeneous dimension . For every we construct a non-divergence form operator and a non-trivial solution to the Dirichlet problem: in , on . This non-uniqueness result shows the impossibility of controlling the maximum of with an norm of when . Another consequence is the impossiblity of an Alexandrov-Bakelman type estimate such as
where is the dimension of the horizontal layer of the Lie algebra and is the symmetrized horizontal Hessian of .
where is the dimension of the horizontal layer of the Lie algebra and is the symmetrized horizontal Hessian of .
3.
If and are countable ordinals such that , denote by the completion of with respect to the implicitly defined norm
where the supremum is taken over all finite subsets of such that and . It is shown that the Bourgain -index of is . In particular, if \alpha =\omega^{\alpha_{1}}\cdot m_{1}+\dots+\omega^{\alpha_{n}}\cdot m_{n}$"> in Cantor normal form and is not a limit ordinal, then there exists a Banach space whose -index is .
where the supremum is taken over all finite subsets of such that and . It is shown that the Bourgain -index of is . In particular, if \alpha =\omega^{\alpha_{1}}\cdot m_{1}+\dots+\omega^{\alpha_{n}}\cdot m_{n}$"> in Cantor normal form and is not a limit ordinal, then there exists a Banach space whose -index is .
4.
Yuri G. Zarhin 《Proceedings of the American Mathematical Society》2003,131(1):95-102
In a previous paper, the author proved that in characteristic zero the jacobian of a hyperelliptic curve has only trivial endomorphisms over an algebraic closure of the ground field if the Galois group of the irreducible polynomial is either the symmetric group or the alternating group . Here 4$"> is the degree of . In another paper by the author this result was extended to the case of certain ``smaller' Galois groups. In particular, the infinite series and were treated. In this paper the case of and is treated.
5.
Richard Delaware 《Proceedings of the American Mathematical Society》2003,131(8):2537-2542
A set is -straight if has finite Hausdorff -measure equal to its Hausdorff -content, where is continuous and non-decreasing with . Here, if satisfies the standard doubling condition, then every set of finite Hausdorff -measure in is shown to be a countable union of -straight sets. This also settles a conjecture of Foran that when , every set of finite -measure is a countable union of -straight sets.
6.
Saharon Shelah 《Proceedings of the American Mathematical Society》2003,131(8):2585-2592
If If is strongly compact and \kappa $"> and is regular (or alternatively cf , then holds for .
7.
Pham Anh Minh 《Proceedings of the American Mathematical Society》2003,131(2):363-368
Let be an odd prime number. The purpose of this paper is to provide a -group whose mod- cohomology ring has a nilpotent element satisfying .
8.
N. Bejhaj Rhouma 《Proceedings of the American Mathematical Society》2003,131(12):3747-3755
We show the existence of principal eigenvalues of the problem in where is an indefinite weight function. The existence of a continuous family of principal eigenvalues is demonstrated. Also, we prove the existence of a principal eigenvalue for which the principal eigenfunction at .
9.
Hidefumi Ohsugi Takayuki Hibi 《Proceedings of the American Mathematical Society》2002,130(7):1913-1922
Let be one of the root systems , , and and write for the set of positive roots of together with the origin of . Let denote the Laurent polynomial ring over a field and write for the affine semigroup ring which is generated by those monomials with , where if . Let denote the polynomial ring over and write for the toric ideal of . Thus is the kernel of the surjective homomorphism defined by setting for all . In their combinatorial study of hypergeometric functions associated with root systems, Gelfand, Graev and Postnikov discovered a quadratic initial ideal of the toric ideal of . The purpose of the present paper is to show the existence of a reverse lexicographic (squarefree) quadratic initial ideal of the toric ideal of each of , and . It then follows that the convex polytope of the convex hull of each of , and possesses a regular unimodular triangulation arising from a flag complex, and that each of the affine semigroup rings , and is Koszul. 相似文献
10.
Rodney Y. Sharp 《Proceedings of the American Mathematical Society》2003,131(10):3009-3017
It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.
11.
David Schrittesser 《Proceedings of the American Mathematical Society》2007,135(4):1213-1222
-absoluteness for forcing means that for any forcing , . `` inaccessible to reals' means that for any real , . To measure the exact consistency strength of `` -absoluteness for forcing and is inaccessible to reals', we introduce a weak version of a weakly compact cardinal, namely, a (lightface) -indescribable cardinal; has this property exactly if it is inaccessible and .
12.
M. Brodmann S. Fumasoli R. Tajarod 《Proceedings of the American Mathematical Society》2003,131(10):2977-2985
Let be a homogeneous Noetherian ring with local base ring and let be a finitely generated graded -module. Let be the -th local cohomology module of with respect to 0}R_n$">. If , the -modules , and are Artinian for all . As a consequence, much can be said on the asymptotic behaviour of the -modules for .
13.
We show that if is an -regular set in for which the triple integral of the Menger curvature is finite and if , then almost all of can be covered with countably many curves. We give an example to show that this is false for .
14.
Jan Kolá r Jan Kristensen 《Proceedings of the American Mathematical Society》2005,133(6):1699-1706
For a -smooth bump function we show that the gradient range is the closure of its interior, provided that admits a modulus of continuity satisfying as . The result is a consequence of a more general result about gradient ranges of bump functions of the same degree of smoothness. For such bump functions we show that for open sets , either the intersection is empty or its topological dimension is at least two. The proof relies on a new Morse-Sard type result where the smoothness hypothesis is independent of the dimension of the space.
15.
Antonios D. Melas 《Proceedings of the American Mathematical Society》2003,131(2):631-636
Let be the th Dirichlet eigenvalue of a bounded domain in . According to Weyl's asymptotic formula we have
The optimal in view of this asymptotic relation lower estimate for the sums has been proven by P.Li and S.T.Yau (Comm. Math. Phys. 88 (1983), 309-318). Here we will improve this estimate by adding to its right-hand side a term of the order of that depends on the ratio of the volume to the moment of inertia of .
The optimal in view of this asymptotic relation lower estimate for the sums has been proven by P.Li and S.T.Yau (Comm. Math. Phys. 88 (1983), 309-318). Here we will improve this estimate by adding to its right-hand side a term of the order of that depends on the ratio of the volume to the moment of inertia of .
16.
Krzysztof Plotka 《Proceedings of the American Mathematical Society》2003,131(4):1031-1041
We say that a function is a Hamel function ( ) if , considered as a subset of , is a Hamel basis for . We prove that every function from into can be represented as a pointwise sum of two Hamel functions. The latter is equivalent to the statement: for all there is a such that . We show that this fails for infinitely many functions.
17.
Robert Gilmer 《Proceedings of the American Mathematical Society》2003,131(8):2337-2346
Let be an integral domain with quotient field and integral closure . An overring of is a subring of containing , and denotes the set of overrings of . We consider primarily two finiteness conditions on : (FO), which states that is finite, and (FC), the condition that each chain of distinct elements of is finite. (FO) is strictly stronger than (FC), but if , each of (FO) and (FC) is equivalent to the condition that is a Prüfer domain with finite prime spectrum. In general satisfies (FC) iff satisfies (FC) and all chains of subrings of containing have finite length. The corresponding statement for (FO) is also valid.
18.
Emre Alkan 《Proceedings of the American Mathematical Society》2003,131(6):1673-1680
Let be a cusp form with integer weight that is not a linear combination of forms with complex multiplication. For , let
Improving on work of Balog, Ono, and Serre we show that for almost all , where is any good function (e.g. such as ) monotonically tending to infinity with . Using a result of Fouvry and Iwaniec, if is a weight 2 cusp form for an elliptic curve without complex multiplication, then we show for all that . We also obtain conditional results depending on the Generalized Riemann Hypothesis and the Lang-Trotter Conjecture.
Improving on work of Balog, Ono, and Serre we show that for almost all , where is any good function (e.g. such as ) monotonically tending to infinity with . Using a result of Fouvry and Iwaniec, if is a weight 2 cusp form for an elliptic curve without complex multiplication, then we show for all that . We also obtain conditional results depending on the Generalized Riemann Hypothesis and the Lang-Trotter Conjecture.
19.
Matej Bresar Ajda Fosner Peter Semrl 《Proceedings of the American Mathematical Society》2003,131(12):3833-3837
Let be be semisimple Banach algebras and let be a unital bijective linear operator that preserves invertibility. If the socle of is an essential ideal of , then is a Jordan isomorphism.
20.
Zhangjian Hu 《Proceedings of the American Mathematical Society》2003,131(7):2171-2179
We define an extended Cesàro operator with holomorphic symbol in the unit ball of as
where is the radial derivative of . In this paper we characterize those for which is bounded (or compact) on the mixed norm space .
where is the radial derivative of . In this paper we characterize those for which is bounded (or compact) on the mixed norm space .