近于凸映照子族全部项齐次展开式的精确估计

本文建立了Cn中单位多圆柱上近于凸映照子族和一类近于准凸映照全部项齐次展开式的精确估计.与此同时,作为推论给出了Cn中单位多圆柱上近于凸映照子族和一类近于准凸映照精确的增长定理和精确的偏差定理上界估计.所得主要结论表明Cn中单位多圆柱上关于近于凸映照子族和一类近于准凸映照的Bieberbach猜想成立,而且与单复变数的经典结论相一致.     

关于一类近于准凸映照推广族齐次展开式的精确估计

在Cn中的单位多圆柱上或复Banach空间的单位球上引入α次的β型近于准凸映照族,并建立了该族在Cn中的单位多圆柱上齐次展开式的精确估计,所得结果包含和推广了许多已知结论.     

一类近于凸映照子族精确的偏差定理

首先建立了C~n中单位多圆柱上一类近于凸映照子族精确的偏差定理,同时在复Banach空间单位球上也建立了该类映照精确的偏差定理的下界估计.其次在复Banach空间单位球上建立了准星形映照精确的偏差定理.所得结果将单复变中近于凸函数和星形函数的偏差定理推广至高维情形,并且对龚升提出的一个公开问题给出肯定的回答.     

近于凸函数族的Fekete－Szegǒ问题

设Ｓ为熟知的单位圆盘内的规范化单叶函数族．Ｆｅｋｅｔｅ－Ｓｚｅｇｏ证明了众所周知的结果最近Ｗ．Ｋｏｅｐｆ考虑了近于凸函数族Ｋ中的相应问题。得到了准确结果［１］．本文讨论了β型近于凸函数族Ｋ（β）中的Ｆｅｋｅｔｅ－Ｓｚｅｇｏ问题，也得到了准确结果，从而推广了文［１］中的结果．     

复Banach空间上推广的Roper-Sufiridge延拓算子

本文研究了推广的Roper-Sufiridge算子保持一些双全纯映照子族的性质.利用一些双全纯映照子族的定义,得到了推广后的Roper-Sufiridge算子在复Banach空间单位球上保持ρ次抛物形β型螺形映照及强α次殆星形映照的性质,由此得到复Hilbert空间上推广的Roper-Sufiridge算子的相应性质,推广了已有的结论.     

复Banach空间上推广的Roper-Suffridge延拓算子

本文研究了推广的Roper-Suffridge算子保持一些双全纯映照子族的性质.利用一些双全纯映照子族的定义,得到了推广后的Roper-Suffridge算子在复Banach空间单位球上保持ρ次抛物形β型螺形映照及强α次殆星形映照的性质,由此得到复Hilbert空间上推广的Roper-Suffridge算子的相应性质,推广了已有的结论.     

有关近于凸函数的一族解析函数

本文引进并研究D^λ算子定义的一族解析函数Bλ(α，β)．导出族中函数的积分表达式；得到该族与近于凸函数之间的关系并借助算子理论讨论了Bλ(α，β)的包含关系，端点性质；由此推出族中函数的偏差定理，证明一个系数不等式．     

单位球上双全纯映照的线性不变族

本文研究单位球上全纯映照的线性不变族.推广了Pommerenke在单位圆盘上建立的不变族理论.给出了单位球上不变族的秩的一些刻划,作为应用,给出不变族的偏差定理的一个简单证明.建立了一种更广泛的偏差定理,并讨论了不变族的单叶半径.最后,研究了不变族极值映照的齐次展开式的三次项系数,建立三次项系数和二次项系数的一些关系式.     

一类多复变全纯映照子族的增长和偏差定理

在一般复Banach空间X中的单位球B上引入一类全纯映照族M_g.考虑B上满足条件(Df(x))~(-1)f(x)∈M_g的正规化局部双全纯映照f(x)(其中x=0是f(x)-x的k+1阶零点)并得到其增长定理.作为应用,也得到了C~n中单位多圆柱D~n上映照f关于Jacobi矩阵Jf(z)的偏差定理,该结果统一和推广了星形映照许多子族的相应结论.     

推广的Roper-Suffridge算子与Loewner链

将Roper-Suffridge箅子在C~n中单位球B~n上做了进一步推广,并考察推广后的算子何时能保持双全纯映照子族的性质.利用k阶零点及双全纯映照子族的增长定理,重点研究了推广后的算子在B~n上保持α次β型螺形映照及强β型螺形映照的性质,并由调和函数的最小值原理及具有正实部函数的性质,揭示了推广后的算子能够嵌入Loewner链,从而得到推广后的算子在B~n上保持α次殆β型螺形映照的性质.     

The sharp estimates of homogeneous expansions for the generalized class of close-to-quasi-convex mappings

In this paper, the class of strongly close-to-quasi-convex mappings of type α and order β is introduced in the unit ball of complex Banach space or unit polydisk in ${\mathbb{C}}^n$, and we obtain the sharp estimates of homogeneous expansions for this class. These results generalize many known results.     

Completion of the mixed unit interval graphs hierarchy

We describe the missing class of the hierarchy of mixed unit interval graphs. This class is generated by the intersection graphs of families of unit intervals that are allowed to be closed, open, and left‐closed‐right‐open. (By symmetry, considering closed, open, and right‐closed‐left‐open unit intervals generates the same class.) We show that this class lies strictly between unit interval graphs and mixed unit interval graphs. We give a complete characterization of this new class, as well as quadratic‐time algorithms that recognize graphs from this class and produce a corresponding interval representation if one exists. We also show that the algorithm from Shuchat et al. [8] directly extends to provide a quadratic‐time algorithm to recognize the class of mixed unit interval graphs.     

Geometric Characterization of Weyl’s Discrepancy Norm in Terms of Its <Emphasis Type="Italic">n</Emphasis>-Dimensional Unit Balls

Weyl’s discrepancy measure induces a norm on ? ⁿ which shows a monotonicity and a Lipschitz property when applied to differences of index-shifted sequences. It turns out that its n-dimensional unit ball is a zonotope that results from a multiple sheared projection from the (n+1)-dimensional hypercube which can be interpreted as a discrete differentiation. This characterization reveals that this norm is the canonical metric between sequences of differences of values from the unit interval in the sense that the n-dimensional unit ball of the discrepancy norm equals the space of such sequences.     

Abelian <Emphasis Type="Italic">ℓ</Emphasis>-Groups with Strong Unit and Perfect MV-Algebras

We investigate the class of abelian ℓ-groups with strong unit corresponding to perfect MV-algebras via the Γ functor, showing that this is a universal subclass of the class of all abelian ℓ-groups with strong unit and describing the formulas that axiomatize it. We further describe results for classes of abelian ℓ-groups with strong unit corresponding to local MV-algebras with finite rank.     

Nonparametric adaptive opportunity-based age replacement strategies

We consider opportunity-based age replacement (OAR) using nonparametric predictive inference (NPI) for the time to failure of a future unit. Based on n observed failure times, NPI provides lower and upper bounds for the survival function for the time to failure X_n+1 of a future unit which lead to upper and lower cost functions, respectively, for OAR based on the renewal reward theorem. Optimal OAR strategies for unit n+1 follow by minimizing these cost functions. Following this strategy, unit n+1 is correctively replaced upon failure, or preventively replaced upon the first opportunity after the optimal OAR threshold. We study the effect of this replacement information for unit n+1 on the optimal OAR strategy for unit n+2. We illustrate our method with examples and a simulation study. Our method is fully adaptive to available data, providing an alternative to the classical approach where the probability distribution of a unit's time to failure is assumed to be known. We discuss the possible use of our method and compare it with the classical approach, where we conclude that in most situations our adaptive method performs very well, but that counter-intuitive results can occur.     

On the Curvature Properties of Manifolds with Deformed <Emphasis Type="Italic">G</Emphasis><Subscript>2</Subscript> Structures

In this paper, we study the curvature properties of a manifold with structure group G₂ whose fundamental 3-form is deformed by a Killing vector field of unit length. We obtain some results concerning conditions under which this manifold is flat, Einstein, or isometric to the unit sphere.     

On quasi-convex mappings of orderαin the unit ball of a complex Banach space Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In this paper, a class of biholomorphic mappings named quasi-convex mapping of order a in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings. Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space X. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order a defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively.     

On quasi-convex mappings of order α in the unit ball of a complex Banach space

In this paper, a class of biholomorphic mappings named quasi-convex mapping of order α in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings.Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space Ⅹ. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order α defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively.     

单位圆内的某族解析函数及其Fekete-Szeg不等式

本文引入了某族定义在单位圆内的解析函数。研究了它们的积分表示,系数估计,最大模估计及其子族的 Ｆｅｋｅｔｅ－Ｓｚｅｇｏ不等式,获得了一些较有关文献更一般的结果．     

Reliability Analysis of a One-Unit System with Unrepairable Spare Units and its Optimization Applications

It is assumed that a unit is either in operation or is in repair. When the main unit is under repair, spare units which cannot be repaired are used. In this system the following quantities are of interest: (i) The time distribution and the mean time to first-system failure, given that the n spare units are provided at time 0. (ii) The probability that the number of the failed spare units are equal to exactly n during the interval (0, t], and its expected number during the interval (0, t]. These quantities are derived by solving the renewal-type equations.Two optimization problems are discussed using the results obtained, viz.: (i) The expected cost of two systems, one with both a main unit and spare units and the other with only spare units is considered. (ii) A preventive maintenance policy of the main unit is considered in order to minimize the expected cost rate. Some policies of the two problems are discussed under suitable conditions. Numerical examples are also presented.