An addition theorem for the color number

There is a close relation between the color number of a continuous map without fixed points and the topological dimension. If  is an involution, the color number is also related to the co-index. An addition theorem for the color number is established thus underscoring the interrelations between color number, dimension and co-index.

     

Synthesis, spectroscopy, and X-ray structure of the polymer catena-[bis(azido-N)-copper(II)-μ-bis(2-benzimidazolyl)butane]

The title compound, catena-[bis(azido-N)-copper(II)-(bis(2-benzimidazolyl)butane), [Cu(C₁₈H₁₈N₄)(N₃)₂]_n, was obtained from the reaction of the ligand bis(2-benzimidazolyl)butane and Cu(N₃)₂. The x-ray crystal structure is reported. The compound crystallizes in the monoclinic space group P2₁/c with a = 8.2524(10), b = 12.765(5), c = 9.1125(15) Å, = 106.423(12)°, Z = 2. The Cu(II) ions are square-planar coordinated with trans-oriented end-on binding azido ligands. The structure is a polynuclear chain with the benzimidazole bridging at each end. In addition a N_(ligand)-H···N_(azido) H-bridge [N_(ligand)···N_(azido) = 2.994(7) Å] is present, resulting in a pseudo 2-dimensional lattice. The characteristic azido infrared vibrations are found at 2060 and 2077 cm^–1 (_as(N₃)) and 1284 and 1297 cm^–1 ((N₃)).     

Morita Equivalence of Sketches

Equivalence of sketches S and T means the equivalence of their categories Mod_S and Mod_T of all Set-valued models. E. Vitale and the second author have characterized equivalence of limit-sketches by means of bimodels, where a bimodel for limit sketches S and T is a model of S in the category Mod_T. For general sketches, we show that an analogous result holds provided that Mod_T is substituted by a more complex category; e.g., in case of limit-coproduct sketches, that category is (Mod_T), the free product completion of Mod_T.     

Cr:Tm:Ho:YAG (2.1 μm) and Nd:YAG (1.444 μm) pulsed-laser lithotripsy of bile duct stones

The Nd:YAG (1.444 m) and Cr:Tm:Ho:YAG (2.1 m) free-running laser systems of the output energy of 300 mJ per pulse and repetition rate 1 Hz have been developed and used for bile duct stones fragmentation study in vitro. A total of 67 human bile duct stones of known sizes, collected from surgical sources were used in the experiments. Insensitivity of the stones fragmentation to the type of the laser used, and insensitivity of the fragmentation efficiency to the type of stone, was observed. No pathological changes of the tissue were observed for non-human soft tissue laser irradiation (in vitro) by 1, 2, and 5 pulses of the Cr:Th:Ho:YAG radiation of the fluency of 1.6 J/cm². The lasers are found to be good candidates for laser lithotripsy.     

On the efficiency of small-angle Čerenkov second harmonic generation in optical waveguides

It is well known that in the non-depleted pump approximation, the efficiency of a second harmonic generation (SHG) of a guided mode in a non-linear optical waveguide increases quadratically with the interaction length (P ₂ L ²), and linearly (P ₂ L) in the erenkov regime. The efficiency of the erenkov SHG in the waveguide with a non-linear substrate and linear guiding layer is known to be strongly peaked at a particular pump wavelength and a particular waveguide thickness, with the erenkov angle approaching zero. The known theory predicts an infinite efficiency value at the peak, however. In this contribution, a simple integral expression for the SHG efficiency in the erenkov regime is derived. For large erenkov angles and interaction lengths it yields the expected P ₂ L dependence, while in the limit of small erenkov angles the dependence is found to have the form of P L ^3/2, possessing also a finite value at the efficiency peak. The condition determining the accurate position of the efficiency peak in the waveguide thickness–pump wavelength plane is given, too.     

制备工艺对p型碲化铋基合金热电性能的影响

利用区熔法、机械合金化、放电等离子烧结(SPS)技术、热压法等多种工艺制备了p型碲化铋基热电材料.在300—500K的温度范围内测量了各热电性能参数，包括电导率(σ)、塞贝克系数(α)和热导率(κ)，研究了制备工艺对热电性能的影响.结果表明，所制备的块体材料与同组成区熔晶体相比，性能优值ZT均有不同程度的提高.其中，利用区熔法结合SPS技术可获得热电性能最佳的块体材料，其ZT值达1.15. 关键词： 碲化铋 放电等离子烧结 区熔法 热电性能     

The possibility to use ‘energy plus transmutation’ set-up for neutron production and transport benchmark studies

The set-up ‘energy plus transmutation’, consisting of a thick lead target and a natural uranium blanket, was irradiated by relativistic proton beams with the energy from 0.7 GeV up to 2 GeV. Neutron field was measured in different places of this set-up using different activation detectors. The possibilities of using the obtained data for benchmark studies are analyzed in this paper. Uncertainties of experimental data are shown and discussed. The experimental data are compared with results of simulation with MCNPX code.      

Preparation and characterization of titania based nanowires

A new method for preparation of titania nanowires with diameter around 10 nm and length up to 2–3 μm is described. The precursor was prepared from sodium titanate by adding ethylene glycole (EG) and heating at temperature of 198°C for 6 h under reflux. The sodium titanate glycolate formed by this way aggregated into 1D nanostructures and was subsequently transformed into titania glycolate during a chemical treatment with 98% sulfuric acid. Titania nanowires with variable amount of anatase and rutile were prepared by heating to temperatures in the range 350–1000°C. The precursor as well as titania based samples were characterized by X-ray diffraction, Infrared spectroscopy, Scanning electron microscopy, High resolution transmission microscopy, Thermogravimetry, Differential thermal analysis, Evolved gas analysis and Emanation thermal analysis. The nitrogen adsorption/desorption was used for surface area and porosity determination. The photoactivity of the prepared titania samples was assessed by the photocatalytic decomposition of 4-chlorophenol in an aqueous slurry under UV irradiation of 365 nm wavelength.     

Synthesis and structural study of 2′‐ and 2′,6′‐positioned methyl‐ and nitro‐substituted 3‐(arylhydrazono)pentane‐2,4‐diones

A systematic series of ortho‐methyl‐ and nitro‐substituted arylhydrazones 2–6 formed by Japp–Klingemann reaction between pentane‐2,4‐dione and the respective aryldiazonium salts have been synthesized and studied by X‐ray crystal structure analysis, with added quantum chemical calculations. The optimized molecular geometries based on DFT calculations, enabling determination of relevant rotational barriers, and the calculated bond and ring critical points, using the method of ‘atoms in molecules’, were found to correspond with the experimental data, involving specific molecular conformations and hydrogen‐bonded ring structure dependent on the ortho‐substitution, thus making possible reliable structural prediction of this compound class. Copyright © 2007 John Wiley & Sons, Ltd.