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71.
Astrid Franz 《Mathematische Nachrichten》2001,223(1):23-32
For a special class of non–injective maps on Riemannian manifolds upper and lower bounds for the Hausdorff dimension of invariant sets are given in terms of the singular values of the tangent map. The upper estimation is based on a theorem by Douady and Oesterlé and its generalization to Riemannian manifolds by Noack and Reitmann , but additionally information about the noninjectivity is used. The lower estimation can be reached by modifying a method, derived by Shereshevskij for geometric constructions on the real line (also described by Barreira , for similar constructions in general metric spaces. The upper and lower dimension estimates for k — 1 — endomorphisms can for instance be applied to Julia sets of quadratic maps on the complex plane. 相似文献
72.
Carl H. FitzGerald Frederick Weening 《Transactions of the American Mathematical Society》2000,352(2):485-513
We consider a generalization of the parallel slit uniformization in which the angle of inclination of each image slit is assigned independently. Koebe proved that for domains of finite connectivity there is, up to a normalization, a unique rectilinear slit map achieving any given angle assignment. Koebe's theorem is partially extended to domains of infinite connectivity. A uniqueness result is shown for domains of countable connectivity and arbitrary angle assignments, and an existence result is proved for arbitrary domains under the assumption that the angle assignment is continuous and has finite range. In order to prove the existence result a new extremal length tool, called the crossing-module, is introduced. The crossing-module allows greater freedom in the family of admissible arcs than the classical module. Several results known for the module are extended to the crossing-module. A generalization of Jenkins' module condition for the parallel slit problem is given for the rectilinear slit problem in terms of the crossing-module and it is shown that rectilinear slit maps satisfying this crossing-module condition exist.
73.
Let {C
i}
0 be a sequence of independent and identically distributed random variables with vales in [0, 4]. Let {X
n}
0 be a sequence of random variables with values in [0, 1] defined recursively by X
n+1=C
n+1
X
n(1–X
n). It is shown here that: (i) E ln C
1<0X
n0 w.p.1. (ii) E ln C
1=0X
n0 in probability (iii) E ln C
1>0, E |ln(4–C
1)| such that (0, 1)=1 and is invariant for {X
n}. (iv) If there exits an invariant probability measure such that {0}=0, then E ln C
1>0 and – ln(1–x) (dx)=E ln C
1. (v) E ln C
1>0, E |ln(4–C
1)|< and {X
n} is Harris irreducible implies that the probability distribution of X
n converges in the Cesaro sense to a unique probability distribution on (0, 1) for all X
00. 相似文献
74.
Pawe Goldstein Pawe Strzelecki Anna Zatorska-Goldstein 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009,26(4):1387-1405
We prove that every polyharmonic map u∈Wm,2(Bn,SN−1) is smooth in the critical dimension n=2m. Moreover, in every dimension n , a weak limit u∈Wm,2(Bn,SN−1) of a sequence of polyharmonic maps uj∈Wm,2(Bn,SN−1) is also polyharmonic. 相似文献
75.
76.
SPECTRUM-PRESERVING ELEMENTARY OPERATORS ON B(X) 总被引:4,自引:0,他引:4
Hou Jinchuan 《数学年刊B辑(英文版)》1998,19(4):511-516
1.IntroductionLetXbeaninfinitedimensionalcomplexBanachspaceandB(X)theBanachalgebraofallboundedlinearoperatorsonX.ForTEB(X),a(T),asusual,willdenotethespectrumofT.Let4bealinearmapfromB(X)intoitself.4isspectrum-preservingifa(di(T))=a(T)forallTEB(X);4isspectrum-compressingifa(4(T))ga(T)forallTEB(X).Itisclearthatif4isunital(i.e.,ac(I)=I),thenacisspectrum-preserving(spectrum-compressing)ifandonlyif4preservesinvertibilityinbothdirections(preservesinvertibility),i.e.,4(T)isinvertibleifando… 相似文献
77.
We study worst-case complexities of visibility and distance structures on terrains under realistic assumptions on edge length ratios and the angles of the triangles, and a more general low-density assumption. We show that the visibility map of a point for a realistic terrain with n triangles has complexity . We also prove that the shortest path between two points p and q on a realistic terrain passes through triangles, and that the bisector of p and q has complexity . We use these results to show that the shortest path map for any point on a realistic terrain has complexity , and that the Voronoi diagram for any set of m points on a realistic terrain has complexity and . Our results immediately imply more efficient algorithms for computing the various structures on realistic terrains. 相似文献
78.
Let X be a real uniformly smooth and uniformly convex Banach space with dual X *. Let A: X → X * be a bounded uniformly submonotone map. It is proved that a Mann-type approximation sequence converges strongly to Jx * where x * ∈ N(A). Furthermore, as an application of this result an iterative sequence which converges strongly to a solution of the Hammerstein equation u+KFu = 0 is constructed where, F:X→X* and K:X*→X are monotone-type mappings. No invertibility assumption is imposed on K. Moreover, neither K nor F need be compact. Finally, our method is of independent interest. 相似文献
79.
《Journal of the Egyptian Mathematical Society》2014,22(2):272-274
Recently Kamran extended the result of Mizoguchi and Takahashi for closed multi-valued mappings and proved a fixed point theorem. In this paper we further extend the result concluded by Kamran and prove a common fixed point theorem by using the concept of lower semi-continuity. 相似文献
80.
该文得到了凸度量空间上混合映射的共同点的一些结果.推广了Ciric在文献[3]中的结论. 相似文献