Convergence and Error Bound for Perturbation of Linear Programs

In various penalty/smoothing approaches to solving a linear program, one regularizes the problem by adding to the linear cost function a separable nonlinear function multiplied by a small positive parameter. Popular choices of this nonlinear function include the quadratic function, the logarithm function, and the x ln(x)-entropy function. Furthermore, the solutions generated by such approaches may satisfy the linear constraints only inexactly and thus are optimal solutions of the regularized problem with a perturbed right-hand side. We give a general condition for such an optimal solution to converge to an optimal solution of the original problem as the perturbation parameter tends to zero. In the case where the nonlinear function is strictly convex, we further derive a local (error) bound on the distance from such an optimal solution to the limiting optimal solution of the original problem, expressed in terms of the perturbation parameter.     

The development of a portable line-shaping optical system for silicon surface treatment

This study proposes a beam shaper for converting a circle beam profile generated with a Gaussian intensity distribution by an 808 nm diode laser into a line beam profile for silicon surface treatment applications. To produce a hand-held and low-cost device with a large spot-size laser, this study uses a portable optical system consisting of a diode laser source, a collimator, a cylindrical lens, and a plano-convex lens to generate an approximately 40 × 3:5mm² line beam profile at a working distance of 200 mm. The silicon surface treated by the line-shaped laser beam has significantly reduced reflectance spectra. The proposed system is also suitable for the surface cleaning of materials.     

Exploring the Origin of Maximum Entropy States Relevant to Resonant Modes in Modern Chladni Plates

The resonant modes generated from the modern Chladni experiment are systematically confirmed to intimately correspond to the maximum entropy states obtained from the inhomogeneous Helmholtz equation for the square and equilateral triangle plates. To investigate the origin of maximum entropy states, the inhomogeneous Helmholtz equation is modified to consider the point interaction coming from the driving oscillator. The coupling strength associated with the point interaction is characterized by a dimensionless factor α. The δ potential of the point interaction is numerically modelled by a truncated basis with an upper index N. The asymptotic behavior for the upper index N is thoroughly explored to verify that the coupling strength of α = 1.0 can make the theoretical resonant modes agree excellently with the maximum entropy states as N→∞. It is further authenticated that nearly the same resonant modes can be obtained by using a larger coupling strength α when a smaller upper index N is exploited in the calculation.     

On the convergence of the exponential multiplier method for convex programming

In this paper, we analyze the exponential method of multipliers for convex constrained minimization problems, which operates like the usual Augmented Lagrangian method, except that it uses an exponential penalty function in place of the usual quadratic. We also analyze a dual counterpart, the entropy minimization algorithm, which operates like the proximal minimization algorithm, except that it uses a logarithmic/entropy proximal term in place of a quadratic. We strengthen substantially the available convergence results for these methods, and we derive the convergence rate of these methods when applied to linear programs.Research supported by the National Science Foundation under Grant DDM-8903385, and the Army Research Office under Grant DAAL03-86-K-0171.     

Broadband Light-Emitting Diodes with One-Dimensional Photonic Crystal Layer

In this article, a broadband gallium-nitride-based light-emitting diode with a one-dimensional photonic crystal layer is investigated. The broadband light-emitting diode using the proposed backside reflector has high reflectance (>95%) over a 270-nm bandwidth in visible light at an arbitrary incidence angle. A broadband light-emitting diode of high output power due to the high reflectivity is achieved. Also reported are the results for light-emitting diodes by the transistor outline can (TO-can) package. The proposed light-emitting diodes possess broadband high reflected spectra, high output power for light extraction, and a good view angle.     

Copolyphenylenes with pendant benzimidazolyl and diethanolaminohexyloxy groups: Synthesis and electron‐transporting application in PLEDs

Two new electron‐transporting copolyphenylenes P1NH and P2NH possessing balanced charges crucial to emission efficiency of polymer light‐emitting diodes (PLEDs) have been synthesized and applied as an electron‐transporting layer (ETL). The main chain structure is all para‐linkage for P1NH and both para‐ and meta‐linkage for P2NH , with the same pendant electron‐withdrawing benzimidazolyl and polar diethanolaminohexyloxy groups. Both copolymers possess excellent thermal stability (T _d > 300 °C, T _g > 100 °C) due to their rigid backbones. In addition, the pendant groups effectively lower LUMO (～ ?2.70 eV) and HOMO (～ ?5.70 eV) levels, resulting in improved electron‐transporting and hole‐blocking capabilities. Multilayer yellow‐emitting PLEDs with a configuration of ITO/PEDOT:PSS/SY/ETL/LiF/Al were successfully fabricated by the spin‐coating process. The maximum luminance and maximum current efficiency of the P1NH ‐based device were 12,881 cd/m² and 10.94 cd/A, respectively, superior to the performance of P2NH ‐based device (4938 cd/m², 3.70 cd/A) and the device without ETL (8690 cd/m², 2.78 cd/A). Current results indicate that P1NH is highly effective in enhancing electron transport and device performance. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55 , 2494–2505     

A circular elastic cylinder under its own weight

An exact analysis of deformation and stress field in a finite circular elastic cylinder under its own weight is presented, with emphasis on the end effect. The problem is formulated on the basis of the state space formalism for axisymmetric deformation of a transversely isotropic body. Upon delineating the Hamiltonian characteristics of the formulation, a rigorous solution which satisfies the end conditions is determined by using eigenfunction expansion. The results show that the end effect is significant but confined to a local region near the base where the displacement and stress distributions are remarkably different from those according to the simplified solution that gives a uniaxial stress state. It is more pronounced in the cylinder with the bottom plane being perfectly bonded than in smooth contact with a rigid base.     

Improvement of <Emphasis Type="Italic">n</Emphasis>-ZnO/<Emphasis Type="Italic">p</Emphasis>-Si photodiodes by embedding of silver nanoparticles

The photo-current of n-ZnO/p-Si heterojunction photodiodes was improved by embedding Ag nanoparticles in the interface (ZnO/nano-P_Ag/p-Si), and the ratio between photo- and dark-current increased by about three orders more than that of a n-ZnO/p-Si specimen. The improvement in the photo-current resulted from the light scattering of embedded Ag nanoparticles. The I–V curve of n-ZnO/p-Si degraded after thermal treatment (A-ZnO/p-Si) because the silicon robbed the oxygen from ZnO to form amorphous silicon dioxide and left an oxygen vacancy. Notably, the properties of ZnO/nano-P_Ag/p-Si were better in the time-dependent photoresponse under 10 V bias. Ag nanoparticles (15–20 nm) scattered the UV light randomly and increased the probability for the absorption of ZnO to enhance the properties of the photodiode.     

Pulsed spark-discharge assisted synthesis of colloidal gold nanoparticles in ethanol

A green method, using pulsed spark-discharge (PSD) to synthesize gold nanoparticles (AuNPs) in ethanol, is studied in this article. Unlike conventional methods for metal nanoparticles synthesis, the PSD method does not require the addition of chemical surfactants and stabilizers. The size of PSD–AuNPs is examined by transmission electron microscopy, with a range 5–50 nm. The chemical compounds, crystal structure, and surface plasmon resonance of PSD–AuNPs are studied using energy dispersive X-ray spectroscopy, X-ray diffraction, and UV–Visible spectroscopy, respectively. Zeta potential analysis shows that a negative charge (−40 mV) on the surface of the PSD–AuNPs may be contributing to the stability of the suspension. During the gold electrodes discharge in the ethanol, under an intensive electric field and thermal energy, bulk metallic gold and ethanol may produce AuNPs and varieties of chemical derivatives, which are also studied by GC/MS and FTIR to investigate the suspension mechanism. The analysis results show that there is an oxidation reaction of ethanol occurring during the PSD process to produce ethanol derivatives, such as acetaldehyde, acetic acid, and ethyl acetate, which may modify the surface of AuNPs by coordination of oxygen atoms. However, only acetic acid can form a negative charge by the deprotonation of the carboxylic group of surface in ethanol, resulting in the creation of a repulsion force between the particles to form the stable colloid system. The experimental results indicate that PSD is an alternative green process to synthesize gold nanoparticles suspension in ethanol. Moreover, with a gold rod consumption rate of 15 mg/L, concentrations of gold nanoparticles ~9 ppm have been observed; therefore, the net production rate is around 60%.