Pooled marginal slicing approach via SIR<Subscript><Emphasis Type="Italic">α</Emphasis></Subscript> with discrete covariables

In this paper, we consider a semiparametric regression model involving both p-dimensional quantitative covariable X and categorical predictor Z, and including a dimension reduction of X via K indices X′β _k . The dependent variable Y can be real or q-dimensional. We propose an approach based on SIR _α and pooled marginal slicing methods in order to estimate the space spanned by the β _k ’s. We establish -consistency of the proposed estimator. Simulation studies show the numerical qualities of our estimator.     

PPV Polymerization through the Gilch Route: Diradical Character of Monomers

Despite various studies on the polymerization of poly(p‐phenylene vinylene) (PPV) through different precursor routes, detailed mechanistic knowledge on the individual reaction steps and intermediates is still incomplete. The present study aims to gain more insight into the radical polymerization of PPV through the Gilch route. The initial steps of the polymerization involve the formation of a p‐quinodimethane intermediate, which spontaneously self‐initiates through a dimerization process leading to the formation of diradical species; chain propagation ensues on both sides of the diradical or chain termination occurs by the formation of side products, such as [2.2]paracyclophanes. Furthermore, different p‐quinodimethane systems were assessed with respect to the size of their aromatic core as well as the presence of heteroatoms in/on the conjugated system. The nature of the aromatic core and the specific substituents alter the electronic structure of the p‐quinodimethane monomers, affecting the mechanism of polymerization. The diradical character of the monomers has been investigated with several advanced methodologies, such as spin‐projected UHF, CASSCF, CASPT2, and DMRG calculations. It was shown that larger aromatic cores led to a higher diradical character in the monomers, which in turn is proposed to cause rapid initiation.     

Highly Segregated Lamello‐Columnar Mesophase Organizations and Fast Charge Carrier Mobility in New Discotic Donor–Acceptor Triads

Four new donor–acceptor triads (D–A–D) based on discotic and arylene mesogens have been synthesized by using Sonogashira coupling and cyclization reactions. This family of triads consists of two side‐on pending triphenylene mesogens, acting as the electron‐donating groups (D), laterally connected through short lipophilic spacers to a central perylenediimide (PI), benzo[ghi]perylenediimide (BI), or coronenediimide (CI) molecular unit, respectively, playing the role of the electron acceptor (A). All D–A–D triads self‐organize to form a lamello‐columnar oblique mesophase, with a highly segregated donor–acceptor (D–A) heterojunction organization, consequent to efficient molecular self‐sorting. The structure consists in the regular alternation of two disrupted rows of triphenylene columns and a continuous row of diimine species. High‐resolution STM images demonstrate that PI‐TP2 forms stable 2D self‐assembly nanostructures with some various degrees of regularity, whereas the other triads do not self‐organize into ordered architectures. The electron‐transport mobility of CI‐TP2, measured by time‐of‐flight at 200 °C in the mesophase, is one order of magnitude higher than the hole mobility. By means of this specific molecular designing idea, we realized and demonstrated for the first time the so‐called p–n heterojunction at the molecular level in which the electron‐rich triphenylene columns act as the hole transient pathways, and the coronenediimide stacks form the electron‐transport channels.     

Controlled Synthesis and Degradation of Poly(N‐(isobutoxymethyl) acrylamide) Homopolymers and Block Copolymers

The homopolymerization of the water‐insoluble N‐(isobutoxymethyl)acrylamide (IBMA) is investigated for the first time by nitroxide‐mediated polymerization. The homopolymerization is characterized by a linear increase in number average molecular weight (M_n) versus conversion (X) to X > 0.80 while maintaining dispersities of M_w/M_n < 1.30. A strong Arrhenius relationship correlates the apparent rate constants and the homopolymerization temperatures between 105 and 120 °C. All poly(IBMA) homopolymers are then successfully chain‐extended with styrene (S) to form well‐defined block copolymers of poly(IBMA)‐b‐poly(S) suggesting a high degree of livingness of the poly(IBMA) macroinitiators. Thermogravimetric analysis and differential scanning calorimetry are both used to characterize the thermal properties of the homopolymers and block copolymers and identify possible unique degradation of the poly(IBMA) block through imide formation at elevated temperatures.

     

Analytical examples of diffusive waves generated by a traveling wave

We construct analytical solutions for a system composed of a reaction–diffusion equation coupled with a purely diffusive equation. The question is to know if the traveling wave solutions of the reaction–diffusion equation can generate a traveling wave for the diffusion equation. Our motivation comes from the calcic wave, generated after fertilization within the egg cell endoplasmic reticulum, and propagating within the egg cell. We consider both the monostable (Fisher–KPP type) and bistable cases. We use a piecewise linear reaction term so as to build explicit solutions, which leads us to compute exponential tails whose exponents are roots of second-, third-, or fourth-order polynomials. These raise conditions on the coefficients for existence of a traveling wave of the diffusion equation. The question of positivity and monotonicity is only partially answered.     

Chebyshev model arithmetic for factorable functions

This article presents an arithmetic for the computation of Chebyshev models for factorable functions and an analysis of their convergence properties. Similar to Taylor models, Chebyshev models consist of a pair of a multivariate polynomial approximating the factorable function and an interval remainder term bounding the actual gap with this polynomial approximant. Propagation rules and local convergence bounds are established for the addition, multiplication and composition operations with Chebyshev models. The global convergence of this arithmetic as the polynomial expansion order increases is also discussed. A generic implementation of Chebyshev model arithmetic is available in the library MC++. It is shown through several numerical case studies that Chebyshev models provide tighter bounds than their Taylor model counterparts, but this comes at the price of extra computational burden.     

"Multi-scan single shot" quantitative 2D NMR: a valuable alternative to fast conventional quantitative 2D NMR

Quantitative Ultrafast (UF) 2D NMR is a very promising methodology enabling the acquisition of 2D spectra in a single scan. The analytical performances of UF 2D NMR have been highly increased in the last few years, however little is known about the sensitivity of ultrafast experiments versus conventional 2D NMR. A fair and relevant comparison has to consider the Signal-to-Noise Ratio (SNR) per unit of time, in order to answer the following question: for a given experiment time, should we run a conventional 2D experiment or is it preferable to accumulate ultrafast acquisitions? To answer this question, we perform here a systematic comparison between accumulated ultrafast experiments and conventional ones, for different experiment durations. Sensitivity issues and other analytical aspects are discussed for the COSY experiment in the context of quantitative analysis. The comparison is first carried out on a model sample, and then extended to model metabolic mixtures. The results highlight the high analytical performance of the "multi-scan single shot" approach versus conventional 2D NMR acquisitions. This result is attributed to the absence of t(1) noise in spatially encoded experiments. The multi-scan single shot approach is particularly interesting for quantitative applications of 2D NMR, whose occurrence in the literature has been greatly increasing in the last few years.     

Third-order nonlinear optical properties of open-shell supermolecular systems composed of acetylene linked phenalenyl radicals

The third-order nonlinear optical (NLO) properties, at the molecular level, the static second hyperpolarizabilities, γ, of supermolecular systems composed of phenalenyl and pyrene rings linked by acetylene units are investigated by employing the long-range corrected spin-unrestricted density functional theory, LC-UBLYP, method. The phenalenyl based superethylene, superallyl, and superbutadiene in their lowest spin states have intermediate diradical characters and exhibit larger γ values than the closed-shell pyrene based superpolyene systems. The introduction of a positive charge into the phenalenyl based superallyl radical changes the sign of γ and enhances its amplitude by a factor of 35. Although such sign inversion is also observed in the allyl radical and cation systems in their ground state equilibrium geometries, the relative amplitude of γ is much different, that is, |γ(regular allyl cation)/γ(regular allyl radical)| = 0.61 versus |γ(phenalenyl based superallyl cation)/γ(phenalenyl based superallyl radical)| = 35. In contrast, the model ethylene, allyl radical/cation, and butadiene systems with stretched carbon-carbon bond lengths (2.0 ?), having intermediate diradical characters, exhibit similar γ features to those of the phenalenyl based superpolyene systems. This exemplifies that the size dependence of γ as well as its sign change by introducing a positive charge on the phenalenyl based superpolyene systems originate from their intermediate diradical characters. In addition, the change from the lowest to the highest π-electron spin states significantly reduces the γ amplitudes of the neutral phenalenyl based superpolyene systems. For phenalenyl based superallyl cation, the sign inversion of γ (from negative to positive) is observed upon switching between the singlet and triplet states, which is predicted to be associated with a modification of the balance between the positive and negative contributions to γ. The present study paves the way toward designing a variety of open-shell NLO supermolecular systems composed of phenalenyl radical building blocks.     

Total synthesis of (+)-ent-cyclizidine: absolute configurational confirmation of antibiotic M146791

The first total synthesis of the enantiomer of the indolizidine alkaloid, cyclizidine, was accomplished from readily available d-serine as the starting chiron. The relevant key reactions involve the stereocontrolled construction of the indolizidine ring system with the required functionality and further elaboration to install the cyclopropyl dienyl side chain. With this total synthesis, the absolute configuration of the natural product based on a redetermination of its X-ray structure has been confirmed.