Uniform fourth order difference scheme for a singular perturbation problem

Summary The numerical solution of a nonlinear singularly perturbed two-point boundary value problem is studied. The developed method is based on Hermitian approximation of the second derivative on special discretization mesh. Numerical examples which demonstrate the effectiveness of the method are presented.This research was partly supported by NSF and SIZ for Science of SAP Vojvodina through funds made available to the U.S.-Yugoslav Joint Board on Scientific and Technological Cooperation (grants JF 544, JF 799)     

Unusual iron(III) ate complexes stabilized by Li-pi interactions

Several iron(III) complexes incorporating diamidoether ligands are described. The reaction between [Li(2)[RN(SiMe(2))](2)O] and FeX(3) (X=Cl or Br; R=2,4,6-Me(3)Ph or 2,6-iPr(2)Ph) form unusual ate complexes, [FeX(2)Li[RN(SiMe(2))](2)O](2) (2, X=Cl, R=2,4,6-Me(3)Ph; 3, X=Br, R=2,4,6-Me(3)Ph; 4, X=Cl, R=2,6-iPr(2)Ph) which are stabilized by Li-pi interactions. These dimeric iron(III)-diamido complexes exhibit magnetic behaviour characteristic of uncoupled high spin (S= 5/2 ) iron(III) centres. They also undergo halide metathesis resulting in reduced iron(II) species. Thus, reaction of 2 with alkyllithium reagents leads to the formation of iron(II) dimer [Fe[Me(3)PhN(SiMe(2))](2)O](2) (6). Similarly, the previously reported iron(III)-diamido complex [FeCl[tBuN(SiMe(2))](2)O](2) (1) reacts with LiPPh(2) to yield the iron(II) dimer [Fe[tBuN(SiMe(2))](2)O](2) but reaction with LiNPh(2) gives the iron(II) product [Fe(2)(NPh(2))(2)[tBuN(SiMe(2))](2)O] (5). Some redox chemistry is also observed as side reactions in the syntheses of 2-4, yielding THF adducts of FeX(2): the one-dimensional chain [FeBr(2)(THF)(2)](n) (7) and the cluster [Fe(4)Cl(8)(THF)(6)]. The X-ray crystal structures of 3, 5 and 7 are described.     

Dependence of the probability of biological effects per hit,induced by radiation emitted by <Superscript>222</Superscript>Rn,from alpha particle energies and the geometry of tracheobronchial tree

Biological effects of radiation in terms of their effect on living cells are considered in this work. In dosimetry of the human lung exist the need to include the influence of the biological effects. The aim of this work is to calculate the probability of biological effects (transformation cell and production of lesion) per hit induced by alpha particle radiation on sensitive cells of human lung. Probability was calculated by applying the analytical model cylinder bifurcation (Nikezić et al., Int J Radiat Biol 79(3):175–180, 2003; Nikezić and Yu, Radiat Environ Biophys 42:49–53, 2003) which was created to simulate the geometry of human lung with the geometric distribution of cell nuclei in the airway wall of the tracheobronchial tree. This analytical model of the human traheobronchial tree represent the exstension of the ICRP66 model, and follows it as much as possible. Reported probabilities are calculated for various targets and alpha particle energies in order to show dependence of the probability of biological effects (transformation cell and production of lesion) per hit from alpha particle energies and the geometry of tracheobronchial tree for the human lung.     

Synthesis, characterization and structural analysis of new copper(II) complexes incorporating a pyridoxal-semicarbazone ligand

The reaction between 3-hydroxy-5-hydroxymethyl-2-methyl-4-pyridinecarboxaldehyde semicarbazone (pyridoxal-semicarbazone or PLSC) and appropriate chloride, sulfate, nitrate or thiocyanate Cu(II) salts in water/alcohol mixtures resulted in the formation of new copper(II) complexes: [Cu(PLSC)Cl₂] (1), [Cu(PLSC)(H₂O)(SO₄)]₂·3H₂O (2), [Cu₂(PLSC)₂(NCS)₂](NCS)₂ (3), [Cu(PLSC)(NO₃)₂(CH₃OH)] (4) and [Cu(PLSC-2H]NH₃·H₂O (5). The complexes were characterized by elemental analysis, conductometric measurements and IR spectroscopy, while complexes 1, 2, 3 and 4 were further characterized by single crystal X-ray diffraction.     

Tuning main group redox chemistry through steric loading: subvalent Group 13 metal complexes of carbazolyl ligands

The ability of substituted carbazol‐9‐yl systems to ligate in σ fashion through the amido N‐donor, or to adopt alternative coordination modes through the π system of the central five‐membered ring, can be tuned by systematic variation in the steric demands of substituents in the 1‐ and 8‐positions. The differing affinities of the two modes of coordination for hard and soft metal centres can be shown to influence not only cation selectivity, but also the redox properties of the metal centre. Thus, the highly sterically sterically demanding 1,3,6,8‐tetra‐tert‐butylcarbazolyl ligand can be used to generate the structurally characterised amido‐indium(I) complex, [{(tBu₄carb)In}_n], (together with its isostructural thallium counterpart) in which the metal centre interacts with the central pyrrolyl ring in η³ fashion [d(In? N)=2.679(3) Å; d(In? C)=2.819(3), 2.899(3) Å]. By contrast, the smaller 3,6‐di‐tert‐butylcarbazolyl system is less able to restrict the metal centre from binding at the anionic nitrogen donor in the plane of the carbazolyl ligand (i.e. in σ fashion). Analogous chemistry with In^I precursors therefore leads to disproportionation to the much harder In^II [and In⁰], and the formation of the mixed‐valence product, [In₂{In₂(tBu₂carb)₆}], a homoleptic molecular [In₄(NR₂)₆] system. This chemistry reveals a flexibility of ligation for carbazolyl systems that contrasts markedly with that of the similarly sterically encumbered terphenyl ligand family.     

A novel pimara-8(9) ,15-diene from lycopus europaeus

Identification of a novel trioxygenated Δ^8(9),15_ pimaric acid methyl ester from plant species Lycopus europaeus by means of two-dimensional ¹H NMR spectroscopy (COSY and NOESY) is reported.     

Novel trioxygenated caryophyllenes from Inula Spiraefolia

The identification of two novel isomeric trioxygenated caryophyllenes from the plant species $\text{Inula Spiraefolia}$ is reported.     

An N,N'-chelated phosphenium cation supported by a beta-diketiminate ligand

The first example of a phosphenium cation supported by N,N'-chelation of a beta-diketiminate ligand has been prepared and structurally characterized.     

Hysteretic behavior of rectangular tube (box) sections based on Preisach model

In the present paper, the Preisach model of hysteresis is applied to model cyclic behavior of elasto-plastic material. Rate of loading and viscous effects will not be considered. The problem of axial loading of rectangular cross-section and cyclic bending of rectangular tube (box) will be studied in details. Hysteretic stress–strain loop for prescribed history of stress change is plotted for material modeled by series connection of three unite element. Also moment–curvature hysteretic loop is obtained for a prescribed curvature change of rectangular tube (box). All obtained results clearly show advantages of the Preisach model for describing cyclic behavior of elasto-plastic material.     

Refractive-index dispersion of glassy semiconductors in the pseudo-binary As2Se3–SbSI system

The bulk chalcogenide glasses in the pseudo-binary system (As₂Se₃)_100?x(SbSI)_x (with x = 20, 30, 50, 70 and 80 at.%) were prepared from high-purity elemental components by melt-quenching technique. It is a system with the variable ratio of classical amorphous compound As₂Se₃ and the molecule of antimony-sulphoiodide, SbSI, which in the monocrystal form is characterized as a ferroelectric. The refractive-index behaviour (magnitude and spectral dispersion) of investigated glasses was determined by the prism method and analyzed. To calculate and discuss the parameters of dispersion in the band gap region three different approaches were used (Cauchy, Sellmeier and Wemple–DiDomenico single-oscillator model). The comparison of the results shows good agreement between all applied models. It was found that the value of the refractive-index shows normal dispersion behaviour and increases with the increase of Sb (or SbSI) content in the investigated system, whereas the optical gap of these glasses E_g slightly decreases.