SOME PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATOR IN THE SIMULTANEOUS SWITCHING AUTOREGRESSIVE MODEL

Abstract. The simultaneous switching autoregressive (SSAR) model proposed by Kunitomo and Sato (A non-linearity in economic time series and disequilibrium econometric models. In Theory and Application of Mathematical Statistics (ed. A. Takemura). Tokyo:University of Tokyo Press (in Japanese), 1994; Asymmetry in economic time series and simultaneous switching autoregressive model. Struct. Change Econ. Dyn. , forthcoming (1994).) is a Markovian non-linear time series model. We investigate the finite sample as well as the asymptotic properties of the least squares estimator and the maximum likelihood (ML) estimator. Due to a specific simultaneity involved in the SSAR model, the least squares estimator is badly biased. However, the ML estimator under the assumption of Gaussian disturbances gives reasonable estimates.     

Continuous emulsion polymerization of vinyl acetate. II Operation in a single Couette–Taylor vortex flow reactor using sodium lauryl sulfate as emulsifier

Continuous emulsion polymerizations of vinyl acetate were conducted at 50°C in a single continuous Couette–Taylor vortex flow reactor (CCTVFR) using sodium lauryl sulfate as emulsifier and potassium persulfate as initiator. The polymerization can be carried out very smoothly and stably, but the steady‐state monomer conversion attained in a CCTVFR is not as high as that in a plug flow reactor (PFR), but only slightly higher than that in a continuous stirred tank reactor (CSTR), even if the Taylor number is adjusted to an optimum value. Also, the effects of operating variables, such as the emulsifier, initiator, and monomer concentrations in the feed and the mean residence time on the kinetic behaviors were almost the same as those observed in a CSTR. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 2755–2762, 2002     

Production of Ceramic Green Bodies Using a Microwave-Reactive Organic Binder

Because the pyrolysis of organic substances can result in the emission of harmful pollutant gases, a reduction in the use of organic binders is one aim of today's ceramics industry. A novel ceramic-forming process was developed that requires considerably less organic binder than conventional techniques. The process involves immobilizing reactive molecules on the surfaces of the particles, which on subsequent irradiation with microwaves, form bridges that bind the entire particle assembly together. The chemical forces involved produce strong bonds, resulting in a significant reduction in the amount of organic binder that is required to maintain the shape of the ceramic green body. This method will help to decrease emissions of harmful gases produced from pyrolysis of the binder.     

Binary phase behavior of 1,3-distearoyl-2-oleoyl-sn-glycerol (SOS) and 1,3-distearoyl-2-linoleoyl-sn-glycerol (SLS)

The binary phase behavior of SOS (1,3-distearoyl-2-oleoyl-sn-glycerol) and SLS (1,3-distearoyl-2-linoleoyl-sn-glycerol) was examined by using DSC and conventional and synchrotron radiation X-ray diffraction. The solid-solution phases were observed in the metastable α and γ forms in all concentration ranges. Results indicated that the miscible γ form did not transform to the β′ form when the mixtures were subjected to simple cooling from a high-temperature liquid to a low-temperature solid phase. However, and α-melt-mediated transformation into β′ and β₂ resulted in the formation of immiscible phases in concentration ranges of SLS below 30%. By contrast, at SLS concentration ranges above 30%, the α-melt-mediated transformation caused crystallization of only the γ form, and β′ and β₂ crystals did not appear. These results show that the specific interactions between SOS and SLS are operative in the phase behavior of the mixture states of SOS and SLS.     

Ring hydrogenation of naphthalene and 1-naphthol over supported metal catalysts in supercritical carbon dioxide solvent

Catalytic ring hydrogenations of naphthalene and 1-naphthol were studied over several supported metal catalysts in supercritical carbon dioxide solvent at low temperature. Higher concentration of hydrogen in supercritical carbon dioxide and lower reaction temperature were responsible for higher catalyst activity and selectivities to the desired partial ring hydrogenated products as compared with those observed in organic solvent for the same catalyst.     

Effect of Grain Boundaries on Thermal Conductivity of Silicon Carbide Ceramic at 5 to 1300 K

The thermal conductivity of a SiC ceramic was measured as 270 W·m⁻¹·K⁻¹ at room temperature. At low temperatures ( T < 25 K), the decrease in the conductivity was proportional to T ³ on a logarithmic scale, which indicated that the conductivity was controlled by boundaries. The calculated phonon mean free path in the ceramic increased with decreased temperature, but was limited to ∼4 μm, a length almost equal to the grain size, at temperatures below 30 K. We concluded that the thermal conductivity of the ceramic below 30 K was influenced significantly by grain boundaries and grain junctions.     

Sintering of Ceria-Doped Tetragonal Zirconia Crystallized in Organic Solvents, Water, and Air

Amorphous CeO₂–ZrO₂ gels were prepared by coprecipitation in ammonia solutions. The onset of crystallization of the gels, from calcining in air, was 420°C, while 200° to 250°C in the presence of water and organic solvents such as methanol and ethanol. The sintering behaviors of CeO₂–ZrO₂ powders were sensitive to the crystallizing conditions, since hard agglomerates formed when the precipitated gels were crystallized by normal calcination in air, whereas soft agglomerates formed when they were crystallized in water or organic solvents. CeO₂–ZrO₂ powders crystallized in methanol and water at 250°C were sintered to full theoretical density at 1150° and 1400°C, respectively, whereas that crystallized by calcination in air at 450°C was sintered to only 95.2% of theoretical density, even at 1500°C.     

Polymorphism of POP and SOS III. Solvent crystallization of β2 and β1 polymorphs

Single crystals of β₁ and polycrystals of β₂ of POP and SOS were obtained from acetonitrile solution. The crystallization behavior of the two polymorphs was almost the same in POP and SOS; rapid cooling of the solution preferentially crystallized the metastable β₂ form, and the most stable β₁ form crystallized in a very low solute concentration at the expense of β₂, via solution-mediated transformation. The single crystal of β₂ revealed needle-like irregular shape, whereas well-defined slender rhombic shape was observed in β₁. The solubilities of the β₁ forms of POP and SOS in tetradecane solution were precisely measured in a temperature range of 10∼20°C. This study showed that the solvent crystallization was the single way to grow the β₁ crystal, since melt-cooling and melt-mediated transformation did not crystallize β₁ both in POP and SOS. Presented at 1988 AOCS Annual Meeting at Phoenix.     

Polymorphic behavior of gondoic acid and phase behavior of its binary mixtures with asclepic acid and oleic acid

Molecular properties of polymorphic forms of gondoic acid [cis-C_20:1Δ11ω9 (GOA)] have been studied by X-ray diffraction (XRD), differential scanning calorimetry (DSC), optical microscopy, and Raman scattering, in comparison to those of six principal unsaturated fatty acids: oleic acid [cis-C_18:1Δ9ω9 (OA)], erucic acid [cis-C_22:1Δ13ω9 (ERA)], petroselinic acid [cis-C_18:1Δ6ω12 (PSA)], asclepic acid [cis-C_18:1Δ11ω7 (APA)], palmitoleic acid [cis-C_16:1Δ9ω7 (POA)], and elaidic acid [trans-C_18:1Δ9ω9 (ELA)]. In addition, phase behavior of binary mixtures of GOA and APA and OA was examined by XRD and DSC. The polymorphic structures of GOA are quite similar to those of APA, ERA, POA, and partly to OA. In particular, DSC and Raman scattering studies have shown that gondoic acid exhibits conformational disordering on heating at the ω-chain, a chain segment between the double bond and CH₃ group, as a transition from all-trans (γ form) to gauche-rich (α form) conformations. A miscible mixing phase was observed in the mixture of GOA and APA, yet eutectic phases were observed in the GOA and OA mixtures. This is a remarkable contrast because the binary mixture systems of varying combinations of cis-unsaturated fatty acids examined so far exhibited either eutectic nature or molecular compound formation. It is expected that specific molecular interactions between GOA and APA that originate from the equivalence of the length of the Δ-chain, the chain segment between the cis-double bond and COOH group, and also from the presence of the γ-α order-disorder transformation would be operating to form the miscible mixing phase.     

Photocatalysts using hexa- and octa-titanates with different tunnel space for water decomposition

Photocatalytic activities for water decomposition were examined for photocatalysts using hexa- and octa-titanates and TiO2(B) with different tunnel space in the structure. Using RuO2 as promoter, M2Ti6O13 (M = Li, Na, K, Rb) showed the stoichiometric production of Hz and O₂ except for Li, whereas H₂Ti₈O₁₇ and TiO₂(B) had very low activity producing only hydrogen as a product. The effects of promoters on Na₂Ti₆O₁₃ showed that the activity increased in the order of RuO₂ > RuO₂ + IrO₂ > IrO₂ > RuO₂ + Pt > MnO₂. These effects along with other related ones are discussed: it emerges that the presence of the tunnels is important for the achievement of high photocatalytic activity.