Solving semi-infinite programs by smoothing projected gradient method

In this paper, we study a semi-infinite programming (SIP) problem with a convex set constraint. Using the value function of the lower level problem, we reformulate SIP problem as a nonsmooth optimization problem. Using the theory of nonsmooth Lagrange multiplier rules and Danskin’s theorem, we present constraint qualifications and necessary optimality conditions. We propose a new numerical method for solving the problem. The novelty of our numerical method is to use the integral entropy function to approximate the value function and then solve SIP by the smoothing projected gradient method. Moreover we study the relationships between the approximating problems and the original SIP problem. We derive error bounds between the integral entropy function and the value function, and between locally optimal solutions of the smoothing problem and those for the original problem. Using certain second order sufficient conditions, we derive some estimates for locally optimal solutions of problem. Numerical experiments show that the algorithm is efficient for solving SIP.     

Thermotropic mesomorphism in a branched chain copper(II) carboxylate and its pyrazine complex

The thermotropic mesomorphism of tetrakis(μ-(2,2-(dioctyl(acetato))-O,O')bis-[copper(II)] has been investigated by optical microscopy and X-ray diffraction. This compound was found to form a hexagonal discotic phase analogous to those reported for the copper(II) salts of n-alkanoic acids, but in contrast to these materials the mesophase of the branched chain compound was found to extend to below room temperature. Complexation of the copper(II) branched chain carboxylate with the difunctional ligands pyrazine and 4,4'-dipyridyl resulted in liquid-crystalline materials whose mesophase structure could not be established. The possibility of these complexes existing as polymeric/oligomeric entities is discussed.     

Hydrolytic stability and high Tg of polyimides derived from the novel 4,9‐bis[4‐(3,4‐dicarboxyphenoxy)phenyl]‐diamantane dianhydride

This work reports the synthesis and characterization of diamantane‐based polyimides obtained from 4,9‐bis[4(3,4‐dicarboxyphenoxy)phenyl]diamantane dianhydride and various aromatic diamines. Interestingly, the diamantane‐based polyimides were very stable to hydrolysis. This novel polyimide exhibits a low dielectric constant (2.65–2.77), low moisture absorption (<0.67%), good solubility, high T_g and unusually high thermal stability. Dynamic mechanical analysis (DMA) reveals that the diamantane‐based polyimides have high T_g ranging from 281 to 379 °C. The high‐temperature β₁ subglass transition around 285 °C was observed in polyimide 6a derived from 2,2′‐bis(trifluoromethyl)benzidine. This class of novel diamantane‐based polyimide is very promising for electronic applications, because of its good mechanical properties, good thermal stability, low dielectric constant, excellent hydrolytic resistance, and low moisture absorption. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 1673–1684, 2009     

COST-BENEFIT ANALYSIS APPLIED TO WILDERNESS PRESERVATION—OPTION VALUE UNCERTAINTY AND DITONICITY

It has been recognized for some time that when cost-benefit analysis is applied to irreversible environmental decisions, such as that of developing or preserving wilderness land, there can be an option value associated with the preservation decision, which arises when there is future uncertainty with respect to the benefits of development or preservation. In this paper the provenance of option value is examined and it is shown that an important cause is a special kind of uncertainty, viz. the possibility of reversals in direction of the relative valuations of wilderness land and developed land, a property we refer to as ditonicity. It is shown that the more ditonic the relative valuation process the greater the deviance between the certainty-equivalence development policy and the stochastically optimal one, and thus by implication the greater the option value. In the two cases with zero ditonicity, when relative wilderness valuations always increase or always decrease (even though in a stochastic fashion), there is zero option value. The model used assumes that service flows from wilderness and developed land are size-dependent, with future relative values known only in terms of a stochastic process, which can take jumps up or down of the same proportional size, at random times. Development can be partial or total and can occur in impulses at any time over an infinite time horizon.     

The educational needs and professional roles of Canadian physicians and nurses regarding genetic testing and adult onset hereditary disease

OBJECTIVE: To investigate the knowledge, professional involvement and confidence of Canadian nurses and physicians in providing genetic services for adult onset hereditary disease. METHODS: 1,425 physicians and 1,425 nurses received a mailed questionnaire with reminders. The response rates were 50% (n = 543) and 79% (n = 975), respectively. RESULTS: Forty-eight percent of physicians and 31% of nurses lacked formal education in genetics. Respondents reported being involved in caring for people at risk for adult onset hereditary disease. Their levels of confidence that they could perform tasks, such as counselling about predictive genetic tests, however, were lower than their levels of expectation that it would be important for them to provide these services. CONCLUSIONS: The expected roles and educational needs of Canadian nurses and physicians have broad areas of overlap suggesting the possibility of combined professional education programs and multiple ways of organizing teams to provide genetic services to people at risk for adult onset hereditary disease.     

Effect of grinding method on the analysis of essential oil from <Emphasis Type="Italic">Baccharis articulata</Emphasis> (Lam.) Pers.

Grinding methods were evaluated aiming to determine yield and composition of essential oils (EOs) from Baccharis articulata (Lam) Pers., called as carqueja, a native plant from South Brazil. Cryogenic, knife (with and without cooling) and ball mills were used. The major constituents found in EOs were β-pinene, caryophyllene, spathulenol and caryophyllene oxide, but differences in 21 compounds were observed. All grinding processes reduced monoterpenes and oxygenated sesquiterpenes with concentration of hydrocarbon sesquiterpenes. The sesquiterpenes (hydrocarbons and oxygenated) were found from 63.55 to 86.02% while the monoterpene hydrocarbons’ concentration ranged from 13.98 to 36.45%. Plants milled with knife mill provided EOs with profile similar to those not grinded. Despite the lower working temperature, cryogenic milling resulted in smaller EO yield (0.40 ± 0.03%) in comparison to other grinding methods (yields from 0.50 ± 0.02 to 0.56 ± 0.03%) and different chromatographic profile. Microscopic analysis showed the smaller particle size provided by cryogenic grinding, which leads to glandular trichome rupture and consequently to loss of EOs. This study showed that grinding should be carefully evaluated to provide reproducible results in essential oil analysis.     

Electrochemical assessment of water|ionic liquid biphasic systems towards cesium extraction from nuclear waste

A room temperature ionic liquid (IL) composed of a quaternary alkylphosphonium (trihexyltetradecylphosphonium, P₆₆₆₁₄⁺) and tetrakis(pentafluorophenyl)borate anion (TB⁻) was employed within a water|P₆₆₆₁₄TB (w|P₆₆₆₁₄TB or w|IL) biphasic system to evaluate cesium ion extraction in comparison to that with a traditional water|organic solvent (w|o) combination. ¹³⁷Cs is a major contributor to the radioactivity of spent nuclear fuel as it leaves the reactor, and its extraction efficiency is therefore of considerable importance. The extraction was facilitated by the ligand octyl(phenyl)-N,N′-diisobutylcarbamoylphosphine oxide (CMPO) used in TRans-Uranium EXtraction processes and investigated through well established liquid|liquid electrochemistry. This study gave access to the metal ion to ligand (1:n) stoichiometry and overall complexation constant, β, of the interfacial complexation reaction which were determined to be 1:3 and 1.6 × 10¹¹ at the w|P₆₆₆₁₄TB interface while the study at w|o elicited an n equal to 1 with β equal to 86.5. Through a straightforward relationship, these complexation constant values were converted to distribution coefficients, δ_α, with the ligand concentrations studied for comparison to other studies present in the literature; the w|o and w|IL systems gave δ_α of 2 and 8.2 × 10⁷, respectively, indicating a higher overall extraction efficiency for the latter. For the w|o system, the metal ion-ligand stoichiometries were confirmed through isotopic distribution analysis of mass spectra obtained by the direct injection of an emulsified water–organic solvent mixture into an electron spray ionization mass spectrometer.