Solving matrix polynomial equations arising in queueing problems

The matrix equation ∑_i=0ⁿA_iXⁱ=0, where the A_i's are m×m matrices, is encountered in the numerical solution of Markov chains which model queueing problems. We provide here a unifying framework in terms of Möbius' mapping to relate different resolution algorithms having a quadratic convergence. This allows us to compare algorithms like logarithmic reduction (LR) and cyclic reduction (CR), which extend Graeffe's iteration to matrix polynomials, and the invariant subspace (IS) approach, which extends Cardinal's algorithm. We devise new iterative techniques having quadratic convergence and present numerical experiments.     

Dinuclear copper complexes based on parallel β-diiminato binding sites and their reactions with O2: evidence for a Cu-O-Cu entity

Investigations concerning the system β-diketiminato-Cu(I)/O(2) have revealed valuable insights that may be discussed in terms of the behavior of mononuclear oxygenases containing copper. On the other hand nature also employs dinuclear Cu enzymes for the activation of O(2). With this background the ligand system [(Me(2))(C(6)H(3))Xanthdim](2-) containing two parallel β-diiminato binding sites linked by a xanthene backbone with 2,3-dimethylphenyl residues at the diiminato units was investigated with respect to its copper coordination chemistry. The diimine [(Me(2))(C(6)H(3))Xanthdim]H(2) was treated with CuOtBu in the presence of acetonitrile, PPh(3), and PMe(3) to yield the corresponding complexes [(Me(2))(C(6)H(3))Xanthdim](Cu(L))(2) (L = CH(3)CN, 1, PPh(3), 2, and PMe(3), 3) that proved to be stable and were fully characterized. Single crystal X-ray diffraction analyses performed for the three complexes showed that considerable steric crowding within the binding pockets of 2 leads to a very long Cu-Cu distance while the structures of 1 and 3 are relaxed. Compounds 2 and 3 are relatively robust toward air, whereas 1 is very sensitive and quantitatively reacts with O(2) at room temperature (r.t.) within less than 2 min to give intractable compounds. At low temperatures the formation of a green intermediate was observed that was identified as a Cu(II)-O-Cu(II) species spectroscopically and chemically. This finding is of relevance also in the context of the results obtained testing 1 as a catalyst for phenol oxidation using O(2): 1 efficiently catalyzes phenol coupling, while there was no evidence for any oxygenation reactions occurring.     

Catalytic phosphorus(V)-mediated nucleophilic substitution reactions: development of a catalytic Appel reaction

Catalytic phosphorus(V)-mediated chlorination and bromination reactions of alcohols have been developed. The new reactions constitute a catalytic version of the classical Appel halogenation reaction. In these new reactions oxalyl chloride is used as a consumable stoichiometric reagent to generate the halophosphonium salts responsible for halogenation from catalytic phosphine oxides. Thus, phosphine oxides have been transformed from stoichiometric waste products into catalysts and a new concept for catalytic phosphorus-based activation and nucleophilic substitution of alcohols has been validated. The present study has focused on a full exploration of the scope and limitations of phosphine oxide catalyzed chlorination reactions as well as the development of the analogous bromination reactions. Further mechanistic studies, including density functional theory calculations on proposed intermediates of the catalytic cycle, are consistent with a catalytic cycle involving halo- and alkoxyphosphonium salts as intermediates.     

Addition of TMSCN to chiral ketimines derived from isatin. Synthesis of an oxindole-based peptidomimetic and a bioactive spirohydantoin

We investigated the Strecker-type reaction of isatin derived chiral ketimines with TMSCN in the presence of a Lewis acid. The desired α-amino nitriles have been obtained in good yields with moderate diastereoselectivity. Further elaboration of the cyanide group allowed the preparation of a new oxindole-based peptidomimetic and a pharmaceutically relevant spirohydantoin.     

Parameter estimation in exponentially fitted hybrid methods for second order differential problems

In this work we deal with exponentially fitted methods for the numerical solution of second order ordinary differential equations, whose solutions are known to show a prominent exponential behaviour depending on the value of an unknown parameter to be suitably determined. The knowledge of an estimation to the unknown parameter is needed in order to apply the numerical method, since its coefficients depend on the value of the parameter. We present a strategy for the practical estimation of the parameter, which is also tested on some selected problems.     

The ENDOR spectrum of bis(p-methoxyphenyl)nitroxide

In this paper we develop useful expansions for the differential cross section in terms of the frequency moments of Van Hove's scattering function, i.e. the Placzek [1] and Wick [3] series. Using only the density independent terms of these series we compare their predictions with those obtained from the models described in paper I. It is concluded that for nitrogen, deuterium chloride and hydrogen chloride the single molecule interference term is given to high accuracy by our Placzek series, so that no density dependent terms are required. For the self terms of nitrogen, and chloride in the HCl and DCl molecules Placzek's series is satisfactory over the range of angles used in most experiments although Wick's series may be needed for angles near 180°. For the self term of D in DCl Wick's series is good over a moderate range of angles, but a realistic model for the rotational behaviour is needed over a wider range and also for all cases involving H in HCl.

The results presented here may be used for the interpretation of a wide range of neutron diffraction experiments, and are shown to be accurate for many cases to ～1 per cent.     

Isolation of ZnO-binding 12-mer peptides and determination of their binding epitopes by NMR spectroscopy

Inorganic-binding peptides are in the focus of research fields such as materials science, nanotechnology, and biotechnology. Applications concern surface functionalization by the specific coupling to inorganic target substrates, the binding of soluble molecules for sensing applications, or biomineralization approaches for the controlled formation of inorganic materials. The specific molecular recognition of inorganic surfaces by peptides is of major importance for such applications. Zinc oxide (ZnO) is an important semiconductor material which is applied in various devices. In this study the molecular fundamentals for a ZnO-binding epitope was determined. 12-mer peptides, which specifically bind to the zinc- or/and the oxygen-terminated sides of single-crystalline ZnO (0001) and (000-1) substrates, were selected from a random peptide library using the phage display technique. For two ZnO-binding peptides the mandatory amino acid residues, which are of crucial importance for the specific binding were determined with a label-free nuclear magnetic resonance (NMR) approach. NMR spectroscopy allows the identification of pH dependent interaction sites on the atomic level of 12-mer peptides and ZnO nanoparticles. Here, ionic and polar interaction forces were determined. For the oxygen-terminated side the consensus peptide-binding sequence (HSXXH) was predicted in silico and confirmed by the NMR approach.     

Optical soliton perturbation in non-Kerr law media: Traveling wave solution

This paper analyses the dynamics of soliton propagation through optical fibers with non-Kerr law nonlinearities. The governing nonlinear Schrödinger equation is integrated in the presence of perturbation terms. The traveling wave hypothesis is used to carry out the integration. Domain restrictions on the soliton parameters are identified in the process. The five forms of nonlinearity that are studied are Kerr-law, power-law, parabolic-law, dual-power law and the log-law nonlinearity. Numerical simulations are presented for each of these nonlinear media.     

Preparation and Characterization of Activated Carbon – nFe3O4, Activated Carbon – nSiO2 and Activated Carbon – nZnO Hybrid Materials

The preparation and physicochemical characterization of activated carbon, nano metal oxides, and activated carbon – nFe₃O₄, activated carbon – nSiO₂ and activated carbon – nZnO hybrid materials has been undertaken. The materials have been characterized by scanning and transmission electron microscopy, x‐ray diffraction, CNH analysis and Fourier transform infrared spectroscopy. Surface area and porosity, ash content, pH, and point of zero charge were also measured. The results showed that the surfaces of activated carbon, nSiO₂, activated carbon – nFe₃O₄, activated carbon – nSiO₂ and activated carbon – nZnO are suitable for the sorption of cationic complexes while the surfaces of nFe₃O₄ and nZnO are favourable to the sorption of anionic complexes of heavy metals. Results also showed that the composition of the activated carbon and nano metal oxides increased the surface and micropore areas of nano metal oxides due to the large number of micropores and crevices on the surface of the hybrid materials.     

Measuring the dielectric constant of materials from valence EELS

Valence EELS combined with STEM provides an approach to determine the dielectric constant of materials in the optical range of frequencies. The paper describes the experimental procedure and discusses the critical aspects of valence electron energy-loss spectroscopy (VEELS) treatment. In particular, the relativistic losses might affect strongly the results, and therefore they have to be subtracted from the spectra prior the analysis. The normalization of the energy-loss function is performed assuming an uniform thickness of the investigated area, which is reasonably fulfilled for carefully prepared FIB samples. This procedure requires the presence of at least one reference material with known dielectric properties to determine the absolute thickness. Examples of measuring the dielectric constant for several materials and structures are presented.