Difference Sets and Recursion Theory

There is a recursive set of natural numbers which is the difference set of some recursively enumerable set but which is not the difference set of any recursive set.     

PARTIAL VERSUS GENERAL STORAGE POLICY: COMMODITIES AND RESOURCES

This paper examines joint storage considerations when both commodities and resources can be stored, e.g., grain and water for irrigation. Results suggest that when separate agencies control public resource and commodity storage, suboptimal storage rules occur unless (i) each agency is sensitive to the policies of the other, (ii) commodity inventories are adjusted in response to prices, and (iii) resource inventories are adjusted in response to both commodity demand and resource supply conditions. For example, the common case where water storage depends on weather and reservoir conditions alone is not sufficiently general. The results imply that water management agencies that tend to be dominated by engineers and hydrological considerations need to incorporate economic considerations into decision processes.     

A remark on the mild solutions of non-local evolution equations

We provide a counterexample to some recent publications concerning the existence of the mild solutions of the non-local evolution equations, and indicate that in the study of the non-local evolution equations, the operators from which the mild solutions may be derived are in general not compact, thus those fixed point theorems requiring the compactness of the operators are not applicable.     

In‐line monitoring of UV photopolymerization with a quartz crystal resonator

An in‐line monitoring device using a quartz crystal resonator for thin film polymerization was proposed, and its performance has been evaluated by implementing in the UV polymerization of 2‐hydroxyethyl methacrylate with a photoinitiator of 1‐chloroanthraquinone. Because the variation of resonant resistance of the resonator is proportional to the square root of viscosity change that is closely related to the polymerization degree, the resistance can be used as a measure of the polymerization degree. The resistance measurements were compared with the outcome of instrumental analyses of polymerization degree using an FTIR spectrometer and a gel permeation chromatograph. The experimental results showed that the resistance measurements were consistent with the experimental outcome of the instrumental analyses, and this indicates the effectiveness of the proposed device. Owing to the simplicity and availability of the resonator system, its wide utilization in the monitoring of a variety of film polymerization processes, including photoresistor application, is expected. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2428–2439, 2006     

Lightly crosslinked,mesomorphic networks obtained through the reaction of dimeric,liquid‐crystalline epoxy–imine monomers and heptanedioic acid

We reacted various dimeric, liquid‐crystalline epoxy–imine monomers, differing in the length of the central aliphatic spacer or the dipolar moments, with heptanedioic acid. The resulting systems showed a liquid‐crystalline phase in some cases, depending on the dimer and on the reaction conditions. The systems were characterized with respect to their mesomorphic properties and then were submitted to dynamic mechanical thermal analysis in both fixed‐frequency and frequency‐sweep modes in the shear sandwich configuration. The arrangement in the liquid‐crystalline phase seemed to be mainly affected both by the polarization of the mesogen and by the reaction temperature, which favored the liquid‐crystalline arrangement when it was lying in the range of stability of the dimer mesophase. In agreement with other recent literature data, dynamic mechanical thermal analysis results suggested that the presence of the mesogen directly incorporated into the main chain increased the lifetimes of the elastic modes both in the isotropic phase and in the liquid‐crystalline phase with respect to side‐chain liquid‐crystalline elastomers and that the time–temperature superposition principle did not hold through the liquid‐crystalline‐to‐isotropic transition. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44:6270–6286, 2006     

Control of the conjugation length and solubility in electroluminescent polymers

A new type of cyclolinear polymer, poly(phenylene vinylene‐alt‐cyclotriphosphazene), was synthesized through Heck‐type coupling reactions to produce π‐conjugated macromolecules with excellent solubility and precise electronic control of the band‐gap energy. This synthesis method is capable of producing well‐defined alternating polymers. The method is highly adaptable and can be readily used for other chromophore systems. The resulting polymers were also capable of accommodating a wide variety of substituents on the cyclophosphazene rings with minimal effect on the electronic properties. The band gap and electron affinities of the polymer were varied through the manipulation of the π‐conjugated unit located between the insulating phosphazene rings. Each chromophore matched the intended conjugation length consistently throughout the macromolecules. The polymers were good film formers because of the chosen substituents on the phosphazene rings. The absorbance of the polymers indicated minimal spectral shift from the monomer absorbance. This suggested an effective insulation of each chromophore unit from its neighbors by the phosphazene rings. Solution photoluminescence efficiencies were found to be up to 44.1%. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 69–76, 2006     

Synthesis and luminescence characteristics of conjugated dendrimers with 2,4,6‐triaryl‐1,3,5‐triazine periphery

We have synthesized conjugated dendrimer with triazine peripheries, and their luminescence properties were investigated. The dendrimers consist of dendritic triazine wedges for electron transport, distyrylbenzene core as an emitting moiety, and t‐butyl peripheral groups for good processing properties. The dendrimers have LUMO values of about ?2.7 eV possibly because of the triazine moiety with high electron affinity. Photoluminescence study indicates that energy transfer occurs from the triazine wedges to the stilbene bridge, and finally to the core chromophore units due to a cascade decrease of bandgap from the peripheral wedge to core moiety. Therefore, the emission wavelength was determined by the structure of the core unit. The energy transfer efficiency of distyrylbenzene‐cored dendrimers was about 75 and 55% for Trz‐1GD‐DSB and Trz‐2GD‐DSB, respectively. A preliminary electroluminescence property also was investigated. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 254–263, 2006     

Mechanical endurance of polymer electrolyte membrane and PEM fuel cell durability

The life of proton exchange membrane fuel cells (PEMFC) is currently limited by the mechanical endurance of polymer electrolyte membranes and membrane electrode assemblies (MEAs). In this paper, the authors report recent experimental and modeling work toward understanding the mechanisms of delayed mechanical failures of polymer electrolyte membranes and MEAs under relevant PEMFC operating conditions. Mechanical breach of membranes/MEAs in the form of pinholes and tears has been frequently observed after long‐term or accelerated testing of PEMFC cells/stacks. Catastrophic failure of cell/stack due to rapid gas crossover shortly follows the mechanical breach. Ex situ mechanical characterizations were performed on MEAs after being subjected to the accelerated chemical aging and relative humidity (RH) cycling tests. The results showed significant reduction of MEA ductility manifested as drastically reduced strain‐to‐failure of the chemically aged and RH‐cycled MEAs. Postmortem analysis revealed the formation and growth of mechanical defects such as cracks and crazing in the membranes and MEAs. A finite element model was used to estimate stress/strain states of an edge‐constrained MEA under rapid RH variations. Damage metrics for accelerated testing and life prediction of PEMFCs are discussed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2346–2357, 2006