ON PARAMETRIC FACTORIZATION OF BI－ORTHOGONAL LAURENT POLYNOMIAL WA VELET FILTERS

In this paper,we study the factorization of bi-orthogonal Laurent polynomial wavelet matrices with degree one into simple blocks.A conjecture about advanced factorization is given.     

Ring‐opening polymerization and block copolymerization of L‐lactide with divalent samarocene complex

Divalent samarocene complex [(C₅H₉C₅H₄)₂Sm(tetrahydrofuran)₂] was prepared and characterized and used to catalyze the ring‐opening polymerization of L ‐lactide (L‐LA) and copolymerization of L‐LA with caprolactone (CL). Several factors affecting monomer conversion and molecular weight of polymer, such as polymerization time, temperature, monomer/catalyst ratio, and solvent, were examined. The results indicated that polymerization was rapid, with monomer conversions reaching 100% within 1 h, and the conformation of L‐LA was retained. The structure of the block copolymer of CL/L‐LA was characterized by NMR and differential scanning calorimetry. The morphological changes during crystallization of poly(caprolactone) (PCL)‐b‐P(L‐LA) copolymer were monitored with real‐time hot‐stage atomic force microscopy (AFM). The effect of temperature on the morphological change and crystallization behavior of PCL‐b‐P(L‐LA) copolymer was demonstrated through AFM observation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2667–2675, 2003     

Gravitational collapse with charge and small asymmetries I. Scalar perturbations

A recent analysis by Richard Price of spherical collapse with small nonspherical perturbations is here generalized to the case of an electrically charged collapsing star (0¦Q¦-M). The perturbations are confined to a scalar field generated by a nonspherical distribution of scalar charge in the star. As in the electrically neutral case, the scalar perturbations are probably a prototype for all others — electromagnetic, gravitational, and higherspin. The collapse is shown to produce a Reissner-Nordström black hole, and the scalar-field perturbations are shown to radiate completely away; but they die out more slowly the larger is the star's electric charge. For charge ¦Q¦M, the -pole part of the perturbation at fixedr and late times is dominated by a tail that dies out ast ^{–(2+ 2)}. But for ¦Q¦=M, the primary outgoing waves emitted from the star's surface are everywhere larger than the tail. At fixedr and late times they die as t^–(+2). Also, a calculation of the redshift shows that a collapsing star becomes black more slowly the larger is the star's electric charge.Supported in part by the National Science Foundation (GP-27304, GP-28027, GP-19887).     

Determination of the electron temperature of the tenuous pulsed argon ion laser plasma by means of the line intensity ratio technique

The validity of the diagnostic line-intensity ratio method for determination of the electron temperature was examined for a tenuous, NLTE pulsed argon ion laser plasma. Recently measured cross sections for simultaneous excitation and ionization of the upper levels of the argon ion laser were used and averaged over the velocity distribution, assumed Maxwellian. The electron temperature was determined by observing the sidelight intensity ratio of doublet 4765 Å and quartet 4806 Å transitions, and it was found to be 1.65 eV. This result is in agreement with electron temperature values obtained by the time resolved measurement and the double probe method, respectively. The theory of the positive column, where wall effects are not considered, gives somewhat larger values as an upper bound.     

Dynamic mechanical properties of two copolymers of styrene and n-hexyl methacrylate

The storage (J′) and loss (J″) shear compliances have been measured for two random copolymers of styrene and n-hexyl methacrylate with styrene contents of 18% and 30% (by weight) in the frequency range 45–4400 Hz and the temperature range 31–107°C. The data at different temperatures were combined by the method of reduced variables, and the WLF coefficients were calculated from the temperature shift factors by the method of Pierson and Kovacs. The data were compared with earlier data for the two homopolymers. The thermal expansion coefficient of the fractional free volume, and the free volume at the glass transition temperature, varied monotonically with composition, but the fractional free volume at a reference temperature of 100°C appeared to pass through a maximum as a function of concentration. Comparison of isothermal plots of J′ at 100°C, plots of the relaxation spectrum at 100°C, the monomer friction coefficient and its temperature dependence, and isochronal plots of the storage shear moduls at 100 radians/see all show that the properties of poly(n-hexyl methacrylate) are very slightly affected by incorporation of 18% styrene and only moderately affected by 30% styrene. By contrast, comparison of styrene–butadiene rubber with 1,4-polybutadiene shows a very large effect of incorporation of 23.5% styrene. These differences may be associated with local packing relations of the comonomer residues and suggest that copolymer properties cannot be readily predicted from those of the component homopolymers.     

Synthetic zeolites A and X as stationary phases in thin-layer chromatography

Summary The possibility of using synthetic zeolites A and X as stationary phases in thin-layer chromatography has been investigated and the method of preparing layers from crystalline zeolites and their gels determined, as was the possibility of separating certain mixtures on the layers obtained. Experiments were performed simultaneously on layers from zeolites A and X dried at room temperature and on layers activated at 120°C, and also on layers from amorphous forms but in this case only on those dried at room temperature. Dyes and inorganic cations were used as test substances. On the basis of the results obtained it has been established that only the crystalline compounds can be successfully used as thin layers for the separation of organic compounds.     

Synthesis and properties of N-hexadecyl ethylenediamine triacetic acid

A new kind of surfactant named N-hexadecyl ethylenediamine triacetic acid (HED3A) was synthesized from anhydrous ethylenediamine, 1-bromohexadecane, and chloroacetic acid. Testing showed stability of HED3A in hard water, wetting power, dispersing power, and surface tension increased along with pH value. Stability in hard water of trisodium N-hexadecyl ethylenediamine triacetate (3NaHED3A) was at level 4, which was better than that of sodium dodecylsulfate (SDS) and sodium dodecylbenzene sulfonate (LAS). Other properties of 3NaHED3A including wetting power, dispersing power, emulsifying power, and surface tension had intermediate value between SDS, LAS, AES, peregal-O, and cetyltrimethylammonium chloride (CTAC). The ethylenediamine triacetic acid (ED3A) group in 3NaHED3A can chelate many kinds of metal ions, which indicates a promising application prospect in many fields including metal anticorrosion, corrosion control agent, additives in electroplating solution, and ore selection and solid surface treatment.     

Isomer separation, conformation control of flexible cyclohexanedicarboxylate ligand in cadmium complexes

Two 2D cadmium coordination polymers have been prepared using flexible 1,4-cyclohexanedicarboxylic acid (chdcH2) under hydrothermal condition, the conformations of chdcH2 were separated completely in the synthetic reactions.     

Long-Time Behaviour of the Solutions for the Multidimensional Kolmogorov-Spieqel-Sivashinsky Equation

In this paper, we study the existence and long-time behaviour of the solutions for the multidimensional Kolmogorov-Spiegel-Sivashinsky equation. We first show the existence of the global solution for this equation, and then prove the existence of the global attractor and establish the estimates of the upper bounds of Hausdorff and fractal dimensions for the attractor. We also obtain the Gevrey class regularity for the solutions and construct an approximate inertial manifold for the system. Received April 15, 1999, Accepted September 6, 2000