Majorization of regular measures and weights with finite and positive critical exponent

For the sets , 1?p<∞, of positive finite Borel measures μ on the real axis with the set of algebraic polynomials P dense in Lp(R,dμ), we establish a majorization principle of their “boundaries,” i.e. for every there exists such that dμ/dν?1. A corresponding principle holds for the sets , p>0, of non-negative upper semi-continuous on R functions (weights) w such that P is dense in the space : For every there exists such that w?ω.     

On some iterated weighted spaces

It is proved that the Hörmander and spaces (Ω₁⊂Rn, Ω₂⊂Rm open sets, 1?p<∞, ki Beurling-Björck weights, k=k₁⊗k₂) are isomorphic whereas the iterated spaces and are not if 1<p≠q<∞. A similar result for weighted Lp-spaces of entire analytic functions is also obtained. Finally a result on iterated Besov spaces is given: and are not isomorphic when 1<q≠2<∞.     

Asymptotic approximations for second-order linear difference equations in Banach algebras, II

A Liouville-Green (WKB) asymptotic approximation theory is developed for some classes of linear second-order difference equations in Banach algebras. The special case of linear matrix difference equations (or, equivalently, of second-order systems) is emphasized. Rigorous and explicitly computable bounds for the error terms are obtained, and this when both, the sequence index and some parameter that may enter the coefficients, go to infinity. A simple application is made to orthogonal matrix polynomials in the Nevai class.     

A new synthetic approach to 7-hydroxynitidine

Benzo[c]phenanthridine alkaloid, 7-hydroxynitidine, was synthesized from readily available 2-benzyloxy-6-bromo-3,4-dimethoxybenzaldehyde 5 and napthylamine 6 using reductive amination followed by radical cyclization in eight steps. This method is highly efficient and better way to synthesize fully aromatized benzo[c]phenanthridine compounds.     

Thermodynamical studies of designed ligands binding to Cel7A using partial-filling capillary electrophoresis

A convenient experimental method for thermodynamical studies based on partial-filling affinity CE is presented. The advantages of this approach are the possibility to determine binding energies from relatively weak interactions as well as the small amounts of samples consumed. In order to explore the affinity and selectivity of the cellobiohydrolase Cel7A, a number of propranolol analogues were recently designed. The affinities of a selection of these ligands were determined in the temperature interval 15-40 degrees C, and DeltaG degrees , DeltaH degrees and DeltaS degrees were obtained by means of Van't Hoff plots. Through these experiments, the importance of the entropy contribution in the complexation between the ligands and Cel7A has been demonstrated.     

Ce和Dy在Cd0.5Zn0.5B4O7中的发光特性及能量双向传递

采用高温固相法制备了白蓝光双发射为一体的Cd0.5Zn0.5B4O7∶Ce/Dy系列发光材料. 由XRD测得Cd0.41Zn0.5B4O7∶Ce0.04/Dy0.02的晶胞参数: a=1.3885 nm, b=0.8020 nm, c=0.8670 nm, 属于正交晶系, Pbca空间群. 在Ce/Dy双掺的体系中存在Ce3+和Dy3+两种发光中心, 254~350 nm激发主要是Dy3+的 4F9/2→6H15/2和4F9/2→6H13/2跃迁发射, 而355—390 nm激发主要为Ce3+的5d→4f跃迁发射. 340 nm激发Ce/Dy双掺发光体的发射强度是同浓度Dy3+单掺的31倍, Ce3+是Dy3+的高效敏化剂, 而355—390 nm激发Dy3+是Ce3+的敏化剂. 体系中存在少见的Ce3+→Dy3+与Dy3+→Ce3+的能量双向传递.     

Synthesis of the water-soluble [Rh(Tpms)(CO)(PTA)] compound, the first transition metal complex bearing the 1,3,5-triaza-7-phosphaadamantane (PTA) and the tris(1-pyrazolyl)methanesulfonate (Tpms) ligands

The water-soluble Rh^I compound [Rh(Tpms)(CO)(PTA)] (1) (Tpms = O₃SC(pz)₃⁻, PTA = 1,3,5-triaza-7-phosphaadamantane) has been easily prepared in high yield by a single-pot reaction of [{Rh(CO)₂(μ-Cl)}₂] with PTA and the tris(1-pyrazolyl)methanesulfonate lithium salt Li(Tpms), in a CH₂Cl₂/MeOH solution at room temperature. This synthetic strategy can be easily applied to the preparation of general [Rh(Tpms)(CO)(L)] (L = phosphine) complexes and constitutes a substantial improvement over the previously described procedures. Compound 1 is air stable in the solid state and water-soluble, affording stable solutions under an inert atmosphere. It has been characterized by IR, ¹H, ³¹P{¹H} and ¹³C{¹H} NMR spectroscopies, elemental and single crystal X-ray diffraction structural analyses. The solid state structure of 1 has a square-planar geometry with the Tpms ligand coordinating the metal centre in a (κ²: N,N) bipodal mode. The title compound has also been investigated by cyclic voltammetry in CH₃CN, and values of the E_L Lever and P_L Pickett electrochemical parameters (which measure the ligand net electron-donor character) are proposed for the PTA ligand. Complex 1 represents the first example of a transition metal complex bearing both PTA and Tpms (or any other tris(1-pyrazolyl)methane or derivative) ligands.     

Synthesis of Some New Heterocycles Derived from Phenylacetyl Isothiocyanate

Phenylacetyl isothiocyanate (1) was reacted with benzoyl hydrazine (2a) in acetonitrile to give thiosemicarbazide derivative 3 which was cyclized by polyphosphoric acid to give 1,2,4-triazoline-5-thione derivative 4. Treatment of 1 with thiosemicarbazide (2b) yielded another 1,2,4-triazoline-5-thione derivative 5. Similar treatment of 1 with phenyl hydrazine (2c) in acetonitrile gave a differently substituted 1,2,4-triazoline-5-thione derivative 6 in one pot-reaction. On the other hand, when the reaction was carried out in acetone, a mixture of 6 and thiadiazolidine derivative 7 was obtained. However, reaction of 1 with hydrazine hydrate (2d) gave hydrazine derivative 8. Reaction of isothiocyanate 1 with anthranilic acid (9) gave benzo[d][1,3,6]oxazin-1-one derivative 10. Treatment of 1 with 2-aminothiophenol (11a), 2-aminophenol (11b) or o-phenylenediamine (11c) produced benzothiazole derivative 12a, benzoxazole derivative 12b and benzimidazole derivative 12c, respectively. The structures of all the products were confirmed by micro-analytical and spectral data.