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.     

Successive Michael reactions on chromone derivatives with dimethyl 1,3-acetonedicarboxylate: one-pot synthesis of functionalized benzophenones, benzo[c]chromones and hydroxybenzoylfuroates

Chromones were reacted with dimethyl acetonedicarboxylate in the presence of DBU in THF at room temperature to furnish good yields of products, their structure depending on the substituent at 3-position. Unsubstituted chromones lead to methyl 7-hydroxy-6-oxo-6H-benzo[c]chromone-8-carboxylates 2, whereas by using 3-bromochromone, the methyl furoate 3c along with the unexpected furylcyclopropyl-chromene carboxylate 4c was isolated. Finally, from 3-formyl-chromones functionalized benzophenones 5 were isolated, in good yields. Plausible mechanisms are proposed.     

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.     

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.     

pH-Specific structural speciation of the ternary V(V)-peroxido-betaine system: a chemical reactivity-structure correlation

Vanadium involvement in cellular processes requires deep understanding of the nature and properties of its soluble and bioavailable forms arising in aqueous speciations of binary and ternary systems. In an effort to understand the ternary vanadium-H(2)O(2)-ligand interactions relevant to that metal ion's biological role, synthetic efforts were launched involving the physiological ligands betaine (Me(3)N(+)CH(2)CO(2)(-)) and H(2)O(2). In a pH-specific fashion, V(2)O(5), betaine, and H(2)O(2) reacted and afforded three new, unusual, and unique compounds, consistent with the molecular formulation K(2)[V(2)O(2)(O(2))(4){(CH(3))(3)NCH(2)CO(2))}]·H(2)O (1), (NH(4))(2)[V(2)O(2)(O(2))(4){(CH(3))(3)NCH(2)CO(2))}]·0.75H(2)O (2), and {Na(2)[V(2)O(2)(O(2))(4){(CH(3))(3)NCH(2)CO(2))}(2)]}(n)·4nH(2)O (3). All complexes 1-3 were characterized by elemental analysis; UV/visible, FT-IR, Raman, and NMR spectroscopy in solution and the solid state; cyclic voltammetry; TGA-DTG; and X-ray crystallography. The structures of 1 and 2 reveal the presence of unusual ternary dinuclear vanadium-tetraperoxido-betaine complexes containing [(V(V)═O)(O(2))(2)] units interacting through long V-O bonds. The two V(V) ions are bridged through the oxygen terminal of one of the peroxide groups bound to the vanadium centers. The betaine ligand binds only one of the two V(V) ions. In the case of the third complex 3, the two vanadium centers are not immediate neighbors, with Na(+) ions (a) acting as efficient oxygen anchors and through Na-O bonds holding the two vanadium ions in place and (b) providing for oxygen-containing ligand binding leading to a polymeric lattice. In 1 and 3, interesting 2D (honeycomb) and 1D (zigzag chains) topologies of potassium nine-coordinate polyhedra (1) and sodium octahedra (3), respectively, form. The collective physicochemical properties of the three ternary species 1-3 project the chemical role of the low molecular mass biosubstrate betaine in binding V(V)-diperoxido units, thereby stabilizing a dinuclear V(V)-tetraperoxido dianion. Structural comparisons of the anions in 1-3 with other known dinuclear V(V)-tetraperoxido binary anionic species provide insight into the chemical reactivity of V(V)-diperoxido systems and their potential link to cellular events such as insulin mimesis and anitumorigenicity modulated by the presence of betaine.     

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.     

Reversible core-interconversion of an iron(III) dihydroxo bridged complex

Complexes [Fe(Hhbi)(2)(NO(3))].2EtOH (1.2EtOH) and [Fe(2)(mu-OH)(2)(Hhbi)(4)].2H(2)O.8EtOH (2.2H(2)O.8EtOH) crystallize in the orthorhombic Fdd2 and P4(2)2(1)2 space groups, respectively (Hhbi(-) = the monoanion of 2-(2'-hydroxyphenyl benzimidazole). Complex 1 exhibits paramagnetic relaxation as evidenced by Mossbauer spectroscopy, and significant axial zero-field splitting (1.5 cm(1) 相似文献   

Slow magnetic relaxation of a ferromagnetic Ni(II)5 cluster with an S = 5 ground state

Complex [Ni 5{pyCOpyC(O)(OMe)py} 2(O 2CMe) 4(N 3) 4(MeOH) 2].2MeOH.2.6H 2O ( 1.2MeOH.2.6H 2O) was synthesized by the reaction of Ni(O 2CMe) 2.4H 2O with pyCOpyCOpy and NaN 3 in refluxing MeOH. It crystallizes in the monoclinic C2/ c space group and consists of five Ni (II) atoms in a helical arrangement. Direct current magnetic susceptibility studies reveal ferromagnetic interactions between the Ni (II) ( S = 1) ions, stabilizing an S = 5 ground state. Alternating current susceptibility experiments revealed the existence of out-of-phase signals indicative of slow magnetic relaxation. Analysis of the signals showed that they are composite, suggesting more than one relaxation process, while analysis of their magnitudes suggests not all molecules undergo slow magnetic relaxation. Magnetization field-sweep experiments revealed hysteresis at 1.8 K, and magnetization decay experiments clearly verified the appearance of slow magnetic relaxation at that temperature.     

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.