A Linear Programming Approach to the Solution of Constrained Multi-Facility Minimax Location Problems where Distances are Rectangular

The problem of locating new facilities with respect to existing facilities is stated as a linear programming problem where inter-facility distances are assumed to be rectangular. The criterion of location is the minimization of the maximum weighted rectangular distance in the system. Linear constraints which (a) limit the new facility locations and (b) enforce upper bounds on the distances between new and existing facilities and between new facilities can be included. The dual programming problem is formulated in order to provide for an efficient solution procedure. It is shown that the duLal variables provide information abouLt the complete range of new facility locations which satisfy the minimax criterion.     

Hestenes' Tetrad and Spin Connections

Defining a spin connection is necessary for formulating Dirac's bispinor equation in a curved space-time. Hestenes has shown that a bispinor field is equivalent to an orthonormal tetrad of vector fields together with a complex scalar field. In this paper, we show that using Hestenes' tetrad for the spin connection in a Riemannian space-time leads to a Yang-Mills formulation of the Dirac Lagrangian in which the bispinor field Ψ is mapped to a set of SL(2,R)× U(1) gauge potentials F_α^K and a complex scalar field ρ. This result was previously proved for a Minkowski space-time using Fierz identities. As an application we derive several different non-Riemannian spin connections found in the literature directly from an arbitrary linear connection acting on the tensor fields (F_α^K, ρ). We also derive spin connections for which Dirac's bispinor equation is form invariant. Previous work has not considered form invariance of the Dirac equation as a criterion for defining a general spin connection.     

SNAr iodination of 6-chloropurine nucleosides: aromatic Finkelstein reactions at temperatures below -40 degrees C

Mesitoyl or toluoyl esters of inosine and 2'-deoxyinosine were deoxychlorinated at C6 to give the crystalline 6-chloropurine nucleoside derivatives, which underwent quantitative conversion to the 6-iodo analogues with NaI/TFA/butanone at -50 to -40 degrees C. The 6-iodo compounds were efficient substrates for SNAr, Sonogashira, and Suzuki-Miyaura reactions, in contrast with the 6-chloro analogues, and gave good to high yields of C-N and C-C coupled products.     

Preparation of 5-hydroxy-1-alkenyboronates from 1-alkynylboronates, Cp2ZrCl2/2EtMgBr, and aldehydes

1-Alkynylboronates form five-membered zirconacycles with Cp(2)ZrCl(2)/2-EtMgBr as indicated by deuterium labeling. The zirconacycles add aldehydes to form seven-membered zirconacycles. Hydrolysis of the latter provides 5-hydroxy-1-alkenylboronates in fair to good isolated yields. Both aliphatic and aromatic aldehydes undergo insertion.     

Cartan-decomposition subgroups of

For and , we give explicit, practical conditions that determine whether or not a closed, connected subgroup of has the property that there exists a compact subset of with . To do this, we fix a Cartan decomposition of , and then carry out an approximate calculation of for each closed, connected subgroup of .

     

Transition to turbulence in particulate pipe flow

We investigate experimentally the influence of suspended particles on the transition to turbulence. The particles are monodisperse and neutrally buoyant with the liquid. The role of the particles on the transition depends upon both the pipe to particle diameter ratios and the concentration. For large pipe-to-particle diameter ratios the transition is delayed while it is lowered for small ratios. A scaling is proposed to collapse the departure from the critical Reynolds number for pure fluid as a function of concentration into a single master curve.     

Formation of electrically active clusterized neural networks

Ordinarily, in vitro neurons self-organize into homogeneous networks of single neurons linked by dendrites and axons. We show that under special conditions they can also self-organize into neuronal clusters, which are linked by bundles of axons. Multielectrode array measurement reveals that the clusterized networks are also electrically active and exhibit synchronized bursting events similar to those observed in the homogeneous networks. From time-lapse recording, we deduced the features required for the neuronal clusterized versus homogeneous self-organization and developed a simple model for testing their validity.