A point-wise criterion for quasi-periodic motions in the KAM theory

We consider initial value problems for nearly integrable Hamiltonian systems. We formulate a sufficient condition for each initial value to admit the quasi-periodic solution with a Diophantine frequency vector, without any nondegeneracy of the integrable part. We reconstruct the KAM theorem under Rüssmann’s nondegeneracy by the measure estimate for the set of initial values satisfying this sufficient condition. Our point-wise version is of the form analogous to the corresponding problems for the integrable case. We compare our framework with the standard KAM theorem through a brief review of the KAM theory.     

The resonance Raman effect of uranyl chloride in dimethyl sulfoxide

A study was carried out of the resonance Raman scattering spectra of uranyl chloride (UO2Cl2) in dimethyl sulfoxide ((CH3)2SO) (DMSO) under laser excitation of the UO2(2+) ion in resonance with the 1sigma(g)+ --> 1phi(g) Laport-forbidden f-f electronic transitions span from 530 to 450 nm by using ten output lines of the argon-ion laser at room temperature. The resonance Raman excitation profile of the totally symmetric stretching vibrational mode of uranyl observed at 832 cm(-1) is presented and analyzed in terms of transform theory within the non-Condon model to give relatively good agreement with experimental results. The disagreement between the experimental data and the calculated resonance Raman excitation profile, at the long-wave part of the the 1sigma(g)+ --> 1phi(g) electronic transitions, may be referred to interference between the weak scattering from the neighboring forbidden electronic states (1delta(g)) and strong preresonance scattering from allowed electronic states at higher levels. An amount of change in the experimental resonance Raman excitation profile of the uranyl-DMSO system depends considerably upon the ligands (L) bound to the uranyl group. Elongation of the U-O equilibrium bond length resulting from the 1sigma(g)+ --> 1phi(g) electronic transitions is related to the magnitude of the change in the excitation profile of UO2L2 (L = NO3, CH3COO, Cl) type uranyl compounds in (DMSO).     

High-Resolution Reflectometry by Optical Multidigitized Coherence

We propose and confirm a novel technique of optical frequency domain reflectometry based on multidigitized coherence using a multimode laser. The proposed system can easily provide the potential for high resolution on the order of 10 μm without scanning frequencies as in frequency domain reflectometers of either continuous or stepwise sweep. The theoretical approach agrees well with the experimental results demonstrated using a commercially available multimode laser diode.     

Copolymerization of carbon dioxide and propylene oxide with supported diethylzinc catalysts

Diethylzinc was allowed to react with various metal oxides in n-heptane at 60°C, and the copolymerization of propylene oxide and carbon dioxide was investigated at 60°C in solution in dioxane with reaction products as catalysts. An alternate copolymer was obtained with every catalyst, but the yield of copolymer and the number-average molecular weight depended significantly on the supporting materials. In a kinetic study of the copolymerization we found that the catalytic efficiency (number of propagating species per number of zinc supported) was only a few percent with every catalyst. The copolymerization was also examined by using several kinds of silica, whose pore diameters are markedly different, as supports. The results obtained strongly suggested that only the active species existing in large pores act as the propagating species.     

Polymerization-induced phase separation in silica sol-gel systems containing formamide

Silica gels with well-defined pores both in micrometer and nanometer ranges were obtained by acid-catalyzed hydrolysis and polymerization of tetramethoxysilane in the presence of formamide. The micrometer-range structures of these gels are studied in terms of the phase diagram of the quasi two-component system, namely solvent-rich and silica-rich end compositions. The resulting interconnected structures and aggregates of particles are related to the occurrence of spinodal phase separation. The composition region that gave interconnected structures for the present system was much more limited and their characteristic sizes were much smaller than those for the previously reported systems containing an organic polymer. These results could be explained qualitatively by the effect of the degree of polymerization on the Flory-Huggins' type free energy change of mixing.     

Radiation-induced oxidation of polyethylene,ethylene–butene copolymer,and ethylene–propylene copolymer

Oxygen consumption and yield of oxidation products during γ-irradiation were studied on five types of polyethylene (PE), ethylene–butene copolymer (EB), and ethylene–propylene copolymer (EPR) using gas chromatography, mass spectrography, and high-resolution NMR. Samples were irradiated in oxygen under pressure from 0 to 500 torr by ⁶⁰Co γ-rays up to 20 Mrad at 22–25°C. In enough oxygen, oxygen consumption and yield of oxidation products are independent of oxygen pressure for low-density PE, EB, and EPR. The G values of oxygen consumption were 14–18.4 for PE, 11.6 for EB at 1 × 10⁶ rad/h, and 8.3 for EPR at 2 × 10⁵ rad/h. The oxidation products determined were carboxylic acid (? CH₂? CO? OH), H₂O, CO₂, and CO. The oxygen consumption and oxidation products for PE were found to increase with increasing crystallinity.     

Synthesis and biological activities of lipid A analogs: modification of a glycosidically bound group with chemically stable polar acidic groups and lipophilic groups on the disaccharide backbone with tetradecanoyl or N-dodecanoylglycyl groups.

Six novel lipid A analogs were synthesized. The first two analogs, 4 and 5, have an alpha-glycosidically bound carboxymethyl or 1,3-dicarboxyisopropyl group on the disaccharide backbone with four tetradecanoyl groups. The next three analogs, 6, 7 and 8, have two or four N-dodecanoylglycyl groups on the 1-alpha-O-phosphonooxyethylated disaccharide backbone. Analog 6 bears N-dodecanoylglycyl groups on the hydroxyl functions at positions 3 and 3', and tetradecanoyl groups on the amino functions at positions 2 and 2'. Analog 7 is a 2, 3, 2' and 3'-tetrakis(N-dodecanoylglycyl) derivative, and analog 8 resembles compound 6, but the binding of the N-dodecanoylglycyl and tetradecanoyl groups at positions 2, 2' and 3, 3' are reversed. The third analog, 9, has the same acyl group configuration as compound 6, but has a 1,3-dicarboxyisopropyl group at position C-1. Compounds 4 and 5 exhibited definite antitumor activity against Meth A fibrosarcoma, indicating that the phosphate group at the C-1 position in lipid A could be replaced by the carboxylic acid without reducing the antitumor activity. In rabbits, compounds 6 and 9 exhibited potent antitumor activity, but their toxicity was extremely low. On the other hand, compounds 7 and 8 showed no antitumor activity. The levels of antitumor activity of 6 and 9 were similar to those of the natural-type lipid A. The antitumor activities of analogs with a N-dodecanoylglycyl group on the disaccharide backbone depended on the connecting sites of the acyl groups.     

Morphology and mechanical properties of ultrahigh molecular weight polypropylene prepared by gelation/crystallization at various temperatures

Films of ultrahigh molecular weight (5.4×10⁶) polypropylene were produced by gelation/crystallization at various temperatures from dilute decalin solutions according to the method of Smith and Lemstra. The temperatures chosen were 20°, 30°, 50°, and 60°C. With increasing the temperature, the long period and crystallinity of the resultant gel film increased. By contrast, when the films were stretched up to 50 } 60 times, the increases in Young's modulus and crystallinity become more significant, as the temperature of the gelation/crystallization became lower. This interesting phenomenon is thought to be due to the dependence of the number of entanglements on the temperatures concerning gelation/crystallization and evaporation of solvent from the gel to form a film.     

Direct chiral resolution of lactic acid in food products by capillary electrophoresis

Chiral resolution of native DL-lactic acid was performed by capillary electrophoresis using 2-hydroxypropyl-beta-cyclodextrin as a chiral selector. Various factors affecting chiral resolution, migration time, and peak area of lactic acid were studied. The running conditions for optimum separation of lactic acid were found to be 90 mM phosphate buffer (pH 6.0) containing 240 mM 2-hydroxypropyl-beta-cyclodextrin with an effective voltage of -30 kV at 16 degrees C, using direct detection at 200 nm. In order to enhance the sensitivity, sample injection was done under a pressure of 50 mbar for 200 s. On-line sample concentration was accomplished by sample stacking. With this system, D- and L-lactic acids in food products were analyzed successfully.