Extending du Bois-Reymond's Infinitesimal and Infinitary Calculus Theory

The discovery of the infinite integer leads to a partition between finite and infinite numbers. Construction of an infinitesimal and infinitary number system, the Gossamer numbers. Du Bois-Reymond's much-greater-than relations and little-o/big-O defined with the Gossamer number system, and the relations algebra is explored. A comparison of function algebra is developed. A transfer principle more general than Non-Standard-Analysis is developed, hence a two-tier system of calculus is described. Non-reversible arithmetic is proved, and found to be the key to this calculus and other theory. Finally sequences are partitioned between finite and infinite intervals.Comment: Resubmission of 6 other submissions. 99 page

Mediterranean marine copepods: basin-scale trends of the calanoid Centropages typicus

The Mediterranean Sea is located in a crossroad of mid-latitude and subtropical climatic modes that enhance contrasting environmental conditions over both latitudinal and longitudinal ranges. Here, we show that the large-scale environmental forcing is reflected in the basin scale trends of the adult population of the calanoid copepod Centropages typicus. The species is distributed over the whole Mediterranean basin, and maximal abundances were found in the north-western basin associated to oceanic fronts, and in the Adriatic Sea associated to shallow and semi enclosed waters. The peak of main abundances of C. typicus correlates with the latitudinal temperature gradient and the highest seasonal abundances occurred in spring within the 14–18°C temperature window. Such thermal cline may define the latitudinal geographic region where C. typicus seasonally dominates the >200 μm-sized spring copepod community in the Mediterranean Sea. The approach used here is generally applicable to investigate the large-scale spatial patterns of other planktonic organisms and to identify favourable environmental windows for population developmentPublicado