Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems

Multi-valued solutions are constructed for 2 × 2 first-order systems using a generalization of the hodograph transformation. The solution is found as a complex analytic function on a complex Riemann surface for which the branch points move as part of the solution. The branch point singularities are envelopes for the characteristics and thus move at the characteristic speeds. We perform an analysis of stability of these singularities with respect to perturbations of the initial data. The generic singularity types are folds, cusps, and nondegenerate umbilic points with non-zero 3-jet. An isolated singularity is generically a square root branch point corresponding to a fold. Two types of collisions between singularities are generic: At a “tangential” collision between two singularities moving at the same characteristic speed, a cube root branch point is formed, corresponding to a cusp. A “non-tangential” collision, between two square root branch points moving at different characteristic speeds, remains a square root branch point at the collision and corresponds to a nondegenerate umbilic point. These results are also valid for a diagonalizable n-th order system for which there are exactly two speeds. © 1993 John Wiley & Sons, Inc.     

Mechanisms of reduced human vascular cell migration after photodynamic therapy

Restenosis results from intimal hyperplasia and constrictive remodeling following cardiovascular interventions. Photodynamic therapy (PDT) has been shown to inhibit intimal hyperplasia in vivo by preventing neointimal repopulation of the treated vessel. This study was undertaken in an attempt to further dissect the mechanisms by which PDT acts on secreted and extracellular matrix proteins to inhibit migration of cultured human vascular cells. PDT of three-dimensional collagen gels inhibited invasive human smooth muscle cell (SMC) migration, whereas cell-derived matrix metalloproteinase production remained unaltered. Additionally, PDT generated cross-links in the collagen gels, a result substantiated in an ex vivo model whereby PDT rendered the treated vessels resistant to pepsin digestion and inhibited invasive migration of SMC and fibroblasts. These data support the premise that by inducing matrix protein cross-links, rendering the vessel resistant to degradation, in vivo PDT inhibits repopulation of the vessel and therefore intimal hyperplasia.     

Rapid determination of corticosteroids in pharmaceuticals by flow injection analysis

The proposed method is based on the reduction of blue tetrazolium by the steroid in an alkaline medium to form a highly colored formazan. The effects of reagent concentration, temperature, flow rate, and manifold design on the reaction are discussed for a typical steroid, methylprednisolone acetate. Analytical readout is obtained within 30 s after sample introduction and up to 100 samples/h can be processed with baseline resolution between peaks. Typical relative standard deviations of 0.5% are obtained with 10-μ1 injection volumes. Results obtained by flow injection analysis are similar to those obtained with the AutoAnalyzer technique.     

Reactivity of secondary metallocene alkyls and the question of dormant sites in catalytic alkene polymerization

The reactivity of [rac-(C2H4(1-indenyl)2)Zr(n-butyl)][MeB(C6F5)3] (4), [rac-(C2H4(1-indenyl)2)Zr(sec-butyl)][MeB(C6F5)3] (5), and [rac-(C2H4(1-indenyl)2)Zr(polypropenyl)][MeB(C6F5)3] with propene, ethene, and hydrogen was studied by low-temperature (<-40 degrees C) 1H and 13C NMR spectroscopy in toluene solutions. In contrast with previous suggestions that 2 degrees zirconium alkyl species such as 5 are dormant sites, these measurements demonstrate reactivity of 2 degrees zirconium alkyls with propene and ethene comparable to the 1 degrees zirconium alkyl species 4 and [rac-(C2H4(1-indenyl)2)Zr(polypropenyl)][MeB(C6F5)3]. Because 2,1-insertion of propene is an infrequent event, these results preclude significant accumulation of catalyst in the form of 2 degrees zirconium alkyls for this metallocene and counterion. The reactivity of 5 with hydrogen is at least 2 orders of magnitude faster than other 1 degrees zirconium alkyls. Such high reactivity accounts for the puzzlingly high fraction of butyl end groups in prior hydrooligomerization studies and implies that catalyst responsivity to H2 as a molecular weight control agent correlates with the regioselectivity of the catalyst.     

Direct observation of insertion events at rac-(C2H4(1-indenyl)2)Zr(MeB(C6F5)3)-polymeryl intermediates: distinction between continuous and intermittent propagation modes

The propagating species for 1-hexene, propene, and ethene polymerization as catalyzed by [rac-(C2H4(1-indenyl)2)Zr(CH3)][CH3B(C6F5)3] has been intercepted at T < -40 degrees C and characterized by NMR methods. Observation of the propagating species permits direct monitoring of initiation, propagation, and termination processes by NMR. Detailed examination of alkene incorporation into Zr-polymeryl species using 13C-labeled 1-alkenes supports a continuous insertion mechanism whereby the anion re-coordinates after each alkene insertion.     

种植沙生植物--沙棘改善内蒙古地区生态环境

结合内蒙古地区现状，对沙棘的生物学和生态学特性、沙棘属植物化学成分和微量元素及种植沙生植物——沙棘的重要性和必要性进行了详细的研究和探讨。研究表明，沙棘属植物具有极强的生态适应性并富含多种营养成分和生物活性物质，并以耐干旱、耐瘠薄、萌蘖及固氮能力强等特点被称为治理非宜林地水土流失、改善生态环境的先锋树种。种植沙棘是治理内蒙古脆弱生态环境最经济、最有效的措施，是贫瘠的不毛之地发展经济、增加收入的经济树种。另外．种植沙棘的技术简便，容易掌握，投资少，见效快。