Stability and robust stability of positive linear Volterra difference equations

We first introduce a class of positive linear Volterra difference equations. Then, we offer explicit criteria for uniform asymptotic stability of positive equations. Furthermore, we get a new Perron–Frobenius theorem for positive linear Volterra difference equations. Finally, we study robust stability of positive equations under structured perturbations and affine perturbations. Two explicit stability bounds with respect to these perturbations are given. Copyright © 2008 John Wiley & Sons, Ltd.     

Poly(p-substituted phenylacetylene) with perfluoroalkyloxydimethylsilyl side groups for oxygen and ethanol permselective membrane

Summary p-(1H,1H,2H,2H-perfluorodecyloxydimethylsilyl)phenylacetylene(ACf8) and p-(1H,1H,2H,2H-Perfluorohexyloxydimethylsilyl)phenylacetylene(ACf4) were synthesized and copolymerized with p-trimethylsilylphenylacetylene(ASi). The resulting copolymers, copoly(ACf8/ASi) and copoly(ACf4/ASi), were fabricated to tough membranes showing high oxygen permeabilities(Po ₂) of 10^-8 cc(STP)·cm/cm²·s·cmHg and high oxygen permselectivities(=Po ₂/Pn ₂) of more than 2.7. In particular, a copoly(ACf4/ASi) containing 15.1 mol% of ACf4 unit showed the best result: Po ₂=3.51x10^-8 cc(STP)·cm/cm²·s·cmHg and =3.04. The values were in a top level and very close to those of upper bound line in an -Po ₂ plot of data in the literature. In addition, copoly(ACfn/ASi) membranes were ethanol permselective owing to water repellency of the perfluoroalkyl groups. Copoly(ACf4/ASi) membranes showed better oxygen and ethanol permselectivity than copoly(ACf8/ASi) membranes.     

Dehydrohalogenation during pyrolysis of brominated flame retardant containing high impact polystyrene (HIPS-Br) mixed with polyvinylchloride (PVC)

Dehydrohalogenation during pyrolysis of brominated flame retardant containing polystyrene (brominated high impact polystyrene (HIPS-Br)) mixed with polyvinylchloride (PVC) was carried out in a laboratory scale batch process. Thermal and catalytic degradation of HIPS-Br mixed with PVC on carbon composite of iron oxide (TR-00301) catalyst was investigated. The thermal degradation of waste plastics (HIPS-Br/PVC) yielded liquid products with 55,000 ppm bromine and 4300 ppm chlorine content in oil. Catalytic degradation (4 g; TR-00301) of HIPS-Br/PVC waste plastics at 430 °C produced halogen-free clean oil, which can be used as a fuel oil or chemical feedstock. The main liquid products during catalytic degradation were benzene, toluene, styrene, ethyl benzene, α-methyl styrene, butyl benzene, 1,2-dimethyl benzene etc. The average carbon number of the liquid products produced during catalytic degradation (9.3) of waste plastics was less than that of the thermal degradation (10.4) and the density of liquid products was found to be lower during the catalytic degradation than the thermal degradation. The possibility of a single step catalytic process for the conversion of halogenated waste plastics into fuel oil with the simultaneous removal of chlorine and bromine content from the oil was demonstrated.     

Gene cloning and characterization of Mycobacterium phlei flavin reductase involved in dibenzothiophene desulfurization

Mycobacterium phlei WU-F1 possesses the ability to convert dibenzothiophene (DBT) to 2-hydroxybiphenyl with the release of inorganic sulfur over a wide temperature range from 20 degrees C to 50 degrees C. The conversion is initiated by consecutive sulfur atom-specific oxidations by two monooxygenases, and a flavin reductase is essential in combination with these flavin-dependent monooxygenases. The flavin reductase gene (frm) of M. phlei WU-F1, which encodes a protein of 162 amino acid residues with a molecular weight of 17,177, was cloned and the deduced amino acid sequence shares approximately 30% identity with those of several flavin reductases in two protein-component monooxygenases. It was confirmed that the coexpression of frm with the DBT-desulfurization genes (bdsABC) from M. phlei WU-F1 was critical for high DBT-desulfurizing ability over a wide temperature range from 20 degrees C to 55 degrees C. The frm gene was overexpressed in Escherichia coli cells, and the enzyme (Frm) was purified to homogeneity from the recombinant cells. The purified Frm was found to be a 34-kDa homodimeric protein with a monomeric molecular mass of 17 kDa. Frm exhibited high flavin reductase activity over a wide temperature range, and in particular, the turnover rate for FMN reduction with NADH as the electron donor reached 564 s(-1) at 50 degrees C, which is one of the highest activities among all of the flavin reductases previously reported. Intriguingly, Frm also exhibited a high ferric reductase activity.     

Facile synthesis of five 2D surface modifiers by highly selective photocyclic aromatization and efficient enhancement of oxygen permselectivities of three polymer membranes by surface modification using a small amount of the 2D surface modifiers

A facile synthesis of novel five 2D (planar) surface modifiers having a triphenylbenzene derivatives as a 2D structure has been achieved by the highly selective photocyclic aromatization reaction. Efficient enhancement of oxygen permselectivities through the three polymer membranes has been achieved by adding a small amount (<5.0 wt%) of the 2D surface modifiers. Among the five 2D surface modifiers, a modifier compound having oligoethylene oxide groups showed the best performance for the enhancement. These improvements were thought to be caused mainly by improvement of the solution selectivity on the membrane surface where the 2D surface modifiers were accumulated. In some of the surface-modified blend membranes, their plots in the PO₂$P_{{\text{O}}_2}$-α graph were over or close to the upper boundary line by Robeson in 1991. Since all the membranes containing the 2D surface modifiers showed better permselectivities than the corresponding substrate membranes, it is very promising for the future.     

Synthesis of poly[2]catenane having rigid linkage by 1,3-dipolar cycloaddition of diazido[2]catenane with 4,4′-diethynylbiphenyl

A novel poly[2]catenane having rigid triazole rings between [2]catenane moieties was synthesized by the 1,3-dipolar cycloaddition of diazido[2]catenane with 4,4′-diethynylbiphenyl. The reaction proceeded effectively under mild conditions and gave a polymer in high yield. The number average molecular weight (M_n) of the polymers was 1.5 × 10⁴-2.5 × 10⁴. A cyclic dimer consisting of two [2]catenane moieties and two biphenylene units was formed along with the polymer. The cyclodimerization was suppressed by performing the reaction at a low temperature without lowering the yield or molecular weight of the polymer. The novel poly[2]catenane had higher solubility in some solvents than the corresponding non-catenated polymer having a similar primary structure.     

Strong Influences of Melting Time and Tm3+ Concentration on Blue Up-Conversion Photoluminescence for Tm3+/Yb3+ Co-Doped TeO2–TlO0.5–ZnO Glass

In this study, by a conventional melt quenching method, we synthesized novel up-conversion phosphors of 60TeO₂–30TlO_0.5–(9−x)ZnO–xTm₂O₃–1Yb₂O₃ (x = 0.1–0.5) glasses, whose system was recently developed in our collaborative group, and their blue up-conversion photoluminescence (UCPL) of Tm³⁺ ions via three-step energy transfer from near-infrared (NIR) sensitizer of Yb³⁺ ions was observed. In particular, the substantial rate of the energy transfer <γ_d5> in the third step from Yb³⁺ to Tm³⁺ under excitation at 975 nm, which determined the final blue UCPL intensity, was estimated as a function of the rare-earth concentration. With an aid of analytical methods of PL lifetime and Judd–Ofelt theory, it was revealed that the highest energy transfer rate <γ_d5> was achieved to be 2.07 × 10⁻¹⁷ cm³/s for x = 0.2, and further increasing Tm₂O₃ content x in the fixed Yb₂O₃ resulted in the decrease in the energy transfer rate <γ_d5>. One of the plausible causes was concentration quenching of Yb³⁺ ions. The other was back-transfer from Tm³⁺ to Yb³⁺ ions. The influence of the condition of glass synthesis and the melting time on <γ_d5> was also discussed.     

Adsorption characteristics of bovine serum albumin onto alumina with a specific crystalline structure

Bone cement containing alumina particles with a specific crystalline structure exhibits the ability to bond with bone. These particles (AL-P) are mainly composed of delta-type alumina (δ-Al₂O₃). It is likely that some of the proteins present in the body environment are adsorbed onto the cement and influence the expression of its bioactivity. However, the effect that this adsorption of proteins has on the bone-bonding mechanism of bone cement has not yet been elucidated. In this study, we investigated the characteristics of the adsorption of bovine serum albumin (BSA) onto AL-P and compared them with those of its adsorption onto hydroxyapatite (HA), which also exhibits bone-bonding ability, as well as with those of adsorption onto alpha-type alumina (α-Al₂O₃), which does not bond with bone. The adsorption characteristics of BSA onto AL-P were very different from those onto α-Al₂O₃ but quite similar to those onto HA. It is speculated that BSA is adsorbed onto AL-P and HA by interionic interactions, while it is adsorbed onto α-Al₂O₃ by electrostatic attraction. The results suggest that the specific adsorption of albumin onto implant materials might play a role in the expression of the bone-bonding abilities of the materials.     

Direct conversion of methane into methanol over MoO3/SiO2 catalyst in an excess amount of water vapor

Well-dispersed MoO₃ on SiO₂ showed a high activity for partial oxidation of methane (mixed with oxygen in a molar ratio of 9:1) into methanol and formaldehyde at 873 K in an excess amount of water vapor, which is attributed to the formation of silicomolybdic acid (SMA) on the catalyst surface during reaction. One of the roles of SMA for the partial oxidation of methane is proved to depress the successive oxidation of methanol and formaldehyde into carbon oxides.