In this Paper we continue to investigate global minimization problems. An integral approach is applied to treat a global minimization problem of a discontinuous function. With the help ofthe theory of measure (Q-meas... In this Paper we continue to investigate global minimization problems. An integral approach is applied to treat a global minimization problem of a discontinuous function. With the help ofthe theory of measure (Q-measure) and integration, optimality conditions of a robust function over arobust set are derived. Algorithms and their implementations for finding global minima are proposed.Numerical tests and applications show that the algorithms are effective.展开更多
In this paper, we construct the function u in L2（Bn, dA） which is unbounded on any neighborhood of each boundary point of Bn such that Tu is the Schatten p-class （0 〈 p 〈 ∞） operator on pluriharmonic Bergman sp...In this paper, we construct the function u in L2（Bn, dA） which is unbounded on any neighborhood of each boundary point of Bn such that Tu is the Schatten p-class （0 〈 p 〈 ∞） operator on pluriharmonic Bergman space h2（Bn, dA） for several complex variables. In addition, we also discuss the compactness of Toeplitz operators with L1 symbols.展开更多
A class of distributions called Box-Cox symmetric was proposed for random variables with asymmetric distributions. This class allows through its structure an interpretation of the parameters in terms of quantiles (in ...A class of distributions called Box-Cox symmetric was proposed for random variables with asymmetric distributions. This class allows through its structure an interpretation of the parameters in terms of quantiles (in particular, the median), relative dispersion and skewness. This study presents the initial </span><span style="font-family:Verdana;">results of the computational development of basic functions of each of the</span><span style="font-family:Verdana;"> distributions that make up the Box-Cox symmetric class. Four functions have been developed to compose a routine in software R up to now. These functions are related to random numbers generation, probability density function, cumulative distribution function, and quantile function associated to a given probability. Examples of implemented functions were presented. The gamlss routine was used to check the performance of developed functions.展开更多
Bernardi has proved that if f(z) is starlike univalent in the unit disk △, then so is the func-tion g(z) given byIn this paper, we extend Bernardi's theorem to certain class φp (α,β,γ,ε,η; A) of p- valent s...Bernardi has proved that if f(z) is starlike univalent in the unit disk △, then so is the func-tion g(z) given byIn this paper, we extend Bernardi's theorem to certain class φp (α,β,γ,ε,η; A) of p- valent starlike functions for operators. We prove that if f(A) e φp (α, β,γ, ε, η; A), then g(A), defined byalso belongs to φp (α, β, γ, ε, η; A) and give a sufficient and necessary vondition with reference to f(A) 6 γp (α,β,γ,ε,η;A)展开更多
In this paper we study the convergence nf 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^(Φ_r)in[3]as special cases....In this paper we study the convergence nf 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^(Φ_r)in[3]as special cases.We obtain weak-type estimates for the associated maximal operators and the maximal mean boundedness for the means.展开更多
In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their...In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α.展开更多
A local probability exponential inequality for the tail of large deviation of an empirical process over an unbounded class of functions is proposed and studied. A new method of truncating the original probability spac...A local probability exponential inequality for the tail of large deviation of an empirical process over an unbounded class of functions is proposed and studied. A new method of truncating the original probability space and a new symmetrization method are given. Using these methods, the local probability exponential inequalities for the tails of large deviations of empirical processes with non-i.i.d. independent samples over unbounded class of functions are established. Some applications of the inequalities are discussed. As an additional result of this paper, under the conditions of Kolmogorov theorem, the strong convergence results of Kolmogorov on sums of non-i.i.d. independent random variables are extended to the cases of empirical processes indexed by unbounded classes of functions, the local probability exponential inequalities and the laws of the logarithm for the empirical processes are obtained.展开更多
We obtain effective lower bounds for certain linear combinations of the valuesat algebraic points of a class of p-adic G-functions defined over a completion of analgebraic closure of a p-adio field.
基金Project supported by National Natural Science Foundation of China
文摘 In this Paper we continue to investigate global minimization problems. An integral approach is applied to treat a global minimization problem of a discontinuous function. With the help ofthe theory of measure (Q-measure) and integration, optimality conditions of a robust function over arobust set are derived. Algorithms and their implementations for finding global minima are proposed.Numerical tests and applications show that the algorithms are effective.
基金Supported by National Natural Science Foundation of China(Grant No.11271092)
文摘In this paper, we construct the function u in L2（Bn, dA） which is unbounded on any neighborhood of each boundary point of Bn such that Tu is the Schatten p-class （0 〈 p 〈 ∞） operator on pluriharmonic Bergman space h2（Bn, dA） for several complex variables. In addition, we also discuss the compactness of Toeplitz operators with L1 symbols.
文摘A class of distributions called Box-Cox symmetric was proposed for random variables with asymmetric distributions. This class allows through its structure an interpretation of the parameters in terms of quantiles (in particular, the median), relative dispersion and skewness. This study presents the initial </span><span style="font-family:Verdana;">results of the computational development of basic functions of each of the</span><span style="font-family:Verdana;"> distributions that make up the Box-Cox symmetric class. Four functions have been developed to compose a routine in software R up to now. These functions are related to random numbers generation, probability density function, cumulative distribution function, and quantile function associated to a given probability. Examples of implemented functions were presented. The gamlss routine was used to check the performance of developed functions.
文摘Bernardi has proved that if f(z) is starlike univalent in the unit disk △, then so is the func-tion g(z) given byIn this paper, we extend Bernardi's theorem to certain class φp (α,β,γ,ε,η; A) of p- valent starlike functions for operators. We prove that if f(A) e φp (α, β,γ, ε, η; A), then g(A), defined byalso belongs to φp (α, β, γ, ε, η; A) and give a sufficient and necessary vondition with reference to f(A) 6 γp (α,β,γ,ε,η;A)
文摘In this paper we study the convergence nf 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^(Φ_r)in[3]as special cases.We obtain weak-type estimates for the associated maximal operators and the maximal mean boundedness for the means.
文摘In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α.
基金This work was supported partially by the National Natural Science Foundation of China(Grant No.19661001)the Social Science Foundation of Ministry of Education of China.
文摘A local probability exponential inequality for the tail of large deviation of an empirical process over an unbounded class of functions is proposed and studied. A new method of truncating the original probability space and a new symmetrization method are given. Using these methods, the local probability exponential inequalities for the tails of large deviations of empirical processes with non-i.i.d. independent samples over unbounded class of functions are established. Some applications of the inequalities are discussed. As an additional result of this paper, under the conditions of Kolmogorov theorem, the strong convergence results of Kolmogorov on sums of non-i.i.d. independent random variables are extended to the cases of empirical processes indexed by unbounded classes of functions, the local probability exponential inequalities and the laws of the logarithm for the empirical processes are obtained.
文摘We obtain effective lower bounds for certain linear combinations of the valuesat algebraic points of a class of p-adic G-functions defined over a completion of analgebraic closure of a p-adio field.
