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The Coefficient Inequalities for a Class of Holomorphic Mappings in Several Complex Variables

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Chinese Annals of Mathematics,Series B 2020年第1期41卷 37-48页

作者： qinghua xu Taishun LIU Xiaosong LIU School of Science Zhejiang University of Science and TechnologyHangzhou 310023China Department of Mathematics Huzhou Teacher’s UniversityHuzhou 313000ZhejiangChina School of Mathematics and Computation Science Lingnan Normal UniversityZhanjiang 524048GuangdongChina

The authors establish the coefficient inequalities for a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in C^n,which are natural extensions to higher dimensions of som... 详细信息

关键词： Coefficient inequality Fekete-Szego problem Quasi-convex mappings

Highly sensitive and selective two-photon sensing of cartap using Au@Ag core-shell nanoparticles

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Science China Chemistry 2016年第1期59卷 78-82页

作者： Peiyan Yuan Rizhao Ma qinghua xu Department of Chemistry National University of Singapore

A highly sensitive and selective two-photon sensing scheme for detection of cartap was developed by using Au@Ag bimetallic core-shell *** was found to induce the aggregation of Au@Ag nanoparticles and up to 700-fold enhancement in two-photon *** enhancement in two-photon photoluminescence allows achieving a detection limit of as low as 0.0062 mg/kg,which is better than the conventional colorimetric *** two-photon sensing scheme has a broad dynamic range and displays excellent selectivity in detection of cartap against over other ten kinds of commonly used insecticides.

关键词： metal nanoparticles bio-sensing two-photon excitation plasmon resonance photoluminescence cartap

Sharp distortion theorems for a subclass of close-to-convex mappings

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Frontiers of Mathematics in China 2013年第6期8卷 1425-1436页

作者： qinghua xu Taishun LIU Xiaosong LIU College of Mathematics and Information Science Jiangxi Normal University Nanchang 330022 China Department of Mathematics Huzhou Teachers College Huzhou 313000 China School of Mathematics and Computation Science Zhanjiang Normal University Zhanjiang 524048 China

We introduce the class of strongly close-to-convex mappings of order c~ in the unit ball of a complex Banach space, and then, we give the sharp distortion theorems for this class of mappings in the unit ball of a complex Hilbert space X or the unit polydisc in Cn. As an application, a sharp growth theorem for strongly close-to-convex mappings of order α is obtained.

关键词： Distortion theorem growth theorem strongly close-to-convexmappings of order α

Fekete and Szeg problem in one and higher dimensions

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Science China Mathematics 2018年第10期61卷 1775-1788页

作者： qinghua xu Taishun Liu Xiaosong Liu School of Science Zhejiang University of Science and Technology Hangzhou 310023 China Department of Mathematics Huzhou University Huzhou 313000 China School of Mathematics and Computation Science Lingnan Normal University Zhanjiang 524048 China

In this paper, we establish the Fekete and Szego inequality for a class of holomorphic functions in the unit disk, and then we extend this result to a class of holomorphic mappings on the unit ball in a complex Banach... 详细信息

关键词： Fekete and Szego problem Bieberbach conjectures in several complex variables subclasses ofstarlike mappings sharp coefficient bound

Fekete and Szego problem for a subclass of quasi-convex mappings in several complex variables

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Frontiers of Mathematics in China 2015年第6期10卷 1461-1472页

作者： qinghua xu Ting YANG Taishun LIU Huiming xu College of Mathematics and Information Science Jiangxi Normal University Nanchang 330022 China Department of Mathematics Huzhou University Huzhou 313000 China College of Mathematics Physics and Information Engineering Zhejiang Normal UniversityJinhua 321004 China

Let K be the familiar class of normalized convex functions in the unit disk. Keogh and Merkes proved the well-known result that maxf∈A ｜a3 - λa22｜ ≤ max{1/3, ｜λ - 1}, ,λ ∈ C, and the estimate is sharp for each ∈. We investigate the corresponding problem for a subclass of quasi-convex mappings of type B defined on the unit ball in a complex Banach space or on the unit polydisk in Cn. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.

关键词： Fekete-Szego problem quasi-convex mappings of type A quasi-convex mappings of type B quasi-convex mappings of type C

A proof of a weak version of the Bieberbach conjecture in several complex variables

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Science China Mathematics 2015年第12期58卷 2531-2540页

作者： LIU XiaoSong LIU TaiShun xu qinghua School of Mathematics and Computation Science Lingnan Normal University Department of Mathematics Huzhou Teachers College College of Mathematics and Information Science Jiangxi Normal University

In this paper, the sharp estimates of all homogeneous expansions for a subclass of starlike mappings on the unit ball in complex Banach spaces are first established. Meanwhile, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in Cnare also obtained. Our results show that a weak version of the Bieberbach conjecture in several complex variables is proved, and the obtained conclusions reduce to the classical results in one complex variable.

关键词： Bieberbach conjecture homogeneous expansion k-fold symmetric mapping a zero of order k + 1 starlike mapping

ON REFINEMENT OF THE COEFFICIENT INEQUALITIES FOR A SUBCLASS OF QUASI-CONVEX MAPPINGS IN SEVERAL COMPLEX VARIABLES

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Acta Mathematica Scientia 2020年第6期40卷 1653-1665页

作者： qinghua xu Yuanping LAI School of Science Zhejiang University of Science and TechnologyHangzhou 310023China

Let K be the familiar class of normalized convex functions in the unit ***[14],Keogh and Merkes proved that for a function f(z)=z+∑k=2∞a k z k in the class K,|a 3−λa 22|≤max{13,|λ−1|},λ∈*** above estimate is sharp for eachλ.In this article,we establish the corresponding inequality for a normalized convex function f on U such that z=0 is a zero of order k+1 of f(z)−z,and then we extend this result to higher *** results generalize some known results.

关键词： Fekete-Szegö problem subclass of quasi-convex mappings sharp coefficient bound

Accurate and robust estimation of phase error and its uncertainty of 50 GHz bandwidth sampling circuit

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Science in China(Series F) 2007年第6期50卷 905-914页

作者： ZHANG Zhe LIN MaoLiu xu qinghua TAN JiuBin Department of Electronics and Communication Harbin Institute of Technology Harbin 150001 China

This paper discusses the dependence of the phase error on the 50 GHz bandwidth oscilloscope＇s sampling circuitry. We give the definition of the phase error as the difference between the impulse responses of the NTN （nose-to-nose） estimate and the true response of the sampling circuit. We develop a method to predict the NTN phase response arising from the internal sampling circuitry of the oscilloscope. For the default sampling-circuit configuration that we examine, our phase error is approximately 7.03° at 50 GHz. We study the sensitivity of the oscilloscope＇s phase response to parametric changes in sampling-circuit component values. We develop procedures to quantify the sensitivity of the phase error to each component and to a combination of components that depend on the fractional uncertainty in each of the model parameters as the same value, ±10%. We predict the upper and lower bounds of phase error, that is, we vary all of the circuit parameters simultaneously in such a way as to increase the phase error, and then vary all of the circuit pa- rameters to decrease the phase error. Based on Type B evaluation, this method qualifies the impresses of all parameters of the sampling circuit and gives the value of standard uncertainty, 1.34°. This result is developed at the first time and has important practical uses. It can be used for phase calibration in the 50 GHz bandwidth large signal network analyzers （LSNAs）.

关键词： uncertainty phase error sampling oscilloscope

Selective enriching of trionic emission in a WS2-ZnO hybrid through type-Ⅱ band alignment

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Science China(Information Sciences) 2023年第6期66卷 63-70页

作者： Jin Feng LEONG Kim Yong LIM Xiao WU qinghua xu Chorng Haur SOW Eng Tuan POH Department of Physics National University of Singapore Department of Chemistry National University of Singapore

Strategies to modulate the exciton dynamics in ultrathin two-dimensional(2D)semiconductors have always been an integral component in the bid towards improved optoelectronics and quantum photonic devices. The capability to non-destructively tune the relaxation dynamics, valley polarization, binding energies, and population ratio of various excitonic species has been well-sought for advanced *** the rationale design of a WS2-ZnO hybrid platform, we present a distinct increment in the trion-toexciton ratio for WS2emission across a patterned heterostructure. The shift in dominant excitonic species arose due to the efficient charge segregation at the spatially confined interface of the type-Ⅱ *** to the charge transfer process, the resultant emission profile presents up to four times amplification in the trion-to-exciton ratio, with temperature variable trion binding energies up to 59 meV. Since trions possess non-zero charge and spin degrees of freedom, the provision of a higher density of trions with increased binding stability would encourage new opportunities for reproducible optoelectronics and quantum emitters.

关键词： heterostructure trions type-II band alignment