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.     

On the accuracy of the IWM–CFC approximation in differentially rotating relativistic stars

A circular restricted three-body problem describes the motion of a test particle around two massive bodies in circular orbits. In this system, orbital decay caused by a gravitational radiation reaction between the two primary bodies is considered but the direct effect of gravitational radiation on the test particle is neglected. We adopt distance- and time-scale transformations to Newtonian problems so that systems without orbital decay will not depend on separation between the primaries but systems with orbital decay will depend on this separation. If a regular or chaotic orbit is given in a Newtonian system, the starting separation of the primaries varies according to the corresponding decay system. Thus, insights into the chaotic behaviour of a third body in a decay case are provided. For a large initial separation between the primaries, the chaos that exists in a Newtonian problem may be retained for a long enough time scale of dissipative evolution before the primaries coalesce. The final state of a third body is escape attributed to orbital decay.     

A New Approach for the Photosynthetic Antenna–Reaction Center Complex with a Model Organized Around an s‐Triazine Linker

Two new artificial mimics of the photosynthetic antenna‐reaction center complex have been designed and synthesized (BDP‐H₂P‐C₆₀ and BDP‐ZnP‐C₆₀). The resulting electron‐donor/acceptor conjugates contain a porphyrin (either in its free‐base form (H₂P) or as Zn‐metalated complex (ZnP)), a boron dipyrrin (BDP), and a fulleropyrrolidine possessing, as substituent of the pyrrolidine nitrogen, an ethylene glycol chain terminating in an amino group C₆₀‐X‐NH₂ (X=spacer). In both cases, the three different components were connected by s‐triazine through stepwise substitution reactions of cyanuric chloride. In addition to the facile synthesis, the star‐type arrangement of the three photo‐ and redox‐active components around the central s‐triazine unit permits direct interaction between one another, in contrast to reported examples in which the three components are arranged in a linear fashion. The energy‐ and electron‐transfer properties of the resulting electron‐donor/acceptor conjugates were investigated by using UV/Vis absorption and emission spectroscopy, cyclic voltammetry, and femtosecond transient absorption spectroscopy. Comparison of the absorption spectra and cyclic voltammograms of BDP‐H₂P‐C₆₀ and BDP‐ZnP‐C₆₀ with those of BDP‐H₂P, BDP‐ZnP and BDP‐C₆₀, which were used as references, showed that the spectroscopic and electrochemical properties of the individual constituents are basically retained, although some appreciable shifts in terms of absorption indicate some interactions in the ground state. Fluorescence lifetime measurements and transient absorption experiments helped to elucidate the antenna function of BDP, which upon selective excitation undergoes a rapid and efficient energy transfer from BDP to H₂P or ZnP. This is then followed by an electron transfer to C₆₀, yielding the formation of the singlet charge‐separated states, namely BDP‐H₂P ^.+‐ C₆₀ ^.? and BDP‐ZnP ^.+‐ C₆₀ ^{. ?}. As such, the sequence of energy transfer and electron transfer in the present models mimics the events of natural photosynthesis.     

Polyoxomolybdenum(V/VI)-sulfite compounds: synthesis, structural, and physical studies

Reaction of Na(2)Mo(VI)O(4) x 2H(2)O with (NH(4))(2)SO(3) in the mixed-solvent system H(2)O/CH(3)CN (pH = 5) resulted in the formation of the tetranuclear cluster (NH(4))(4)[Mo(4)(VI)SO(16)] x H(2)O (1), while the same reaction in acidic aqueous solution (pH = 5) yielded (NH(4))(4)[Mo(5)(VI)S(2)O(21)] x 3H(2)O (2). Compound {(H(2)bipy)(2)[Mo(5)(VI)S(2)O(21)] x H(2)O}(x) (3) was obtained from the reaction of aqueous acidic solution of Na(2)Mo(VI)O(4) x 2H(2)O with (NH(4))(2)SO(3) (pH = 2.5) and 4,4'-bipyridine (4,4'-bipy). The mixed metal/sulfite species (NH(4))(7)[Co(III)(Mo(2)(V)O(4))(NH(3))(SO(3))(6)] x 4H(2)O (4) was synthesized by reacting Na(2)Mo(VI)O(4) x 2H(2)O with CoCl(2) x 6H(2)O and (NH(4))(2)SO(3) with precise control of pH (5.3) through a redox reaction. The X-ray crystal structures of compounds 1, 2, and 4 were determined. The structure of compound 1 consists of a ring of four alternately face- and edge-sharing Mo(VI)O(6) octahedra capped by the trigonal pyramidal sulfite anion, while at the base of the Mo(4) ring is an oxo group which is asymmetrically shared by all four molybdenum atoms. Compound 3 is based on the Strandberg-type heteropolyion [Mo(5)(VI)S(2)O(21)](4-), and these coordinatively saturated clusters are joined by diprotonated 4,4'-H(2)bipy(2+) through strong hydrogen bonds. Compound 3 crystallizes in the chiral space group C2. The structure of compound 4 consists of a novel trinuclear [Co(III)Mo(2)(V)SO(3)(2-)] cluster. The chiral compound 3 exhibits nonlinear optical (NLO) and photoluminescence properties. The assignment of the sulfite bands in the IR spectrum of 4 has been carried out by density functional calculations. The cobalt in 4 is a d(6) octahedral low-spin metal atom as it was evidenced by magnetic susceptibility measurements, cw EPR, BVS, and DFT calculations. The IR and solid-state UV-vis spectra as well as the thermogravimetric analyses of compounds 1-4 are also reported.     

Block-coordinate and incremental aggregated proximal gradient methods for nonsmooth nonconvex problems

Mathematical Programming - This paper analyzes block-coordinate proximal gradient methods for minimizing the sum of a separable smooth function and a (nonseparable) nonsmooth function, both of...