Bromine hydrolysis control and two consecutive oscillatory domains in closed, cerium-catalyzed glyoxylic acid Belousov-Zhabotinsky systems

In closed, cerium-catalyzed glyoxylic acid Belousov-Zhabotinsky systems we found a new dynamic behavior, viz. the observation of two oscillatory regimes separated by a nonoscillatory region. Mechanisms for this intermediate nonoscillatory domain are discussed.

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LC-MS Quantitative Determination of Atropine and Scopolamine in the Floral Nectar of Datura Species

The present study aimed at determining selected alkaloid components in the nectar of Datura species, to elucidate whether the alkaloid content of the floral nectar can lead to intoxication. A simple and rapid liquid chromatography coupled with electrospray mass spectrometry analysis was developed for the quantitative determination of atropine and scopolamine, the main toxic alkaloids of the Datura species. This method allowed the direct coupling of an electrospray mass selective detector to the LC system. Under these conditions, atropine and scopolamine were well separated from other components and detected with mass spectrometry (mass selective detector). Simultaneous determination of atropine and scopolamine was performed with gradient elution on an Ascentis Express C₁₈ (Supelco) reversed-phase column based on a new fused core particle design. Liquid chromatography coupled with electrospray mass spectrometry was used in positive ion mode. Atropine and scopolamine produced protonated species at m/z 290 and 304 (which are also the base peaks). Our data confirmed that the alkaloid characteristics for the vegetative and reproductive parts of the Datura plants may also occur in the nectar secreted by the flowers. In Datura species with large flowers and high nectar amounts, the alkaloid content increases proportionately and thus the nectar may be a potential source of intoxication.     

Stability of the path-path Ramsey number

Here we prove a stability version of a Ramsey-type Theorem for paths. Thus in any 2-coloring of the edges of the complete graph K_n we can either find a monochromatic path substantially longer than 2n/3, or the coloring is close to the extremal coloring.     

Perfect matchings in large uniform hypergraphs with large minimum collective degree

We define a perfect matching in a k-uniform hypergraph H on n vertices as a set of ⌊n/k⌋ disjoint edges. Let δk−1(H) be the largest integer d such that every (k−1)-element set of vertices of H belongs to at least d edges of H.In this paper we study the relation between δk−1(H) and the presence of a perfect matching in H for k?3. Let t(k,n) be the smallest integer t such that every k-uniform hypergraph on n vertices and with δk−1(H)?t contains a perfect matching.For large n divisible by k, we completely determine the values of t(k,n), which turn out to be very close to n/2−k. For example, if k is odd and n is large and even, then t(k,n)=n/2−k+2. In contrast, for n not divisible by k, we show that t(k,n)∼n/k.In the proofs we employ a newly developed “absorbing” technique, which has a potential to be applicable in a more general context of establishing existence of spanning subgraphs of graphs and hypergraphs.     

Adaptive finite element methods in electrochemistry

In this article, we review some of our previous work that considers the general problem of numerical simulation of the currents at microelectrodes using an adaptive finite element approach. Microelectrodes typically consist of an electrode embedded (or recessed) in an insulating material. For all such electrodes, numerical simulation is made difficult by the presence of a boundary singularity at the electrode edge (where the electrode meets the insulator), manifested by the large increase in the current density at this point, often referred to as the edge effect. Our approach to overcoming this problem has involved the derivation of an a posteriori bound on the error in the numerical approximation for the current that can be used to drive an adaptive mesh-generation algorithm, allowing calculation of the quantity of interest (the current) to within a prescribed tolerance. We illustrate the generic applicability of the approach by considering a broad range of steady-state applications of the technique.     

Synthesis of aminomethylazetidines regioselective reactions of mesyloxymethylazetidinones with nucleophiles II

Two efficient methods have been developed for the synthesis of variously substituted 2‐aminomethylazetidine derivatives 5 by regioselective nucleophilic substitution of 4‐mesyloxymethylazetidin‐2‐ones 3 followed by reduction or by reduction of the appropriate 4‐oxo‐azetidine‐2‐carboxamides 7 . A novel ring transformation of 4‐oxoazetidine‐2‐carboxamides 7 into tetrahydroquinolines 16 by reaction with lithium aluminium hydride/aluminium trichloride has been investigated.     

Monochromatic Matchings in the Shadow Graph of Almost Complete Hypergraphs

Edge colorings of r-uniform hypergraphs naturally define a multicoloring on the 2-shadow, i.e., on the pairs that are covered by hyperedges. We show that in any (r – 1)-coloring of the edges of an r-uniform hypergraph with n vertices and at least (1-e)( *20c nr)(1-\varepsilon)\left( {\begin{array}{*{20}c} n\\ r\\ \end{array}}\right) edges, the 2-shadow has a monochromatic matching covering all but at most o(n) vertices. This result confirms an earlier conjecture and implies that for any fixed r and sufficiently large n, there is a monochromatic Berge-cycle of length (1 – o(1))n in every (r – 1)-coloring of the edges of K^(r)_n{K^{(r)}_{n}}, the complete r-uniform hypergraph on n vertices.