Ws Cheung

On Ostrowski type inequalities for Stieltjes integrals with absolutely continuous integrands and integrators of bounded variation

Some Ostrowski type inequalities are given for the Stieltjes integral where the integrand is absolutely continuous while the integrator is of bounded variation. The case when |f^| is convex is explored. Applications for the mid-point rule and a generalised trapezoid type rule are also presented.

Ostrowski and trapezoid type inequalities for the Stieltjes integral with Lipschitzian integrands or integrators

Some Ostrowski and trapezoid type inequalities for the Stieltjes integral in the case of Lipschitzian integrators for both Holder continuous and monotonic integrals are obtained. The dual case is also analysed. Applications for the midpoint rule are pointed out as well.

Two Ostrowski type inequalities for the Stieltjes integral of monotonic functions

Two integral inequalities of Ostrowski type for the Stieltjes integral nare given. The first is for monotonic integrators and Holder continuous nintegrands while the second considers the dual case, i.e., for monotonic integrands nand Holder continuous integrators. Applications for the mid-point ninequality that are useful in the numerical analysis of Stieltjes integrals are nexhibited. Some connections with the generalised trapezoidal rule are also npresented.

Plastic dynamics of the Al0.5CoCrCuFeNi high entropy alloy at cryogenic temperatures: Jerky flow, stair-like fluctuation, scaling behavior, and non-chaotic state

This study investigates the plastic behavior of the Al0.5CoCrCuFeNi high-entropy alloy at cryogenic temperatures. The samples are uniaxially compressed at 4.2u2009K, 7.5u2009K, and 9u2009K. A jerky evolution of stress and stair-like fluctuation of strain are observed during plastic deformation. A scaling relationship is detected between the released elastic energy and strain-jump sizes. Furthermore, the dynamical evolution of serrations is characterized by the largest Lyapunov exponent. The largest Lyapunov exponents of the serrations at the three temperatures are all negative, which indicates that the dynamical regime is non-chaotic. This trend reflects an ordered slip process, and this ordered slip process exhibits a more disordered slip process, as the temperature decreases from 9u2009K to 4.2u2009K or 7.5u2009K.

InGaN light-emitting diode stripes with reduced luminous exitance

InGaN light-emitting diodes of stripe geometries have been demonstrated. The elongated geometry facilitates light spreading in the longitudinal direction. The chips are further shaped by laser-micromachining to have partially-inclined sidewalls. The light extraction efficiencies of such 3D chip geometries are enhanced by ~12% (~8% according to ray-trace simulations), leading to a reduction of junction temperatures. The effective emission area is also increased four times compared to a cubic chip. The stripe LEDs are thus more efficient emitters with reduced luminous exitance, making them more suitable for a wide range of lighting applications.

Confocal microscopic analysis of optical crosstalk in GaN micro-pixel light-emitting diodes

The optical crosstalk phenomenon in GaN micro-pixel light-emitting diodes (LED) has been investigated by confocal microscopy. Depth-resolved confocal emission images indicate light channeling along the GaN and sapphire layers as the source of crosstalk. Thin-film micro-pixel devices are proposed, whereby the light-trapping sapphire layers are removed by laser lift-off. Optical crosstalk is significantly reduced but not eliminated due to the remaining GaN layer. Another design involving micro-pixels which are completely isolated is further proposed; such devices exhibited low-noise and enhanced optical performances, which are important attributes for high-density micro-pixel LED applications including micro-displays and multi-channel optical communications.

Orlicz Dual Brunn-Minkowski Theory: Addition, Dual Quermassintegrals, and Inequalities

We further consider the Orlicz dual Brunn-Minkowski theory. An Orlicz radial harmonic addition is introduced, which generalizes the Lp-radial addition and the Lp-harmonic addition to an Orlicz space, respectively. The variational formula for the dual mixed quermassintegrals with respect to the Orlicz radial harmonic addition is proved, and the new Orlicz dual quermassintegrals generalizes the Lp-dual quermassintegrals. The fundamental notions and conclusions of the dual quermassintegrals and the Minkoswki and Brunn-Minkowski inequalities for the dual quermassintegrals are extended to an Orlicz setting. The new Orlicz-Minkowski and Brunn-Minkowski inequalities in special case yield the Orlicz dual Minkowski inequality and Orlicz dual Brunn-Minkowski inequality, which also imply the Lp-dual Minkowski inequality and Lp-dual Brunn-Minkowski inequality for the dual quermassintegrals. As application, a dual log-Minkowski inequality is proved.

Emission characteristics of light-emitting diodes by confocal microscopy

The emission profiles of light-emitting diodes have typically be measured by goniophotometry. However this technique suffers from several drawbacks, including the inability to generate three-dimensional intensity profiles as well as poor spatial resolution. These limitations are particularly pronounced when the technique is used to compared devices whose emission patterns have been modified through surface texturing at the micrometer and nanometer scales,. In view of such limitations, confocal microscopy has been adopted for the study of emission characteristics of LEDs. This enables three-dimensional emission maps to be collected, from which two-dimensional cross-sectional emission profiles can be generated. Of course, there are limitations associated with confocal microscopy, including the range of emission angles that can be measured due to the limited acceptance angle of the objective. As an illustration, the technique has been adopted to compare the emission profiles of LEDs with different divergence angles using an objective with a numerical aperture of 0.8. It is found that the results are consistent with those obtained by goniophotometry when the divergence angle is less that the acceptance angle of the objective.

A Survey on Ostrowski Type Inequalities for Riemann-Stieltjes Integral

Some Ostrowski type inequalities for the Riemann–Stieltjes integral for various classes of integrands and integrators are surveyed. Applications for the midpoint rule and a generalised trapezoidal type rule are also presented.

On the Quermassintegrals of Convex Bodies

AbstractThe well-known question for quermassintegrals is the following: For which values of i∈N and every pair of convex bodies K and L, is it true thatn Wi(K+L)Wi+1(K+L)≥Wi(K)W˜i+1(K)+Wi(L)Wi+1(L)?n In 2003, the inequality was proved if and only if i=n−1 or i=n−2. Following the problem, in the paper, we prove some interrelated results for the quermassintegrals of a convex body.MSC:26D15, 52A30.