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.     

Boundedness of semilinear Duffing equations at resonance in a critical situation

In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation $\ddot{x}+n^{2}x+g(x)=p(t)$ with the critical situation that $|{\int }_0^{2\pi }p(t)e^{?int}dt|=2|g(+\infty )?g(?\infty )|$ on g and p, where $n\in {\mathbb{N}}^{+}$, $p(t)$ is periodic and $g(x)$ is bounded.     

Metabolic profiles of dioscin in rats revealed by ultra‐performance liquid chromatography quadrupole time‐of‐flight mass spectrometry

Dioscin (DIS), one of the most abundant bioactive steroidal saponins in Dioscorea sp., is used as a complementary medicine to treat coronary disease and angina pectoris in China. Although the pharmacological activities and pharmacokinetics of DIS have been well demonstrated, information regarding the final metabolic fates is very limited. This study investigated the in vivo metabolic profiles of DIS after oral administration by ultra‐performance liquid chromatography quadrupole time‐of‐flight mass spectrometry method. The structures of the metabolites were identified and tentatively characterized by means of comparing the molecular mass, retention time and fragmentation pattern of the analytes with those of the parent compound. A total of eight metabolites, including seven phase I and one phase II metabolites, were detected and tentatively identified for the first time. Oxidation, deglycosylation and glucuronidation were found to be the major metabolic processes of the compound in rats. In addition, a possible metabolic pathway on the biotransformation of DIS in vivo was proposed. This study provides valuable and new information on the metabolism of DIS, which will be helpful for further understanding its mechanism of action. Copyright © 2015 John Wiley & Sons, Ltd.     

Identifying anomalous Floquet edge modes via bulk-edge correspondence

Floquet engineering appears as a new protocol for designing topological states of matter,and features anomalous edge modes pinned at quasi-energy π/T with vanished topological index.We propose how to predict the anomalous edge modes via the bulk Hamiltonian in frequency space,and use Zak phase to quantitatively index the topological properties.The above methods are clarified by the example of time periodic Kitaev chain with chemical potential of harmonic driving and pulse driving,and topological phase transitions are manifested at different driving frequencies.     

Photoisomerisation in Aminoazobenzene‐Substituted Ruthenium(II) Tris(bipyridine) Complexes: Influence of the Conjugation Pathway

Transition‐metal complexes containing stimuli‐responsive systems are attractive for applications in optical devices, photonic memory, photosensing, as well as luminescence imaging. Amongst them, photochromic metal complexes offer the possibility of combining the specific properties of the metal centre and the optical response of the photochromic group. The synthesis, the electrochemical properties and the photophysical characterisation of a series of donor–acceptor azobenzene derivatives that possess bipyridine groups connected to a 4‐dialkylaminoazobenzene moiety through various linkers are presented. DFT and TD‐DFT calculations were performed to complement the experimental findings and contribute to their interpretation. The position and nature of the linker (ethynyl, triazolyl, none) were engineered and shown to induce different electronic coupling between donor and acceptor in ligands and complexes. This in turn led to strong modulations in terms of photoisomerisation of the ligands and complexes.     

Design and development of a two‐dimensional system based on hydrophilic and reversed‐phase liquid chromatography with on‐line sample treatment for the simultaneous separation of excreted xenobiotics and endogenous metabolites in urine

In the present work we describe a two‐dimensional liquid chromatographic system (2D‐LC) with detection by mass spectrometry (MS) for the simultaneous separation of endogenous metabolites of clinical interest and excreted xenobiotics deriving from exposure to toxic compounds. The 2D‐LC system involves two orthogonal chromatographic modes, hydrophilic interaction liquid chromatography (HILIC) to separate polar endogenous metabolites and reversed‐phase (RP) chromatography to separate excreted xenobiotics of low and intermediate polarity. Additionally, the present proposal has the novelty of incorporating an on‐line sample treatment based on the use of restricted access materials (RAMs), which permits the direct injection of urine samples into the system. The work is focused on the instrumental coupling, studying all possible options and attempting to circumvent the problems of solvent incompatibility between the RAM device and the two chromatographic columns, HILIC and RP. The instrumental configuration developed, RAM‐HILIC‐RPLC‐MS/MS, allows the simultaneous assessment of urinary metabolites of clinical interest and excreted compounds derived from exposure to toxic agents with minimal sample manipulation. Thus, it may be of interest in areas such as occupational and environmental toxicology in order to explore the possible relationship between the two types of compounds. Copyright © 2015 John Wiley & Sons, Ltd.     

Convergence of the viscosity solution of non-autonomous Hamilton-Jacobi equations

In this paper,we investigate the non-autonomous Hamilton-Jacobi equation ■ where H is 1-periodic with respect to t and M is a compact Riemannian manifold without boundary.We obtain the viscosity solution denoted by T_(t_0)~tφ(x) and show T_(t_0)~tφ(x) converges uniformly to a time-periodic viscosity solution u~*(x,t) of ?_tu+H(t,x,?_xu,u)=0.