Path Integration and Separation of Variables in Spaces of Constant Curvature in Two and Three Dimensions

In this paper path integration in two- and three-dimensional spaces of constant curvature is discussed: i.e. the flat spaces R² and R³, the two- and three-dimensional sphere and the two- and three-dimensional pseudosphere. We are going to discuss all coordinates systems where the Laplace operator admits separation of variables. In all of them the path integral formulation will be stated, however in most of them an explicit solution in terms of the spectral expansion can be given only on a formal level. What can be stated in all cases, are the propagator and the corresponding Green function, respectively, depending on the invariant distance which is a coordinate independent quantity. This property gives rise to numerous identities connecting the corresponding path integral representations and propagators in various coordinate systems with each other.     

Numerical approach for generic three-phase flow based on cut-cell and ghost fluid methods

In this paper, we introduce numerical methods that can simulate complex multiphase flows. The finite volume method, applying Cartesian cut-cell is used in the computational domain, containing fluid and solid, to conserve mass and momentum. With this method, flows in and around any geometry can be simulated without complex and time consuming meshing. For the fluid region, which involves liquid and gas, the ghost fluid method is employed to handle the stiffness of the interface discontinuity problem. The interaction between each phase is treated simply by wall function models or jump conditions of pressure, velocity and shear stress at the interface. The sharp interface method “coupled level set (LS) and volume of fluid (VOF)” is used to represent the interface between the two fluid phases. This approach will combine some advantages of both interface tracking/capturing methods, such as the excellent mass conservation from the VOF method and good accuracy of interface normal computation from the LS function. The first coupled LS and VOF will be generated to reconstruct the interface between solid and the other materials. The second will represent the interface between liquid and gas.     

Thermal diffusion of dilute aqueous NH4Cl,Me4NCl,Et4NCl,n-Pr4NCl,andn-Bu4NCl solutions at 25°C

The Soret effect (thermal diffusion) of dilute aqueous solutions of NH₄Cl, Me₄NCl, Et₄NCl, n-Pr₄NCl, and n-Bu₄NCl has been investigated potentiometrically using the silver, silver chloride thermocell. The molar entropies (heats) of transport have been derived from the initial and final thermoelectric powers. The concentration dependence of the entropy of transport has been examined and the effect of the ionic size on the heat of transport is discussed. The molar entropy of tetrabutylammonium chloride exhibits a sharp minimum in the neighborhood of 0.002M, the reason of which is as yet unclear.     

Rh(I)-catalyzed carbonylative ring opening of diazabicycles with acyl anion equivalents

A catalytic desymmetrization of strained alkenes by ring-opening of meso-diazabicycles with acyl anion nucleophiles is reported. Densely functionalized trans-1,2-hydrazinoacyl cyclopentene building blocks are obtained stereoselectively. The acyl anion equivalent is generated in situ under very mild conditions from readily available organoboron precursors.     

Immunomodulatory Properties of Masticadienonic Acid and 3α-Hydroxy Masticadienoic Acid in Dendritic Cells

Dendritic cells are antigen-presenting cells, which identify and process pathogens to subsequently activate specific T lymphocytes. To regulate the immune responses, DCs have to mature by the recognition of TLR ligands, TNFα or IFNγ. These ligands have been used as adjuvants to activate DCs in situ or in vitro, with toxic effects. It has been shown that some molecules affect the immune system, e.g., Masticadienonic acid (MDA) and 3α-hydroxy masticadienoic acid (3α-OH MDA) triterpenes naturally occurring in several medicinal plants, since they activate the nitric oxide synthase in macrophages and induce T lymphocyte proliferation. The DCs maturation induced by MDA or 3a-OH MDA was determined by incubating these cells with MDA or 3α-OH MDA, and their phenotype was afterwards analyzed. The results showed that only 3α-OH MDA was able to induce DCs maturation. When mice with melanoma were inoculated with DCs/3α-OH MDA, a decreased tumor growth rate was observed along with an extended cell death area within tumors compared to mice treated with DCs incubated with MDA. In conclusion, it is proposed that 3α-OH MDA may be an immunostimulant molecule. Conversely, it is proposed that MDA may be a molecule with anti-inflammatory properties.