The Geometry of Barotropic Flow

In this paper we construct a new noninvariant Riemannian metric on the semidirect product of the diffeomorphism group of a manifold and the space of positive functions on that manifold, which has the property that certain geodesics give the equations of barotropic fluid mechanics. We compute a formula for its curvature, analyze the sign of the curvature, and determine directly the growth of Jacobi fields in a few special cases.     

Spectroscopic fingerprints of valence and spin states in manganese oxides and fluorides

We performed a systematic study of soft X-ray absorption spectroscopy in various manganese oxides and fluorides. Both Mn L-edges and ligand (O and F) K-edges are presented and compared with each other. Despite the distinct crystal structure and covalent/ionic nature in different systems, the Mn-L spectra fingerprint the Mn valence and spin states through spectral lineshape and energy position consistently and evidently. The clear O- and F-K pre-edge features in our high resolution spectra enable a quantitative definition of the molecular orbital diagram with different Mn valence. In addition, while the binding energy difference of the O-1s core electrons leads to a small shift of the O-K leading edges between trivalent and quadrivalent manganese oxides, a significant edge shift, with an order of magnitude larger in energy, was found between divalent and trivalent compounds, which is attributed to the spin exchange stabilization of half-filled 3d system. This shift is much enhanced in the ionic fluoride system. This work provides the spectroscopic foundation for further studies of complicated Mn compounds.     

APPLICATIONS OF MULTICOMPONENT ASSEMBLY PROCESSES TO THE FACILE SYNTHESES OF DIVERSELY FUNCTIONALIZED NITROGEN HETEROCYCLES

Several multicomponent assembly processes have been developed for the synthesis of intermediates that may be elaborated by a variety of cyclizations to generate a diverse array of highly functionalized heterocycles from readily-available starting materials. The overall approach enables the efficient preparation of libraries of small molecules derived from fused, privileged scaffolds.     

Distinctive field dependence of the longitudinal muon polarization for Mu* in polycrystalline silicon

A distinctive longitudinal magnetic field dependence of the muon polarization for anomalous muonium in polycrystalline semiconductor targets has been predicted. The polarization exhibits a cusp,i.e., a discontinuous jump in the slope from negative to positive. Measurements of the longitudinal polarization for polycrystalline silicon in fields up to 0.5 T, and temperatures 53 and 200 K have been made at LAMPF. A cusp in the field dependence indeed occurs at 0.345 T, in excellent agreement with the prediction. No cusp is observed at 200 K because Mu^* has been thermally ionized.     

Variational conditions with smooth constraints: structure and analysis

 This is an expository paper about the analysis of variational conditions over sets defined in finite-dimensional spaces by fairly smooth functions satisfying a constraint qualification. The primary focus is on results that can provide quantitative and computable sensitivity information for particular instances of the problems under study, and our objective is to give a personal view of the state of current knowledge in this area and of gaps in that knowledge that require future work. The writing style is informal, in keeping with the objective of focusing the reader's attention on the basic concepts and the relationships between them, rather than on details of the particular results themselves. Received: December 1, 2002 / Accepted: April 25, 2003 Published online: May 28, 2003 Key words. variational condition – variational inequality – complementarity – sensitivity – stability – nondegeneracy Mathematics Subject Classification (2000): Primary: 90C31. Secondary: 47J20, 49J40, 49J53, 90C33     

Strategic commitment to price to stimulate downstream innovation in a supply chain

It is generally in a firm’s interest for its supply chain partners to invest in innovations. To the extent that these innovations either reduce the partners’ variable costs or stimulate demand for the end product, they will tend to lead to higher levels of output for all of the firms in the chain. However, in response to the innovations of its partners, a firm may have an incentive to opportunistically increase its own prices. The possibility of such opportunistic behavior creates a hold-up problem that leads supply chain partners to underinvest in innovation. Clearly, this hold-up problem could be eliminated by a pre-commitment to price. However, by making an advance commitment to price, a firm sacrifices an important means of responding to demand uncertainty. In this paper we examine the trade-off that is faced when a firm’s channel partner has opportunities to invest in either cost reduction or quality improvement, i.e. demand enhancement. Should it commit to a price in order to encourage innovation, or should it remain flexible in order to respond to demand uncertainty. We discuss several simple wholesale pricing mechanisms with respect to this trade-off.     

An Application of Branch and Cut to Open Pit Mine Scheduling

The economic viability of the modern day mine is highly dependent upon careful planning and management. Declining trends in average ore grades, increasing mining costs and environmental considerations will ensure that this situation will remain in the foreseeable future. The operation and management of a large open pit mine having a life of several years is an enormous and complex task. Though a number of optimization techniques have been successfully applied to resolve some important problems, the problem of determining an optimal production schedule over the life of the deposit is still very much unresolved. In this paper we will critically examine the techniques that are being used in the mining industry for production scheduling indicating their limitations. In addition, we present a mixed integer linear programming model for the scheduling problems along with a Branch and Cut solution strategy. Computational results for practical sized problems are discussed.