CD-independent subsets in meet-distributive lattices

A subset $X$ of a finite lattice $L$ is CD-independent if the meet of any two incomparable elements of $X$ equals 0. In 2009, Cz\'edli, Hartmann and Schmidt proved that any two maximal CD-independent subsets of a finite distributive lattice have the same number of elements. In this paper, we prove that if $L$ is a finite meet-distributive lattice, then the size of every CD-independent subset of $L$ is at most the number of atoms of $L$ plus the length of $L$. If, in addition, there is no three-element antichain of meet-irreducible elements, then we give a recursive description of maximal CD-independent subsets. Finally, to give an application of CD-independent subsets, we give a new approach to count islands on a rectangular board.Comment: 14 pages, 4 figure

Chemical composition and antimicrobial activity of Nigella sativa crude and essential oil

Nigella sativa L. (black cumin) is well known for its benefits in the field of traditional medicine. The aim of this study was to determine the chemical composition and investigate the antimicrobial activity of cold pressed oil (CO) and essential oil (EO) of Nigella sativa L. on food-borne pathogenic and spoilage bacteria. The microdilution method was used to determine the minimal inhibitory concentration (MIC) of Nigella sativa crude oil (CO) and essential oil (EO) against 4 Gram-positive (Bacillus cereus, Bacillus subtilis, Staphylococcus aureus, and Listeria monocytogenes) and 3 Gram-negative (Salmonella Hartford, Pseudomonas aeruginosa, and Escherichia coli) foodborne pathogenic and spoilage bacteria occurring in food products. Total fatty acid composition of CO was analysed by GLC, while the EO was analysed by GC-MS to detect its active compounds. The results showed that the major fatty acid of CO was palmitic acid (C16:0), as saturated fatty acid, however, linoleic acid (C18:2) was the main unsaturated fatty acid. The major compounds of the EO were p-cymene and thymoquinone. The inhibition on all tested bacteria of EO was 10 times higher than of CO, and the lowest concentration value was observed in case of Bacillus subtilis (0.003%). Hence, results reinforce the ambition to apply Nigella sativa oils in food as natural preservative

Yield and composition of supercritical fluid extracts of different Lamiaceae herbs

In our work the effectiveness of supercritical carbon dioxide extraction was studied on volatile components of Lamiaceae herbs. The aim of our investigations was to determine the optimal extraction parameters yielding high amount of volatiles in a desirable composition. As plant materials, dried and powdered cude drugs of Thymus vulgaris, Thymus pannonicus, Satureja hortensis, Ocimum basilicum, Rosmarinus officnalis and Salvia officinalis were chosen. Pressure (8-30 MPa), temperature (35-60 °C) and time (5-60 min) of extraction were regulated. Results obtained by supercritical fluid extraction (SFE) were compared to that of the conventional extraction procedur, hydrodistillation (HD). In the case of Thymus vulgaris, Thymus pannonicus and Salvia officnalis, extract yield of SFE was comparable to the essential oil amount obtained by hydrodistillation from the same drug. Essential oil rich thyme extracts were analysed by GC-FID. We have found that yield and quality of SFE extracts highly depend on the conditions of extraction

Yield and composition of supercritical fluid extracts of different Lamiaceae herbs

In our work the effectiveness of supercritical carbon dioxide extraction was studied on volatile components of Lamiaceae herbs. The aim of our investigations was to determine the optimal extraction parameters yielding high amount of volatiles in a desirable composition. As plant materials, dried and powdered cude drugs of Thymus vulgaris, Thymus pannonicus, Satureja hortensis, Ocimum basilicum, Rosmarinus officnalis and Salvia officinalis were chosen. Pressure (8-30 MPa), temperature (35-60 °C) and time (5-60 min) of extraction were regulated. Results obtained by supercritical fluid extraction (SFE) were compared to that of the conventional extraction procedur, hydrodistillation (HD). In the case of Thymus vulgaris, Thymus pannonicus and Salvia officnalis, extract yield of SFE was comparable to the essential oil amount obtained by hydrodistillation from the same drug. Essential oil rich thyme extracts were analysed by GC-FID. We have found that yield and quality of SFE extracts highly depend on the conditions of extraction

Paul Erdős and Probabilistic Reasoning

One of the major contributions of Paul Erdős is the development of the Probabilistic Method and its applications in Combinatorics, Graph Theory, Additive Number Theory and Combinatorial Geometry. This short paper describes some of the beautiful applications of the method, focusing on the long-term impact of the work, questions and results of Erdős. This is mostly a survey, but it contains a few novel results as well