In this paper, with the help of modulus of smoothness ω2r(f,t), we discuss the pointwise approximation properties for the iterated Boolean sums of Bernstein operator B n and obtain direct and inverse theorems when ...In this paper, with the help of modulus of smoothness ω2r(f,t), we discuss the pointwise approximation properties for the iterated Boolean sums of Bernstein operator B n and obtain direct and inverse theorems when 1-1/r ≤λ≤ 1, r ∈N.展开更多
In order to measure the correlation propeties of two Boolean functions,the global avalanche characteristics of Boolean functions constructed by concatenation are discussed,i.e.,f_1‖f_2and f_1‖f_2‖f_3‖f_4.Firstly,f...In order to measure the correlation propeties of two Boolean functions,the global avalanche characteristics of Boolean functions constructed by concatenation are discussed,i.e.,f_1‖f_2and f_1‖f_2‖f_3‖f_4.Firstly,for the function f = f_1‖f_2,the cross-correlation function of f_1,f_2 in the special condition are studied.In this case,f,f_1,f_2 must be in desired form.By computing their sum-of-squares indicators,the crosscorrelation function between f_1,f_2 is obtained.Secondly,for the function g = f_1‖f_2‖f_3‖f_4,by analyzing the relation among their auto-correlation functions,their sum-of-squares indicators are investigated.Based on them,the sum-of-squares indicators of functions obtained by Canteaut et al.are investigated.The results show that the correlation property of g is good when the correlation properties of Boolean functions f_1,f_2,f_3,f_4 are good.展开更多
In this paper, we investigate not only the acceleration problem of the q-Bernstein polynomials Bn（f, q; x） to B∞ （f, q; x） but also the convergence of their iterated Boolean sum. Using the methods of exact estima...In this paper, we investigate not only the acceleration problem of the q-Bernstein polynomials Bn（f, q; x） to B∞ （f, q; x） but also the convergence of their iterated Boolean sum. Using the methods of exact estimate and theories of modulus of smoothness, we get the respective estimates of the convergence rate, which suggest that q-Bernstein polynomials have the similar answer with the classical Bernstein polynomials to these two problems.展开更多
文摘In this paper, with the help of modulus of smoothness ω2r(f,t), we discuss the pointwise approximation properties for the iterated Boolean sums of Bernstein operator B n and obtain direct and inverse theorems when 1-1/r ≤λ≤ 1, r ∈N.
基金Sponsored by the National Natural Science Foundations of Anhui Higher Education Institutions of China(Grant No.KJ2014A220,KJ2014A231)the Anhui Provincial Natural Science Foundation(Grant No.1608085MF143)the Key Program in the Youth Elite Support Plan in Universities of Anhui Province(Grant No.gxyq ZD2016112)
文摘In order to measure the correlation propeties of two Boolean functions,the global avalanche characteristics of Boolean functions constructed by concatenation are discussed,i.e.,f_1‖f_2and f_1‖f_2‖f_3‖f_4.Firstly,for the function f = f_1‖f_2,the cross-correlation function of f_1,f_2 in the special condition are studied.In this case,f,f_1,f_2 must be in desired form.By computing their sum-of-squares indicators,the crosscorrelation function between f_1,f_2 is obtained.Secondly,for the function g = f_1‖f_2‖f_3‖f_4,by analyzing the relation among their auto-correlation functions,their sum-of-squares indicators are investigated.Based on them,the sum-of-squares indicators of functions obtained by Canteaut et al.are investigated.The results show that the correlation property of g is good when the correlation properties of Boolean functions f_1,f_2,f_3,f_4 are good.
文摘In this paper, we investigate not only the acceleration problem of the q-Bernstein polynomials Bn（f, q; x） to B∞ （f, q; x） but also the convergence of their iterated Boolean sum. Using the methods of exact estimate and theories of modulus of smoothness, we get the respective estimates of the convergence rate, which suggest that q-Bernstein polynomials have the similar answer with the classical Bernstein polynomials to these two problems.
