Number of ℬ -free numbers in short intervals

The ℬ-free number is a generalization of the well-known squarefree numbers. The result that if θ > 33/80, then the interval [x-x^θ,x] must contain a B-free number for largex has been proved.     

A generalized funk’s section theorem for measures

If L is a star body in R~n whose central(n-i)-slices have the same(n-i)-dimensional measure μ_(n-i)(with appropriate density)as the central(n-i)-slices of an origin-symmetric star body K,then the corresponding n-dimensional measures μ_n of K and L satisfy μ_n(K)≤μ_n(L).This extends a generalized Funk’s section theorem for volumes to that for measures.     

Implicational lattices and generalization of Stone’s representation theorem

Let F(S) be the free algebra of type (,∨,→) generated by the non_empty set S, it is proved that the logical equivalent relation defined by means of R 0_semantics is a congruence relation on F(S) and the corresponding quotient algebra is said to be the R 0_semantic Lindenbaum algebra. Taking R 0_semantic Lindenbaum algebra as a prototype, the concepts of implicational lattices and regular implicational lattices which are generalizations of the concept of Boolean algebras are introduced. Besides, the concept of fuzzy implicational spaces is introduced and the representation theorem of regular implicational lattices is obtained by means of fuzzy implicational spaces. In case of Boolean algebras, the corresponding fuzzy implicational spaces are zero_dimensional compact Hausdorff spaces and herefrom it is proved that the famous Stone's representation theorem of Boolean algebras is a corollary of the representation theorem of regular implicational lattices.     

Nonlinear version of Holub’s theorem and its application

Holub proved that any bounded linear operator T or -T defined on Banach space L 1(μ) satisfies Daugavet equation1+‖T‖=Max{‖I+T‖, ‖I-T‖}.Holub's theorem is generalized to the nonlinear case: any nonlinear Lipschitz operator f defined on Banach space l 1 satisfies1+L(f)=Max{L(I+f), L(I-f)},where L(f) is the Lipschitz constant of f. The generalized Holub theorem has important applications in characterizing the invertibility of nonlinear operator.     

Lightning in Saturn’s atmosphere

There exists large-scale lightning in Saturn’s water cloud. Based on the powerful moist convection in the water cloud, we establish a thermal-induced convective model to interpret the mechanism for the processes of charge generation and separation. We also estimate the breakdown field of Saturn’s atmosphere quantitatively and interpret the discharge process.     

Wessex in Hardy’s Novel

Thomas Hardy is a novelist and poet, generally regarded as one of the outstanding figures in English literature. Most of his novels take place in the "partly-real, partly-dream" county of Wessex (named after the Anglo-Saxon kingdom which existed in the area) and called Wessex Novel. It is regarded as the reflection of his hometown Dorset. His novel creation could be generally divided into three periods. The first period was romantic and pastoral; the masterpieces are Under the Green Tree and Far from the Madding Crowd. His second period mainly focuses on the social tragedy of Wessex, such as The Return of the Native and The Mayor of Casterbridge .In the last period of his creation, he began to write the pessimistic fate of the villagers in Wessex, this could be seen through Tess of the D'Urbervilles and Jude the Obscure. From the evolution of Wessex we can know the English society in the 19th century as well as Hardy's love for his hometown and his individual philosophy.     

Teacher’s Role in Intensive Reading

本文介绍了教师在精读课中的作用及在不同课堂步骤当中的教学活动和教学策略。根据这种教学步骤,学生能更好的掌握语言技能。     

Elliptic curves in Huff’s model

In this paper,we present the generalized Huff curves that contain Huff’s model as a special case.First,it is proved that every elliptic curve with three points of order 2 is isomorphic to a generalized Huff curve.Then,the fast and explicit formulae are derived for generalized Huff curves in projective coordinates.This paper also enumerates the number of isomorphism classes of generalized Huff curves over finite fields.Finally,the explicit formulae are presented for the doubling step and addition step in Miller’s algorithm to compute the Tate pairing on generalized Huff elliptic curves.     

Rebellious Spirit in Shelley’s Poetry

雪莱的诗歌反映了他争取平等和自由的反叛思想。诗歌中揭示了他对上层阶级的诅咒 ,对下层劳动阶级的激励和鼓舞以及他对命运的不屈服和斗争的信念     

Xi stresses engineering’s role in development

Beijing, June 3 （Xinhua）- President Xi Jinping has vowed China will innovate in engineering to realize peaceful and sustainable development.     

Management Communication in University’s Digital Library

IntroductionAmericanfuturologistNaisbitthadsaid :“Futurecompetitionisthecompetitionofmanagement,thefocusofwhichistheeffectivepersonnelcommunicationandcross organizationalcommunication.”[1]Communicationisthetransferringprocessofinformation ,knowledgeandemotionamongindividualsandgroups,throughwhichaf fectothers’attitudesandfeelings,andeventuallyaffecttheirbehaviors.Forknowledgehasbeentheprimacyele ment,managementcommunicationinknowledgeeconomicagesismoreimportantthananyotherepoch ,whosestyle…     

A Milestone in China’s Space History —The White Paper on China’s Space Activities

The white paper document titled“China’s Space Activities”,released in November２０００by the Information Office of the State Council,represents the first time for China to fully,systematically and publicly introduce to the world China’s space development strategy and concerned policies．Its release is a milestone event in the country’s space history,bearing great importance and profound influence to its future space efforts．The paper here describes the shaping processes of some important new ideas and concepts,including the connotative meaning of“space activities in a broad sense”and the roles and positions of different sectors in such activities．It also briefly discusses related policies concerning the country’s space development and short term concepts and plans on its civil space activities．     

Evidence for tritium production in the Earth’s interior

We have made a new investigation on the vertical profiles of tritium and helium isotopes in Lakes Van and Nemrut （Eastern Turkey）, using experimental data from the reference by Kipfer et al. for study of long-term vertical mixing and deep water renewal in Lake Van. Lakes Van and Nemrut are crater lakes. Lake Nemrut is at the western border of Lake Van. The ^3He and ^4He are injected at the bottom of Lakes Van and Nemrut, and the both helium isotopes are confirmed from the mantle source. From ^3H （tritium） data in Lakes Van and Nemrut, we have observed ＂^3H anomaly＂ at the vertical profile of ^3H concentrations in Lake Nemrut. The ^3H concentration at the lake bottom is 10% higher than at the surface. The difference of ^3H concentrations between surface and bottom is about 3.7±1.2 TU. This excess ^3H should be injected from the lake bottom. An investigation on the origin of the injected tritium has been made. The results show the conventional origins are excluded, such as residence of precipitation tritium from nuclear testing in the early 1950s--1960s and tritium from known nuclear reactions. Based on the correlation of excess ^3H with ^3He and heat flow in Lake Nemrut, we infer that the ^3He and ^3H might be all from the mantle source, and produced by the supposed natural-nuclear-fusion, which might occur in an environment rich in water （H） and （U ＋ Th） at high temperature and high pressure in the deep Earth. Detection of tritium in the Earth＇s interior is a key evidence for exploration of natural nuclear fusion in the deep Earth. Based on the published data, we have found that the excess ^3He and ^3H injected at the bottom of Lake Laacher （Germany） were also released from the mantle source. The present work will be helpful to the further study of mechanism of natural nuclear fusion in the Earth＇s interior.     

High-speed flowing plasmas in the Earth’s plasma sheet

A research topic of great interest to the space physics community is the observation of plasmas flowing at hundreds of kilometers per second in the Earth’s plasma sheet. Although considerable effort has been made to understand the source of fast-flowing plasmas, many questions remain unanswered about the mechanisms that produce high-speed flows and the effects they have on magnetospheric disturbances, especially their contributions to magnetospheric convection and substorms. In this paper, we discuss briefly the history of high-speed flows and review the proposed mechanisms, signatures of high-speed flows in auroras and their interaction with the background plasma. We then summarize the relationships between high-speed flows and magnetic structures, discuss questions associated with substorms, and finally pose several important scientific questions that need to be addressed.     

Characteristics of carbon storage in Shanghai’s urban forest

Urban forest has undergone rapid development in China over the last three decades because of the acceleration of urbanization.Urban forest thus plays an increasingly important role in carbon sequestration at a regional and national scale.As one of the most urbanized cities in China,Shanghai showed an increase of forest coverage from 3% in the 1990s to 13% in 2009.Based on CITY-green model and the second soil survey of Shanghai,the forest biomass carbon(FBC) was estimated to be 0.48 Tg in the urban area and,forest soil organic carbon(SOC)(0-100 cm soil depth) is 2.48 Tg in the urban and suburban areas,respectively.These values are relatively within the median and lower level compared with other Chinese megacities,with the FBC of 0.02 Tg in Harbin to 47.29 Tg in Chongqing and the forest SOC of 1.74 Tg in Nanjing to 418.67 Tg in Chongqing.For the different land-use types in Shanghai,the SOC density ranges from 13.8(tidal field) to 38.6 t ha-1(agricultural land).On average,the forest SOC density(31.5 t ha-1) in Shanghai is lower than that in agricultural lands(38.6 t ha-1) and higher than that in lawns(26.5 t ha-1) and gardens(21.3 t ha-1).In Shanghai,the SOC density in newly established urban parks is generally lower than that in older parks.In the northern and southeastern suburban areas(e.g.,Baoshan,Yangpu,and Nanhui districts),greenspace SOC density is higher than that in the central commercial areas(Hongkou,Putuo,Changning,and Zhabei districts) and in newly developed district(Pudong District).Uncertainties still exist in the estimation of urban forest carbon in Shanghai,as well as in other Chinese cities.Thus,future research directions are also discussed in this paper.     

The Nature of Linguistic Signs in Saussure’s Course in General Linguistics

The paper mainly discusses the nature of linguistic signs in Saussure’s Course in General Linguistics. In the book, Saussure promoted semiology and regarded language as a system of signs and expounded the basic features of language from the aspect of semiology. In Saussure’s opinion, one of the most important characteristics of linguistic signs is arbitrariness. Saussure regarded the arbitrariness of the sign asfirst principle.At the same time, Saussure also discussed the linear character of the linguistic ...     

Solution of Cauchy’s problem for wave equations in higher space dimensions by means of D’Alembert’s formula

A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown. Foundation item: Supported by the Natural Science Foundation of Hubei Province (992P0307) and the National Natural Science Foundation of China (39970203) Biography: YAO Duan-zheng (1946-), female, Professor, Research direction: mathematical physics and nonlinear optics.     

Editor’s Note

Wallace (Wally) S. Broecker is Newberry Professor of Earth and Environmental Sciences at La- mont-Doherty Earth Observatory of Columbia University, New York. He received his PhD (1958) from Columbia University. He is a fellow of numerous renowned scientif…