On Kernel polynomials and self-perturbation of orthogonal polynomials

Given an orthogonal polynomial system {Q _n (x)} _n=0 ^∞, define another polynomial system by where α _n are complex numbers and t is a positive integer. We find conditions for {P _n (x)} _n=0 ^∞ to be an orthogonal polynomial system. When t=1 and α₁≠0, it turns out that {Q _n (x)} _n=0 ^∞ must be kernel polynomials for {P _n (x)} _n=0 ^∞ for which we study, in detail, the location of zeros and semi-classical character. Received: November 25, 1999; in final form: April 6, 2000?Published online: June 22, 2001     

Modified Mini finite element for the Stokes problem in ℝ2 or ℝ3

We analyze a modified version of the Mini finite element (or the Mini* finite element) for the Stokes problem in ℝ² or ℝ³. The cross‐grid element of order one in ℝ³ is also analyzed. The stability is verified with the aid of the macroelement technique introduced by Stenberg. Each of these methods converges with first order in h as the Mini element does. Numerical tests are given for the Mini* element in comparison with the Mini element when Ω is a unit square on ℝ². This revised version was published online in June 2006 with corrections to the Cover Date.     

Novel fabrication route for carbon-free and dense CuInSe2 (CIS) thin films via a non-vacuum process for solar cell application

Carbon-free CuInSe₂ (CIS) thin film with a dense microstructure has been prepared using a novel non-vacuum based fabrication route. Cu_xS_y and In₂Se₃ binary nanoparticles, approximately 10 nm in size, were synthesized by a low temperature colloidal process. The precursor film was deposited using the coating ink formulated with the binary nanoparticles and pyridine, and then annealed in the rapid thermal annealing (RTA) chamber at 540 °C for 15 min under selenium (Se) atmosphere. Scanning electron micrographs, X-ray diffraction patterns and Raman spectra showed a phase pure carbon-free and dense CIS thin film was prepared in this method. A solar cell device fabricated using this CIS thin film showed the following photovoltaic characteristics: V_OC = 350 mV, J_SC = 24.72 mA cm⁻², FF = 38.73% and η = 3.36% under standard AM 1.5 condition.     

Graphene Modified Lipophilically by Stearic Acid and its Composite With Low Density Polyethylene

Graphene, prepared by the thermal reduction of graphite oxide (GO), was modified with stearic acid to enhance its lipophilicity. A novel method, using the intrinsic epoxy groups on the graphene, was utilized for reaction with stearic acid to minimize the negative impact of the normal functionalization method on the π-electronic system of graphene. Gravimetric analysis, thermogravimetric analysis (TGA), Fourier transform infrared (FTIR) spectroscopy, and X-ray photoelectron spectroscopy (XPS) showed that the stearic acid was effectively attached to the graphene. In addition, Raman spectroscopy and electric conductivity of the graphene showed that this novel modification method, utilizing intrinsic defects, did not damage the π-electronic system of the sp² bonded carbons. The dispersion of graphene in a low density polyethylene (LDPE) matrix was enhanced; consequently, the reinforcing effect in tensile testing was improved by the lipophilic modification. The crystallization behavior observed by differential scanning calorimetry (DSC) showed that the crystallization of LDPE was hindered by dispersed graphene, more evidently when dispersed uniformly.     

Solving the Generalized Machine Assignment Problem in Group Technology

Many existing solution methodologies for machine assignment problems in group technology do not consider factors such as part demand, operation sequence and cost of intercellular moves. We formulate a 0-1 quadratic programming model that takes into account these factors in machine assignment. Two approaches are proposed to solve this problem. The first is an A*-based approach that generates optimal solutions. The second is a heuristic approach developed to solve problems with large number of machines and/or parts. The heuristic approach is shown to be efficient in producing good solutions in a computational study.     

Acoustic attenuation of hybrid silencers

The acoustic attenuation of a single-pass, perforated concentric silencer filled with continuous strand fibers is investigated first theoretically and experimentally. The study is then extended to a specific type of hybrid silencer that consists of two single-pass perforated filling chambers combined with a Helmholtz resonator. One-dimensional analytical and three-dimensional boundary element methods (BEM) are employed for the predictions of the acoustic attenuation in the absence of mean flow. To account for the wave propagation in absorbing fiber, the complex-valued characteristic impedance and wave number are measured. The perforation impedance facing the fiber is also presented in terms of complex-valued characteristic impedance and wave number. The effects of outer chamber diameter and the fiber density are examined. Comparisons of predictions with the experiments illustrate the need for multi-dimensional analysis at higher frequencies, while the one-dimensional treatment provides a reasonable accuracy at lower frequencies, as expected. The study also shows a significant improvement in the acoustic attenuation of the silencer due to fiber absorption. Multi-dimensional BEM predictions of a hybrid silencer demonstrate that a reactive component such as a Helmholtz resonator can improve transmission loss at low frequencies and a higher duct porosity may be effective at higher frequencies.     

Evolution of a stress-driven pattern in thin bilayer films: spinodal wrinkling

We report the full spectrum of the evolution of the wrinkle pattern formation in a thin bilayer film of an elastic metal on a viscoelastic polymer. Although the origin is different, the transition of an initial islandlike pattern to a labyrinthine structure without any change in the wavelength (q approximately t(0)) and the overall evolutionary process is strikingly similar to that in the spinodal system but the process is robust and takes place on a long time scale (about 10 days). The change into a mountainous topography in the late stages is accompanied by an increase in the length scale from an initial wavelength to another. This change, due to the relaxation of the confined polymer that results in a transition from elastic- to viscouslike behavior, induces wave coarsening (q approximately t(-1.04+/-0.08)) and macroscopic roughening.     

A Note on the Morozov Principle via Lagrange Duality

Considering a general linear ill-posed equation, we explore the duality arising from the requirement that the discrepancy should take a given value based on the estimation of the noise level, as is notably the case when using the Morozov principle. We show that, under reasonable assumptions, the dual function is smooth, and that its maximization points out the appropriate value of Tikhonov’s regularization parameter. The numerical relevance of our approach is established by means of an illustrative example from nonparametric instrumental regression, a standard problem in statistics.     

Magnetized SPR sensor for enhanced functionality

It is known that a magnetic field changes the RI and the SPR angle of specific analytes. We have applied an external magnetic field to a surface plasmon resonance (SPR) sensor to exploit this phenomenon. A gold film is used for excitation of SPR in the sensor with a Kretschmann configuration. According to the concentration of 4-type analyte, we observed unique changes of the SPR angle due to the magnetic field, providing better classification of material type than a conventional SPR sensor.     

Improved dimensional stability of Nafion membrane modified using a layer by layer self-assembly of biophilic polymers

The modification of perfluorinated proton exchange membranes (e.g. Nafion) utilizing a layer by layer (LbL) electrostatic assembly of oppositely charged biophilic polymers such as poly-l-lysine as positive layer and dsDNA as a negative layer is developed to protect the interface between the catalyst layer and the membrane in a low temperature fuel cell. Various physicochemical measurements including water uptake, proton conductivity and surface tension were investigated for both the as-received Nafion and the biopolymeric LbL modified Nafion. The smaller water contact angle and the less swelling characteristics of the biopolymer modified Nafion membrane was founded compared to that of as-received Nafion. This clearly indicates that the more hydrophilic surface of biopolymeric layers on Nafion plays an important role in the enhanced dimensional stability. In addition, a potential hypothesis explaining the higher proton conductivity from the LbL biopolymeric film coated Nafion is suggested.