The optical-mechanical analogy in general relativity: Exact Newtonian forms for the equations of motion of particles and photons

In many metrics of physical interest, the gravitational field can be represented as an optical medium with an effective index of refraction. We show that, in such a metric, the orbits of both massive and massless particles are governed by a variational principle which involves the index of refraction and which assumes the form of Fermat's principle or of Maupertuis's principle. From this variational principle we derive exact equations of motion of Newtonian form which govern both massless and massive particles. These equations of motion are applied to some problems of physical interest.     

Periodic solutions of nonlinear integral equations

The existence of a continuous periodic solution of the system

Analysis of anions by solid-state spot-tests

Trituration and capillary solid-state spot-tests for 25 anions with a number of organic and inorganic reagents have been examined. A comparative study of the corresponding reactions in solution has also been made. Incorporation of a glass-wool plug in the capillary improves the selectivity. Schemes are presented for possible use of the technique.     

Effect of Ba and Bi doping on the synthesis and sintering of Ge-based apatite phases

Recently, high oxide ion conduction has been observed in the apatite-type systems La_9.33+x(Si/Ge)₆O_26+x/2, with conductivities approaching and even exceeding that of yttria-stabilized zirconia. The Ge-based phases have been reported to suffer from Ge loss and undergo irreversible structural changes on sintering at the high temperatures required to obtain dense pellets. In this paper we discuss doping studies (Ba, Bi for La) aimed at stabilizing the hexagonal apatite lattice to high temperature, and/or lowering the synthesis and sintering temperatures. The results show that doping with Ba helps to stabilize the hexagonal lattice at high temperatures, although Ge loss appears to still be a problem. Conductivity data show that, as previously reported for the Si-based systems, non-stoichiometry in the form of cation vacancies and/or oxygen excess is required to achieve high oxide ion conduction in these Ge-based systems. Neutron diffraction structural data for the fully stoichiometric phase La₈Ba₂Ge₆O₂₆ shows that the channel oxygen atoms show little anisotropy in their thermal displacement parameters, consistent with the low oxide ion conductivity of this phase. Bi doping is shown to lower the synthesis and sintering temperatures, although the presence of Bi means that these samples are not stable at high temperatures under reducing conditions.Presented at the OSSEP Workshop Ionic and Mixed Conductors: Methods and Processes, Aveiro, Portugal, April 10–12, 2003     

Construction of solid-liquid phase diagrams in ternary systems by titration calorimetry

Titration calorimetry was used to construct the solid-liquid equilibrium line in ternary systems containing the solute and an aqueous mixed solvent by measuring the heat of dissolution of the solid solute during successive additions of the liquid solvent. The plot of cumulated heats versus the mole ratio, n_solvent/n_solute, yields two (almost) linear increases of different slopes. These two lines represent successively the enthalpy of dissolution then the enthalpy of dilution of the medium; their intersection gives the solubility and the enthalpy of dissolution of the solute. Phase diagrams have been established over the whole concentration range for o-anisaldehyde, 1,3,5-trimethoxybenzene and vanillin, in water + methanol, +ethanol, or +n-propanol at 303, 313 and 318 K.     

A Method for the Acetylation of Alcohols Catalyzed by Heteropolyoxometallates

Summary. Esterifications of acetic acid with some linear, secondary, tertiary, and benzylic alcohols mediated by catalytic amounts of Keggin, Wells–Dawson, and Preyssler type heteropolyacids were carried out under reflux at mild reaction conditions with good to excellent yields. Among the examined catalysts, H₃PW₁₂O₄₀ and H₁₄NaP₅W₃₀O₁₁₀ revealed better results than other heteropolyacids. This work was performed with the aim of simplifying the esterification process by omitting any solvents and mineral acid catalysts. Easy work-up, low cost, and acidic waste reduction, which are all important features from the environmental and economical points of view, are distinct aspects of this protocol. Heteropolyacid catalysts could be separated after a simple work-up and reused for several times.     

Water as an Efficient Solvent for Oxygenation Transformations with 34% Hydrogen Peroxide Catalyzed by some Heteropolyoxometalates

Summary. A highly efficient, selective, fast, and cheap protocol is developed for oxidation of aromatic amines and alcohols utilizing 34% hydrogen peroxide in water catalyzed by some W- and Mo-based heteropolyoxometalates. Findings showed that dodecatungstophosphoric acid, H₃PW₁₂O₄₀, was the most efficient catalyst in the examined oxidation reactions. This methodology may prove to be a valuable alternative for eco-friendly green oxidation. Inherent simplicity, easy work up, and using regenerable catalysts were other key aspects of this oxidation protocol.     

Headspace solvent microextraction of trihalomethane compounds into a single drop

Headspace solvent microextraction (HSME) into a single drop is developed for the determination of six trihalomethanes, CH2Cl2, CHCl3, C4H9Cl, CCl4, C2HCl3, and C2Cl4, in aqueous solution. A drop of benzyl alcohol containing bromoform, as an internal standard, is used for extraction. The analytes are extracted by suspending a 3-microL drop directly from the needle of a microsyringe. The needle passes through the septum of a vessel, and the needle tip appears above the surface of the solution. After the prescribed extraction time, the drop is drawn back into the syringe. The syringe is then removed, and its content is injected directly into a gas chromatography column for analysis. The main parameters affecting the HSME process, such as stirring speed, microdrop volume, sample solution temperature, microsyringe needle temperature, sample volume, solution pH, extracting solvent, and ionic strength of the solution, are studied. Also, the linear range and precision of the method are examined.     

以金属硫酸氢盐为催化剂在无溶剂条件下高效合成3,4-二氢嘧啶-2(1H)-酮

以金属硫酸氢盐M(HSO4)n(Ca(HSO4)2,Zn(HSO4)2和过硫酸氢钾制剂oxone○R)为催化剂催化醛、1,3-二羰基化合物和尿素进行缩合反应,在90℃及无溶剂的条件下高收率、一锅法合成了3,4-二氢嘧啶-2(1H)-酮.     

SnCl4 and SbCl5 promoted aromatization of enamines

Aromatic amines have been synthesized efficiently from enamines using SnCl₄ and SbCl₅ in CH₂Cl₂ at room temperature.