Synthesis of linear and tripoidal oligo(phenylene ethynylene)-based building blocks for application in modular DNA-programmed assembly

Rigid linear and tripoidal organic modules based on the oligo(phenylene ethynylene) backbone having salicylaldehyde-derived termini are synthesized. A highly functionalized 5-iodosalicyl aldehyde was prepared and coupled to each ethynyl group of 1,4-diethynylbenzene or 1,3,5-triethynylbenzene in Sonogashira couplings. The two or three termini of the compounds are functionalized for incorporation in linear and branched oligonucleotide strands. For the linear module (LM), the two termini are equipped with amide spacers, and one of these was functionalized with a DMTr (dimethoxytrityl)-protected hydroxy group and the other with a phosphoramidite. One of the tripoidal modules is prepared with DMTr groups in two of its three termini. A tripoidal module is also synthesized with three different groups on its hydroxy termini: a phosphoramidite, a DMTr group, and an Fmoc group. Extended studies have shown that these rigid linear and tripoidal organic modules can be incorporated into short oligonucleotides. Several of these modules can be applied for DNA-directed assembly and covalent coupling into structures of predetermined connectivity. Such structures have potential application for molecular electronics and nanotechnology.     

Nonlinear Approximation with Dictionaries I. Direct Estimates

We study various approximation classes associated with m-term approximation by elements from a (possibly redundant) dictionary in a Banach space. The standard approximation class associated with the best m-term approximation is compared to new classes defined by considering m-term approximation with algorithmic constraints: thresholding and Chebychev approximation classes are studied, respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space, and we prove that assuming a certain structure of the dictionary is sufficient and (almost) necessary to obtain stronger results. We give examples of classical dictionaries in L^p spaces and modulation spaces where our results recover some known Jackson type estimates, and discuss some new estimates they provide.     

Fiber Bragg gratings for pure dispersion-slope compensation

Single-fiber Bragg gratings designed to compensate for pure third-order dispersion are demonstrated. The devices are designed by use of a layer-peeling inverse-scattering technique and exhibit dispersion profiles across their reflection bandwidths of -20, +/- 40, and -225 ps/nm2 over bandwidths of 4.5, 6, and 3 nm, respectively. Furthermore, they have almost constant peak reflectivities of approximately 75% and are, respectively, only 8, 23, and 40 mm long.     

On Transience Conditions for Markov Chains

Siberian Mathematical Journal -     

On a cycle partition problem

Let G be any graph and let c(G) denote the circumference of G. We conjecture that for every pair c₁,c₂ of positive integers satisfying c₁+c₂=c(G), the vertex set of G admits a partition into two sets V₁ and V₂, such that V_i induces a graph of circumference at most c_i, i=1,2. We establish various results in support of the conjecture; e.g. it is observed that planar graphs, claw-free graphs, certain important classes of perfect graphs, and graphs without too many intersecting long cycles, satisfy the conjecture.This work is inspired by a well-known, long-standing, analogous conjecture involving paths.     

Influence of HPAM on W/O emulsion separation properties

The present study reports on the influence of partially hydrolyzed polyacrylamide (HPAM) on essential w/o emulsion properties. The characterization has been undertaken with low field NMR to follow droplet sizes and distributions, sedimentation and coalescence kinetic, bench-scale electrocoalescence (E_crit) experiments to follow emulsion stability changes, and electrorheology to detect changes in the viscosity upon applying an external electric field. The result is that HPAM does not basically influence the droplet size distribution (DSD) and the stability level of the emulsions as can be expected of bulk polymers. However, there seems to be an interaction between added demulsifiers either through direct molecular interaction or via an interfacial complexation.     

Impact of network topology on cationic diffusion and hardness of borate glass surfaces

The connection between bulk glass properties and network topology is now well established. However, there has been little attention paid to the impact of network topology on the surface properties of glass. In this work, we report the impact of the network topology on both the transport properties (such as cationic inward diffusion) and the mechanical properties (such as hardness) of borate glasses with modified surfaces. We choose soda lime borate systems as the object of this study because of their interesting topological features, e.g., boron anomaly. An inward diffusion mechanism is employed to modify the glass surface compositions and hence the surface topology. We show that accurate quantitative predictions of the hardness of the modified surfaces can be made using topological constraint theory with temperature-dependent constraints. Experimental results reveal that Ca(2+) diffusion is most intense in glasses with lowest BO(4) fraction, whereas Na(+) diffusion is only significant when nonbridging oxygens start to form. These phenomena are interpreted in terms of the atomic packing and the local electrostatic environments of the cations.     

Mechanistic proposal for the zeolite catalyzed methylation of aromatic compounds

Alkylation and methylation reactions are important reactions in petrochemical production and form part of the reaction mechanism of many hydrocarbon transformation processes. Here, a new reaction mechanism is explored for the zeolite catalyzed methylation of arenes using quantum chemical calculations. It is proposed that the most substituted methylbenzenes, which will reside predominantly on the protonated form when adsorbed in a zeolite, can react directly with a neutral methanol molecule in the vicinity, thereby initiating the methylation reaction without having to return a proton to the zeolite surface. The calculated barriers are quite low, indicating that the suggested mechanism is plausible. This route might explain how the most substituted methylbenzenes can function as efficient reaction intermediates in the methanol to hydrocarbons reaction without themselves acting as catalyst poisons as a consequence of their high proton affinities.