Subgroup Separability and Linearity of Certain Graphs of Groups

We show that if the fundamental group of a finite graph of groups with finitely generated Abelian vertex groups is subgroup separable, then it is linear.     

Psuedosymmetry and pseudomerodry or nonmerohedral twinning for the known structure of diaquabis(quinolin‐8‐olato‐κ2N,O)zinc(II)

The structure of the title centrosymmetric compound, [Zn(C₉H₆NO)₂(H₂O)₂], has already been solved three times [Merritt, Cady & Mundy (1954). Acta Cryst. 7 , 473–476; Palenik (1964). Acta Cryst. 17 , 696–700; Chen, Zhang, Shi, Huang, Liang & Zhou (2003). Acta Cryst. E 59 , m814–m815]. The authors of the two most recent papers state that they attained lower R1 values than that obtained in the 1954 paper, but they do not mention that Merritt et al. had derived the structural model from a twinned crystal. Also, from a structural point of view, there are strong indications that the most recent report is in fact the isostructural Cu^II complex already reported by Okabe & Saishu [Acta Cryst. (2001), E 57 , m251–m252] and not the Zn^II complex. The structure of the title compound is reported here based on data obtained from a twinned crystal.     

A [24-MC-6] zinc metallacoronate with a nonsteroidal antiinflammatory drug as the constructing ligand

The interaction of ZnCl(2) with 2-dipyridylketonoxime (=Hpko) and flufenamic acid (=Hfluf) in a basic methanolic solution leads to the formation of a hexanuclear 24-membered metallacoronate, [Zn(6)(OH)(2)(pko)(4)(fluf)(6)] (1), with a [Zn-O-C-O] repeat unit and a nonsteroidal antiinflammatory drug as the constructing ligand. Compound 1 retains its structure in a dimethyl sulfoxide solution, as shown by (1)H NMR spectroscopy and molar conductance.     

Investigation of the zinc(II)-benzoate-2-pyridinealdoxime reaction system

The employment of pyridine-2-carbaldehyde oxime (paoH) in zinc(II) benzoate chemistry, in the absence or presence of azide ions, is described. The syntheses, crystal structures and spectroscopic characterization are reported for the complexes [Zn(O(2)CPh)(2)(paoH)(2)] (1), [Zn(12)(OH)(4)(O(2)CPh)(16)(pao)(4)] (2) and [Zn(4)(OH)(2)(pao)(4)(N(3))(2)] (3). The Zn(II) centre in octahedral 1 is coordinated by two monodentate PhCO(2)(-) groups and two N,N'-chelating paoH ligands. The metallic skeleton of 2 describes a tetrahedron encapsulated in a distorted cube. The {Zn(12)(μ-OH)(4)(μ(3)-ΟR)(4)}(16+) core of the cluster can be conveniently described as consisting of a central {Zn(4)(μ(3)-ΟR)(4)}(4+) cubane subunit (RO(-) = pao(-)) linked to four {Zn(2)(μ-OH)}(3+) subunits via the OH(-) group of each of the latter, which becomes μ(3). The molecule of 3 has an inverse 12-metallacrown-4 topology. Two triply bridging hydroxido groups are accommodated into the metallacrown ring. Each pao(-) ligand adopts the η(1)?:?η(1)?:?η(1)?:?μ coordination mode, chelating one Zn(II) atom and bridging a Zn(II)(2) pair. Complexes 1 and 2 display photoluminescence with maxima at ～355 nm and ～375 nm, upon maximum excitation at 314 nm; the origin of the photoluminescence is discussed.     

Evans Function for Lax Operators with Algebraically Decaying Potentials

We study the instability of algebraic solitons for integrable nonlinear equations in one spatial dimension that include modified KdV, focusing NLS, derivative NLS, and massive Thirring equations. We develop the analysis of the Evans function that defines eigenvalues in the corresponding Lax operators with algebraically decaying potentials. The standard Evans function generically has singularities in the essential spectrum, which may include embedded eigenvalues with algebraically decaying eigenfunctions. We construct a renormalized Evans function and study bifurcations of embedded eigenvalues, when an algebraically decaying potential is perturbed by a generic potential with a faster decay at infinity. We show that the bifurcation problem for embedded eigenvalues can be reduced to cubic or quadratic equations, depending on whether the algebraic potential decays to zero or approaches a nonzero constant. Roots of the bifurcation equations define eigenvalues which correspond to nonlinear waves that are formed from unstable algebraic solitons. Our results provide precise information on the transformation of unstable algebraic solitons in the time-evolution problem associated with the integrable nonlinear equation. Algebraic solitons of the modified KdV equation are shown to transform to either travelling solitons or time-periodic breathers, depending on the sign of the perturbation. Algebraic solitons of the derivative NLS and massive Thirring equations are shown to transform to travelling and rotating solitons for either sign of the perturbation. Finally, algebraic homoclinic orbits of the focusing NLS equation are destroyed by the perturbation and evolve into time-periodic space-decaying solutions.     

Activation de la Ponction Hydroxyle Anomere via les Sels d'Iminium. O-Glycosylation des Tri-O-benzyl-2,3,5-D-arabino et -ribotorannoses

Abstract

The glycosylation reaction based upon anomeric free hydroxyl group activation by its transformation into an alkcxyiminium salt by the action of the N,N-dimethylformamide/phosgene complex has been extended to the pentofuranose series. The mechanism of this glycosylation is discussed. Nine glycosides have been prepared.     

On the Hardness of the Quadratic Assignment Problem with Metaheuristics

Meta-heuristics are a powerful way to approximately solve hard combinatorial optimization problems. However, for a problem, the quality of results can vary considerably from one instance to another. Understanding such a behaviour is important from a theoretical point of view, but also has practical applications such as for the generation of instances during the evaluation stage of a heuristic.In this paper we propose a new complexity measure for the Quadratic Assignment Problem in the context of metaheuristics based on local search, e.g. simulated annealing. We show how the ruggedness coefficient previously introduced by the authors, in conjunction with the well known concept of dominance, provides important features of the search space explored during a local search algorithm, and gives a rather precise idea of the complexity of an instance for these heuristics. We comment previous experimental studies concerning tabu search methods and genetic algorithms with local search in the light of our complexity measure. New computational results with simulated annealing and taboo search are presented.     

Expanding the 3d-4f heterometallic chemistry of the (py)2CO and pyCOpyCOpy ligands: structural, magnetic and Mössbauer spectroscopic studies of two Fe(II)-Gd(III) complexes

Complex [Fe(II)Gd(III){pyCO(OEt)pyCOH(OEt)py}(3)](ClO(4))(2) (1) crystallizes in the Cc space group and contains one hexacoordinate ferrous ion and one enneacoordinate Gd(III) ion. Complex [Fe(2)(II)Gd(III){pyCO(OEt)py}(4)(NO(3))(H(2)O)][Gd(NO(3))(5)](0.5)(ClO(4)) (2) crystallizes in the C2/c space group and contains two hexacoordinate ferrous ions and one octacoordinate Gd(III) ion. Both complexes have been prepared by the metal-assisted ethanolysis of ligands di-2,6-(2-pyridylcarbonyl)pyridine (pyCOpyCOpy, dpcp) and di-2-pyridyl ketone ((py)(2)CO, dpk), which exhibit similar structures. M?ssbauer spectroscopic studies of 2 revealed the presence of two quadrupole-split doublets of equal intensities, each assigned to a ferrous site. These doublets exhibit similar isomer shifts (δ(1) = 1.14 mm s(-1), δ(2) = 1.11 mm s(-1)) but quite different quadrupole splittings (ΔE(Q1) = 3.55 mm s(-1), ΔE(Q2) = 2.74 mm s(-1)). Magnetic studies revealed weak ferromagnetic Fe(II)-Gd(III) interactions for both complexes (J(FeGd) = +0.68 cm(-1), D(Fe) = 12.0 cm(-1) for 1 and J(FeGd) = +0.03 cm(-1), J(FeFe) = -1.73 cm(-1) for 2, according to the -JS(i)S(j) spin-Hamiltonian formalism).     

Special issue on global flow instability and control

This special issue is intended to provide a snapshot of current research in the area of ??Global Flow Instability and Control??. The original papers, and to a certain extent the topic itself, are intimately linked with the series of symposia by the same name that were held in Crete, Greece, between 2001 and 2009. As members of the organizing committees of the Crete symposia, we invited all past participants to contribute, and all papers were reviewed following the strict standards of the journal. This preface gives a brief historical account of events that have shaped ideas in the field over the past decade, followed by a synopsis of the papers published herein.     

An example where separation of variables fails

We present in detail a linear, constant-coefficient initial/boundary value problem for which the classical method of eigenfunction expansions fails. We note that the new method recently introduced by A. Fokas and B. Pelloni (2005) in [3] can be successfully applied to the same problem.