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Nikulin has classified all finite abelian groups acting symplectically on a K3 surface and he has shown that the induced action on the K3 lattice U⊕E8(−1) depends only on the group but not on the K3 surface. For all the groups in the list of Nikulin we compute the invariant sublattice and its orthogonal complement by using some special elliptic K3 surfaces.

While the equation above is correct, it is not very useful for incremental updates since the equation above updates the checksum C, rather than the 1’s complement of the checksum, ̃C, which is the value stored in the checksum field. In addition, it suffers because the notation does not clearly specify that all arithmetic, including the unary negation, must be performed one’s complement, and so i...

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...