Magneto-photoluminescence of AlGaN/GaN quantum wells

The magneto-luminescence of GaN/AlGaN quantum wells in fields up to 52 T shows a field dependence that is strongly dependent on the well width. Strong redshifts are seen for the narrowest wells that are attributed to a Zeeman splitting. This is unexpected, since in bulk GaN epilayers the electron and hole g-factors of the lowest valence band cancel each other almost exactly. Therefore, we attribute this splitting to a reordering of the valence band due to the different band offsets caused by the strain and the aluminium component in the AlGaN barriers. The field dependence also gives information on the size of the exciton that has been converted into values for the exciton binding energy, and these values agree reasonably well with a theory that includes the presence of the electric field.     

Kolmogorov-Smirnov two-sample test based on regression rank scores

We derive the two-sample Kolmogorov-Smirnov type test when a nuisance linear regression is present. The test is based on regression rank scores and provides a natural extension of the classical Kolmogorov-Smirnov test. Its asymptotic distributions under the hypothesis and the local alternatives coincide with those of the classical test. (Supplement to the special issue of Appl. Math. 53 (2008), No. 3) This work was supported by the Czech Science Foundation under Grant No. 201/05/H007 and by Research Project LC06024.     

Numerical study of wave propagation in compressible two‐phase flow

We propose a new model and a solution method for two‐phase two‐fluid compressible flows. The model involves six equations obtained from conservation principles applied to a one‐dimensional flow of gas and liquid mixture completed by additional closure governing equations. The model is valid for pure fluids as well as for fluid mixtures. The system of partial differential equations with source terms is hyperbolic and has conservative form. Hyperbolicity is obtained using the principles of extended thermodynamics. Features of the model include the existence of real eigenvalues and a complete set of independent eigenvectors. Its numerical solution poses several difficulties. The model possesses a large number of acoustic and convective waves and it is not easy to upwind all of these accurately and simply. In this paper we use relatively modern shock‐capturing methods of a centred‐type such as the total variation diminishing (TVD) slope limiter centre (SLIC) scheme which solve these problems in a simple way and with good accuracy. Several numerical test problems are displayed in order to highlight the efficiency of the study we propose. The scheme provides reliable results, is able to compute strong shock waves and deals with complex equations of state. Copyright © 2006 John Wiley & Sons, Ltd.     

Optimal designs for estimating the coefficients of the lower frequencies in trigonometric regression models

In the common Fourier regression model we determine the optimal designs for estimating the coefficients corresponding to the lower frequencies. An analytical solution is provided which is found by an alternative characterization of c-optimal designs. Several examples are provided and the performance of the D-optimal design with respect to the estimation of the lower order coefficients is investigated. The results give a complete answer to an open question which was recently raised in the literature.     

一类三次系统极限环的唯一性和唯二性

讨论了一类三次系统x=-y(1-βx2)-(a1x a2x2 a3x3),y=b1x b2x2 b3x3的极限环问题.对包含一个奇点或多个奇点的极限环的唯一性和唯二性给出了若干充分条件.     

Focus on economy or ecology? A three‐dimensional trade‐off based on ecological carrying capacity in southwest China

Economic growth and human activities challenge the regional harmony of the economy and environment. Based on an evaluation of ecological carrying capacity (ECC), we have constructed a three‐dimensional trade‐off model for socially harmonious development for the Sichuan and Yunnan regions in southwest China. The results demonstrate that there is a continuous increase in socioeconomic coordination (SEC; slope > 0.23) and a change in the ECC in the study area, characterized by subtle fluctuations from 2000 through 2008. This was primarily due to the loss of resource and environment carrying capacity wiping out the profits of SEC. Significant government aid during the postdisaster reconstruction and more attention being paid to the environment in policy resulted in a faster increase in ECC (slope > 0.38) from 2008 to 2016. Based on this trade‐off model, managers could deeply understand the relationship between resources, the economy, and ecology. Summary for Managers

• Ecological environment protection is increasingly crucial in Sichuan and Yunnan regions as they feel the effects of climate change and human activities.
• The three‐dimensional trade‐off model measuring socially coordinated development is a modified multiobjective, decision‐making model.
• Based on this trade‐off model, managers could, understand the relationship between resources, the economy, and ecology.
• It can help manage our environmental assets and plan ecological conservation, to ensure that the environment maintains its capacity to serve the societal development.

     

The Banach manifold Ck(M,N)

Let M be a compact manifold without boundary and let N be a connected manifold without boundary. For each $k\in \mathbb{N}$ the set of k times continuously differentiable maps between M and N has the structure of a smooth Banach manifold where the underlying manifold topology is the compact-open $C^k$ topology. We provide a detailed and rigorous proof for this important statement which is already partially covered by existing literature.     

Effect of Monomer Composition on the Performance of Polymer‐Stabilized Liquid Crystals with Two‐Step Photopolymerization

Polymer‐stabilized cholesteric liquid crystal (PSCLC) films with broadband reflection based on two‐step photopolymerization are fabricated. Owing to the helical twisting power (HTP) value of the chiral dopant (CD) decreasing with increasing temperature, PSCLC films with broadband reflection are obtained by two‐step polymerization anchoring helical pitch of different length at two different temperature points. The effect of monomer composition on the PSCLC reflection properties before and after polymerization was studied. The results show that the free‐radical monomers with appropriate concentration and cationic monomers with sufficient concentration are vital for the formation of PSCLC films with broadband reflection. In addition, the experiments show that the increase in the functionality and rigidity of the cationic monomer has a positive effect on the broadening of the reflection band. This study can provide guidance and reference for the selection of monomer species and concentration in PSCLC preparation. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1126–1132