Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

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)

Mapping the landscape of the lymphocytic choriomeningitis virus stable signal peptide reveals novel functional domains

The stable signal peptide (SSP) of the lymphocytic choriomeningitis virus surface glycoprotein precursor has several unique characteristics. The SSP is unusually long, at 58 amino acids, and contains two hydrophobic domains, and its sequence is highly conserved among both Old and New World arenaviruses. To better understand the functions of the SSP, a panel of point and deletion mutants was created by in vitro mutagenesis to target the highly conserved elements within the SSP. We were also able to confirm critical residues required for separate SSP functions by trans-complementation. Using these approaches, it was possible to resolve functional domains of the SSP. In characterizing our SSP mutants, we discovered that the SSP is involved in several distinct functions within the viral life cycle, beyond translocation of the viral surface glycoprotein precursor into the endoplasmic reticulum lumen. The SSP is required for efficient glycoprotein expression, posttranslational maturation cleavage of GP1 and GP2 by SKI-1/S1P protease, glycoprotein transport to the cell surface plasma membrane, formation of infectious virus particles, and acid pH-dependent glycoprotein-mediated cell fusion.

Improved display of synthetic IgG-binding domains on the baculovirus surface

Improved display of foreign protein moieties in combination with beneficial alteration of the viral surface properties should be of value for targeted and enhanced gene delivery. Here, we describe a vector based on Autographa californica multiple nucleopolyhedrovirus (AcMNPV) displaying synthetic IgG-bincling domains (ZZ) of protein A fused to the transmembrane anchor of vesicular stomatitis virus (VSV) G protein. This display vector was equipped with a GFP/EGFP expression cassette enabling fluorescent detection in both insect and mammalian cells. The virus construct displayed the biologically active fusion protein efficiently and showed increased binding capacity to IgG. As the display is carried out using a membrane anchor of foreign origin, gp64 is left intact for virus entry, which may increase gene expression in the transduced mammalian cells. In addition, the viral vector can be targeted to any desired cell type via binding of ZZ domains when an appropriate IgG antibody is available.

Mapping CD55 function: the structure of two pathogen-binding domains at 1.7 A

Decay-accelerating factor (CD55), a regulator of the alternative and classical pathways of complement activation, is expressed on all serum-exposed cells. It is used by pathogens, including many enteroviruses and uropathogenic Escherichia coli, as a receptor prior to infection. We describe the x-ray structure of a pathogen-binding fragment of human CD55 at 1.7 A resolution containing two of the three domains required for regulation of human complement. We have used mutagenesis to map biological functions onto the molecule; decay-accelerating activity maps to a single face of the molecule, whereas bacterial and viral pathogens recognize a variety of different sites on CD55.

Anion-directed synthesis of metal-organic frameworks based on 2-picolinate Cu(II) complexes: a ferromagnetic alternating chain and two unprecedented ferromagnetic fish backbone chains

Three new polynuclear copper(II) complexes of 2-picolinic acid (Hpic), {[Cu-2(pic)(3)(H2O)]ClO4}(n) (1), {[Cu-2(pic)(3)(H2O)]BF4}(n) (2), and [Cu-2(pic)3(H2O)(2)(NO3)](n) (3), have been synthesized by reaction of the "metalloligand" [Cu-(pic)(2)] with the corresponding copper(II) salts. The compounds are characterized by single-crystal X-ray diffraction analyses and variable-temperature magnetic measurements. Compounds 1 and 2 are isomorphous and crystallize in the triclinic system with space group P (1) over bar, while 3 crystallizes in the monoclinic system with space group P2(1)/n. The structural analyses reveal that complexes 1 and 2 are constructed by "fish backbone" chains through syn-anti (equatorial-equatorial) carboxylate bridges, which are linked to one another by syn-anti (equatorial-axial) carboxylate bridges, giving rise to a rectangular grid-like two-dimensional net. Complex 3 is formed by alternating chains of syn-anti carboxylate-bridged copper(II) atoms, which are linked together by strong H bonds involving coordinated nitrate ions and water molecules and uncoordinated oxygen atoms from carboxylate groups. The different coordination ability of the anions along with their involvement in the H-bonding network seems to be responsible for the difference in the final polymeric structures. Variable-temperature (2-300 K) magnetic susceptibility measurement shows the presence of weak ferromagnetic coupling for all three complexes that have been fitted with a fish backbone model developed for 1 and 2 (J = 1.74 and 0.99 cm(-1); J' = 0.19 and 0.25 cm(-1), respectively) and an alternating chain model for 3 (J = 1.19 cm(-1) and J' = 1.19 cm(-1)).

Pyrene-functionalised, alternating copolyimide for sensing nitroaromatic compounds

A novel, pyrene-functionalised copolymer has been synthesised in a single step via imidisation of poly(maleic anhydride-alt-1-octadecene) with 1-pyrenemethylamine, and its potential for the detection of volatile nitro aromatic compounds (NACs) evaluated. The new copolymer forms complexes in solution with NACs such as 2,5-dinitrobenzonitrile, as shown by H-1 NMR, UV-vis and fluorescence spectroscopy. Moreover, thin films of this copolymer, cast from THF solution, undergo almost instantaneous fluorescence quenching when exposed to the vapour of 2,5-dinitrobenzonitrile (a model for TNT) at ambient temperatures and pressures.

Two new mu-(1,3-azido)-bridged polymers: alternating single and double bridges in a 1D nickel(II) complex and uniform bridge in a 2D copper(II) complex: Syntheses, single-crystal structures and magnetic studies

Two polymeric azido bridged complexes [Ni2L2(N-3)(3)](n)(ClO4). (1) and [Cu(bpdS)(2)(N-3)],(ClO4),(H2O)(2.5n) (2) [L = Schiff base, obtained from the condensation of pyridine-2-aldehyde with N,N,2,2-tetramethyl-1,3-propanediamine; bpds = 4,4'-bipyridyl disulfide] have been synthesized and their crystal structures have been determined. Complex 1, C26H42ClN15Ni2O4, crystallizes in a triclinic system, space group P1 with a 8.089(13), b = 9.392(14), c = 12.267(18) angstrom, a = 107.28(l), b 95.95(1), gamma = 96.92(1)degrees and Z = 2; complex 2, C20H21ClCuN7O6.5S4, crystallizes in an orthorhombic system, space group Pnna with a = 10.839(14), b = 13.208(17), c = 19.75(2) angstrom and Z = 4. The crystal structure of I consists of 1D polymers of nickel(L) units, alternatively connected by single and double bridging mu-(1,3-N-3) ligand with isolated perchlorate anions. Variable temperature magnetic susceptibility data of the complex have been measured and the fitting,of magnetic data was carried out applying the Borris-Almenar formula for such types of alternating one-dimensional S = 1 systems, based on the Hamiltonian H = -J Sigma(S2iS2i-1 + aS(2i)S(2i+1)). The best-fit parameters obtained are J = -106.7 +/- 2 cm(-1); a = 0.82 +/- 0.02; g = 2.21 +/- 0.02. Complex 2 is a 2D network of 4,4 topology with the nodes occupied by the Cu-II ions, and the edges formed by single azide and double bpds connectors. The perchlorate anions are located between pairs of bpds. The magnetic data have been fitted considering the complex as a pseudo-one-dimensional system, with all copper((II)) atoms linked by [mu(1,3-azido) bridging ligands at axial positions (long Cu...N-3 distances) since the coupling through long bpds is almost nil. The best-fit parameters obtained with this model are J = -1.21 +/- 0.2 cm(-1), g 2.14 +/- 0.02. (c) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2005).

Cu-II acetate complexes involving N,N,O donor Schiff base ligands: Mono-atomic oxygen bridged dimers and alternating chains of the dimers and Cu-2(OAc)(4)

Two tridentate N,N,O donor Schiff bases, HL1 (4-(2-ethylamino-ethylimino)-pentan-2-one) and HL2 (3-(2-amino-propylimino)-1-phenyl-butan-1-one) on reaction with Cu-II acetate in presence of triethyl amine yielded two basal-apical, mono-atomic acetate oxygen-bridging dimeric copper(II) complexes, [Cu2L21(OAc)(2)] (1), [Cu2L22(OAc)(2)] (2). Whereas two other similar tridentate ligands HL3 (4-(2-amino-propylimino)-pentane-2-one) and HL3 (3-(2-amino-ethylimino)-1-phenyl-butan-1-one) under the same conditions produced a mixture of the corresponding dinners and a one-dimensional alternating chain of the dimer and copper acetate moiety, [Cu4L23(OAc)(6)](n) (3) and [Cu4L24(OAc)(6)](n) (4), formed by a very rare mu(3) bridging mode of the acetate ion. All four complexes (1-4) have been characterized by X-ray crystallography. The isotropic Hamiltonian, H = -JS(1)S(2) has been used to interpret the magnetic data. Magnetic measurements of 1 and 2 in the temperature range 2-300 K reveal a very weak antiferromagnetic coupling for both complexes U = -0.56 and -1.19 cm(-1) for 1 and 2, respectively). (C) 2008 Elsevier Ltd. All rights reserved.

Microblock ionomers: a new concept in high temperature, swelling-resistant membranes for PEM fuel cells

A novel series of polyaromatic ionomers with similar equivalent weights but very different sulphonic acid distributions along the ionomer backbone has been designed and prepared. By synthetically organising the sequence-distribution so that it consists of fully defined ionic segments (containing singlets, doublets or quadruplets of sulphonic acid groups) alternating strictly with equally well-defined nonionic spacer segments, a new class of polymers which may be described as microblock ionomers has been developed. These materials exhibit very different properties and morphologies from analogous randomly substituted systems. Progressively extending the nonionic spacer length in the repeat unit (maintaining a constant equivalent weight by increasing the degree of sulphonation. of the ionic segment) leads to an increasing degree of nanophase separation between hydrophilic and hydrophobic domains in these materials. Membranes cast from ionomers with the more highly phase-separated morphologies show significantly higher onset temperatures for uncontrolled swelling in water. This new type of ionomer design has enabled the fabrication of swelling-resistant hydrocarbon membranes, suitable for fuel cell operation, with very much higher ion exchange capacities (>2 meq g(-1)) than those previously reported in the literature. When tested in a fuel cell at high temperature (120 degrees C) and low relative humidity (35% RH), the best microblock membrane matched the performance of Nafion 112. Moreover, comparative low load cycle testing of membrane -electrode assemblies suggests that the durability of the new membranes under conditions of high temperature and low relative humidity is superior to that of conventional perfluorinated materials.

Ontology supported comparison in vague domains

It is problematic to use standard ontology tools when describing vague domains. Standard ontologies are designed to formally define one view of a domain, and although it is possible to define disagreeing statements, it is not advisable, as the resulting inferences could be incorrect. Two different solutions to the above problem in two different vague domains have been developed and are presented. The first domain is the knowledge base of conversational agents (chatbots). An ontological scripting language has been designed to access ontology data from within chatbot code. The solution developed is based on reifications of user statements. It enables a new layer of logics based on the different views of the users, enabling the body of knowledge to grow automatically. The second domain is competencies and competency frameworks. An ontological framework has been developed to model different competencies using the emergent standards. It enables comparison of competencies using a mix of linguistic logics and descriptive logics. The comparison results are non-binary, therefore not simple yes and no answers, highlighting the vague nature of the comparisons. The solution has been developed with small ontologies which can be added to and modified in order for the competency user to build a total picture that fits the user’s purpose. Finally these two approaches are viewed in the light of how they could aid future work in vague domains, further work in both domains is described and also in other domains such as the semantic web. This demonstrates two different approaches to achieve inferences using standard ontology tools in vague domains.

Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth

We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth. We show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions. We also prove that in very general situations the free boundary is necessarily the graph of a function.

A simple method of calculating eigenvalues and resonances in domains with infinite regular ends

A new approach is presented for the solution of spectral problems on infinite domains with regular ends, which avoids the need to solve boundary-value problems for many trial values of the spectral parameter. We present numerical results both for eigenvalues and for resonances, comparing with results reported by Aslanyan, Parnovski and Vassiliev.