Even Cycles in Graphs with Many Odd Cycles

It will be shown that if G is a graph of order n which contains a triangle, a cycle of length n or n−1 and at least cn odd cycles of different lengths for some positive constant c, then there exists some positive constant k=k(c) such that G contains at least kn ^1/6 even cycles of different lengths. Other results on the number of even cycle lengths which appear in graphs with many different odd length cycles will be given. Received: October 15, 1997     

Global existence and collisions for symmetric configurations of nearly parallel vortex filaments

We consider the Schrödinger system with Newton-type interactions that was derived by R. Klein, A. Majda and K. Damodaran (1995) [17] to modelize the dynamics of N nearly parallel vortex filaments in a 3-dimensional homogeneous incompressible fluid. The known large time existence results are due to C. Kenig, G. Ponce and L. Vega (2003) [16] and concern the interaction of two filaments and particular configurations of three filaments. In this article we prove large time existence results for particular configurations of four nearly parallel filaments and for a class of configurations of N   nearly parallel filaments for any N?2$N?2$. We also show the existence of travelling wave type dynamics. Finally we describe configurations leading to collision.     

HPLC determination of majdine in Vinca herbacea

A reliable HPLC method coupled with DAD detection was developed and validated for determination of majdine in Vinca herbacea. The chromatographic separation was carried out on a Symmetry C18 column (250 mm x 4.6 mm, 5 microm, Waters) with an isocratic solvent system of 25 mM potassium phosphate buffer (pH = 3.0)-acetonitrile. UV detection was performed at 225 nm. Good linear behavior over the investigated concentration range was observed with the value of r2 > 0.9978. The method was reproducible with intra- and inter-day variations of less than 4.38%. The proposed method was linear, accurate, precise and specific. The validated method was successfully applied to quantify majdine in various parts of V. herbacea, which was collected during the flowering months of April and May. The results indicated that the developed HPLC method could be used for the quality control of V. herbacea and for the standardization of its extracts in majdine.     

Formation of nanometric HT-LiCoO(2) by a precipitation and aging process in an alcoholic solution

In this paper, we detailed the formation/evolution of precipitates in alcoholic media containing Co(II+) and Li(+) species, together with the evolution of the composition and structure/texture of the resulting solid phases during the aging process at controlled constant temperature. While the end product is found to be well-crystallized HT-LiCoO(2), its formation is shown to result from a two-step process enlisting the initial fast precipitation of β-HCoO(2) and then its slow dissolution followed by recrystallization of the lithium-containing material. These results were obtained through combined X-ray diffraction, Raman and IR spectroscopy, elemental and oxidation-state analysis, and high-resolution transmission electron microscopy/selected-area electron diffraction observations. Depending on the cationic concentration, the size of the precipitated material can be controlled within the nanometric range. The electrochemical performances of these aged materials are slightly improved compared to those of the directly precipitated ones that we previously reported. The main limitation of these materials remains the presence of surface protons.     

Antiplasmodial activity of three bisbenzylisoquinoline alkaloids from the tuber of Stephania rotunda

Three bisbenzylisoquinoline alkaloids were isolated for the first time from Stephania rotunda tuber. Their structures were elucidated by spectroscopic methods and their antiplasmodial activity was investigated in vitro on chloroquine resistant Plasmodium falciparum strain W2. These alkaloids were identified as 2-norcepharanthine (1), cepharanoline (2) and fangchinoline (3). In vitro, they displayed significant antiplasmodial activity with inhibitory concentration 50 values of 0.3, 0.2 and 0.3 μM.     

Metabolic phenotyping of human plasma by 1H‐NMR at high and medium magnetic field strengths: a case study for lung cancer

Accurate identification and quantification of human plasma metabolites can be challenging in crowded regions of the NMR spectrum with severe signal overlap. Therefore, this study describes metabolite spiking experiments on the basis of which the NMR spectrum can be rationally segmented into well‐defined integration regions, and this for spectrometers having magnetic field strengths corresponding to ¹H resonance frequencies of 400 MHz and 900 MHz. Subsequently, the integration data of a case–control dataset of 69 lung cancer patients and 74 controls were used to train a multivariate statistical classification model for both field strengths. In this way, the advantages/disadvantages of high versus medium magnetic field strength were evaluated. The discriminative power obtained from the data collected at the two magnetic field strengths is rather similar, i.e. a sensitivity and specificity of respectively 90 and 97% for the 400 MHz data versus 88 and 96% for the 900 MHz data. This shows that a medium‐field NMR spectrometer (400–600 MHz) is already sufficient to perform clinical metabolomics. However, the improved spectral resolution (reduced signal overlap) and signal‐to‐noise ratio of 900 MHz spectra yield more integration regions that represent a single metabolite. This will simplify the unraveling and understanding of the related, disease disturbed, biochemical pathways. Copyright © 2017 John Wiley & Sons, Ltd.     

Phase-Transfer Catalytic Alkylation of Hydroperoxides: A Convenient Route to Mixed Dialkyl Peroxides

The solid-liquid phase transfer catalytic alkylation of hydroperoxides using solid potassium hydroxide as a base and TEBAC as a phase transfer catalyst is reported. When the alkylating agent is a primary bromide, this reaction represents a simple and quick method for the synthesis of mixed dialkyl peroxides in fair yields.