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81.
Ryo Ikehata 《Journal of Mathematical Analysis and Applications》2003,288(2):803-818
We generalize a previous result of Ikehata (Math. Methods Appl. Sci., in press), which studies the critical exponent problem of a semilinear damped wave equation in the one-dimensional half space, to the general N-dimensional half space case. That is to say, one can show the small data global existence of solutions of a mixed problem for the equation utt−Δu+ut=|u|p with the power p satisfying p∗(N)=1+2/(N+1)<p?N/[N−2]+ if we deal with the problem in the N-dimensional half space. 相似文献
82.
Yong-Gao Chen 《Journal of Number Theory》2003,98(2):310-319
In this paper we prove that if (r,12)?3, then the set of positive odd integers k such that kr−2n has at least two distinct prime factors for all positive integers n contains an infinite arithmetic progression. The same result corresponding to kr2n+1 is also true. 相似文献
83.
B. Banaschewski 《Journal of Pure and Applied Algebra》2003,177(3):231-236
The familiar equivalence between σ-frames and σ-coherent frames, given by the frame envelopes of σ-frames, is shown to induce an equivalence between stably continuous σ-frames and stably continuous frames. Similarly, the analogue of the former for σ-biframes is proved to provide an equivalence between compact regular σ-biframes and compact regular biframes. As an application we obtain the equivalence between stably continuous σ-frames and compact regular σ-biframes due to Matutu as an easy consequence of its frame counterpart established earlier by Banaschewski and Brümmer. This provides an affirmative answer to a question posed by Dana Scott. 相似文献
84.
Reduced rank regression assumes that the coefficient matrix in a multivariate regression model is not of full rank. The unknown rank is traditionally estimated under the assumption of normal responses. We derive an asymptotic test for the rank that only requires the response vector have finite second moments. The test is extended to the nonconstant covariance case. Linear combinations of the components of the predictor vector that are estimated to be significant for modelling the responses are obtained. 相似文献
85.
86.
87.
We develop constructive techniques to show that non-isomorphic 3-connected
matroids that are representable over a fixed finite field and that have the same Tutte
polynomial abound. In particular, for most prime powers q,
we construct infinite families
of sets of 3-connected matroids for which the matroids in a given set are non-isomorphic,
are representable over GF(q), and have the same Tutte
polynomial. Furthermore, the
cardinalities of the sets of matroids in a given family grow exponentially as a function of
rank, and there are many such families.In Memory of Gian-Carlo Rota 相似文献
88.
For an integer n3 and any positive number , we establish the existence of smooth functions K on
n
{0} with |K–1|, such that the equation
has a smooth positive solution which blows up at the origin (i.e., u does not have slow decay near the origin). Furthermore, we show that in some situations K can be extended as a Lipschitz function on
n
. These provide counter-examples to a conjecture of C.-S. Lin when n>4, and a question of Taliaferro.
Mathematics Subject Classification (2000)Primary 35J60; Secondary 53C21 相似文献
89.
In this paper we study the direct decomposability of free Tarski algebras. We
show that infinite freely generated Tarski algebras are directly indecomposable, whereas
finite freely generated Tarski algebras can only be decomposed into a direct product of two
factors, one of which is the two-element Tarski algebra. 相似文献
90.
Jean-Paul Penot 《Bulletin des Sciences Mathématiques》2003,127(9):815-833
We introduce a notion of “firm” (or uniform) asymptotic cone to an unbounded subset of a normed space. We relate this notion to a concept of “firm” asymptotic function. We use these notions to study boundedness properties which can be applied to continuity questions for some operations on sets and functions. Such questions arise in stability analysis of Hamilton-Jacobi equations. We present some other applications such as an extension of a theorem of Dieudonné and existence results in optimization and fixed point theory. 相似文献