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91.
92.
Let () be the set of all continuous functions on which have a derivative ( , respectively) at least at one point . B. R. Hunt (1994) proved that is Haar null (in Christensen's sense) in .
In the present article it is proved that neither nor its complement is Haar null in . Moreover, the same assertion holds if we consider the approximate derivative (or the ``strong' preponderant derivative) instead of the ordinary derivative; these results are proved using a new result on typical (in the sense of category) continuous functions, which is of interest in its own right.
93.
2 Abstract For the 2-D quasilinear wave equation(?_t~2-?_x)u+2∑ij=0g~(ij)(?u)?_(ij)u = 0 satisfying i,j=0 null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consider a more general 2-D quasilinear wave equation(?_t~2-?_x)_u+2∑ij=0g~(ij)(?u)?_(ij)u = 0 satisfying null conditions with small initial data and the coefficients i,j=0 depending simultaneously on u and ?u. Through construction of an approximate solution,combined with weighted energy integral method, a quasi-global or global existence solution are established by continuous induction. 相似文献
94.
利用1981-2014年华南台风灾情数据,选取受灾人口、农作物受灾面积和直接经济损失,应用Copula函数理论,计算灾情重现期,分析台风灾害的灾情.首先,借助Clayton Copula函数构造三变量的联合分布,计算单变量重现期、联合重现期及同现重现期,并求出该重现期下的设计值.计算结果表明联合重现期的设计值要优于单变量重现期和同现重现期的设计值.因此,选取联合重现期的设计值作为防灾标准的最优参考,并将联合重现期记为灾情重现期.然后,计算2015-2017年登陆华南台风灾害的灾情重现期,并对台风灾害的灾情进行分析.发现台风灾情重现期越长的台风造成的灾情越严重.最后,利用灾情重现期与致灾重现期对台风灾害的发生频率作综合性分析,可以为台风灾害的风险评估提供一种新思路. 相似文献
95.
Diego Dominici 《Journal of Difference Equations and Applications》2018,24(6):916-940
We derive a system of difference equations satisfied by the three-term recurrence coefficients of some families of discrete orthogonal polynomials. 相似文献
96.
Null‐space methods for solving saddle point systems of equations have long been used to transform an indefinite system into a symmetric positive definite one of smaller dimension. A number of independent works in the literature have identified that we can interpret a null‐space method as a matrix factorization. We review these findings, highlight links between them, and bring them into a unified framework. We also investigate the suitability of using null‐space factorizations to derive sparse direct methods and present numerical results for both practical and academic problems. 相似文献
97.
A. Avilés 《Journal of Functional Analysis》2010,259(11):2776-2792
Di Piazza and Preiss asked whether every Pettis integrable function defined on [0,1] and taking values in a weakly compactly generated Banach space is McShane integrable. In this paper we answer this question in the negative. Moreover, we give a counterexample where the target Banach space is reflexive. 相似文献
98.
In this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ?2 and ?. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly nonmeasurable subset of the real line, which has different properties than classical non‐measurable subsets of reals. We shall also consider the question whether all images of bounded measurable subsets of the plane via a such mapping are non‐measurable (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
99.
100.