On the structure of stationary sets

We isolate several classes of stationary sets of [k]ωand investigate implications among them. Under a large cardinal assumption, we prove a structure theorem for stationary sets.     

Some properties of rapidly varying sequences

We investigate the class R∞,s of rapidly varying sequences from different points of view. It is shown: (1) a sequence (cn)_n∈N of positive real numbers is rapidly varying if and only if the corresponding function x→c[x], x?1, is rapidly varying; (2) the class R∞,s satisfies some selection properties, as well as game-theoretical and Ramsey-theoretical conditions.     

Maximum principle for functional equations in the space of discontinuous functions of three variables

The paper is devoted to the maximum principles for functional equations in the space of measurable essentially bounded functions. The necessary and sufficient conditions for validity of corresponding maximum principles are obtained in a form of theorems about functional inequalities similar to the classical theorems about differential inequalities of the Vallee Poussin type. Assertions about the strong maximum principle are proposed. All results are also true for difference equations, which can be considered as a particular case of functional equations. The problems of validity of the maximum principles are reduced to nonoscillation properties and disconjugacy of functional equations. Note that zeros and nonoscillation of a solution in a space of discontinuous functions are defined in this paper. It is demonstrated that nonoscillation properties of functional equations are connected with the spectral radius of a corresponding operator acting in the space of essentially bounded functions. Simple sufficient conditions of nonoscillation, disconjugacy and validity of the maximum principles are proposed. The known nonoscillation results for equation in space of functions of one variable follow as a particular cases of these assertions. It should be noted that corresponding coefficient tests obtained on this basis cannot be improved. Various applications to nonoscillation, disconjugacy and the maximum principles for partial differential equations are proposed.     

基于向量Liapunov函数不连续系统的稳定性研究

基于局部Lipschitz连续且正则(Clarke意义下)的向量Liapunov函数,讨论不连续自治系统的稳定性(Filippov解意义下)．通过定义一类新的向量Liapunov函数的“集值导数”,给出了关于不连续系统的广义比较原理．基于Lipschitz连续且正则的向量Liapunov函数,进一步的给出不连续自治系统的Liapunov稳定性定理．     

Penta-SiC5 monolayer: A novel quasi-planar indirect semiconductor with a tunable wide band gap

In this paper, by using of the first principles calculations in the framework of the density functional theory, we systematically investigated the structure, stability, electronic and optical properties of a novel two-dimensional pentagonal monolayer semiconductors namely penta-SiC₅ monolayer. Comparing elemental silicon, diamond, and previously reported 2D carbon allotropes, our calculation shows that the predicted penta-SiC₅ monolayer has a metastable nature. The calculated results indicate that the predicted monolayer is an indirect semiconductor with a wide band gap of about 2.82 eV by using Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional level of theory which can be effectively tuned by external biaxial strains. The obtained exceptional electronic properties suggest penta-SiC₅ monolayer as promising candidates for application in new electronic devices in nano scale.     

Mn掺杂LiFePO4的第一性原理研究

采用基于密度泛函理论的第一性原理方法, 计算了不同Mn掺杂浓度LiFe_1-xMn_xPO₄ (x=0,0.25,0.50,0.75) 的电子结构. 同时采用流变相辅助高温固相碳热还原法制备了LiFe_1-xMn_xPO₄ (x= 0,0.25,0.50,0.75) 材料. 理论计算表明: LiFePO₄具有E_g = 0.725 eV的带隙宽度, 为半导体材料. 通过Fe位掺杂25%的Mn离子可最大程度地 减小材料带隙宽度、降低Fe---O键及Li---O键键能, 进而提高材料的电子电导率及锂离子扩散速率. 实验结果亦表明, 当Mn掺杂量x=0.25时, 材料具有最优的电化学性能, 其具有约为158 mAh· g^-1的放电比容量以及551 Wh· kg^-1的能量密度. 理论计算与实验结果非常符合.     

On the Validity of Entropy Production Principles for Linear Electrical Circuits

We explain the (non-)validity of close-to-equilibrium entropy production principles in the context of linear electrical circuits. Both the minimum and the maximum entropy production principles are understood within dynamical fluctuation theory. The starting point are Langevin equations obtained by combining Kirchoff’s laws with a Johnson-Nyquist noise at each dissipative element in the circuit. The main observation is that the fluctuation functional for time averages, that can be read off from the path-space action, is in first order around equilibrium given by an entropy production rate. That allows to understand beyond the schemes of irreversible thermodynamics (1) the validity of the least dissipation, the minimum entropy production, and the maximum entropy production principles close to equilibrium; (2) the role of the observables’ parity under time-reversal and, in particular, the origin of Landauer’s counterexample (1975) from the fact that the fluctuating observable there is odd under time-reversal; (3) the critical remark of Jaynes (1980) concerning the apparent inappropriateness of entropy production principles in temperature-inhomogeneous circuits.     

基于第一性原理计算Mn掺杂MoS2对油中溶解气体的吸附性能

CO、C₂H₂、CH₄是溶解在变压器油中的典型故障特征气体,其种类和浓度能够反映油浸式变压器绝缘故障的不同类型和严重程度,进行油中溶解气体分析是在线检测变压器运行状态的重要方法.基于第一性原理,通过Mn-MoS₂单层对三种气体的吸附能、转移电荷、态密度和形变电荷密度等参数以及解吸性能分析和灵敏度计算,提出了一种基于Mn-MoS₂材料的气敏传感器对油中溶解气体进行分析的方法.结果表明Mn-MoS₂对CH₄是物理吸附,对CO和C₂H₂是化学吸附.对于Mn-MoS₂来说,CH₄在常温下吸附能力差且灵敏度低,CO在不同温度下均有较强的吸附能力,而C₂H₂在常温下吸附稳定,高温下易解吸且响应灵敏度高.因此,Mn掺杂的MoS₂体系可预期作为CO的气体吸附剂和检测C₂H     

Electronic structure,mechanical and optical properties of ternary semiconductors Si1-xGexC (X = 0, 0.25, 0.50, 0.75, 1)

The electronic structure of silicon carbide with increasing germanium content have been examined using first principles calculations based on density functional theory. The structural stability is analysed between two different phases, namely, cubic zinc blende and hexagonal phases. The zinc blende structure is found to be the stable one for all the Si_1-xGe_xC semiconducting carbides at normal pressure. Effect of substitution of Ge for Si in SiC on electronic and mechanical properties is studied. It is observed that cubic SiC is a semiconductor with the band gap value 1.243?eV. The band gap value of SiC is increased due to the substitution of Ge and the band gap values of Si _0.75 Ge _0.25 C, Si _0.50 Ge _0.50 C, Si _0.25 Ge _0.75 C and GeC are 1.322 eV, 1.413 eV, 1.574 eV and 1.657?eV respectively. As the pressure is increased, it is found that the energy gap gets decreased for Si_1-x Ge_xC (X?=?0, 0.25, 0.50, 0.75, 1). The elastic constants satisfy the Born – Huang elastic stability criteria. The bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio are also calculated and compared with the other available results.