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.     

Eicosapentaenoic acid in tissue lipids ofPieris brassicae

Summary Larvae of the cabbage white butterfly,Pieris brassicae, have a dietary requirement for linolenic acid (C183n3) and were found to accumulate two other members of the n-3 family, C203n3 and C205n3 (eicosapentaenoic acid) especially in testicular phospholipids. Arachidonic acid was observed in trace amounts only. During diapause the relative titer of eicosapentaenoic acid increased in testicular phospholipids to about 4.2% of the fatty acids. Eicosapentaenoic acid is a possible precursor of prostaglandins, suggesting that prostaglandins of the 3-series predominate in this insect.     

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.     

Sex pheromone of the pine sawflyDiprion pini (Hymenoptera: Diprionidae): Chemical identification,synthesis and biological activity

The main component of the sex pheromone secretion of femaleDiprion pini L. (Hymenoptera: Diprionidae) from insects collected both in Finland and in France has been identified as athreo-3,7-dimethyl-2-tridecanol (8 ng per female) stereoisomer by GC-MS and synthesis. The secretion also contains lower and higher homologues in small amounts (1–4% of the main component). Combined gas chromatographic-electroantennographic detection showed activity in both natural and esterified extracts (acetates and propionates); the esters of the main component gave the largest responses. The acetates and propionates of the eight stereoisomers of 3,7-dimethyl-2-tridecanol were synthesized from enantiomerically highly enriched (>99% ee) building blocks. The stereochemistry of the main component was established to be (2S,3R,7R)-3,7-dimethyl-2-tridecanol by GC analysis of the natural material. It was purified by liquid chromatography prior to the GC analysis of both its pentafluorobenzoates and its isopropylcarbamates on a non-chiral polar column (ECD) and a chiral column (NPD), respectively. Field tests demonstrated that both the acetate and propionate of the main component (100 g of each applied on cotton roll dispensers) were active in attracting males, with or without the presence of several of the minor compounds. Experiments with smaller amounts of the acetate and the propionate (1 g in France and 50 g in Finland) demonstrated that the propionate was more active than the acetate, and that it also caught more males than a blend of the two compounds.     

In vitro inactivation of corpora allata of the bugOncopeltus fasciatus by precocene II

Summary Corpora allata fromOncopeltus fasciatus incubated in vitro in medium containing 10^–5.35 M (1 g/ml) of precocene II lose their ability to secrete juvenile hormone when reimplanted into last instar larvae.Acknowledgments. We thank Mr K. Dorn, Mrs L. Dolezal, Mrs V. Nötzli-Graf, Mr K.H. Trautmann and Mr A. Schuler for technical help, Dr W. Vogel and Dr A. Dübendorfer for valuable discussions.     

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.