Direct Proof of Determinant Representation for Scalar Products of the XXZ Gaudin Model with Generic Non-Diagonal Boundary Terms

After constructing the Bethe state of the XXZ Gaudin model with generic non-diagonal boundary terms,we analyze the properties of this state and obtain the determinant representations of the scalar products for this XXZ Gaudin model.     

Reflection of plane waves in generalized thermoelasticity of type III with nonlocal effect

The generalized thermoelasticity theory based upon the Green and Naghdi model III of thermoelasticity as well as the Eringen's nonlocal elasticity model is used to study the propagation of harmonic plane waves in a nonlocal thermoelastic medium. We found two sets of coupled longitudinal waves, which are dispersive in nature and experience attenuation. In addition to the coupled waves, there also exists one independent vertically shear-type wave, which is dispersive but experiences no attenuation. All these waves are found to be influenced by the elastic nonlocality parameter. Furthermore, the shear-type wave is found to face a critical frequency, while the coupled longitudinal waves may face critical frequencies conditionally. The problem of reflection of the thermoelastic waves at the stress-free insulated and isothermal boundary of a homogeneous, isotropic nonlocal thermoelastic half-space has also been investigated. The formulae for various reflection coefficients and their respective energy ratios are determined in various cases. For a particular material, the effects of the angular frequency and the elastic nonlocal parameter have been shown on phase speeds and the attenuation coefficients of the propagating waves. The effect of the elastic nonlocality on the reflection coefficients and the energy ratios has been observed and depicted graphically. Finally, analysis of the various results has been interpreted.     

攒尖四坡屋面风致雪漂移的数值模拟

为获得攒尖四坡屋面的风致雪漂移规律，基于欧拉-欧拉方法和风雪单向耦合假定，运用计算流体动力学软件，选取Mixture模型分别对立方体周边和高低屋面上的风致雪漂移运动进行数值模拟，将模拟结果与两者的实地观测数据对比，探讨分析数值风洞的关键技术和参数设置，验证数值模拟方法的合理性与可靠性。依据攒尖四坡房屋的使用功能要求，设计分析模型与分析工况，在试算的基础上对屋面进行分区。以风速5 m/s，7 m/s，9 m/s，11 m/s，13 m/s和15 m/s，风向角0°，15°，30°和45°以及屋面坡度25°，30°，34°，40°和45°为分析参数，对攒尖四坡房屋的120种工况进行数值模拟，得到屋面各分区侵蚀沉积的基本规律，提出可用于抗雪设计的屋面积雪分布系数。研究表明，风向角的改变会使屋面积雪分布状态发生较大程度的变化，风速和屋面坡度的变化对屋面整体积雪量有较大影响。     

Judiciously 3‐partitioning 3‐uniform hypergraphs

Bollobás, Reed, and Thomason proved every 3‐uniform hypergraph ? with m edges has a vertex‐partition V()=V₁?V₂?V₃ such that each part meets at least edges, later improved to 0.6m by Halsegrave and improved asymptotically to 0.65m+o(m) by Ma and Yu. We improve this asymptotic bound to , which is best possible up to the error term, resolving a special case of a conjecture of Bollobás and Scott.