Aizerman's Problem for Discrete Systems

Absolute stability conditions for nonlinear difference equations are derived. In particular, it is proved that equations with positive Green's functions (impulse responses) satisfy the generalized Aizerman conjecture.     

Non-Exponential Stabilization of Nonlinear Discrete-Time Systems

In this paper, we investigate the stabilization problem for a class of nonlinear discrete-time control systems. We consider semilinear systems with a nonlinear perturbation satisfying a Hölder-type condition. Based on a new discrete inequality of Gronwall type, we establish sufficient conditions for the global and local weak stabilizability of semilinear and nonlinear discrete-time systems, respectively.     

One-pot synthesis of imidazoles from aromatic nitriles with nickel catalysts

Nickel(0) catalysts were used to produce substituted imidazoles in good to high yields using benzonitrile, p-substituted benzonitriles and 4-cyanopyridine as starting materials.     

Stimuli-responsive binary mixed polymer brushes and free-standing films by LbL-SIP

We report a facile approach to preparing binary mixed polymer brushes and free-standing films by combining the layer-by-layer and surface-initiated polymerization (LbL-SIP) techniques. Specifically, the grafting of mixed polymer brushes of poly(n-isopropylacrylamide) and polystyrene (pNIPAM-pSt) onto LbL-macroinitiator-modified planar substrates is described. Atom transfer radical polymerization (ATRP) and free radical polymerization (FRP) techniques were employed for the syntheses of pNIPAM and pSt, respectively, yielding pNIPAM-pSt mixed polymer brushes. The composition of the two polymers was controlled by varying the number of macroinitiator layers deposited on the substrate (i.e., LbL layers = 4, 8, 12, 16, and 20); consequently, mixed brushes of different thicknesses and composition ratios were obtained. Moreover, the switching behavior of the LbL-mixed brush films as a function of solvent and temperature was demonstrated and evaluated by water contact angle and atomic force microscopy (AFM) experiments. It was found that both the solvent and temperature stimuli responses were a function of the mixed brush composition and thickness ratio where the dominant component played a larger role in the response behavior. Furthermore, the ability to obtain free-standing films was exploited. The LbL technique provided the macroinitiator density variation necessary for the preparation of stable free-standing mixed brush films. Specifically, the free-standing films exhibited the rigidity to withstand changes in the solvent and temperature environment and at the same time were flexible enough to respond accordingly to external stimuli.     

Permeability of anti-fouling PEGylated surfaces probed by fluorescence correlation spectroscopy

The present work reports on in situ observations of the interaction of organic dye probe molecules and dye-labeled protein with different poly(ethylene glycol) (PEG) architectures (linear, dendron, and bottle brush). Fluorescence correlation spectroscopy (FCS) and single molecule event analysis were used to examine the nature and extent of probe-PEG interactions. The data support a sieve-like model in which size-exclusion principles determine the extent of probe-PEG interactions. Small probes are trapped by more dense PEG architectures and large probes interact more with less dense PEG surfaces. These results, and the tunable pore structure of the PEG dendrons employed in this work, suggest the viability of electrochemically-active materials for tunable surfaces.     

Novel biobased resins from blends of functionalized soybean oil and unsaturated polyester resin

Biobased unsaturated polyester (UPE) materials containing epoxidized methyl soyate (EMS) were processed with cobalt naphthenate as a promoter and 2‐butanone peroxide as an initiator. A certain amount of the UPE resin was replaced by EMS. The combination of the UPE and EMS resulted in an excellent combination for a new biobased thermoset material with a relatively high elastic modulus and a constant glass transition temperature with up to 25 wt % replacement with EMS. The Izod impact strength was almost constant while the amount of EMS was changed. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 698–704, 2007     

Homopolymer and block copolymer brushes on gold by living anionic surface‐initiated polymerization in a polar solvent

Living anionic surface‐initiated polymerization on flat gold substrates has been conducted to create uniform homopolymer and diblock copolymer brushes. A 1,1‐diphenylethylene (DPE) self‐assembled monolayer was used as the immobilized precursor initiator. n‐BuLi was used to activate the DPE in tetrahydrofuran at –78 °C to initiate the polymerization of different monomers (styrene, isoprene, ethylene oxide, and methyl methacrylate). Poly(styrene) (PS) and poly(ethylene oxide) (PEO) in particular were first investigated as grafted homopolymers, followed by their copolymers, including poly(isoprene)‐b‐poly(methylmethacrylate) (PI‐b‐PMMA). A combined approach of spectroscopic (Fourier transform infrared spectroscopy, surface plasmon spectroscopy, ellipsometry, X‐ray photoelectron spectroscopy) and microscopic (atomic force microscopy) surface analysis was used to investigate the formation of the polymer brushes in polar solvent media. The chemical nature of the outermost layer of these brushes was studied by water contact angle measurements. The effect of the experimental conditions (solvent, temperature, initiator concentration) on the surface properties of the polymer brushes was also investigated. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 769–782, 2006     

The freezing method for abstract nonlinear difference equations

The freezing method for ordinary differential systems is extended to a class of semilinear difference equations in a Hilbert space, whose linear parts have slowly varying coefficients and nonlinearities satisfying local Lipschitz conditions. The main methodology is based on a combined use of recent norm estimates for operator-valued functions with the freezing method as well as the multiplicative representation of solutions. Thus, explicit stability and boundedness conditions are derived. Applications to infinite dimensional delay difference systems are discussed.     

Incorporation of silver/carbon nanoparticles into poly(methyl methacrylate) via in situ miniemulsion polymerization and its influence on the glass‐transition temperature

Silver/carbon nanoparticles (9 nm) were incorporated, as reinforcements, into a matrix of poly(methyl methacrylate) via in situ miniemulsion polymerization. It was found by differential scanning calorimetry that the glass‐transition temperature of the poly(methyl methacrylate) showed an improvement of 14 °C with only 0.5 wt % nanoparticles in comparison with a pure poly(methyl methacrylate) control, which was also obtained by miniemulsion polymerization under the same conditions. This increase was related to a polymer chain mobility restriction due to a combination of bound plastic and joint plastic shell effects at the interphase and the surrounding regions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 511–518, 2007.