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New copolymers of norbornene and 1,5-bis(hexenyl-5)-1,1,3,3,5,5-hexamethyltrisiloxane containing flexible siloxane and rigid norbornene fragments in the main chain are synthesized. Synthesis is carried out using three types of olefin metathesis reactions: the ring-opening metathesis polymerization of norbornene, the metathesis of nonconjugated diene 1,5-bis(hexenyl-5)-1,1,3,3,5,5-hexamethyltrisiloxane, and the interchain macromolecular cross-metathesis between polynorbornene and siloxane-containing polyene. The latter reaction is studied for the first time. With its help, new statistical multiblock copolymers of norbornene and 1,5-bis(hexenyl-5)-1,1,3,3,5,5-hexamethyltrisiloxane with different average block lengths are obtained and characterized by 1H and 13C NMR and IR spectroscopy. The effect of the copolymer structure on their thermal properties is investigated. [ABSTRACT FROM AUTHOR]

The gas permeability of hydrocarbons (CH4, C2H6, n-C4H10) through four polynorbornenes obtained by modification of the addition poly(5-vinyl-2-norbornene) is studied. Upon modification, both polar (oxirane and thioacetyl fragments) and nonpolar substituents (cyclopropyl and ethyl groups) are introduced into side substituents. The introduction of polar groups leads to a decrease in gas permeability, while the hydrogenation or cyclopropanation of addition poly(5-vinyl-2-norbornene) causes an increase in gas permeability. Despite the fact that the synthesized polymers are glassy and nonmicroporous materials, they have an unusual feature for such polymers—the selectivity of hydrocarbon separation controlled by solubility (α(n‑C4H10/CH4) ≫ 1). Among the studied polymers, the optimal combination of gas permeability and selectivity is observed for the cyclopropanated polymer. [ABSTRACT FROM AUTHOR]

Previously undescribed norbornene monomer 3,3,4-trifluoro-4-perfluorohexyltricyclononene-7 is synthesized by the [2+2+2] cycloaddition reaction. The monomer is involved in the ring-opening polymerization metathesis in the presence of the first-generation Grubbs catalyst to give rise to the amorphous, glassy unsaturated polymer. The gas-transport properties of the metathesis polymer is studied, the gas permeability and diffusion coefficients for a wide range of gases (He, H2, O2, N2, CO2, CH4) are determined, and the solubility coefficients of gases in this polymer are calculated. [ABSTRACT FROM AUTHOR]

The nonzero sum four-person game was considered. We show that the game can be reduced to a global optimization problem by extending Mills' result (J Soc Ind Appl Math 8(2):397-402, 1960). For solving the problem, we propose a global optimization method that combines the ideas of the classical multistart and an estimation of a convexity degree of the function. The proposed algorithm was tested numerically on some problems created by the well-known generator GAMUT (GAMUT is a Suite of Game Generators. http://gamut.stanford.edu) and allowed us to find solutions to the four-person game. [ABSTRACT FROM AUTHOR]

The effect of postpolymerization epoxidation of metathesis polynorbornenes on their gas-transport behavior is studied. For two polymers, unsubstituted polynorbornene and poly(trimethylsilylnorbornene), postpolymerization modification via double bonds is implemented by epoxidation under the action of m-chloroperbenzoic acid to high conversions (95-100%). For initial polymers and their epoxidation products, the permeability and diffusion coefficients are measured and the solubility coefficients are estimated. It is shown that, for both initial polymers, functionalization leads to a marked reduction in permeability (by a factor of 2-10) and diffusion coefficients (by a factor of 3-10); simultaneously, the separation factors increase by a factor of 2-6. Although for all gases the solubility coefficients decrease as a result of epoxidation, the coefficients of CO solubility in both epoxidated polymers increase. This effect may be explained by specific interactions of a СО molecule possessing the quadrupole moment with С-О-С bonds appearing in a polymer. [ABSTRACT FROM AUTHOR]

Numerical methods for solving optimal control problems with equality constraints at the right end of the trajectory are discussed. Algorithms for optimal control search are proposed that are based on the multimethod technique for finding an approximate solution of prescribed accuracy that satisfies terminal conditions. High accuracy is achieved by applying a second-order method analogous to Newton's method or Bellman's quasilinearization method. In the solution of problems with direct control constraints, the variation of the control is computed using a finite-dimensional approximation of an auxiliary problem, which is solved by applying linear programming methods. [ABSTRACT FROM AUTHOR]

For an optimal control problem with state constraints, an iterative solution method is described based on reduction to a finite-dimensional problem, followed by applying a successive linearization algorithm with the use of an augmented Lagrangian. The efficiency of taking into account state constraints in optimal control computation is illustrated by numerically solving several application problems. [ABSTRACT FROM AUTHOR]

Aims: To compare methods to measure time outdoor and light levels, two possible predictors of myopia, in Singapore children.Methods: Outdoor time from a diary and portable light meter over a 1-week period was compared in 117 Singapore children aged 6-12 years with and without myopia. All children wore a (HOBO Pendant temp/light Part # UA-002-64) light meter for 1 week and the parents filled the 7-day outdoor diary to track the outdoor activity.Results: Mean outdoor time from diary and time with light levels was 5.44 hours per week and 7.91 hours per week, respectively, during school term and school holidays. Time spent with light levels of >1000 Lux from the light meter were 7.08 h per week and 9.81 h per week, respectively, during school term and school holidays. The intraclass correlation coefficients were 0.21 and 0.28 for outdoor time from the diary and light meter (1000 Lux cut-off) during the school term and holidays, respectively. The correlation coefficient was 0.34 (95% CI 0.05, 0.58) for a weekday during school holidays, 0.17 (-0.14, 0.45) for a weekday during school term, 0.07 (-0.16, 0.29) for a weekday during school term, and 0.25 (0.02, 0.46) for a weekend during school term.Conclusions: The agreement between the light meter and 1-week diary was poor to fair. Both instruments measure different parameters, time outdoors and light intensity, and could therefore capture different aspects of risk in future myopia studies. [ABSTRACT FROM AUTHOR]

The 'obesity paradox' refers to observations that run counter to the thesis that normal weight (BMI 18.5-24.9 g/m(2)) provides the lowest mortality and higher weight is associated with greater mortality. We argue that the weight of lowest mortality is influenced by aging and chronic disease, with mortality advantage extending into the overweight and even class I obese ranges under some circumstances. A focus on quality nutrition, physical activity, fitness, and maintaining function in these weight ranges may be preferable to a focus on intentional weight loss, which has uncertain effects. The 'obesity paradox' is no 'paradox' if one defines and interprets 'ideal' weight appropriately. [ABSTRACT FROM AUTHOR]

The concentration of psoralens in celery ( Apium graveolens L.), variety 'Tender Crisp', harvested 120 days after planting, was 12 μg g f.wt, compared with 18 μg g f.wt in celery harvested 150 days after planting. After 1 month of storage at 2°C, concentrations of psoralens in the 120- and 150-day-old celery were 82 and 118 μg g f.wt, respectively. Concentrations of psoralens in the 120- and 150-day-old celery inoculated with Botrytis cinerea Pers., after 1 month of storage at 2°C, were 266 and 294 μg g f.wt, respectively. [ABSTRACT FROM AUTHOR]

A response from the author of the article "Comparison of measurements of time outdoors and light levels as risk factors for myopia in young Singapore children" in the 2012 issue is presented.