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1.
Hypersurfaces in a sphere with constant mean curvature 总被引:13,自引:0,他引:13
Zhong Hua Hou 《Proceedings of the American Mathematical Society》1997,125(4):1193-1196
Let be a closed hypersurface of constant mean curvature immersed in the unit sphere . Denote by the square of the length of its second fundamental form. If , is a small hypersphere in . We also characterize all with .
2.
A. Eduardo Gatto Stephen Vá gi 《Proceedings of the American Mathematical Society》1997,125(4):1149-1152
On a space of homogeneous type we consider functions in , , which are potentials of order of functions. We show that these functions belong to the class of smooth functions of Calderón-Scott. This result has applications to tangential convergence.
3.
Paul S. Bourdon 《Proceedings of the American Mathematical Society》1997,125(4):1187-1192
Let be a holomorphic function taking the open unit disk into itself. We show that the set of nonnegative powers of is orthogonal in if and only if the Nevanlinna counting function of , , is essentially radial. As a corollary, we obtain that the orthogonality of for a univalent implies for some constant . We also show that if is orthogonal, then the closure of must be a disk.
4.
Gennady Bachman 《Proceedings of the American Mathematical Society》1997,125(4):1001-1003
We evaluate , where the is taken over sequences satisfying . In particular we show that it is attained by taking for all , which reduces the summation over to a Ramanujan sum .
5.
Edgar M. E. Wermuth 《Proceedings of the American Mathematical Society》1997,125(6):1685-1688
In a previous paper the author proved that for square matrices with algebraic entries expexpexpexp if and only if . This result is extended here to bounded operators on an arbitrary Banach space.
6.
On the von Neumann-Jordan constant for Banach spaces 总被引:2,自引:0,他引:2
Let be the von Neumann-Jordan constant for a Banach space . It is known that for any Banach space ; and is a Hilbert space if and only if . We show that: (i) If is uniformly convex, is less than two; and conversely the condition implies that admits an equivalent uniformly convex norm. Hence, denoting by the infimum of all von Neumann-Jordan constants for equivalent norms of , is super-reflexive if and only if . (ii) If , (the same value as that of -space), is of Rademacher type and cotype for any with , where ; the converse holds if is a Banach lattice and is finitely representable in or .
7.
Katsuro Sakai 《Proceedings of the American Mathematical Society》1997,125(9):2809-2813
Let be the -dimensional universal Menger compactum, a -set in and a metrizable zero-dimensional compact group with the unit. It is proved that there exists a semi-free -action on such that is the fixed point set of every . As a corollary, it follows that each compactum with can be embedded in as the fixed point set of some semi-free -action on .
8.
A. Edward Nussbaum 《Proceedings of the American Mathematical Society》1997,125(12):3541-3545
Let and be semibounded (bounded from below) operators in a Hilbert space and a dense linear manifold contained in the domains of , , , and , and such that for all in . It is shown that if the restriction of to is essentially self-adjoint, then and are essentially self-adjoint and and commute, i.e. their spectral projections permute.
9.
Changyu Xia 《Proceedings of the American Mathematical Society》1997,125(6):1801-1806
Let be an ()-dimensional compact Riemannian manifold with nonnegative Ricci curvature and nonempty boundary . Assume that the principal curvatures of are bounded from below by a positive constant . In this paper, we prove that the first nonzero eigenvalue of the Laplacian of acting on functions on satisfies with equality holding if and only if is isometric to an -dimensional Euclidean ball of radius . Some related rigidity theorems for are also proved.
10.
The purpose of this paper is to classify invariant hypercomplex structures on a -dimensional real Lie group . It is shown that the -dimensional simply connected Lie groups which admit invariant hypercomplex structures are the additive group of the quaternions, the multiplicative group of nonzero quaternions, the solvable Lie groups acting simply transitively on the real and complex hyperbolic spaces, and , respectively, and the semidirect product . We show that the spaces and possess an of (inequivalent) invariant hypercomplex structures while the remaining groups have only one, up to equivalence. Finally, the corresponding hyperhermitian -manifolds are determined.
11.
James Cummings 《Proceedings of the American Mathematical Society》1997,125(9):2703-2709
Let be a singular cardinal in , and let be a model such that for some -cardinal with . We apply Shelah's pcf theory to study this situation, and prove the following results. 1) is not a -c.c generic extension of . 2) There is no ``good scale for ' in , so in particular weak forms of square must fail at . 3) If then and also . 4) If then .
12.
Marion Scheepers 《Proceedings of the American Mathematical Society》1997,125(9):2719-2724
An open cover of an infinite separable metric space is an -cover of if and for every finite subset of there is a such that . Let be the collection of -covers of . We show that the partition relation holds if, and only if, the partition relation holds.
13.
J. Marshall Ash Gang Wang David Weinberg 《Proceedings of the American Mathematical Society》1997,125(1):219-228
If is a lacunary sequence of integers, and if for each , and are trigonometric polynomials of degree then must tend to zero for almost every whenever does. We conjecture that a similar result ought to hold even when the sequence has much slower growth. However, there is a sequence of integers and trigonometric polynomials such that tends to zero everywhere, even though the degree of does not exceed for each . The sequence of trigonometric polynomials tends to zero for almost every , although explicit formulas are developed to show that the sequence of corresponding conjugate functions does not. Among trigonometric polynomials of degree with largest Fourier coefficient equal to , the smallest one ``at' is while the smallest one ``near' is unknown.
14.
Let be a reductive group and a parabolic subgroup. For every -regular dominant weight let denote the variety embedded in the projective space by the embedding corresponding to the ample line bundle . Writing , we prove that the degree of the dual variety to is a polynomial with nonnegative coefficients in . In the case of homogeneous spaces we find an expression for the constant term of this polynomial.
15.
Let be a commutative Noetherian ring, and let be an -module. In earlier papers by Bass (1963) and Roberts (1980) the Bass numbers were defined for all primes and all integers by use of the minimal injective resolution of . It is well known that . On the other hand, if is finitely generated, the Betti numbers are defined by the minimal free resolution of over the local ring . In an earlier paper of the second author (1995), using the flat covers of modules, the invariants were defined by the minimal flat resolution of over Gorenstein rings. The invariants were shown to be somehow dual to the Bass numbers. In this paper, we use homologies to compute these invariants and show that
for any cotorsion module . Comparing this with the computation of the Bass numbers, we see that is replaced by and the localization is replaced by (which was called the colocalization of at the prime ideal by Melkersson and Schenzel).
16.
Jeffrey Bergen Piotr Grzeszczuk 《Proceedings of the American Mathematical Society》1997,125(12):3481-3488
If is an automorphism and is a -derivation of a ring , then the subring of invariants is the set The main result of this paper is Theorem. Let be a -derivation of an algebra over a commutative ring such that
for all , where and .
- (i)
- If , then .
- (ii)
- If is a -stable left ideal of such that , then .
17.
It is shown that for every closed, convex and nowhere dense subset of a superreflexive Banach space there exists a Radon probability measure on so that for all . In particular, closed, convex, nowhere dense sets in separable superreflexive Banach spaces are Haar null. This is unlike the situation in separable nonreflexive Banach spaces, where there always exists a closed convex nowhere dense set which is not Haar null.
18.
Keiji Izuchi 《Proceedings of the American Mathematical Society》1997,125(4):1153-1159
Let be a sequence of bounded linear operators on such that and for every . It is proved that for every .
19.
Robert C. Stolz 《Proceedings of the American Mathematical Society》1997,125(4):1215-1220
For each function that satisfies the law of large numbers with values in a certain class of locally convex spaces with the Radon-Nikodym property the following decomposition holds: , where is integrable by seminorm, and is a Pettis integrable function which is scalarly 0.
20.
Eric K. van Douwen David J. Lutzer 《Proceedings of the American Mathematical Society》1997,125(4):1237-1245
In this paper, we show that for generalized ordered spaces, paracompactness is equivalent to Property D, where a space is said to have Property D if, given any collection of open sets in satisfying for each , there is a closed discrete subset of satisfying .