A Generating Tree Approach to <Emphasis Type="Italic">k</Emphasis>-Nonnesting Partitions and Permutations

We describe a generating tree approach to the enumeration and exhaustive generation of k-nonnesting set partitions and permutations. Unlike previous work in the literature which uses the connections of these objects to Young tableaux and restricted lattice walks, our approach deals directly with partition and permutation diagrams. We provide explicit functional equations for the generating functions, with k as a parameter. Key to the solution is a superset of diagrams that permit semi-arcs. Many of the resulting counting sequences also count other well-known objects, such as Baxter permutations, and Young tableaux of bounded height.     

Local Stability and Local Convergence of the Basic Trust-Region Method

It is proved that the iterative sequence constructed by the Basic Trust-Region Algorithm (see Conn et al. in Trust-region methods, MPS-SIAM series on optimization, Philadelphia, 2000), which uses the Cauchy point method, is locally stable and linearly convergent in a neighborhood of a nonsingular local minimizer.     

Facile Fabrication of PEGylated Fluorescent Organic Nanoparticles with Aggregation‐Induced Emission Feature via Formation of Dynamic Bonds and Their Biological Imaging Applications

Driven by the high demand for sensitive and specific tools for optical imaging, fluorescent nanoprobes with various working mechanisms and advanced functionalities are flourishing at an incredible speed. This work reports the design and fabrication of aggregation‐induced emission (AIE)‐active fluorescent organic nanoparticles (FNPs) via forming dynamic phenyl borate between diol containing hydrophobic AIE dye (APD‐PhCHO) and phenylboronic acid pendant hydrophilic polymers (PEGMA‐VPBA) within 30 min. The final AIE‐active APD‐PhCHO‐PEGMA‐VPBA FNPs display high water dispersibility and strong fluorescence emission because of their amphiphilic properties and AIE feature. Biological evaluation suggests that APD‐PhCHO‐PEGMA‐VPBA FNPs possess negative effect on HeLa cells and desirable optical properties for biological imaging. More importantly, phenyl borate is a dynamic bond with pH and glucose responsiveness. Furthermore, different functions can be designed and introduced into these AIE‐active systems through adoption of different monomers for good applicability of free radical polymerization. Therefore, this work provides a novel platform for preparation of multifunctional AIE‐active nanosystems with responsiveness for various biomedical applications.

     

A new pH sensitive fluorescent and white light emissive material through controlled intermolecular charge transfer

A new, pH dependent and water-soluble, conjugated oligomer (amino, trimethylammonium oligophenylene vinylene, ATAOPV) was synthesized with a quaternary ammonium salt and an aromatic amine at the two ends of a π-conjugated oligomer, thus creating a strong dipole across the molecule. A unique white light LED is successfully fabricated from a stimuli responsive organic molecule whose emission properties are dominated by the pH value of the solution through controlled intermolecular charge transfer.     

Information initiatives of mobile retailers: a regression analysis of zero‐truncated count data with underdispersion

Our paper presents an empirical analysis of the association between firm attributes in electronic retailing and the adoption of information initiatives in mobile retailing. In our attempt to analyze the collected data, we find that the count of information initiatives exhibits underdispersion. Also, zero‐truncation arises from our study design. To tackle the two issues, we test four zero‐truncated (ZT) count data models—binomial, Poisson, Conway–Maxwell–Poisson, and Consul's generalized Poisson. We observe that the ZT Poisson model has a much inferior fit when compared with the other three models. Interestingly, even though the ZT binomial distribution is the only model that explicitly takes into account the finite range of our count variable, it is still outperformed by the other two Poisson mixtures that turn out to be good approximations. Further, despite the rising popularity of the Conway–Maxwell–Poisson distribution in recent literature, the ZT Consul's generalized Poisson distribution shows the best fit among all candidate models and suggests support for one hypothesis. Because underdispersion is rarely addressed in IT and electronic commerce research, our study aims to encourage empirical researchers to adopt a flexible regression model in order to make a robust assessment on the impact of explanatory variables. Copyright © 2014 John Wiley & Sons, Ltd.     

Synthesis and unexpected electrochemical behavior of the triphenylamine‐based aramids with ortho‐ and para‐trimethyl‐protective substituents

Two series of new organosoluble polyamides with methyl‐substituted triphenylamine (MeTPA) units showing anodically electrochromic characteristic were prepared from the phosphorylation polyamidation reaction of two diamine monomers, 4,4′‐diamino‐2″,4″,6″‐trimethyltriphenylamine (Me₃TPA‐diamine; 2 ) and 4,4′‐diamino‐4″‐methyltriphenylamine (MeTPA‐diamine; 2 ′), with various dicarboxylic acids, respectively. These polymers were readily soluble in many polar solvents and showed useful levels of thermal stability associated with relatively high glass‐transition temperatures (T_g) (314–329 °C) and high char yields (higher than 62% at 800 °C in nitrogen). In addition, the polymer films showed reversible electrochemical oxidation, high coloration efficiency (CE), low switching time, and anodic green electrochromic behavior. The unexpected electrochemical behavior of higher oxidation potential and lower electrochemical stability of Me₃TPA‐polyamides I than MeTPA corresponding polymers could be attributed to the higher steric hindrance of ortho‐substituents in Me₃TPA moieties, thus made the resonance stabilization of cation radical much more difficult for the Me₃‐substituted phenyl ring. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

A green epoxidation system with poly(4‐vinylpyridine) microsphere‐supported molybdenum catalyst

The immobilization of molybdenum (Mo) compounds on poly(4‐vinylpyridine) (P4VP) microspheres for catalytic epoxidation was reported. P4VP‐supported Mo compounds were highly efficient and selective for the epoxidation of cis‐cyclooctene using hydrogen peroxide (H₂O₂) as oxygen source. When ethanol was used as solvents, outstanding catalytic activity and selectivity were observed for Mo‐containing catalysts in the epoxidation of cis‐cyclooctene. A completely green epoxidation system based on H₂O₂ and cleaner solvent has been achieved, and the heterogenized Mo catalyst can be recovered for five times without loss of its activity. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 558–562, 2010     

Call Option Prices Based on Bessel Processes

As a complement to some recent work by Pal and Protter (2007, 2009), we show that the call option prices associated with the Bessel strict local martingales are integrable over time, and we discuss the probability densities obtained thus.     

In situ formation of Sn(IV) catalyst with increased activity in ε‐caprolactone and L‐lactide polymerization using stannous(II) 2‐ethylhexanoate

Ring‐opening polymerization (ROP) of ε‐caprolactone and L‐lactide (LA) was studied using stannous(II) 2‐ethylhexanoate (Sn(Oct)₂) with N,N‐dimethylformamide‐dimethyl acetal (DMF‐DMA). DMF‐DMA showed a tenfold improvement in catalytic activity over that of Sn(Oct)₂ under the same conditions. It also enhanced the capability to control molecular weight in the synthesis of small molecular weight polymers of polycaprolactone and polylactide (PLA). The high molecular weight polymerization demonstrated a strong capability to control molecular weight for the polymerization of LA: a molecular weight of PLA exceeding 400,000 was obtained at very low catalytic loadings. The individual polymerization rates of other tin reagents with DMF‐DMA also clearly increased. Applying this methodology could drastically reduce the time and cost required for the fabrication of these products to increase the competitive advantage of manufacturers. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012