Thioetherphenolate group 4 metal complexes in the ring opening polymerization of rac‐β‐Butyrolactone

Group 4 complexes 1 – 3 [ 1 = (t‐BuOS)₂Ti(O‐i‐Pr)₂; 2 = (t‐BuOS)₂Zr(O‐t‐Bu)₂; 3 = (t‐BuOS)₂Hf(O‐t‐Bu)₂] supported by two phenolate bidentate ligands (t‐BuOS‐H = 4,6‐di‐tert‐butyl‐2‐phenylsulfanylphenol) promote the well‐controlled ring opening polymerization of rac‐β‐butyrolactone. In presence of isopropanol, low dispersities and molecular weights proportional to the equivalents of isopropanol are achieved. Moreover, the zirconium complex is effective in the copolymerization of rac‐β‐butyrolactone with rac‐lactide. The 13 C nuclear magnetic resonance analysis revealed that the obtained copolymers have a tapered diblock microstructure consisting of an initial block composed of lactide sequences and a terminal block composed of butyrolactone sequences. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 3132–3139     

A Novel [OSSO]-Type Chromium(III) Complex as a Versatile Catalyst for Copolymerization of Carbon Dioxide with Epoxides

A new chromium(III) complex, bearing a bis-thioether-diphenolate [OSSO]-type ligand, was found to be an efficient catalyst in the copolymerization of CO₂ and epoxides to achieve poly(propylene carbonate), poly(cyclohexene carbonate), poly(hexene carbonate) and poly(styrene carbonate), as well as poly(propylene carbonate)(cyclohexene carbonate) and poly(propylene carbonate)(hexene carbonate) terpolymers.     

Quantum curves and q-deformed Painlevé equations

Letters in Mathematical Physics - We propose that the grand canonical topological string partition functions satisfy finite-difference equations in the closed string moduli. In the case of genus...     

Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control

This article proposes a new fractional-order discrete-time chaotic system, without equilibria, included two quadratic nonlinearities terms. The dynamics of this system were experimentally investigated via bifurcation diagrams and largest Lyapunov exponent. Besides, some chaotic tests such as the 0–1 test and approximate entropy (ApEn) were included to detect the performance of our numerical results. Furthermore, a valid control method of stabilization is introduced to regulate the proposed system in such a way as to force all its states to adaptively tend toward the equilibrium point at zero. All theoretical findings in this work have been verified numerically using MATLAB software package.     

Copper‐Catalyzed Propargylic Substitution of Dichloro Substrates: Enantioselective Synthesis of Trisubstituted Allenes and Formation of Propargylic Quaternary Stereogenic Centers

An easy and versatile Cu‐catalyzed propargylic substitution process is presented. Using easily prepared prochiral dichloro substrates, readily available Grignard reagents together with catalytic amount of copper salt and chiral ligand, we accessed a range of synthetically interesting trisubstituted chloroallenes. Substrate scope and nucleophile scope are broad, providing generally high enantioselectivity for the desired 1,3‐substitution products. The enantioenriched chloroallenes could be further transformed into the corresponding trisubstituted allenes or terminal alkynes bearing all‐carbon quaternary stereogenic centers, through the copper‐catalyzed enantiospecific 1,1/1,3‐substitutions. The two successive copper‐catalyzed reactions could be eventually combined into a one‐pot procedure and different desired allenes or alkynes were obtained respectively with high enantiomeric excesses.     

Hyperinstantons,the Beltrami equation,and triholomorphic maps

We consider the Beltrami equation for hydrodynamics and we show that its solutions can be viewed as instanton solutions of a more general system of equations. The latter are the equations of motion for an sigma model on 4‐dimensional worldvolume (which is taken locally HyperKähler) with a 4‐dimensional HyperKähler target space. By means of the 4D twisting procedure originally introduced by Witten for gauge theories and later generalized to 4D sigma‐models by Anselmi and Fré, we show that the equations of motion describe triholomophic maps between the worldvolume and the target space. Therefore, the classification of the solutions to the 3‐dimensional Beltrami equation can be performed by counting the triholomorphic maps. The counting is easily obtained by using several discrete symmetries. Finally, the similarity with holomorphic maps for sigma on Calabi‐Yau space prompts us to reformulate the problem of the enumeration of triholomorphic maps in terms of a topological sigma model.     

Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems

This article investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behaviors of the system are explored and discussed via several numerical simulations. This system displays complex hidden dynamics such as inversion property, chaotic bursting oscillation, multistabilty, and coexisting attractors. Besides, by means of adapting certain controlled constants, it is shown that this system possesses a three-variable offset boosting system. In conformity with the performed simulations, it also turns out that the resultant hidden attractors can be distributively ordered in a grid of three dimensions, a lattice of two dimensions, a line of one dimension, and even arbitrariness in the phase space. Through considering the Caputo fractional-order operator in all performed simulations, phase portraits in two- and three-dimensional projections, Lyapunov exponents, and the bifurcation diagrams are numerically reported in this work as beneficial exit results.     

A relationship between atomic correlation energy of neutral atoms and generalized entropy

In a previous article, hereafter named as Paper I, we have showed a relationship between atomic correlation energy of neutral atoms with 2 < Z < 29 and Tsallis entropy. In this article, we generalize this relation showing the link between the atomic correlation energy and a general form of entropy obtained from deformed algebra. The results evidence the role of both q and Δ parameters of the general entropy, in terms of contribution of the long‐range interactions in the correlation energy. The q and Δ values, obtained as best fit of the atomic correlation energies 2 < Z < 29, indicate that this general form of entropy reduces to the Tsallis one, reproducing well the trend of the correlation energy for low Z. Moreover, as a consequence of these values of the parameters, the state atomic wave function is more localized with respect to the wave function calculated in the limit of Shannon entropy. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011