Crown ether complexes of sodium and potassium 2-(benzotriazol-2-yl)phenolates: Synthesis and catalysis towards the ring-opening polymerization of rac-lactide

Crown ether complexes of sodium and potassium 2-(benzotriazol-2-yl)phenolates were synthesized and characterized. In the presence of BnOH these complexes are highly active catalysts for the controlled ring-opening polymerization of rac-lactide. The polymerizations are iso-selective and the P_m of polylactide reached 0.77 when the polymerization was performed in toluene at ?60°C; whereas heterorich-polylactide was obtained when the polymerization was carried out in CH₂Cl₂ or THF.     

Precise large deviations for sums of random vectors with dependent components of consistently varying tails

Let {X _i = (X _1,i ,...,X _m,i )^?, i ≥ 1} be a sequence of independent and identically distributed nonnegative m-dimensional random vectors. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Here, the components of X ₁ are allowed to be generally dependent. Moreover, let N(·) be a nonnegative integer-valued process, independent of the sequence {X _i , i ≥ 1}. Under several mild assumptions, precise large deviations for S _n = Σ _i=1 ⁿ X _i and S _N(t) = Σ _i=1 ^N(t) X _i are investigated. Meanwhile, some simulation examples are also given to illustrate the results.     

Standard molar enthalpy of formation of [(C12H8N2)2Bi(O2NO)3] and its biological activity on Schizosaccharomyces pombe

The title complex [(C₁₂H₈N₂)₂Bi(O₂NO)₃] was synthesized by reaction of 1,10-phenanthroline (phen) and Bi(NO₃)₃·5H₂O. The structure of the complex was characterized by single-crystal X-ray diffraction, IR spectroscopy, and elemental analysis. An advanced solution-reaction isoperibol microcalorimeter was applied to determine the standard molar enthalpies of formation at 298.15 K of the complex and Bi(NO₃)₃·5H₂O, giving –(798.92 ± 5.99) and –(1986.87 ± 0.20) kJ mol⁻¹, respectively. The biological effect of the complex was evaluated by microcalorimetry on the growth of Schizosaccharomyces pombe (S. pombe). According to thermogenic curves, the corresponding thermokinetics and thermodynamic parameters were derived. The complex had good bioactivity on the growth metabolism of S. pombe, with the value of IC₅₀ being 2.8 × 10⁻⁵ mol L⁻¹.

     

Self-catalytic synthesis of hydrophilic polypyrrole/tellurium nanocomposite and its capacitance performance

Journal of Solid State Electrochemistry - A hydrophilic polypyrrole/tellurium (PPy/Te) nanocomposite was synthesized by a facile approach in which H2TeO3 was used as the oxidizing agent of pyrrole...     

Nickel‐Catalyzed Barton Decarboxylation and Giese Reactions: A Practical Take on Classic Transforms

Two named reactions of fundamental importance and paramount utility in organic synthesis have been reinvestigated, the Barton decarboxylation and Giese radical conjugate addition. N ‐hydroxyphthalimide (NHPI) based redox‐active esters were found to be convenient starting materials for simple, thermal, Ni‐catalyzed radical formation and subsequent trapping with either a hydrogen atom source (PhSiH₃) or an electron‐deficient olefin. These reactions feature operational simplicity, inexpensive reagents, and enhanced scope as evidenced by examples in the realm of peptide chemistry.     

Thioether‐derived Macrocycle for Peptide Secondary Structure Fixation

Recently, we developed methods to stabilize peptides into various secondary structures, including α‐helix, type III turn and β‐hairpin via proper thioether based macrocyclization. These conformationally constrained peptidomimetics confer enhanced biophysical properties and provide a valuable avenue towards clinically‐relevant therapeutic molecules. In this personal account, thioether‐derived macrocyclization methods developed by our group for stabilization of α‐helix, type‐III β turn and β‐hairpin conformations are discussed.     

Global dynamics of a Vector‐Borne disease model with two delays and nonlinear transmission rate

In this paper, we investigate a Vector‐Borne disease model with nonlinear incidence rate and 2 delays: One is the incubation period in the vectors and the other is the incubation period in the host. Under the biologically motivated assumptions, we show that the global dynamics are completely determined by the basic reproduction number R₀. The disease‐free equilibrium is globally asymptotically stable if R₀≤1; when R₀>1, the system is uniformly persistent, and there exists a unique endemic equilibrium that is globally asymptotically. Numerical simulations are conducted to illustrate the theoretical results.     

自由Rota-Baxter代数的因子分解

近年来,Rota-Baxter代数在数学和物理学中有着广泛的应用,受到越来越多的关注,自由Rota-Baxter代数分别用括号字,根树以及Motzkin路径得到了构造.因子分解在代数学中是一个很重要的问题.本文主要考虑用括号字构造的自由RotaBaxter代数,得到了自由Rota-Baxter代数中基元素的因子分解.     

Analytic invariant curves for an iterative equation related to dissipative standard map

In this paper, we study existence of invariant curves of an iterative equation which is from dissipative standard map. By constructing an invertible analytic solution g (x ) of an auxiliary equation of the form invertible analytic solutions of the form g (λ g  ^? 1(x )) for the original iterative functional equation are obtained. Besides the hyperbolic case 0 < |λ | < 1, we focus on those λ on the unit circle S ¹, that is, |λ | = 1. We discuss not only those λ at resonance, that is, at a root of the unity, but also those λ near resonance under the Brjuno condition. Copyright © 2016 John Wiley & Sons, Ltd.     

Composite generalized Laguerre spectral method for nonlinear Fokker–Planck equations on the whole line

In this paper, we propose a composite Laguerre spectral method for the nonlinear Fokker–Planck equations modelling the relaxation of fermion and boson gases. A composite Laguerre spectral scheme is constructed. Its convergence is proved. Numerical results show the efficiency of this approach and coincide well with theoretical analysis. Some results on the Laguerre approximation and techniques used in this paper are also applicable to other nonlinear problems on the whole line. Copyright © 2016 John Wiley & Sons, Ltd.