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.     

Facile strategies for the synthesis and crystallization of linear trinuclear nickel(II)-Schiff base complexes with carboxylate bridges: Tuning of coordination geometry and magnetic properties

Three new linear trinuclear nickel(II) complexes, [Ni₃(salpen)₂(OAc)₂(H₂O)₂]·4H₂O (1) (OAc = acetate, CH₃COO⁻), [Ni₃(salpen)₂(OBz)₂] (2) (OBz = benzoate, PhCOO⁻) and [Ni₃(salpen)₂(OCn)₂(CH₃CN)₂] (4) (OCn = cinnamate, PhCHCHCOO⁻), H₂salpen = tetradentate ligand, N,N′-bis(salicylidene)-1,3-pentanediamine have been synthesized and characterized structurally and magnetically. The choice of solvent for growing single crystal was made by inspecting the morphology of the initially obtained solids with the help of SEM study. The magnetic properties of a closely related complex, [Ni₃(salpen)₂(OPh)₂(EtOH)] (3) (OPh = phenyl acetate, PhCH₂COO⁻) whose structure and solution properties have been reported recently, has also been studied here. The structural analyses reveal that both phenoxo and carboxylate bridging are present in all the complexes and the three Ni(II) atoms remain in linear disposition. Although the Schiff base ligand and the syn–syn bridging bidentate mode of the carboxylate group remain the same in complexes 1–4, the change of alkyl/aryl group of the carboxylates brings about systematic variations between six- and five-coordination in the geometry of the terminal Ni(II) centres of the trinuclear units. The steric demand as well as hydrophobic nature of the alkyl/aryl group of the carboxylate is found to play a crucial role in the tuning of the geometry. Variable-temperature (2–300 K) magnetic susceptibility measurements show that complexes 1–4 are antiferromagnetically coupled (J = −3.2(1), −4.6(1), −3.2(1) and −2.8(1) cm⁻¹ in 1–4, respectively). Calculations of the zero-field splitting parameter indicate that the values of D for complexes 1–4 are in the high range (D = +9.1(2), +14.2(2), +9.8(2) and +8.6(1) cm⁻¹ for 1–4, respectively). The highest D value of +14.2(2) and +9.8(2) cm⁻¹ for complexes 2 and 3, respectively, are consistent with the pentacoordinated geometry of the two terminal nickel(II) ions in 2 and one terminal nickel(II) ion in 3.     

Rheological representation of fractional order viscoelastic material models

We develop rheological representations, i.e., discrete spectrum models, for the fractional derivative viscoelastic element (fractional dashpot or springpot). Our representations are generalized Maxwell models or series of Kelvin-Voigt units, which, however, maintain the number of parameters of the corresponding fractional order model. Accordingly, the number of parameters of the rheological representation is independent of the number of rheological units. We prove that the representations converge to the corresponding fractional model in the limit as the number of units tends to infinity. The representations extend to compound fractional derivative models such as the fractional Maxwell model, fractional Kelvin-Voigt model, and fractional standard linear solid. Computational experiments show that the rheological representations are accurate approximations of the fractional order models even for a small number of units.     

Dinuclear Lanthanide(III) Complexes from the Use of Methyl 2-Pyridyl Ketoxime: Synthetic,Structural, and Physical Studies

The first use of methyl 2-pyridyl ketoxime (mepaoH) in homometallic lanthanide(III) [Ln(III)] chemistry is described. The 1:2 reactions of Ln(NO₃)₃·nH₂O (Ln = Nd, Eu, Gd, Tb, Dy; n = 5, 6) and mepaoH in MeCN have provided access to complexes [Ln₂(O₂CMe)₄(NO₃)₂(mepaoH)₂] (Ln = Nd, 1; Ln = Eu, 2; Ln = Gd, 3; Ln = Tb, 4; Ln = Dy, 5); the acetato ligands derive from the Ln^III—mediated hydrolysis of MeCN. The 1:1 and 1:2 reactions between Dy(O₂CMe)₃·4H₂O and mepaoH in MeOH/MeCN led to the all-acetato complex [Dy₂(O₂CMe)₆(mepaoH)₂] (6). Treatment of 6 with one equivalent of HNO₃ gave 5. The structures of 1, 5, and 6 were solved by single-crystal X-ray crystallography. Elemental analyses and IR spectroscopy provide strong evidence that 2–4 display similar structural characteristics with 1 and 5. The structures of 1–5 consist of dinuclear molecules in which the two Ln^III centers are bridged by two bidentate bridging (η¹:η¹:μ₂) and two chelating-bridging (η¹:η²:μ₂) acetate groups. The Ln^III atoms are each chelated by a N,N’-bidentate mepaoH ligand and a near-symmetrical bidentate nitrato group. The molecular structure of 6 is similar to that of 5, the main difference being the presence of two chelating acetato groups in the former instead of the two chelating nitrato groups in the latter. The geometry of the 9-coordinate Ln^III centers in 1, 5 and 6 can be best described as a muffin-type (MFF-9). The 3D lattices of the isomorphous 1 and 5 are built through H-bonding, π⋯π stacking and C-H⋯π interactions, while the 3D architecture of 6 is stabilized by H bonds. The IR spectra of the complexes are discussed in terms of the coordination modes of the organic and inorganic ligands involved. The Eu(III) complex 2 displays a red, metal-ion centered emission in the solid state; the Tb^III atom in solid 4 emits light in the same region with the ligand. Magnetic susceptibility studies in the 2.0–300 K range reveal weak antiferromagnetic intramolecular Gd^III…Gd^III exchange interactions in 3; the J value is −0.09(1) cm⁻¹ based on the spin Hamiltonian Ĥ = −J(Ŝ_Gd1·Ŝ_Gd2).     

Dynamic Optimization of Molecular Weight Distribution Using Orthogonal Collocation on Finite Elements and Fixed Pivot Methods: An Experimental and Theoretical Investigation

In the present study, two numerical methods, namely the orthogonal collocation on finite elements and the fixed pivot technique, are employed to calculate the MWD in an MMA free‐radical batch suspension polymerization reactor operating up to very high conversions (e.g., ≥95%). The theoretical MWD predictions are directly compared with experimentally measured MWDs, obtained from a pilot‐scale batch MMA suspension polymerization reactor. It is shown that there is a very good agreement between model predictions and experimental measurements on both monomer conversion and MWD. Subsequently, two different time‐optimal temperature trajectories are calculated to obtain a polymer having either a narrow or a bimodal MWD in minimum batch time. The calculated time optimal trajectories are then applied, as set point temperature changes, to a pilot plant batch polymerization reactor. It is shown that the measured MWDs are in very good agreement with the off‐line calculated optimal MWDs.