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P. M. Gadea J. Muñ oz Masqué 《Proceedings of the American Mathematical Society》1996,124(5):1437-1443
Let be a finite-dimensional commutative algebra over and let , and be the ring of -differentiable functions of class , the ring of real analytic mappings with values in and the ring of -analytic functions, respectively, defined on an open subset of . We prove two basic results concerning -differentiability and -analyticity: ) , ) if and only if is defined over .
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Dusan Repovs Arkadij B. Skopenkov Evgenij V. Scepin 《Proceedings of the American Mathematical Society》1996,124(4):1219-1226
We give the characterization of -homogeneous compacta in : Let be a locally compact (possibly nonclosed) subset of . Then is -homogeneous if and only if is a -submanifold of .
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Douglas R. Farenick Phillip B. Morenz 《Transactions of the American Mathematical Society》1997,349(5):1725-1748
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Osamu Saeki Kazuhiro Sakuma 《Transactions of the American Mathematical Society》1996,348(7):2585-2606
We give two congruence formulas concerning the number of non-trivial double point circles and arcs of a smooth map with generic singularities --- the Whitney umbrellas --- of an -manifold into , which generalize the formulas by Szücs for an immersion with normal crossings. Then they are applied to give a new geometric proof of the congruence formula due to Mahowald and Lannes concerning the normal Euler number of an immersed -manifold in . We also study generic projections of an embedded -manifold in into and prove an elimination theorem of Whitney umbrella points of opposite signs, which is a direct generalization of a recent result of Carter and Saito concerning embedded surfaces in . The problem of lifting a map into to an embedding into is also studied.
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John R. Stembridge 《Transactions of the American Mathematical Society》1997,349(2):763-788
An (ordinary) -partition is an order-preserving map from a partially ordered set to a chain, with special rules specifying where equal values may occur. Examples include number-theoretic partitions (ordered and unordered, strict or unrestricted), plane partitions, and the semistandard
tableaux associated with Schur's -functions. In this paper, we introduce and develop a theory of enriched -partitions; like ordinary -partitions, these are order-preserving maps from posets to chains, but with different rules governing the occurrence of equal values. The principal examples of enriched -partitions given here are the tableaux associated with Schur's -functions. In a sequel to this paper, further applications related to commutation monoids and reduced words in Coxeter groups will be presented.
tableaux associated with Schur's -functions. In this paper, we introduce and develop a theory of enriched -partitions; like ordinary -partitions, these are order-preserving maps from posets to chains, but with different rules governing the occurrence of equal values. The principal examples of enriched -partitions given here are the tableaux associated with Schur's -functions. In a sequel to this paper, further applications related to commutation monoids and reduced words in Coxeter groups will be presented.
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Alejandro Illanes 《Proceedings of the American Mathematical Society》1996,124(4):1243-1246
A topological space is -resolvable if has disjoint dense subsets. In this paper, we prove that if is -resolvable for each positive integer , then is -resolvable.
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Zaqueu Coelho Anthony N. Quas 《Transactions of the American Mathematical Society》1998,350(8):3257-3268
Bernoullicity is the strongest mixing property that a measure-theoretic dynamical system can have. This is known to be intimately connected to the so-called metric on processes, introduced by Ornstein. In this paper, we consider families of measures arising in a number of contexts and give conditions under which the measures depend -continuously on the parameters. At points where there is -continuity, it is often straightforward to establish that the measures have the Bernoulli property.
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Robert W. Fitzgerald 《Proceedings of the American Mathematical Society》1997,125(5):1309-1313
We improve Kula's bounds on the size of possible -regular Witt rings.
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Michael Marsalli 《Proceedings of the American Mathematical Society》1997,125(3):779-784
Let be a von Neumann algebra with a faithful, finite, normal tracial state , and let be a finite, maximal subdiagonal algebra of . Let be the closure of in the noncommutative Lebesgue space . Then possesses several of the properties of the classical Hardy space on the circle, including a commutant lifting theorem, some results on Toeplitz operators, an factorization theorem, Nehari's Theorem, and harmonic conjugates which are bounded.
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For characterization of best nonlinear approximation, DeVore,
Howard, and Micchelli have recently suggested the nonlinear -width of a subset in a normed linear space . We proved by a topological method that for and the well-known Aleksandrov -width in a Banach space the following inequalities hold: . Let be the unit ball of Besov space , of multivariate periodic functions. Then for approximation in , with some restriction on and , we established the asymptotic degree of these -widths: .
Howard, and Micchelli have recently suggested the nonlinear -width of a subset in a normed linear space . We proved by a topological method that for and the well-known Aleksandrov -width in a Banach space the following inequalities hold: . Let be the unit ball of Besov space , of multivariate periodic functions. Then for approximation in , with some restriction on and , we established the asymptotic degree of these -widths: .
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Kanghui Guo 《Proceedings of the American Mathematical Society》1997,125(5):1329-1340
A uniform estimate of Bessel functions is obtained, which is used to get a characterization of the measures on the unit sphere of in terms of the mixed norm of the Fourier transform of the measures.
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Goutam Mukherjee 《Proceedings of the American Mathematical Society》1997,125(4):1229-1236
We determine conditions for a -CW-complex to be a Hopfian or a co-Hopfian object in the -homotopy category of -path-connected -CW-complexes with base points.
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An infinite sequence is -complete if every sufficiently large integer is the sum of such that no one divides the other. We investigate -completeness of sets of the form and with nonnegative.
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Pawe l Kolwicz Ryszard Pluciennik 《Proceedings of the American Mathematical Society》1998,126(8):2315-2322
A characterization of -convexity of arbitrary Banach space is given. Moreover, it is proved that the Orlicz-Bochner function space is P-convex if and only if both spaces and are -convex. In particular, the Lebesgue-Bochner space with is -convex iff is -convex.
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Robert Tubbs 《Transactions of the American Mathematical Society》1997,349(7):2605-2617
In this paper we study the structure of analytic subgroups and of -submodules of -modules.
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A. Candel 《Proceedings of the American Mathematical Society》1996,124(3):899-905
We study the -algebras of proper foliations. In case of finite depth they are described by a tower of exact sequences. We conclude with remarks about foliations almost without holonomy and AF-embeddability.
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Let be the \u{C}ech-Stone remainder . We show that there exists a large class of images of such that whenever is a subset of of cardinality at most the continuum, then is again an image of . The class contains all separable compact spaces, all compact spaces of weight at most and all perfectly normal compact spaces.
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A -semigroup is of contractions if for , . Using the Hille-Yosida space, we completely characterize the generators of contraction -semigroups. We also give the Lumer-Phillips theorem for -semigroups in several special cases.