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.     

Identification of metabolites of rupestonic acid in rat urine by liquid chromatography combined with electrospray ionization quadrupole time‐of‐flight tandem mass spectrometry

Rupestonic acid, a potential anti‐influenza agent, is an important and characteristic compound in Artemisia rupestris L., a well‐known traditional Uighur medicine for the treatment of colds. In the present study, high‐performance liquid chromatography combined with electrospray ionization quadrupole time‐of‐flight tandem mass spectrometry was used to detect and identify the metabolites in rat urine after oral administration of rupestonic acid. A total of 10 metabolites were identified or partially characterized. The structure elucidations of the metabolites were performed by comparing the changes in accurate molecular masses and fragment ions with those of the parent compound. The results showed that the main metabolites of rupestonic acid in rat urine were formed by oxidation, hydrogenation and glucuronidation. A metabolism pathway was proposed for the first time based on the characterized structures. This metabolism study can provide essential information for drug discovery, design and clinical application of rupestonic acid. Copyright © 2014 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.     

Cancer Initiation,Progression and Resistance: Are Phytocannabinoids from Cannabis sativa L. Promising Compounds?

Cannabis sativa L. is a source of over 150 active compounds known as phytocannabinoids that are receiving renewed interest due to their diverse pharmacologic activities. Indeed, phytocannabinoids mimic the endogenous bioactive endocannabinoids effects through activation of CB1 and CB2 receptors widely described in the central nervous system and peripheral tissues. All phytocannabinoids have been studied for their protective actions towards different biological mechanisms, including inflammation, immune response, oxidative stress that, altogether, result in an inhibitory activity against the carcinogenesis. The role of the endocannabinoid system is not yet completely clear in cancer, but several studies indicate that cannabinoid receptors and endogenous ligands are overexpressed in different tumor tissues. Recently, in vitro and in vivo evidence support the effectiveness of phytocannabinoids against various cancer types, in terms of proliferation, metastasis, and angiogenesis, actions partially due to their ability to regulate signaling pathways critical for cell growth and survival. The aim of this review was to report the current knowledge about the action of phytocannabinoids from Cannabis sativa L. against cancer initiation and progression with a specific regard to brain, breast, colorectal, and lung cancer as well as their possible use in the therapies. We will also report the known molecular mechanisms responsible for such positive effects. Finally, we will describe the actual therapeutic options for Cannabis sativa L. and the ongoing clinical trials.     

Simultaneous determination of major components of Huangqi–Honghua extract in rat plasma using LC–MS/MS and application to a pharmacokinetic study

A sensitive and reliable LC–MS/MS method was developed and validated for simultaneous quantification of the major components of Huangqi–Honghua extact in rat plasma, including hydroxysafflor yellow A (HSYA), astragaloside IV (ASIV), calycosin‐7‐O‐β‐d ‐glucoside (CAG), calycosin, calycosin‐3′‐O‐glucuronide (C‐3′‐G) and calycosin‐3′‐O‐sulfate (C‐3′‐S). After extraction by protein precipitation with acetonitrile and methanol from plasma, the analytes were separated on a Hypersil BDS C₁₈ column by gradient elution with acetonitrile and 5 mM ammonium acetate. The detection was carried out on a triple quadrupole tandem mass spectrometer equipped with electrospray ionization source switched between negative and positive modes. HSYA was monitored in negative ionization mode from 0 to 4.9 min, and ASIV, CAG, calycosin, C‐3′‐G and C‐3′‐S were determined in positive ionization mode from 4.9 to 10 min. The lower limits of quantification of the analytes were 6.25 ng/mL for HSYA, 0.781 ng/mL for CAG and 1.56 ng/mL for ASIV and calycosin. The intra‐ and inter‐assay precision (RSD) values were within 13.43%, and accuracy (RE) ranged from ?8.75 to 9.92%. The validated method was then applied to the pharmacokinetic study of HSYA, ASIV, CAG, calycosin, C‐3′‐G and C‐3′‐S in rat after an oral administration of Huangqi–Honghua extract.     

Gravitational wave imprint of new symmetry breaking

It is believed that there are more fundamental gauge symmetries beyond those described by the Standard Model of particle physics. The scales of these new gauge symmetries are usually too high to be reachable by particle colliders. Considering that the phase transition (PT) relating to the spontaneous breaking of new gauge symmetries to the electroweak symmetry might be strongly first order, we propose considering the stochastic gravitational waves (GW) arising from this phase transition as an indirect way of detecting these new fundamental gauge symmetries. As an illustration, we explore the possibility of detecting the stochastic GW generated from the PT of \begin{document}$ {\bf{B}}-{\bf{L}}$\end{document} in the space-based interferometer detectors. Our study demonstrates that the GW energy spectrum is reachable by the LISA, Tianqin, Taiji, BBO, and DECIGO experiments only for the case where the spontaneous breaking of \begin{document}$ {\bf{B}}-{\bf{L}}$\end{document} is triggered by at least two electroweak singlet scalars.     

An algebraic characterization ofB-convergent Runge-Kutta methods

Summary In the analysis of discretization methods for stiff intial value problems, stability questions have received most part of the attention in the past.B-stability and the equivalent criterion algebraic stability are well known concepts for Runge-Kutta methods applied to dissipative problems. However, for the derivation ofB-convergence results — error bounds which are not affected by stiffness — it is not sufficient in many cases to requireB-stability alone. In this paper, necessary and sufficient conditions forB-convergence are determined.This paper was written while J. Schneid was visiting the Centre for Mathematics and Computer Science with an Erwin-Schrödinger stipend from the Fonds zur Förderung der wissenschaftlichen Forschung     

Experimental intensity patterns obtained from a 2D shearing interferometer with adaptable sensitivity

The interferometric intensity patterns from a 2D shearing interferometer are shown and discussed. The intensity patterns can be obtained in two different approaches incorporating differential and extended wavefront controlled displacements. The reliable directional sensitivity of this interferometer allows the optimization of the measurement parameters to estimate the wavefront of the intensity patterns by regularization techniques.     

A nilpotent Roth theorem

Let T and S be invertible measure preserving transformations of a probability measure space (X, ℬ, μ). We prove that if the group generated by T and S is nilpotent, then exists in L ²-norm for any u, v∈L ^∞(X, ℬ, μ). We also show that for A∈ℬ with μ(A)>0 one has . By the way of contrast, we bring examples showing that if measure preserving transformations T, S generate a solvable group, then (i) the above limits do not have to exist; (ii) the double recurrence property fails, that is, for some A∈ℬ, μ(A)>0, one may have μ(A∩T _-n A∩S ^{- n} A)=0 for all n∈ℕ. Finally, we show that when T and S generate a nilpotent group of class ≤c, in L ²(X) for all u, v∈L ^∞(X) if and only if T×S is ergodic on X×X and the group generated by T ^-1 S, T ^-2 S ²,..., T ^-c S ^c acts ergodically on X. Oblatum 19-V-2000 & 5-VII-2001?Published online: 12 October 2001