The aliasing‐phenomenon in visual terms

In a recent paper it was shown that the aliasing phenomenon, which leads to a severe identification problem in the estimation of stochastic differential equations, can be overcome by using a polygonal (or higher) approximation for the time paths of the exogenous variables. This work attempts to visualize the problem and presents several simulated trajectories of a continuous time AR(2)‐process (Ornstein‐Uhlenbeck‐process) together with the observationally equivalent structures. Furthermore it is shown that aliasing can even change the analytical properties of the time paths of the system: whereas the first component of the Ornstein‐Uhlenbeck‐process is differentiable, the trajectories of the aliasing structures are continuous, but not differentiable any more.     

The equation of state of the hard-disc fluid revisited

Some points about the search for analytical expressions for the equation of state of the hard-disc fluid are discussed in the light of the most recent advances in the field. New and accurate equations of state for this fluid are proposed.     

A Singular Limit Problem for Conservation Laws Related to the Camassa–Holm Shallow Water Equation

We consider a shallow water equation of the Camassa–Holm type, which contains nonlinear dispersive effects as well as fourth order dissipative effects. We prove that as the diffusion and dispersion parameters tend to zero, with a condition on the relative balance between these two parameters, smooth solutions of the shallow water equation converge to discontinuous weak solutions of a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L ^p setting.     

Correlations between quantum and stochastic systems with a dephasing coupling

Correlations between single qubit and classical environment are studied by means of the stochastic Liouville equation, where a dephasing coupling between them is assumed. When the dephasing of the qubit is characterized by the two-state-jump Markov process, the properties of the total, classical and quantum correlations are examined.     

New Methacrylate Copolymers Based on the Benzofurane Ring: Synthesis,Characterization, Monomer Reactivity Ratios and Biological Activity

The free radical copolymerization of (5-bromo-1-Benzofuran-2-yl)(phenyl)-O-methacrylketoxime (BPMKO) with 2-(4-acetylphenoxy)-2-oxoethyl-2-methylacrylate(AOEMA) has been carried out in 1, 4-dioxane at 65°C ± 1 and was analyzed by Fourier transform infrared, ¹H-NMR, ¹³C-NMR and gel permeation chromatography. Elemental analysis was used to determine the molar fractions of BPMKO and AOEMA in the copolymers. The monomer–reactivity ratios were calculated according to the general copolymerization equation using Kelen-Tüdõs and Finemann-Ross linearization methods. The reactivity ratios indicated a tendency toward random copolymerization. The polydispersity indices of the polymers were determined by gel permeation chromatography and suggested a strong tendency for chain termination by disproportionation. The thermal behaviors of copolymers with various compositions were investigated by differential scanning calorimetry and thermogravimetric analysis. The glass-transition temperature of the copolymers increased with increasing BPMKO content in the copolymers. All the products showed moderate activity against different strains of bacteria and fungi.     

The use of relative residues in fitting experimental data: an example from fluid mechanics

A curve fitting model is presented which minimizes the sum of squares of relative residues and expressions for the fit coefficients and their respective errors are derived. The new model is compared to the normal least squares model, using as an example the Reynolds number-drag coefficient data for a sphere. The results show that the best fit was obtained with the new model, indicating it may provide a useful tool for data analysis.     

Ranking Oxidant Sensitiveness: A Guide for Synthetic Utility

Common oxidants used in chemical synthesis, including newly developed perruthenates, were evaluated in the context of understanding (and better appreciating) the sensitiveness and associated potential hazards of these reagents. Analysis using sealed cell differential scanning calorimetry (scDSC) facilitated Yoshida correlations, which were compared to impact sensitiveness and electrostatic discharge experiments (ESD), that enabled sensitiveness ranking. Methyltriphenylphoshonium perruthenate (MTP3, 8 ), isoamyltriphenylphosphonium perruthenate (ATP3, 7 ) and tetraphenylphosphonium perruthenate (TP3, 9 ) were found to be the most sensitive followed by 2-iodoxybenzoic acid (IBX, 2 ) and benzoyl peroxide (BPO, 10 ), whereas the most benign were observed to be Oxone ( 12 ), manganese dioxide (MnO₂, 13 ), and N-bromosuccinimide (NBS, 17 ).     

Contribution à l'étude Électrochimique de Dérivés de l'Acide Mercapto-2 Pyridinecarboxylique-5. II

Abstract

Electrochemical caracteristics of 2-mercaptopyridine-5-carboxylic acid and its methylic ester have been determined using recent polarographic techniques. Measurements have been carried out as a function of parameters such as frequency, others surimposed signals and as a function of concentration and pH. Results are compared to those obtained for selectively methylated on sulfur or nitrogen atoms derivatives. Interpretations of the data are given. The optimal conditions for a quantitative determination by D.C. and differential pulse polarography are fixed.