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151.
Convergence rates of cascade algorithms   总被引:2,自引:0,他引:2  
We consider solutions of a refinement equation of the form


where is a finitely supported sequence called the refinement mask. Associated with the mask is a linear operator defined on by . This paper is concerned with the convergence of the cascade algorithm associated with , i.e., the convergence of the sequence in the -norm.

Our main result gives estimates for the convergence rate of the cascade algorithm. Let be the normalized solution of the above refinement equation with the dilation matrix being isotropic. Suppose lies in the Lipschitz space , where 0$"> and . Under appropriate conditions on , the following estimate will be established:


where and is a constant. In particular, we confirm a conjecture of A. Ron on convergence of cascade algorithms.

  相似文献   

152.
The set of continuous or Baire class 1 functions defined on a metric space is endowed with the natural pointwise partial order. We investigate how the possible lengths of well-ordered monotone sequences (with respect to this order) depend on the space .

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153.
Recently, the authors studied the connection between each maximal monotone operator and a family of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities.

The aim of this paper is to establish the converse of the latter fact. Namely, that every convex function satisfying those two particular inequalities is associated to a unique maximal monotone operator.

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154.
We present a new inversion formula for the classical, finite, and asymptotic Laplace transform of continuous or generalized functions . The inversion is given as a limit of a sequence of finite linear combinations of exponential functions whose construction requires only the values of evaluated on a Müntz set of real numbers. The inversion sequence converges in the strongest possible sense. The limit is uniform if is continuous, it is in if , and converges in an appropriate norm or Fréchet topology for generalized functions . As a corollary we obtain a new constructive inversion procedure for the convolution transform ; i.e., for given and we construct a sequence of continuous functions such that .

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155.
笔者依据所能获得的资料———《瓶罐玻璃行业企业经济信息汇编》[6],建立了一套经济实用的瓶罐玻璃行业企业绩效评价指标体系;提供了一种科学评价方法和计算机化的评价技术;能适时地对该行业内各企业绩效进行评价和比较分析;及时获得各企业在全行业内竞争位次;及时发现影响企业绩效的主要因素;为高层管理者制定和调整企业管理决策提供了参考依据。  相似文献   
156.
In this paper, we present-optimality criteria for convex programming problems associated with exact penalty functions. Several authors have given various criteria under the assumption that such convex problems and the associated dual problems can be solved. We assume the solvability of neither the convex problem nor the dual problem. To derive our criteria, we estimate the size of the penalty parameter in terms of an-solution for the dual problem.  相似文献   
157.
Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exists a convex representation of the operator which is a fixed point of this conjugation.

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158.
We proposed for the first time the concept of the nano liquid-metal fluid, aiming to establish an engineering route to make the highest conductive coolant. Using several widely accepted theoretical models for characterizing the nano fluid, the thermal conductivity enhancement of the liquid-metal fluid due to addition of more conductive nano particles was predicted. Further, the effects of particle size, cluster of nano particle, solid-like layer due to adsorption, volume fraction and particle types were evaluated. Having the highest conductivity, being electromagnetically drivable, the liquid metal with low melting point is expected to be an idealistic base fluid for making super conductive solution which may lead to the ultimate coolant in a wide variety of heat transfer enhancement area.  相似文献   
159.
160.
H. Weigel 《Pramana》2003,61(5):921-930
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