ON THE UNIMODALITY OF THE EXACT LIKELIHOOD FUNCTION FOR NORMAL AR(2) SERIES

Abstract. For stationary second-order autoregressive normal processes, the conjecture of uniqueness of the solution of the exact likelihood equations is examined. A sufficient condition for uniqueness is given; this condition is satisfied with very high probability if the number of observations is not extremely small. Moreover, it is shown that not more than two maxima may exist. Examples of data which actually produce a likelihood function with two local maxima are given.     

Pervaporation performance analysis and prediction—using a hybrid solution-diffusion and pore-flow model

A hybrid mathematic model for pervaporation is proposed which incorporates the concepts of solution-diffusion model and pore model. The model allows performance prediction as well as the establishment of the internal concentration and pressure profiles within the membrane. The model parameters specific to the particular membrane and mixture system are determined using liquid sorption and pervaporation experimental data. The model is experimentally examined using ethanol–water mixtures and poly(dimethyl siloxane)–poly(vinyldiene fluoride) (PDMS–PVDF) composite membranes. The characteristics of flux and separation factor predicted using the model are in fair agreement with the experimental data under various feed concentrations and downstream pressures for different membrane arrangements, including single-layer, reverse single-layer and double-layer PDMS–PVDF composite membranes. Internal profiles of pressure, concentration and component mole fraction can be established using the model. Concentration polarization phenomena for ethanol and water are located at membrane interfaces and vapor–liquid interfaces, respectively. Performances of several different membrane designs are compared using the model.     

Packed-microtubes model for flowthrough chromatography of protein

A mathematical model for flowthrough (perfusion) chromatography, namely packed-microtubes (PMT) model, has been proposed for a column packed with biporous (BiP) anion exchanger in which the mesopores and flowthrough pores are created with liquid and solid porogens, respectively. The model is established based on the assumption that the BiP particle is made up of packed microtubes. Bovine serum albumin (BSA) is used as a model protein and three kinds of anion exchangers (i.e., mesoporous, macroporous and BiP resins) are used as adsorbents to determine the model parameters and to evaluate the model. Adsorption equilibrium and finite bath experiments are performed to determine the adsorption isotherms and kinetics parameters. Both the bound amounts of the protein on the surface of the mesopores and macropores are experimentally determined and taken into account in the mathematical model. With all the model parameters determined by independent experiments or calculated from available correlations, model simulations are performed and compared with the experimentally determined breakthrough profiles of the BiP column. It is found that the model predictions agree reasonably well with the experimental data obtained under various conditions and the PMT model fit experimental data better than the modified double linear driving force (LLDF) model proposed by Leitão and Rodriogues (1999. Biochemical Engineering Journal 3, 131) in which the adsorbent particle is considered to be made up of packed microparticles. The results indicate that the PMT model is more reasonable for this kind of BiP adsorbent.     

The prediction of transport parameters in filamentous fermentation broths based on results obtained in pseudoplastic polymer solutions

Transport phenomena studies on single phase “model” fluids are of limited value in biochemical engineering if they cannot be translated to the heterogeneous systems encountered in real fermentation processes. In this paper we discuss the utility of polymer solutions as models of filamentous fermentation broths for evaluation of: pipeline friction factors and impeller power numbers (turbine and helical ribbon). To a first approximation, polymer solutions can serve as suitable models for the prediction of laminar flow pressure drop in pipelines and turbulent power consumption in stirred tanks. However, results obtained on polymer solutions do not directly apply to filamentous fermentation broths for predictions of laminar flow impeller power consumption and the transition point for turbulent flow in stirred tanks. These discrepancies are believed to result from the existence of a time dependent yield stress in filamentous fermentation broths.     

Thermodynamic assessment of MCl–YCl3 (M=Na,K, Rb,Cs) systems

Thermodynamic properties and phase diagrams of the MCl–YCl₃ (M=Na, K, Rb, Cs) systems were reassessed by using the CALPHAD method with the latest phase diagram data. A two-sublattice ionic solution model (M⁺)_P(Cl⁻, ${\mathrm{YCL}}_6^{3-}$, YCl₃)_Q reflecting the ionic behavior of the components was adopted to describe the liquid phase in the systems. A new set of optimized model parameters was found, and the calculated phase diagrams and enthalpies of mixing have good agreement with experimental data. The calculated liquidus near to YCl₃ side agrees much better with experimental data compared with previous work. In consideration of high and low temperature modifications as well as stability of intermediate compounds, Gibbs energies of formation of these compounds evaluated in the present work are more reasonable.     

Critical transistors nexus based circuit-level aging assessment and prediction

Accurate age modeling, and fast, yet robust reliability sign-off emerged as mandatory constraints in Integrated Circuits (ICs) design for advanced process technology nodes. In this paper we introduce a novel method to assess and predict the circuit reliability at design time as well as at run-time. The main goal of our proposal is to allow for: (i) design time reliability optimization; (ii) fine tuning of the run-time reliability assessment infrastructure, and (iii) run-time aging assessment. To this end, we propose to select a minimum-size kernel of critical transistors and based on them to assess and predict an IC End-Of-Life (EOL) via two methods: (i) as the sum of the critical transistors end-of-life values, weighted by fixed topology-dependent coefficients, and (ii) by a Markovian framework applied to the critical transistors, which takes into account the joint effects of process, environmental, and temporal variations. The former model exploits the aging dependence on the circuit topology to enable fast run-time reliability assessment with minimum aging sensors requirements. By allowing the performance boundary to vary in time such that both remnant and nonremnant variations are encompassed, and imposing a Markovian evolution, the probabilistic model can be better fitted to various real conditions, thus enabling at design-time appropriate guardbands selection and effective aging mitigation/compensation techniques. The proposed framework has been validated for different stress conditions, under process variations and aging effects, for the ISCAS-85 c499 circuit, in PTM 45 nm technology. From the total of 1526 transistors, we obtained a kernel of 15 critical transistors, for which the set of topology dependent weights were derived. Our simulation results for 15 critical transistors kernel indicate a small approximation error (i.e., mean smaller than 15% and standard deviation smaller than 6%) for the considered circuit estimated end-of-life (EOL), when comparing to the end-of-life values obtained from Cadence simulation, which quantitatively confirm the accuracy of the IC lifetime evaluation. Moreover, as the number of critical transistors determines the area overhead, we also investigated the implications of reducing their number on the reliability assessment accuracy. When only 5 transistors are included into the critical set instead of 15, which results in a 66% area overhead reduction, the EOL estimation accuracy diminished with 18%. This indicates that area vs. accuracy trade-offs are possible, while maintaining the aging prediction accuracy within reasonable bounds.     

气化炉复合炉衬的传热计算

新型 (多喷嘴对置 )水煤浆气化炉拟采用水冷管和耐火浇铸料组成的复合炉衬结构 .炉内的高温高压对复合炉衬的高温侵蚀十分严重 ,是影响其寿命的重要因素 ,因此合理设计气化炉复合炉衬的结构对充分发挥其材质的作用具有十分重要的意义 .建立了气化炉复合炉衬的传热计算的数学模型 ,同时编制了模型求解的计算程序 ,并用某工艺条件对复合炉衬的温度分布进行了计算 .结果表明 ,该方法可有效计算出复合炉衬的温度分布情况 ,为复合炉衬的设计、运行和维护提供理论依据     

基于BP网络的保护渣性能预测模型的研究

结合BP网络计算机实验研究 ,建立了保护渣化学组成与性能的预测模型 ,并利用化学组成与性能的关系 ,对网络的实用性进行了检验 ,结果符合保护渣化学组成与性能的关系。保护渣粘度随着保护渣碱度的增大而减小 ,而半球点温度随碱度增大而增大 ;保护渣的半球点温度和粘度都随着渣中CaF2 含量的增加而减小。用BP网络的误差反向传播算法建立的保护渣的化学组成与性能的预测模型 ,得出的预测值与实际值的误差小 ,对保护渣的设计与应用都有一定的指导作用。     

ASYMPTOTIC PROPERTIES OF SOME PRELIMINARY ESTIMATORS FOR AUTOREGRESSIVE MOVING AVERAGE TIME SERIES MODELS

Abstract. Some simple preliminary estimators for the coefficients of mixed autoregressive moving average time series models are considered. As the first step the estimators require the fitting of a long autoregression to the data. The first two methods of the paper are non-iterative and generally inefficient. The estimators are Yule-Walker type modifications of the least squares estimators of the coefficients in auxiliary linear regression models derived, respectively, for the coefficients of the long autoregression and for the coefficients of the corresponding long moving average approximation of the model. Both of these estimators are shown to be strongly consistent and their asymptotic distributions are derived. The asymptotic distributions are used in studying the loss in efficiency and in constructing the third estimator of the paper which is an asymptotically efficient two-step estimator. A numerical illustration of the third estimator with real data is given.