Electron-impact and chemical ionization detection of nicotine and cotinine by gas chromatography-mass spectrometry in rat plasma and brain.

Nicotine and its metabolite, cotinine, were measured in rat plasma and brain by gas chromatography-mass spectrometry. Both agents were extracted from plasma and brain, separated on a capillary column, and quantified by single-ion monitoring. The major fragment ions of nicotine and cotinine at m/z 84 and m/z 98, respectively, were monitored by electron-impact ionization detection and the protonated molecular ions at m/z 163 and m/z 177, respectively, were monitored by chemical ionization detection. Both compounds were quantified using deuterium-labeled nicotine and cotinine, respectively, as internal standards.     

Linear selections for the metric projection

A characterization is given of those proximinal subspaces of a normed linear space whose (set-valued) metric projections admit linear selections. This characterization is applied in each of the classical Banach spaces C₀(T) and L_p (1 ? p ? ∞), resulting in an intrinsic characterization of those one-dimensional subspaces whose metric projections admit linear selections.     

A mean-field theory for self-propelled particles interacting by velocity alignment mechanisms

A mean-field approach (MFA) is proposed for the analysis of orientational order in a two-dimensional system of stochastic self-propelled particles interacting by local velocity alignment mechanism. The treatment is applied to the cases of ferromagnetic (F) and liquid-crystal (LC) alignment. In both cases, MFA yields a second order phase transition for a critical noise strength and a scaling exponent of 1/2 for the respective order parameters. We find that the critical noise amplitude η_c at which orientational order emerges in the LC case is smaller than in the F-alignment case, i.e. η^LC_C<η^F_C. A comparison with simulations of individual-based models with F- resp. LC-alignment shows that the predictions about the critical behavior and the qualitative relation between the respective critical noise amplitudes are correct.     

The mutual transformation of magnetoacoustic waves in plane inhomogeneous systems

In this paper an approach is given to the generation of slow magnetoacoustic waves by fast ones and vice versa and to the reflection of magnetoacoustic waves at plasma and magnetic field inhomogeneities. The cases of very strong and very weak fields as well as the case when the Alfvén velocity is of the order of the sound velocity are closely investigated. General conclusions are drawn on the mutual transformation of magnetoacoustic waves.     

Ionization Cross Sections of Gas Molecules for Plasma Chemistry

Using the recently tested formula of Gryzinski electron impact ionization cross sections for several molecules are calculated. The additivity rule and the statistical approach by Fitch and Sauter are discussed. With new experimental ionization cross sections it is possible to derive the regression coefficients also for P, As, B, and Si, which are presented together with the previously obtained values as a function of the atomic number. It appears to be possible to obtain coefficients for other atoms by interpolation. First attemps to determine regression coefficients also for 20 and 35 eV electron energy are discussed.     

An alternate proof of Cohn's four squares theorem

While various techniques have been used to demonstrate the classical four squares theorem for the rational integers, the method of modular forms of two variables has been the standard way of dealing with sums of squares problems for integers in quadratic fields. The case of representations by sums of four squares in was resolved by Götzky, while those of and were resolved by Cohn. These efforts utilized modular forms. In previous work, the author was able to demonstrate Götzky's theorem by means of the geometry of numbers. Here Cohn's theorem on representation by the sum of four squares for is proven by a combination of geometry of numbers and quaternionic techniques.     

Congenitally corrected transposition of the great arteries (L-TGA) with situs inversus totalis in adulthood: findings with magnetic resonance imaging

Diagnosis of congenitally corrected transposition of the great arteries (L-TGA) with situs inversus totalis in two adult patients was made by magnetic resonance imaging (MRI). Visualization of the complete anatomy and quantification of ventricular function was possible. Relevant concomitant disease such as perimembraneous ventricular septal defect, atrial secundum septal defect, tricuspid regurgitation, valvular pulmonic stenosis, and pulmonary artery dilatation were clearly depicted by MRI using standard spin-echo and gradient-echo techniques. Findings were confirmed by cardiac catheterization in both patients. In this rare and complex congenital cardiac anomaly, MRI is an excellent imaging modality as echocardiography may be difficult to interpret due to restricted imaging windows. MRI may help in the decision about the necessity to undergo further invasive evaluation and may help to make cardiac catheterization a straightforward procedure.     

Short proofs of the universality of certain diagonal quadratic forms

In a paper of Kim, Chan, and Rhagavan, the universal ternary classical quadratic forms over quadratic fields of positive discriminant were discovered. Here a proof of the universality of some of these quadratic forms is given using a technique of Liouville. Another quadratic form over the field of discriminant 8 is shown universal by a different elementary approach. Received: 30 October 2007