Sigma Models and Minimal Surfaces

Correspondence is established between sigma models, minimal surfaces and the Monge–Ampére equation. The Lax pairs of the minimality condition of the minimal surfaces and the Monge–Ampére equations are given. Existence of infinitely many nonlocal conservation laws is shown and some Bäcklund transformations are also given.     

Some Further Properties of the Accelerated Kerr-Schild Metrics

We extend the previously found accelerated Kerr-Schild metrics for Einstein-Maxwell-null dust and Einstein-Born-Infeld-null dust equations to the cases including the cosmological constant. This way we obtain the generalization of the charged de Sitter metrics in static space-times. We also give a generalization of the zero acceleration limit of our previous Einstein-Maxwell and Einstein-Born-Infeld solutions.     

On the strong almost convergence of double sequences

In this paper, necessary and sufficient conditions that the real doubly infinite matrixA sums every strongly almost convergent double sequence, leaving the limit invariant, have been determined.     

An auto-coherent variational scheme for Yukawa potential

The variational principle is used to obtain solutions to Schrödinger's equation for a particle in the Yukawa potential. A Laguerre basis set extended by an extra function is employed in the calculations. A special parameter used in the extra function and its relation with the systems energy results in utilizing an auto-coherent scheme. Considerable improvement seems to be achieved especially in the critical region where the screening parameter approaches its threshold value.     

Optimal control of classical molecular dynamics: A perturbation formulation and the existence of multiple solutions

This paper considers the prospect for there being multiple solutions to the control of classically modelled molecular dynamical systems. The research presented here follows up on a parallel study based on quantum mechanics. For polyatomic molecules it is generally expected that a classical mechanical model will be adequate and necessary as a means for designing optical fields for molecular control. The prospect for multiple control field solutions existing in this domain is important to establish in terms of ultimate laboratory realization of molecular control. A general formulation of the multiplicity problem is considered and the existence of a denumerably infinite number of solutions for the control field amplitude is shown to be the case under certain mild limitations on the physical variables.     

The bromination of 3-bromo-6,7-benzobicyclo[3.2.1]octa-2,6-diene

The bromination of 3-bromo-6, 7-benzobicyclo [3.2.1] octa-2, 6-diene at ?50°C has been found to give only one product, the tribromide(7) produced via Wagner-Meerwein rearrangement with accompanying aryl migration. The bromination at 0°C produced nonrearranged tribromides beside the rearranged product. The structures of the products were determined by means of spectral data. The addition mechanism is discussed in terms of exo- and endo-attack.     

Designing of an Intensification Process for Biosynthesis and Recovery of Menaquinone-7

A nutritional food rich in menaquinone-7 has a potential in preventing osteoporosis and cardiovascular diseases. The static fermentation of Bacillus subtilis natto is widely regarded as an optimum process for menaquinone-7 production. The major issues for the bulk production of menaquinone-7 are the low fermentation yield, biofilm formation and the use of organic solvents for the vitamin extraction. In this study, we demonstrate that the dynamic fermentation involving high stirring and aeration rates enhances the yield of fermentation process significantly compared to static system. The menaquinone-7 concentration of 226 mg/L was produced at 1,000 rpm, 5 vvm, 40 °C after 5 days of fermentation. This concentration is 70-fold higher than commercially available food products such as natto. Additionally, it was found that more than 80 % of menaquinone-7 was recovered in situ in the vegetable oil that was gradually added to the system as an anti-foaming agent. The intensification process developed in this study has a capacity to produce an oil rich in menaquinone-7 in one step and eliminate the use of organic solvents for recovery of this compound. This oil can, therefore, be used for the preparation of broad range of supplementary and dietary food products rich in menaquinone-7 to reduce the risk of osteoporotic fractures and cardiovascular diseases.     

A finite element-spherical harmonics radiation transport model for photon migration in turbid media

In this paper, we solve the steady-state form of the Boltzmann transport equation in homogeneous and heterogeneous tissue-like media with a finite element-spherical harmonics (FE-P_N) radiation transport method. We compare FE-transport and diffusion solutions in terms of the ratio of absorption to reduced scattering coefficient, (μ_a/μ_s′) and the anisotropy factor g. Two different scattering phase function formulas are employed to model anisotropic scattering in the slab media with high g-value. Influence of void-like heterogeneities, and of their boundaries with the surrounding medium on the transport of photons are also examined.