On the Hopficity of HNN-Extensions of Polycyclic Groups

For a group G, an HNN-extension of polycyclic groups, we give two necessary and sufficient conditions for G to be hopfian. One is based on the nature of the endomorphism of G and the other on the nature of the associated subgroups of G. At the end, we give an application for HNN-extensions of nilpotent groups.     

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.

     

Anisotropic exchange interactions in dinuclear systems (Ln = Dy, Tm, Yb): Magnetometry and Dual Mode X-band Electron Paramagnetic Resonance spectroscopic study

A recently developed experimental and theoretical procedure is used in order to calculate the magnitude and anisotropy of interaction between a lanthanide and a 3d-metal ion. The general formula of the molecular compounds is [Ln(H₂O)₃(dmf)₄(μ-CN)Fe–(CN)₅] · nH₂O where 1  n  1,5 and dmf = N,N′-dimethylformamide, abbreviated as [LnFe] from now on. The main parts of this procedure are (a) the evaluation of the effective g-parameters of the lanthanide ion with the help of EPR measurements. (b) The use of dual mode EPR spectroscopy to define the anisotropic exchange interactions with the help of an anisotropic Hamiltonian model. (c) Use of the same magnetic model to fit magnetization and susceptibility data in order to verify the EPR findings.It was possible to define some trends concerning the exchange components of the [DyFe] dimer according to which the antiferromagnetic isotropic exchange constant is smaller than 4 cm⁻¹ and the anisotropic components are [D_exc, E_exc] = [6(1), 0.0] cm⁻¹. Also for the case of [TmFe] and [YbFe] dimers the antiferromagnetic isotropic exchange constant is smaller than 0.3 cm⁻¹ while the anisotropic components are [D_exc, E_exc] = [12.0, 0.0] cm⁻¹ and [D_exc, E_exc] = [0.4(1), 0.0] cm⁻¹, respectively.     

Review of a fast simulation method for the analysis of queueing networks

This paper presents a review of and refinements to a class of discrete-event models for the analysis of unreliable queueing systems. In contrast to conventional piece-by-piece simulators, these models observe a number of rare events that affect the inflow and outflow rates at each queue. Between events, the evolution of the system is approximated by a linear function. Several experiments confirm the accuracy of this approximation and its computational efficiency over conventional simulation. © 1997 by John Wiley & Sons, Ltd.     

Ion exchange of Pb(2+), Cu(2+), Fe(3+), and Cr(3+) on natural clinoptilolite: selectivity determination and influence of acidity on metal uptake

In the present study ion exchange of Pb(2+), Cu(2+), Fe(3+), and Cr(3+) on natural Greek clinoptilolite was examined in terms of selectivity toward the above heavy metals in single- and multicomponent solutions in batch systems. Also examined are the influence of clinoptilolite on solution acidity and the effect of acidity on the ion exchange process. Clinoptilolite increases solution acidity due to the exchange of H(+) cations with the cations initially present in its structure. H(+) cations should be considered as competitive ones in ion exchange processes, and consequently ion exchange of metals is favored at high acidity values. Cu(2+) and Cr(3+) are the most sensitive cations with respect to acidity. Selectivity determination demonstrates that the selectivity at total concentration 0.01 N and acidity 2 in both single- and multicomponent solutions is following the order Pb(2+)>Fe(3+)>Cr(3+) > or =Cu(2+). This order is set since the first days of equilibration. However, Cu(2+) shows remarkable changes in selectivity and generally its uptake and selectivity are increasing with time. On the other hand selectivity in single metal solutions where acidity is not adjusted is following the order Pb(2+)>Cr(3+)>Fe(3+) congruent with Cu(2+).     

Criteria for convexity in Banach spaces

In this paper two convexity criteria are proven. The first one characterizes compact convex sets in a locally convex space and extends a previous result by G. Aumann, while the second one characterizes closed bounded convex sets with the Radon-Nikodým property in a Banach space.