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Journal of environmental sciences 2009年第12期21卷 1667-1672页

作者： ZHENG Weishuang, FEI Yingheng, HUANG Yi College of environmental sciences and Engineering, peking university, beijing 100871, china. College of environmental sciences and Engineering Peking University Beijing 100871 China

Fungi and their symbionts can alleviate heavy metal stress by exuding soluble proteins and enzymes. This study examined the role of soluble protein and acid phosphatase （APase） exuded by Xerocomus chrysenteron, an ectomycorrhizal fungus, and the seedlings of its symbiont, Chinese pine （Pinus tabulaeformis）, under conditions of excessive Cu and Cd. The growth type showed that this poorly studied ectomycorrhizal fungus was capable of tolerating high concentrations of Cu, and may be useful in phytoremediation. X. chrysenteron grew well at 80 mg/L Cu, and the EC50 for Cd was 17.82 mg/L. X. chrysenteron also showed enhanced exudation of soluble protein in both isolated and inoculated cultivations under the influence of Cu and Cd. Soluble protein exudation, however, differed under Cu and Cd stress in isolates. In mediums containing Cu, soluble protein exudation increased with concentration, but in mediums containing Cd the content of soluble protein increased to a comparable level at all concentrations. This study demonstrated that soluble protein was related to heavy metal tolerance, although the different ions played different roles. While APase activity in exudates of fungi and seedlings decreased under Cu and Cd stress in comparison to the control, the APase activity in seedlings was maintained by inoculation. Thus, X. chrysenteron facilitated the ability of plant to maintain a normal nutrient uptake, and therefore to protect it from heavy metal toxicity.

关键词： soluble protein acid phosphatase exudate Cu, Cd Xerocomus chrysenteron

On multiply of sections of line bundles on compact Riemann surfaces

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Science china Mathematics 2008年第4期51卷 721-727页

作者： TAN XiaoJiang LMAM and school of Mathematical sciences peking university beijing 100871 china LMAM and school of Mathematical sciences Peking University Beijing China

In this paper,we give some conditions on the surjective of multiply maps H^0(R,L)×H^0(R,K)→H^0(R,L(?)K).Here R is a compact Riemann surface,L a line bundle on R and K is the canonical line bundle.

关键词： compact Riemann surfaces line bundles 14E20 14F24

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,beijing 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 25000 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 25000—12000 a B.P.; runoff occurring during 12000—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 25000—12000 a B.P.; and the runoff occurring during 25000—12000 a B.P., 12000—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 25000 years are indicated by these comparisons.

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

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, china 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 2g × 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

Wavelets associated with Hankel transform and their Weyl transforms

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Science china Mathematics 2004年第3期47卷 393-400页

作者： PENG Lizhong MA Ruiqin LMAM, school of Mathematical sciences, peking university, beijing 100871, china LMAM School of Mathematical Sciences Peking University Beijing China

The Hankel transform is an important transform. In this paper, westudy the wavelets associated with the Hankel transform, thendefine the Weyl transform of the wavelets. We give criteria of itsboundedness and compactne... 详细信息

关键词： Bessel function, Hankel transform, wavelets, Weyltransform, boundedness, compactness.

Oblique derivative problem for general Chaplygin-Rassias equations

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Science china Mathematics 2008年第1期51卷 5-36页

作者： WEN GuoChun LMAM, school of Mathematical sciences, peking university, beijing 100871, china LMAM School of Mathematical Sciences Peking University Beijing China

The present paper deals with the oblique derivative problem for general second order equations of mixed (elliptic-hyperbolic) type with the nonsmooth parabolic degenerate line $$K_1 (y)u_{xx} + \left| {K_2 (x)} \right|u_{yy} + a(x,y)u_x + b(x,y)u_y + c(x,y)u = - d(x,y)$$ in any plane domain D with the boundary ?D=Γ ∪ L 1 ∪ L 2 ∪ L 3 ∪ L 4, where Γ(? {y > 0}) ∈ C μ 2 (0 4 are four characteristics with the slopes ?H 2(x)/H 1(y), H 2(x)/H 1(y),?H 2(x)/H 1(y),H 2(x)/H 1(y) (H 1(y) = √|K 1(y)|, H 2(x) = √|K 2(x)| in {y 4 , \operatorname{Im} \left[ {\overline {\lambda (z)} u_{\tilde z} } \right]\left| {_{z = z_l } } \right. = b_l ,l = 1,2, u( - 1) = b_0 ,u(1) = b_3 ,$$ in which z 1, z 2 are the intersection points of L 1, L 2, L 3, L 4 respectively. The above equations can be called the general Chaplygin-Rassias equations, which include the Chaplygin-Rassias equations $$K_1 (y)(M_2 (x)u_x )_x + M_1 (x)(K_2 (y)u_y )_y + r(x,y)u = f(x,y), in D$$ as their special case. The above boundary value problem includes the Tricomi problem of the Chaplygin equation: K(y)u xx+u yy = 0 with the boundary condition u(z) = ?(z) on Γ ∪ L 1 ∪ L 4 as a special case. Firstly some estimates and the existence of solutions of the corresponding boundary value problems for the degenerate elliptic and hyperbolic equations of second order are discussed. Secondly, the solvability of the Tricomi problem, the oblique derivative problem and Frankl problem for the general Chaplygin-Rassias equations are proved. The used method in this paper is different from those in other papers, because the new notations W(z) = W(x + iy) = $u_{\tilde z} $ = [H

关键词： oblique derivative problem equations of mixed type nonsmooth degenerate line 35J70 35L80 35N99

Global well-posedness for the 2D critical dissipative quasi-geostrophic equation

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Science china Mathematics 2007年第4期50卷 485-494页

作者： Zhi-fei ZHANG school of Mathematical sciences, peking university, beijing 100871, china school of Mathematical sciences Peking University Beijing China

We study the initial value problem for the 2D critical dissipative quasi-geostrophic equation. We prove the global existence for small data in the scale invariant Besov spaces ? p,1 2/p , 1 ? p ? ∞. In particular, for p = ∞, our result does not impose any regularity on the initial data. Our proofs are based on an exponential decay estimate of the semigroup $e^{{ - t\kappa ( - \Delta )}^{\alpha}} $ and the use of space-time Besov spaces.

关键词： quasi-geostrophic equation Besov space Littlewood-Paley decomposition well-posedness 35Q35

Fluxes of NH_3 and HNO_3 over heathland in the Netherlands:implications for chemical interactions

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Journal of environmental sciences 1997年第1期9卷 49-58页

作者： Zhang Yuanhang Center of environmental sciences,peking university,beijing 100871,china Center of environmental sciences Peking University Beijing 100871 China

The surface exchange of NH_3 and HNO_3 gases over heathland was measured with the aerodynamic gradient method in Leende,the Netherlands during April 25 and May 9,*** to reactions in the system NH_3,HNO_3 and NH_4NO_3,the NH_3 deposition flux is overestimated,while HNO_3 shows apparent emission fluxes mostly during the field *** reveal that NH_3 gradients are influenced slightly by HNO_3 and the HNO_3 gradients are strongly controlled by the NH_3.A clear relationship between NH_3 and HNO_3 gradient is suggested by the Leende experiment. Before the late afternoon,NH_3 deposition gradients will cause HNO_3 upward gradients,meanwhile the NH_3 gradients themselves will become *** the HNO_3 upward gradient reaches maxi- mum,the NH_3 deposition gradients will be enlarged or the emission gradients depressed,while the HNO_3 upward gradients become smaller.

关键词： dry deposition ammonia nitric acid equilibrium,fluxes.

REGULARITY OF SOLUTIONS TO THE DIRICHLET PROBLEM FOR DEGENERATE ELLIPTIC EQUATION

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Chinese Annals of Mathematics,Series B 2003年第4期24卷 529-540页

作者： CHEN YEMIN school of Mathematics, peking university, beijing 100871, china. school of Mathematics Peking University Beijing 100871 China

In this paper, the author studies the regularity of solutions to the Dirichlet problem forequation Lu = f, where L is a second order degenerate elliptic operator in divergence form inΩ, a bounded open subset of Rn (n... 详细信息

关键词： Regularity Dirichlet problem Degenerate Weighted spaces

Maslov-type index and brake orbits in nonlinear Hamiltonian systems

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Science china Mathematics 2007年第6期50卷 761-772页

作者： Duan-zhi ZHANG school of Mathematical sciences, peking university, beijing 100871, china school of Mathematical sciences Peking University Beijing China

In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian s... 详细信息

关键词： brake orbit Maslov-type index relative Morse index dual variational method 58E05 70H05 34C25