Elusive properties of infinite graphs

A graph property is said to be elusive (or evasive) if every algorithm testing this property by asking questions of the form “is there an edge between vertices $x$ and $y$?” requires, in the worst case, to ask about all pairs of vertices. The unsettled Aanderaa–Karp–Rosenberg conjecture is that every nontrivial monotone graph property is elusive for any finite vertex set. We show that the situation is completely different for infinite vertex sets: the monotone graph properties “every vertex has degree at least $n$” and “every connected component has size at least $m$,” where $n\ge 1$ and $m\ge 2$ are natural numbers, are not elusive for infinite vertex sets, but the monotone graph property “the graph contains a cycle” is elusive for arbitrary vertex set. On the other hand, we also prove that every algorithm testing some natural monotone graph properties, for example, “every vertex has degree at least $n$” or “connected” on the vertex set $\omega$ should check “lots of edges,” more precisely, all the edges of an infinite complete subgraph.     

Ein neuer Zugang zu 2,6,6-Trimethylcyclohexa-2,4-dienon aus 4-Oxoisophoron

A New Access to 2,6,6-Trimethylcyclohexa-2,4-dienone from 4-Oxoisophorone 2,6,6-Trimethylcyclohexa-2,4-dienone ( 1 ), a versatile starting material for the preparation of some carotenoids and several natural products, was efficiently (73% yield) prepared from oxoisophorone 3 . After conversion of 3 to the alcohol 4 or the acetate 5 , H₂O was eliminated ( 4→1 ) under acidic distillative conditions, whereas AcOH could be eliminated ( 5→l ) under Pd(O) catalysis.     

Simple Physical Model of Generation of the Low-Pressure Radio Frequency Supersonic Plasma Jet

The paper presents a simple theoretical model of the breakdown of the supersonic plasma jet generated by the hollow cathode discharge inside the nozzle in the low pressure RF plasma-chemical reactor. Through the nozzle which is drilled in the RF electrode the working gas flows to the reactor chamber. If at the outlet of the nozzle the gas flow is supersonic the well defined plasma jet is created inside the reactor chamber. The results of our model are in qualitative agreement with experimental data.     

Laser deposited YBaCuO thin films

YBa₂Cu₃O_7-x thin films were deposited by laser ablation using KrF excimer laser. In deposition on polycrystalline ZrO₂/(1–102) sapphire substrates influence of deposition conditions on film properties were studied. Zero resistance temperatureT _z of 83 K of epitaxially grown YBaCuO films on poly-ZrO₂/sapphire substrates was reached. Epitaxially grown yttria stabilized zirconia (YSZ) buffer layers were deposited by laser ablation on (1–102) sapphire substrates. On YSZ/sapphire, SrTiO₃ and NdGaO₃ substrates, temperatures T_z between 89–90 K were measured. Results of X-ray diffraction and SEM are also presented.We would like to express our thanks to L. Cibulka, L. and L. Rouek, and J. Stránský for their efficient help during the solution of technological problems connected with the construction of experimental apparatus.     

Optical filters with panchromatic emulsion layers for image processing

Amplitude filters with non-linear adaptive performance in the Fourier plane of a mirror optical system are considered. Panchromatic silver bromide layers with a printout effect are employed. The processing of binary and grey-scale images with the aid of a passively adaptive mirror filtering block is investigated.     

Nagata's conjecture and countably compact hulls in generic extensions

Nagata conjectured that every M-space is homeomorphic to a closed subspace of the product of a countably compact space and a metric space. Although this conjecture was refuted by Burke and van Douwen, and A. Kato, independently, but we can show that there is a c.c.c. poset P of size ω² such that in VP Nagata's conjecture holds for each first countable regular space from the ground model (i.e. if a first countable regular space X∈V is an M-space in VP then it is homeomorphic to a closed subspace of the product of a countably compact space and a metric space in VP). By a result of Morita, it is enough to show that every first countable regular space from the ground model has a first countable countably compact extension in VP. As a corollary, we also obtain that every first countable regular space from the ground model has a maximal first countable extension in model VP.     

Die Verwendung des Cupferrons in der quantitativen Analyse

Ohne Zusammenfassung Die Zitate zu diesem Referat folgen ausnahmsweise am Schlusse des ganzen Artikels S. 66.     

Quantification of soy isoflavones and their conjugative metabolites in plasma and urine: an automated and validated UHPLC-MS/MS method for use in large-scale studies

The biotransformation of isoflavones by gut microbiota and by drug metabolizing enzymes plays a crucial role in the understanding of their potential health-promoting effects. The purpose of our work was to develop a simultaneous, sensitive, and robust automated ultra high performance liquid chromatography tandem mass spectrometry (UHPLC-MS/MS) method to quantify the soy isoflavones daidzein and genistein, their conjugative metabolites, as well as their major microbial degradation products in order to provide a method for use in large clinical trials or animal studies. An automated, 96-well solid-phase extraction method was used to extract the isoflavone analytes from plasma and urine. Separation of genistein, daidzein, and 19 of its metabolites, including five glucuronides, seven sulfates, and two sulfoglucuronides, as well as five microbial metabolites, was achieved in less than 25 min using a sub-2 μm particle column and a gradient elution with acetonitrile/methanol/water as mobile phases. Analysis was performed under negative ionization electrospray MS via the multiple reaction monitoring (MRM). Validation was performed according to the analytical method validation guidelines of Food and Drug Administration (FDA) and International Conference on Harmonization of Technical Requirements for Registration of Pharmaceuticals for Human Use (ICH) consisting of selectivity, accuracy, precision, linearity, limit of detection, recovery, matrix effect, and robustness. All validated parameters essentially matched the FDA and ICH requirements. The application of this method to a pharmacokinetic study in postmenopausal women showed that isoflavones are extensively metabolized in vivo. A robust automated analytical approach was developed, which allows the handling of large sample sizes but nevertheless provides detailed information on the isoflavone metabolite profile leading to a better understanding and interpretation of clinical and animal studies.