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Vladimir Andrievskii 《Journal of Approximation Theory》2000,105(2):317
For an arbitrary continuum E in the complex plane with connected complement Ω we study the rate of approximation of ∂E from outside by lemniscates in terms of level lines of a conformal mapping of Ω onto the exterior of the unit disk. 相似文献
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V. N. Dubinin 《Mathematical Notes》2006,80(1-2):31-35
It is shown that if P(z) = z n + ? is a polynomial with connected lemniscate E(P) = {z: ¦P(z)¦ ≤ 1} and m critical points, then, for any n? m+1 points on the lemniscate E(P), there exists a continuum γ ? E(P) of logarithmic capacity cap γ ≤ 2?1/n which contains these points and all zeros and critical points of the polynomial. As corollaries, estimates for continua of minimum capacity containing given points are obtained. 相似文献
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We study the attractors of a finite system of planar contraction similarities S
j
(j=1,...,n) satisfying the coupling condition: for a set {x
0,...,x
n} of points and a binary vector (s
1,...,s
n
), called the signature, the mapping S
j
takes the pair {x
0,x
n} either into the pair {x
j-1,x
j
} (if s
j
=0) or into the pair {x
j
, x
j-1} (if s
j
=1). We describe the situations in which the Jordan property of such attractor implies that the attractor has bounded turning, i.e., is a quasiconformal image of an interval of the real axis. 相似文献
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借助于球调和多项式的de la Vallée Poussin和构造出了单位球面S^q上一类带形平移网络算子,并给出了其对L^p(S^q)中函数一致逼近的收敛速度.
相似文献
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This paper gives a formula of integral for the rectifiable curves in the plane by the Hausdorff fractional derivation and integral. Received August 10, 1999, Revised December 27, 1999, Accepted January 14, 2000 相似文献
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We study the attractors γ of a finite system
of contraction similarities S
j
(j = 1,..., m) in ℝd which are Jordan arcs. We prove that if a system
possesses a structure parametrization (ℐ,ϕ) and ℱ(ℐ) is the associated family of ℐ then we have one of the following cases:1. The identity mapping Id does not belong to the closure of ℱ(ℐ). Then
(if properly rearranged) is a Jordan zipper.2. The identity mapping Id is a limit point of ℱ(ℐ). Then the arc γ is a straight line segment.3. The identity mapping Id is an isolated point of
.We construct an example of a self-similar Jordan curve which implements the third case.Original Russian Text Copyright © 2005 Aseev V. V. and Tetenov A. V.The authors were supported by the Program “Universities of Russia” (Grant UR.04.01.456).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 733–748, July–August, 2005. 相似文献
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本文利用摄动的思想,以摄动有理曲线(曲面)的系数的无穷模作为优化目标,给出了用多项式曲线(曲面)逼近有理曲线(曲面)的一种新方法.同以前的各种方法相比,该方法不仅收敛而且具有更快的收敛速度,并且可以与细分技术相结合,得到有理曲线与曲面的整体光滑、分片多项式的逼近. 相似文献
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用广义特征矩阵计算若当链 总被引:1,自引:0,他引:1
In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system of linear equations and they can be used to compute Jordan basis. 相似文献
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In this note we study the connection between the spectra of the products AB and BA of unbounded closed operators A and B acting in Banach spaces. Under the condition that the resolvent sets of these products are not empty we show that the spectra of AB and BA coincide away from zero and prove the commutation relation 𝕀 . Further, we prove statements concerning the relationship between the spectra of the operator AB and the block operator matrix . 相似文献
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研究了闭值域稠定闭算子的Moore-Penrose广义逆的有限维逼近问题.由于可接受条件相当强,我们提出更弱的条件P_(G(T_n))■P_(G(T))来研究稠定闭算子MoorePenrose广义逆的有限维逼近,也能得到相同的结论.特别地,当T为有界算子且T_n=Q_nTP_n时,条件P_(G(T_n))■P_(G(T))自然成立,于是有界线性算子Moore-Penrose广义逆的有限维逼近的一些结果会成为定理3.3的推论. 相似文献
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有心2-环绕系统中心距离的几何不等式 总被引:1,自引:0,他引:1
定义了无心2-环绕系统S~((m)){Γ,A,A_+,l}和有心2-环绕系统S~((2)){P,Γ,A,A_+,l}.借助于等周不等式理论对于有心2-环绕系统建立了如下的一类几何不等式. 相似文献
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M. Bognár 《Acta Mathematica Hungarica》2003,98(1-2):79-83
The proof of the following theorem of Gy. Pál is simplified: Each locally connected planar continuum with at least two points
is the orthogonal projection of a closed Jordan curve of the Euclidean 3-space.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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§ 1 . Introduction Itisaveryimportantstudytoapproximatenonboundedcontinuousfunctionsdefinedonalargerange.Aneffectivemethodcalledthemethodofmultiplierenlargementhasbeenputfor wardandgreatlydevelopedbyHSULCandWANGReng Hong [1— 3].Thesecondauthorofthispaperinparticularhasprovedin [2 ]almostuniformlythatanynonboundedcontinuousfunctionsdefinedonawholerealaxiscanbeapproximatedbypolynomialoperators.We’llgen eralizeinthispaperthebasicprincipleofthismethod,andasanexample,Bernsteinpolynomial… 相似文献
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We study approximation properties of certain nonlinear integral operators L
n
* obtained by a modification of given operators L
n
. The operators L
n;r
and L
n;r
* of r-times differentiable functions are also studied.
We give theorems on approximation orders of functions by these operators in polynomial weight spaces. 相似文献
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Let r ∈ ? be a complex number, and d ∈ ?≥2 a positive integer greater than or equal to 2. Ashihara and Miyamoto [4] introduced a vertex operator algebra V 𝒥 of central charge dr, whose Griess algebra is isomorphic to the simple Jordan algebra of symmetric matrices of size d. In this article, we prove that the vertex operator algebra V 𝒥 is simple if and only if r is not an integer. Further, in the case that r is an integer (i.e., V 𝒥 is not simple), we give a generator system of the maximal proper ideal I r of the VOA V 𝒥 explicitly. 相似文献
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Let K be a field of characteristic zero and V a vector space of dimension m>1 with a nondegenerate symmetric bilinear form f:V×V→K. The Jordan algebra Bm = K⊕V of the form f is a ?2-graded algebra with this decomposition. We prove that the ideal of all the ?2-graded identities of Bm satisfies the Specht property and we compute the ?2-graded cocharacter sequence of Bm. 相似文献