SOME TOPICS ON WAVELET ANALYSIS

A review of the advance in the theory of wavelet analysis in recent years is given.     

伴有边界摄动的三阶拟线性向量微分方程边值问题的奇摄动

本文研究伴有边界摄动的三阶拟线性向量微分方程边值问题的奇摄动,在适当的假设下,利用对角化技巧和不动点原理证明了摄动问题解的存在唯一性并给出解的任意阶的一致有效的渐近展开式和余项的估计。     

Modeling high-pressure densities at wide temperature range with volume scaling: Cyclohexane + n-hexadecane mixtures

High-pressure density data for cyclohexane + n-hexadecane mixtures at a wide temperature range was modeled with several classical equations of state (EOS) and correlative models. A modification for softening the co-volume and another for a volume scaling of the Peng–Robinson EOS (VS-PR) were proposed. The VS-PR model is able to correlate the pure component experimental data employing only five adjustable parameters, with root-mean-square deviation (RMSD) between calculated and experimental densities essentially within the experimental error. This result is superior to widely used approaches, i.e., a six parameter Tait model and six parameter volume translations (temperature and pressure dependent) for Peng–Robinson and Patel–Teja EOS. The VS-PR model also represents well the isobaric thermal expansion and the isothermal compressibility coefficients of the pure cyclohexane, a small naphthenic substance as well as a long chain n-alkane hydrocarbon, n-hexadecane. When modeling the mixture data, the use of VS-PR model of pure components along with the Redlich–Kister expansion, truncated at the first term, the density was correlated within a RMSD only 60% greater than the experimental error. The proposed model is able to accurately represent all the tested mixture data with a relatively small number of parameters.     

Joule-Thomson inversion curve prediction by using equation of state

In this paper five equations of state are tested for checking their ability to predict the Joule-Thomson inversion curve.These five equations of state are:Mohsennia-Modarres-Mansoori(MMM),Ji-Lemp(JL),modified Soave-Redlich-Kwang(SRK)equation of state by Graboski(MSRK1),modified SRK equation of state by Peneloux and Rauzy(MSRK2),and modified Peng-Robinson (PR)equation of state by Rauzy(PRmr).The investigated equations of state give good prediction of the low-temperature branch of the inversion curve,except for MMM equation of state.The high-temperature branch and the peak of the inversion curve have been observed,in general,to be sensitive to the applied equation of state.The values of the maximum inversion temperature and maximum inversion pressure are calculated for each component used in this work.     

On-line testing of gas chromatographic columns with a programmable computing integrator

Summary A program is described which calculates the number of effective plates and the coating efficiency over the entire range of a test chromatogram. The peak widths at half height are derived by assuming a Gaussian peak shape. The interpolated peak width at k=4 is used for computing a standardized number of effective plates. Plate height, column permeability, overall performance and a novel parameter called sampling efficiency are calculated from 5 other figures — i. e. carrier gas code, pressure drop, column length, column temperature and particle size.Dedicated to Dr. Leslie S. Ettre for his 60th birthday.     

Effect of combining rules for cubic equations of state on the prediction of double retrograde vaporization

In this work, the phenomenon of double retrograde vaporization (DRV) is simulated using the Peng–Robinson equation of state with the classical mixing rules and several combining rules for the cross-energy and cross-co-volume parameters. The binary interaction parameters are set equal to zero in all cases, i.e., the calculations are entirely predictive. An interesting conclusion is that the predictions using the classical combining rules (geometric mean rule for a_ij and arithmetic mean rule for b_ij) provide the best agreement with the experimental data for all the systems tested: methane + n-butane, methane + n-pentane, ethane + limonene, and ethane + linalool. Another interesting observation is that several combining rules for b_ij, other than the arithmetic mean rule, predict the existence of three phases in equilibrium in a very narrow temperature range close to the critical temperature of methane in the methane + n-pentane system, even though, literature data indicates that n-hexane is the first n-alkane to present partial liquid phase immiscibility with methane.     

Frequent analytical/experimental problems in lipase-mediated synthesis in solvent-free systems and how to avoid them

Compared with chemical catalysis, enzymatic catalysis is a relatively new topic. Experimental work involving lipases deserves careful attention and accurate procedures still need to be implemented. A rapid but careful survey of published data immediately demonstrates that experiments performed under similar conditions with similar reagents have led to very different results. The aim of this work is to point out the importance of accurate and systematic procedures in order to ensure the reproducibility of experimental data. We strongly believe that different results found by different labs are due to problems detected in the procedures used. Quantification of the immobilisation efficiency of lipase on several supports through UV/visible methods and sampling methods used to obtain correct enzymatic activity values are specifically analysed. After a brief review which demonstrates the big discrepancies found in the literature, original data from Candida rugosa lipase adsorption on polypropylene powder and its use in the solvent-free synthesis of ethyl oleate are introduced in order to exemplify the difficulties found in these kinds of systems. Several procedures described in the literature are assayed and the accuracy of the results obtained is carefully analysed. The aim of the whole analysis performed is that it would be useful for any powdered solid to be used as a support for a lipase in a solvent-free system for any synthesis reaction, especially for those involving a volatile reagent. Throughout this contribution, special emphasis is placed on how catalytic reaction results using enzymes (free and immobilised) are reported so as to allow comparison between published data, something which is usually difficult since very different units are used and often complementary data are not included.     

THE SOLID STATE REACTIONS AND TRANSITIONS IN HIGH POLYMERIC SYSTEMS Ⅲ. THE BULK CRYSTALLIZATION OF LANTHANIDECATALYTICALLY POLYMERIZED POLYDIENES

For the mechanism of isothermal bulk crystallization of high polymers, beside the nucleation and growth steps, the unimpingement of growing crystal aggregates should be taken into account for the modification of the Avrami equation. Starting from Poisson distribution function of growing crystal aggregates, the probability of the unimpinging ones should be P(0)+P(1), then the Q-modified Avrami equation thus derived can be expressed aswhere V0 represents the volume fraction of crystal aggregates at crystallization time t at a given temperature, while the exponent n on t relates to the mode of nucleation and growth, and K_q is the corresponding shape factor. This Q-modified one is verified satisfactory by the isothermal bulk crystallization of lanthanidecatalytically polymerized polybutadiene (Ln-PB), polyisoprene (Ln-PIR) and their copolymers (LnPB/IR). Furthermore, the proposed mechanism is well identified by the change of morphological state during the course of crystallization of the corresponding east film of Ln-PB TR (92/8) at-60°(Fig. 1).Upon examination of the influence of the number of entanglement on crystallization rate, it reveals the existence of two stages of entanglementation, the primary and the secondary ones (Fig. 19)The equation for dependence of molecular weight and entanglement on bulk crystallization rate has been derived as Eq. 13 or 18 for Ln-PB, and verified by the experimental rate data of well fractionated Ln-PB samples crystallized at -9.1 to -15℃(Fig.20).     

New In-situ Sampling and Analysis of the Production of CeO<Subscript>2</Subscript> Powders from Liquid Precursors using a Novel Wet Collection System in a rf Inductively Coupled Thermal Plasma Reactor. Part 1: Reactor System and Sampling Probe

A new reactor and a novel in-situ sampling technique were developed for the study of the synthesis of CeO₂ powders produced from dissolved cerium nitrate salts. The conical reactor minimized particle recirculation and provided a highly symmetrical and undisturbed plasma flow suitable for the analysis of the phenomena affecting the formation of CeO₂ powders. Both a calorimetric study of the reactor and a thermodynamic analysis of CeO₂ formation were conducted. The sampling probe is described and near-isokinetic sampling was achieved. The sampled particles were collected using a miniature wet collection system, i.e. a mist atomizer and a custom-made spray chamber. A numerical simulation of the velocity and temperature fields of the plasma gas in the reactor was done using Fluent. A comprehensive droplet-to-particle formation mechanism presented elsewhere is revisited and expanded based on calorimetry, thermodynamics of CeO₂ formation, numerical simulations and collected particles. No traces of other oxidation states other than CeO₂ were found.