We describe explicitly the algebras of degree zero operations in connective and periodic p-local complex K-theory. Operations are written uniquely in terms of certain infinite linear combinations of Adams operations, and we give formulas for the product and coproduct structure maps. It is shown that these rings of operations are not Noetherian. Versions of the results are provided for the Adams...

We provide direct proofs of product and coproduct formulae for Schur functions where the coefficients (Littlewood–Richardson coefficients) are defined as counting puzzles. The product formula includes a second alphabet for the Schur functions, allowing in particular to recover formulae of [Molev–Sagan ’99] and [Knutson–Tao ’03] for factorial Schur functions. The method is based on the quantum i...

Resumptions appear in many forms as a convenient abstraction, such as in semantics of concurrency and as a programming pattern. In this paper we introduce generalised resumptions in a categorytheoretic, coalgebraic context and show their basic properties: they form a monad, they come equipped with a corecursion scheme in the sense of Adámek et al.’s notion of completely iterative monads (cims),...

The presence of variability in life cycle analysis (LCA) is inherent due to both inexact LCA procedures and variation of numerical inputs. Variability in LCA needs to be clearly distinguished from uncertainty. This paper uses specific examples from the production of diesel and jet fuels from 14 different feedstocks to demonstrate general trends in the types and magnitudes of variability present...

The dicarboxylic acid malic acid synthesized as part of the tricarboxylic acid cycle can be produced in excess by certain microorganisms. Although malic acid is produced industrially to a lesser extent than citric acid, malic acid has industrial applications in foods and pharmaceuticals as an acidulant among other uses. Only recently has the production of this organic acid from coproducts of in...

Let D be the set of isomorphism types of finite double partially ordered sets, that is sets endowed with two partial orders. On ZD we define a product and a coproduct, together with an internal product, that is, degree-preserving. With these operations ZD is a Hopf algebra, self-dual with respect to a scalar product which counts the number of pictures (in the sense of Zelevinsky) between two do...

This paper evaluates the o-hydroxycinnamic platform for designing efficient caging groups with fluorescence reporting upon one- and two-photon excitation. The model cinnamates are easily prepared in one step by coupling commercial or readily available synthons. They exhibit a large one-photon absorption that can be tuned in the near-UV range. Uncaging after one-photon excitation was investigate...

This paper introduces a notion of equivalence for higher-dimensional automata, called weak equivalence. Weak focuses mainly on traditional trace language and new homology language, which captures the overall independence structure an HDA. It is shown that compatible with both tensor product coproduct HDAs that, under certain conditions, may be reduced to weakly equivalent smaller ones by mergin...