Co‐syndiospecific Alternating Copolymerization of Functionalized Propylenes and Styrene by Rare‐Earth Catalysts

The precise control of monomer sequence and stereochemistry in copolymerization is of much interest and importance for the synthesis of functional polymers, but studies toward this goal have met with only limited success to date. Now, the co‐syndiospecific alternating copolymerization of methoxyphenyl‐ and N,N‐dimethylaminophenyl‐functionalized propylenes with styrene by half‐sandwich rare‐earth catalysts is reported. This reaction efficiently afforded the corresponding functionalized propylene‐alt‐styrene copolymers with a perfect alternating sequence and excellent co‐syndiotacticity (rrrr >99 %), thus constituting the first example of co‐stereospecific alternating copolymerization of polar and non‐polar olefins.     

Hidden Markov models revealing the stress field underlying the earthquake generation

The application of the hidden Markov models (HMMs) is attempted for revealing key features for the earthquake generation which are not accessible to direct observation. Considering that the states of the HMM correspond to levels of the stress field, our objective is to identify these states. The observations are considered after grouping earthquake magnitudes and the cases of different number of states are examined. The problems of HMMs theory are solved and the ensuing HMMs are compared on the basis of Akaike and Bayesian information criteria. A new insight on the evaluation of future seismic hazard is given by calculating the mean number of steps for the first visit to a particular state, along with the respective variance. We further calculate an estimator of the mean number of steps for the first visit to a particular state and we construct its confidence interval. Additionally, a second approach to the problem is followed by assuming a different determination of observations. The HMMs applied to both approaches, contribute significantly to seismic hazard assessment via revealing the number of the stress levels as well as the way in which these levels are associated with certain earthquake occurrence.     

Dependence of electronic and optical properties of multilayer SiC and GeC on stacking sequence and external electric field

The electronic and optical properties of different stacked multilayer SiC and GeC are investigated with and without external electric field (EEF). The band gaps of multilayer SiC and GeC are found smaller than that of monolayer SiC and GeC due to the interlayer coupling effect. When EEF is applied, the direct band gaps (ΔK–M) of multilayer SiC and direct band gaps (ΔK–K) of multilayer GeC all turn to indirect band gaps (ΔK–G) as the band at the G point drops dramatically toward zero. The imaginary part ε₂(ω)s of multilayer SiC and GeC show that new absorption peaks between 2–5 eV appear when the polarized direction is perpendicular to the layer plane, and new absorption peaks in infrared region appear as the EEF is higher than a certain point when the polarized direction is parallel to the layer plane. Our calculations reveal that different stacking sequences and EEF can provide a wide tunable band structures and optical properties for multilayer SiC and GeC.     

A model of product line design and introduction sequence with reservation utility

Cannibalization is a major concern for a firm when designing a product line. In addition, external options from outside the firm’s product line may also play a significant role. In this paper, we investigate the impact of external options, represented by reservation utility, on product line design and introduction sequence. We find that: (a) heterogeneous reservation utility defines the relative attractiveness of segments and corresponding product line; (b) reservation utility makes it more favorable to introduce products sequentially rather than simultaneously; (c) aggregating segments is an effective way to mitigate cannibalization when it becomes too difficult to manage with different values of reservation utility across multiple segments; and (d) introducing products in a non-monotone order of quality can improve profit from simultaneous introduction when the value of reservation utility of a middle segment is particularly high.     

Book review of spectral theory of linear operators and spectral systems in banach algebras,operator theory: advances and applications,Vladimir Müller,Birkhäuser Verlag,Basel-Boston-Berlin, 2003, Volume 139, 381 pages. ISBN 3-7643-6912-4

We explore how randomization can help asymptotic convergence properties of simple directional search-based optimization methods. Specifically, we develop a cheap, iterative randomized Hessian estimation scheme. We then apply this technique and analyse how it enhances a random directional search method. Then, we proceed to develop a conjugate-directional search method that incorporates estimated Hessian information without requiring the direct use of gradients.     

Reactivity Ratios and Sequence Distribution Characterization by Quantitative 13C NMR for RAFT Synthesis of Styrene‐Acrylonitrile Copolymers

The kinetics and reactivity ratios of styrene‐acrylonitrile (SA) copolymerization have been studied extensively in bulk and in a variety of solution media using conventional free radical polymerizations (FRPs). Due to the significant difference in the two reactivity ratios for this monomer pair, at certain feed ratios the copolymers display composition drift with conversion due to monomer depletion. In this study, the kinetics of SA copolymerization using Reversible Addition‐Fragmentation Chain Transfer (RAFT) has been studied in bulk at 80 °C. The reactivity ratios for the terminal model were calculated from the comonomer sequence distributions for the RAFT process at low conversion for nine different compositions and found to be in the same range as those reported for conventional FRP of SA. The changes in the composition and sequence distribution with conversion were studied for three feed compositions. The copolymers show compositional drift with conversion, except at the azeotropic composition, and match the predictions from the reactivity ratios obtained at low conversion. From quantitative ¹³C NMR the triad distributions of these copolymers were estimated and found to match the predicted triad distributions as conversion increased. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 919–927     

The q-Calkin-Wilf tree

We define a q-analogue of the Calkin-Wilf tree and the Calkin-Wilf sequence. We show that the nth term f(n;q) of the q-analogue of the Calkin-Wilf sequence is the generating function for the number of hyperbinary expansions of n according to the number of powers that are used exactly twice. We also present formulae for branches within the q-analogue of the Calkin-Wilf tree and predecessors and successors of terms in the q-analogue of the Calkin-Wilf sequence.     

字符串匹配算法在DNA序列比对中的应用

高通量测序技术的飞速发展让生物信息领域迎来了大数据时代。新技术在提供海量生物遗传信息的同时,也给分析这些数据带来了新的挑战。DNA序列比对是信息分析流程中的关键步骤,为后续的变异检测提供序列比对信息。2015“深圳杯”数学建模夏令营B题以DNA序列比对为研究课题,希望参赛学生给出序列快速比对的最佳方案。本文简要点评了各参赛队伍的解答情况,然后介绍了现有DNA序列比对软件中用到的算法和数据结构。     

Determination of the Chemical Structure of Poly-β (-)-pinene by NMR Spectroscopy

This paper is dedicated to the memory of our friend and colleague Annalaura Segre.

The chemical structure of a series of β (-)-pinene polymers (PBP) obtained by radiation-induced polymerization, free radical initiation, cationic polymerization over a Friedel-Craft catalyst and by coordinative polymerization over a Ziegler-Natta catalyst has been fully elucidated by ¹H and ¹³C-NMR spectroscopy. 2D NMR techniques have been applied in order to assign all the NMR resonances to the structures of the PBP investigated. The NMR spectra show that the most regular PBP structure is obtained by radiation-induced polymerization followed by the free radical initiated polymerization. The most defective structure has been observed in the case of PBP prepared by cationic mechanism over a Friedel-Crafts catalyst. The discussion accounts for different types of defects and cross-links present in the PBPs investigated whose fundamental structure is based on the p-menthene repeating unit.

NMR self-diffusion measurements have been performed to evaluate the molecular weight of all the PBP investigated. The highest molecular weight (2600 Dalton) was found in the case of PBP prepared by Ziegler-Natta catalyst, while the lowest molecular weight was found in the case of PBP prepared by radiation-induced polymerization (about 1000 Dalton).     

N‐Vinylpyrrolidone and Ethoxyethyl Methacrylate Copolymer: Synthesis,Characterization and Reactivity Ratios

Free radical copolymerization of N‐vinyl‐2‐pyrrolidone with 2‐ethoxyethyl methacrylates was carried out with 2,2′‐azobisisobutyronotrile as an initiator in 1,4‐dioxane. The resulting copolymer was characterized by FTIR, H¹‐NMR and C¹³‐NMR spectroscopic techniques thermal properties of copolymer were determined by DSC and TGA. The reactivity ratios of the monomers were computed by the Fineman‐Rose (F‐R), Kelen‐Tudos (K‐T) and extended Kelen‐Tudos (EK‐T) method at lower conversion, using the data obtained from both FTIR and elemental analysis studies; the results are in good agreement with each other. The average reactivity ratio, Alfrey‐Price Q and e values were found to be r ₁=0.769, r ₂=0.266 and Q ₁=0.0859, e ₁=0.4508, respectively for NVP/EOEMA copolymer. The distribution of monomer sequence along the copolymer chain was calculated using a statistical method based on obtained reactivity ratio. The number average molecular weight and polydispersity were determined by GPC.