Global Regularity of the 3D Axi-Symmetric Navier–Stokes Equations with Anisotropic Data

In this paper, we study the 3D axisymmetric Navier–Stokes equations with swirl. We prove the global regularity of the 3D Navier–Stokes equations for a family of large anisotropic initial data. Moreover, we obtain a global bound of the solution in terms of its initial data in some L ^p norm. Our results also reveal some interesting dynamic growth behavior of the solution due to the interaction between the angular velocity and the angular vorticity fields.     

Existence of positive solutions to semilinear elliptic systems with supercritical growth

We establish the existence of positive entire solutions to cooperative systems of semilinear elliptic equations involving nonlinearities with critical and supercritical growth. Consequently, we obtain existence results to several well-known model examples such as systems of the Hénon, Lane–Emden, and stationary Schrödinger types. The main technique for generating our results relies on a topological approach for the shooting method combined with nonexistence results to closely related boundary value problems.     

MoO3催化碳酸二甲酯与乙酸苯酯合成碳酸二苯酯

采用焙烧法制备了MoO3催化剂并将其用于碳酸二甲酯(DMC)与乙酸苯酯(PA)合成碳酸二苯酯(DPC)反应,考察了焙烧温度对催化荆性能的影响,并用X射线衍射(XRD)对催化剂结构进行了表征.结果发现,在400或500℃焙烧的催化剂具有良好的催化性能,DMC转化率为73.9%,DPC和甲基苯基碳酸酯的选择性分别为39.5%和56.5%.XRD结果表明,该催化剂物相组成为正交晶系MoO3,且(021)或/和(110)晶面有利于酯交换反应.催化剂使用5次后DMC转化率从73.9%降至10.2%,多次重复使用后的催化剂在窄气气氛中于400或500℃焙烧即可再生,再生后催化剂的性能几乎和新鲜催化剂相当.     

Tailored preparation of dual phase concomitant methylcellulose/poly(vinyl alcohol) physical hydrogel with tunable thermosensivity

A novel dual phase concomitant, methylcellulose sol@poly(vinyl alcohol) (MC/PVA) hydrogel, was prepared via physical mixing and subsequent freezing/thawing. MC/PVA hydrogel was stable within a wide temperature range, and exhibited reversible thermoresponsivity. The initial sol-gel transition temperatures of MC/PVA hydrogels containing 40, 45 and 50 wt% MC were 45.9, 42.0 and 45.5 °C, respectively. It was found that the crystallinity of these samples was 41.1%, 38.3% and 40.3%, respectively; all of them were lower than that of MC and PVA. The thermal responding rates of MC/PVA hydrogel composed of 30, 40, 45 and 50 wt% MC were about 2.85, 3.17, 5.74 and 8.58%/min, respectively. The fluorescence micrograph and scanning electron microscopy of MC/PVA hydrogel revealed that the micro MC sol phases were dispersed in whole PVA network. Moreover, the thermal transition behavior and interior morphology of MC/PVA hydrogel could be tailored with its composition.     

CLASSIFICATION OF POSITIVE SOLUTIONS FOR NONLINEAR DIFFERENTIAL AND INTEGRAL SYSTEMS WITH CRITICAL EXPONENTS

We classify all positive solutions for the following integral system：{ui（x）=∫Rn1/│x-y│^n-α fi（u（y））dy,x∈R^n,i=1,…,m,0〈α〈n,and u（x）=（u1（x）,u2（x）…,um（x））.Here fi（u）, 1 ≤ i ≤m, monotone nondecreasing are real-valued functions of homogeneous degree n＋α/n-α and are monotone nondecreasing with respect to all the independent variables U1, u2, ..., urn.In the special case n ≥ 3 and α = 2. we show that the above system is equivalent to thefollowing elliptic PDE system：This system is closely related to the stationary SchrSdinger system with critical exponents for Bose-Einstein condensate     

有界区域上非线性 Schrodinger 方程解的全局性质

本文解决了 H.Bréis 在文[1]中提出的一个问题,对于非线性 Schr(?)dinger 方程(?) (1)H.Brézis 在文[1]中证明了,如果 Ω=R~2,p=3,K≤0或k>0,同时K integral from R~2|u_0|~2dx<4,(1)式有解 u(x,t),u∈C~1([0,∞),L~2(R~2))∩C([0,∞),H~2(R~2)).并且指出,在 Ω=R~2的情形,如果 p≥3,并且初值 u_0满足     

Prescribing gaussian curvatures on surfaces with conical singularities

We consider prescribing Gaussian curvatures on surfaces with conical singularities. In a critical case, we obtain the best constant in an inequality. Then, by using the “distribution of mass” analysis, we are able to provide some sufficient conditions for a function to be the Gaussian curvature of some pointwise conformai metric.     

Identification of the major metabolites of quinocetone in swine urine using ultra‐performance liquid chromatography/electrospray ionization quadrupole time‐of‐flight tandem mass spectrometry

Quinocetone (QCT), 3‐methyl‐2‐cinnamoylquinoxaline‐1,4‐dioxide, is a quinoxaline‐N,N‐dioxide used in veterinary medicine as a feed additive. QCT is broadly used in China to promote animal growth, but few studies have been performed to reveal the metabolism of QCT in animals until now. In the present study, the metabolites of QCT in swine urine were investigated using ultra‐performance liquid chromatography/electrospray ionization quadrupole time‐of‐flight mass spectrometry (UPLC/ESI‐QTOF‐MS). Multiple scans of metabolites in MS and MS/MS modes and accurate mass measurements were performed simultaneously through data‐dependent acquisition. Most measured mass errors were less than ±5 mDa for both protonated molecules and product ions using external mass calibration. The structures of metabolites and their product ions were easily and reliably characterized based on the accurate MS² spectra and known structure of QCT. As expected, extensive metabolism was observed in swine urine. Thirty‐one metabolites were identified in swine urine, most of which were reported for the first time. The results reveal that the N‐O group reduction at position 1 and the hydroxylation reaction occurring at the methyl group, the side chain or on the benzene ring are the main metabolic pathways of quinocetone in swine urine. There was abundant production of 1‐desoxyquinocetone and hydroxylation metabolites of 1‐desoxyquinocetone. The proposed metabolic pathway of quinocetone in vivo can be expected to play a key role in food safety evaluations. Copyright © 2010 John Wiley & Sons, Ltd.     

关于共轭温度系统的 Herz-型Hardy 空间

记（ｎ－１）／ｎ〈ｐ〈ｑ〈∞,１〈ｐ,且α＝ｎ（１／ｐ－１／ｑ）。本文引进了关于Ｒ＾（ｎ＋１）上温度函数的共轭系统的Ｈｅｒ－型Ｈａｒｄｙ空间ＴＨＫｑ＾（α,ｐ）（Ｒ＾ｎ）,并且证明了它们的边值分布等同于通常的调和函数的共轭系统的Ｈｅｒｚ－型Ｈａｒｄｙ空间ＨＫｑ＾（α,ｐ）（Ｒ＾ｎ）。     

Synthesis and in vitro degradation of poly(alkylene carbonate anhydride)

A novel degradable poly(alkylene carbonate anhydride) (PACA) was synthesized by the melt polycondensation reaction of the corresponding mixed anhydrides of the dicarboxylic acid derived from oligo(tetramethylene carbonate)diol (OTMCD) and oligo(hexamethylene carbonate)diol (OHMCD). The polymer's structure was confirmed by IR and ¹H NMR spectroscopy. DSC analysis showed PACA had a low T_g (< –30°C). In vitro degradation tests indicated that the degradation rate of poly(alkylene carbonate) was more controlled with the incorporation of anhydride groups.