A numerical model of multimode fiber PON frequency response

Frequency response of passive optical network (PON) based on multimode fibers is investigated. The network comprises fibers, connectors and splitters/couplers. It is shown that due to mode filtering at splitters, the frequency response is different for different network nodes in otherwise symmetrical network.     

Normality of orbit closures for Dynkin quivers¶of type ?n

It is known that the orbit closures for the representations of the equioriented Dynkin quivers ? _n are normal and Cohen–Macaulay varieties with rational singularities. In the paper we prove the same for the Dynkin quivers ? _n with arbitrary orientation. Received: 25 October 2000 / Revised version: 28 February 2001     

Multivariate approximation in the worst case setting over reproducing kernel Hilbert spaces

We study the worst case setting for approximation of d variate functions from a general reproducing kernel Hilbert space with the error measured in the L_∞ norm. We mainly consider algorithms that use n arbitrary continuous linear functionals. We look for algorithms with the minimal worst case errors and for their rates of convergence as n goes to infinity. Algorithms using n function values will be analyzed in a forthcoming paper.We show that the L_∞ approximation problem in the worst case setting is related to the weighted L₂ approximation problem in the average case setting with respect to a zero-mean Gaussian stochastic process whose covariance function is the same as the reproducing kernel of the Hilbert space. This relation enables us to find optimal algorithms and their rates of convergence for the weighted Korobov space with an arbitrary smoothness parameter α>1, and for the weighted Sobolev space whose reproducing kernel corresponds to the Wiener sheet measure. The optimal convergence rates are n^-(α-1)/2 and n^-1/2, respectively.We also study tractability of L_∞ approximation for the absolute and normalized error criteria, i.e., how the minimal worst case errors depend on the number of variables, d, especially when d is arbitrarily large. We provide necessary and sufficient conditions on tractability of L_∞ approximation in terms of tractability conditions of the weighted L₂ approximation in the average case setting. In particular, tractability holds in weighted Korobov and Sobolev spaces only for weights tending sufficiently fast to zero and does not hold for the classical unweighted spaces.     

Solvent extraction of Cu,Mo, V,and U from leach solutions of copper ore and flotation tailings

A micro-cloud point extraction method was discussed for preconcentration and spectrophotometric quantification of U(VI). The method depends on complex formation between U(VI) and 2-(4-sulphophenyloazo)-1,8-dihydroxy-3,6-naphtalenedisulphonic acid (SPADNS) at pH 7.0 and subsequent extraction of the complex in a mixed surfactant medium (cethyltrimethyl ammonium bromide and Triton X-114). The separation was carried out in the presence of 1% Na₂SO₄ at room temperature. The calibration curve was linear up to 3000 µg L^?1. The enrichment factor, detection limit and precision were 16.0, 1.05 µg L^?1, and 2.3%, respectively. The method was employed for the determination of U(VI) in real samples with different matrices.     

Circular logic: nonribosomal peptide-like macrocyclization with a ribosomal peptide catalyst

A protease from ribosomal peptide biosynthesis macrocyclizes diverse substrates, including those resembling nonribosomal peptide and hybrid polyketide-peptide products. The proposed mechanism is analogous to thioesterase-catalyzed chemistry, but the substrates are amide bonds rather than thioesters.     

Mononuclear and dinuclear chiral vanadium(V) complexes with tridentate Schiff bases derived from R(−)-1,2-diaminopropane: Synthesis,structure, characterization and catalytic properties

A series of vanadium(V) complexes with unsymmetrical tridentate Schiff base ligands, obtained by the single condensation of R(−)-1,2-diaminopropane with salicylaldehyde and its derivatives, 2-hydroxy-1-naphthaldehyde, 2-hydroxyacetophenone, 1-hydroxy-2-acetonaphthone and 2-hydroxybenzophenone, were prepared. The complexes were characterized by elemental analysis and by their IR, CD, UV–Vis, 1D (¹H, ⁵¹V) and 2D (COSY, NOESY, gHSQC) NMR spectra. Crystal structures of the mononuclear complex {R(−)-2-amino-1-N-[(2′-oxido-κO-4′,6′-dimethoxyphenyl)methylene]aminopropane-κ²N}dioxidovanadium(V), VO₂(C₁₂H₁₇N₂O₃), 4, and of the dinuclear complex, di-μ-oxido-bis({R(−)-2-[1-(2-aminopropylimino)ethyl]-4-methylphenolato-κ³N,N′,O}oxidovanadium(V)), V₂O₄(C₁₁H₁₅N₂O)₂, 5, have been obtained by X-ray diffraction studies. The structure of 4 was revealed to be a distorted trigonal–bipyramidal coordination geometry, rarely encountered in VO₂(tridentate Schiff base) complexes. Complexes 2 and 3 have the ability to catalyze the oxidation of prochiral sulfide substrates PhSR (R = Me, Bz) utilizing hydrogen peroxide or cumene hydroperoxide (CHPO) as the oxidant.     

Determination of selenomethionine, selenocysteine, and inorganic selenium in eggs by HPLC–inductively coupled plasma mass spectrometry

A method for the simultaneous determination of selenomethionine (SeMet), selenocysteine (SeCys), and selenite [Se(IV)] in chicken eggs was developed. A sample preparation protocol including defatting, protein denaturation, and carbamidomethylation was optimized in order to achieve complete protein digestion and to avoid SeCys losses. Quantification was carried out by reversed-phase HPLC–inductively coupled plasma mass spectrometry (ICP MS) after quantitative isolation of the selenium-containing fraction by size-exclusion liquid chromatography. The detection limits were 0.06, 0.003, and 0.01 μg g⁻¹ (dry weight) for SeCys, Se(IV) and SeMet, respectively, and the precision was 5–10%. The end products of carbamidomethylation of the different selenium species were identified for the first time by electrospray QTOF MS after custom-designed 2D HPLC purification. Differences in selenium speciation in egg yolk and white were highlighted, the yolk containing more SeCys and the white more SeMet. An insight into selenium bioaccessibility in eggs was obtained by digestion with simulated gastric and gastrointestinal juices and size-exclusion HPLC-ICP MS.     

Solid state NMR spectroscopy as a precise tool for assigning the tautomeric form and proton position in the intramolecular bridges of o-hydroxy Schiff bases

Two analogous Schiff bases, (S,E)-2-((1-hydroxy-3-methyl-1,1-diphenylbutan-2-ylimino)methyl)phenol (1) and (S,Z)-2-hydroxy-6-((1-hydroxy-3-methyl-1,1-diphenylbutan-2-ylamino)methylene)cyclohexa-2,4-dienone (2), exist in the solid state as phenol-imine and keto-amine tautomers, respectively. Their crystal structures were solved using the X-ray diffraction method. Sample 1 forms orthorhombic crystals of space group P2(1)2(1)2(1), while 2 forms monoclinic crystals of space group P2(1). In each sample, one molecule is in the asymmetric unit of the crystal structure. One-dimensional and two-dimensional solid state NMR techniques were used for structure assignment and for inspection of the (13)C and (15)N δ(ii) of the chemical shift tensor (CST) values. NMR study indicates that the span (Ω = δ(11)-δ(33)) and the skew (κ = 3(δ(22)-δ(iso)/Ω) are extremely sensitive to change in the tautomeric form of the Schiff bases. Theoretical calculations of NMR shielding parameters for 1 and 2 and a model compound with reduced aliphatic residue were performed using the GIAO method with B3LYP functional and 6-311++g(d,p) basis sets. From comparative analysis of the experimental and theoretical parameters, it was concluded that the position of hydrogen in the intramolecular bridge has tremendous influence on (13)C and (15)N CST parameters. Inspection of Ω and κ parameters allowed for the establishment of the nature of the hydrogen bonding and the assignment of the equilibrium proton position in the intramolecular bridges in the solid state.     

Characterization of 1,3-alternate calix[4]arene-silica bonded stationary phases and their comparison to selected commercial columns by using principal component analysis

Twelve calix[4]arene stationary phases in 1,3-alternate conformation, synthesized in the authors’ laboratory, were characterized in terms of their surface coverage, hydrophobic selectivity, aromatic selectivity, shape selectivity, hydrogen bonding capacity and ion-exchange capacity. The set of tests commonly used for evaluation of commercially available stationary phases was applied to assess fundamental chromatographic properties of the calixarene phases. The new calixarene phases were compared to each other, to Caltrex and LiChrosorb C-18 columns. Principal component analysis has been used to provide comparison between 1,3-alternate calix[4]arene phases and commercially available phenyl, fluorophenyl and fluoroalkyl columns.