Discrete Yamabe problem for polyhedral surfaces

We introduce a new discretization of the Gaussian curvature on piecewise at surfaces. As the prime new feature the curvature is scaled by the factor 1/r2 upon scaling the metric globally with the factor r. We develop a variational principle to tackle the corresponding discrete uniformisation theorem – we show that each piecewise at surface is discrete conformally equivalent to one with constant discrete Gaussian curvature. This surface is in general not unique. We demonstrate uniqueness for particular cases and disprove it in general by providing explicit counterexamples. Special attention is paid to dealing with change of combinatorics

Fatty acids, minerals, phenolics and vitamins in the seeds of <i>Inocarpus fagifer</i>, a Pacific Island underutilized legume

Recently, Pacific nations have faced to alarming increase in prevalence of noncommunicable diseases connected with consumption of non-traditional processed food. It is believed that re-introduction of native diet may mitigate these negative trends. One of the traditional staple food of Pacific region are seeds of underutilized leguminous tree Inocarpus fagifer. Nevertheless, information on their chemical composition and nutritional properties are missing. Therefore we decided to analyze this crop for the presence of fatty acids, minerals, phenolics and vitamins. Performed analyses revealed a slightly predominating portion of unsaturated (e.g. 18:2 n-6; 18:1 n-9 and 18:3α n-3) over saturated (e.g. C18 and C16) fatty acids. Considering minerals, the substantial concentrations of copper, magnesium, manganese, potassium and zinc (19.32; 1823.21; 8.44; 23308.41 and 77.99 mg kg-1 of dry matter respectively) were recorded. Ferulic and coumaric acids were the most abundant phenolics (3.23 and 1.48 mg kg-1 of dry matter respectively), whereas flavonoids, isoflavonoids and coumestrol were also present. Regarding vitamins, niacin and riboflavin were found in respective concentrations 131.80 and 4.47 mg kg-1 of dry matter. Our findings suggest I. fagifer seeds as a prospective food source of several health-beneficial constituents which might contribute to the well-being of Pacific islanders.   The online version of this article (doi: 10.5073/JABFQ.2016.089.034) contains a supplementary file

Discrete yamabe problem for polyhedral surfaces

We study a new discretization of the Gaussian curvature for polyhedral surfaces. This discrete Gaussian curvature is defined on each conical singularity of a polyhedral surface as the quotient of the angle defect and the area of the Voronoi cell corresponding to the singularity. We divide polyhedral surfaces into discrete conformal classes using a generalization of discrete conformal equivalence pioneered by Feng Luo. We subsequently show that, in every discrete conformal class, there exists a polyhedral surface with constant discrete Gaussian curvature. We also provide explicit examples to demonstrate that this surface is in general not unique

Thymoquinone vapor significantly affects the results of Staphylococcus aureus sensitivity tests using the standard broth microdilution method

The broth microdilution (BMD) method is widely used for the determination of minimum inhibitory concentrations of antimicrobial agents, including volatile oils and their components. In this series of various experiments, we have demonstrated the influence of thymoquinone (TQ) vapor on the results of the BMD test performed with Staphylococcus aureus as a model organism. The spread of vapor from the TQ containing wells (32–512 μg/mL) caused the complete inhibition of staphylococcal growth in adjoining wells initially containing bacterium-inoculated pure Mueller–Hinton broth only and thus produced false positive results of the test. The ability of TQ to pass into the adjoined wells was subsequently confirmed by gas chromatography–mass spectrometry, whereas TQ at concentrations up to 84 μg/mL was detected in these wells after five hours. Based on these results, we suppose that vapors of TQ as well as of other naturally occurring volatile compounds and their mixtures (for example essential oils and plant extracts) can significantly influence results of the standard BMD assay. These observations, therefore, call for development of new appropriate BMD method suitable for assessment of antimicrobial activity of volatile substances

Antioxidant activity of selected phenols and herbs used in diets for medical conditions.

The antioxidant capacity of some herbs used in dietology practice was determined by the DPPH free radical method, which was calibrated with ascorbic acid. Partially hydrophilic phenolic compounds are the most active compounds in plants, and therefore water was used as the extraction agent. Besides antioxidant capacity, the content of total phenolic compounds was also measured and a strong correlation between these two variables was found. The extracts of lemon balm (Melissa officinalis L.), peppermint (Mentha x piperita L.), oregano (Origanum vulgare L.), Greek oregano (Origanum heracleoticum L.), sage (Salvia officinalis L.) and winter savory (Satureja montana L.) showed very significant activity. It was comparable with the activity of green tea in the case of oregano and peppermint. Lower activity was observed in the case of rosemary (Rosmarinus officinalis L.), marjoram (Majorana hortensis), hyssop (Hyssopus officinalis L.), sweet basil (Ocimum basilicum), and lovage (Levisticum officinale Koch.). The inhibitory activity of the herb extracts was monitored also during the autooxidation of lard. Very high antioxidant capacity was observed mainly in sage samples, but also in marjoram and Greek oregano. The extracts of peppermint, oregano, rosemary, winter savory, lemon balm and hyssop showed middle activity comparable to that of alpha-tocopherol. The antioxidant capacity of sweet basil and lovage was insignificant