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.     

Induction of hemopoietic chimerism in the caprine fetus by intraperitoneal injection of fetal liver cells

Summary Intraperitoneal injection of allogeneic liver cells from 43-day-old male fetuses into normal 60-day female goat fetuses resulted in persistent hemopoietic chimerism in surviving recipients without clinical evidence of graft-versus-host disease. Transplantation of normal fetal liver cells into preimmunocompetent goat fetuses affected with -D-mannosidosis may provide an alternative strategy for evaluating hemopoietic stem cell transplantation in the treatment of human lysosomal storage diseases.     

Changes in glycosaminoglycan sulfation and protein kinase C subcellular distribution during differentiation of the human colon tumor cell line Caco-2

Summary During the spontaneous differentiation (day 5 to day 15 of the culture) of Caco-2 cells, the sulfation of cell layer glycosaminoglycans increased, whereas protein kinase C activity was concomitantly redistributed from the membrane to the cytosol. The protein kinase C activators, 4-phorbol 12-myristate, 13-acetate and 1,2-dioctanoyl-glycerol inhibited glycosaminoglycan sulfation. By contrast, 4-phorbol 12, 13 didecanoate was ineffective.These results suggest that membrane-bound PKC may exert a modulatory effect on glycosaminoglycan sulfation, and this effect is gradually attenuated as Caco-2 cell differentiation progresses.     

Using genetically-defined rodent strains for the identification of hippocampal traits relevant for two-way avoidance behavior: a non-invasive approach

Summary Genetically-defined rodent strains permit the identification of hippocampal traits which are of functional relevance for the performance of two-way avoidance behavior. This is exemplified here by analyzing the relationship between infrapyramidal mossy fibers (a tiny projection terminating upon the basal dendrites of hippocampal pyramidal neurons) and two-way avoidance learning in about 800 animals. The necessary steps include 1) identification of structural traits sensitive to selective breeding for extremes in two-way avoidance, 2) testing the robustness of the associations found by studying individual and genetical correlations between hippocampal traits and behavior, 3) establishing causal relationships by Mendelian crossing of strains with extreme structural traits and studying the behavioral consequences of such structural randomization, 4) confirming causal relationships by manipulating the structural variable in inbred (isogenic) strains, thereby eliminating the possibility of genetic linkage, and 5) ruling out the possibility of spurious associations by studying the correlations between the hippocampal trait and other behaviors known to depend on hippocampal functioning.In comparison with the classical lesion approach for identifying relationships between brain and behavior, the present procedure appears to be superior in two aspects: it is non-invasive, and it focuses automatically on those brain traits which are used by natural selection to shape behaviorally-defined animal populations, i.e., it reveals the natural regulators of behavior.     

In vivo effects of immunostimulating lipopeptides on mouse liver microsomal cytochromes P-450 and on paracetamol-induced toxicity

Summary Immunomodulating lipopeptides lauroyl-L-Ala--D-Glu-LL-A2pmNH2-Gly (RP 44.102) and lauroyl-L-Ala--D-Glu-LL-A2pmNH2 (RP 56.142) were found to protect mice against the hepatotoxicity of paracetamol, which is due to cytochrome P-450 dependent formation of toxic metabolites and radicals. In fact they decreased the amount of hepatic microsomal cytochrome P-450, and the level of CCl₄-induced lipid peroxidation. In contrast lauroyl-L-Ala--D-Glu-DD-A2pmNH2 (RP 53.204), which only differs by the configuration of the two chiral carbons of A2pm (diaminopimelic acid) and is not an immunomodulating agent, failed to protect against poisoning by paracetamol and had no effect on the level of hepatic cytochrome P-450 or the microsomal CCl₄-induced lipid peroxidation. This provides a clear connection between the immunostimulating properties of a compound and its effects on xenobiotic biotransformations.     

Evolutionary and ecological implications of cardenolide sequestration in the monarch butterfly

Summary Monarch butterflies sequester cardenolides from their larval host plants in the milkweed genusAsclepias for use in defense against predation. Of 108Asclepias species in North America, monarchs are known to feed as larvae on 27. Research on 11 of these has shown that monarchs sequester cardenolides most effectively, to an asymptote of approximately 350 g/0.1 g dry butterfly, from plants with intermediate cardenolide contents rather than from those with very high or very low cardenolide contents. SinceAsclepias host plant species are distributed widely in space and time across the continent, monarchs exploit them by migration between breeding and overwintering areas. After overwintering in central Mexico, spring migrants east of the Rocky Mountains exploit three predominantAsclepias species in the southern USA that have moderately high cardenolide contents. Monarchs sequester cardenolides very effectively from these species. First generation butterflies are thus well protected against predators and continue the migration north. Across the northern USA and southern Canada most summer breeding occurs on a fourthAsclepias species and in autumn most of these monarchs migrate back to Mexican overwintering sites. The ecological implications of this cycle of cardenolide sequestration for the evolution of monarch migration are discussed.     

Comments on “aggregation of equivalence relations” by P. C. Fishburn and A. Rubinstein

The theorem of the paper Aggregation of Equivalence Relations, by Fishburn and Rubinstein, states a result already known. This theorem improves a result from Mirkin (1975) and appears as a corollary occurring in Leclerc (1984).

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Resume L'unique théorème de l'article Aggregation of Equivalence Relations de Fishburn et Rubinstein est déja connu. Il améliore, en fait, un résultat de Mirkin (1975) et apparait en tant que corollaire dans Leclerc (1984).

     

Methodological foundations of systems methodologies

In social systems science generally, and in management science particularly, recent developments in the variety of types of specific problem-solving methodologies (under the rubric of hard and soft systems approaches) have given an impetus to a line of inquiry, as well as debate on the nature of those methodologies. On the one hand, there has been the view that what we are witnessing is a form of Kuhnian crisis. On the other hand, a complementarist view of developments has been argued and a contingency approach proposed. But one thing has been common among the competing views: a belief that the prospects for further advances in the design and application of those methodologies, and in resolving the current controversies, lie in serious attempts to reconsider and clarify the underlying metatheoretical assumptions and concerns. This paper is an attempt to contribute to such an endeavor. A brief exposition of three methodological foundations (namely, empiricism, hermeneutics, and critique) is made, not only with the purpose of highlighting the nature as well as the limits of their epistemological and ethical claims, but also as a basis for illuminating both the nature of contemporary work on systems inquiry, design, and problem solving and the ongoing debate on what constitutes appropriate criteria for choice of specific methodologies.     

The contents of the pygidial gland of the primitive antNothomyrmecia macrops (Hymenoptera:Formicidae)

Summary The principal constituent of the pygidial gland ofNothomyrmecia macrops is 3,7-dimethyloct-6-en-2-one, a substance not previously identified in insects. Also identified were 2,6-dimethylhept-5-enal, 2-nonanone, indole, -dodecalactone, and the hydrocarbons pentadecane, heptadecane, heptadecene and heptadecadiene, all in low nanogram quantities.