Periodicity of equilibrium structures in a time dependent markov model under stochastic environment

The problem of periodicity for a non–homogeneous Markov model in a stochastic environment is studied. The stochastic concept is established through the notion of optional scenarios applied on the transition process. It is proved that the sequence of so–called aggregate structures follows a certain periodic pattern that can split into converging subsequences according to alternative policies. These limits are highly influenced by the different scenarios utilized in the model, but always lie on a convex region that also depends on the pool of alternatives.     

Solution of the planar Newtonian stick–slip problem with the singular function boundary integral method

A singular function boundary integral method (SFBIM) is proposed for solving biharmonic problems with boundary singularities. The method is applied to the Newtonian stick–slip flow problem. The streamfunction is approximated by the leading terms of the local asymptotic solution expansion which are also used to weight the governing biharmonic equation in the Galerkin sense. By means of the divergence theorem the discretized equations are reduced to boundary integrals. The Dirichlet boundary conditions are weakly enforced by means of Lagrange multipliers, the values of which are calculated together with the singular coefficients. The method converges very fast with the number of singular functions and the number of Lagrange multipliers, and accurate estimates of the leading singular coefficients are obtained. Comparisons with the analytical solution and results obtained with other numerical methods are also made. Copyright © 2005 John Wiley & Sons, Ltd.     

A far-red emitting probe for unambiguous detection of mobile zinc in acidic vesicles and deep tissue

Imaging mobile zinc in acidic environments remains challenging because most small-molecule optical probes display pH-dependent fluorescence. Here we report a reaction-based sensor that detects mobile zinc unambiguously at low pH. The sensor responds reversibly and with a large dynamic range to exogenously applied Zn²⁺ in lysosomes of HeLa cells, endogenous Zn²⁺ in insulin granules of MIN6 cells, and zinc-rich mossy fiber boutons in hippocampal tissue from mice. This long-wavelength probe is compatible with the green-fluorescent protein, enabling multicolor imaging, and facilitates visualization of mossy fiber boutons at depths of >100 μm, as demonstrated by studies in live tissue employing two-photon microscopy.     

New Calix[4]arene‐Cored Peripherally Functionalized Dendrimers: Synthesis and Conformational Characteristics

New calixarene‐based dendrimers, containing calix[4]arene as the core and different generations of Fréchet‐type poly(benzyl ether) dendrons as building blocks, which possess either Br‐atoms or COO^tBu groups at their surface were synthesized and presented herein for the first time. The new calix[4]arene‐cored dendritic macromolecules were fully characterized and found to prefer strictly the cone conformation.     

Heat transfer due to harmonic variation in the free stream temperatures in a flat plate exposed on both sides

The heat transfer through an infinite flat plate is studied when the temperatures of the two free streams surrounding it are varying harmonically with time and out of phase, with a delay period τ_d. The configuration is a simplified model for the heat transfer through the separating wall in the isochoric counter-current heat exchanger. The results show that apart from the τ_d effect, the perturbation parameters depend mainly on the cavity passing frequency f. At the thick plate solution, the combined passing frequency–delay time influences are significant only when the dimensionless frequency is smaller than 10. Within this range τ_d affects seriously not only the temperature perturbation amplitudes (which determine the thermal stresses) but also the heat fluxes and the accumulated energy ones. When f ≥ 10, the plate behaves as two separate semi-infinite slabs. Heat penetration delays greater than one cavity passing period may be possible.     

Aspects of heterogeneous enantioselective catalysis by metals

Some aspects of metal-catalyzed heterogeneous enantioselective reactions are reviewed with specific reference to four different systems where the phenomena that control enantioselection appear to be very different. In the case of glucose electro-oxidation, it is clear that any intrinsic chirality present at the metal surface plays a vital role. With α-keto hydrogenation, achiral surfaces modified by the adsorption of chiral agents become effective enantioselective catalysts and the formation of extended arrays of chiral species appears not to be of importance: instead a 1:1 docking interaction controlled by hydrogen bonding between the adsorbed chiral modifier and the prochiral reactant determines the outcome. Hydrogen bonding also plays a central role in β-ketoester hydrogenation, but here fundamental studies indicate that the formation of ordered arrays involving the reactant and chiral ligand is of importance. Asymmetric C═C hydrogenation, though relatively little studied, has the potential for major impact in synthetic organic chemistry both on the laboratory scale and in the manufacture of fine chemicals and pharmaceuticals. The structural attributes that determine whether a given chiral ligand is effective have been identified; the ability to form strong covalent bonds with the metal surface while also resisting hydrogenation and displacement by the strongly adsorbing reactant under reaction conditions is an essential necessary condition. Beyond this, ligand rigidity in the vicinity of the chirality center coupled with resistance to SAM formation is a critically important factor whose absence results in racemic chemistry.     

Poly(sodium styrene sulfonate)-b-poly(methyl methacrylate) diblock copolymers through direct atom transfer radical polymerization: Influence of hydrophilic–hydrophobic balance on self-organization in aqueous solution

A series of poly(sodium styrene sulfonate)-b-poly(methyl methacrylate), PSSNa-b-PMMA, amphiphilic diblock copolymers have been synthesized through atom transfer radical polymerization (ATRP) of methyl methacrylate (MMA) in N,N-dimethylformamide/water mixtures, starting from a PSSNa macroinitiator. The kinetics of the polymerization was followed by ¹H NMR, while the chemical composition of the copolymers was verified by a variety of techniques, such as ¹H NMR, FTIR and TGA. The MMA content of the copolymers ranges from 0 up to 60 mol%, while the number–average molecular weight of the PSSNa macroinitiator was 9000 g/mol. The self-association of the diblock copolymers in aqueous solution was compared to the respective behavior of similar random P(SSNa-co-MMA) copolymers through optical density measurements, pyrene fluorescence probing, dynamic light scattering and surface tension measurements. It is shown that the diblock copolymers form micellar structures in water, characterized by an increasing hydrophobic character and a decreasing size as the length of the PMMA block increases. These micelle-like structures turn from surface inactive to surface active as the length of the PMMA block increases. Moreover, contrary to the MMA-rich random copolymers, the respective diblock copolymers form water insoluble polymer/surfactant complexes with cationic surfactants such as hexadecyltrimethyl ammonium bromide (HTAB), leading to materials with antimicrobial activity.     

Monte Carlo simulations of a coarse grained model for an athermal all-polystyrene nanocomposite system

The structure of a polystyrene matrix filled with tightly cross-linked polystyrene nanoparticles, forming an athermal nanocomposite system, is investigated by means of a Monte Carlo sampling formalism. The polymer chains are represented as random walks and the system is described through a coarse grained Hamiltonian. This approach is related to self-consistent-field theory but does not invoke a saddle point approximation and is suitable for treating large three-dimensional systems. The local structure of the polymer matrix in the vicinity of the nanoparticles is found to be different in many ways from that of the corresponding bulk, both at the segment and the chain level. The local polymer density profile near to the particle displays a maximum and the bonds develop considerable orientation parallel to the nanoparticle surface. The depletion layer thickness is also analyzed. The chains orient with their longest dimension parallel to the surface of the particles. Their intrinsic shape, as characterized by spans and principal moments of inertia, is found to be a strong function of position relative to the interface. The dispersion of many nanoparticles in the polymeric matrix leads to extension of the chains when their size is similar to the radius of the dispersed particles.     

A Lie symmetry analysis and explicit solutions of the two‐dimensional ∞‐Polylaplacian

In this work, we consider the Lie point symmetry analysis of a strongly nonlinear partial differential equation of third order, the ∞‐Polylaplacian, in two spatial dimensions. This equation is a higher order generalization of the ∞‐Laplacian, also known as Aronsson's equation, and arises as the analog of the Euler–Lagrange equations of a second‐order variational principle in L^∞. We obtain its full symmetry group, one‐dimensional Lie subalgebras and the corresponding symmetry reductions to ordinary differential equations. Finally, we use the Lie symmetries to construct new invariant ∞‐Polyharmonic functions.