On the Increments of Stable Subordinators

Let be a stable subordinator defined on a probability space and let at for t>0?be a non-negative valued function. In this paper, it is shown that under varying conditions on at, there exists a function such that where , , and .

The measure functions of random Cantor set and fractals determined by subordinators

Let （Ω, F, P）=（[0, 1], [0, 1], μ）N （μ is the Lebesque measure, N={1, 2,…}）.{Xn}n=1∞ are independent random variables on （Ω, F, P） with Xn（ω）=ωn, where ω=（ω1, ω2,…）. The {Xn}n=1∞ are almost surely distinct. Thus to almost all sample points ω there is a random partial order 【 of the integers given

Packing measure functions of subordinators sample paths

X(t)(t∈[0,∞)) is a subordinator with its upper index β less than one, g(u) is the index function of X(t), and X[0,1]={x∈R:X(t)=x}, for some t∈ }. If (s)(s∈(0,1) ) is a measure function and h(s)=(s)g1s, then h-p(X)=0\ \ a.s. +∞\ a.s. according as ∫ 1 0φ 2(s)s d s<+∞, =+∞.The packing dimension of X(t) is the upper index β .

Multifractal structure of the product measure of two independent general subordinators'occupation measures

In this paper, we mainly investigate the multifractal spectrum of the random measure derived from two independent general subordinators.

On new classes of strongly Janowski type functions of complex order

We investigate some new subclasses of analytic functions of Janowski type of complex order.We also study inclusion properties,distortion theorems,coefficient bounds and radius of convexity of the functions.Moreover,analytic properties of these classes under certain integral operator are also discussed.Our findings are more comprehensive than the existing results in the literature.

一类包含广义Mittag-Leffler函数的积分算子的从属与超从属结果

In the paper,by making use of the principle of subordination between analytic functions with the multiplier transforms defined by generalized Mittag-Leffler function,the authors investigate subclasses of univalent analytic functions,such as starlike functions,convex functions,close-to-convex functions and quasiconvex functions.Several inclusion relationships,inequality properties,subordination and superordination results associated with the multiplier transforms are proved and the sandwich-type results are also obtained.

关于Subordinator的指数与维数

设Ｘ（ｔ）是Ｒｄ（ｄ为正整数）中的Ｌｅｖｙ过程，本文首先对前人所定义的Ｘ（ｔ）的各种指数给出了另外一种刻划，事实上它们可以用极限的形式表达．这种刻划使得这些指数的几何意义非常明确．且适合于构造各种各样的例子．若Ｘ（ｔ）是一个Ｓｕｂｏｒｄｉｎａｔｏｒ，本文证明了Ｘ（ｔ）的象集的填充维数就是Ｘ（ｔ）的上指数β，并且举例说明存在Ｓｕｂｏｒｄｉｎａｔｏｒ，它的象集的Ｈａｕｓｄｏｒｆ维数为０而填充维数为１．

On the Usage of the Subjunctive Mood in English

The subjunctive mood is one of the most difficult English grammar items for most English learners. In this thesis,the author discusses the usage of the subjunctive mood in English,especially its usage in English subordinate clauses. At the same time,the author provides a lot of examples. In the author's opinion,as long as the English learners find out the rules of it and practice it more,they will definitely grasp the subjunctive mood and use it correctly and skillfully.

On Hyponymy and Semantic Fields

This paper aims at elaborating on the semantics. The concept of hyponymy is mentioned first. Then the concept of semantic fields is mentioned. In order to make a comparison between hyponymy and semantic fields, there are some examples in the paper.

ON THE COEFFICIENTS OF SEVERAL CLASSES OF BI-UNIVALENT FUNCTIONS

In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve of generalize the recent works of other authors.

ON CERTAIN CLASS OF ANALYTIC FUNCTIONS DEFINED BY DIFFERENTIAL SUBORDINATION

In this paper, the new subclass B-n(lambda,alpha,A,B) of analytic functions is introduced. Its subordination relations, inclusion relations, the inequality properties and convering theorem are discussed. The results obtained in this paper are sharp, which generalize the related works of some authors and some other new results are obtained.

ON A CLASS OF ANALYTIC FUNCTIONS RELATED TO CONIC DOMAINS AND ASSOCIATED WITH CARLSON-SHAFFER OPERATOR

Making use of the Carlson-Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. We also show that this class is closed under convolution with a convex function. Some applications are also discussed.

HARMONIC FUNCTION WITH CORRELATED COEFFICIENTS

In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri and Silverman. Next we define classes of harmonic functions with correlated coefficients in terms of generalized Dziok-Srivastava operator. By using extreme points theory, we obtain estimations of classical convex functionals on the defined classes of functions. Some applications of the main results are also considered.

Fuzzy Complex Index in Water Quality Assessment of Municipalities

Donghu Lake in Wuhan is a multipurpose complex water body. However, its eutrophication phenomenon becomes increasingly serious. By making use of detailed and accurate contamination monitoring data and several mathematics models, we probe into the dynamic state of water quality. The year’s average value of major contamination index in Donghu Lake from 2001 to 2008 and fuzzy complex index are used to assess its short-term state of water quality. The results show that its water quality is basically stable in the 4th class of water quality standard GB3838-2002.

CLASSES OF MEROMORPHIC FUNCTIONS ASSOCIATED WITH CONIC REGIONS

The object of this article is to introduce new classes of meromorphic functions associated with conic regions. Several properties like the coefficient bounds, growth and distortion theorems, radii of starlikeness and convexity, partial sums, are investigated. Some consequences of the main results for the well-known classes of meromorphic functions are also pointed out.

A UNIFIED CLASS OF ANALYTIC FUNCTIONS WITH FIXED ARGUMENT OF COEFFICIENTS

In this paper we introduce new classes of analytic functions with fixed argument of coefficients defined by subordination. Coefficient estimates, distortion theorems, integral means inequalities, and the radii of convexity and starlikeness are investigated. Convolution properties are also pointed out.

Polarity for a Class of Levy Processes

Polar set of Markov processes is an important concept in probabilistic potential theory, but it is not easy to judge the polarity of the sets. In this paper, we give some results which can be easily used to examine the polarity of the sets whenX t belongs to a special class of Levy processes. We also give a result about polar functions of symmetric stable processes.

Properties for Certain Subclass of Analytic Functions Involving Carlson-Shaffer Operators

Let Hn(p)be the class of functions of the form f(z)=z p+ +∞Σ k=n akzk+p,which are analytic in the open unit disk U={z:|z|<1}.In the paper,we introduce a new subclass Bn(μ,a,c,α,p;φ)of Hn(p)and investigate its subordination relations,inclusion relations and distortion theorems.The results obtained include the related results of some authors as their special case.

Coefficient Estimates for a Subclass of Bi-univalent Strongly Quasi-starlike Functions

The aim of this paper is to establish the Fekete-Szego inequality for a subclass of bi-univalent strongly quasi-starlike functions which is defined in the open unit disk. Furthermore, the coefficients a2 and a3 for functions in this new subclass are estimated.

Coefficient Estimates for a Class of m-fold Symmetric Bi-univalent Function Defined by Subordination

In this paper, we investigate the coefficient estimates of a class of m-fold bi-univalent function de?ned by subordination. The results presented in this paper improve or generalize the recent works of other authors.