Poisson structures due to Lie algebra representations

Using a unitary solution of the classical Yang-Baxter equation on a Lie algebraG we describe a particular way of constructing homogeneous quadratic Poisson structures on the dual of aG-moduleV and study some local features of the symplectic foliation due to the involutive distribution of the Hamiltonian vector fields. We also give some examples where the symplectic leaves are explicitly calculated.     

Eigenvalues of the form valued Laplacian for Riemannian submersions

Let be a Riemannian submersion of closed manifolds. Let be an eigen -form of the Laplacian on with eigenvalue which pulls back to an eigen -form of the Laplacian on with eigenvalue . We are interested in when the eigenvalue can change. We show that , so the eigenvalue can only increase; and we give some examples where , so the eigenvalue changes. If the horizontal distribution is integrable and if is simply connected, then , so the eigenvalue does not change.

     

A synthetic approach to the phorboxazoles – A strategy for the synthesis of the C1–C19 polyketide fragment

A synthetic approach to the C1–C19 polyketide fragment of the phorboxazoles is disclosed here. While an initial two-directional approach was efficient, it did not proceed in a high enough yield to justify moving forward. A subsequent successful strategy for the generation of the C11–C15 pyrans of both of the phorboxazoles was achieved, and the installation of the C9 stereocenter was able to be demonstrated. Furthermore, an efficient route for the preparation of the C1–C8 fragment with suitable functionality to allow for elaboration into the complete C1–C19 fragment, with the capricious C2–C3 Z-geometry installed, was also achieved.     

An air sparging CFD model for heap bioleaching of chalcocite

A computational fluid dynamics (CFD) solver CFX4.4 is used to implement a steady state model of heap bioleaching of chalcocite, which includes air sparging (forced aeration) based on a previous model entirely under natural convection. The model assumes the oxygen supply limits the reaction rate. A parameter analysis is performed which shows that the factors important to copper leaching are liquid and air flow rates, permeability and fraction of pyrite to chalcocite leached (FPY). The ability to control which parts of the bed received the highest extraction as a function of the liquid and air flow rates was established. Sparging is found to increase the oxygen concentration throughout the heap compared to the circumstance with no sparging (natural convection), and consequently improves the copper extraction significantly. The results show that sparging does not provide any better copper extraction for very high heap permeabilities. The arrangement and spacing of air sparging inlets is analysed in regard to the existence of oxygen starved regions between the inlets.     

A synthetic approach to the phorboxazoles – Synthesis of the C20–C32 central core

An enantiospecific synthesis of the C20–C32 central core of the phorboxazole scaffold, including the non-macrocyclic oxazole is detailed in 17 steps (longest linear sequence) from methacrolein in 7.8% overall yield. All of the stereocenters are communicated from a single Evans aldol reaction, and the final compound is suitably functionalized for further elaboration to the natural products.