ASYMPTOTIC PROPERTIES OF THE SAMPLE AUTOCORRELATIONS AND PARTIAL AUTOCORRELATIONS OF A MULTIPLICATIVE ARIMA PROCESS

Abstract. We shall investigate the asymptotic behaviour of the sample autocorrelations and partial autocorrelations of a multiplicative ARIMA process and derive their limiting distributions. Some simulations are presented to illustrate the results obtained.     

Analysis of supersaturation and nucleation in a moving solution droplet with flowing supercritical carbon dioxide

A supercritical antisolvent (SAS) process is employed for production of solid nanoparticles from atomized droplets of dilute solution in a flowing supercritical carbon dioxide (SC CO₂) stream by attaining extremely high, very rapid, and uniform supersaturation. This is facilitated by a two‐way mass transfer of CO₂ and solvent, to and from the droplet respectively, rendering rapid reduction in equilibrium solubility of the solid solute in the ternary solution. The present work analyses the degree of supersaturation and nucleation kinetics in a single droplet of cholesterol solution in acetone during its flight in a flowing SC CO₂ stream. Both temperature and composition are assumed to be uniform within the droplet, and their variations with time are calculated by balancing the heat and mass transfer fluxes to and from the droplet. The equilibrium solubility of cholesterol with CO₂ dissolution has been predicted as being directly proportional to the Partial Molar Volume Fraction (PMVF) of acetone in the binary (CO₂–acetone) system. The degree of supersaturation has been simulated up to the time required to attain almost zero cholesterol solubility in the droplet for evaluating the rate of nucleation and the size of the stable critical nuclei formed. The effects of process parameters have been analysed in the pressure range of 7.1–35.0 MPa, temperature range of 313–333 K, SC CO₂ flow rate of 0.1136–1.136 mol s^?1, the ratio of the volumetric flow rates of CO₂‐to‐solution in the range of 100–1000, and the initial mole fraction of cholesterol in acetone solution in the range of 0.0025–0.010. The results confirm an extremely high and rapid increase in degree of supersaturation, very high nucleation rates and stable critical nucleus diameter of the order of a nanometre. Copyright © 2005 Society of Chemical Industry     

Decreasing miscibility with greater heterogeneity in ternary polymer blend: poly(cyclohexyl methacrylate), poly(α‐methyl styrene) and poly(4‐methyl styrene)

A ternary blend system comprising poly(cyclohexyl methacrylate) (PCHMA), poly(α‐methyl styrene) (PαMS) and poly(4‐methyl styrene) (P4MS) was investigated by thermal analysis, optical and scanning electron microscopy. Ternary phase behaviour was compared with the behaviour for the three constituent binary pairs. This study showed that the ternary blends of PCHMA/PαMS/P4MS in most compositions were miscible, with an apparent glass transition temperature (T_g) and distinct cloud‐point transitions, which were located at lower temperatures than their binary counterparts. However, in a closed‐loop range of compositions roughly near the centre of the triangular phase diagram, some ternary blends displayed phase separation with heterogeneity domains of about 1 µm. Therefore, it is properly concluded that ternary PCHMA/PαMS/P4M is partially miscible with a small closed‐loop immisciblity range, even though all the constituent binary pairs are fully miscible. Thermodynamic backgrounds leading to decreased miscibility and greater heterogeneity in a ternary polymer system in comparison with the binary counterparts are discussed. © 2003 Society of Chemical Industry     

Study on Factors Affecting the Structure of High SpeedSteel Ingot Produced by ESR

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On the design of multiple key hashing files for concurrent orthogonal range retrieval between two disks

This paper concerns the following problem: given a set of multi-attribute records, a fixed number of buckets and a two-disk system, arrange the records into the buckets and then store the buckets between the disks in such a way that, over all possible orthogonal range queries (ORQs), the disk access concurrency is maximized. We shall adopt the multiple key hashing (MKH) method for arranging records into buckets and use the disk modulo (DM) allocation method for storing buckets onto disks. Since the DM allocation method has been shown to be superior to any other allocation methods for allocating an MKH file onto a two-disk system for answering ORQs, the real issue is knowing how to determine an optimal way for organizing the records into buckets based upon the MKH concept.

A performance formula that can be used to evaluate the average response time, over all possible ORQs, of an MKH file in a two-disk system using the DM allocation method is first presented. Based upon this formula, it is shown that our design problem is related to a notoriously difficult problem, namely the Prime Number Problem. Then a performance lower bound and an efficient algorithm for designing optimal MKH files in certain cases are presented. It is pointed out that in some cases the optimal MKH file for ORQs in a two-disk system using the DM allocation method is identical to the optimal MKH file for ORQs in a single-disk system and the optimal average response time in a two-disk system is slightly greater than one half of that in a single-disk system.     

Development of calibration models for quality control in the production of ethylene/propylene copolymers by FTIR spectroscopy,multivariate statistical tools,and artificial neural networks

Principal component regression (PCR), partial least squares (PLS), StepWise ordinary least squares regression (OLS), and back‐propagation artificial neural network (BP‐ANN) are applied here for the determination of the propylene concentration of a set of 83 production samples of ethylene–propylene copolymers from their infrared spectra. The set of available samples was split into (a) a training set, for models calculation; (b) a test set, for selecting the correct number of latent variables in PCR and PLS and the end point of the training phase of BP‐ANN; (c) a production set, for evaluating the predictive ability of the models. The predictive ability of the models is thus evaluated by genuine predictions. The model obtained by StepWise OLS turned out to be the best one, both in fitting and prediction. The study of the breakdown number of samples to be included in the training set showed that at least 52 experiments are necessary to build a reliable and predictive calibration model. It can be concluded that FTIR spectroscopy and OLS can be properly employed for monitoring the synthesis or the final product of ethylene–propylene copolymers, by predicting the concentration of propylene directly along the process line. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Optically tuned superconductive-dielectric resonators with whispering-gallery modes

An analytical method is presented for calculating the resonant frequency andQ-factor of a superconducting dielectric disk resonator operating in millimeter-wave regime with whispering-gallery mode. Resonant frequency shift due to the optical generation of quasi-particles in superconducting film is investigated as a function of photon flux. An optically tunable resonant frequency of about 500 MHz is estimated, and good agreement is found between numerical results and experimental ones.     

THE ANALYSIS OF THE SEPARATED LAYERS ALGORITHM BY DOMAIN DECOMPOSITION METHOD

From the principle of of the Domain Decomposition Method (DDM), we analyse the 2nd-order linear elliptic partial differential problems and link the Separated-Layers Algorithm (SLA) with DDM. The mathematical properties of SLA and numerical example are presented to obtain satisfactory computation results. For general linear differential ones, also are the structure of SLA and its characteristics discussed.     

红外与可见光复合寻的制导中的快速图像配准方法

对现有多传感器图像配准方法在红外与可见光复合寻的制导应用中存在的计算量大等不足,提出了一种基于部分Hausdorff距离的快速方法和一种两集合相似度的定义,从而实现了有效减小误匹配特征点对的红外与可见光图像快速配准方法.此算法通过分别提取两幅图像边缘上显著特征点,再根据提出的快速方法和两集合相似度定义,粗略估计出图像间的旋转角度、平移量;然后依据此估计值,缩小特征点匹配时匹配特征点搜索范围,求得一致特征点对;最后用最小二乘法求解最优变换参数.实验结果表明了该方法的有效性、快速性.     

基于解析解的四阶PDE曲面裁剪方法

该文提出了一种可以广泛应用于四阶PDE曲面的裁剪方法。利用PDE的参数域内的曲线在曲面上投影,得到所求裁剪曲面的边界曲线,然后通过边界曲线的导矢与曲面在边界曲线处的法向量得到边界曲线处的跨界导矢,最后以求得的裁剪曲面的边界曲线以及裁剪曲面在边界曲线处的跨界导矢为PDE曲面的边界条件,用四阶的PDE曲面方程求得PDE裁剪曲面。