In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on comp...In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.展开更多
In this paper, we deal with the complex Baskakov-Szasz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth...In this paper, we deal with the complex Baskakov-Szasz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth in DR = {z ∈ C; ｜z｜ 〈 R}. Also, the exact order of approximation is found. The method used allows to construct complex Szasz-type and Baskakov-type approximation operators without involving the values on [0,∞）.展开更多
A simple method to fabricate one-dimensional(1-D) and two-dimensional(2-D) ordered micro- and nano-scale patterns is developed based on the original masters from optical discs, using nanoimprint technology and soft st...A simple method to fabricate one-dimensional(1-D) and two-dimensional(2-D) ordered micro- and nano-scale patterns is developed based on the original masters from optical discs, using nanoimprint technology and soft stamps. Polydimethylsiloxane(PDMS) was used to replicate the negative image of the 1-D grating pattern on the masters of CD-R, DVD-R and BD-R optical discs, respectively, and then the 1-D pattern on one of the PDMS stamps was transferred to a blank polycarbonate(PC) substrate by nanoimprint. The 2-D ordered patterns were fabricated by the second imprinting using another PDMS stamp. Different 2-D periodic patterns were obtained depending on the PDMS stamps and the angle between the two times of imprints. This method may provide a way for the fabrication of complex 2-D patterns using simple 1-D masters.展开更多
Suppose that {b(n)} and {c(n)} are two positive sequences. Let F({b(n)}, {c(n)}) = {f(z) : f(z) is analytic in \z\ < 1, f(z) = z - Sigma(n=2)(+infinity) a(n)z(n), a(n) greater than or equal to 0, Sigma(n=2)(+infini...Suppose that {b(n)} and {c(n)} are two positive sequences. Let F({b(n)}, {c(n)}) = {f(z) : f(z) is analytic in \z\ < 1, f(z) = z - Sigma(n=2)(+infinity) a(n)z(n), a(n) greater than or equal to 0, Sigma(n=2)(+infinity) b(n)a(n) less than or equal to 1 and Sigma(n=2)(+infinity) c(n)a(n) less than or equal to 1}. This article obtains the extreme points and support points of F({b(n)}, {c(n)}).展开更多
By the author denotes the areal measure on the unit disk . Let H'p = {f(z): f(z) is analytic in D and . Let B H 'p and. This article researches the support points and extreme points of B(H'p).
文摘In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.
文摘In this paper, we deal with the complex Baskakov-Szasz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth in DR = {z ∈ C; ｜z｜ 〈 R}. Also, the exact order of approximation is found. The method used allows to construct complex Szasz-type and Baskakov-type approximation operators without involving the values on [0,∞）.
基金supported by the National Natural Science Foundation of China(Nos.11504259,21575098 and 21505098)the Shanxi International Cooperation Project(No.2015081019)+2 种基金the Shanxi Scholarship Council(No.2013-038)the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(No.2015123)the Scientific Research Starting Foundation from Taiyuan University of Technology(No.tyut-rc201162a)
文摘A simple method to fabricate one-dimensional(1-D) and two-dimensional(2-D) ordered micro- and nano-scale patterns is developed based on the original masters from optical discs, using nanoimprint technology and soft stamps. Polydimethylsiloxane(PDMS) was used to replicate the negative image of the 1-D grating pattern on the masters of CD-R, DVD-R and BD-R optical discs, respectively, and then the 1-D pattern on one of the PDMS stamps was transferred to a blank polycarbonate(PC) substrate by nanoimprint. The 2-D ordered patterns were fabricated by the second imprinting using another PDMS stamp. Different 2-D periodic patterns were obtained depending on the PDMS stamps and the angle between the two times of imprints. This method may provide a way for the fabrication of complex 2-D patterns using simple 1-D masters.
文摘Suppose that {b(n)} and {c(n)} are two positive sequences. Let F({b(n)}, {c(n)}) = {f(z) : f(z) is analytic in \z\ < 1, f(z) = z - Sigma(n=2)(+infinity) a(n)z(n), a(n) greater than or equal to 0, Sigma(n=2)(+infinity) b(n)a(n) less than or equal to 1 and Sigma(n=2)(+infinity) c(n)a(n) less than or equal to 1}. This article obtains the extreme points and support points of F({b(n)}, {c(n)}).
文摘By the author denotes the areal measure on the unit disk . Let H'p = {f(z): f(z) is analytic in D and . Let B H 'p and. This article researches the support points and extreme points of B(H'p).
