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On the Multiplier Conjecture

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Acta Mathematica Sinica,English Series 1994年第1期10卷 49-58页

作者： Qiu Weisheng department of Mathematics peking university {2.,100871 china 1. department of Mathematics Peking University 100871 Beijing China

The Multiplier Theorem is a celebrated theorem in the Design *** condition p>λis crucial to all known proofs of the multiplier *** in all known examples of difference sets μp is a multiplier for every prime p with（p,v）=1 and *** there is the multiplier conjecture:"The multiplier theorem holds without the assumption that p> λ."The general form of the multiplier theorem may be viewed as an attempt to partially resolve the multiplier conjecture,where the assumption"p>λ"is replaced by "n1>λ".Since then Newman（1963）,Turyn（1964）,and McFarland（1970）attempted to partially resolve the multiplier conjecture（see[7],[8],[9]）.This paper will prove the following result using the representation theory of finite groups and the algebraic number theory:Let G be an abelian group of order v,v0 be the exponent of G,and D be a（v, k,λ）-difference set in *** n=2.1, then the general form of the multiplier theorem holds without the assumption that n1>λin any of the following cases: （1）2.n1; （2.2.×n1,and（v,7）=1; （3） 2.×n1,7|v,and t≡1 or 2.or 4（mod 7）.

关键词： On the Multiplier Conjecture Math

Excessive Cu and Zn affecting on distribution of the metals and activities of glycolytic and nitrogen incorporating key enzymes in mycelia of ectomycorrhizal fungi Suillus bovinus

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Journal of Environmental Sciences 2001年第3期13卷 337-341页

作者： HUANG Yi, TAO Shu(department of Urban and Environmental Sciences, peking university,{2., china. department of Urban and Environmental Sciences Peking University Beijing 100871 China. yhuang@***

Concentration of copper and zinc in isolated Suillus bovinus mycelia, used nutrient solution and 0.5 mol/L EDTA mycelia washing solution were measured to investigate the distribution of heavy metals in mycelia growth in excess copper or zinc nutrient solution. Treated with zinc, most of added zinc maintained in used solution, and 9.8%/14.6% was in/on mycelia in treatment, and in treatment 2.was 3.9%/8.0% in/on mycelia. In the copper applications, copper stimulated in more than on mycelia, i.e., 2..9%/4.5% in/on mycelia in treatment, and 7%/18.8% in/on mycelia while most of copper retained in used nutrient solution. Certain amount of copper or zinc uptake by mycelia led to pronounced influence on glycolysis and nitrogen incorporating process of Suillus bovinus, while the tested enzymes kept constant in treatment. In crude extracts of copper treatment 2.mycelia, activities of HK, PFK and GS were inhibited and decrease to 63%, 48% and 38% and GIDH increased by 68% of the control, respectively. The behaviors of these tested enzymes toward zinc corresponded in general with that towards copper. The potential protection of Suillus bovinus for its host plant under excess copper or zinc threaten was discussed.

关键词： Suillus bovinus ectomycorrhizal fungous copper zinc glycolysis nitrogen incorporate enzymes

On the Linear Representations of Circle Expanding Maps

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Acta Mathematica Sinica,English Series 1994年第2期10卷 202-208页

作者： Cui Guizhen department of Mathematics peking university {2., 100871 china 1. department of Mathematics Peking University 100871 Beijing China

In this paper, it is proved that the two real analytic expanding endomorphisms of the unit circle are equivalent if and only if they have equal eigenvalues along corresponding cycles. A sufficient and necessary condit... 详细信息

关键词： Expand maps Circles representations Real number If and only if Equivalent Unit circle Corresponding

Some Results on Entire Functions of Finite Lower Order

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Acta Mathematica Sinica,English Series 1994年第2期10卷 168-178页

作者： Wu Shengjian department of Mathematics peking university {2., 100871 china 1. department of Mathematics Peking University 100871 Beijing China

Let f（z） be an entire function of order λ and of finite lower order μ. If the zeros of f（z） accumulate in the vicinity of a finite number of rays, then （a） λ is finite; （b） for every arbitrary number k1>1, there exists k2./sub>>1 such that T（k1r, f）≤k2./sub>T（r, f） for all r≥r0. Applying the above results, we prove that if f（z） is extremal for Yang’s inequality p=g/2. then （c） every deficient value of f（z） is also its asymptotic value; （d） every asymptotic value of f（z） is also its deficient value; （e） λ=μ; （f） ∑a≠∞δ5（a, f）≤1-k（μ）.

关键词： Some Results on Entire Functions of Finite Lower Order

Palaeorunoff estimations achieved from palaeoclimatic information for the southwest part of the North china Plain: an attempt to apply a climatological approach to palaeohydrology

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Journal of Environmental Sciences 2000年第3期12卷 330-336页

作者： WANG Hong\|ya, XIE Qiang (department of Urban and Environmental Sciences, peking university,{2. 100871, china) 北京大学北京 1 0 0 871

Palaeoclimatic scenario projecting annual temperature and annual precipitation is firstly formalized with data available and speculations for the southwest part of the North china Plain (35— 37°N, 115—119°E) during the last 2.000 years. Then, with three regression equations relating annual runoff to annual precipitation and derived with data of modern hydrological and meteorological records, values of annual runoff are calculated in terms of the corresponding values of annual precipitation from this palaeoclimatic scenario for this region during this temporal interval. These results indicate that runoff is the most during 8000—3000 a B.P. and the least during 2.000—12.00 a B.P.; runoff occurring during 12.00—8000 a B.P. and during 3000—0 a B.P. is less than the one occurring during 8000—3000 a B.P. and more than the one occurring during 2.000—12.00 a B.P.; and the runoff occurring during 2.000—12.00 a B.P., 12.00—8000 a B.P., and 3000—0 a B.P. is respectively 43, 46 and 66 percent of the one occurring during 8000—3000 a B.P. Values of bankfull discharge for palaeochannels of the Yellow River flowing in this region during the same interval are calculated from available estimates of slope of stream bed of these palaeochannels with a regression equation relating bankfull discharge to slope of stream bed and ratios of bankfull discharge are further calculated from these values for different groups of palaeochannel formed during different time spans embraced in this interval. To conduct a cross check, these values and ratios of bankfull discharge are compared to the corresponding values and ratios of runoff occurring during roughly the same time spans. The same direction and similar relative magnitude of changes of the surface water occurring in this region during the last 2.000 years are indicated by these comparisons.

关键词： palaeorunoff the southwest part of the North china Plain palaeoclimate

|m| Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

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Science china(Physics,Mechanics & Astronomy) 2004年第6期47卷 676-684页

作者： WANG Jing & ZENG Jinyan department of Physics,Tsinghua university,{2. 100084,china School of Physics,peking university,{2. 100871,china department of Physics Tsinghua University Beijing 100084 China School of Physics Peking University Beijing 100871 China

The symmetry and |m| partial-wave analysis for two-dimensional (2.) Coulomb-scattering is investigated. As a function of energyE, the |m| partial-wave scattering amplitudef |m|(θ) is analytically continuated to the, negativeE (complexk) plane, and it is found that the bound state energy eigenvalues (E<0) are just located at the poles off |m|(θ) on the positive imaginaryk axis as is expected. In addition, as a function of |m|,f |m|(θ) is analytically continuated to the complex |m| plane, the bound state energy eigenvalues are just located at the poles off |m|(θ) on the positive real |m| axis.

关键词： two-dimensional Coulomb scattering, |m| partial-wave, Regge pole.

BRILL-NOETHER MATRIX FOR RANK TWO VECTOR BUNDLES

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chinese Annals of Mathematics,Series B 2002年第4期23卷 531-538页

作者： TAN XIAOJIANGSchool of Mathematical Sciences, peking university, beijing 100871,{2.a School of Mathematical Sciences Peking University Beijing 100871 China

Let X be an arbitrary smooth irreducible complex projective curve, E (?)X a rank two vector bundle generated by its sections. The author first represents ?as a triple {D1,D2.f}, where D1 , D2.are two effective divisors with d = deg(D1) + deg(D2., and f ∈ H?X, [D1] |D2. is a. collection of polynomials. E is the extension of [D2. by [D1] which is determined by f. By using / and the Brill-Noether matrix of D1+D2. the author constructs a 2. × d matrix WE whose zero space gives Im{H0(X,[D1]) (?) H0(X, [D1] |D1)}(?) Im{H?X, E) (?) H0(X,[D2.) (?) H0(X, [D2.|D2.} From this and H0(X,E) = H0(X,[D1]) (?)Im{H0(X,E) (?) H0(X, [D2.)}, it is got in particular that dimH0(X, E) = deg(E) - rank(WE) + 2.

关键词： Brill-Noether matrix Vector bundle Effective divisor

The study of two-color excitation upconversion of Pr(0.5)Yb(3):ZBLAN

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Science china(Physics,Mechanics & Astronomy) 2006年第2期49卷 169-177页

作者： CHEN Xiaobo1 & SONG Zengfu2.1. Applied Optics beijing Area Major Laboratory, Analysis and testing center, beijing Normal {2., beijing 100875, china 2. peking university, Physics School, beijing 100871, china Applied Optics beijing Area Major Laboratory Analysis testing center Beijing Normal University Beijing 100875 China Physics School Peking University Beijing 100871 China

The excited state absorption upconversion of Pr(0.5)Yb(3):ZBLAN glass material, under two-color excitation of the 960 nm semiconductor laser and the Xe lamp light simultaneously, is reported in this article. It was found that the upconversion emission spectra of 480.1, 519.0, 601.9 and 631.8 nm coincide with the common emission spectra. Meanwhile, the upconversion-excitation spectrum has three obvious peaks under two-color excitation, and they respectively correspond to the 856.0 nm upconversion ex-citation transition [1G4(Pr3+)→1I6(Pr3+) and 1G4(Pr3+)→3P1(Pr3+)], the 789.0 nm upconver-sion excitation transition 1G4(Pr3+)→3P2.Pr3+), and the 803.7 nm upconversion excitation transition 3H6(Pr3+)→1D2.Pr3+). The upconversion excitation transition 1G4(Pr3+)→1I6(Pr3+) is strong because its oscillator strength f = 2..040×10?6 is large, which results in a large peak appearing in the upconversion excitation spectrum. That is just the new interesting two-color excitation upconversion luminescence phenomenon of Pr(0.5)Yb(3):ZBLAN induced by one laser and one continuous normal light simultaneously.

关键词： upconversion volumetric three-dimensional display two-color excitation.

AutoProc: An automatic proactive replication scheme for P2. storage

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Science china(Information Sciences) 2011年第6期54卷 1151-1160页

作者： YANG Zhi & DAI YaFei Computer Science department, peking university,{2., china 1. Computer Science department Peking University Beijing 100871 China

Due to the prevalence of peer departures, P2. storage systems need to constantly generate replicas for high durability. However, few existing systems are able to select the right replication rate that balances replication cost and durability, e.g., minimizing replication cost without threatening the durability target. In this paper, we propose a method called AutoProc to automate the replication process in P2. storage systems. AutoProc employs two key techniques to enable cost-effective replication: correctly adapting replication rate with a reliability model, and replicating objects at the right order with a reliability indicator. Extensive simulations based on the real system failure trace show that AutoProc achieves the near-optimal performance.

关键词： P2. storage churn durability fault tolerance proactive replication resource usage