On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions

We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely related to the definition in BISH of ‘locally compact’. Possible approaches to this problem are discussed. Topology seems to be a key to understanding many issues. We offer several new simplifying axioms, which can form bridges between the various branches of constructive mathematics and classical mathematics (‘reuniting the antipodes’). We give a simplification of basic intuitionistic theory, especially with regard to so-called ‘bar induction’. We then plead for a limited number of axiomatic systems, which differentiate between the various branches of mathematics. Finally, in the appendix we offer BISH an elegant topological definition of ‘locally compact’, which unlike the current definition is equivalent to the usual classical and/or intuitionistic definition in classical and intuitionistic mathematics, respectively.     

Position of the Y-chromosome at somatic metaphase in patients with chronic myelogenous leukemia (CML)

Summary A random distribution of the Y-chromosome at somatic metaphase was found in 50 patients with Ph' positive chronic myelogenous leukemia (CML). Thus, it is concluded that the positive of the Y-chromosome at somatic metaphase does not appear to influence the loss from bone marrow cells.     

A novel mechanism for jumping in the indian ant<Emphasis Type="Italic">Harpegnathos saltator</Emphasis> (Jerdon) (Formicidae,Ponerinae)

The Indian antHarpegnathos saltator may be unique among insects in using its jumping capacity not only as an escape mechanism but also as a normal means of locomotion, and for catching its prey in flight. High-speed cinematography used to analyse the various phases of the jump suggests thatHarpegnathos employs a novel jumping mechanism to mediate these behaviours: namely the synchronous activation of its middle and hindlegs. Electrophysiological recordings from muscles or nerves in pairs of middle and hindlegs show remarkably synchronous activity during fictive jumping, supporting the synchronous activation hypothesis.Harpegnathos is not the only ant to jump, and a cladistic analysis suggests that jumping behaviour evolved independently three times during ant evolutionary history.     

Chromosome variations inXenopsylla astia Rothschild, 1911 (Siphonaptera). A preliminary report

Summary 2 populations of rat fleas,Xenopsylla astia, collected from (A) Bombay and (B) Trivandrum, were found to differ in chromosome number as follows; (A) 2n=10 in both sexes; (B) 2n=18 (male) and 20 (female). Preliminary observations have further shown that the 2 populations differ in certain morphological characters and that their reciprocal hybrids are sterile in the male and partially sterile in the female sex.Acknowledgments. We wish to express our deepest gratitude to Dr Robert E. Lewis, Professor of Entomology, Iowa State University, USA, for confirming our identification of the 2 samples of rat fleas. We are indebted to Dr N.R. Prabhoo, Reader in Zoology, University of Kerala, Trivandrum, for his advice and helpful suggestions. We are also indebted to Prof. K.M. Alexander, for encouragement and providing facilities. Financial help of the University Grants Commission, India, to one of us (C.T.) is also gratefully acknowledged.     

Lightning activity on the central Tibetan Plateau and its response to convective available potential energy

Lightning flash activities on the central Tibetan Plateau have been studied by using the satellite-based Lightning Imaging Sensor(LIS)database from January 1998 to July 2002.The lightning activity shows a clear diurnal variation on the central Plateau.The peak lightning activity appears at about 17:00 which is 3 h earlier than that in Jingxhou,Hubei in the same latitude belt nearby,indicating that the lightning activity is a sensitive indicator of solar heating on the Plateau.The lightning discharge is weaker on the Plateau than Jingzhou.Hubei and other low-altitude continental regions because of the lower convective available potential energy(CAPE)on the Plateau.The CAPE on the Plateau is 12 times lower than that in Jingzhou,Hubei,and 20 times lower than that in the sea-level region,such as Guangzhou and Florida.However,the sensitivity of lightning activity to CAPE changes on the Plateau is up to 30 times more sensitive than other prominent low-altitude regions.     

C－isotope composition and significance of the Sinian on the Tarim plate

102 samples of limestones,mudrocks shales and tillites from the Sinian in Kuluketage have been analyzed ,Four formations in the Sinian belong to glacial deposits in which the differences in δ^13C are distinct (-14.7‰- 4.2‰),Distinctly negative δ^13C excursions for three times support the viwe of three glacial deposits in this area suggested by previous authors,except for the durations of them ,δ^13C values are generally positive in the Beiyixi Formation of lower part of the Lower Sinian ,representing probably the rock records of a continental rift related to break-up of the Rodinian supercontinent,There are three times of distinct excursions of δ^13C curve in all strata,The first one is from positive values at the bottom to about -5‰ at the top of the Beiyixi Formation ,The second one,from 0‰-3‰ in the Arletonggou Formation of upper part of the Lower Sinian to -3.4‰---14.4‰ in the Teruiaiken Formation.The third one,from positive values in the Zhamoketi Formation of lower part of the Upper Sinian to negative values in glacial varves at the top of the Hankeerqiaoke Formation.     

A new Euprox from the Late Miocene of Yuanmou,Yunnan Province,China,with interpretation of its paleoenvironment

The Yuanmou Basin of Yunnan Province is a hotspot for the research of early homind evolution and its environmental background.During the implementation of the Program“Research of the Origin and Evolution of Early Man and Its Environmental Baqckground” from 1998 to 2001,a huge quantity of hominoid and mammal fossils were collected.The present report systematically describes an Euprox robustus sp.nov.identified during the recent laboratory work on the collected material.Euprox is a group of earliest cervids with true antlers.The new species is the third one of the genus discovered in China.Judged by its morphologic characteristics,the new species feed on juicy and tender leaves of dicotyledon.It implies that the vegetation of its epoch in the Yuanmou Basin is a kind of southern subtropical evergreen forest and the climate is humid and temperate with evident seasonality.The latter is mostly influenced by the monsoon and secondly by the latitude.     

Inorganic chemical composition and source signature of PM2.5 in Beijing during ACE-Asia period

Aerosol samples for PM2.5 were collected in Beijing for 38 consecutive days from March to April 2001 using an IMPROVE Sampler. Concentrations of 20 elements in PM2.5 were determined using a PIXE method. Results show that the average mineral dust concentration of PM2.5 was 14.6 Ilg/m3 during the observation period. On the sand-dust event days of March 21 and April 10, dust PM2.5 mass concentrations were 62.4 and 54.1 μg/m^3, respectively.These demonstrate that fine particle pollution by dust event in Beijing was very severe. The enrichment factors of S and Cu reached minimums on the dusty days and were high on the non-dusty days. It is considered that enrichment factors of elements in PM2.5, which are associated with human activities, can probably provide an effective method to distinguish local sources from external sources of dust. Factor analysis on the chemical composition in PM2.5 shows that sources of crustal matters, anthropogenic emission, and oil combustion contributed to PM2.5 levels in air in the springtime of 2001 in Beijing.     

Progress in the study of tectophysicochemistry

Tectophysicochemistry is a research area that deals with the interrelations between physical and chemical changes of crustal materials caused by tectonism. A given tectonic force may be resolved into two parts: homogeneous stress and differential stress. Homogeneous stress refers to isotopic pressure, which is superimposed on the original pressure and affects the equilibrium of various chemical reactions. It is also a factor that influences petrogenesis,metallogenesis and metamorphism. Differential stress is commonly produced when external forces act on a given solid body. It may cause deformation of crustal materials and generate various kinds of structural features. Tectophysicochemistry pays special attention to pressure, temperature and other physicochemical conditions produced or induced by tectonism and studies the influences of additional tectonic parameters on various chemical equilibria, so it gradually develops into an independent area of science.     

Automatic evolutionary modeling by the Lattice-Boltzmann method

The Lattice-Boltzmann method is an effective tool for solving fluid mechanics problems, but there isn’t still a good scheme to determinate some parameters in Boltzmann equations. In this paper, a technique using evolutionary algorithm to automatically model Boltzmann equations is introduced. Numerical simulation shows that the designed scheme is fast and efficient. Biography: Chen Ju-hua ( 1963-), male, Associate professor, research direction: Lattice-Boltzmann method, evolutionary algorithm.