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Some New Results in Waring's Problem

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Acta Mathematica Sinica,English Series 1996年第3期12卷 262-267页

作者： Meng Zaizhao, department of Mathematics peking university beijing 100871 china department of Mathematics Peking University Beijing China

Let G(k) denote the smallest number s such that every sufficiently large natural number is the sum of, at most, s k-th powers of natural numbers. In this paper, we give new bounds for G(12), G(13) and G(19).

关键词： Waring’s problom Circle method Iterative method Difference

Steady motion and spiral patterns in typhoon

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Acta Oceanologica Sinica 1999年第4期18卷 495-504页

作者： Liu Shikuo Liang Fuming Liu Shida and Xin Guojun (department of geophysics, peking university, beijing 100871, china) department of geophysics Peking University Beijing 100871 China

By using the equations describing typhoons in the atmosphere, the steady three-dimensional stream fieldand the corresponding pressure and temperature fields are obtained. The three-dimensional velocity fields construct anonlinear autonomuos system in the physical space. It is shown that the center of typhoon is a local minimum pressurewith positive vertical vorticity and horizontal convergence in lower levels and a local maximum pressure with negativevertical vorticity and horizontal divergence in the upper levels. Because there exits two saddle-focus points in the autnomous system, there exist the spiral patterns, in which the winds blow spirally in and out of the center in the lowerand upper levels in the Northern Hemisphere and cause the ascending motion near the center and dascending motionnear the edge, respectively . All these are in fair conformity with the observations. It implies that the rotation of earthand the viscosity of air play an important role in the spiral structure of typhoons.

关键词： Typhoon steady motion spiral pattern

Experimental measurement of growth patterns on fossil corals:Secular variation in ancient Earth-Sun distances

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Chinese Science Bulletin 2010年第35期55卷 4010-4017页

作者： ZHANG WeiJia1,3,4,LI ZhengBin2,3 & LEI Yang1 1 department of Physics,peking university,beijing 100871,china 2.department of Electrical Engineering and Computer Science,peking university,beijing 100871,china 3 State Key Laboratory of Advanced Optical Communication Systems & Networks,peking university,beijing 100871,china 4 Committee of Yuanpei Honors Program,peking university,beijing 100871,china department of Physics Peking University Beijing 100871 China State Key Laboratory of Advanced Optical Communication Systems & Networks Peking University Beijing 100871 China Committee of Yuanpei Honors Program Peking University Beijing 100871 China department of Electrical Engineering and Computer Science Peking University Beijing 100871 China

In recent years,much attention has been given to the increase in the Earth-Sun distance,with the modern rate reported as 5-15 m/cy on the basis of astronomical ***,traditional methods cannot measure the ancient leaving rates,so a myriad of research attempting to provide explanations were met with unmatched *** this paper we consider that the growth patterns on fossils could reflect the ancient Earth-Sun *** mechanical analysis of both the Earth-Sun and Earth-Moon systems,these patterns confirmed an increase in the Earth-Sun *** a large number of well-preserved specimens and new technology available,both the modern and ancient leaving rates could be measured with high precision,and it was found that the Earth has been leaving the Sun over the past 0.53 billion *** Earth's semi-major axis was 146 million kilometers at the beginning of the Phanerozoic Eon,equating to 97.6% of its current *** modern leaving rates are 5-14 m/cy,whereas the ancient rates were much *** results indicate a special expansion with an average expansion coefficient of 0.57H0 and deceleration in the form of Hubble *** the basis of experimental results,the Earth's semi-major axis could be represented by a simple formula that matches fossil measurements.

关键词：地球太阳古代距离生长模式实验石珊瑚量化

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, beijing 100871, 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., 25.9%/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 Essential Self-Adjointness of Pseudodifferential Operators

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Acta Mathematica Sinica,English Series 1994年第1期10卷 72-79页

作者： Fan Qihong department of Mathematics peking university beijing,100871 china 1. department of Mathematics Peking University 100871 Beijing China

In this paper we investigate the self-adjointness for a kind of pseudodifferential operators,which include the nonsemi-bounded Schr（o|¨）dinger operator,-△+v（x）,v（x）→-∞, as |x|→∞,and the relativistic correc... 详细信息

关键词： On the Essential Self-Adjointness of Pseudodifferential Operators

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 beijing,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=2n1, 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

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 beijing, 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>1 such that T（k1r, f）≤k2T（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

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 beijing, 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

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