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Mean Value on the Difference Between a Quadratic Residue and Its Inverse Modulo p

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Acta Mathematica Sinica,English Series 2007年第5期23卷 915-924页

作者： Hua Ning liu wen Peng zhang Department of Mathematics Northwest University Xi'an 710069 P. R. China

The main purpose of this paper is to use the generalized Bernoulli numbers, Gauss sums and the mean value theorems of Dirichlet L-functions between a quadratic residue and its inverse modulo p value formula. to study ... 详细信息

关键词： An integer and its inverse Bernoulli numbers Cochrane sums

General Kloosterman Sums and the Difference Between an Integer and Its Inverse Modulo Q

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Acta Mathematica Sinica,English Series 2007年第1期23卷 77-82页

作者： Hua Ning liu wen Peng zhang Department of Mathematics Northwest University Xi'an 710069 P. R. China

The main purpose of this paper is to use the generalized Bernoulli numbers, Gauss sums and the mean value theorems of Dirichlet L-functions to study the asymptotic property of one class of number-theoretic functions, ... 详细信息

关键词： An integer and its inverse Bernoulli numbers Gauss sums

Principal Quasi-Baerness of Formal Power Series Rings

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Acta Mathematica Sinica,English Series 2010年第11期26卷 2231-2238页

作者： Zhong Kui liu wen Hui zhang Department of Mathematics Northwest Normal University Lanzhou 730070 P. R. China

Let R be a ring. We consider left （or right） principal quasi-Baerness of the left skew formal power series ring R[[x;α]] over R where a is a ring automorphism of R. We give a necessary and sufficient condition under which the ring R[[x; α]] is left （or right） principally quasi-Baer. As an application we show that R[[x]] is left principally quasi-Baer if and only if R is left principally quasi- Baer and the left annihilator of the left ideal generated by any countable family of idempotents in R is generated by an idempotent.

关键词： Left principally quasi-Baer ring skew power series ring right semicentral idempotent

On a Problem of D. H. Lehmer

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Acta Mathematica Sinica,English Series 2006年第1期22卷 61-68页

作者： Hua Ning liu wen Peng zhang Department of Mathematics Northwest University Xi'an Shaanxi 710069 P R China

The main purpose of this paper is to use the Fourier expansion for character sums and the mean value theorem of Dirichlet L-functions to study the asymptotic property of the difference between a D. H. Lehmer number an... 详细信息

关键词： Lehmer problem Error term Mean square value formula

A Parallel Quantum Algorithm for the Satisfiability Problem

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Communications in Theoretical Physics 2008年第3期49卷 629-630页

作者： liu wen-zhang zhang Jing-Fu LONG Gui-Lu Key Laboratory for Atomic and Molecular NanoSciences and Department of Physics Tsinghua University Beijing 100084 China Tsinghua National Laboratory for Information Science and Technology Beijing 100084 China

In this paper we present a classical parallel quantum algorithm for the satisfiability problem. We have exploited the classical parallelism of quantum algorithms developed in [G.L. Long and L. Xiao, Phys. Rev. A 69 （2004） 052303], so that additional acceleration can be gained by using classical parallelism. The quantum algorithm first estimates the number of solutions using the quantum counting algorithm, and then by using the quantum searching algorithm, the explicit solutions are found.

关键词： satisfiability problem quantum search algorithm long algorithm

Decoupling Bang-Bang Group for Adiabatic Decoherence Control in a Three-Level Atom

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Communications in Theoretical Physics 2005年第5X期44卷 810-814页

作者： liu Xiao-Shu WU Re-Bing liu Yang liu wen-zhang LONG Gui-Lu Key Laboratory for Quantum Information and Measurements and Department of Physics Tsinghua University Beijing 100084 China Department of Automation Tsinghua University Beijing 100084 China Key Laboratory for Atomic and Molecular Nano-sciences Tsinghua University Beijing 100084 China

In this paper, we study the control problem of adiabatic decoherence in a three-level atom. We will find the decoupling bang-bang group for various configurations, including the V configuration and the cascade type of three-levelatom subjected to adiabatic decoherence. We also give the programs to design a sequence of periodic twinborn pulses to suppress the decoherence.

关键词： decoupling bang-bang group three-level atom adiabatic decoherence

Several Remarks on Ball-Coverings of Normed Spaces

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Acta Mathematica Sinica,English Series 2010年第9期26卷 1667-1672页

作者： Li Xin CHENG Zheng Hua LUO Xue Fang liu wen zhang Department of Mathematics Xiamen University Xiamen 361005 P. R. China

This paper presents two counterexamples about ball-coverings of Banach spaces and shows a new characterization of uniformly non-square Banach spaces via ball-coverings.

关键词： Uniformly non-square ball-covering Banach space

Distribution and Estimation of Aboveground Biomass of Alpine Shrubs along an Altitudinal Gradient in a Small Watershed of the Qilian Mountains, China

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Journal of Mountain Science 2015年第4期12卷 961-971页

作者： liu zhang-wen CHEN Ren-sheng SONG Yao-xuan HAN Chun-tan Qilian Alpine Ecology & Hydrology Research Station Key Laboratory of Ecohydrology of Inland Basin Cold and Arid Regions Environmental and Engineering Research Institute Chinese Academy of Sciences University of Chinese Academy of Sciences

Shrublands serve as an important component of terrestrial ecosystems, and play an important role in structure and functions of alpine *** estimation of biomass is critical to examination of the productivity of alpine ecosystems, due to shrubification under climate change in past *** this study, 14 experimental plots and 42 quadrates of the shrubs Potentilla fruticosa and Caragana jubata were selected along altitudes gradients from 3220 to 3650 m a.s.l.(above sea level) on semi-sunny and semi-shady slope in Hulu watershed of Qilian Mountains, *** foliage, woody component and total aboveground biomass per quadrate were examined using a selective destructive method, then the biomass were estimated via allometric equations based on measured parameters for two shrub *** results showed that *** accounted for 1–3 times more biomass(480.98 g/m2) than ***(191.21 g/m2).The aboveground biomass of both the shrubs varied significantly with altitudinal gradient(P<0.05).Woody component accounted for the larger proportion than foliage component in the total aboveground *** biomass on semi-sunnyslopes(200.27 g/m2 and 509.07 g/m2) was greater than on semi-shady slopes(182.14 g/m2 and 452.89g/m2) at the same altitude band for *** and *** contrast, the foliage biomass on semi-shady slopes(30.50 g/m2) was greater than on semi-sunny slopes(27.51 g/m2) for two *** deceased with increasing altitude for ***, whereas *** showed a hump-shaped pattern with *** equations were obtained from the easily descriptive parameters of height(H), basal diameter(D) and crown area(C) for biomass of *** and *** the equations type and variables comprising of the best model varied among the species, all equations related to biomass were significant(P < 0.005), with determination coefficients(R2) ranging from 0.81 to *** allometric equations satisfied the requirements of t

关键词： Aboveground biomass Allometric equations Alpine shrub Altitudinal gradient Qilian Mountains

Aboveground Biomass and Water Storage Allocation in Alpine Willow Shrubs in the Qilian Mountains in China

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Journal of Mountain Science 2015年第1期12卷 207-217页

作者： liu zhang-wen CHEN Ren-sheng SONG Yao-xuan HAN Chun-tan Qilian Alpine Ecology & Hrdrolody Research Station Key Laboratory of Ecohydrology of Inland River Basin Cold and Arid Regions Environmental and Engineering Research Institute Chinese Academy of Sciences

The aboveground biomass allocation and water relations in alpine shrubs can provide useful information on analyzing their ecological and hydrological functions in alpine regions. The objectives of this study were to compare the aboveground biomass allocation, water storage ratio and distribution between foliage/woody components,and to investigate factors affecting aboveground biomass allocation and water storage ratio in alpine willow shrubs in the Qilian Mountains, China. Three experimental sites were selected along distance gradients from the riverside in the Hulu watershed in the Qilian Mountains. The foliage, woody component biomass, and water allocation of Salix cupularis *** Salix oritrepha Schneid. shrubs were measured using the selective destructive method. The results indicated that the foliage component had higher relative water and biomass storage than the woody component in the upper part of the crown in individual shrubs. However, the woody component was the major biomass and water storage component in the whole shrub level for S. cupularis and ***. Moreover, the foliage/woody component biomass ratio decreased from the top to the basal level of shrubs. The relative water storage allocation was significantly affected by species types, but was not affected by sites and interaction between species and sites. Meanwhile, relative water storage was affectedby sites as well as by interaction between sites and species type.

关键词： Water storage Aboveground biomass Alpine shrubs Willow Qilian Mountains