Neighborhood unions and the cycle cover number of a graph

For several years, the study of neighborhood unions of graphs has given rise to important structural consequences of graphs. In particular, neighborhood conditions that give rise to hamiltonian cycles have been considered in depth. In this paper we generalize these approaches to give a bound on the smallest number of cycles in G containing all the vertices of G. We show that if for all x, y ? V(G), |N(x) ∩ N(y)| ≧ 2n/5 + 1, then V(G) is coverable by at most two cycles. Several related results and extensions to t cycles are also given.     

Native ethylene glycol in wine: Application of a dead volume free,very fast “deans heart-cut” system on-line with multi-chromatography

Data about the existence of native HO? CH₂? CH₂? OH (MEG) in natural wines and champagne has led to delicate questions because of legal decisions already made to declare wine or champagne illegal for sale if the MEG concentrations found are above 10 mg/liter. Action has been taken because of the DEG (diethylene glycol) disaster in European wines of 1985…86. An incorrect legal decision was made due to the belief that MEG cannot be produced biochemically by grape vines. A further reason may be lack of correct data on native MEG trace concentrations, as a result of the special behavior of this diol. As first member of a homologous series whose higher members (C₄) are normally found in all wines at quite high concentration levels, MEG shows extremely adsorptive behavior. The solution of the chromatographic problems is summarized in this paper. MEG concentrations in Riesling as example are in the range of 2 to 6 mg/liter and can easily be increased by biotechnological steps to a level of around 10 to 60 mg/liter. This is again due to the specific adsorptive behavior of MEG, which can be enriched on filter surfaces and displaced when the wine acidity changes with changing types. In order to control and guarantee the qualitative and quantitative results of MEG analyses we used a combination of Deans heart cutting on-line with Multi-Chromatography. It was easy to produce false data by many otherwise useful single column or two-dimensional separation processes, etc.     

Determination of a double Lie groupoid by its core diagram

In a double groupoid S, we show that there is a canonical groupoid structure on the set of those squares of S for which the two source edges are identities; we call this the core groupoid of S. The target maps from the core groupoid to the groupoids of horizontal and vertical edges of S are now base-preserving morphisms whose kernels commute, and we call the diagram consisting of the core groupoid and these two morphisms the core diagram of S. If S is a double Lie groupoid, and each groupoid structure on S satisfies a natural double form of local triviality, we show that the core diagram determines S and, conversely, that a locally trivial double Lie groupoid may be constructed from an abstractly given core diagram satisfying some natural additional conditions.

In the algebraic case, the corresponding result includes the known equivalences between crossed modules, special double groupoids with special connection (Brown and Spencer), and cat¹-groups (Loday). These cases correspond to core diagrams for which both target morphisms are (compatibly) split surjections.     

Validation of a thermal decomposition mechanism of formaldehyde by detection of CH2O and HCO behind shock waves

The thermal decomposition of formaldehyde was investigated behind shock waves at temperatures between 1675 and 2080 K. Quantitative concentration time profiles of formaldehyde and formyl radicals were measured by means of sensitive 174 nm VUV absorption (CH₂O) and 614 nm FM spectroscopy (HCO), respectively. The rate constant of the radical forming channel (1a), CH₂O + M → HCO + H + M, of the unimolecular decomposition of formaldehyde in argon was measured at temperatures from 1675 to 2080 K at an average total pressure of 1.2 bar, k_1a = 5.0 × 10¹⁵ exp(‐308 kJ mol^?1/RT) cm³ mol^?1 s^?1. The pressure dependence, the rate of the competing molecular channel (1b), CH₂O + M → H₂ + CO + M, and the branching fraction β = k_1a/(kA_1a + k_1b) was characterized by a two‐channel RRKM/master equation analysis. With channel (1b) being the main channel at low pressures, the branching fraction was found to switch from channel (1b) to channel (1a) at moderate pressures of 1–50 bar. Taking advantage of the results of two preceding publications, a decomposition mechanism with six reactions is recommended, which was validated by measured formyl radical profiles and numerous literature experimental observations. The mechanism is capable of a reliable prediction of almost all formaldehyde pyrolysis literature data, including CH₂O, CO, and H atom measurements at temperatures of 1200–3200 K, with mixtures of 7 ppm to 5% formaldehyde, and pressures up to 15 bar. Some evidence was found for a self‐reaction of two CH₂O molecules. At high initial CH₂O mole fractions the reverse of reaction (6), CH₂OH + HCO ? CH₂O + CH₂O becomes noticeable. The rate of the forward reaction was roughly measured to be k₆ = 1.5 × 10¹³ cm³ mol^?1 s^?1. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 157–169 2004     

A short synthesis of koniamborine, a naturally occurring pyrano[3,2-b]indole

An expedient synthesis of the alkaloid koniamborine, the only to date isolated naturally occurring pyrano[3,2-b]indole is presented. The key pyrano[3,2-b]indole forming step is a palladium-catalyzed reductive N-heteroannulation of 2-(4-methoxy-2-nitrophenyl)-(4H)-pyrane-4-one.     

Dendritic cells: In the forefront of immunopathogenesis and vaccine development – A review

Dendritic cellls (DCs) comprise an essential component of the immune system. These cells, as antigen presenting cells (APCs) to na?ve T cells, are crucial in the initiation of antigen specific immune responses. In the past years, several DC subsets have been identified in different organs which exert different effects in order to elicit adaptive immune responses. Thus, identification of such DC subsets has led to a better understanding of their distribution and function in the body. In this review, several key properties of the immunobiology, immunopathogenesis and vaccine strategies using DCs will be discussed.     

Pulsed-Field-Gradient Measurements of Time-Dependent Gas Diffusion

Pulsed-field-gradient NMR techniques are demonstrated for measurements of time-dependent gas diffusion. The standard PGSE technique and variants, applied to a free gas mixture of thermally polarized xenon and O₂, are found to provide a reproducible measure of the xenon diffusion coefficient (5.71 × 10⁻⁶m²s⁻¹for 1 atm of pure xenon), in excellent agreement with previous, non-NMR measurements. The utility of pulsed-field-gradient NMR techniques is demonstrated by the first measurement of time-dependent (i.e., restricted) gas diffusion inside a porous medium (a random pack of glass beads), with results that agree well with theory. Two modified NMR pulse sequences derived from the PGSE technique (named the Pulsed Gradient Echo, or PGE, and the Pulsed Gradient Multiple Spin Echo, or PGMSE) are also applied to measurements of time dependent diffusion of laser polarized xenon gas, with results in good agreement with previous measurements on thermally polarized gas. The PGMSE technique is found to be superior to the PGE method, and to standard PGSE techniques and variants, for efficiently measuring laser polarized noble gas diffusion over a wide range of diffusion times.     

The location of median paths on grid graphs

In this paper we consider the location of a path shaped facility on a grid graph. In the literature this problem was extensively studied on particular classes of graphs as trees or series-parallel graphs. We consider here the problem of finding a path which minimizes the sum of the (shortest) distances from it to the other vertices of the grid, where the path is also subject to an additional constraint that takes the form either of the length of the path or of the cardinality. We study the complexity of these problems and we find two polynomial time algorithms for two special cases, with time complexity of O(n) and O(nℓ) respectively, where n is the number of vertices of the grid and ℓ is the cardinality of the path to be located. The literature about locating dimensional facilities distinguishes between the location of extensive facilities in continuous spaces and network facility location. We will show that the problems presented here have a close connection with continuous dimensional facility problems, so that the procedures provided can also be useful for solving some open problems of dimensional facilities location in the continuous case.