A semi-discrete convergent scheme for a quasilinear hyperbolic equation

We establish here the convergence (thereby proving the existence) of a semi-discrete scheme for the quasilinear hyperbolic equation where x ∈ Rⁿ, t ∈ [0,T], and ? ∈ L^∞ (Rⁿ). It is well known that the above problem does not necessarily have global classical solutions and the usual concepts of weak solution. do not lead to a unique solution The existence of a unique solution to the above problem in a suitable sense was established in [3], where a parabolic problem obtained by introducing the term ??Δu was studied and then the behavior as ? → 0 was discussed. A difference scheme approach to a problem of the above type where ?_i does not depend on x and t and Ψ does not depend on u was also studied in [2]. The aim of this paper is to present a proof for the case when ? depends on x, Ψ depends on u, and the technical complications in this case are nontrivial. The discussions in this paper my be considered as continuation of the ideas in the above papers.     

Local and global chirality at surfaces: succinic acid versus tartaric acid on Cu110

A detailed comparison of tartaric acid (HOOC-CHOH-CHOH-COOH) and succinic acid (HOOC-CH(2)-CH(2)-COOH) molecules on a Cu(110) surface is presented with a view to elucidate how the two-dimensional chirality exhibited by such robust, chemisorbed systems is affected when both OH groups of the former molecule are replaced with H groups, a stereochemical change that leaves the metal-bonding functionalities of the molecule untouched but destroys both chiral centers. It is found that this change does not significantly affect the thermodynamically preferred chemical forms that are adopted, namely the doubly deprotonated bicarboxylate at low coverages (theta 相似文献   

Inexpensive device for measurements with ion-selective and pH electrodes

The design and construction of a simple device for measuring ionic concentrations (or pH) with ion-selective electrodes are described. The automated system includes a special electronic circuit with an operational amplifier, a signal conditioner and a personalcomputer. A digital multimeter can be used if automation is not required. The results obtained in tests with iodide-, chloride- and nitrate-selective electrodes and glass electrodes show very good agreement with those obtained with sophisticated commercial apparatus.     

Monolayers of hydrogen-bonded polymer blends at the air–water interface: poly(vinylacetate)+poly (4-hydroxystyrene)

 The surface pressure (Π) vs surface concentration (Γ_s) curves of the hydrogen-bonded polymer blend poly(vinylacetate)+ poly(4-hydro-xystyrene) (PVAc+P4HS) have been measured at 25 °C onto a water subphase at pH=2.0. While PVAc forms extended monolayers, and the free surface of water is found to be a good solvent for it, P4HS forms compressed monolayers, and the surface is a near Θ-type solvent for it. PVAc and P4HS form miscible non-ideal monolayers until near the collapse pressure through the whole concentration range. The composition dependence of the Π–Γ_s curves is rather complex. Contrary to what might be expected, the addition of PVAc to the blend does not reduce the rigidity of the monolayer until its weight fraction is larger than 0.5. The compressibility data of the P4HS-rich monolayers suggest the existence of a second maximum at high surface coverages, a result already observed in some polysiloxanes. Received: 11 March 1998 Accepted: 7 May 1998     

Optimisation and validation of an automated solid phase extraction technique coupled on-line to enzyme-based biosensor detection for the determination of phenolic compounds in surface water samples

Summary A fully integrated screening system for phenolic compounds was developed incorporating on-line solid phase extraction, fractionation and biosensor detection. Two different types of biosensors, solid graphite and carbon paste electrodes incorporating the enzyme tyrosinase, were compared and used in the screening system. Interfacing of the solid phase extraction and fractionation with the biosensor detection was given special attention since the biosensors were not compatible with the organic modifier used for desorption of phenols from the solid phase extraction step. The system was validated with conventional analytical techniques. Surface water samples from the Ebro river were spiked with 1,10, and 25g L^–1 of catechol, phenol,p-cresol, respectively. Three out of seven samples were spiked and the correct samples were identified, containing phenols equivalent to the spiked concentrations.     

The reaction of β-aminoenones with substituted acetonitriles. Regiospecific synthesis of 2(1H)-pyridones

Unsymmetrically substituted β-aminoenones react with malononitrile, cyanomethylphenylsulfone, benzoyl-acetonitrile and ethyl cyanoacetate, in very mild conditions, to yield regiospecifically 3-functionalized 2(1H)-pyridones in high yields.     

Shift reagent 1H NMR study of methoxycoumarins

The complete assignment of the proton chemical shifts of coumarin ( 1 ), all monomethoxy derivatives and the six possible dimethoxyl substituted compounds at the aromatic ring was achieved at 60 MHz in a quantitative study utilizing Pr(fod)₃ as the shift reagent. It was found that in addition to the complexation at the lactone carbonyl a second interaction of the lanthanide shift reagent occurs when two methoxyl groups are found in an ortho distribution. The results are discussed in comparison to data published for flavones in the presence of Pr(fod)₃ shift reagent.     

Langmuir monolayers of the zwitterionic surfactant hexadecyl 1-N-L-tryptophan glycerol ether

We report the formation of Langmuir monolayers of pure zwitterionic hexadecyl 1-N-L-tryptophan glycerol ether (C(16)-TGE) surfactant and mixed monolayers of cationic-zwitterionic surfactant obtained modifying the pH of the subphase. The pressure-area and surface potential-area isotherms and fluorescence microscopy measurements have been used to characterize the surface phase transitions in the monolayers. These transitions appeared at larger areas as the pH decreased from 6.0 to 2.0 and almost disappeared as the pH decreased further. The analysis of the surface potential and the infrared reflection-absorption spectroscopy data suggests that the phase transition is associated with a change of orientation of both the hydrocarbon chain and the aromatic group of the surfactant with respect to the air-water surface. The surface rheology of the monolayers was studied by quasielastic light scattering and by the oscillatory barrier technique. The results indicate that there is at least one relaxation process in the monolayer.     

Combined Dynamic Model for the Kinetics of Electron Transfer from Cytochrome to a Bacteriochlorophill Dimer in Reaction Centers of Rps. Sulfoviridis

The electron transfer from the heme of cytochrome c to the bacteriochlorophill dimer in reaction centers of photosynthetic purple bacteria Rps. sulfoviridis is studied by laser flash photolysis at 40–296 K in conditions where one, two, or three cytochrome hemes are chemically reduced. In the model used for the electron transfer kinetics, the protein relaxation is described with a temperature-independent oscillatory coordinate and a temperature-dependent diffusion coordinate, with the protein dielectric relaxation times widely distributed along the diffusion coordinate. It is found that all the protein complexes can be divided into proteins with fast (k _et = 10⁷ to 10^–4 s^–1) and slow (k _et 100 s^–1) electron transfer. These populations presumably differ by the protonation state of the functional group. The contribution of the oscillatory and diffusion coordinates alters, which severely affects k _et. Parameters V _ab, G, , ₀, and for these reactions are determined.     

The applicability of DTA and DSC techniques to the study of the kinetics of phase transition reactions

Differential thermal analysis and differential scanning calorimetry techniques have been used to study the kinetics of phase transitions. The aragonite/calcite transformation was chosen as test reaction.Marked discrepancies were observed between the DTA kinetic results and those obtained from isothermal kinetic measurements. This disagreement is associated with the difficulty of determining accurately the reaction rate of the process from a DTA curve.In contrast, in DSC measurements, where the reaction rate is given by the height of the peak from the base-line, it is possible to get a satisfactory fit of the data, and the kinetic results obtained with this technique are in good agreement with the isothermal ones.

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Zusammenfassung Die Differentialthermoanalyse und DSC wurden zur Untersuchung der Kinetik von Phasenübergängen eingesetzt. Die Umwandlung Aragonit/Calcit wurde als Testreaktion gewählt.Bedeutende Diskrepanzen wurden zwischen den kinetischen Ergebnissen der DTA und den durch isotherme kinetische Messungen erhaltenen Ergebnissen beobachtet. Diese Abweichungen sind damit verbunden, daß es schwierig ist, die Reaktionsgeschwindigkeit des Vorgangs aus einer DTA-Kurve genau zu ermitteln.Bei DSC-Messungen,wo die Reaktionsgeschwindigkeit durch die Höhe des Peaks von der Grundlinie gegeben ist, kann eine befriedigende Anpassung der Daten erhalten werden, und die durch diese Technik erhaltenen kinetischen Ergebnisse sind in guter Übereinstimmung mit den isothermen Ergebnissen.

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