In order to quantitatively analyze air traffic operation complexity,multidimensional metrics were selected based on the operational characteristics of traffic flow.The kernel principal component analysis method was ut...In order to quantitatively analyze air traffic operation complexity,multidimensional metrics were selected based on the operational characteristics of traffic flow.The kernel principal component analysis method was utilized to reduce the dimensionality of metrics,therefore to extract crucial information in the metrics.The hierarchical clustering method was used to analyze the complexity of different airspace.Fourteen sectors of Guangzhou Area Control Center were taken as samples.The operation complexity of traffic situation in each sector was calculated based on real flight radar data.Clustering analysis verified the feasibility and rationality of the method,and provided a reference for airspace operation and management.展开更多
In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,...In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.展开更多
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 article, some proper ties of complex Wiener-Ito multiple integrals and complex Ornstein-Uhlenbeck opera tors and semigroups are obtained. Those include Stroock's formula, Hu-Meyer formula, Clark-Ocone form...In this article, some proper ties of complex Wiener-Ito multiple integrals and complex Ornstein-Uhlenbeck opera tors and semigroups are obtained. Those include Stroock's formula, Hu-Meyer formula, Clark-Ocone formula, and the hypercontractivity of complex Ornstein-Uhlenbeck semigroups. As an application, several expansions of the fourth moments of complex Wiener-Ito multiple integrals are given.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
In the present article, we deal with the so-called overconvergence phenomenon in C of a slightly modified Post-Widder operator of real variable, that is with the extension of its approximation properties from the real...In the present article, we deal with the so-called overconvergence phenomenon in C of a slightly modified Post-Widder operator of real variable, that is with the extension of its approximation properties from the real axis in the complex plane.In this sense, error estimates in approximation and a quantitative Voronovskaya-type asymptotic formula are established.展开更多
The Meyer-König and Zeller operator is one of the most challenging operators. Sometimes the study of its properties will rely on the weighted approximation by Baskakov operator. In this paper, this relation i...The Meyer-König and Zeller operator is one of the most challenging operators. Sometimes the study of its properties will rely on the weighted approximation by Baskakov operator. In this paper, this relation is extended to complex space;the quantitative estimates and the Voronovskaja type results for analytic functions by complex Meyer-König and Zeller operators were obtained.展开更多
Given f being Holder continuous in a region GC. For the Cauchy principal integral where G is a smooth closed contour,lt is established that,if a sequence or smooth closed contours G(n ∈N ) smoothly convergent top,the...Given f being Holder continuous in a region GC. For the Cauchy principal integral where G is a smooth closed contour,lt is established that,if a sequence or smooth closed contours G(n ∈N ) smoothly convergent top,then the corresponding sequence I(Γm,f)is convergent to I (,f). Furthermore,when Γ is approximated by a sequence of complex cubic splines(Γ)interpolatory to Γ,the error is estimated.展开更多
基金co-supported by the National Natural Science Foundation of China(No.61304190)the Fundamental Research Funds for the Central Universities of China(No.NJ20150030)the Youth Science and Technology Innovation Fund(No.NS2014067)
文摘In order to quantitatively analyze air traffic operation complexity,multidimensional metrics were selected based on the operational characteristics of traffic flow.The kernel principal component analysis method was utilized to reduce the dimensionality of metrics,therefore to extract crucial information in the metrics.The hierarchical clustering method was used to analyze the complexity of different airspace.Fourteen sectors of Guangzhou Area Control Center were taken as samples.The operation complexity of traffic situation in each sector was calculated based on real flight radar data.Clustering analysis verified the feasibility and rationality of the method,and provided a reference for airspace operation and management.
基金supported by the Natural Science Foundation of Guangdong Province(2021A1515010058)。
文摘In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.
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.
基金Supported by NSFC(11871079)NSFC (11731009)Center for Statistical Science,PKU
文摘In this article, some proper ties of complex Wiener-Ito multiple integrals and complex Ornstein-Uhlenbeck opera tors and semigroups are obtained. Those include Stroock's formula, Hu-Meyer formula, Clark-Ocone formula, and the hypercontractivity of complex Ornstein-Uhlenbeck semigroups. As an application, several expansions of the fourth moments of complex Wiener-Ito multiple integrals are given.
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,∞).
文摘In the present article, we deal with the so-called overconvergence phenomenon in C of a slightly modified Post-Widder operator of real variable, that is with the extension of its approximation properties from the real axis in the complex plane.In this sense, error estimates in approximation and a quantitative Voronovskaya-type asymptotic formula are established.
基金NSF of China (11571089, 11871191) NSF of Hebei Province (2012205028+1 种基金 ZD2019053) Science foundation of Hebei Normal University
文摘The Meyer-König and Zeller operator is one of the most challenging operators. Sometimes the study of its properties will rely on the weighted approximation by Baskakov operator. In this paper, this relation is extended to complex space;the quantitative estimates and the Voronovskaja type results for analytic functions by complex Meyer-König and Zeller operators were obtained.
文摘Given f being Holder continuous in a region GC. For the Cauchy principal integral where G is a smooth closed contour,lt is established that,if a sequence or smooth closed contours G(n ∈N ) smoothly convergent top,then the corresponding sequence I(Γm,f)is convergent to I (,f). Furthermore,when Γ is approximated by a sequence of complex cubic splines(Γ)interpolatory to Γ,the error is estimated.
基金partially supported by the CRC TRR 191:“Symplectic Structures in Geometry,Algebra and Dynamics”partially supported by Taiwan Ministry of Science of Technology project(Grant No.104-2628-M-001-003-MY2)+1 种基金the Golden-Jade fellowship of Kenda Foundationsupported by National Natural Science Foundation of China(Grant No.11501422)
文摘In this paper, we give an explicit formula for the Szego kernel for (0, q) forms on the Heisenberg group Hn+1.