Synthesis and crystal structure of a novel octa-aqua bridged star-shaped Ni4K complex

A penta-nuclear. star-shaped hetero-metallic compound containing a unique Ni4KO8 core has been synthesized. The X-ray single crystal structure analysis reveals that in the complex, [K(Ni(LH)(2))(4)(OH2)(8)](Br)(ClO4)(8)center dot 11H(2)O (LH=(CH3)(2)HN+(CH2)(3)N=CHC6H4O-) the eight coordinate central K+ ion is encapsulated by four terminal [Ni(LH)(2)](2+) units through the double water bridges between K+ and each Ni(II) ions.

Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

A new frequency-uniform coercive boundary integral equation for acoustic scattering

A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this integral operator is coercive in L2(Γ) (where Γ is the surface of the scatterer) for all Lipschitz star-shaped domains. Moreover, the coercivity is uniform in the wavenumber k = ω/c, where ω is the frequency and c is the speed of sound. The new boundary integral operator, which we call the “star-combined” potential operator, is a slight modification of the standard combined potential operator, and is shown to be as easy to implement as the standard one. Additionally, to the authors' knowledge, it is the only second-kind integral operator for which convergence of the Galerkin method in L2(Γ) is proved without smoothness assumptions on Γ except that it is Lipschitz. The coercivity of the star-combined operator implies frequency-explicit error bounds for the Galerkin method for any approximation space. In particular, these error estimates apply to several hybrid asymptoticnumerical methods developed recently that provide robust approximations in the high-frequency case. The proof of coercivity of the star-combined operator critically relies on an identity first introduced by Morawetz and Ludwig in 1968, supplemented further by more recent harmonic analysis techniques for Lipschitz domains.

Vekua theory for the Helmholtz operator

Vekua operators map harmonic functions defined on domain in \mathbb R2R2 to solutions of elliptic partial differential equations on the same domain and vice versa. In this paper, following the original work of I. Vekua (Ilja Vekua (1907–1977), Soviet-Georgian mathematician), we define Vekua operators in the case of the Helmholtz equation in a completely explicit fashion, in any space dimension N ≥ 2. We prove (i) that they actually transform harmonic functions and Helmholtz solutions into each other; (ii) that they are inverse to each other; and (iii) that they are continuous in any Sobolev norm in star-shaped Lipschitz domains. Finally, we define and compute the generalized harmonic polynomials as the Vekua transforms of harmonic polynomials. These results are instrumental in proving approximation estimates for solutions of the Helmholtz equation in spaces of circular, spherical, and plane waves.

Stability results for the time-harmonic Maxwell equations with impedance boundary conditions

We consider the time-harmonic Maxwell equations with constant coefficients in a bounded, uniformly star-shaped polyhedron. We prove wavenumber-explicit norm bounds for weak solutions. This result is pivotal for convergence proofs in numerical analysis and may be a tool in the analysis of electromagnetic boundary integral operators.

Is the Helmholtz equation really sign-indefinite?

The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in the sense that the bilinear forms cannot be bounded below by a positive multiple of the appropriate norm squared. This is often for a good reason, since in bounded domains under certain boundary conditions the solution of the Helmholtz equation is not unique at wavenumbers that correspond to eigenvalues of the Laplacian, and thus the variational problem cannot be sign-definite. However, even in cases where the solution is unique for all wavenumbers, the standard variational formulations of the Helmholtz equation are still indefinite when the wavenumber is large. This indefiniteness has implications for both the analysis and the practical implementation of finite element methods. In this paper we introduce new sign-definite (also called coercive or elliptic) formulations of the Helmholtz equation posed in either the interior of a star-shaped domain with impedance boundary conditions, or the exterior of a star-shaped domain with Dirichlet boundary conditions. Like the standard variational formulations, these new formulations arise just by multiplying the Helmholtz equation by particular test functions and integrating by parts.

New radiocarbon accelerator dates on artefacts from the early Mesolithic site of Star Carr, North Yorkshire

For the well-known early Mesolithic site of Star Carr, dating of organic artefacts by accelerator mass spectrometry (AMS) has been hampered by treatment of bone and antler recovered during the original excavations with preservatives. Some, untreated, artefacts were, however, collected after Clark's excavation in 1950. Four of these artefacts were AMS dated in 1995, but two of the dates were significantly younger than the others, and were questionable due to their low collagen yields. These suspect samples have now been re-analysed, demonstrating that all four artefacts are of similar date. The significance of these dates for the chronology of Star Carr is discussed.

Water-soluble, unimolecular containers based on amphiphilic multiarm star block copolymers

A new class of water-soluble, amphiphilic star block copolymers with a large number of arms was prepared by sequential atom transfer radical polymerization (ATRP) of n-butyl methacrylate (BMA) and poly( ethylene glycol) methyl ether methacrylate (PEGMA). As the macroinitiator for the ATRP, a 2-bromoisobutyric acid functionalized fourth-generation hyperbranched polyester (Boltorn H40) was used, which allowed the preparation of star polymers that contained on average 20 diblock copolymer arms. The synthetic concept was validated by AFM experiments, which allowed direct visualization of single molecules of the multiarm star block copolymers. DSC and SAXS experiments on bulk samples suggested a microphase-separated structure, in agreement with the core-shell architecture of the polymers. SAXS experiments on aqueous solutions indicated that the star block copolymers can be regarded as unimolecular micelles composed of a PBMA core and a diffuse PPEGMA corona. The ability of the polymers to encapsulate and release hydrophobic guests was evaluated using H-1 NMR spectroscopy. In dilute aqueous solution, these polymers act as unimolecular containers that can be loaded with up to 27 wt % hydrophobic guest molecules.

Mapping fibre orientation in complex-shaped biological systems with micrometre resolution by scanning X-ray microdiffraction

A fully automated procedure to extract and to image local fibre orientation in biological tissues from scanning X-ray diffraction is presented. The preferred chitin fibre orientation in the flow sensing system of crickets is determined with high spatial resolution by applying synchrotron radiation based X-ray microbeam diffraction in conjunction with advanced sample sectioning using a UV micro-laser. The data analysis is based on an automated detection of azimuthal diffraction maxima after 2D convolution filtering (smoothing) of the 2D diffraction patterns. Under the assumption of crystallographic fibre symmetry around the morphological fibre axis, the evaluation method allows mapping the three-dimensional orientation of the fibre axes in space. The resulting two-dimensional maps of the local fibre orientations - together with the complex shape of the flow sensing system - may be useful for a better understanding of the mechanical optimization of such tissues.

Fastidiosipila sanguinis gen. nov., sp nov., a new Gram-positive, coccus-shaped organism from human blood

Phenotypic and phylogenetic studies were performed on two strains of an unidentified Gram-positive, fastidious, non-spore-forming, coccus-shaped bacterium recovered from human blood. The organism was catalase-negative and grew under strictly anaerobic conditions and in the presence of 2 and 6% O-2. Comparative 16S rRNA gene sequencing demonstrated that the unidentified bacterium was, phylogenetically, far removed from peptostreptococci and related Gram-positive coccus-shaped organisms, but exhibited a phylogenetic association with Clostridium rRNA cluster III [as defined by Collins et al, Int J Syst Bacteriol 44 (1994), 812-826]. Sequence divergence values of 15% or more were observed between the unidentified bacterium and all other recognized species within this and related rRINIA clostridial clusters. Treeing analysis showed that the unknown bacterium formed a deep line branching at the periphery of rRNA cluster III and represents a hitherto unknown genus within this supra-generic grouping. On the basis of both phylogenetic and phenotypic evidence, it is proposed that the unknown bacterium from blood be classified in a new genus, Fastidiosipila gen. nov., as Fastidiosipila sanguinis sp, nov. The type strain of Fastidiosipila sanguinis is CCUG 47711(T) (= CIP 108292(T)).

Atopococcus tabaci gen. nov., sp nov., a novel Gram-positive, catalase-negative, coccus-shaped bacterium isolated from tobacco

A novel Gram-positive, aerobic, catalase-negative, coccus-shaped organism originating from tobacco was characterized using phenotypic and molecular taxonomic methods. The organism contained a cell wall murein based on L-lysine (variation A4 alpha, type L-lysine-L-glutamic acid), synthesized long-chain cellular fatty acids of the straight-chain saturated and monounsaturated types (with C(16:1)omega 9, C-16:0 and C(18:1)omega 9 predominating) and possessed a DNA G+C content of 46 mol%. Based on morphological, biochemical and chemical characteristics, the coccus-shaped organism did not conform to any presently recognized taxon. Comparative 16S rRNA gene sequencing studies confirmed the distinctiveness of the unknown coccus, with the bacterium displaying sequence divergence values of greater than 7% with other recognized Gram-positive taxa. Treeing analysis reinforced its distinctiveness, with the unidentified organism forming a relatively long subline branching at the periphery of an rRNA gene sequence cluster which encompasses the genera Alloiococcus, Allolustis, Alkalibacterium, Atopostipes, Dolosigranulum and Marinilactibacillus. Based on phenotypic and molecular phylogenetic evidence, it is proposed that the unknown organism from tobacco be classified as a new genus and species, Atopococcus tabaci gen. nov., sp. nov. The type strain of Atopococcus tabaci is CCUG 48253(T) (= CIP 108502(T)).

Allofustis seminis gen. nov., sp. nov., a novel Gram-positive, catalase-negative, rod-shaped bacterium from pig semen

An unknown Gram-positive, catalase-negative, facultatively anaerobic, non-spore-forming, rod-shaped bacterium originating from semen of a pig was characterized using phenotypic, molecular chemical and molecular phylogenetic methods. Chemical studies revealed the presence of a directly cross-linked cell wall murein based on L-lysine and a DNA G + C content of 39 mol%. Comparative 16S rRNA gene sequencing showed that the unidentified rod-shaped organism formed a hitherto unknown subline related, albeit loosely, to Alkalibacterium olivapovliticus, Alloiococcus otitis, Dolosigranulum pigrum and related organisms, in the low-G + C-content Gram-positive bacteria. However, sequence divergence values of > 11 % from these recognized taxa. clearly indicated that the novel bacterium represents a separate genus. Based on phenotypic and phylogenetic considerations, it is proposed that the unknown bacterium from pig semen be classified as a new genus and species, Allofustis seminis gen. nov., sp. nov. The type strain is strain 01-570-1(T) (=CCUG 45438(T)=CIP 107425(T)).

Largest connected component of a star graph with faulty vertices

In order to make a full evaluation of an interconnection network, it is essential to estimate the minimum size of a largest connected component of this network provided the faulty vertices in the network may break its connectedness. Star graphs are recognized as promising candidates for interconnection networks. This article addresses the size of a largest connected component of a faulty star graph. We prove that, in an n-star graph (n >= 3) with up to 2n-4 faulty vertices, all fault-free vertices but at most two form a connected component. Moreover, all fault-free vertices but exactly two form a connected component if and only if the set of all faulty vertices is equal to the neighbourhood of a pair of fault-free adjacent vertices. These results show that star graphs exhibit excellent fault-tolerant abilities in the sense that there exists a large functional network in a faulty star graph.