On existence,uniqueness, and numerical evaluation of solutions of ordinary and hyperbolic differential equations

Summary After a preliminary survey of related results, a general uniqueness theorem for the ordinary differential equation dy/dx=f(x, y) is given in section 4. The general uniqueness theorem for the hyperbolic partial differential equation u_xy=f(x, y, u), proved in section 5, is an exact analogue of the general uniqueness theorem for the ordinary differential equation dy/dx=f(x, y). This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research and Development Command under Contract No. AF 49(638)-228. This is a detailed account of lectures given at the Sixth Conference of Arsenal Mathematicians, held at Duke University Durham, North Carolina, June 1, 2, 1960, and at the Symposium on the Numerical Treatment of Ordinary Differential Equations, Integral and Integro-Differential Equations, Rome, 20–24 September 1960.     

Energy method and localization of solutions of equations of continuum mechanics

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 18–25, March–April, 1989.     

Application of the method of brather for the determination of complex dielectric permittivity from measurements of isothermal polarization current

Some years ago, Brather proposed a method for calculation of the real and imaginary parts of the complex dielectric permittivity starting from measurements of isothermal polarization current. This method shows some advantages over the Hamon method, which is normally used. Both methods are applied in this work to the β relaxation of poly(butyl methacrylate). It is concluded that, with the usual accuracy of measurement, a combination of the two methods is advisable; Hamon's method is taken to be a first approximation to that of Brather. Results following the two procedures are compared, and their respective advantages and disadvantages are discussed.     

Properties of pp annihilations into strange particles at 702 and 757 MeV/c

$\text{p}\text{p}$ annihilations, leading to the production of at least one neutral K meson in the final state, have been studied in the incident momentum region of 700–760 MeV/c. Topological cross sections and cross sections for the various exclusive final states are presented. Detailed analyses of the different final states have been carried out to study the importance of resonance production and of quasi two-body and quasi three-body processes. A detailed study of the $\text{K}\text{K}\text{π}$ system in the four-body final states shows that the F₁ meson is a spurious effect due to systematic biases. In the momentum range investigated, the C = +1 final states are strongly suppressed.     

Investigation of factors affecting the adsorption of functional molecules onto gel silicas. 1. Flow microcalorimetry and infrared spectroscopy

Flow microcalorimetry and infrared spectroscopy were used to study the surface structure and adsorptive properties of a series of calcined and uncalcined porous silicas. The adsorbates DL-menthol, (R)-(+)-limonene, (+/-)-citronellal and carvone were selected for their functionality, that included carbonyl, vinylic and hydroxyl groups. The amounts of probe retained by the silicas together with the energy exchange involved in the adsorption/desorption process were determined by flow microcalorimetry. The functional groups involved in these interactions were studied by means of infrared spectroscopy. It was observed that the strongest interactions with the silica surface took place through hydrogen bonding onto the surface silanol. The most retentive probes were found to be those with a carbonyl group in their structure. Adsorption onto calcined silicas was found to be less energetic than onto the equivalent calcined samples. The adsorption densities were compared with theoretical predictions based on molecular models. In all cases apart from citronellal monolayer coverage were not observed due to steric effects.     

Complexes of osmium (III) obtained from OsO4 and ethylenethioureas. A kinetic study of the reduction in HClO4 solutions

Summary OsO₄ reacts with imidazolidine-2-thione and itsN-methyl andN-ethyl derivatives in acidified 11 vol. H₂O:EtOH to give [OsL₆]³⁺. Complexes obtained in the presence of HClO₄ or HBF₄ have been isolated as crystals and characterized by elemental analysis, i.r. spectroscopy and magnetic measurements.All the ligands bind the metal through the sulphur atom and the magnetic measurements are consistent with low spin osmium(III). The kinetics of [OsL₆]³⁺ formation has been followed spectrophotometrically. Thepseudo-first order rate constants are linear both with respect to the acid and the ligand concentrations, indicating that the kinetically significant process involves one proton and one molecule of the ligand. A comparison of these results with those obtained for the analogous reaction with thiourea is reported.     

Validation and quality control of methylmercury determinations by means of capillary electrophoresis

Methyl-Hg is one of the most dangerous pollutants in the environment. It is highly toxic and accumulates through the food chain. Tuna fish especially tends to concentrate Hg in the form of methyl-Hg. Quality assurance is a well established routine in analytical laboratories to control the variability of analytical results and to maintain adequate stability, detection power and reproducibility. Capillary electrophoresis (CE) has shown in recent years powerful capabilities for the resolution and analysis of very complex samples. The high resolution and peak capacity characteristics of this technique could be used favourably in speciation studies of organo-Hg compounds. Since the time needed for separation is usually very short in this technique, it lends itself to routine analysis. The application of quality control approaches in the analysis of methyl-Hg in tuna freeze-dried materials using CE is reported.     

Surface‐enhanced Raman scattering and density functional theory studies of bis(4‐aminophenyl)sulfone

Raman and surface‐enhanced Raman scattering (SERS) spectra of dapsone by using colloidal silver nanoparticles have been recorded. Density functional theory was used for the optimization of ground state geometries and simulation of the vibrational spectrum of this molecule. The SERS spectrum with a large silver cluster as a model metallic surface was simulated for the first time. Taking into account the experimental and calculated Raman as well as the SERS normal modes and the corresponding assignments, along with the modeling of the free dapsone and the one in the presence of the colloidal silver nanoparticles, the importance of the sulfone group on the SERS effect in dapsone was inferred. Copyright © 2009 John Wiley & Sons, Ltd.     

Coherence and wavefront characterization of Si‐111 monochromators using double‐grating interferometry

A study of the coherence and wavefront properties of a pseudo‐channel‐cut monochromator in comparison with a double‐crystal monochromator is presented. Using a double‐grating interferometer designed for the hard X‐ray regime, the complex coherence factor was measured and the wavefront distortions at the sample position were analyzed. A transverse coherence length was found in the vertical direction that was a factor of two larger for the channel‐cut monochromator owing to its higher mechanical stability. The wavefront distortions after different optical elements in the beam, such as monochromators and mirrors, were also quantified. This work is particularly relevant for coherent diffraction imaging experiments with synchrotron sources.