Robust Stabilization for a Class of Uncertain Nonlinear Systems with Time-Varying Delay: Razumikhin-Type Approach

In this paper, using a Razumikhin-type approach, the stabilization of a class of uncertain nonlinear systems with time-varying delay is considered. The proposed controller is based on a specific optimal control problem. Global asymptotic stability is guaranteed for the proposed control if some algebraic condition is met. An example illustrates the use of the main result.     

Synthesis,photophysics, and electroluminescent performance of stable blue‐light‐emitting copoly(9,9‐diarylfluorene)s

A series of fluorene derivatives containing nonsymmetric and bulky aromatic groups at C‐9 position were synthesized and used for the preparation of blue‐light‐emitting copolyfluorenes ( P1 – P4 ) by the Suzuki coupling polycondensation. The copolymers were characterized by molecular weight determination, elemental analysis, differential scanning calorimeter, thermogravimetric analysis, absorption and emission spectroscopy, cyclic voltammetry, and differential pulse voltammetry. Their decomposition temperatures and glass transition temperatures are 423–441 °C and >120 °C, respectively. In film state, the copolyfluorenes exhibit blue photoluminescence at 425–450 nm, which remains almost unchanged after annealing at 200 °C in air for 60 min. Polymer light‐emitting diodes [ITO/PEDOT:PSS/ P1 – P4 /Ca(50 nm)/Al(100 nm)] show stable blue‐light emission under device operation with the CIE co‐ordinates being between (0.16, 0.07) and (0.17, 0.09). The light‐emitting diodes devices from P1 and P3 containing electron‐deficient oxadiazole units display enhanced performance, with the maximum brightness and maximum current efficiency being (4510 cd/m² and 2.40 cd/A) and (2930 cd/m², 1.19 cd/A), respectively. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 2821–2834, 2009     

Film protection of polymers

Polymer membranes, slabs, etc. can be effectively protected in time against permeation by an environmental polluting agent by self-regenerating, thin surface films of suitable film-forming materials initially dispersed in small amounts (less than 5 weight percent) in the polymer. These thin surface films (about 0.5 micrometers) can be either chemically passive to the polluting agent or be designed to react or catalyze a reaction with the agent in the presence of atmospheric oxygen or water vapor. We have studied the effectiveness of a number of passive film formers and a reactive film former in protecting a polyurethane elastomer, polyvinyl chloride and polyethylene towards a model polluting agent, tributyl phosphate. The presence on the polymer surface of the film former and its regeneration (within minutes) on scratching was followed by advancing contact angles of water, optical microscopy and scanning electron microscopy. Permeation weight loss of the polluting agent in a modified cup apparatus yielded both steady state permeation fluxes and the Barrer—Daynes time lags. In all cases the film-protected polymers exhibited smaller steady state fluxes and longer time lags than control polymers without the surface film. The decrease due to the presence of the surface film of the effective permeability and diffusion coefficient was sufficiently large to make this a promising method of protection.     

Nanoscale deformation measurement by using the hybrid method of gray-level and holographic interferometry

This study extends the use of holographic interferometry to measure the nanoscale out-of-plane displacement with high surface resolution. It is noted that if the deformation is less than half of the optical wavelength, it is hard to find an obvious fringe pattern. Under such a situation, in general, the phase shift method is used. However, it needs to take more than 3 images for phase shifting and phase reconstruction In this paper, a more simple hybrid method of gray-level and holographic interferometry is used to extract fringe skeletons, in which it just needs to take one or two images for the normal deformation measurement directly, even if there exists no obvious fringe pattern. The displacement field with high surface resolution can also be obtained. The proposed method yielded a theoretical precision of 0.15 nm for out-of-plane displacement with a monochromatic CCD camera of 10-bit gray scale (1024 gray scales) sensitivity and microscale surface resolution for millimeter scale object with 640×480 pixels image resolution by an He–Ne LASER (632.8 nm wavelength) light source. The gray-level method is proposed to calculate the non-obvious interferometry fringe by traditional holographic interferometry hologram, and the result showed that this method works for this purpose.     

Fast fractal image compression using spatial correlation

Fractal image compression is time consuming in the encoding process. The time is essentially spent on the search for the best-match block in a large domain pool. In this paper, the spatial correlations in both the domain pool and the range pool are utilized to reduce the searching space. With this technique, the encoding speed is 2.6 times faster than that of the full search method while the quality of the retrieved image is almost the same. Moreover, since the searching space is limited to the matched blocks of the previous range blocks, fewer bits are required to represent the transform. The bit rate is thus improved by about 20%.     

Impingement cooling in a rotating curved square annular duct with crossflow effect from Rib-roughened surfaces

An experimental investigation was carried out to determine the effects of jets in crossflow on impingement heat transfer from rib-roughened curved duct with rotational speeds of 120 and 240 rpm. The jet impinged on curved surface in crossflow having repeated square ribs (3 2 3mm). The curvature of the duct was fixed and has a value of 300 mm. The rib height (e) was fixed at 1.5 mm and pitch-to-height ratio (p/e) kept at 2. The study covered jet Reynolds number in the range 6500 to 26000, and duct stream crossflow Reynolds number from 3250 to 13000 based on jet nozzle diameter, respectively, which gave M = 0.12 to 2. Results were presented for rotational, crossflow, roughened surfaces and curvature effects on local Nusselt numbers. Significant heat transfer enhancement was found for the present physical geometry and within the ranges of operating parameters considered in the study.     

Ultrafine hydrogel fibers with dual temperature‐ and pH‐responsive swelling behaviors

Ultrafine hydrogel fibers that were responsive to both temperature and pH signals were prepared through the electrospinning of poly(N‐isopropylacrylamide) (PNIPAAm) and poly(acrylic acid) mixtures in dimethylformamide. Both the diameters (700 nm to 1.2 μm) and packing of the fibers could be controlled through changes in the polymer compositions and PNIPAAm molecular weights. These fibers were rendered water‐insoluble by the addition of either Na₂HPO₄ or poly(vinyl alcohol) (PVA) to the solution, followed by the heat curing of the fibers. The fibers crosslinked with Na₂HPO₄ swelled to 30–120 times in water; this was significantly higher than the swelling of those crosslinked with PVA. The PVA‐crosslinked hydrogel fibers, however, exhibited faster swelling kinetics; that is, they reached equilibrium swelling in less than 5 min at 25 °C. They were also more stable after 1 week of water exposure; that is, they lost less mass and retained their fibrous form better. All the hydrogel fibers showed a drastic increase in the swelling between pH 4 and 5. The PVA‐crosslinked hydrogel fibers exhibited distinct temperature‐responsive phase‐transition behavior of PNIPAAm, whereas the Na₂HPO₄‐crosslinked hydrogel fibers showed altered two‐stage phase transitions that reflected side‐chain modification of PNIPAAm. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 6331–6339, 2004     

Some results on a heat conduction problem by Myshkis

An infinite homogeneous d-dimensional medium initially is at zero temperature. A heat impulse is applied at the origin, raising the temperature there to a value greater than a constant value u₀>0. The temperature at the origin then decays, and when it reaches u₀, another equal-sized heat impulse is applied at a normalized time τ₁=1. Subsequent equal-sized heat impulses are applied at the origin at the normalized times τ_n, n=2,3,…, when the temperature there has decayed to u₀. This sequence of normalized waiting times τ_n can be defined recursively by a difference equation and its asymptotic behavior was known recently. This heat conduction problem was first studied in [J. Difference Equations Appl. 3 (1997) 89–91].

A natural subsequent question is what happens if the problem is set in a finite region, like in a laboratory, with the temperature at the boundary being kept zero forever. In this paper we obtain the asymptotic behavior of the heating times for the one-dimensional case.     

Minimal model for genome evolution and growth

Textual analysis of typical microbial genomes reveals that they have the statistical characteristics of a DNA sequence of a much shorter length. This peculiar property supports an evolutionary model in which a genome evolves by random mutation but primarily grows by random segmental duplication. That genomes grew mostly by duplication is consistent with the observation that repeat sequences in all genomes are widespread and intragenomic and intergenomic homologous genes are preponderant across all life forms.