A probabilistic approach to spectral analysis of growth-fragmentation equations

The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual.     

Full counting statistics of transport electrons through a two-level quantum dot with spin–orbit coupling

We study the full counting statistics of transport electrons through a semiconductor two-level quantum dot with Rashba spin–orbit (SO) coupling, which acts as a nonabelian gauge field and thus induces the electron transition between two levels along with the spin flip. By means of the quantum master equation approach, shot noise and skewness are obtained at finite temperature with two-body Coulomb interaction. We particularly demonstrate the crucial effect of SO coupling on the super-Poissonian fluctuation of transport electrons, in terms of which the SO coupling can be probed by the zero-frequency cumulants. While the charge currents are not sensitive to the SO coupling.     

The character and the wave front set correspondence in the stable range

We relate the distribution characters and the wave front sets of unitary representation for real reductive dual pairs of type I in the stable range.     

Studies on metabolites and metabolic pathways of bulleyaconitine A in rat liver microsomes using LC‐MSn combined with specific inhibitors

Bulleyaconitine A (BLA) from Aconitum bulleyanum plants is usually used as anti‐inflammatory drug in some Asian countries. It has a variety of bioactivities, and at the same time some toxicities. Since the bioactivities and toxicities of BLA are closely related to its metabolism, the metabolites and the metabolic pathways of BLA in rat liver microsomes were investigated by HPLC–MSⁿ. In this research, the 12 metabolites of BLA were identified according to the results of HPLC‐MSⁿ data and the relevant literature. The results showed that there are multiple metabolites of BLA in rat liver microsomes, including demethylation, deacetylation, dehydrogenation deacetylation and hydroxylation. The major metabolic pathways of BLA in rat liver microsomes were clarified by HPLC‐MS combined with specific inhibitors of CYP450 isoforms. As a result, CYP3A and 2C were found to be the principal CYP isoforms contributing to the metabolism of BLA. Moreover, CYP2D6 and 2E1 are also more important CYP isoforms for the metabolism of BLA. While CYP1A2 only affected the formation rate of M11, its effect on the metabolism of BLA is very small. Copyright © 2014 John Wiley & Sons, Ltd.     

The behavior of differential forms under purely inseparable extensions

Let F be a field of characteristic 2. In this paper we give a complete computation of the kernel of the homomorphism $H_2^{m+1}(F)?H_2^{m+1}(L)$ induced by scalar extension, where $L/F$ is a purely inseparable extension (of any degree), $H_2^{m+1}(F)$ is the cokernel of the Artin–Schreier operator $?:{\mathrm{\Omega }}_F^m?{\mathrm{\Omega }}_F^m/\mathrm{d}{\mathrm{\Omega }}_F^{m?1}$ given by: $x\frac{\mathrm{d}{x}_1}{x_1}\wedge ?\wedge \frac{\mathrm{d}{x}_m}{x_m}?(x^2?x)\frac{\mathrm{d}{x}_1}{x_1}\wedge ?\wedge \frac{\mathrm{d}{x}_m}{x_m}+\mathrm{d}{\mathrm{\Omega }}_F^{m?1}$, where ${\mathrm{\Omega }}_F^m$ is the space of absolute m-differential forms over F and d is the differential operator. Other related results are included.     

Perturbative manifolds and the Noether generators of nth-order Poisson equations

A manifold that contains small perturbations will induce a perturbed partial differential equation. The partial differential equation that we select is the Poisson equation – in order to explore the interplay between the geometry of the manifold and the perturbations. Specifically, we show how the problem of symmetry determination, for higher-order perturbations, can be elegantly expressed via geometric conditions.     

Development and validation of a reversed‐phase HPLC method for CYP1A2 phenotyping by use of a caffeine metabolite ratio in saliva

CYP1A2 is important for metabolizing various clinically used drugs. Phenotyping of CYP1A2 may prove helpful for drug individualization therapy. Several HPLC methods have been developed for quantification of caffeine metabolites in plasma and urine. Aim of the present study was to develop a valid and simple HPLC method for evaluating CYP1A2 activity during exposure in xenobiotics by the use of human saliva. Caffeine and paraxanthine were isolated from saliva by liquid‐liquid extraction (chlorophorm/isopropanol 85/15v/v). Extracts were analyzed by reversed‐phase HPLC on a C₁₈ column with mobile phase 0.1% acetic acid/methanol/acetonitrile (80/20/2 v/v) and detected at 273nm. Caffeine and paraxanthine elution times were <13min with no interferences from impurities or caffeine metabolites. Detector response was linear (0.10–8.00µg/ml, R²>0.99), recovery was >93% and bias <4.47%. Intra‐ and inter‐day precision was <5.14% (n=6). The limit of quantitation was 0.10µg/ml and the limit of detection was 0.018±0.002µg/mL for paraxanthine and 0.032±0.002µg/ml for caffeine. Paraxanthine/caffeine ratio of 34 healthy volunteers was significantly higher in smokers (p<0.001). Saliva paraxanthine/caffeine ratios and urine metabolite ratios were highly correlated (r=0.85, p<0.001). The method can be used for the monitoring of CYP1A2 activity in clinical practice and in studies relevant to exposure to environmental and pharmacological xenobiotics. Copyright © 2015 John Wiley & Sons, Ltd.     

Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme.