A boundary value problem associated with the second painlevé transcendent and the Korteweg-de Vries equation

The differential equation considered is \(y'' - xy = y|y|^\alpha \) . For general positive α this equation arises in plasma physics, in work of De Boer & Ludford. For α=2, it yields similarity solutions to the well-known Korteweg-de Vries equation. Solutions are sought which satisfy the boundary conditions (1) y(∞)=0 (2) (1) $$y{\text{(}}\infty {\text{)}} = {\text{0}}$$ (2) $$y{\text{(}}x{\text{) \~( - }}\tfrac{{\text{1}}}{{\text{2}}}x{\text{)}}^{{{\text{1}} \mathord{\left/ {\vphantom {{\text{1}} \alpha }} \right. \kern-\nulldelimiterspace} \alpha }} {\text{ as }}x \to - \infty $$ It is shown that there is a unique such solution, and that it is, in a certain sense, the boundary between solutions which exist on the whole real line and solutions which, while tending to zero at plus infinity, blow up at a finite x. More precisely, any solution satisfying (1) is asymptotic at plus infinity to some multiple kA i(x) of Airy's function. We show that there is a unique k^*(α) such that when k=k^*(α) the condition (2) is also satisfied. If 0 ^*, the solution exists for all x and tends to zero as x→-∞, while if k>k ^* then the solution blows up at a finite x. For the special case α=2 the differential equation is classical, having been studied by Painlevé around the turn of the century. In this case, using an integral equation derived by inverse scattering techniques by Ablowitz & Segur, we are able to show that k^*=1, confirming previous numerical estimates.     

Comparison between discrete dipole approximation and other modelling methods for the plasmonic response of gold nanospheres

We investigate the plasmonic response of gold nanospheres calculated using discrete dipole approximation validated against the results from other discretization methods, namely the finite-difference time-domain method and the finite-element methods. Comparisons are also made with calculations from analytical methods such as the Mie solution and the null-field method with discrete sources. We consider the nanoparticle interacting with the incident field both in free space and sitting on a planar substrate. In the latter case, discrete dipole approximation with surface interaction is used; this includes the interaction with the ‘image dipoles’ using Sommerfeld integration.     

Screening of Tea (Camellia sinensis) for Trait-Associated Molecular Markers

This study was done to identify random amplified polymorphic DNA (RAPD) markers that may associate with seven important traits in tea. Sixty RAPD primers were first screened using 18 cultivars under each of the 7 traits, followed by confirmatory screening of 20 promising primers with 32 tea cultivars. Six RAPD primers generated a total of nine specific bands that associated with six desired traits: black tea quality and tolerance to drought, high temperature, low temperature, Phomopsis theae, and high yield. These markers would allow early identification of plant material with the desired traits that can be advanced to the next stage of selection and enhance targeted choice of breeding stocks with the desirable traits. The nine RAPD markers identified in this study could improve precision and efficiency in tea breeding and selection and are an important contribution towards the establishment of marker-assisted selection in tea breeding programmes.     

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Ohne Zusammenfassung     

Eigenvalue Distribution in the Self-Dual Non-Hermitian Ensemble

We consider an ensemble of self-dual matrices with arbitrary complex entries. This ensemble is closely related to a previously defined ensemble of anti-symmetric matrices with arbitrary complex entries. We study the two-level correlation functions numerically. Although no evidence of non-monotonicity is found in the real space correlation function, a definite shoulder is found. On the analytical side, we discuss the relationship between this ensemble and the β=4 two-dimensional one-component plasma, and also argue that this ensemble, combined with other ensembles, exhausts the possible universality classes in non-hermitian random matrix theory. This argument is based on combining the method of hermitization of Feinberg and Zee with Zirnbauer's classification of ensembles in terms of symmetric spaces.     

Spectral Gap and Exponential Decay of Correlations

We study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short-range interactions on a wide class of lattices. We prove that, if two observables anticommute with each other at large distance, then the nonvanishing spectral gap implies exponential decay of the corresponding correlation. When two observables commute with each other at large distance, the connected correlation function decays exponentially under the gap assumption. If the observables behave as a vector under the U(1) rotation of a global symmetry of the system, we use previous results on the large distance decay of the correlation function to show the stronger statement that the correlation function itself, rather than just the connected correlation function, decays exponentially under the gap assumption on a lattice with a certain self-similarity in (fractal) dimensions D < 2. In particular, if the system is translationally invariant in one of the spatial directions, then this self-similarity condition is automatically satisfied. We also treat systems with long-range, power-law decaying interactions.     

Structure and magnetism of Eu2IrD5

A powder neutron diffraction study of Eu¹⁵³₂IrD₅ has shown it to be isostructural with Sr₂IrD₅ at room temperature. Unlike the latter compound, it does not undergo a deuterium-ordering transition at low temperatures. Magnetic scattering at helium temperatures confirms the suggestion that it becomes ferromagnetic below 20 K with a moment corresponding to that of divalent europium.     

Isobaric metabolite interferences and the requirement for close examination of raw data in addition to stringent chromatographic separations in liquid chromatography/tandem mass spectrometric analysis of drugs in biological matrix

In addition to matrix effects, common interferences observed in liquid chromatography/tandem mass spectrometry (LC/MS/MS) analyses can be caused by the response of drug-related metabolites to the multiple reaction monitoring (MRM) channel of a given drug, as a result of in-source reactions or decomposition of either phase I or II metabolites. However, it has been largely ignored that, for some drugs, metabolism can lead to the formation of isobaric or isomeric metabolites that exhibit the same MRM transitions as parent drugs. The present study describes two examples demonstrating that interference caused by isobaric or isomeric metabolites is a practical issue in analyzing biological samples by LC/MS/MS. In the first case, two sequential metabolic reactions, demethylation followed by oxidation of a primary alcohol moiety to a carboxylic acid, produced an isobaric metabolite that exhibits a MRM transition identical to the parent drug. Because the drug compound was rapidly metabolized in rats and completely disappeared in plasma samples, the isobaric metabolite appeared as a single peak in the total ion current (TIC) trace and could easily be quantified as the drug since it was eluted at a retention time very close to that of the drug in a 12-min LC run. In the second example, metabolism via the ring-opening of a substituted isoxazole moiety led to the formation of an isomeric product that showed an almost identical collision-induced dissociation (CID) MS spectrum as the original drug. Because two components were co-eluted, the isomeric product could be mistakenly quantified and reported by data processing software as the parent drug if the TIC trace was not carefully inspected. Nowadays, all LC/MS data are processed by computer software in a highly automated fashion, and some analysts may spend much less time to visually examine raw TIC traces than they used to do. Two examples described in this article remind us that quality data require both adequate chromatographic separations and close examination of raw data in LC/MS/MS analyses of drugs in biological matrix.