Concentrated steady vorticities of the Euler equation on 2-d domains and their linear stability

We consider concentrated vorticities for the Euler equation on a smooth domain $\mathrm{\Omega }?{\mathbf{R}}^2$ in the form of

$\omega =\sum _{j=1}^N{\omega }_j{\chi }_{{\mathrm{\Omega }}_j},|{\mathrm{\Omega }}_j|=\pi r_j^2,\underset{{\mathrm{\Omega }}_j}{\int }{\omega }_{j}d\mu ={\mu }_j\ne 0,$

supported on well-separated vortical domains ${\mathrm{\Omega }}_j$, $j=1,\dots ,N$, of small diameters $O(r_j)$. A conformal mapping framework is set up to study this free boundary problem with ${\mathrm{\Omega }}_j$ being part of unknowns. For any given vorticities ${\mu }_1,\dots ,{\mu }_N$ and small $r_1,\dots ,r_N\in {\mathbf{R}}^{+}$, through a perturbation approach, we obtain such piecewise constant steady vortex patches as well as piecewise smooth Lipschitz steady vorticities, both concentrated near non-degenerate critical configurations of the Kirchhoff–Routh Hamiltonian function. When vortex patch evolution is considered as the boundary dynamics of $?{\mathrm{\Omega }}_j$, through an invariant subspace decomposition, it is also proved that the spectral/linear stability of such steady vortex patches is largely determined by that of the 2N-dimensional linearized point vortex dynamics, while the motion is highly oscillatory in the 2N-codim directions corresponding to the vortical domain shapes.     

Setting local rank constraints by orthogonal projections for image resolution analysis: Application to the determination of a low dose pharmaceutical compound

Raman chemical imaging provides chemical and spatial information about pharmaceutical drug product. By using resolution methods on acquired spectra, the objective is to calculate pure spectra and distribution maps of image compounds. With multivariate curve resolution-alternating least squares, constraints are used to improve the performance of the resolution and to decrease the ambiguity linked to the final solution. Non negativity and spatial local rank constraints have been identified as the most powerful constraints to be used.     

Response surface methodology toward the optimization of high-energy carotenoid extraction from Aristeus antennatus shrimp

High-energy assisted extraction techniques, like ultrasound assisted extraction (UAE) and microwave assisted extraction (MAE), are widely applied over the last years for the recovery of bioactive compounds such as carotenoids, antioxidants and phenols from foods, animals and herbal natural sources. Especially for the case of xanthophylls, the main carotenoid group of crustaceans, they can be extracted in a rapid and quantitative way with the use of UAE and MAE.     

Condensation of all-cis-tetraphenylcyclotetrasiloxanetetraol in ammonia: new method for preparation of ladder-like polyphenylsilsesquioxanes

1. Download : Download high-res image (68KB)
2. Download : Download full-size image

     

Triacetic acid lactone as a bioprivileged molecule in organic synthesis

1. Download high-res image (148KB)
2. Download full-size image

     

Synthesis and antimycobacterial activity of purine conjugates with (S)-lysine and (S)-ornithine

1. Download high-res image (115KB)
2. Download full-size image

     

Stability of O3 + N2, O3 + O2 and O3 + CO2 double hydrates: DFT study

1. Download : Download high-res image (151KB)
2. Download : Download full-size image

     

Development of an LC‐MS/MS method for determining the pharmacokinetics of clonidine following oral administration of Zhenju antihypertensive compound

Zhenju antihypertensive compound (ZJAHC) is a combined Chinese–Western medicine formula including clonidine (CLO), hydrochlorothiazide (HCT), rutin, Chrysanthemum indicum extract and pearl powder. Compared with CLO preparations, ZJAHC shows improved activities and decreased adverse effects. It is believed that the side effects of CLO are caused by its high peak plasma concentration. Hence, study of the influence of ZJAHC on the pharmacokinetic behaviors of clonidine seems essential. In present study, the plasma concentrations of CLO were determined with a liquid chromatography–tandem mass spectrometry (LC‐MS/MS) method. The MS/MS transitions monitored for clonidine and internal standard were 230.2 → 213.1 and 152.2 → 110.2, respectively. The analyte was quantified in a single run within 3 min. The pharmacokinetic study showed that the area under the plasma concentration–time curve of CLO in ZJAHC (60 µg/kg CLO) was similar to that of CLO‐HCT‐high (120 µg/kg CLO) but the peak concentration was much lower than that in CLO‐HCT‐high. ZJAHC could enhance the bioavailability without greatly increasing peak concentration of clonidine. This comprehensive effect of enhancing the bioavailability and avoiding the high peak plasma concentration for CLO might mainly result from the co‐contribution of Western medicine and traditional Chinese medicine (TCM), while the effect of TCM was stronger than that of Western medicine. Copyright © 2014 John Wiley & Sons, Ltd.