When the degree of intersections A∩B of events A,B is unknown arises a problem: how to evaluate the probability P(A ∩ B) and P(A ∩B) from P(A) and P(B). To treat related problems two models of valuation: interval and paired probabilities are proposed. It is shown that the valuation corresponding to the set operations ∩ (intersection), ∪ (union) and ∼ (complement) can be described by the truth f...

An efficient chiral squaramide-catalysed enantioselective Michael addition of pyrazolin-5-ones to 3-nitro-2H-chromenes for the synthesis of chiral heterocyclic systems containing both chroman and pyrazolone derivatives has been developed. This reaction afforded the desired products in high to excellent yields (up to 98%) with high enantioselectivities (up to 96%) and excellent diastereoselectiv...

An efficient chiral squaramide-catalysed enantioselective Michael addition of pyrazolin-5-ones to nitroalkenes has been developed. This reaction afforded the chiral pyrazol-3-ol derivatives in high to excellent yields (up to >99%) with high enantioselectivities (up to 94% ee) for most substrates under very low catalyst loading (0.25 mol%). This catalytic asymmetric reaction provides valuable an...

Mathematical models are used to determine if infection wave fronts could occur by traveling geographically in a loop around a region or continent. These infectionwave fronts arise by Hopf bifurcation for some spatial models for infectious disease transmission with distributed-contacts. Periodic traveling waves are shown to exist for the spatial analog of the SIRS endemic model, in which the tem...

This paper describes a simple means for embedding a checksum within a FITS header, providing a mechanism for later verifying the integrity of the FITS le. The method uses ASCII coded 32-bit 1's complement arithmetic to force the checksum of each FITS HDU to zero. This technique requires no extension of the FITS standard to be used by any given project, in fact the technique may be used to zero ...