This article is devoted to presenting a recapitulative introduction for the theory of Besov-type and Triebel-Lizorkin-type spaces developed in recent years.
The main purpose of this paper is to introduce some approximation properties of a Kantorovich kind q-Bernstein operators related to B′ezier basis functions with shape parameterλ∈[−1,1].Firstly,we compute some basic...The main purpose of this paper is to introduce some approximation properties of a Kantorovich kind q-Bernstein operators related to B′ezier basis functions with shape parameterλ∈[−1,1].Firstly,we compute some basic results such as moments and central moments,and derive the Korovkin type approximation theorem for these operators.Next,we estimate the order of convergence in terms of the usual modulus of continuity,for the functions belong to Lipschitz-type class and Peetre’s K-functional,respectively.Lastly,with the aid of Maple software,we present the comparison of the convergence of these newly defined operators to the certain function with some graphical illustrations and error estimation table.展开更多
Bumetanide has been shown to lessen cerebral edema and reduce the infarct area in the acute stage of cerebral ischemia. Few studies focus on the effects of bumetanide on neuroprotection and neurogenesis in the chronic...Bumetanide has been shown to lessen cerebral edema and reduce the infarct area in the acute stage of cerebral ischemia. Few studies focus on the effects of bumetanide on neuroprotection and neurogenesis in the chronic stage of cerebral ischemia. We established a rat model of cerebral ischemia by injecting endothelin-1 in the left cortical motor area and left corpus striatum. Seven days later, bumetanide 200 μg/kg/day was injected into the lateral ventricle for 21 consecutive days with a mini-osmotic pump. Results demonstrated that the number of neuroblasts cells and the total length of dendrites increased, escape latency reduced, and the number of platform crossings increased in the rat hippocampal dentate gyrus in the chronic stage of cerebral ischemia. These findings suggest that bumetanide promoted neural precursor cell regeneration, dendritic development and the recovery of cognitive function, and protected brain tissue in the chronic stage of ischemia.展开更多
In this paper we introduce a generalization of Bernstein polynomials based on q calculus. With the help of Bohman-Korovkin type theorem, we obtain A-statistical approximation properties of these operators. Also, by us...In this paper we introduce a generalization of Bernstein polynomials based on q calculus. With the help of Bohman-Korovkin type theorem, we obtain A-statistical approximation properties of these operators. Also, by using the Modulus of continuity and Lipschitz class, the statistical rate of convergence is established. We also gives the rate of A-statistical convergence by means of Peetre＇s type K-functional. At last, approximation properties of a rth order generalization of these operators is discussed.展开更多
In this paper,we first give characterizations of weighted Besov spaces with variable exponents via Peetre’s maximal functions.Then we obtain decomposition characterizations of these spaces by atom,molecule and wavele...In this paper,we first give characterizations of weighted Besov spaces with variable exponents via Peetre’s maximal functions.Then we obtain decomposition characterizations of these spaces by atom,molecule and wavelet.As an application,we obtain the boundedness of the pseudo-differential operators on these spaces.展开更多
This article is devoted to the study of variable 2-microlocal Besov-type and Triebel- Lizorkin-type spaces. These variable function spaces are defined via a Fourier-analytical approach. The authors then characterize t...This article is devoted to the study of variable 2-microlocal Besov-type and Triebel- Lizorkin-type spaces. These variable function spaces are defined via a Fourier-analytical approach. The authors then characterize these spaces by means of Q-transforms, Peetre maximal functions, smooth atoms, ball means of differences and approximations by analytic functions. As applications, some re- lated Sobolev-type embeddings and trace theorems of these spaces are Mso established. Moreover, some obtained results, such as characterizations via approximations by analytic functions, are new even for the classical variable Besov and Triebel-Lizorkin spaces.展开更多
In this paper an asymptotic formula of Voronovskaja type for a multivariate extension of the Kantorovich generalized sampling series is given. Moreover a quantitative version in terms of some moduli of smoothness is e...In this paper an asymptotic formula of Voronovskaja type for a multivariate extension of the Kantorovich generalized sampling series is given. Moreover a quantitative version in terms of some moduli of smoothness is established. Finally some particular examples of kernels are discussed, as the Bochner-Riesz kernel and the multivariate splines.展开更多
基金supported by the National Natural Science Foundation of China(11171027and 11101038)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20120003110003)+1 种基金the Fundamental Research Funds for Central Universities of China(2012LYB26)supported by the Alexander von Humboldt Foundation
文摘This article is devoted to presenting a recapitulative introduction for the theory of Besov-type and Triebel-Lizorkin-type spaces developed in recent years.
基金This work is supported by the Natural Science Foundation of Fujian Province of China(Grant No.2020J01783)the Project for High-Level Talent Innovation and Entrepreneurship of Quanzhou(Grant No.2018C087R)the Program for New Century Excellent Talents in Fujian Province University.
文摘The main purpose of this paper is to introduce some approximation properties of a Kantorovich kind q-Bernstein operators related to B′ezier basis functions with shape parameterλ∈[−1,1].Firstly,we compute some basic results such as moments and central moments,and derive the Korovkin type approximation theorem for these operators.Next,we estimate the order of convergence in terms of the usual modulus of continuity,for the functions belong to Lipschitz-type class and Peetre’s K-functional,respectively.Lastly,with the aid of Maple software,we present the comparison of the convergence of these newly defined operators to the certain function with some graphical illustrations and error estimation table.
文摘Bumetanide has been shown to lessen cerebral edema and reduce the infarct area in the acute stage of cerebral ischemia. Few studies focus on the effects of bumetanide on neuroprotection and neurogenesis in the chronic stage of cerebral ischemia. We established a rat model of cerebral ischemia by injecting endothelin-1 in the left cortical motor area and left corpus striatum. Seven days later, bumetanide 200 μg/kg/day was injected into the lateral ventricle for 21 consecutive days with a mini-osmotic pump. Results demonstrated that the number of neuroblasts cells and the total length of dendrites increased, escape latency reduced, and the number of platform crossings increased in the rat hippocampal dentate gyrus in the chronic stage of cerebral ischemia. These findings suggest that bumetanide promoted neural precursor cell regeneration, dendritic development and the recovery of cognitive function, and protected brain tissue in the chronic stage of ischemia.
文摘In this paper we introduce a generalization of Bernstein polynomials based on q calculus. With the help of Bohman-Korovkin type theorem, we obtain A-statistical approximation properties of these operators. Also, by using the Modulus of continuity and Lipschitz class, the statistical rate of convergence is established. We also gives the rate of A-statistical convergence by means of Peetre＇s type K-functional. At last, approximation properties of a rth order generalization of these operators is discussed.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12161022 and 12061030)Hainan Provincial Natural Science Foundation of China(Grant No.122RC652)the Science and Technology Project of Guangxi(Grant No.Guike AD23023002)。
文摘In this paper,we first give characterizations of weighted Besov spaces with variable exponents via Peetre’s maximal functions.Then we obtain decomposition characterizations of these spaces by atom,molecule and wavelet.As an application,we obtain the boundedness of the pseudo-differential operators on these spaces.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11571039,11671185,11471042 and 11701174)supported by the Construct Program of the Key Discipline in Hu’nan Province+1 种基金the Scientific Research Fund of Hu’nan Provincial Education Department(Grant No.17B159)the Scientific Research Foundation for Ph.D.Hu’nan Normal University(Grant No.531120-3257)
文摘This article is devoted to the study of variable 2-microlocal Besov-type and Triebel- Lizorkin-type spaces. These variable function spaces are defined via a Fourier-analytical approach. The authors then characterize these spaces by means of Q-transforms, Peetre maximal functions, smooth atoms, ball means of differences and approximations by analytic functions. As applications, some re- lated Sobolev-type embeddings and trace theorems of these spaces are Mso established. Moreover, some obtained results, such as characterizations via approximations by analytic functions, are new even for the classical variable Besov and Triebel-Lizorkin spaces.
文摘In this paper an asymptotic formula of Voronovskaja type for a multivariate extension of the Kantorovich generalized sampling series is given. Moreover a quantitative version in terms of some moduli of smoothness is established. Finally some particular examples of kernels are discussed, as the Bochner-Riesz kernel and the multivariate splines.
