A new class of coefficients for the Hopf-cyclic homology of module algebras and coalgebras is introduced. These coefficients, termed stable anti-Yetter-Drinfeld contramodules, are both modules and contramodules of a Hopf algebra that satisfy certain compatibility conditions. 1. Introduction. It has been demonstrated in [8], [9] that the Hopf-cyclic homology developed by Connes and Moscovici [5]...

The symbol bootstrap has proven to be a powerful tool for calculating polylogarithmic Feynman integrals and scattering amplitudes. In this Letter, we initiate the elliptic integrals. Concretely, of twelve-point two-loop double-box integral in four dimensions, which depends on nine dual-conformal cross ratios. We obtain alphabet, contains 100 logarithms as well simple integrals, via Schubert-typ...

Symmetric ordering and Weyl realizations for non-commutative quantum Minkowski spaces are reviewed. of Lie deformed corresponding star products, as well twist to realization coproduct momenta, presented. Drinfeld twists understood in Hopf algebroid sense also discussed. A few examples given. We show that the original Snyder space, there exists symmetric but no realization. Quadratic deformation...

Corn-ethanol production is expanding rapidly with the adoption of improved technologies to increase energy efficiency and profitability in crop production, ethanol conversion, and coproduct use. Life cycle assessment can evaluate the impact of these changes on environmental performance metrics. To this end, we analyzed the life cycles of cornethanol systems accounting for the majority of U.S. c...

We assessed the water requirements of ethanol from corn grain and crop residue. Estimates are explicit in terms of sources-green (GW) and blue (BW) water, consumptive and nonconsumptive requirements across the lifecycle, including evapotranspiration, application and conveyance losses, biorefinery uses, and water use of energy inputs, and displaced requirements or credits due to coproducts. Etha...

Corn gluten meal (CGM) is a major coproduct of corn wet milling; it has value because of high protein. However, variation in composition and high P content reduce market value. Data that characterize gluten streams would be helpful in identifying key processing steps that could be modified to improve the quality of CGM and increase processing efficiency. Few data are published in the literature...

For an endofunctor H on a hyper-extensive category preserving countable coproducts we describe the free corecursive algebra on Y as the coproduct of the final coalgebra for H and the free Halgebra on Y . As a consequence, we derive that H is a cia functor, i.e., its corecursive algebras are precisely the cias (completely iterative algebras). Also all functors H(−) + Y are then cia functors. For...

Motivated by a new approach in the categorical semantics of linear logic, we investigate some speciic categories of coalgebras. They all arise from the canonical comonad that one has on a category of algebras. We obtain a very simple model of linear logic where linear formulas are complete lattices and intuitionistic formulas are just sets. Also, in another, domain theoretic example, we give a ...