Global well-posedness of the critical Burgers equation in critical Besov spaces

We make use of the method of modulus of continuity \cite{K-N-S} and Fourier localization technique \cite{A-H} to prove the global well-posedness of the critical Burgers equation $\partial_{t}u+u\partial_{x}u+\Lambda u=0$ in critical Besov spaces $\dot{B}^{\frac{1}{p}}_{p,1}(\mathbb{R})$ with $p\in[1,\infty)$, where $\Lambda=\sqrt{-\triangle}$.Comment: 21page

Global Wellposedness for a Modified Critical Dissipative Quasi-Geostrophic Equation

In this paper we consider the following modified quasi-geostrophic equation \partial_{t}\theta+u\cdot\nabla\theta+\nu |D|^{\alpha}\theta=0, \quad u=|D|^{\alpha-1}\mathcal{R}^{\bot}\theta,\quad x\in\mathbb{R}^2 with $\nu>0$ and $\alpha\in ]0,1[\,\cup \,]1,2[$. When $\alpha\in]0,1[$, the equation was firstly introduced by Constantin, Iyer and Wu in \cite{ref ConstanIW}. Here, by using the modulus of continuity method, we prove the global well-posedness of the system with the smooth initial data. As a byproduct, we also show that for every $\alpha\in ]0,2[$, the Lipschitz norm of the solution has a uniform exponential bound.Comment: In this version we extend the range of $\alpha$ from (0,1) to (0,2), we also show that for every $\alpha\in (0,2)$, the Lipschitz norm of the solution has a uniform exponential bound. 27page

The peroxisome proliferator-activated receptor delta +294T > C polymorphism and alcohol consumption on serum lipid levels

<p>Abstract</p> <p>Background</p> <p>The single nucleotide polymorphism (SNP) of peroxisome proliferator-activated receptor delta (<it>PPARD</it>) gene affects serum lipid profiles, but to what extent alcohol consumption interferes with this association remains unknown. The present study was undertaken to compare the association of <it>PPARD </it>+294T > C (rs2016520) polymorphism and serum lipid levels in the nondrinkers and drinkers.</p> <p>Methods</p> <p>A total of 685 unrelated nondrinkers and 497 drinkers aged 15-82 were randomly selected from our previous stratified randomized cluster samples. Genotyping of the <it>PPARD </it>+294T > C was performed by polymerase chain reaction and restriction fragment length polymorphism. Interactions of the <it>PPARD </it>+294T > C genotypes and alcohol consumption on serum lipid levels were detected by using a factorial regression analysis after controlling for potential confounders.</p> <p>Results</p> <p>The levels of triglyceride (TG), high-density lipoprotein cholesterol (HDL-C), apolipoprotein (Apo) A1, and the ratio of ApoA1 to ApoB were higher in drinkers than in nondrinkers (<it>P </it>< 0.05-0.001). There were no significant differences in the levels of total cholesterol (TC), low-density lipoprotein cholesterol (LDL-C) and ApoB between the two groups (<it>P </it>> 0.05 for all). The frequencies of TT, TC and CC genotypes were 56.0%, 36.4% and 7.6% in nondrinkers, and 57.2%, 38.0% and 4.8% in drinkers (<it>P </it>> 0.05); respectively. The frequencies of T and C alleles were 74.2% and 25.8% in nondrinkers, and 76.2% and 23.8% in drinkers (<it>P </it>> 0.05); respectively. There was also no significant difference in the genotypic and allelic frequencies between males and females in both groups (<it>P </it>> 0.05 for all). The levels of TC in nondrinkers were different among the three genotypes (<it>P </it>= 0.01), the C allele carriers had higher serum TC levels than the C allele noncarriers. The levels of all seven lipid traits in drinkers were not different among the three genotypes (P > 0.05 for all). The interactions of <it>PPARD </it>+294T > C genotypes and alcohol consumption on serum lipid levels were not detected in the drinkers (<it>P ></it>0.05 for all). Multiple linear regression analysis showed that serum TC, HDL-C, LDL-C, ApoA1, and ApoB levels were correlated with genotypes in drinkers but not in nondrinkers (<it>P </it>< 0.05-0.01).</p> <p>Conclusions</p> <p>These results suggest that the great majority of our study populations are beneficial from alcohol consumption. But there is no interaction between the <it>PPARD </it>+294T > C genotypes and alcohol consumption on serum lipid levels in the drinkers.</p

3-Hy­droxy-1,2-dimeth­oxyxanthone

The title compound (systematic name: 3-hy­droxy-1,2-dimeth­oxy-9H-xanthen-9-one), C15H12O5, was isolated from Polygala arillata. The tricyclic unit is essentially planar (r.m.s. deviation = 0.039 Å). In the crystal, the mol­ecules form stacks along the a axis. Inter­molecular O—H⋯O hydrogen bonds link the mol­ecules into chains parallel to [010]

4-Hy­droxy-3,5-dimeth­oxy-N-{4-[(5-methyl-1,2-oxazol-3-yl)sulfamo­yl]phen­yl}benzamide methanol monosolvate

The title compound, C19H19N3O7S·CH3OH, was synthesized from syringic acid and sulfamethoxazole. The benzene rings make a dihedral angle of 41.8 (1)° and the isoxazole ring is twisted by 74.3 (1)° from the central benzene ring. The crystal packing features O—H⋯O and O—H⋯N hydrogen bonds in which the hy­droxy groups from the main mol­ecule and methanol solvent mol­ecules serve as donor groups

Polarization control proposal for Shanghai deep ultraviolet free electron laser

In this paper, a fully coherent radiation option with controllable polarization is proposed for Shanghai deep ultraviolet free electron laser (FEL) test facility. Intensive start-to-end simulation suggests that, the two crossed planar undulators which generate the horizontal and vertical linear polarized FEL respectively, should be placed as close as possible for avoiding the polarization performance degradation of the final combined FEL radiation. With the existence of the phase-shifter between the two crossed radiators, Fourier-Transform-Limited output radiation with 100 nJ order pulse energy, 5 ps full pulse length and circular polarization degree above 90% could be achieved.Comment: 9 pages, 5 figures, 1 tabl

Interactions of Several Lipid-Related Gene Polymorphisms and Cigarette Smoking on Blood Pressure Levels

The interactions of single nucleotide polymorphisms (SNPs) and cigarette smoking on blood pressure levels are limited. The present study was undertaken to detect nine lipid-related SNPs and their interactions with cigarette smoking on blood pressure levels. Genotyping of ATP-binding cassette transporter A1 (ABCA-1) V825I, acyl-CoA:cholesterol acyltransferase-1 (ACAT-1) rs1044925, low density lipoprotein receptor (LDL-R) AvaⅡ, hepatic lipase gene (LIPC) -250G>A, endothelial lipase gene (LIPG) 584C>T, methylenetetrahydrofolate reductase (MTHFR) 677C>T, proprotein convertase subtilisin-like kexin type 9 (PCSK9) E670G, peroxisome proliferator-activated receptor delta (PPARD) +294T>C, and Scavenger receptor class B type 1 (SCARB1) rs5888 was performed in 935 nonsmokers and 845 smokers. The interactions were detected by factorial regression analysis. The frequencies of genotypes (ACAT-1 and LIPG), alleles (ABCA-1), and both genotypes and alleles (LDL-R, LIPC, PPARD and SCARB1) were different between nonsmokers and smokers (P < 0.05-0.001). The levels of pulse pressure (PP, ABCA-1), and systolic, diastolic blood pressure (SBP, DBP) and PP (LIPC) in nonsmokers were different among the genotypes (P < 0.01-0.001). The levels of SBP (ABCA-1, ACAT-1, LIPG and PCSK9), DBP (ACAT-1, LDL-R, LIPC, PCSK9 and PPARD), and PP (LIPC, LIPG, MTHFR and PCSK9) in smokers were different among the genotypes (P < 0.01-0.001). The SNPs of ABCA-1, ACAT-1 and PCSK9; ACAT-1, LDL-R, MTHFR and PCSK9; and ABCA-1, LIPC, PCSK9 and PPARD were shown interactions with cigarette smoking to influence SBP, DBP and PP levels (P < 0.05-0.001); respectively. The differences in blood pressure levels between the nonsmokers and smokers might partly result from different interactions of several SNPs and cigarette smoking

Design of Tunable Nanophotonic Devices

This tutorial addresses design of tunable nanophotonic arrays, enabling dynamic, active control of the properties of light - amplitude, phase, wavevector, wavelength and polarization - opening new applications such as optical beam steering, focusing and wavefront engineering