Liouville theorem for weighted p-Lichnerowicz equation on smooth metric measure space

In this paper, let $(M^n,g,d\mu )$ be n-dimensional noncompact metric measure space which satisfies Poincaré inequality with some Ricci curvature condition. We obtain a Liouville theorem for positive weak solutions to weighted p-Lichnerowicz equation

${△}_{p,f}v+c{v}^{\sigma }=0,$

where $c\le 0,m>n\ge 1,1<p<\frac{m?1+\sqrt{(m?1)(m+3)}}{2},\sigma \le p?1$ are real constants.     

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.     

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.     

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.     

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.     

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.