Efficient optimization of the reward-risk ratio with polyhedral risk measures

In problems of portfolio selection the reward-risk ratio criterion is optimized to search for a risky portfolio offering the maximum increase of the mean return, compared to the risk-free investment opportunities. In the classical model, following Markowitz, the risk is measured by the variance thus representing the Sharpe ratio optimization and leading to the quadratic optimization problems. Several polyhedral risk measures, being linear programming (LP) computable in the case of discrete random variables represented by their realizations under specified scenarios, have been introduced and applied in portfolio optimization. The reward-risk ratio optimization with polyhedral risk measures can be transformed into LP formulations. The LP models typically contain the number of constraints proportional to the number of scenarios while the number of variables (matrix columns) proportional to the total of the number of scenarios and the number of instruments. Real-life financial decisions are usually based on more advanced simulation models employed for scenario generation where one may get several thousands scenarios. This may lead to the LP models with huge number of variables and constraints thus decreasing their computational efficiency and making them hardly solvable by general LP tools. We show that the computational efficiency can be then dramatically improved by alternative models based on the inverse ratio minimization and taking advantages of the LP duality. In the introduced models the number of structural constraints (matrix rows) is proportional to the number of instruments thus not affecting seriously the simplex method efficiency by the number of scenarios and therefore guaranteeing easy solvability.     

Effect of extraction method on phenolic content and antioxidant activity of mistletoe extracts from Viscum album subsp. abietis

The total content of polyphenols and flavonoids determined in the same plant and their corresponding antioxidant activities may vary widely, depending on the extraction conditions applied. This study was conducted to optimise the extraction conditions of phenolics and flavonoids from the mistletoe plant. Various extraction methods, i.e. ultrasound-assisted extraction technology, maceration, maceration with stirring, accelerated solvent extraction (ASE), and extraction under reflux were evaluated for their percentage extraction of polyphenols (TPC) and flavonoids (TFC) from Viscum album subsp. abietis. In addition, the anti-radical activity of extracts was analysed using the 2,2-diphenyl-1-picrylhydrazyl method. The effects of temperature, solvent type, and concentration on the phenolic extraction efficiency and antioxidant activity were studied using chemometric and statistical methods. The results showed that the extracts of V. album subsp. abietis contained large amounts of polyphenols and flavonoids (up to 57.673 mg g^?1 and 9.955 mg g^?1 of dry extract, respectively) and exhibited potent antioxidant activity, hence representing promising sources of powerful antioxidants. Due to its high extraction efficiency and considerable saving of time and solvent, ASE was more effective than the other extraction techniques. Extracts prepared with water-polar solvent mixtures displayed the highest TPC, TFC, and antioxidant activity, while organic polar solvents were the least efficient extractants.     

Influence of cryogenic modification of silica on thermal properties and flammability of cross-linked nitrile rubber

The article presents the results of testing thermal properties and combustibility of butadieneacrylonitrile rubber with 18% contents of bounded acrylonitrile, NBR 18. Two types of silica, Zeosil 175C and Ultrasil VN-3, with different specific surfaces were used as filler. Zeosil 175C and Ultrasil VN-3 were modified via cryogenic dezaggregation method. The activity of unmodified and cryogenic modified silica toward butadiene-acrylonitrile rubber were investigated. The sulphur and peroxide vulcanizates contained 20, 30, 40, and 50 phr. of the filler were studied. The article discusses also the test results of thermal stability and flammability of NBR 18 containing silica prepared "in situ" from alkoxysilane precursor. The test results were obtained with the use of derivatograph, measurements of flammability by the method of oxygen index, and in air. The effect of the silica modification on the SEM and AFM was also examined. The method of cryogenic modification enables to achieve increase of mineral fillers activity towards elastomer and reduction in the flammability of NBR 18 vulcanizates. It has been found that the modification of the vulcanizates of NBR 18 with tetraethoxysilane that makes it possible to form silica "in situ" reduces the flammability of cross-linked rubbers.     

On tame operators between non-archimedean power series spaces

Let p ∈ {1, ∞}. We show that any continuous linear operator T from A1 (a) to Ap (b) is tame, i.e., there exists a positive integer c such that sup x||Tx||k/|x|ck ∞ for every k ∈ N. Next we prove that a similar result holds for operators from A∞(a) to Ap(b) if and only if the set Mb,a of all finite limit points of the double sequence (bi /aj ) i,j∈N is bounded. Finally we show that the range of every tame operator from A∞(a) to A∞(b) has a Schauder basis.     

Hyperbolic Coxeter groups of large dimension

We construct examples of Gromov hyperbolic Coxeter groups of arbitrarily large dimension. We also extend Vinbergs theorem to show that if a Gromov hyperbolic Coxeter group is a virtual Poincaré duality group of dimension n, then n 61.Coxeter groups acting on their associated complexes have been extremely useful source of examples and insight into nonpositively curved spaces over last several years. Negatively curved (or Gromov hyperbolic) Coxeter groups were much more elusive. In particular their existence in high dimensions was in doubt.In 1987 Gabor Moussong [M] conjectured that there is a universal bound on the virtual cohomological dimension of any Gromov hyperbolic Coxeter group. This question was also raised by Misha Gromov [G] (who thought that perhaps any construction of high dimensional negatively curved spaces requires nontrivial number theory in the guise of arithmetic groups in an essential way), and by Mladen Bestvina [B2].In the present paper we show that high dimensional Gromov hyperbolic Coxeter groups do exist, and we construct them by geometric or group theoretic but not arithmetic means.     

Passive sampling application to control air quality in interior of new vehicles

The investigation of air pollution is a highly important field of research. Air quality in a vehicle’s interior has attracted growing attention since people spend much of their time in vehicles and those frequently travelling in new cars are exposed to harmful compounds. The main air pollutants inside new vehicles are volatile organic compounds (VOCs), present as a result of interior materials’ de-gassing. Among the sampling methods used in indoor air quality research, active sampling for VOCs collection is one method that has been extensively described and applied. The present study sought to implement passive sampling with Radiello® samplers to collect air samples directly in the car factory. The results from passive sampling were compared with results derived from active sampling using Carbograph 1TD and silicagel coated with 2,4-dinitrophenylhydrazine cartridges, based on previously validated methods. The identification and quantification of organic compounds was performed using gas chromatography with flame ionisation coupled with a mass spectrometer after thermal desorption. Aldehydes were determined by means of high-performance liquid chromatography. In the present study, the results obtained with the use of active and passive methods of air sampling were compared, correlations between the two sampling methods were designated and the repeatability of passive sampling was detailed.     

LC-ESI-MS/MS Polyphenolic Profile and In Vitro Study of Cosmetic Potential of Aerva lanata (L.) Juss. Herb Extracts

The aim of the present study was to investigate the phenolic composition and the biological properties of different Aerva lanata (L). Juss. herb extracts obtained with the use of accelerated solvent extraction (ASE), i.e., a green, ecological method, for cosmetic purposes. All samples exhibited high DPPH^• (9.17–119.85 mg TE/g) and ABTS^•+ (9.90–107.58 mg TE/g) scavenging activity. The extracts exhibited considerable anti-lipoxygenase (EC₅₀ between 1.14 mg/mL and 3.73 mg/mL) and anti-xanthine oxidase (EC₅₀ between 1.28 mg/mL and 3.72 mg/mL) activities, moderate chelating activity (EC₅₀ between 1.58 mg/mL and 5.30 mg/mL), and high antioxidant potential in the ORAC assay (0.36–3.84 mM TE/g). Changes in the polyphenol profile of the analysed samples depending on the solvent and temperature used for the extraction were determined with the liquid chromatography/electrospray mass spectrometry (LC-ESI-MS/MS) method. Twenty-one phenolic compounds, including flavonoids and phenolic acids, were detected and quantified. It was shown that tiliroside was one of the main phenolic metabolites in the A. lanata (L.) Juss. herb., which may suggest that this compound may be largely responsible for the observed anti-inflammatory activity of the extracts. In addition, the studied extracts exhibited promising skin-related (anti-tyrosinase, anti-elastase, anti-collagenase, and anti-hyaluronidase) activity. This study showed that Aerva lanata (L.) Juss. contains high amounts of phenolic compounds, including tiliroside, and has good skin-related activities. Therefore, the plant may be interesting as a novel source of bioactive agents for cosmetic industries.