Well-posed boundary value problems for integrable evolution equations on a finite interval

We consider boundary value problems posed on an interval [0,L] for an arbitrary linear evolution equation in one space dimension with spatial derivatives of order n. We characterize a class of such problems that admit a unique solution and are well posed in this sense. Such well-posed boundary value problems are obtained by prescribing N conditions at x=0 and n–N conditions at x=L, where N depends on n and on the sign of the highest-degree coefficient n in the dispersion relation of the equation. For the problems in this class, we give a spectrally decomposed integral representation of the solution; moreover, we show that these are the only problems that admit such a representation. These results can be used to establish the well-posedness, at least locally in time, of some physically relevant nonlinear evolution equations in one space dimension.

Integrable evolution equations in time-dependent domains

We discuss the implementation of a method of solving initial boundary value problems in the case of integrable evolution equations in a time-dependent domain. This method is applied to a dispersive linear evolution equation with spatial derivatives of arbitrary order and to the defocusing nonlinear Schrödinger equation, in the domain l(t)

Sonogashira coupling on an extended gold surface in vacuo: reaction of phenylacetylene with iodobenzene on Au(111)

Temperature-programmed reaction measurements supported by scanning tunneling microscopy have shown that phenylacetylene and iodobenzene react on smooth Au(111) under vacuum conditions to yield biphenyl and diphenyldiacetylene, the result of homocoupling of the reactant molecules. They also produce diphenylacetylene, the result of Sonogashira cross-coupling, prototypical of a class of reactions that are of paramount importance in synthetic organic chemistry and whose mechanism remains controversial. Roughened Au(111) is completely inert toward all three reactions, indicating that the availability of crystallographically well-defined adsorption sites is crucially important. High-resolution X-ray photoelectron spectroscopy and near-edge X-ray absorption fine structure spectroscopy show that the reactants are initially present as intact, essentially flat-lying molecules and that the temperature threshold for Sonogashira coupling coincides with that for C−I bond scission in the iodobenzene reactant. The fractional-order kinetics and low temperature associated with desorption of the Sonogashira product suggest that the reaction occurs at the boundaries of islands of adsorbed reactants and that its appearance in the gas phase is rate-limited by the surface reaction. These findings demonstrate unambiguously and for the first time that this heterogeneous cross-coupling chemistry is an intrinsic property of extended, metallic pure gold surfaces: no other species, including solvent molecules, basic or charged (ionic) species are necessary to mediate the process.

Evaluation of NRC, UC Davis and ADAS approaches to estimate the metabolizable energy values of feeds at maintenance energy intake from equations utilizing chemical assays and in vitro determinations

Feed samples received by commercial analytical laboratories are often undefined or mixed varieties of forages, originate from various agronomic or geographical areas of the world, are mixtures (e.g., total mixed rations) and are often described incompletely or not at all. Six unified single equation approaches to predict the metabolizable energy (ME) value of feeds determined in sheep fed at maintenance ME intake were evaluated utilizing 78 individual feeds representing 17 different forages, grains, protein meals and by-product feedstuffs. The predictive approaches evaluated were two each from National Research Council [National Research Council (NRC), Nutrient Requirements of Dairy Cattle, seventh revised ed. National Academy Press, Washington, DC, USA, 2001], University of California at Davis (UC Davis) and ADAS (Stratford, UK). Slopes and intercepts for the two ADAS approaches that utilized in vitro digestibility of organic matter and either measured gross energy (GE), or a prediction of GE from component assays, and one UC Davis approach, based upon in vitro gas production and some component assays, differed from both unity and zero, respectively, while this was not the case for the two NRC and one UC Davis approach. However, within these latter three approaches, the goodness of fit (r(2)) increased from the NRC approach utilizing lignin (0.61) to the NRC approach utilizing 48 h in vitro digestion of neutral detergent fibre (NDF:0.72) and to the UC Davis approach utilizing a 30 h in vitro digestion of NDF (0.84). The reason for the difference between the precision of the NRC procedures was the failure of assayed lignin values to accurately predict 48 h in vitro digestion of NDF. However, differences among the six predictive approaches in the number of supporting assays, and their costs, as well as that the NRC approach is actually three related equations requiring categorical description of feeds (making them unsuitable for mixed feeds) while the ADAS and UC Davis approaches are single equations, suggests that the procedure of choice will vary dependent Upon local conditions, specific objectives and the feedstuffs to be evaluated. In contrast to the evaluation of the procedures among feedstuffs, no procedure was able to consistently discriminate the ME values of individual feeds within feedstuffs determined in vivo, suggesting that the quest for an accurate and precise ME predictive approach among and within feeds, may remain to be identified. (C) 2004 Elsevier B.V. All rights reserved.

Host niches and defensive extended phenotypes structure parasitoid wasp communities

Oak galls are spectacular extended phenotypes of gallwasp genes in host oak tissues and have evolved complex morphologies that serve, in part, to exclude parasitoid natural enemies. Parasitoids and their insect herbivore hosts have coevolved to produce diverse communities comprising about a third of all animal species. The factors structuring these communities, however, remain poorly understood. An emerging theme in community ecology is the need to consider the effects of host traits, shaped by both natural selection and phylogenetic history, on associated communities of natural enemies. Here we examine the impact of host traits and phylogenetic relatedness on 48 ecologically closed and species-rich communities of parasitoids attacking gall-inducing wasps on oaks. Gallwasps induce the development of spectacular and structurally complex galls whose species- and generation-specific morphologies are the extended phenotypes of gallwasp genes. All the associated natural enemies attack their concealed hosts through gall tissues, and several structural gall traits have been shown to enhance defence against parasitoid attack. Here we explore the significance of these and other host traits in predicting variation in parasitoid community structure across gallwasp species. In particular, we test the "Enemy Hypothesis,'' which predicts that galls with similar morphology will exclude similar sets of parasitoids and therefore have similar parasitoid communities. Having controlled for phylogenetic patterning in host traits and communities, we found significant correlations between parasitoid community structure and several gall structural traits (toughness, hairiness, stickiness), supporting the Enemy Hypothesis. Parasitoid community structure was also consistently predicted by components of the hosts' spatiotemporal niche, particularly host oak taxonomy and gall location (e.g., leaf versus bud versus seed). The combined explanatory power of structural and spatiotemporal traits on community structure can be high, reaching 62% in one analysis. The observed patterns derive mainly from partial niche specialisation of highly generalist parasitoids with broad host ranges (>20 hosts), rather than strict separation of enemies with narrower host ranges, and so may contribute to maintenance of the richness of generalist parasitoids in gallwasp communities. Though evolutionary escape from parasitoids might most effectively be achieved via changes in host oak taxon, extreme conservatism in this trait for gallwasps suggests that selection is more likely to have acted on gall morphology and location. Any escape from parasitoids associated with evolutionary shifts in these traits has probably only been transient, however, due to subsequent recruitment of parasitoid species already attacking other host galls with similar trait combinations.

Extended-chain, multinuclear transition metal complexes bridged by cyanodiazenido(1-), [N=N-C=N](-), ligands

Extended-chain complexes containing multiple transition metal centres linked by conjugated mu-cyanodiazenido(1-) ligands [N= N-C N]-have been obtained by reaction of trans-[BrW(dppe)(2)(N2CN)], 1, [dppe = 1,2-bis(diphenylphosphino) ethane] with dirhodium(II) tetra-acetate, bis(benzonitrile) palladium(II) dichloride, and bis(aqua) M(II) bis(hexa. uoroacetylacetonate) (M = Mn, Ni, Cu, Zn): stronger Lewis acids such as tetrakis(acetonitrile) palladium(II) tetra. uoroborate and boron trifl. uoride promote hydrolysis of complex 1, leading to the isolation of a novel carbamoylhydrazido(2-) complex, trans-[BrW(dppe) 2(N2HC=ONH2)](+)[BF4](-).

A reaction surface Hamiltonian study of malonaldehyde

We report calculations using a reaction surface Hamiltonian for which the vibrations of a molecule are represented by 3N-8 normal coordinates, Q, and two large amplitude motions, s(1) and s(2). The exact form of the kinetic energy operator is derived in these coordinates. The potential surface is first represented as a quadratic in Q, the coefficients of which depend upon the values of s(1),s(2) and then extended to include up to Q(6) diagonal anharmonic terms. The vibrational energy levels are evaluated by solving the variational secular equations, using a basis of products of Hermite polynomials and appropriate functions of s(1),s(2). Our selected example is malonaldehyde (N=9) and we choose as surface parameters two OH distances of the migrating H in the internal hydrogen transfer. The reaction surface Hamiltonian is ideally suited to the study of the kind of tunneling dynamics present in malonaldehyde. Our results are in good agreement with previous calculations of the zero point tunneling splitting and in general agreement with observed data. Interpretation of our two-dimensional reaction surface states suggests that the OH stretching fundamental is incorrectly assigned in the infrared spectrum. This mode appears at a much lower frequency in our calculations due to substantial transition state character. (c) 2006 American Institute of Physics.