Peripheral spectrum of positive quasi-compact operators onC 0(X)

LetX be a locally compact space, andT, a quasi-compact positive operator onC ₀(X), with positive spectral radius,r. Then the peripheral spectrum ofT is a finite set of poles containingr, and the residue of the resolvent ofT at each peripheral pole is of finite rank. Using the concept of closed absorbing set, we develop an iterative process that gives the order,p, ofr, some special bases of the algebraic eigenspaces ker(T-r) ^p and ker(T ^*-r) ^p , and finally the dimension of the algebraic eigenspace associated to each peripheral pole.     

Stereocontrol of diene polymers by topochemical polymerization of substituted benzyl muconates and their crystallization properties

We report the stereocontrol of diene polymers by the topochemical polymerization of alkoxy-substituted benzyl muconates in the solid state. A monomer stacking structure is controlled by the weak intermolecular interactions in the monomer crystals, depending on the structure and position of the alkoxy-substituent. The translational and alternating types of molecular stacking structures in a column provide diisotactic and disyndiotactic polymers, respectively, by the solid-state polymerization under UV and γ-ray irradiation. On the other hand, the meso and racemo structures of the resulting polymers are determined by the molecular symmetry of the used muconate monomers. The various substituted benzyl ester polymers are transformed into the same ethyl ester polymers with the four types of tacticities. The structure and crystallization behavior of the substituted benzyl ester polymers as well as the ethyl ester polymers have been revealed in detail. We clarify the effects of the tacticity on the crystallization property of the stereoregular polymuconates. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4952–4965, 2006     

Synthesis of silicon nitride based ceramic nanoparticles by the pyrolysis of silazane block copolymer micelles

Diblock copolymer poly(1,1,3,N,N′‐pentamethyl‐3‐vinylcyclodisilazane)‐block‐polystyrene (polyVSA‐b‐polySt) and triblock copolymer poly(1,1,3,N,N′‐pentamethyl‐3‐vinylcyclodisilazane)‐block‐polystyrene‐block‐poly(1,1,3,N,N′‐pentamethyl‐3‐vinylcyclodisilazane) (polyVSA‐b‐polySt‐b‐polyVSA), consisting of silazane and nonsilazane segments, were prepared by the living anionic polymerization of 1,1,3,N,N′‐pentamethyl‐3‐vinylcyclodisilazane and styrene. PolyVSA‐b‐polySt formed micelles having a poly(1,1,3,N,N′‐pentamethyl‐3‐vinylcyclodisilazane) (polyVSA) core in N,N‐dimethylformamide, whereas polyVSA‐b‐polySt and polyVSA‐b‐polySt‐b‐polyVSA formed micelles having a polyVSA shell in n‐heptane. The micelles with a polyVSA core were core‐crosslinked by UV irradiation in the presence of diethoxyacetophenone as a photosensitizer, and the micelles with a polyVSA shell were shell‐crosslinked by UV irradiation in the presence of diethoxyacetophenone and 1,6‐hexanedithiol. These crosslinked micelles were pyrolyzed at 600 °C in N₂ to give spherical ceramic particles. The pyrolysis process was examined by thermogravimetry and thermogravimetry/mass spectrometry. The morphologies of the particles were analyzed by atomic force microscopy and transmission electron microscopy. The chemical composition of the pyrolysis products was analyzed by X‐ray fluorescence spectroscopy and Raman scattering spectroscopy. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4696–4707, 2006     

纳米晶Y_2SiO_5∶Eu的浓度猝灭研究

报道了分别用溶胶－凝胶法合成的Ｙ２ＳｉＯ５∶Ｅｕ纳米晶和用高温固相法合成常规尺度的Ｙ２ＳｉＯ５∶Ｅｕ材料的光致发光光谱和猝灭浓度的实验研究．结果表明：纳米Ｙ２－ｘＥｕｘＳｉＯ５比常规尺度的Ｙ２－ｘＥｕｘＳｉＯ５有更高的猝灭浓度和更高的发光亮度．理论分析认为这是由于在纳米材料中能量共振传递被阻断和猝灭中心在各个纳米晶内分布的涨落造成的．这个结果为高亮度的Ｙ２ＳｉＯ５∶Ｅｕ纳米材料的实际开发应用展示了广阔前景．     

A generalization of the katona theorem for crosst-intersecting families

LetX be ann-element set and letA and? be families of subsets ofX. We say thatA and? are crosst-intersecting if |A ∩ B| ≥ t holds for all A ∈A and for allB ∈ ?. Suppose thatA and ? are crosst-intersecting. This paper first proves a crosst-intersecting version of Harper's Theorem:

1. There are two crosst-intersecting Hamming spheresA ₀,? ₀ with centerX such that |A| ≤ |A ₀| and|?| ≤ |? ₀| hold.
2. Suppose thatt ≥ 2 and that the pair of integers (|A) is maximal with respect to direct product ordering among pairs of crosst-intersecting families. Then,A and? are Hamming spheres with centerX.

Using these claims, the following conjecture of Frankl is proven:

1. Ifn + t = 2k ? 1 then |A| |?| ≤ max \(\left\{ {\left( {K_k^n + \left( {_{k - 1}^{n - 1} } \right)} \right)^2 ,K_k^n K_{k - 1}^n } \right\}\) holds, whereK _l ⁿ is defined as \(\left( {_n^n } \right)\left( {_{n - 1}^n } \right) + \cdots + \left( {_l^n } \right).\)
2. Ifn + t = 2k then |A| |? ≤ (K _k ⁿ )² holds.

The extremal configurations are also determined.     

Emulsion stability and potassium leakage in emulsion liquid membrane systems

Potassium leakage was studied in liquid membrane systems containing various emulsifiers and compared with emulsion, stability in the storage test. The effects of various parameters upon emulsion stability and the leakage of standard traces are discussed. The transfer of cations can be caused by emulsion breaking, by transport with the specific carrier and/or with surfactants used as emulsifiers. The latter case becomes especially important when hydrophilic surfactants, e.g. ones containing polyoxyethylene chains, are present in liquid membranes. In systems containing hydrophobic emulsifiers the transfer of potassium is relatively low. In each case considered the effect of emulsifiers upon the transfer of the standard tracer should be checked prior to using the leakage test to characterize emulsion stability.     

Enhanced rectal absorption of insulin in rabbits from hollow-type suppositories containing insulin and glyceryl-1-monooctanoate.

The absorption of two kinds of insulin (from porcine or bovine pancreas) from the rectum of rabbits after the administration of hollow-type suppositories containing insulin and glyceryl-1-monooctanoate (GMO) as an absorption-enhancing agent was investigated. Two types of suppositories were employed: type I containing insulin in an aqueous solution (approx. 25 IU/mg/100 microliters citric buffer solution at pH 3.0) in the cavity of the suppository and GMO mixed with a base material (Witepsol H-15), and type II containing insulin in a crystalline form in the same amount as in type I. Without GMO, the insulin and glucose levels in plasma were unchanged, whereas a marked increase in the plasma levels of insulin and a decrease of glucose concentrations were found following coadministration of insulin and GMO by the type I suppository. Similar enhancement of rectal absorption of insulin was obtained from porcine and bovine sources. In the case of the crystalline insulin, despite the use of the same amount of GMO, porcine insulin was more efficiently absorbed than bovine insulin by the type II suppository. GMO enhances the absorption of insulin in an aqueous solution or a crystalline form, and the dissolution rate of insulin may be an important factor in the rectal absorption of insulin.