P-doped CoSe2 nanoparticles embedded in 3D honeycomb-like carbon network for long cycle-life Na-ion batteries

We report for the first time a Na-ion battery anode material composed of P-doped CoSe2 nanoparticles(P-CoSe2)with the size of 5-20 nm that are uniformly embed in a 3D porous honeycomb-like carbon network.High rate capability and cycling stability are achieved simultaneously.The honeycomb-like carbon network is rationally designed to support high electrical conductivity,rapid Na-ion diffusion as well as the accommodation of the volume expansion from the active P-CoSe2 nanoparticles.In particular,heteroatom P-doping within CoSe2 introduces stronger P-Co bonds and additional P-Se bonds that signif-icantly improve the structure stability of P-CoSe2 for highly stable sodiation/desodiation over long-term cycling.P-doping also improves the electrical conductivity of the CoSe2 nanoparticles,leading to highly elevated electrochemical kinetics to deliver high specific capacities at high current densities.Benefiting from the unique nanostructure and atomic-level P-doping,the P-CoSe2(2∶1)/C anode delivers an excel-lent cycle stability with a specific capacity of 206.9 mA h g-1 achieved at 2000 mA g-1 after 1000 cycles.In addition,this material can be synthesized using a facile pyrolysis and selenization/phosphorization approach.This study provides new opportunities of heteroatom doping as an effective method to improve the cycling stability of Na-ion anode materials.     

Crystallographic characteristics and microwave dielectric properties of Ni-modified MgTa2O6 ceramics

Ni²⁺ modified MgTa₂O₆ ceramics with a trirutile phase and space group P4₂/mnm were obtained. The correlations between crystallographic characteristics and microwave dielectric performance of MgTa₂O₆ ceramics were systematically studied based on the chemistry bond theory (PVL theory) for the first time. The results indicate that the introduction of Ni²⁺ causes a change in polarizability and the Mg–O bond ionicity, which contributes to the variation of dielectric constant. Moreover, the lattice energy, and packing fraction, full width at half maximum of the Raman peak of Ta–O bond, as the quantitative characterization of crystallographic parameters, regulate the dielectric loss of MgTa₂O₆ ceramics in GHz frequency band. In addition, the study of sintering behavior shows that the densification and micromorphology are the crucial factors affecting the microwave dielectric performance. Typically, Ni²⁺ doping on the A-site of MgTa₂O₆ can effectively promote the Q × f values to 173,000 GHz (at 7.43 GHz), which ensures its applicability in 5G communication technology.     

Investigation of crystal characteristics,Raman spectra,and microwave dielectric properties of Mg1-xZnxTa2O6 ceramics

Mg_(1-x)Zn_xTa₂O₆ (x = 0.00?0.08) dielectric ceramics were synthesized via the traditional solid-state reaction method. We used XRD and Rietveld refinement to demonstrate that a pure Mg_(1-x)Zn_xTa₂O₆ phase with trirutile structure was formed. Zn²⁺ substitution helped to decrease the Raman full width at half width of the A_1g mode at 703 cm^?1, which resulted in an increase in the order and rigidity of the TaO₆ octahedron, this in turn contributed to improving the Q×f values. Additionally, the introduction of Zn²⁺ significantly promoted grain growth and increased the dense, and the molecular polarizability, these factors lead to a higher permittivity. Moreover, enhanced Ta-O bond energy resulted in a more stable TaO₆ octahedron in the Mg_(1?x)Zn_xTa₂O₆ system, which contributed to enhanced τ_f values via substitution of Zn²⁺ doped on the A-site. Correspondingly, the microwave dielectric properties were significantly improved for 0.04-doped samples, obtaining: ε_r = 27, Q × f = 185,000 GHz (at 7.47 GHz), τ_f =32 ppm/°C.     

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.     

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.