The intertwining lifting theorem for ordered groups

Sz.-Nagy's dilation theorem for a contraction on a Hilbert space has been extended by Mlak to the case of a contraction semigroup whose indices are the positive elements of a totally ordered discrete group. We generalize to this case the intertwining lifting theorem of Sz.-Nagy and Foias. Some previous interpolation results on ordered groups are obtained as consequences.     

Complex morphology of melt-spun nylon-6 fibres investigated by 1H double-quantum-filtered NMR spin-diffusion experiments.

The complex morphology of high-speed melt-spun nylon-6 fibres hydrated with D2O was investigated using 1H double-quantum-filtered spin-diffusion NMR experiments. The magnetisation exchange from selected crystalline domains along the fibrils and interfibrils was simulated with the help of a three-dimensional solution of a spin-diffusion equation approximated by a product of one-dimensional analytical NMR signals, which correspond to a lamellar morphology. This allows to measure the sizes of crystalline and less-mobile amorphous domains along the fibrils, as well as the diameter of the fibrils and interfibril distances. A series of nylon-6 fibres with extreme values of winding speed and draw ratio was investigated. The changes detected in the domain size along the fibrils and interfibrils show the same trend in the data obtained from wide-angle X-ray diffraction and small-angle X-ray scattering.     

How to Exhibit Toroidal Maps in Space

Steinitz's theorem states that a graph is the 1-skeleton of a convex polyhedron if and only if it is 3-connected and planar. The polyhedron is called a geometric realization of the embedded graph. Its faces are bounded by convex polygons whose points are coplanar. A map on the torus does not necessarily have such a geometric realization. In this paper we relax the condition that faces are the convex hull of coplanar points. We require instead that the convex hull of the points on a face can be projected onto a plane so that the boundary of the convex hull of the projected points is the image of the boundary of the face. We also require that the interiors of the convex hulls of different faces do not intersect. Call this an exhibition of the map. A map is polyhedral if the intersection of any two closed faces is simply connected. Our main result is that every polyhedral toroidal map can be exhibited. As a corollary, every toroidal triangulation has a geometric realization.     

A highly sensitive and rapid assay for protein determination in human urine and penicillin using a Rayleigh light-scattering technique with benzeneazo-8-acetylamino-1-naphthol-3,6-disulfonic acid sodium salt.

A simple and sensitive method was conducted for the determination of trace amounts of proteins with benzeneazo-8-acetylamino-1-naphthol-3,6-disulfonic acid sodium salt (azophloxine, AP) using a Rayleigh light-scattering (RLS) technique. At pH 2.60 and in the presence of an emulsifier OP microemulsion, the RLS of AP can be greatly enhanced by proteins, owing to the interaction between AP and protein. The enhanced intensity is proportional to the concentration of proteins. Four proteins, including bovine serum albumin (BSA), human serum albumin (HSA), lysozyme (Lys) and gamma globulin (gamma-G) have been tested. For example, the linear range of BSA was 0 - 0.06 microg mL(-1) with detection limits of 2.38 ng mL(-1). The method was applied to the analysis of protein in human urine and penicillin samples with satisfactory results. The relative standard deviation was in all instances less than 4.0%, and the recovery was in the range of 97.5 - 104%.     

The newton filtration and d-determination of bifurcation problems related to C 0 contact equivalence

In this paper, from the Newton filtration’s point of view, we construct the singular Riemannian metric and use the method in singular theory to study the bifurcation problems, and give the sufficient condition of d-determination of bifurcation problems with respect to C ⁰ contact equivalence. The special cases of the main result in this paper are the results of Sun Weizhi and Zou Jiancheng.     

Rapid Fabrication of Hollow SiO2 Spheres with Novel Morphology

The hydrolysis of tetraethoxysilane (TEOS) occurred on the surface of poly(methyl methacrylate) (PMMA) microshperes immediately after these microshperes were prepared in TEOS. Micron-sized hollow SiO2 spheres were obtained by calcination of the coated PMMA microshperes. It was found that the final hollow spheres were constituted by small SiO2 particles.     

Construction of multiporphyrin arrays using ruthenium and rhodium coordination to phosphines

The synthesis of linear multiporphyrin arrays with mono- and bisphosphine-substituted porphyrins as ligand donors and ruthenium(II) or rhodium(III) porphyrins as ligand acceptors is described. With appropriate amounts of the building blocks mixed, linear dimeric and trimeric arrays have been synthesized and analyzed by (1)H NMR and (31)P NMR spectroscopy. The Ru/Rh acceptor porphyrins can be located either at the periphery or in the center of the array. Likewise, the monophosphine porphyrins can be positioned at the periphery, thus allowing a high degree of freedom in the overall composition of the arrays. This way, both donor and acceptor porphyrins can act as chain extenders or terminators. One of the trimeric complexes with two nickel and one ruthenium porphyrin has also been analyzed by X-ray crystallography. Attempts have also been made to synthesize higher order arrays by mixing appropriate amounts of the porphyrins; however, from the NMR data it cannot be concluded if monodisperse five, seven, or nine porphyrin arrays are present or if the solutions are composed of a statistical mixture of smaller and larger arrays.     

Headspace Solid-phase Microextraction–Gas Chromatographic–Mass Spectrometric Analysis of the Essential Oils of Two Traditional Chinese Medicines, Angelica pubescens and Angelica sinensis

Angelica pubescens and Angelica sinensis belong to the Umbelliferae family and both are used as traditional Chinese medicines. In the present study, headspace solid-phase microextraction (HS-SPME) with gas chromatography-mass spectrometry (GC-MS) was used for the analysis of the volatile constituents present in their roots. Eighty-seven compounds in Angelica pubescens and thirty-six compounds in Angelica sinensis were identified by GC-MS. Their relative contents were calculated by the peak area ratio. HS-SPME was compared to steam distillation (SD) by analyzing the volatile constituents of Angelica sinensis root. A good agreement between results obtained with both techniques was found. As a conclusion, HS-SPME is a powerful tool for determining the volatile constituents present in the TCMs.