The embedding of General Relativity in five dimensions

We argue that General Relativistic solutions can always be locally embedded in Ricci-flat 5-dimensional spaces. This is a direct consequence of a theorem of Campbell (given here for both a timelike and spacelike extra dimension, together with a special case of this theorem) which guarantees that anyn-dimensional Riemannian manifold can be locally embedded in an (n+1)-dimensional Ricci-flat Riemannian manifold. This is of great importance in establishing local generality for a proposal recently put forward and developed by Wesson and others, whereby vacuum (4+1)-dimensional field equations give rise to (3+1)-dimensional equations with sources. An important feature of Campbell's procedure is that it automatically guarantees the compatibility of Gauss-Codazzi equations and therefore allows the construction of embeddings to be in principle always possible. We employ this procedure to construct such embeddings in a number of simple cases.     

Mathematical simulation of oil reservoir properties

The study and computational representation of porous media properties are very important for many industries where problems of fluid flow, percolation phenomena and liquid movement and stagnation are involved, for example, in building constructions, ore processing, chemical industries, mining, corrosion sciences, etc. Nevertheless, these kinds of processes present a noneasy behavior to be predicted and mathematical models must include statistical analysis, fractal and/or stochastic procedures to do it. This work shows the characterization of sandstone berea core samples which can be found as a porous media (PM) in natural oil reservoirs, rock formations, etc. and the development of a mathematical algorithm for simulating the anisotropic characteristics of a PM based on a stochastic distribution of some of their most important properties like porosity, permeability, pressure and saturation. Finally a stochastic process is used again to simulated the topography of an oil reservoir.     

Triterpene glycosides of Astragalus quisqualis. I. The structure of quisquagenin

The hydrolysis of the glycoside quisqualoside B, isolated from the herbAstragalus quisqualis Bunge, has given the new cycloartane triterpenoid quisquagenin, which has the structure of 20(R),24(S)-epoxycycloartane-3β,16β,25-triol.     

Determining Optimum Fertilizer Combinations Through Goal Programming with Penalty Functions: An Application to Sugar Beet production in Spain

A goal programming model was used to analyse optimum fertilizer combinations. Under this approach, the fertilizer requirements, instead of being fixed values as in traditional linear programming, are considered targets which may or may not be achieved. A penalty system coupled to the goal programming model makes the specified lower and upper levels of nutrients more flexible and realistic. A simple example is used to expound the model, and then applied to real data to give optimum combinations of fertilizers for sugar beet in Western Andalusia (Spain).     

A study of hadronic decays of the ϒ′

We present a detailed study of the decays ?′ → π⁺π^?? and ?′ → π⁰π⁰?, where the ? decays subsequently to e⁺e^? or μ⁺μ^?. The results are obtained from a sample of 146 000 ?′ decays observed with the CUSB detector at the Cornell Electron Storage Ring. We derive branching fractions of (18.9 ± 2.6)% for ?′ → π′π^?? and (10.3 ± 2.3)% for ?′ → π⁰π⁰?, and determined partial widths for these decays. Invariant mass and angular distributions of both the π⁺π^? and π⁰π⁰ systems are presented. We also set a limit on the branching fraction for ?′ → η? of less than 0.2% at the 90% confidence level.     

Synthesis and structure of 1,10-phenanthroline bis{[2-(2-pyrrole)-methylimino]4-methylphenolato}nickel(II)

Summary Electrochemical oxidation of nickel in an acetonitrile solution containing 2-pyrrole-[N-(2-hydroxy-4-methyl-phenyl)methylimine] (H₂L) and 1,10-phenanthroline (phen) yielded Ni(HL)₂·phen, whose crystal structure was determined by XRD. The nickel atom has a distorted octahedral geometry, and is coordinated to the phenolic oxygen and imino nitrogen atoms of two Schiff base ligands. The i.r. and u.v.-vis. spectra of the complex are discussed and related to the structure.     

Potential-dependent sum frequency generation study of 5-methylbenzotriazole on polycrystalline copper, platinum, and gold

In situ sum frequency generation vibrational spectroscopy, at varied potentials and polarization combinations, was performed on polycrystalline copper, polycrystalline platinum, and polycrystalline gold samples in 0.5 M HClO4 with 50 mM 5-methylbenzotriazole (5-methylBTAH) added. These studies were performed to determine the orientation of 5-methylBTAH on the surface at different potentials. For copper surfaces, orientation of the molecule on the surface is not affected by potential within the potential window studied (-500 to -100 mV vs saturated calomel electrode (SCE)). Sum frequency generation spectra of 5-methylBTAH on platinum show a change in orientation over the potential range studied (-250 to 750 mV vs SCE). The orientation of the methyl group tilts more toward the plane of the interface as the potential is scanned in the positive direction. This orientation change is correlated to hydrogen coadsorption on the platinum surface at low potentials. 5-Methylbenzotriazole lies in the surface plane or does not orient on gold at lower potentials but the orientation is tilted toward normal at more positive potentials over the potential range studied (-500 to 900 mV vs SCE). To compliment these results, cyclic voltammetry and electrochemical impedance spectroscopy measurements were performed. Cyclic voltammograms of copper show that addition of 5-methylBTAH protects the surface from copper dissolution, increasing the electrochemical window by 450 mV. Cyclic voltammetry of 5-methylBTAH on platinum showed a partial blockage of adsorbed hydrogen and also prevented the adsorption of oxygenated species at 450-600 mV. Cyclic voltammetry on gold shows that 5-methylBTAH blocks oxide formation for 400 mV thus increasing the electrochemical window. Electrochemical impedance spectroscopy has been performed to determine the potential of zero charge of 5-methylBTAH on copper.