Minimal Cantor Systems and Unimodal Maps

We consider the restriction of unimodal maps f to the omega-limit set y ( c ) of the critical point for certain cases where y ( c ) is a Minimal Cantor set. We investigate the relation of these minimal systems to enumeration scales (generalized adding machines), to Vershik adic transformations on ordered Bratelli diagrams and to substitution shifts. Sufficient conditions are given for ( y ( c ), f ) to be uniquely ergodic.     

单峰扩张映射的捏制序列

设Ｐ及ＡＣ均是准素序列并满足ｍｉｎ｛Ｐ，ＡＣ｝ＲＬＲ∞，ρ（Ｐ）及ρ（ＡＣ）分别是Ｐ及ＡＣ的特征值．设ｆ∈Ｃ０（Ｉ，Ｉ）是个单峰扩张映射并具有扩张常数λ，ｍ是个非负整数．本文证明了若λ（ρ（Ｐ））１／２ｍ，则ｆ的捏制序列Ｋ（ｆ）（ＲＣ）ｍＰ；若λ＞（ρ（ＡＣ））１／２ｍ，则对任极大序列Ｅ，Ｋ（ｆ）＞（ＲＣ）ｍＡＣＥ．（ρ（Ｐ））１／２ｍ及（ρ（ＡＣ））１／２ｍ均是下述意义下的最佳值，即若其中任一个被较小的值代替，则相应的结论便不成立．     

具有稠密临界轨道和预不动临界轨道的单峰映射的丰富性

证明了对于实二次族在参数空间存在正Ｌｅｂｅｓｇｕｅ测度集合Ｅ,使得Ｅ中几乎所有的参数,相应的映射在不变测度的支集上具有稠密的临界轨道;还证明了Ｅ中存在稠密集合使得相应映射的临界轨道进入它的反向不动点。     

Anosov映射的性质

设f是紧致度量空间M上的自覆盖映射,本文证明(a)?(c)结合[2](a)?(b)且(a)?(c)     

Spectral Properties of Interval Exchange Maps

 In [7], Nogueira and Rudolph proved that for irreducible permutations not of rotation class almost every (a.e.) interval exchange transformation (i.e.t.) is topological weak mixing. It is conjectured that the claim holds if topological weak mixing is replaced by weak mixing. Here we study the behaviour of eigenfunctions of i.e.t. Our analysis gives alternative proofs of results due to Katok and Stepin [4] and Veech [10]: for certain permutations a.e. i.e.t. is weak mixing and for irreducible permutations a.e. i.e.t. is totally ergodic.     

Enumerative Properties of Rooted Circuit Maps

In 1966, Barnette introduced a set of graphs, called circuit graphs, which are obtained from 3-connected planar graphs by deleting a vertex. Circuit graphs and 3-connected planar graphs share many interesting properties which are not satisfied by general 2-connected planar graphs. Circuit graphs have nice closure properties which make them easier to deal with than 3-connected planar graphs for studying some graph-theoretic properties. In this paper, we study some enumerative properties of circuit graphs. For enumeration purpose, we define rooted circuit maps and compare the number of rooted circuit maps with those of rooted 2-connected planar maps and rooted 3-connected planar maps.     

Spectral Properties of Interval Exchange Maps

 In [7], Nogueira and Rudolph proved that for irreducible permutations not of rotation class almost every (a.e.) interval exchange transformation (i.e.t.) is topological weak mixing. It is conjectured that the claim holds if topological weak mixing is replaced by weak mixing. Here we study the behaviour of eigenfunctions of i.e.t. Our analysis gives alternative proofs of results due to Katok and Stepin [4] and Veech [10]: for certain permutations a.e. i.e.t. is weak mixing and for irreducible permutations a.e. i.e.t. is totally ergodic. (Received 1 February 2001)     

锥凸集值映射的基本性质

本文首先在R~m的幂集上定义了一种锥序关系并借助这种序关系定义锥凸集值映射,证明了普通单值凸函数的一些基本性质拓广到这种锥凸集值映射时仍成立.     

Banach空间中全纯映射的若干性质

本文将全纯映射的若干性质推广到Ｂａｎａｃｈ空间，并应用这些性质研究有界域中的凸映射与星形映射．     

Unimodal mappings and Li-Yorke chaos

Conditions for unimodal mappings to have domains with a Li-Yorke chaotic behavior of trajectories are found. Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 679–689, May, 1998.     

Statistical Properties of Covariance Tapers

Compactly supported autocovariance functions reduce computations needed for estimation and prediction under Gaussian process models, which are commonly used to model spatial and spatial-temporal data. A critical issue in using such models is the loss in statistical efficiency caused when the true autocovariance function is not compactly supported. Theoretical results indicate the value of specifying the local behavior of the process correctly. One way to obtain a compactly supported autocovariance function that has similar local behavior to an autocovariance function K of interest is to multiply K by some smooth compactly supported autocovariance function, which is called covariance tapering. This work extends previous theoretical results showing that covariance tapering has some asymptotic optimality properties as the number of observations in a fixed and bounded domain increases. However, numerical experiments show that for purposes of parameter estimation, covariance tapering often does not work as well as the simple alternative of breaking the observations into blocks and ignoring dependence across blocks. When covariance tapering is used for spatial prediction, predictions near the boundary of the observation domain are affected most. This article proposes an approach to modifying the taper to ameliorate this edge effect. In addition, a justification for a specific approach to carrying out conditional simulations based on tapered covariances is given. Supplementary materials for this article are available online.     

Linear Maps Preserving Invertibility or Related Spectral Properties

We survey some recent results on linear maps on operator algebras that preserve invertibility. We also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various parts of spectrum, spectral radius, quasinilpotents, etc. We present some results on elementary operators and additive operators preserving invertibility or related properties. In particular, we give a negative answer to a problem posed by Gao and Hou on characterizing spectrumpreserving elementary operators. Several open problems are also mentioned.     

Unimodal Polynomials Arising from Lie Superalgebras

Using the existence of a principal five-dimensional subalgebra for several types of basic Lie superalgebras, the unimodality of the principally specialized character of a typical finite-dimensional module with highest weight Λ is derived. This gives rise to some remarkable unimodal partition polynomials.     

On Some Properties of Bilinear Maps of Order Bounded Variation

In this paper we study properties of bilinear maps of order bounded variation. Theorems of preservation of properties in passage to the triadjoint and the tensor product are presented.     

Topological Properties of the Space of Convex Minimal Usco Maps

Set-Valued and Variational Analysis - We investigate the space of convex minimal usco maps from a Tychonoff space to the space of real numbers. Its elements are set-valued maps that are important...     

弱P-调和映射流的紧性性质

分别考虑了映入球面及紧致的齐性Ｒｉｅｍａｎｎｉａｎ空间的弱Ｐ－调和映射流；通过球面及齐性Ｒｉｅｍａｎｎｉａｎ空间的对称性质，证明了弱Ｐ－调和映射流的紧性性质．     

Properties for a Class of Holomorphic Mapson Hilbert Space

Itiswell-knownthattheanalyticfunctionwithpositiverealpartintheunitdiscofthecomplexplaneplaysaveryimportantroleinthegeometrictheoryofcomplexvariablefunc-tions.Ithasbeenremarkablehowtoextendtheclassicalresultofthetheoryoffunctionstoabstractspacesinrecentyears[2].Inthisnotewedefineageneralizedhalf-planeinHilbertspaceandfindthebiholomorphicmapoftheunitballonHilbertspaceontothishalf-plane.Asacorollary,wegiveashortproofofaresultin[5].UsingtheaboveholomooorphicmapweobtainthedistortiontheoremandPick…