For the vorticity–velocity–pressure form of the Navier–Stokes equations on a bounded plane domain with corners

We show existence and regularity for the boundary value problems of the Navier–Stokes equations with non-standard BCs on a bounded plane domain with non-convex corners. We assign the vorticity value $\omega ={\omega }_0$ and the velocity normal component $u?n=u_0?n$ over the non-convex corner, the dynamic pressure value $p+{\left|u\right|}^2/2=p_0$ over inflow and outflow boundaries, and so on. We construct the corner singularity functions for the Stokes operator with zero vorticity and velocity normal component BCs, subtract its leading singularity from the solution by defining the coefficient of the singularity and show increased regularity for the remainder. The solution is determined by the smoother part and the coefficients of the singularities. It is seen from the singularity that the dynamic pressure has a transition layer that changes the sign (at $\theta =\pi /2$ in the domain). The obtained results can be applied to general polygonal domains and the cavity flows.     

Dynamic changes of gangliosides expression during the differentiation of embryonic and mesenchymal stem cells into neural cells

Stem cells are used for the investigation of developmental processes at both cellular and organism levels and offer tremendous potentials for clinical applications as an unlimited source for transplantation. Gangliosides, sialic acid-conjugated glycosphingolipids, play important regulatory roles in cell proliferation and differentiation. However, their expression patterns in stem cells and during neuronal differentiation are not known. Here, we investigated expression of gangliosides during the growth of mouse embryonic stem cells (mESCs), mesenchymal stem cells (MSCs) and differentiated neuronal cells by using high-performance thin-layer chromatography (HPTLC). Monosialoganglioside 1 (GM1) was expressed in mESCs and MSCs, while GM3 and GD3 were expressed in embryonic bodies. In the 9-day old differentiated neuronal cells from mESCs cells and MSCs, GM1 and GT1b were expressed. Results from immunostaining were consistent with those observed by HPTLC assay. These suggest that gangliosides are specifically expressed according to differentiation of mESCs and MSCs into neuronal cells and expressional difference of gangliosides may be a useful marker to identify differentiation of mESCs and MSCs into neuronal cells.     

Site-specific amide hydrogen exchange in melittin probed by electron capture dissociation Fourier transform ion cyclotron resonance mass spectrometry

Electron capture dissociation (ECD) has been proposed to be a non-ergodic process, i.e. to provide backbone dissociation of gas-phase peptides faster than randomization of the imparted energy. One potential consequence could be that ECD can fragment deuterated peptides without causing hydrogen scrambling and thereby provide amino acid residue-specific amide hydrogen exchange rates. Such a feature would improve the resolution of approaches involving solution-phase amide hydrogen exchange combined with mass spectrometry for protein structural characterization. Here, we explore this hypothesis using melittin, a haemolytic polypeptide from bee venom, as our model system. Exchange rates in methanol calculated from consecutive c-type ion pairs show some correlation with previous NMR data: the amide hydrogens of leucine 13 and alanine 15, located at the unstructured kink surrounding proline 14 in the melittin structure adopted in methanol, appear as fast exchangers and the amide hydrogens of leucine 16 and lysine 23, buried within the helical regions of melittin, appear as slow exchangers. However, calculations based on c-type ions for other amide hydrogens do not correlate well with NMR data, and evidence for deuterium scrambling in ECD was obtained from z*-type ions.     

Blue upconversion luminescence of CaMoO4:Li+/Yb3+/Tm3+ phosphors prepared by complex citrate method

Li⁺/Tm³⁺/Yb³⁺ co-doped CaMoO₄ upconversion (UC) phosphor was prepared by complex citrate-gel method and UC luminescence properties were investigated. Li⁺/Tm³⁺/Yb³⁺ co-doped CaMoO₄ has intense blue emission induced by ¹G₄??³H₆ transition at 476?nm that is improved 10 times more than that of Li⁺ undoped sample and weak red emission at 647 nm generated by ³F₂??³H₆ transition under excitation at 980?nm. The optimum doping concentration of Li⁺ ions was investigated and UC mechanism of Li⁺/Tm³⁺/Yb³⁺ co-doped CaMoO₄ was discussed in detail.