Intersection properties of open sets, II.

A topological space is called P_2 ( P_3, P_{<omega} ) if and only if it does not contain two (three, finitely many) uncountable open sets with empty intersection. We show that (i) there are 0-dimensional P_{<omega} spaces of size 2^omega, (ii) there are compact P_{<omega} spaces of size omega_1, (iii) the existence of a Psi-like examples for a compact P_{<omega} space of size omega_1 is independent of ZFC, (iv) it is consistent that 2^omega is as large as you wish but every first countable (and so every compact) P_2 space has cardinality<=omega_1

Two-Source Dispersers for Polylogarithmic Entropy and Improved Ramsey Graphs

In his 1947 paper that inaugurated the probabilistic method, Erd\H{o}s proved the existence of $2\log{n}$-Ramsey graphs on $n$ vertices. Matching Erd\H{o}s' result with a constructive proof is a central problem in combinatorics, that has gained a significant attention in the literature. The state of the art result was obtained in the celebrated paper by Barak, Rao, Shaltiel and Wigderson [Ann. Math'12], who constructed a $2^{2^{(\log\log{n})^{1-\alpha}}}$-Ramsey graph, for some small universal constant $\alpha > 0$. In this work, we significantly improve the result of Barak~\etal and construct $2^{(\log\log{n})^c}$-Ramsey graphs, for some universal constant $c$. In the language of theoretical computer science, our work resolves the problem of explicitly constructing two-source dispersers for polylogarithmic entropy

The Use of a Line Scan Ratemeter for the X-Ray Microanalytic Evaluation of Membrane-Bound Histochemical Endproducts

Although X-ray microanalysis represents a useful tool for identifying electron dense histochemical end-products, quantitative microanalytic measurements are seriously hampered in the case of the activities of certain membrane-bound enzymes. For example, the electron histochemical methods revealing K+-dependent pNPPase activity result in a very fine, granular reaction product of lead phosphate. Therefore microanalytic, densitometric or similar evaluations of the reaction, even in semiquantitative terms are not practical by the usual procedures. This paper describes a method of X-ray microanalysis of thick sections (0.5 μm) processed for K+-pNPPase, where a sufficient amount of lead is present for X-ray microanalytic determination. The analysis is performed in the line scan mode on transversely cut membrane profiles by means of the line scan ratemeter of an EDAX System F. This yields quantitative data on the relative lead concentrations in the vicinity of the cell membrane. A method is proposed for calculation of relative enzyme activities based on the Pb-signal of the ratemeter curve and the average noise -level of the cytoplasm, containing also non-specifically bound lead. This method avoids the necessity of measuring the section thickness; it may be useful for a variety of purposes in the electron microscopic histochemistry of membrane-bound enzymes

Investigation of antinutritive components in Hungarian potato cultivars depending on production technology

We have investigated the Total Glycoalcaloid (TGA), nitrite, and nitrate contents of some Hungarian and foreign potato cultivars in relation to the effect of different combination of fertilisers and green manure, late blight management strategies (none, programmed, or prediction based spraying), and irrigation regime for three years. The Hungarian cultivars have exotic potato species like S. acaule, S. demissum, S. stoloniferum, S. vernei, or S. tub. ssp. andigenum in their genetic background as sources of resistance genes. No effect of fertilisers or irrigation was found on the level of glycoalkaloids and nitrate contents, which were influenced mostly by the genotype and season. In conclusion, the absolute amount and the presence of different antinutritive components of potato tubers were influenced by the technology, genotype, and season in a complex manner. These results in general prove that ware potato production utilising intensive commercial agrotechnical practices and common cultivars is safe regarding the nitrate and TGA content of tubers

Detailed survey of the phase space around Nix and Hydra

We present a detailed survey of the dynamical structure of the phase space around the new moons of the Pluto - Charon system. The spatial elliptic restricted three-body problem was used as model and stability maps were created by chaos indicators. The orbital elements of the moons are in the stable domain both on the semimajor axis - eccentricity and - inclination spaces. The structures related to the 4:1 and 6:1 mean motion resonances are clearly visible on the maps. They do not contain the positions of the moons, confirming previous studies. We showed the possibility that Nix might be in the 4:1 resonance if its argument of pericenter or longitude of node falls in a certain range. The results strongly suggest that Hydra is not in the 6:1 resonance for arbitrary values of the argument of pericenter or longitude of node.Comment: Published in MNRAS. 10 pages, 7 figures, 4 table