Weyl's geometry and physics

It is proposed to remove the difficulty of nonitegrability of length in the Weyl geometry by modifying the law of parallel displacement and using standard vectors. The field equations are derived from a variational principle slightly different from that of Dirac and involving a parameter . For =0 one has the electromagnetic field. For <0 there is a vector meson field. This could be the electromagnetic field with finite-mass photons, or it could be a meson field providing the missing mass of the universe. In cosmological models the two natural gauges are the Einstein gauge and the cosmic gauge. With the latter the universe has a fixed size, but the sizes of small systems decrease with time and their masses and energies increase, thus producing the Hubble effect. The field of a particle in this gauge is investigated, and it leads to an interesting solution of the Einstein equations that raises a question about the Schwarzschild solution.     

Is there stereoselectivity in spin trapping superoxide by 5-tert-butoxycarbonyl-5-methyl-1-pyrroline N-oxide?

[reaction: see text] Ester-containing nitrones, including 5-tert-butoxycarbonyl-5-methyl-1-pyrroline N-oxide 5, have been reported to be robust spin traps for superoxide (O2*-). Using a chiral column, we have been able to isolate the two enantiomers of nitrone 5. With enantiomerically pure nitrone 5a and 5b we explored whether one of these isomers was solely responsible for the EPR spectrum of aminoxyl 6. Data obtained demonstrate that the spin trapping of O2*- by nitrone 5a and nitrone 5b affords the identical EPR spectra and lifetimes in homogeneous aqueous solution and exhibits the same ratio of cis and trans isomers. Quantum chemical modeling in vacuo also finds no difference, aside from the expected optical activity, arising from the difference in stereochemistry.     

Purification,Crystallization, and Preliminary Crystallographic Studies of Human As(III) S-Adenosylmethionine Methyltransferase (hAS3MT)

Crystallography Reports - Exposure to environmental arsenic is associated with serious of health issues such as cancer, diabetes and developmental delays in infants and children. In human liver,...     

A parallel algorithm for solving the linear complementarity problem

The concept of multitasking mathematical programs is discussed, and an application of multitasking to the multiple-cost-row linear programming problem is considered. Based on this, an algorithm for solving the Linear Complementarity Problem (LCP) in parallel is presented. A variety of computational results are presented using this multitasking approach on the CRAY X-MP/48. These results were obtained for randomly generated LCP's where thenxn dense matrixM has no special properties (hence, the problem is NP-hard). based on these results, an average time performance ofO(n ⁴) is observed.     

Algebraic interpretation of the Yang-Mills field

Einstein's principle of general relativity is a dynamical-group approach in that all dynamics is implied by the invariance and no force is introduced (as an external, symmetry-breaking factor). In this spirit we take a Poincaré-invariant free wave equation and, deforming the Poincaré group to the de Sitter group, obtain interaction. This illustrates our algebraic approach to gauge invariance, whereby the (generalized) Maxwell tensor of the Yang-Mills field appears as structure constants of the homogeneous algebra obtained as a deformation of an inhomogeneous one, with interaction appearing via the same tensor, which plays a role corresponding to the curvature tensor in Einstein's general relativity.     

Multi-funnel optimization using Gaussian underestimation

In several applications, underestimation of functions has proven to be a helpful tool for global optimization. In protein–ligand docking problems as well as in protein structure prediction, single convex quadratic underestimators have been used to approximate the location of the global minimum point. While this approach has been successful for basin-shaped functions, it is not suitable for energy functions with more than one distinct local minimum with a large magnitude. Such functions may contain several basin-shaped components and, thus, cannot be underfitted by a single convex underestimator. In this paper, we propose using an underestimator composed of several negative Gaussian functions. Such an underestimator can be computed by solving a nonlinear programming problem, which minimizes the error between the data points and the underestimator in the L ¹ norm. Numerical results for simulated and actual docking energy functions are presented.