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.     

Pseudoparabolic variational inequalities without initial conditions

We consider a pseudoparabolic variational inequality in a cylindrical domain semibounded in a variable t. Under certain conditions imposed on the coefficients of the inequality, we prove theorems on the unique existence of a solution for a class of functions with exponential growth as t → ∞. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 919–929, July, 1998.     

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.