Asymptotic Properties of Quasi-Maximum Likelihood Estimators for ARMA Models with Time-Dependent Coefficients

For about thirty years, time series models with time-dependent coefficients have sometimes been considered as an alternative to models with constant coefficients or non-linear models. Analysis based on models with time-dependent models has long suffered from the absence of an asymptotic theory except in very special cases. The purpose of this paper is to provide such a theory without using a locally stationary spectral representation and time rescaling. We consider autoregressive-moving average (ARMA) models with time-dependent coefficients and a heteroscedastic innovation process. The coefficients and the innovation variance are deterministic functions of time which depend on a finite number of parameters. These parameters are estimated by maximising the Gaussian likelihood function. Deriving conditions for consistency and asymptotic normality and obtaining the asymptotic covariance matrix are done using some assumptions on the functions of time in order to attenuate non-stationarity, mild assumptions for the distribution of the innovations, and also a kind of mixing condition. Theorems from the theory of martingales and mixtingales are used. Some simulation results are given and both theoretical and practical examples are treated. Received 2004; Final version 23 December 2004     

关于Tchebycheff—Fourier级数的（H,λ）平均的逼近

我们定义了（Ｈ，λ）求和法，它含有（Ｎ，ｐｎ），（Ｒ＾ｒｎ）和（Ｖｍｎ）求和法。讨论了函数ｆ（ｘ）∈Ｃ＾ｒ［－１，１］（ｒ∈Ｎ０）以及ｆ（ｘ）∈Ｗ＾ｒＨ＾ａ（ｒ∈Ｎ０，０＜ａ＜１）的切比晓夫－富里埃级数的逼近阶。     

Copolymer of Di (methacryloyloxymethyl) naphthalene and divinylbenzene as a column packing for high-performance liquid chromatography

Summary A new porous polyaromatic ester packing was synthetized for high performance liquid chromatography. The relationship between retention and chain length of the members of homologous series of alkylbenzenes, N-alkylanilines, alkylarylethers, alkylbenzoates and alkylarylketones on this new stationary phase using different eluents was investigated. Using the alkylarylketone scale the retention indices of the homologues and test compounds were calculated. The results were compared with those obtained for poly (styrene-divinylbenzene) polymers. For both types of packing the first members of each homologous series gave non-linear behaviour. The methylene group index increments are different for the studied homologous series; thus there is no simple additivity of the retention indices. The efficiency of the porous polymeric columns is a function of the capacity factor of the solute and the organic component of the eluent.     

Cu离子A位掺杂对LaSrCoO4复合氧化物氧化性能的影响

采用聚丙烯酰胺法制备了La1-xCuxSrCoO4(x=0.2-0.8)复合氧化物,考察了Cu离子掺杂量(x)对CO及C3H8氧化反应活性的影响,并运用XRD、IR、TPR和TPD等多种手段对复合氧化物催化剂进行了表征。结果表明,催化剂活性随x的变化而变化,Cu部分取代A位La能提高LaSrCoO4催化剂的CO及C3H8氧化反应活性,当x=0.4时La1-xCuxSrCoO4催化剂的晶格氧和Co3 含量较多,晶格氧的活动性较高,催化活性最佳。     

铁系元素冠醚配合物的研究——Ⅱ. 铁系氯化物与4''-碘苯并-15-冠-5固态配合物的合成与性质

对碱金属、希土与苯并-15-冠-5冠醚配合物的研究指出,4′-取代单苯并冠醚的阳离子配合物的稳定性及其他性质,受取代基电子效应的影响,给电性取代基可增加芳醚氧原子上的电子密度,改变冠氧的极性,从而影响其配位能力,扩大希土配合物之间性质上的差别,达到分离的目的。对于铁系元素,文献报导甚少。我们继Ⅰ之后,又合成了三氯化铁水合物与4′-碘苯并-15-冠-5固态配合物,并研究了其性质。     

Mixed crystals in the system Cu2MnGexSn1−xS4: Phase analytical investigations and inspection of tetrahedra volumes

Cu₂MnGeS₄ crystallizes orthorhombic in a wurtzite superstructure type while Cu₂MnSnS₄ crystallizes in a tetragonal sphalerite superstructure type. Lattice constants and thermal analyses of the solid solution series Cu₂MnGe_xSn_1−xS₄ are presented. A two-phase region is found from Cu₂MnGe_0.3Sn_0.7S₄ to Cu₂MnGe_0.5Sn_0.5S₄. The cell volume of the mixed crystals increases with increasing Sn content. The melting points increase smoothly with increasing Ge content to x=0.5 and then steeply for higher Ge contents. The single crystal X-ray structure analysis of Cu₂MnGe_0.55Sn_0.45S₄ is presented. The refinement converges to R=0.0270 and wR₂=0.0586, Z is 2. The volumes of the tetrahedra [MS₄] (M=Cu, Mn, Ge, Sn) are calculated. From these volumes the differences in size of the tetrahedra are derived and compared with the corresponding differences in the end members of the solid solution series. It turns out that the resulting structure type in these materials depends on the volume differences of the constituting tetrahedra [MS₄].     

铁系元素冠醚配合物的研究——V.三氯化铁与4′-溴苯并-15-冠-5固态配合物的合成和性质

本文报导了三氯化铁(水合物)与4′-溴苯并-15-冠-5(L)固态配合物的合成,对合成的新配合物,进行了元素定量分析及摩尔电导测定,并作了红外光谱、紫外光谱,热重和差热以及X-射线粉末衍射分析的性质表征。从而证明,该配合物中FeCl₃与配体L比为1:1,是溶化剂,含有结晶水的固态配合物。     

Simultaneous determination of radionuclides separable into natural decay series by use of time-interval analysis

A delayed coincidence method, time-interval analysis (TIA), has been applied to successive – decay events on the millisecond time-scale. Such decay events are part of the ²²⁰Rn²¹⁶Po (T_1/2 145 ms) (Th-series) and ²¹⁹Rn²¹⁵Po (T_1/2 1.78 ms) (Ac-series). By using TIA in addition to measurement of ²²⁶Ra (U-series) from -spectrometry by liquid scintillation counting (LSC), two natural decay series could be identified and separated. The TIA detection efficiency was improved by using the pulse-shape discrimination technique (PSD) to reject -pulses, by solvent extraction of Ra combined with simple chemical separation, and by purging the scintillation solution with dry N₂ gas. The U- and Th-series together with the Ac-series were determined, respectively, from alpha spectra and TIA carried out immediately after Ra-extraction. Using the ²²¹Fr²¹⁷At (T_1/2 32.3 ms) decay process as a tracer, overall yields were estimated from application of TIA to the ²²⁵Ra (Np-decay series) at the time of maximum growth. The present method has proven useful for simultaneous determination of three radioactive decay series in environmental samples.     

STUDY ON 1-HEXENE POLYMERIZATION BASED ON ZIEGLER-NATTA CATALYSTS WITH DOPED SUPPORT

A series of Ti/Mg supported catalysts are prepared by using ball-milled mixtures of MgCl2-ethanol adducts and NaCl as supports, and 1-hexene polymerizations catalyzed by the novel catalysts are studied. It is found that the molecular weight distribution of poly(1-hexene) becomes apparently narrower when catalysts with doped supports are used, indicating that changing the structure of the support is an effective way to regulate the active center distribution of heterogeneous Ziegler-Natta catalyst.     

Semi‐classical formulation of time‐dependent discrete variable representation method

In this article, we apply a novel time‐dependent discrete variable representation (TDDVR) method proposed by Barkakaty and Adhikari to investigate tunneling through an Eckart barrier. This semi‐classical method is theoretically rigorous and straightforward to implement. Among the TDDVR formulations, this report presents the first derivation of a rigorous form of quantum force (QF) for the present perspective. The validity of this semi‐classical approach is demanded based on the excellent agreement of the tunneling probability with the corresponding quantum results. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004