Electrospray ionization mass spectrometric study of 1,3,4-oxadiazole–copper complexes

The complexes of 2,5-disubstituted-1,3,4-oxadiazoles, namely 2,5-diphenyl-1,3,4-oxadiazole (1), 2,5-bis(2-pyridyl)-1,3,4-oxadiazole (2) and 2,5-bis(4-pyridyl)-1,3,4-oxadiazole (3), with copper cation were studied by electrospray ionization mass spectrometry (ESI-MS). The ability of the compounds studied to form complexes with copper (under the ESI conditions) can be ordered as 2 > 1 > 3. The compounds studied tend to form both 1 : 1 and 2 : 1 chelate complexes with both copper(II) and copper(I). The complexes with copper(I) are formed in the ESI process. The influence of solvent polarity, solution flow-rate, counter ions (Cl⁻, NO₃⁻, CH₃COO⁻, SO₄²⁻, acetylacetonates) on the type of the ions observed was studied. Copyright © 2004 John Wiley & Sons, Ltd.     

On the equivalence of the parallel channel and the correlated cluster relaxation models

The question of the origins of nonexponential relaxation is addressed in terms of the probabilistic approach to relaxation. The interconnection between two differently rooted probabilistic models, i.e., between the parallel channel and the correlated cluster models, is presented. We show that clearly different probabilistic origins yield in both approaches a well-defined class of universally valid two-power-law responses with the stretched-exponential and exponential decay laws as special cases. The equivalence of both models indicates that variations in the local environment of the relaxing configurational units (parallel channel relaxation) can provide a basis for self-similar relaxation dynamics without the need for hierarchically constrained dynamics (correlated clusters relaxation).     

Noncommuting Domination in Krein Spaces Via Commutators of Block Operator Matrices

The commutators of 2 × 2 block operator matrices with (unbounded) operator entries are investigated. The matrix representation of a symmetric operator in a Krein space is exploited. As a consequence, the domination result due to Cichoń, Stochel and Szafraniec is extended to the case of Krein spaces.     

Modified Alternating $$\vec{k}$$–generators

This paper deals with a class of pseudorandom bit generators – modified alternating –generators. This class is constructed similarly to the class of alternating step generators. Three subclasses of are distinguished, namely linear, mixed and nonlinear generators. The main attention is devoted to the subclass of linear and mixed generators generating periodic sequences with maximal period lengths. A necessary and sufficient condition for all sequences generated by the linear generators of to be with maximal period lengths is formulated. Such sequences have good statistical properties, such as distribution of zeroes and ones, and large linear complexity. Two methods of cryptanalysis of the proposed generators are given. Finally, three new classes of modified alternating –generators, designed especially to be more secure, are presented.     

Coordination ability of trans-cyclohexane-1,2-diamine-N,N,N',N'-tetrakis(methylenephosphonic acid) towards lanthanide(III) ions

The proton and metal complex equilibria of trans-cyclohexane-1,2-diamine-N,N,N',N'-tetrakis(methylenephosphonic acid) (CDTP) with lanthanide(iii) ions, where Ln(III) = La(III), Nd(III), Sm(III), Eu(III), Gd(III), Tb(III), Ho(III) and Lu(III) were studied. The stoichiometry, protonation and complex formation constants were determined by potentiometric titration at 25.0 degrees C and ionic strength of 0.1 mol dm(-3) (KCl). All metal ions form several species: [LnH4L]-, [LnH3L](2-), [LnH2L](3-), [LnHL](4-), [LnL](5-), [LnH(-1)L](6-) and [LnH(-2)L](7-) in the pH range between 2 and 11. The stability constants log beta(LnL) were found to be between 14.7 and 16.7. The studied complexes were also characterized by spectroscopic methods (31P NMR, UV-Vis absorption and emission spectroscopy). These studies allowed to reveal a distinct structural change of the Ln(III)-CDTP complex which occurs between protonated and hydroxy species in solutions at pH around 7.5. The major change is caused by the involvement of both nitrogen donors in the metal ion coordination occurring in ML species. The data obtained from UV-Vis spectroscopy allowed to draw conclusions about complex symmetry and to estimate a number of coordinated water molecules. The hydration number or more precisely the number of two OH oscillators was found to be approximately one in all species formed over the pH range between 5 and 10. The structure of the major hydroxy complex was supported by X-ray crystallographic data. The crystal structures of the Eu(III) and Tb(III) complexes clearly show that the CDTP ligand is coordinated to the Ln(III) ion by two nitrogen and four oxygen atoms in such a way that only one oxygen atom from each phosphonic group is placed in the lanthanide inner sphere. The monomeric complex anion is connected to a symmetry related ion through short hydrogen bonds formed by two hydroxy ions and one water molecule. In this way the two neighbouring anions form a quasi-dimer in which one of the Ln(III) ion is seven-coordinate (two N atoms, four O atoms and one hydroxy ion) and the other is eight-coordinate (two N atoms, four O atoms, one hydroxy ion and one water molecule).     

Influence of solvent and counter ion on copper complexes with N-alkyl-pyridine-2-carboxamides as studied by electrospray ionization mass spectrometry

The interactions of copper(II) with N-alkyl-pyridine-2-carboxamides (M) were studied by electrospray ionization mass spectrometry. The influence of solvent and counter ion (Cl-, ClO4-) on the type of ions (complexes) observed was discussed. By cone voltage increase, the fragmentation "in source" of the ions discussed was achieved. In methanol solution containing N-alkyl-pyridine-2-carboxamide (M) and CuCl2 the singly- and doubly charged-ions [M+CuCl]+ and [M2+Cu]+2 were detected. In acetonitrile solution containing N-alkyl-pyridine-2-carboxamide and CuCl2, the copper(I)-containing ions [M+CH3CN+Cu]+ were formed. The use of Cu(ClO4)2 instead of CuCl2 resulted in more abundant doubly-charged ions in both methanol and acetonitrlile solutions and, for the former solution, the ions containing methoxyl anion, namely [M+CuOCH3]+, were observed. When water was used as a solvent, the abundant ions corresponding to the protonated ligands were formed, while the ions corresponding to copper complexes were characterised by low abundances.     

Influence of solvent and counter ion on complexes of 2,5-bis(2-pyridyl)-1,3,4-oxadiazole with iron (II) and (III) studied by electrospray ionization mass spectrometry

The effect of solvent and counter ion on the complexes of 2,5-bis(2-pyridyl)-1,3,4-oxadiazole (1) with Fe+2 and Fe+3 has been studied by electrospray ionization mass spectrometry (ESI/MS). As expected, upon ESI conditions the metal reduction proceeds, but it can be deduced that complexes with Fe+2 are favored over those with Fe+3. When methanol is used as solvent, the formation of complexes of stoichiometry 2:1 and 1:1 with counter ion attached (monovalent anion) is favored, for example, [1(2)+FeCl]+ ion. The use of methanol/water (1/1) as solvent favors the formation of complexes of stoichiometry 2:1 and 3:1, namely doubly charged [1(2)+Fe]+2 and [1(3)+Fe]+2 ions. The complexes containing anion of oxidative properties (ClO4-, NO3-), when the higher cone voltage is applied, yield unusual species [1n+FeOm]+ (n=1, 2; m=1, 2). The use of divalent counter ion (SO4(-2)) resulted in formation of complexes containing two iron cations, namely [1n+Fe2SO4]+2 (n=2, 3, 4) ions. These ions can be regarded as Fe-1 complexes bridged by a sulfate anion.     

Affine representations of Fibonacci groups and flat manifolds

We construct examples of affine representations for a family of Fibonacci groups. As an application, we prove that all Hantzsche–Wendt groups of the same dimension are epimorphic images of the same Fibonacci group.     

Rearrangement of conditionally convergent series on a small set

We consider ideals I of subsets of the set of natural numbers such that for every conditionally convergent series _∑n∈ωan and every there is a permutation such that _∑n∈ωaπr(n)=r and