In this paper we establish direct local and global approximation theorems for Baskakov type operators and Szasz - Mirakjan type operators, respectively.
This article proves the existence of Julia directions of value distribution of holomorphic mapping f from the unit disk into the n-dimensional complex projective spacePn（C） under the assumption limsupT（r,f）/log 1/...This article proves the existence of Julia directions of value distribution of holomorphic mapping f from the unit disk into the n-dimensional complex projective spacePn（C） under the assumption limsupT（r,f）/log 1/1-r = ＋∞ for hypersurfaces in general position. A heuristic principle concerning the existence of Julia directions of holomorphic mappings from the unit disk into Pn（C） is given also.展开更多
A spatial array of wave gauges installed on an observatoion platform has been designed and arranged to measure the local features of winter monsoon directional waves off Taishi coast of Taiwan. A new method, named the...A spatial array of wave gauges installed on an observatoion platform has been designed and arranged to measure the local features of winter monsoon directional waves off Taishi coast of Taiwan. A new method, named the Bayesian Parameter Estimation Method(BPEM), is developed and adopted to determine the main direction and the directional spreading parameter of directional spectra. ne BPEM could be considered as a regression analysis to find the maximum joint probability of parameters, which best approximates the observed data from the Bayesian viewpoint. The result of the analysis of field wave data demonstrates the highly dependency of the characteristics of normalized directional spreading on the wave age. The Mitsuyasu type empirical formula of directional spectrum is therefore modified to be representative of monsoon wave field. Moreover, it is suggested that S-max could be expressed as a function of wave steepness. The values of S-max decrease with increasing steepness. Finally, a local directional spreading model, which is simple to be utilized in engineering practice, is proposed.展开更多
It is well-known that Bernstein polynomials are very important in studying the characters of smoothness in theory of approximation. A new type of combinations of Bernstein operators are given in [1]. In this paper, we...It is well-known that Bernstein polynomials are very important in studying the characters of smoothness in theory of approximation. A new type of combinations of Bernstein operators are given in [1]. In this paper, we give the Bernstein-Markov inequalities with step-weight functions for combinations of Bernstein polynomials with inner singularities as well as direct and inverse theorems.展开更多
New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous differ...New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous difference equations is negative definite. In this paper, we consider the case that the Liapunov function is only positive definite and its variation is semi-negative definite. At these weaker conditions, we put forward a new asymptotical stability theorem of nonautonomous difference equations by adding to extra conditions on the variation. After that, in addition to the hypotheses of our new asymptotical stability theorem, we obtain a new uniformly asymptotical stability theorem of nonautonomous difference equations provided that the Liapunov function has an indefinitely small upper bound. Example is given to verify our results in the last.展开更多
By using function one direction S-rough sets (function one direction singular rough sets),the concept of one direction rough law is proposed,where one direction rough law is the law pair {w(x)-,w(x)-} composed by w(x)...By using function one direction S-rough sets (function one direction singular rough sets),the concept of one direction rough law is proposed,where one direction rough law is the law pair {w(x)-,w(x)-} composed by w(x)-and w(x)-. If the attribute set {α-,α-} of function one direction S-rough sets changes,then one direction rough law {w(x)-,w(x)-} will change,too. By employing ellipse curves,the concept of one direction rough law security is presented,the security theorem of one direction rough law is proposed and the applications are given. One direction rough law security,which is generated by the intersection and penetration between function one direction S-rough sets and ellipse curves,is a new applied research direction of function S-rough sets.展开更多
由使用一个方向双单个不平的集合，(F) 知识的概念和它的 F 减小被给；(F) 知识和属性补充的 F 减小定理 F 减小的冗余的原则被介绍；一个方向双单个不平的集合是单个不平的集合的基本形式之一；知识减小是不平的集合和不平的系统理论...由使用一个方向双单个不平的集合，(F) 知识的概念和它的 F 减小被给；(F) 知识和属性补充的 F 减小定理 F 减小的冗余的原则被介绍；一个方向双单个不平的集合是单个不平的集合的基本形式之一；知识减小是不平的集合和不平的系统理论上的一个新研究方向。展开更多
In the present paper, we establish direct and converse theorems for weight-ed Bernstein-Durrmeyer operators under weighted L^p-norm with Jacobi weight w（x）=x^a（1-x）β.All the results involved have no restriction a...In the present paper, we establish direct and converse theorems for weight-ed Bernstein-Durrmeyer operators under weighted L^p-norm with Jacobi weight w（x）=x^a（1-x）β.All the results involved have no restriction a,β〈1-1/p,which indicates that the weighted Bemstein-Durrmeyer operators have some better approxi- mation properties than the usual Bernstein-Durrmeyer operators.展开更多
文摘In this paper we establish direct local and global approximation theorems for Baskakov type operators and Szasz - Mirakjan type operators, respectively.
基金project supported in part by the National Natural Science Foundation of China(10971156)
文摘This article proves the existence of Julia directions of value distribution of holomorphic mapping f from the unit disk into the n-dimensional complex projective spacePn（C） under the assumption limsupT（r,f）/log 1/1-r = ＋∞ for hypersurfaces in general position. A heuristic principle concerning the existence of Julia directions of holomorphic mappings from the unit disk into Pn（C） is given also.
文摘A spatial array of wave gauges installed on an observatoion platform has been designed and arranged to measure the local features of winter monsoon directional waves off Taishi coast of Taiwan. A new method, named the Bayesian Parameter Estimation Method(BPEM), is developed and adopted to determine the main direction and the directional spreading parameter of directional spectra. ne BPEM could be considered as a regression analysis to find the maximum joint probability of parameters, which best approximates the observed data from the Bayesian viewpoint. The result of the analysis of field wave data demonstrates the highly dependency of the characteristics of normalized directional spreading on the wave age. The Mitsuyasu type empirical formula of directional spectrum is therefore modified to be representative of monsoon wave field. Moreover, it is suggested that S-max could be expressed as a function of wave steepness. The values of S-max decrease with increasing steepness. Finally, a local directional spreading model, which is simple to be utilized in engineering practice, is proposed.
文摘It is well-known that Bernstein polynomials are very important in studying the characters of smoothness in theory of approximation. A new type of combinations of Bernstein operators are given in [1]. In this paper, we give the Bernstein-Markov inequalities with step-weight functions for combinations of Bernstein polynomials with inner singularities as well as direct and inverse theorems.
文摘New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous difference equations is negative definite. In this paper, we consider the case that the Liapunov function is only positive definite and its variation is semi-negative definite. At these weaker conditions, we put forward a new asymptotical stability theorem of nonautonomous difference equations by adding to extra conditions on the variation. After that, in addition to the hypotheses of our new asymptotical stability theorem, we obtain a new uniformly asymptotical stability theorem of nonautonomous difference equations provided that the Liapunov function has an indefinitely small upper bound. Example is given to verify our results in the last.
基金Natural Science Foundation of Fujian Province of China( No.2009J01293)Open Project of Brain-like Key Laboratory Research of Fujian Province of China (No. BLISSOS20101015)
文摘By using function one direction S-rough sets (function one direction singular rough sets),the concept of one direction rough law is proposed,where one direction rough law is the law pair {w(x)-,w(x)-} composed by w(x)-and w(x)-. If the attribute set {α-,α-} of function one direction S-rough sets changes,then one direction rough law {w(x)-,w(x)-} will change,too. By employing ellipse curves,the concept of one direction rough law security is presented,the security theorem of one direction rough law is proposed and the applications are given. One direction rough law security,which is generated by the intersection and penetration between function one direction S-rough sets and ellipse curves,is a new applied research direction of function S-rough sets.
基金Supported by the Nature Science Foundation of Henan Province（102300410153） Supported by the Natural Science Foundation of Shandong Province（Y2007H02）
文摘由使用一个方向双单个不平的集合，(F) 知识的概念和它的 F 减小被给；(F) 知识和属性补充的 F 减小定理 F 减小的冗余的原则被介绍；一个方向双单个不平的集合是单个不平的集合的基本形式之一；知识减小是不平的集合和不平的系统理论上的一个新研究方向。
文摘In the present paper, we establish direct and converse theorems for weight-ed Bernstein-Durrmeyer operators under weighted L^p-norm with Jacobi weight w（x）=x^a（1-x）β.All the results involved have no restriction a,β〈1-1/p,which indicates that the weighted Bemstein-Durrmeyer operators have some better approxi- mation properties than the usual Bernstein-Durrmeyer operators.
