Hardy平均及其不等式

本文研究了涉及Hardy平均的不等式问题.借助于优超理论,获得了2维Hardy平均不等式成立的充要条件及n维Hardy平均不等式的充分条件.并为建立解析不等式和高维结果提供了一些方法.     

On weighted extensions of Cauchy's means

We show that every Cauchy mean in (0,∞) can be embedded into two parameter family of weighted means. Some basic properties and examples are presented. A functional equation which appears in the problem of symmetry of these means is considered. As an application a natural extension of Stolarsky's means is obtained and a two parameter subclass of weighted power means is determined.     

一种稳健的聚类方法

本文讨论一种新的聚类方法 :属性均值聚类 .通过理论分析 ,属性均值聚类是比模糊均值聚类更稳健的聚类方法 .数值实验说明了该方法的有效性     

Invariance of means

We give a survey of results dealing with the problem of invariance of means which, for means of two variables, is expressed by the equality \(K\circ \left( M,N\right) =K\). At the very beginning the Gauss composition of means and its strict connection with the invariance problem is presented. Most of the reported research was done during the last two decades, when means theory became one of the most engaging and influential topics of the theory of functional equations. The main attention has been focused on quasi-arithmetic and weighted quasi-arithmetic means, also on some of their surroundings. Among other means of great importance Bajraktarevi? means and Cauchy means are discussed.     

A dynamical characterization of quasilinear means

The theory of dyadic iterations of two-variables continuous means is revised and extended in order to introduce the concept of base family of a continuous mean. Besides other results of interest, a new analytic characterization of quasilinear means is obtained by studying the means admitting a unique base mean.     

Inequalities for differences of power means in two variables

Using classical analytic techniques, a double inequality for differences of power means and geometric means in two variables is generalized and sharpened. A new inequality for differences of power means involving four parameters is established.     

Operator means and networks

The operator means of two variables are known to be weighted arithmetic averages of weighted harmonic means. The passage from 2 to 3 or more variables offers conceptual difficulties, and besides the symmetric means of Anderson, Morley, and Trapp next to nothing is known.In this paper we construct and study a new family of operator means in any number of variables. Our construction is motivated by network considerations and it generalizes the above mentioned symmetric means.Research partially supported by NSF Grant No. DMS 8702371.     

Knowledge trees in complex knowledge bases

We extend the use of knowledge trees as a means for questioning knowledge bases with linguistic information. Using Zadeh's theory of approximate reasoning as a tool we provide means for questioning large knowledge bases which have relational, implicational and data type information. We provide a means for answering questions of truth as well as questions of value.     

In-betweenness,a geometrical monotonicity property for operator means

We introduce the notions of in-betweenness and monotonicity with respect to a metric for operator means. These notions can be seen as generalising their natural counterpart for scalar means, and as a relaxation of the notion of geodesity. We exhibit two classes of non-trivial means that are monotonic with respect to the Euclidean metric. We also show that all Kubo–Ando means are monotonic with respect to the trace metric, which is the natural metric for the geometric mean.     

Convergence of a class of means of Hp functions (0<p<1) on compact lie groups

In this paper we study the convergence of a class of means on H^p(G) (0<p<1), the means take the Bochner-Riesz means in [1], the generalized Bochner-Riesz means in [2], and the operators T^σ, in [3] as special cases. We obtain weak-type estimates for the associated maximal operators and the maximal mean boundedness for the means. Supported by NSFC     

Run length not required: Optimal-mse dynamic batch means estimators for steady-state simulations

This paper addresses the estimation of the variance of the sample mean from steady-state simulations without requiring the knowledge of simulation run length a priori. Dynamic batch means is a new and useful approach to implementing the traditional batch means in limited memory without the knowledge of the simulation run length. However, existing dynamic batch means estimators do not allow one to control the value of batch size, which is the performance parameter of the batch means estimators. In this work, an algorithm is proposed based on two dynamic batch means estimators to dynamically estimate the optimal batch size as the simulation runs. The simulation results show that the proposed algorithm requires reasonable computation time and possesses good statistical properties such as small mean-squared-error (mse).     

球面Hardy空间上Riesz平均的逼近

引进了球面Hrady空间上Riesz平均算子及Peetre K模。讨论了Riesz平均算子在Hardy空间上的逼近性质。证明了Riesz平均算子与Peetre K模的强渐近等价关系。所得结果表明Peetre K模完全刻划了Riesz平均的逼近。     

VaR方法在证券市场尖峰、胖尾分布中的实证分析

标准 Va R方法的假设条件与实际数据之间存在较大的差距 ,而差距是必严重影响 Va R方法的实际应用效果 .为此 ,本文从实际数据的基本特征出发 ,讨论了 Va R方法在尖峰、胖尾分布中的计算公式 ,并使用该计算公式对我国证券市场的实际数据进行了实证分析 .分析结果表明 ,推广的 Va R计算方法对证券市场风险预警有更可靠的揭示作用 .     

正态分布的均值被简单树半序约束方差为未知的最大似然估计

对给定的 k个总体 ,均值和方差均未知 ,本文讨论了均值被简单树半序约束 ,方差为未知的最大似然估计 ,并给出了一个求解方法 .     

On the order of approximation by Riesz means in multiplicative systems in the classes E X [ɛ]

We establish the order of approximation by Riesz means of the Fourier series in a multiplicative system of a class of functions with given majorant of the sequence of best approximations. In some cases, approximations by Riesz means and best approximations are considered in a specific space, but, in other cases, approximations by Riesz means are considered in spaces with a stronger norm.     

On the meaning of mean shape: manifold stability, locus and the two sample test

Various concepts of mean shape previously unrelated in the literature are brought into relation. In particular, for non-manifolds, such as Kendall’s 3D shape space, this paper answers the question, for which means one may apply a two-sample test. The answer is positive if intrinsic or Ziezold means are used. The underlying general result of manifold stability of a mean on a shape space, the quotient due to an proper and isometric action of a Lie group on a Riemannian manifold, blends the slice theorem from differential geometry with the statistics of shape. For 3D Procrustes means, however, a counterexample is given. To further elucidate on subtleties of means, for spheres and Kendall’s shape spaces, a first-order relationship between intrinsic, residual/Procrustean and extrinsic/Ziezold means is derived stating that for high concentration the latter approximately divides the (generalized) geodesic segment between the former two by the ratio 1:3. This fact, consequences of coordinate choices for the power of tests and other details, e.g. that extrinsic Schoenberg means may increase dimension are discussed and illustrated by simulations and exemplary datasets.     

Three-Dimensional Maneuvering and Control of Flexible Robots

This paper develops a general approach to the three-dimensional maneuver and vibration control of a robot in the form of a chain of flexible links. The equations for the rigid-body maneuvering motions are derived by means of Lagrange equations in terms of quasi-coordinates and the equations for the elastic deformations by means of ordinary Lagrange equations. The equations of motion are derived for the full system simultaneously, using recursive equations to relate the motions of a given link to the motions of the preceding links in the chain. The maneuver is carried out by means of joint torques and the vibration is suppressed by means of point actuators dispersed throughout the links. The controls are designed by the Liapunov direct method. A numerical example demonstrates the theoretical developments.     

On large deviations for some sequences of weighted means of Gaussian processes

In this paper we study some sequences of weighted means of continuous real valued Gaussian processes. More precisely we consider suitable generalizations of both arithmetic and logarithmic means of a Gaussian process with covariance function which satisfies either an exponential decay condition or a power decay condition. Our aim is to provide limits of variances of functionals of such weighted means which allow the application of some large deviation results in the literature.     

Theory of operator means

New properties of operator connections and means are established. Specifically, representations of an arbitrary connection by means of a concave representing function, an estimate of the norm of a connection in a von Neumann-Schatten ideal, a relation between operator means and convolutions onto operator domains are obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 6, pp. 723–730, June, 1990.     

Exact Inference for Random Dirichlet Means

Two characterisations of a random mean from a Dirichlet process, as a limit of finite sums of a simple symmetric form and as a solution of a certain stochastic equation, are developed and investigated. These are used to reach results on and new insights into the distributions of such random means. In particular, identities involving functional transforms and recursive moment formulae are established. Furthermore, characterisations for several choices of the Dirichlet process parameter (leading to symmetric, unimodal, stable, and finite mixture distributions) are provided. Our methods lead to exact simulation recipes for prior and posterior random means, an approximation algorithm for the exact densities of these means, and limiting normality theorems for posterior distributions. The theory also extends to mixtures of Dirichlet processes and to the case of several random means simultaneously.