New evolution PDEs with many isochronous solutions

Certain nonlinear evolution PDEs in 1+1 variables (time and space) are identified, featuring a positive parameter ω and evolving, for a large class of initial data, periodically with the fixed period T=2π/ω (or perhaps with p a small integer). They are autonomous (i.e., they do not feature any explicit dependence on the time variable), but they generally (although not quite all of them) depend explicitly on the space variable hence are not translation-invariant. They are integrable, having been obtained by applying an appropriate change of dependent and independent variables to certain nonlinear evolution PDEs whose integrable character has been recently ascertained. Solutions of some of these PDEs are exhibited.     

Comparison of liquid-liquid partition, HS-SPME and static HS GC/MS analysis for the quantification of (-)-linalool in human whole blood samples

The aim of this investigation was to develop a fast and convenient method for the determination of (-)-linalool in human whole blood to facilitate pharmacokinetic studies. Analytical protocols were elaborated for three different GC/MS sampling techniques, i.e., static headspace (s-HS), headspace solid phase micro extraction (HS-SPME), and liquid-liquid partition. In principle, all tested methods were feasible, but s-HS had the greatest benefit because of the easy handling of the blood samples and its short analysis time. For s-HS two different incubation temperatures were tested (40 degrees C and 60 degrees C). The limit of detection was slightly lower when samples were incubated at 60 degrees C, but the same quantitative results were achieved using alpha-terpineol as internal standard. An accurate and sensitive method for the quantification of (-)-linalool in blood samples after either inhalation or percutaneous application, as well as pharmacokinetic data are presented.     

The small core of the German corporate board network

We consider the bipartite graph of German corporate boards and identify a small core of directors who are highly central in the entire network while being densely connected among themselves. To identify the core, we compare the actual number of board memberships to a random benchmark, focusing on deviations from the benchmark that span several orders of magnitude. The board appointment decisions of largely capitalized companies appear to be the driving force behind the existence of a core in Germany’s corporate network.     

Self-energy and vertex radiative corrections in LQG

We consider the elementary radiative-correction terms in loop quantum gravity. These are a two-vertex “elementary bubble” and a five-vertex “ball”; they correspond to the one-loop self-energy and the one-loop vertex correction of ordinary quantum field theory. We compute their naive degree of (infrared) divergence.     

Extrinsic symplectic symmetric spaces

We define the notion of extrinsic symplectic symmetric spaces and exhibit some of their properties. We construct large families of examples and show how they fit in the perspective of a complete classification of these manifolds. We also build a natural ?$?$-quantization on a class of examples.     

Coherence transfer between spy nuclei and nitrogen-14 in solids

Coherence transfer from 'spy nuclei' such as (1)H or (13)C (S=1/2) was used to excite single- or double-quantum coherences of (14)N nuclei (I=1) while the S spins were aligned along the static field, in the manner of heteronuclear single-quantum correlation (HSQC) spectroscopy. For samples spinning at the magic angle, coherence transfer can be achieved through a combination of scalar couplings J(I,S) and second-order quadrupole-dipole cross-terms, also known as residual dipolar splittings (RDS). The second-order quadrupolar powder patterns in the two-dimensional spectra allow one to determine the quadrupolar parameters of (14)N in amino acids.     

Sur une attaque inhabituelle de l'hetérocycle du benzofuranne,par action de chlorure de sulfuryle sur l'acétamido-3 nitro-2 benzofuranne

Sulphuryl chloride transforms 3-acetamido-2-nitrobenzofuran into 3-acetylimino-2-chloro-2-nitro-2,3-dihydrobenofuran instead of proceeding to the expected chlorination. When the reaction was carried out in the presence of an alcohol, 3-acetamido3-alkoxy-2-chloro-2-nitro-2,3-dihydrobenzofuran was obtained.     

Spatially homogeneous solutions of the Vlasov–Nordström–Fokker–Planck system

The Vlasov–Nordström–Fokker–Planck system describes the evolution of self-gravitating matter experiencing collisions with a fixed background of particles in the framework of a relativistic scalar theory of gravitation. We study the spatially-homogeneous system and prove global existence and uniqueness of solutions for the corresponding initial value problem in three momentum dimensions. Additionally, we study the long time asymptotic behavior of the system and prove that even in the absence of friction, solutions possess a non-trivial asymptotic profile. An exact formula for the long time limit of the particle density is derived in the ultra-relativistic case.