Why did a minor math error that would occur only once every 27,000 years so enrage customers that it briefly threatened to derail Intel's Pentium chip? And how could a feature as trivial as an inexpensive cup holder swing millions of customers to purchase a $17,000 automobileparticularly when only three years later, the same cup holder had hecome almost invisible to buyers? Is it possible to de...

Contents 0 Notations and conventions 5 1 The Eisenstein symbol and the cup product construction 6 1.1 A residue sequence in K-theory. .

We present here a combinatorial method for computing cup-i products and Steenrod squares of a simplicial set X. This method is essentially based on the determination of explicit formulae for the component morphisms of a higher diagonal approximation (i.e., a family of morphisms measuring the lack of commutativity of the cup product on the cochain level) in terms of face operators of X. A genera...

The article proposes a scheme of the process manufacturing bimetallic tubular elements by extraction cylindrical cup two dissimilar metals without thinning and with cup. At same time, in heated state, layers alloys are connected desired shape product is obtained. A mathematical model deformation joint heating flat deformed state developed. influence value on dispersion mechanical energy bimetal...

Abstract We prove that the cup product of ?-decomposable quasimorphisms, Brooks quasimorphisms or Rolli with any bounded cohomology class arbitrary positive degree is trivial.

We give a short proof of a formula of de Shalit, expressing the cup product of two vector valued one forms of the second kind on a Mumford curve in terms of Coleman integrals and residues. The proof uses the notion of double indices on curves and their reciprocity laws.

For any Lie algebra g there is a notion of Leibniz cohomology HL(g), which is defined like the classical Lie cohomology, but with the n-th tensor product g⊗n in place of the n-th exterior product Λ g. This Leibniz cohomology is defined on a larger class of algebras : the Leibniz algebras (cf. [L1], [L2]). A Leibniz algebra is a vector space equipped with a product satisfying a variation of the ...