On the Howson property of HNN-extensions with abelian base group and amalgamated free products of abelian groups

We give necessary and sufficient conditions under which an HNN-extension with abelian base group or an amalgamated free product of abelian groups is a Howson group (that is the intersection of any two finitely generated subgroups is finitely generated). We describe HNN-extensions and amalgamated free products which are Howson groups without satisfying the Burns–Cohen statements.     

On solving the master equation in spatially periodic systems

We present a new method for solving the master equation for a system evolving on a spatially periodic network of states. The network contains 2(ν) images of a "unit cell" of n states, arranged along one direction with periodic boundary conditions at the ends. We analyze the structure of the symmetrized (2(ν)n) × (2(ν)n) rate constant matrix for this system and derive a recursive scheme for determining its eigenvalues and eigenvectors, and therefore analytically expressing the time-dependent probabilities of all states in the network, based on diagonalizations of n × n matrices formed by consideration of a single unit cell. We apply our new method to the problem of low-temperature, low-occupancy diffusion of xenon in the zeolite silicalite-1 using the states, interstate transitions, and transition state theory-based rate constants previously derived by June et al. [J. Phys. Chem. 95, 8866 (1991)]. The new method yields a diffusion tensor for this system which differs by less than 3% from the values derived previously via kinetic Monte Carlo (KMC) simulations and confirmed by new KMC simulations conducted in the present work. The computational requirements of the new method are compared against those of KMC, numerical solution of the master equation by the Euler method, and direct molecular dynamics. In the problem of diffusion of xenon in silicalite-1, the new method is shown to be faster than these alternative methods by factors of about 3.177 × 10(4), 4.237 × 10(3), and 1.75 × 10(7), respectively. The computational savings and ease of setting up calculations afforded by the new method of master equation solution by recursive reduction of dimensionality in diagonalizing the rate constant matrix make it attractive as a means of predicting long-time dynamical phenomena in spatially periodic systems from atomic-level information.     

Photodegradable Polymers for Biotechnological Applications

Photodegradable polymers constitute an emerging class of materials that finds numerous applications in biotechnology, biomedicine, and nanoscience. This article highlights some of the emerging applications of photodegradable polymers in the form of homopolymers, particles and self‐assembled constructs in solution, hydrogels for tissue engineering, and photolabile polymers for biopatterning applications. Novel photochemistries have been combined with controlled polymerization methods, which result in well‐defined photodegradable materials that exhibit light mediated and often controlled fragmentation processes.     

A singular perturbation analysis with applications to delay differential equations

We prove an approximation result for the solutions of a singularly perturbed, nonautonomous ordinary differential equation which has interesting applications to problems in higher dimensions. Here our result is applied to a singularly perturbed, delay differential equation with state dependent time-lags (i.e., aninfinite dimensional problem). We find a new dynamical system (also in infinite dimensions), which describes, in a certain sense, the dynamics of our delay equations for very small values of the singular parameter.     

Douglas–Rachford splitting and ADMM for nonconvex optimization: accelerated and Newton-type linesearch algorithms

Computational Optimization and Applications - Although the performance of popular optimization algorithms such as the Douglas–Rachford splitting (DRS) and the ADMM is satisfactory in convex...     

Study of poly(N,N-dimethylacrylamide)/CdS nanocomposite organic/inorganic gels

CdS nanoparticles have been synthesized and stabilized in poly(N,N-dimethylacrylamide) hydrogels. The properties of the composite material have been characterized by UV-vis spectroscopy, scanning electron microscopy, X-ray diffraction, thermogravimetric analysis, and steady-state and time-resolved luminescence spectroscopy. This material can be obtained in three different states: swollen, shrunk, and freeze-dried. The swollen and the freeze-dried states correspond to a nanocomposite organic/inorganic (wet or dry) gel containing CdS nanoparticles of approximately 50 nm diameter while the shrunk state is a two-phase system containing CdS crystals, which precipitate forming interesting geometrical shapes.     

Protein adsorption on the mesoporous molecular sieve silicate SBA-15: effects of pH and pore size

A mesoporous molecular sieve silicate, SBA-15, with three pore sizes (38.1 A, 77.3 A, and 240 A) has been synthesized using a non-ionic, tri-block copolymer as a template in a sol-gel method. The effects of synthesis conditions on the pore size and pore-size distribution of this adsorbent have been described. The adsorption of proteins on these crystalline, ordered, materials has been studied. The kinetics of adsorption and equilibrium capacity have been probed with three proteins of different dimensions. The effects of electrostatic interactions and protein size are illustrated. It has been shown that SBA-15 materials can be tailored to show size selectivity for proteins, and very high capacities (450 mg/g) can be obtained. Furthermore, the rates of adsorption are shown to be dependent on the pore size, protein structure and solution pH.     

Heterogeneous oxidation of ethanol over Cu(OH)2/-α-Fe2O3 under visible light

A Cu(OH)₂/α-Fe₂O₃ photocatalyst is shown to be active in the gas phase oxidation of ethanol under visible light. The calculated initial quantum efficiency of the ethanol photooxidation is 0.1-1%. However, ethanol is oxidized only into acetic acid, which deactivates the catalyst. This revised version was published online in August 2006 with corrections to the Cover Date.