共查询到20条相似文献,搜索用时 156 毫秒
1.
Alina Carmen Cojocaru Igor E. Shparlinski 《Proceedings of the American Mathematical Society》2008,136(6):1977-1986
We prove that the set of Farey fractions of order , that is, the set , is uniformly distributed in residue classes modulo a prime provided for any fixed . We apply this to obtain upper bounds for the Lang-Trotter conjectures on Frobenius traces and Frobenius fields ``on average' over a one-parametric family of elliptic curves.
2.
Ali Abkar 《Proceedings of the American Mathematical Society》2003,131(1):155-164
Let denote the unit disk in the complex plane. We consider a class of superbiharmonic weight functions whose growth are subject to the condition for some constant . We first establish a Reisz-type representation formula for , and then use this formula to prove that the polynomials are dense in the weighted Bergman space with weight .
3.
Jiazhong Yang 《Proceedings of the American Mathematical Society》2003,131(9):2715-2720
We prove that on , except for those germs of vector fields whose linear parts are conjugated to , any two Poincaré type vector fields are at least conjugated to each other provided their linear approximations have the same eigenvalues and the nonlinear parts are generic.
4.
Hitoshi Tanaka 《Proceedings of the American Mathematical Society》2005,133(3):763-772
Let , , be the Kakeya (Nikodým) maximal operator defined as the supremum of averages over tubes of eccentricity . The (so-called) Fefferman-Stein type inequality:
is shown in the range , where and are some constants depending only on and the dimension and is a weight. The result is a sharp bound up to -factors.
is shown in the range , where and are some constants depending only on and the dimension and is a weight. The result is a sharp bound up to -factors.
5.
Yong Zhou 《Proceedings of the American Mathematical Society》2006,134(1):149-156
In this paper we establish a Serrin-type regularity criterion on the gradient of pressure for the weak solutions to the Navier-Stokes equations in . It is proved that if the gradient of pressure belongs to with , , then the weak solution is actually regular. Moreover, we give a much simpler proof of the regularity criterion on the pressure, which was showed recently by Berselli and Galdi (Proc. Amer. Math. Soc. 130 (2002), no. 12, 3585-3595).
6.
A. Lins Neto J. C. Canille Martins 《Transactions of the American Mathematical Society》2004,356(7):2963-2988
In this paper we consider the problem of uniformization of the leaves of a holomorphic foliation by curves in a complex manifold . We consider the following problems: 1. When is the uniformization function , with respect to some metric , continuous? It is known that the metric induces the Poincaré metric on the leaves. 2. When is the metric complete? We extend the concept of ultra-hyperbolic metric, introduced by Ahlfors in 1938, for singular foliations by curves, and we prove that if there exists a complete ultra-hyperbolic metric , then is continuous and is complete. In some local cases we construct such metrics, including the saddle-node (Theorem 1) and singularities given by vector fields with the first non-zero jet isolated (Theorem 2). We also give an example where for any metric , is not complete (§3.2).
7.
Mark S. Ashbaugh Rafael D. Benguria 《Transactions of the American Mathematical Society》2001,353(3):1055-1087
For a domain contained in a hemisphere of the -dimensional sphere we prove the optimal result for the ratio of its first two Dirichlet eigenvalues where , the symmetric rearrangement of in , is a geodesic ball in having the same -volume as . We also show that for geodesic balls of geodesic radius less than or equal to is an increasing function of which runs between the value for (this is the Euclidean value) and for . Here denotes the th positive zero of the Bessel function . This result generalizes the Payne-Pólya-Weinberger conjecture, which applies to bounded domains in Euclidean space and which we had proved earlier. Our method makes use of symmetric rearrangement of functions and various technical properties of special functions. We also prove that among all domains contained in a hemisphere of and having a fixed value of the one with the maximal value of is the geodesic ball of the appropriate radius. This is a stronger, but slightly less accessible, isoperimetric result than that for . Various other results for and of geodesic balls in are proved in the course of our work.
8.
Sean Sather-Wagstaff 《Transactions of the American Mathematical Society》2002,354(3):993-1005
The recent work of Kurano and Roberts on Serre's positivity conjecture suggests the following dimension inequality: for prime ideals and in a local, Cohen-Macaulay ring such that we have . We establish this dimension inequality for excellent, local, Cohen-Macaulay rings which contain a field, for certain low-dimensional cases and when is regular.
9.
Ahmad El Soufi Saï d Ilias 《Proceedings of the American Mathematical Society》2003,131(5):1611-1618
Let be a compact manifold. First, we give necessary and sufficient conditions for a Riemannian metric on to be extremal for with respect to conformal deformations of fixed volume. In particular, these conditions show that for any lattice of , the flat metric induced on from the standard metric of is extremal (in the previous sense). In the second part, we give, for any , an upper bound of on the conformal class of and exhibit a class of lattices for which the metric maximizes on its conformal class.
10.
Tadej Kotnik. 《Mathematics of Computation》2004,73(246):949-956
The paper describes a search for increasingly large extrema (ILE) of in the range . For , the complete set of ILE (57 of them) was determined. In total, 162 ILE were found, and they suggest that . There are several regular patterns in the location of ILE, and arguments for these regularities are presented. The paper concludes with a discussion of prospects for further computational progress.
11.
Matthias Birkner José Alfredo Ló pez-Mimbela Anton Wakolbinger 《Proceedings of the American Mathematical Society》2002,130(8):2431-2442
We present a probabilistic approach which proves blow-up of solutions of the Fujita equation in the critical dimension . By using the Feynman-Kac representation twice, we construct a subsolution which locally grows to infinity as . In this way, we cover results proved earlier by analytic methods. Our method also applies to extend a blow-up result for systems proved for the Laplacian case by Escobedo and Levine (1995) to the case of -Laplacians with possibly different parameters .
12.
Takeshi Okano 《Proceedings of the American Mathematical Society》2002,130(6):1603-1605
13.
Jeremy T. Tyson 《Proceedings of the American Mathematical Society》2000,128(11):3361-3367
For any , there is a compact set of (Hausdorff) dimension whose dimension cannot be lowered by any quasiconformal map . We conjecture that no such set exists in the case . More generally, we identify a broad class of metric spaces whose Hausdorff dimension is minimal among quasisymmetric images.
14.
S. Artstein-Avidan O. Friedland V. Milman 《Proceedings of the American Mathematical Society》2006,134(6):1735-1742
In this paper we show that the euclidean ball of radius in can be approximated up to , in the Hausdorff distance, by a set defined by linear inequalities. We call this set a ZigZag set, and it is defined to be all points in space satisfying or more of the inequalities. The constant we get is , where is some universal constant. This should be compared with the result of Barron and Cheang (2000), who obtained . The main ingredient in our proof is the use of Chernoff's inequality in a geometric context. After proving the theorem, we describe several other results which can be obtained using similar methods.
15.
Christopher Croke 《Proceedings of the American Mathematical Society》2005,133(12):3663-3668
We consider compact Riemannian manifolds with boundary and metric on which a finite group acts freely. We determine the extent to which certain rigidity properties of descend to the quotient . In particular, we show by example that if is boundary rigid, then need not be. On the other hand, lens rigidity of does pass to the quotient.
16.
Horst Alzer 《Proceedings of the American Mathematical Society》2007,135(11):3641-3648
Let and be real numbers. The inequality holds for all positive real numbers if and only if . The reverse inequality is valid for all if and only if .
17.
Let be a finite-dimensional self-injective algebra. We study the dimensions of spaces of stable homomorphisms between indecomposable -modules which belong to Auslander-Reiten components of the form or . The results are applied to representations of finite groups over fields of prime characteristic, especially blocks of wild representation type. 相似文献
18.
M. J. Jacobson Jr. Á . Pinté r P. G. Walsh. 《Mathematics of Computation》2003,72(244):2099-2110
We present a computational approach for finding all integral solutions of the equation for even values of . By reducing this problem to that of finding integral solutions of a certain class of quartic equations closely related to the Pell equations, we are able to apply the powerful computational machinery related to quadratic number fields. Using our approach, we determine all integral solutions for assuming the Generalized Riemann Hypothesis, and for unconditionally.
19.
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.
20.
Suppose that we are given a set of powers of a prime and that . A technique is presented that enables the construction of a -group of specified nilpotence class such that its set of irreducible character degrees is exactly . If , then this can be done for and if , then the only requirement is .