共查询到20条相似文献,搜索用时 843 毫秒
1.
成圣江 《高等学校计算数学学报》1982,(1)
用插值节点的均匀性,在空间中函数具有嵌入性质的条件下,导出了最佳逼近的误差估计,本文仍利用插值节点均匀性假设,对空间中的一般函数,也导出了逼近的误差估计,不再要求函数的嵌入性质; Ciarlet在仿射等价和空间函数具有嵌入性质的条件下,对一个二阶椭圆边值问题论证数值积分并不影响有限元子空间近似解逼近变分问题真解的速度。本文借助於空间中的一般函数的有限元逼近理论,对这一特殊的二阶椭圆边值问题,在基函数满足均匀性条件下,不要嵌入性质同样得到上面结果。 相似文献
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均匀性度量是构作均匀设计的基础,本文从距离概念出发,通过对称的方法,得到一种新的距离函数-势函数,并将势函数作为衡量任意凸多面体上布点均匀性好坏的准则.数值例子和多变量Kendall 协和系数检验表明,当试验区域限制在单位立方体上时,势函数与目前常用的两种偏差-中心化L_2-偏差和可卷L_2.偏差在度量布点均匀性方面结论一致. 相似文献
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非线性抛物组非均匀网格差分解的唯一性和稳定性 总被引:4,自引:1,他引:3
1.引言 1.对一维非线性抛物组,在文献山中已构造一般非均匀网格差分格式,其中差分逼近的组合系数对不同的网格点和不同的网格层可以不同,并且运用不动点原理证明了差分解的存在性和收敛性.在非均匀网格差分格式中差分逼近的组合系数为常数的情形,文献[2]证明了具有有界二阶差商的离散向量解的存在性、唯一性和稳定性.本文将对文献[1]中构造的一般非均匀网格差分格式,证明所得到的差分解的唯一性和稳定性. 考虑如下非线性抛物组其中是未知的m-维向量函数是给定的矩阵函数,j(x,t,u,p)。是给定的m-维向量函数… 相似文献
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定义了二维Haar尺度函数,构造了长方形区域上的二维非均匀Haar小波函数,给出了非均匀 Haar 小波的分解和重构公式,最后得到了单值重构算法. 相似文献
6.
传输特征值在反散射唯一性理论中具有十分重要的意义.在含空隙的各向同性非均匀介质折射率扰动下,研究了Helmholtz方程传输特征值的存在性问题.首先,通过构造Neumann-Dirichlet算子,建立传输特征值问题的等价形式.然后,进一步构造特征值函数,将扰动的传输特征值问题转化为算子为零特征值的扰动问题.最后,利用隐函数定理的扰动方法证明传输特征值的存在性. 相似文献
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利用三次非均匀有理B样条,给出了一种构造局部插值曲线的方法,生成的插值曲线是C2连续的.曲线表示式中带有一个局部形状参数,随着一个局部形状参数值的增大,所给曲线将局部地接近插值点构成的控制多边形.基于三次非均匀有理B样条函数的局部单调性和一种保单调性的准则,给出了所给插值曲线的保单调性的条件. 相似文献
11.
Su-Ion Ih 《Compositio Mathematica》2002,134(1):35-57
We recall the main result of L. Caporaso, J. Harris, and B. Mazur's 1997 paper of Uniformity of rational points. It says that the Lang conjecture on the distribution of rational points on varieties of general type implies the uniformity for the numbers of rational points on curves of genus at least 2. In this paper we will investigate its analogue for their heights under the assumption of the Vojta conjecture. Basically, we will show that the Vojta conjecture gives a naturally expected simple uniformity for their heights. 相似文献
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E. P. Golubeva 《Journal of Mathematical Sciences》1984,25(2):988-998
Under the assumption on the boundary of the zeros of the Dirichlet L-functions, one obtains a refinement of the results of Yu. V. Linnik and B. F. Skubenko on the uniformity of the distribution of integral points on the hyperboloids D=b2–ac (D0). As a corollary one obtains the asymptotic behavior of the number of reduced indefinite binary quadratic forms of discriminant 4D.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 112, pp. 26–40, 1981. 相似文献
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Su-ion Ih 《Transactions of the American Mathematical Society》2006,358(4):1657-1675
We recall the result of D. Abramovich and its generalization by P. Pacelli on the uniformity for stably integral points on elliptic curves. It says that the Lang-Vojta conjecture on the distribution of integral points on a variety of logarithmic general type implies the uniformity for the numbers of stably integral points on elliptic curves. In this paper we will investigate its analogue for their heights under the assumption of the Vojta conjecture. Basically, we will show that the Vojta conjecture gives a naturally expected simple uniformity for their heights.
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Jaap Eldering 《Comptes Rendus Mathematique》2012,350(11-12):617-620
We prove a persistence result for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. The bounded geometry of the ambient manifold is a crucial assumption in order to control the uniformity of all estimates throughout the proof. 相似文献
15.
José Manuel Gutiérrez 《TOP》2014,22(2):739-748
Beyond its mathematization, preference intensity is a relevant concept, more general than cardinal representable preference, and an according axiomatic definition is introduced, dispensing with the Archimedean assumption. Given a preference intensity, a uniform space (generating the order topology of the induced preference) is associated to it. If the preference intensity is representable, this uniformity is semimetrizable. A “uniqueness” result for preference intensities leads naturally to the hypothesis of compactness. Through the uniformity corresponding to the preference intensity, compactness can be characterized. 相似文献
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In this paper, we consider two dependent classes of insurance business with heavy‐tailed claims. The dependence comes from the assumption that claim arrivals of the two classes are governed by a common renewal counting process. We study two types of ruin in the two‐dimensional framework. For each type of ruin, we establish an asymptotic formula for the finite‐time ruin probability. These formulae possess a certain uniformity feature in the time horizon. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
17.
Martin Aigner 《Aequationes Mathematicae》1977,16(1-2):37-50
In a geometric lattice every interval can be mapped isomorphically into an upper interval (containing 1) by a strong map. A natural question thus arises as to what extent certain assumptions on the upper interval structure determine the whole lattice. We consider conditions of the following sort: that above a certain levelm any two upper intervals of the same length be isomorphic. This property, called uniformity, is studied for binary geometries. The geometries satisfying the strongest uniformity condition (m = 1) are determined (except for one open case). As is to be expected the corresponding problem for lower intervals is easier and is solved completely. 相似文献
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Anna Di Concilio 《Monatshefte für Mathematik》1989,107(4):303-308
LetX be a completely regular space and 2
X
the hyperspace ofX. It is shown that the uniform topologies on 2
X
arising from Nachbin uniformity onX, which is the weak uniformity generated byC(X, ), and from Tukey—Shirota uniformity onX, generated by all countable open normal coverings ofX, agree. They, both, coincide with a Vietoris-type topology on 2
X
, the countable locally finite topology, iffX is normal. 相似文献
19.
Approximation in the finite element method 总被引:2,自引:0,他引:2
Gilbert Strang 《Numerische Mathematik》1972,19(1):81-98
Summary The rate of convergence of the finite element method depends on the order to which the solutionu can be approximated by the trial space of piecewise polynomials. We attempt to unify the many published estimates, by proving that if the trial space is complete through polynomials of degreek–1, then it contains a functionv
h
such that |u–v
h
|
s
ch
k–s|u|
k
. The derivatives of orders andk are measured either in the maximum norm or in the mean-square norm, and the estimate can be made local: the error in a given element depends on the diameterh
i
of that element. The proof applies to domains in any number of dimensions, and employs a uniformity assumption which avoids degenerate element shapes.This research was supported by the National Science Foundation (GP-13778). 相似文献
20.
The question of the finiteness of simplicial branch-and-bound algorithms employing only -subdivisions is considered. In Ref. 1, it was shown that this algorithm is convergent; here, it is proved that the algorithm is also finite if two assumptions are fulfilled. The first assumption requires the function values at vertices of the initial simplex to be lower than the optimal value of the problem. The second assumption requires each vertex of the initial simplex to violate at most one of the constraints defining the feasible polytope. The first assumption is mild from a theoretical point of view; the second assumption is strong, but holds always for instance when the feasible region is a hypercube. 相似文献