On the capacity of the state‐dependent interference relay channel

This paper considers the state‐dependent interference relay channel (SIRC) in which one of the two users may operate as a secondary user and the relay has a noncausal access to the signals from both users. For discrete memoryless SIRC, we first establish the achievable rate region by carefully merging Han‐Kobayashi rate splitting encoding technique, superposition encoding, and Gelfand‐Pinsker encoding technique. Then, based on the achievable rate region that we derive, the capacity of the SIRC is established in many different scenarios including (a) the weak interference regime, (b) the strong interference regime, and (c) the very strong interference regime. This means that our capacity results contain all available known results in the literature. Next, the achievable rate region and the associated capacity results are also evaluated in the case of additive Gaussian noise. Additionally, many numerical examples are investigated to show the value of our theoretical derivations.     

The generalized discrete ‐centroid problem

The ‐centroid problem or leader–follower problem is generalized considering different customer choice rules where a customer may use facilities belonging to different firms, if the difference in travel distance (or time) is small enough. Assuming essential goods, some particular customer choice rules are analyzed. Linear programming formulations for the generalized ‐medianoid and ‐centroid problems are presented and an exact solution approach is applied. Some computational examples are included.     

Adaptive compensation of persistent actuator failures of nonlinear systems

In this article, adaptive compensation designs are developed for nonlinear systems with uncertainties from the system functions and persistent actuator failures of characterizations that (i) some unknown system inputs are stuck at some unknown fixed or varying values at unknown time instants and (ii) the failure pattern always switches from one to another and the switching does not stop. Such a controlled plant is described by an uncertain time-varying nonlinear system, and some robust adaptive feedback linearization based failure compensation results are studied for closed-loop system stabilization and bounded output tracking for some specific conditions. To improve the tracking performance in the presence of persistent actuator failures, a new adaptive control scheme is developed, using the failure indicator function which contains the failure pattern and failure time in the formulation. Detailed stability and tracking performance are shown. Simulation results are shown to verify the effectiveness of the proposed adaptive actuator failure compensation method.     

Structural,optical and electrical properties of indium doped Cu2ZnSn(S,Se)4 thin films synthesized by the DC and RF reactive magnetron cosputtering

Element doping into the Cu₂ZnSn(S,Se)₄ (CZTSSe) absorber is an effective method to optimize the performance of thin film solar cells. In this study, the Cu₂In_xZn_1-xSn(S,Se)₄ (CIZTSSe) precursor film was deposited by magnetron cosputtering technique using indium (In) and quaternary Cu₂ZnSnS₄ (CZTS) as targets. Meanwhile, the In content was controlled using the direct current (DC) power on In target (P_In). A single kesterite CIZTSSe alloy was formed by successfully doping a small number of In³⁺ into the main lattice of CZTSSe. The partial Zn²⁺ cations were substituted by In³⁺ ions, resulting in improving properties of CZTSSe films. Morphological analysis showed that large grain CIZTSSe films could be obtained by doping In. The well-distributed, smooth, and dense film was obtained when the P_In was 30 W. The band gap of CIZTSSe could be continuously adjusted from 1.27 to 1.05 eV as P_In increased from 0 to 40 W. In addition, the CIZTSSe alloy thin film at P_In = 30 W exhibited the best p-type conductivity with Hall mobility of 6.87 cm²V^?1s^?1, which is a potential material as the absorption layer of high-performance solar cells.     

Assessing students' conceptual understanding using an online three‐tier diagnostic test

When solving a mathematical problem, students who do not have sufficient conceptual understanding may perform poorly and exhibit misconceptions. This study was aimed to examine students' conceptual understanding and significant misconceptions when solving number sense‐related problems. An online three‐tier diagnostic test was administered to 125 fifth‐grade students with varied socio‐economic backgrounds in Hong Kong. Only 14.40% of the students exhibited high performance with high confidence, indicating that these students had a profound conceptual understanding of number sense. In addition, the majority of the students (66.40%) did not demonstrate number sense; these students exhibited several significant misconceptions and could solve the questions only by using a rule‐based method or guessing. Accordingly, most students performed unsatisfactorily on number sense‐related problems. This study is imperative in identifying early predictors and provides information for further compatible interventions in the teaching and learning of number sense in Hong Kong in particular and worldwide in general.     

Evolution of Local Structural Ordering and Chemical Distribution upon Delithiation of a Rock Salt–Structured Li1.3Ta0.3Mn0.4O2 Cathode

Lithium‐rich disordered rock‐salt oxides have attracted great interest owing to their promising performance as Li‐ion battery cathodes. While experimental and theoretical efforts are critical in advancing this class of materials, a fundamental understanding of key property changes upon Li extraction is largely missing. In the present study, single‐crystal synthesis of a new disordered rock‐salt cathode material, Li_1.3Ta_0.3Mn_0.4O₂ (LTMO), and its use as a model compound to investigate Li concentration–driven evolution of local cationic ordering, charge compensation, and chemical distribution are reported. Through the combined use of 2D and 3D X‐ray nanotomography, it is shown that Li removal accompanied by oxygen oxidation is correlated with the development of morphological defects such as particle cracking. Chemical heterogeneity, quantified by subparticle level distribution of Mn valence state, is minimal during Mn redox, which drastically increases upon the formation of cracks during oxygen redox. Density functional theory and bond valence sum mismatch calculations reveal the presence of local short‐range ordering in the pristine oxide, which gradually disappears along with the extraction of Li. The study suggests that with cycling the transformation into true cation–disordered state can be expected, which likely impacts the voltage profile and obtainable energy density of the oxide cathodes.     

Toughness enhancement and equivalent initial fracture toughness of cementitious composite reinforced with aligned steel fibres

Based on theoretical analysis and numerical simulation, the impact of steel fibres on the stress intensity factor (SIF) at the crack tip for cementitious composite was studied. The enhanced toughness of steel fibre reinforced cementitious composite (SFRC) in resisting cracks was explained by the decrement of SIF caused by steel fibre inclusions at the crack tip of the composite. The equivalent initial fracture toughness was used to characterize the crack initiation of SFRC. A simplified method for determining the of SFRC was proposed based on a linear regression method. Fracture tests were conducted on three‐point bending notched beams with different steel fibre volume fractions and specimen sizes to study the crack initiation behaviour of aligned steel fibre reinforced cementitious composite (ASFRC). of ASFRC was calculated, and the size effect of was analysed. The results showed that slightly increased with the steel fibre volume fraction and gradually became stable. For the tested specimens, whose heights varied between 40 and 100 mm, the specimen size had little impact on the .     

Study of haze emission efficiency based on new co-opetition data envelopment analysis

As haze intensifies in China, controlling haze emission has become the country's top priority for environmental protection. Because haze moves across different regions, it is necessary to develop a data envelopment analysis (DEA) model underpinned by both competition and cooperation to evaluate the haze emission efficiency in different provinces. This study innovatively adopts the spatial econometrics to construct the co-opetition matrices of Chinese provinces, then builds the co-opetition DEA model to evaluate the haze emission efficiency of them, and finally uses the haze data of 2015 as an example to assess the applicability of the model. The results of the study include the following: First, compared with the traditional CCR (A. Charnes & W. W. Cooper & E. Rhodes) model, this study constructs the co-opetition DEA cross-efficiency model that integrates haze's feature of cross-border moving; thus, it is more in line with the reality of haze emission and movement. Second, compared with the efficiency value gained from the CCR model, the haze emission efficiency values for Tianjin and Guangdong, two decision-making units, register greater variance when using the DEA model. The reason might lie in that they have a different spatial transportation relationship with their surrounding provinces. Third, the haze emission efficiency of provinces, according to the evaluation based on the co-opetition DEA method, varies greatly: Those with high efficiency are mostly inland provinces with slow economic growth and adverse climatic conditions, whereas many of the provinces with low efficiency are located in the relatively prosperous East China. The specific co-opetition DEA model constructed in this study enriches the research on the DEA model, which can be applied to the emission efficiency evaluation of similar pollutants around the world and can contribute empirical support to the haze reducing efforts of the government with its empirical results.     

Association of solid fuel use with risk of stunting in children living in China

Stunting adversely affects physical and mental outcomes of children. It has not been examined whether household air pollution from solid fuel combustion is a risk factor for stunting in children. In a total of 41,439 children aged 6-17 across China, height was measured using a unified protocol. Multivariable linear regression models and logistic regression models were used to assess the associations of solid fuel use for cooking/heating with stunting in children. Adjusted for covariates, cooking/heating with solid fuel was significantly associated with a lower z-score for height for age and sex (β = −0.21 [−0.32 to −0.09] and −0.17 [−0.31 to −0.03], respectively) and an increased risk of stunting with an estimated ORs of 1.34 [1.07~1.68] and 1.37 [1.02~1.83], respectively. The risk of stunting associated with solid fuel use was statistically significant in high-age children. And the effect was greater on girls than on boys, though the difference was not statistically significant. Our study suggested that Chinese children living in households using solid fuel had a significantly higher risk of stunting than those living in households using cleaner fuel.