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.     

The induction of secondary seed dormancy by oxygen deficiency in a barnyard grassEchinochloa crus-galli

At 25°C, secondary dormancy was induced in seeds ofE. crus-galli exposed for 100 days to oxygen deficiency. By contrast, hypoxia did not induce dormancy at 15°C or prevent dormancy termination at 7°C. Secondary dormancy was terminated after 2 months stratification at 7°C. Oxygen deficiency may increase the proportion of dormant seeds in the soil, and affect the dynamics of the barnyard-grass soil seed bank.We thank Miss Jitka Králová for her excellent technical assistance.     

Photoperiodic summation is temperature-dependent inPyrrhocoris apterus (L.) (Heteroptera)

Summary InPyrrhocoris apterus, a low temperature, 15°C, prevented the termination of diapause by long days and, unexpectedly, also the induction of diapause by short days. Both responses were enabled at a higher temperature, 26°C. In contrast to current concepts, it was proved that the summation of photoperiodic signals was temperature-dependent, since the morphogenetic development was prevented by starvation.     

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.     

The use of cyclophosphamide as an enhancer of the vaccine against foot-and-mouth disease

The immunization of biungulate animals with killed foot-and-mouth disease virus (FMDV) requires periodic vaccinations due to a low vaccine immunogenicity. Therefore, FMDV antigens need to be combined with adjuvants such as aluminum hydroxide, saponin or oil emulsions. Animal handling for periodic inoculations, and the repeated doses of vaccines that have to be administered increase the commercialization costs. Moreover, the use of adjuvants may induce adverse effects.In the present work we show that it is possible to increase the life span of neutralizing antibodies in serum when a single dose of cyclophosphamide (Cy) is administered four days before vaccination with aluminum hydroxidesaponin FMDV vaccine.     

Nicotianamine,the ‘normalizing factor’ for the auxotroph tomato mutantChloronerva; a representative of a new class of plant effectors

Summary The article surveys our knowledge of the normalizing factor, gained from its discovery a quarter of a century ago up to the present time, under the following headings: Discovery; Physiological properties; Isolation and characterization; Structure determination (Identity of the normalizing factor with nicotianamine); Chemical properties; Analysis; Synthesis; Occurrence and physiological role; Related compounds; Prospects.     

Oxygen consumption in rat skeletal muscle at various rates of oxygen delivery

Summary Resting oxygen consumption of the vascularly isolated gracilis anticus muscle of the rat perfused by natural circulation via the femoral artery with diluted or undiluted blood depends on oxygen delivery (the product of flow rate and arterial oxygen concentration-DO₂) only when DO₂ falls below 16 l/min/g.     

Reciprocal changes in serum free thyroxine fraction and thyrotropin level after administration of thiocyanate to rats

Summary The administration of thiocyanate to rats caused a significant increase of serum free thyroxine fraction, which coincided with the significant decrease of TSH level. The other components (AFT₄, T₄, T₃) in serum at this time were decreased or unchanged. The finding suggests the role of free thyroxine fraction in feed-back regulation of TSH secretion.Acknowledgment. We thank Dr A. Parlow and the NIAMDD, Rat Pituitary Hormone Distribution Program, for material for rat TSH immunoassay; Dr J. Nauman (Inst. Postgrad. Med., Warsaw, Poland) for T₃ antibody, and to Ing. J. Sadlo, Mrs M. t'astná and Miss R Fajkoová for technical assistance.     

Protein degradation in human T-lymphocytes

Summary Protein from resting or phytohemagglutinin-stimulated human peripheral blood T-lymphocytes, pulse-labeled in vitro for 1 h with³H-leucine, had a half-life of 30 h.     

Complete replacement of serum in primary cultures of chick embryo brain cells by growth-promoting alpha-globulin

Summary Growth-promoting alpha-globulin (GPAG), a specific serum protein complex which induces mitotic activity in continually replicating metazoan cells in vitro, was shown in this study to support growth of astrocytes and mesenchymal cells as well as process formation of nerve cells isolated from cerebral hemispheres of chick embryos.