Well-posedness of The Prandtl Equation in Sobolev Spaces

We develop a new approach to study the well-posedness theory of the Prandtl equation in Sobolev spaces by using a direct energy method under a monotonicity condition on the tangential velocity field instead of using the Crocco transformation. Precisely, we firstly investigate the linearized Prandtl equation in some weighted Sobolev spaces when the tangential velocity of the background state is monotonic in the normal variable. Then to cope with the loss of regularity of the perturbation with respect to the background state due to the degeneracy of the equation, we apply the Nash-Moser-Hormander iteration to obtain a well-posedness theory of classical solutions to the nonlinear Prandtl equation when the initial data is a small perturbation of a monotonic shear flow

Women and Matrimony: A Study of Mona Lisa Smile

This study intended to use the film Mona Lisa Smile (1993) as an example to examine how women in the traditional generation of 1950 were gender stereotyped and used to trade themselves off through marriage in consideration of a cost-and-benefit analysis. However, as the change of women’s gender consciousness from the conservative to the feminist in the USA of 1950, women began to realize their potential and subjectivity, hence questing for liberal spirit and autonomy to choose their career and husbands based on love. The researchers used the qualitative method, with both the primary and secondary data, to facilitate a latent-content analysis. After conducting a content analysis of the film and the script of Mona Lisa Smile, the researchers took notes regarding gender stereotyping and conventional gender norms in social interactions and conducted a literature review of Becker’s side bet theory and Homan’s social exchange theory to investigate how women in America in the 1950s were disciplined to meet the expectation of social norms to fit the notion of conventional matrimony, and how people, both men and women, while choosing their mates, seek the maximum interest and minimum cost. The film Mona Lisa Smile lets readers have a chance to see the transformation of a marital relationship from the old days to modern ones. With raised gender consciousness, women may now subject their choices to their own will and, hence, apply a different definition to the word “marriage.

2,2′-[Ethane-1,2-diylbis(sulfanedi­yl)]bis­(pyridine N-oxide)

The tile compound, C12H12N2O2S2, lies on an inversion center. The two pyridyl rings are parallel to each other. The structure is devoid of any classical hydrogen bonds due to lack of appropriate donors and acceptors for such bonds. However, non-classical hydrogen bonds of the types C—H⋯O and C—H⋯S stabilize the structure

Nonextensive effects on QCD chiral phase diagram and baryon-number fluctuations within Polyakov-Nambu-Jona-Lasinio model

In this paper, a version of the Polyakov-Nambu-Jona-Lasinio (PNJL) model based on nonextensive statistical mechanics is presented. This new statistics summarizes all possible factors that violate the assumptions of the Boltzmann-Gibbs (BG) statistics to a dimensionless nonextensivity parameter $q$, and when $q$ tends to 1, it returns to the BG case. Within the nonextensive PNJL model, we found that as $q$ increases, the location of the critical end point (CEP) exhibits non-monotonic behavior. That is, for $q<1.15$, CEP moves in the direction of lower temperature and larger quark chemical potential. But for $q>1.15$, CEP turns to move in the direction of lower temperature and lower quark chemical potential. In addition, we studied the moments of the net-baryon number distribution, that is, the variance ($\sigma^{2}$), skewness (S), and kurtosis ($\kappa$). Our results are generally consistent with the latest experimental data, especially for $\sqrt{S_{NN}}>19.6\ \mathrm{GeV}$, when $q$ is set to $1.07$

Bis[μ-4-methyl-2-(2-pyridyl­methyl­sulfan­yl)pyrimidine-κN 1]bis­[(trifluoro­methanesulfonato-κO)silver(I)]

In the centrosymmetric dinuclear title complex, [Ag2(CF3SO3)2(C11H11N3S)2], the AgI atom is coordinated by two N atoms from two 4-methyl-2-(2-pyridyl­methyl­sulfan­yl)pyrimidine ligands and one O atom from a trifluoro­methane­sulfonate anion in a distorted T-type coordination geometry. The ligand adopts a bidentate bridging coordination mode through one pyridyl N atom and one pyrimidine N atom. In the crystal structure, π–π inter­actions are present between adjacent pyrimidine rings, with a centroid-to-centroid distance of 3.875 (7) Å

_In vivo_ photoacoustic molecular imaging with simultaneous multiple selective targeting using antibody-conjugated gold nanorods

The use of gold nanorods for photoacoustic molecular imaging in vivo with simultaneous multiple selective targeting is reported. The extravasation of multiple molecular probes is demonstrated, and used to probe molecular information of cancer cells. This technique allows molecular profiles representing tumor characteristics to be obtained and a heterogeneous population of cancer cells in a lesion to be determined. The results also show that the image contrast can be enhanced by using a mixture of different molecular probes. In this study, HER2, EGFR, and CXCR4 were chosen as the primary target molecules for examining two types of cancer cells, OECM1 and Cal27. OECM1 cells overexpressed HER2 but exhibited a low expression of EGFR, while Cal27 cells showed the opposite expression profile. Single and double targeting resulted in signal enhancements of up to 3 dB and up to 5 dB, respectively, and hence has potential in improving cancer diagnoses

Effects of natto extract on endothelial injury in a rat model

Vascular endothelial damage has been found to be associated with thrombus formation, which is considered to be a risk factor for cardiovascular disease. A diet of natto leads to a low prevalence of cardiovascular disease. The aim of the present study was to investigate the effects of natto extract on vascular endothelia damage with exposure to laser irradiation. Endothelial damage both in vitro and in vivo was induced by irradiation of rose bengal using a DPSS green laser. Cell viability was determined by MTS assay, and the intimal thickening was verified by a histological approach. The antioxidant content of natto extract was determined for the free radical scavenging activity. Endothelial cells were injured in the presence of rose bengal irradiated in a dose-dependent manner. Natto extract exhibits high levels of antioxidant activity compared with purified natto kinase. Apoptosis of laser-injured endothelial cells was significantly reduced in the presence of natto extract. Both the natto extract and natto kinase suppressed intimal thickening in rats with endothelial injury. The present findings suggest that natto extract suppresses vessel thickening as a synergic effect attributed to its antioxidant and anti-apoptosis properties