A Weak Formulation of the Boltzmann Equation Based on the Fourier Transform

In this article we present an alternative formulation of the spatially homogeneous Boltzmann equation. Rewriting the weak form of the equation with shifted test functions and using Fourier techniques, it turns out that the transformed problem contains only a three-fold integral. Explicit formulas for the transformed collision kernel are presented in the case of VHS models for hard and soft potentials. For isotropic Maxwellian molecules, a classical result by Bobylev is recovered, too.     

Catalytic asymmetric intramolecular aminopalladation: improved palladium(II) catalysts

[reaction: see text] Cobalt oxazoline palladacyclic (COP) complex 4 containing acetate as a bridging ligand is an excellent catalyst for asymmetric intramolecular aminopalladation to synthesize 4-vinyloxazolidin-2-ones in 91-98% ee. In contrast to previously reported Pd(II) catalysts, COP-OAc (4) promotes the asymmetric cyclization of (Z)-allylic N-tosylcarbamates without prior activation by silver salts.     

The low temperature heat capacity and electrical resistivity of ReO3

Low temperature heat capacity and electrical resistivity measurements are reported for ReO₃. The heat capacity data give an acoustical mode Debye temperature θ = 327 K, and an electrronic density of states parameter γ = 2.83 mJ/mole-K². The observed temperature dependence of the resistivity is consistent with the existence of electron scattering both from acoustic mode phonons and from optical mode phonons of characteristic temperature θ_E = 1080 K. The above measurements are used to evaluate the electron-phonon interaction parameter λ = 0.24.     

Regioselective Isomerisation of Highly Substituted 1-Methylenecyclohexenepoxides to the Corresponding Allylic Alcohols. Influence of the Base and of the Protecting Groups

Summary. Highly substituted 1-methylenecyclohexenepoxides 3, useful building blocks for a projected synthesis of wailupemycin A (1), were synthesized from (R)-carvone in eight synthetic steps in 23–40% overall yield. The regioselectivity of the subsequent isomerisation to the corresponding allylic alcohols was shown to depend on the basicity of the reagent and on the bulkiness of the protecting groups existing in 3. With diethylaluminum 2,2,6,6-tetramethylpiperidid (DATMP), secondary allylic alcohols 5 were formed exclusively. With strong bases such as a mixture of lithium di-iso-propylamide and potassium tert-butoxide (LIDAKOR), the tertiary allylic alcohol 6 was obtained as predominant product.To whom inquiries about the X-ray analysis should be addressed     

Optimization of rod antennas of mobile phones

Two types of rod antennas of mobile phones are optimized so that the radiated energy absorbed by the head or body of the user is reduced and the radiation intensity to other areas especially to the receiver is increased. The mathematical modelling of this problem leads to an infinite dimensional bicriterial optimization problem. It is shown that this optimization problem and a discretized version of this problem are solvable. The relationship between the infinite and finite dimensional optimization problem is investigated. Numerical results are presented for mobile phones working with the GSM standards 900 and 1800.     

On Asymptotic Expansions and Scales of Spectral Universality in Band Random Matrix Ensembles

 We consider real random symmetric N × N matrices H of the band-type form with characteristic length b. The matrix entries are independent Gaussian random variables and have the variance proportional to , where u(t) vanishes at infinity. We study the resolvent in the limit and obtain the explicit expression for the leading term of the first correlation function of the normalized trace . We examine on the local scale and show that its asymptotic behavior is determined by the rate of decay of u(t). In particular, if u(t) decays exponentially, then . This expression is universal in the sense that the particular form of u determines the value of C > 0 only. Our results agree with those detected in both numerical and theoretical physics studies of spectra of band random matrices. Received: 8 April 2000 / Accepted: 7 June 2002 Published online: 21 October 2002 RID="*" ID="*" Present address: Département de Mathématiques, Université de Versailles Saint-Quentin, 78035 Versailles, France.     

Characterization of polymer dispersions by Fourier transform rheology

Fourier transform rheology is a very sensitive technique to characterize non-linear rheological fluid properties. It has been applied here for the first time to polymer dispersions in water and the results are compared to those from conventional rheology, namely steady and small amplitude oscillatory shear experiments. The investigated systems are mainly based on styrene and n-butylacrylate. A first attempt was made to evaluate how far colloidal parameters like particle volume fraction and ionic strength as well as chemical composition and surface characteristics of the dispersed particles are reflected in FT-rheology spectra. Significantly different non-linearities are observed for highly concentrated dispersions of particles with different T_g. These differences are not detected in linear oscillatory shear and show up in steady shear only at significantly higher shear rates. Particle surface characteristics influence the non-linear response in oscillatory shear significantly and the intensity of the overtones is found to be higher for a dispersion of particles with a “hairy” swollen surface layer as compared to a system of smooth particles, although the solids content was adjusted to match the steady shear viscosity. The intensity of the overtones in FT-rheology strongly decrease upon dilution. At a solid content below 35% no differences are observed in the FT-experiments for the systems investigated here, whereas the differences in steady shear are very pronounced in this concentration range. A significant influence of added salt onto the non-linear response is detected for some systems, which might be correlated to the stability of these systems. The observed phenomena certainly cannot be explained in terms of constitutive equations or microstructural statistical mechanical models at present. Thus, FT-rheology yields information complementary to classical steady or linear oscillatory shear experiments. Received: 11 December 2000 Accepted: 8 April 2001     

Near-Infrared Spectroscopy: Applications in the Analysis of Tablets and Solid Pharmaceutical Dosage Forms

Introduction

The popularity of near-infrared (near-IR) spectroscopy is rapidly increasing for many reasons. Availability of inexpensive yet powerful computers and chemometric software for spectral data analysis is fostering the growth of new applications of the technique. The development of rapid-scanning spectrometers offering very high signal-to-noise ratios, an increased understanding and acceptance of the method in a variety of industries, and the need to maintain real-time process control in an era of total quality management are other reasons this method has begun to receive such attention. Near-IR spectroscopy has been used for a wide range of analyses in industries as diverse as biomedicine and petrochemicals. Although the pharmaceutical industry has been relatively slow to embrace this technique, a variety of pharmaceutical applications of near-IR have been identified and investigated. This review will discuss the development of near-IR spectroscopy for the analysis of pharmaceutical dosage forms, specifically solid dosage from matrices, capsules, and tablets. The chemometric techniques used extensively in these analyses will also be discussed briefly.