On Potential Theoretic Skeletons of Polyhedra

We prove that any polyhedron in two dimensions admits a type of potential theoretic skeleton called mother body. We also show that the mother bodies of any polyhedron in any number of dimensions are in one-to-one correspondence with certain kinds of decompositions of the polyhedron into convex subpolyhedra. A consequence of this is that there can exist at most finitely many mother bodies of any given polyhedron. The main ingredient in the proof of the first mentioned result consists of showing that any polyhedron in two dimensions contains a convex subpolyhedron which sticks to it in the sense that every face of the subpolyhedron has some part in common with a face of the original polyhedron.     

Electron capture detector performance parameters in view of the response presentation forms

Summary Four most frequently used presentation forms of the ECD response are described. Equations describing the dependence of the sensitivity, linearity and minimum detectable concentration of the ECD working under constant frequency mode of operation on the pulse period are derived from Wenthworth’s kinetic model for all four forms mentioned above. The forms presented are compared on the basis of equations derived. Results of the calculations are given and some predictions are experimentally tested for sulphur hexafluoride. Good agreement was found between the predicted and observed relationships. Presented at the 15th International Symposium on Chromatography, Nürnberg, October 1984     

Domino allylation and cyclization of ortho-alkynylbenzaldehydes with allyltrimethylsilane catalyzed by Pd(II)-Cu(II) bimetallic systems

The reaction of ortho-alkynylated benzaldehydes 1 with allyltrimethylsilane under the Pd(OAc)₂-CuCl₂ catalyst system gave the isochromene derivatives 2 together with the chlorinated products 3. When the reaction was conducted in the presence of half equiv of H₂O, the formation of 3 was suppressed and 2 was obtained in good to high yields. When the reaction of 1a was carried out with trimethylsilylcyanide instead of allylsilane, the cyano group-substituted isochromene 9 was obtained in 94% yield.     

Homotopy of ends and boundaries of CAT(0) groups

For n ≥ 0, we exhibit CAT(0) groups that are n-connected at infinity, and have boundary which is (n − 1)-connected, but this boundary has non-trivial nth-homotopy group. In particular, we construct 1-ended CAT(0) groups that are simply connected at infinity, but have a boundary with non-trivial fundamental group. Our base examples are 1-ended CAT(0) groups that have non-path connected boundaries. In particular, we show all parabolic semidirect products of the free group of rank 2 and have a non-path connected boundary.     

Links in an open book decomposition and in the standard contact structure

We study a relationship between arc presentations of links in and Legendrian links in with the standard tight contact structure. We determine the arc indices of torus knots.

     

Canonical symbolic dynamics for one-dimensional generalized solenoids

We define canonical subshift of finite type covers for Williams' one-dimensional generalized solenoids, and use resulting invariants to distinguish some closely related solenoids.

     

大豆蛋白基茶碱控释片的制备及稳定性研究

以茶碱为模型药物,大豆蛋白和海藻酸钠作为骨架材料,采用混合压片法制备了不同比例的药物片剂。采用紫外比色法测定释放效果,考察了大豆蛋白与海藻酸钠不同比例以及不同pH释放介质和高湿度对茶碱片稳定性的影响。结果表明:大豆蛋白和海藻酸钠作为骨架材料的片剂释药时间都达到了8h以上,在pH6.8PBS中的释药率相对pH1.2盐酸溶液要快,具有良好的定向控释特性。随着湿度的增加,茶碱释放率略有下降,具有较好的湿度稳定性。通过适度调节大豆蛋白和海藻酸钠的比例可实现不同控释效果。实验结果表明大豆蛋白和海藻酸钠共混物是一种良好的天然药物缓控释骨架材料,其释放过程符合一级动力学特征,是药物扩散和骨架溶蚀二者共同作用的结果。     

Localization Phenomena in Liquid-Saturatedand Empty Porous Solids

Localization phenomena occur as a result of local concentrations of plastic deformations in small bands of finite width (shear bands). Porous materials, as, for instance, soil, rock, concrete and sinter materials as well as polymeric and metallic foams exhibit a strong tendency towards shear banding caused by plastic dilatation in the brittle deformation range. This kind of behaviour is of great practical importance in engineering design, for example in the study and computation of failure mechanisms in soil mechanics (base failure, slope failure, etc.). From the mathematical point of view, the computation of localization phenomena, for example within the framework of the finite element method (FEM), yields an ill-posed problem, since each mesh refinement leads to smaller shear bands until one obtains (ideally) a singular surface. Following this, regularization mechanisms should be introduced to obtain reliable and robust results.In the present article, two natural regularization mechanisms for liquid-saturated and empty granular porous materials are discussed. These mechanisms are (1) the inclusion of additional independent degrees of freedom in the sense of the Cosserat brothers for the granular porous solid and (2) the inclusion of pore-fluid viscosity in the saturated case.     

Integral presentations of Catalan numbers

We compute in three different ways the same definite parametric integral. By-products are the derivation of a combinatorial identity and two integral presentations of Catalan numbers. One of them leads to a presentation using the γ function.     

Naturally occurring bioactive 5-ethylidenehydantoins as inspiration for the development of analogues

Many naturally occurring 5-ethylidenehydantoins and their derivatives exhibit extensive biological activities; this characteristic has inspired us to prepare analogues. Fourteen such analogues with the core structure of 5-ethylidenehydantoin were synthesized from readily available components with yields of up to 82%.