Conics in finite projective planes

There does not exist a general theory of conics in finite projective planes, because the many definitions of conics which are equivalent in desarguesian projective planes yield different types of conics in more general situations. Thus even the use of the word conic can lead to confusion, particularly in the finite case. This note is an attempt to clarify these various definitions and give as an example in a finite projective plane a von Staudt conic which is not an Ostrom conic. We conjecture that any finite projective plane admitting an Ostrom conic must be desarguesian.     

Biomimetic pH/redox dual stimuli‐responsive zwitterionic polymer block poly(L‐histidine) micelles for intracellular delivery of doxorubicin into tumor cells

A series of pH/redox dual stimuli‐responsive poly(2‐methacryloyloxyethyl phosphorylcholine)₂₅‐block‐poly(l ‐histidine)_n (p[MPC])₂₅‐b‐p[His]_n, n = 20, 35, 50, and 75) copolymers consisting of a pH‐responsive p(His)_n block and a biocompatible phospholipid analog p(MPC) block connected by a redox‐responsive disulfide linker have been synthesized. The block copolymers are self‐assembled into uniform micelles (～100 nm) in which doxorubicin (Dox) is efficiently encapsulated. The in vitro release profile shows an enhanced release of Dox at low pH (5.0) in 10 mM glutathione (GSH). The in vitro cell viability assays performed using various cell lines show that the blank hybrid micelles have no acute or intrinsic toxicity. A pH‐dependent cytotoxicity is observed with the Dox‐loaded micelles, especially at pH 5.0. Moreover, confocal microscopy images and flow cytometry results show the pH‐dependent cellular uptake of Dox‐loaded micelles. Therefore, the Dox‐loaded micelles can be considered a good candidate for cancer therapy. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 2061–2070     

One-Dimensional Particle Processes with Acceleration/Braking Asymmetry

The slow-to-start mechanism is known to play an important role in the particular shape of the Fundamental Diagram of traffic and to be associated to hysteresis effects of traffic flow. We study this question in the context of exclusion and queueing processes, by including an asymmetry between deceleration and acceleration in the formulation of these processes. For exclusions processes, this corresponds to a multi-class process with transition asymmetry between different speed levels, while for queueing processes we consider non-reversible stochastic dependency of the service rate w.r.t. the number of clients. The relationship between these 2 families of models is analyzed on the ring geometry, along with their steady state properties. Spatial condensation phenomena and metastability are observed, depending on the level of the aforementioned asymmetry. In addition, we provide a large deviation formulation of the fundamental diagram which includes the level of fluctuations, in the canonical ensemble when the stationary state is expressed as a product form of such generalized queues.     

Synthesis and structure–property relationship of carbazole‐alt‐benzothiadiazole copolymers

A series of four π‐conjugated carbazole‐alt‐benzothiadiazole copolymers (PCBT) were prepared by Suzuki cross‐coupling reaction between synthesized dibromocarbazoles as electron‐rich subunits and 4,7‐bis(4,4,5,5‐tetramethyl‐1,3,2‐dioxaborolan‐2‐yl)?2,1,3‐benzothiadiazole as electron‐deficient subunits. The subunits were directly linked through 2,7‐ or 3,6‐ positions of the carbazole. In addition, the carbazole monomers have been N‐substituted by a branched or a linear side‐chain. The chemical structure of the copolymers and their precursors was confirmed by NMR and IR spectroscopies, and their molar masses were estimated by SEC. Thermal analysis under N₂ atmosphere showed no weight loss below 329°C, and no glass transition was observed in between 0 and 250°C. The band gaps of all PCBTs evaluated by optical spectroscopies and by cyclic voltammetry analysis were consistent with expectations and ranged between 2.2 and 2.3 eV. Finally, 2,7 and 3,6 linkages were shown to influence optical properties of PCBTs. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2059–2068     

Characterization of polyoxometalate/polymer photo-composites: A toolbox for the photodegradation of organic pollutants

Different inorganic/organic photocomposites based on polyoxometalate (POM) nanoparticles have been developed for photocatalytic applications. Currently, polyoxometalate nanoparticles have been successfully in-situ embedded into an acrylate polymer network by photopolymerization upon mild visible light irradiation at 405 nm. The proposed POM/polymer photocomposites have been characterized using complementary techniques for a better understanding of their photocatalytic activity. Interestingly, the obtained photocomposites exhibit high rigidity, excellent thermal stability, a non-negligible porosity and new functionalities such as light reactivity and redox properties. Moreover, developed composites showed efficient catalytic activity for the color removal of aqueous solutions of erythrosine and rose Bengal under Light Emitting Diodes LED@375 nm irradiation reaching 80 and 90% as a final color removal, respectively.     

Successions in Words and Compositions

We consider words over the alphabet [k] = {1, 2, . . . , k}, k ?? 2. For a fixed nonnegative integer p, a p-succession in a word w ₁ w ₂ . . . w _n consists of two consecutive letters of the form (w _i , w _i ?+ p), i = 1, 2, . . . , n ? 1. We analyze words with respect to a given number of contained p-successions. First we find the mean and variance of the number of p-successions. We then determine the distribution of the number of p-successions in words of length n as n (and possibly k) tends to infinity; a simple instance of a phase transition (Gaussian-Poisson-degenerate) is encountered. Finally, we also investigate successions in compositions of integers.