L p -dual Quermassintegral sums

In this paper, we first introduce a concept of L _p -dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L _p -dual Quermassintegral sums. Moreover, by using Lutwak’s width-integral of index i, we establish the L _p -Brunn-Minkowski inequality for the polar mixed projection bodies. As applications, we prove some interrelated results. This work was partially supported by the National Natural Science Foundation of China (Grant No. 10271071), Zhejiang Provincial Natural Science Foundation of China (Grant No. Y605065) and Foundation of the Education Department of Zhejiang Province of China (Grant No. 20050392)     

Chromatographic investigations of furocoumarins fromHeracleum genus fruits

Summary Furocoumarins from extracts ofHeracleum genus fruits were separated using normal and reversed phase TLC and HPLC and isolated in the milligram scale using overloaded systems of column chromatography. Binary or ternary solvents containing a polar modifier (methanol, diisopropyl ether or acetonitrile) were used as the mobile phases. Preliminary report on this work was presented at the 47th International Congress of Pharmaceutical Sciences of F.I.P. in Amsterdam. The Netherlands, 30 August–5 September 1987.     

Li2O-B2O3-P2O5系统非晶态混合骨架效应的NMR研究

用核磁共振对非晶态中B³⁺离子的微观结构进行了测定,结合Raman光谱的研究,对Li₂O-B₂O₃-P₂O₅系统非晶态的性能(电导率、密度等)在P₂O₅/B₂O₃比约等于1时产生极值的原因从理论上作了阐明。     

On the Isoperimetric Type Problems with Current Hyperplanes

Analytical approach is presented to the isoperimetric type problems of finding convex figures separated by current hyperplanes.     

Detailed Description of Mixed Symmetry States in 94Mo Using Interacting Boson Model

We have investigated the low-lying collective states and electromagnetic transitions in 94Mo within the framework of the interacting boson model. The influence of model parameters on the energy levels and electromagnetic properties has been investigated. The analysis of the obtained results and the parameter values predict that the 23+state is the lowest mixed symmetry state with pure F = Fmax - 1 in this nucleus. The calculated results predicate that the 25+ (two-Q-phonon) mixed symmetry state is closed to the J = 2+ at 2.870 MeV in the experimental data, and the 2.965 MeV state is the lowest mixed symmetry with J = 3+.     

New methodologies in trace analysis of volatile organic compounds

Two methods for sampling and concentration of volatile organic compounds are reported. In the first method, traps coated with a very thick film (ca. 100 μm) of cross-linked silicone stationary phase are employed. Such thick films can be prepared with a modified dynamic coating procedure, which is briefly described. The low phase ratio traps can be utilized for enrichment of volatiles from gaseous as well as aqueous matrices. The second technique is based on chromatographic evaporation of a solvent in a capillary tube, where the process is sustained by a repeated sample injection and a cyclic flow reversal. In this way, large solvent volumes can be handled by a small volume system. Under optimal conditions, when using a solvent barrier, quantitative recovery is possible even for compounds of comparatively high volatility. Another important application of the technique is extraction of trace components from gases such as headspace samples, polluted air, etc.     

Studies on pre-hump and main fractions of cellulose-2,5-acetate in acetone

Technical cellulose-2.5-acetates (CA 2.5) were characterized regarding their carbohydrate composition in comparison to the raw material. The association of the CA 2.5 samples in acetone was studied by size exclusion chromatography (SEC) using various acetone grades and styrene divinylbenzene copolymer columns. In HPLC grade acetone with and without addition of 1% water up to three different pre-humps eluted in front of the main fraction of the polymer. The evaluation of the main peak by light scattering measurements resulted in high molar masses indicating that for these technical CA 2.5 samples even the main fraction is not dissolved without association. No pre-humps or association phenomena were observed after addition of 1 ppm LiBr to HPLC grade acetone or with p.a. grade acetone. In addition pre-hump enriched and pre-hump free fractions were isolated by fractionated precipitation. The carbohydrate composition of these fractions was determined and correlated with their association pattern in SEC investigations.     

Uniform convergence of Galerkin‐multigrid methods for nonconforming finite elements for second‐order problems with less than full elliptic regularity

In this article we prove uniform convergence estimates for the recently developed Galerkin‐multigrid methods for nonconforming finite elements for second‐order problems with less than full elliptic regularity. These multigrid methods are defined in terms of the “Galerkin approach,” where quadratic forms over coarse grids are constructed using the quadratic form on the finest grid and iterated coarse‐to‐fine intergrid transfer operators. Previously, uniform estimates were obtained for problems with full elliptic regularity, whereas these estimates are derived with less than full elliptic regularity here. Applications to the nonconforming P₁, rotated Q₁, and Wilson finite elements are analyzed. The result applies to the mixed method based on finite elements that are equivalent to these nonconforming elements. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 203–217, 2002; DOI 10.1002/num.10004