On a free group of transformations defined by an automaton

We prove that three automorphisms of the rooted binary tree defined by a certain 3-state automaton generate a free non-Abelian group of rank 3. Both authors are supported by the NSF grants DMS-0308985 and DMS-0456185. Yaroslav Vorobets is supported by a Clay Research Scholarship.     

Correction to: Lithium ion conductivity of solid solutions based on Li8ZrO6

Journal of Solid State Electrochemistry - Lithium ion conductivity of lithium hexaoxozirconate Li8ZrO6 doped by Mg2+, Sr2+, Nb5+, V5+, and Ce4+ cations was studied using impedance spectroscopy. The...     

Enhanced spin capturing polymerization: Numerical investigation of mechanism

Simulation on the kinetic scheme of enhanced spin capturing polymerizations (ESCP) were performed to reveal the influence of different parameters, e.g., initiation rate, spin capturing and side reactions on the properties (the monomer conversion, degree of polymerization, polydispersity index, and the fraction of “living” chains) of polymer obtained. The kinetic scheme of ESCP was solved numerically as well as the method of statistical moments of molecular weight distribution was applied to get some numerical expressions for analysis. The simulations showed that fast initiation rate can lead to decrease of living fraction and broadening of molecular weight distribution. Whereas high rate of spin capturing makes the polymer chains shorter but increases living character. And side reactions always decrease livingness of the polymer obtained. Finally in the case of absence of side reaction we were able to formulate criteria for formation of polymer with target molecular weight and quota of living chains via ESCP process. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2546–2556     

Synthesis,X-ray and DFT Studies of 6-halo-3-(hydroxymethyl)cinnolin-4(1H)-ones

Chemistry of Heterocyclic Compounds - The Richter cyclization was used for the synthesis of 6-halo-3-(hydroxymethyl)cinnolin-4(1H)-ones. X-ray analysis revealed that these compounds exist as dimers...     

CeO2/Pd Nanoparticles Incorporated Fly Ash Zeolite: An Efficient and Recyclable Catalyst for Csp2-Csp2 Bond Formation Reactions

The catalytic activity of CeO₂ and palladium nanoparticles supported fly ash zeolite (CeO₂/Pd@FAZ) for C_sp²-C_sp² bond formation was studied. CeO₂/Pd@FAZ was characterized by FTIR, XRD, EDAX and TEM studies. In the Suzuki-Miyauracross-coupling reaction, biphenyl derivatives with excellent yields were obtained, and the reaction conditions were optimized. The catalytic activity was explored using a wide variety of diversely substituted aryl bromides and chlorides with aryl boronic acid under optimized reaction conditions. The recyclability of the catalyst was established for three cycles, with the conversion rate from 99 to 40%, which gained the advantage of heterogeneous catalysis.     

Integral representation of a solution to the Stokes–Darcy problem

With methods of potential theory, we develop a representation of a solution of the coupled Stokes–Darcy model in a Lipschitz domain for boundary data in H^?1/2. Copyright © 2014 John Wiley & Sons, Ltd.     

A Versatile Solid-Phase Approach to the Synthesis of Oligonucleotide Conjugates with Biodegradable Hydrazone Linker

One of the ways to efficiently deliver various drugs, including therapeutic nucleic acids, into the cells is conjugating them with different transport ligands via labile or stable bonds. A convenient solid-phase approach for the synthesis of 5′-conjugates of oligonucleotides with biodegradable pH-sensitive hydrazone covalent bonds is proposed in this article. The approach relies on introducing a hydrazide of the ligand under aqueous/organic media to a fully protected support-bound oligonucleotide containing aldehyde function at the 5′-end. We demonstrated the proof-of-principle of this approach by synthesizing 5′-lipophilic (e.g., cholesterol and α-tocopherol) conjugates of modified siRNA and non-coding RNAs imported into mitochondria (antireplicative RNAs and guide RNAs for Mito-CRISPR/system). The developed method has the potential to be extended for the synthesis of pH-sensitive conjugates of oligonucleotides of different types (ribo-, deoxyribo-, 2′-O-methylribo-, and others) with ligands of different nature.     

A soft multi-criteria decision analysis model with application to the European Union enlargement

This paper proposes a new multi-criteria decision analysis (MCDA) model that uses a series of existing intuitive and analytical methods to systematically capture both objective and subjective beliefs and preferences from a group of decision makers (DMs). A defuzzification method that combines entropy and the theory of displaced ideal synthesizes crisp values from the DMs’ subjective judgments. This approach assists the DMs in their selection process by plotting alternatives in a four quadrant graph and considering their Euclidean distance from the “ideal” choice. A pilot study illustrates the details of the proposed method. The DMs were a group of graduate students from the University of Paderborn in Germany. The pilot study concerned the addition of new members into the European Union (EU), a decision that has profound economic and political effects on both the entering and existing members of the Union. The DMs were required to consider a large number of internal strengths and weaknesses and external opportunities and threats in assessing the decision to enlarge the EU. Although the pilot study was not performed by actual DMs from the EU, it was an excellent platform for testing the proposed model.     

Crystallization and stereocomplexation behavior of poly(D‐ and L‐lactide)‐b‐poly(N,N‐dimethylamino‐2‐ethyl methacrylate) block copolymers

The thermal properties, crystallization, and morphology of amphiphilic poly(D ‐lactide)‐b‐poly(N,N‐dimethylamino‐2‐ethyl methacrylate) (PDLA‐b‐PDMAEMA) and poly (L ‐lactide)‐b‐poly(N,N‐dimethylamino‐2‐ethyl methacrylate) (PLLA‐b‐PDMAEMA) copolymers were studied and compared to those of the corresponding poly(lactide) homopolymers. Additionally, stereocomplexation of these copolymers was studied. The crystallization kinetics of the PLA blocks was retarded by the presence of the PDMAEMA block. The studied copolymers were found to be miscible in the melt and the glassy state. The Avrami theory was able to predict the entire crystallization range of the PLA isothermal overall crystallization. The melting points of PLDA/PLLA and PLA/PLA‐b‐PDMAEMA stereocomplexes were higher than those formed by copolymer mixtures. This indicates that the PDMAEMA block is influencing the stability of the stereocomplex structures. For the low molecular weight samples, the stereocomplexes particles exhibited a conventional disk‐shape structure and, for high molecular weight samples, the particles displayed unusual star‐like shape morphology. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1397–1409, 2011