This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The definition of quasi-linearity is dis...This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The definition of quasi-linearity is discussed, in addition to the examination of properties and classifications of linear ring spaces. Particularly, the ring of holomorphic functions on a region of the complex plane is examined, and the manner in which it generates an iterated linear ring space under the complex derivative operator. This notion is then generalized to all rings with nth order linear and surjective operators. Basic operator theory regarding the classifications of linear ring maps is also covered.展开更多
水系锌离子电池(ZIBs)以其低成本、高安全性和环境友好的优点受到了研究者的广泛关注,成为大规模电化学储能系统的理想选择之一。然而锌金属负极在应用时面临着锌枝晶生长、腐蚀反应和副反应等难以克服的障碍,严重制约了水系锌离子电池...水系锌离子电池(ZIBs)以其低成本、高安全性和环境友好的优点受到了研究者的广泛关注,成为大规模电化学储能系统的理想选择之一。然而锌金属负极在应用时面临着锌枝晶生长、腐蚀反应和副反应等难以克服的障碍,严重制约了水系锌离子电池的发展。探索可替代锌金属的储锌负极是应对上述问题的有效策略,因此研究者围绕过渡金属氧化物、硫化物和导电聚合物开展了深入研究。以TiX_(2)(X=S,Se)为代表的二维过渡金属硫族化合物(TMDs)具有较大的层间距和快速的离子传输通道,可作为锌离子电池的负极,但其储锌反应机制尚未得到完整的揭示。在本文中,我们使用密度泛函理论(DFT)计算方法系统地研究锌离子在TiX_(2)中的嵌入反应。首先我们采用群论去描述嵌锌TiX_(2)的稳定层间构型的特点,定义了一个依赖于超胞并且只涉及平移旋转两种对称操作的群,其子群可以用来描述层间构型的对称性,而且用来描述最稳定构型的子群总是倾向于有最大的阶数。基于该计算得到的一系列对应于不同放电深度的TiX_(2)的稳定结构,我们发现TiS_(2)和TiSe_(2)两种材料在锌嵌入/脱出过程中的开路电压(OCV)均低于0.5V。态密度(DOS)的计算结果表明TiX_(2)具有很好的电子导电性,而分波态密度(PDOS)的结果显示随着锌的嵌入闭壳层的Ti^(4+)还原成开壳层的Ti^(3+),并且伴随着Zn―X键的生成。Bader电荷分析的结果表明随着X的嵌入,X相比Ti得到了更多的负电荷,意味着X也参与了TiX_(2)的氧化还原过程。爬坡弹性带方法(CINEB)计算的结果证实了Zn^(2+)在TiX_(2)中具有较低的扩散能垒(对于TiS_(2)是0.333 e V,对于TiSe_(2)是0.338e V)。本文的研究结果不仅从本质上证明了TiX_(2)适合作为锌离子电池的嵌锌负极材料,而且为其他高性能TMDs电池材料的DFT研究提供了新的见解。展开更多
Parallel mechanisms(PMs) having the same motion characteristic with a UP kinematic chain(U denotes a universal joint, and P denotes a prismatic joint) are called UP-equivalent PMs. They can be used in many application...Parallel mechanisms(PMs) having the same motion characteristic with a UP kinematic chain(U denotes a universal joint, and P denotes a prismatic joint) are called UP-equivalent PMs. They can be used in many applications, such as machining and milling. However, the existing UP-equivalent PMs suffer from the disadvantages of strict assembly requirements and limited rotational capability. Type synthesis of UP-equivalent PMs with high rotational capability is presented.The special 2 R1 T motion is briefly discussed and the fact that the parallel module of the Exechon robot is not a UP-equivalent PM is disclosed. Using the Lie group theory, the kinematic bonds of limb chains and their mechanical generators are presented. Structural conditions for constructing such UP-equivalent PMs are proposed,which results in numerous new architectures of UP-equivalent PMs. The high rotational capability of the synthesized mechanisms is illustrated by an example. The advantages of no strict assembly requirements and high rotational capability of the newly developed PMs will facilitate their applications in the manufacturing industry.展开更多
苯(C 6 H 6)作为大气和室内环境中的主要污染物,具有强烈致癌性,是大气环境主要监测的内容之一。基于群论方法分析建立一种苯分子的泛频跃迁谱线计算方法,利用苯分子简正振动模式与光谱活性,获得30个振动模式的振动频率及其不可约表示...苯(C 6 H 6)作为大气和室内环境中的主要污染物,具有强烈致癌性,是大气环境主要监测的内容之一。基于群论方法分析建立一种苯分子的泛频跃迁谱线计算方法,利用苯分子简正振动模式与光谱活性,获得30个振动模式的振动频率及其不可约表示。基于D 6点群乘法规则,给出苯分子泛频跃迁的振动模式、光谱活性与谱线位置,为后续精确测量近红外区域苯分子未知谱线跃迁提供了数据与理论支撑。展开更多
文摘This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The definition of quasi-linearity is discussed, in addition to the examination of properties and classifications of linear ring spaces. Particularly, the ring of holomorphic functions on a region of the complex plane is examined, and the manner in which it generates an iterated linear ring space under the complex derivative operator. This notion is then generalized to all rings with nth order linear and surjective operators. Basic operator theory regarding the classifications of linear ring maps is also covered.
文摘水系锌离子电池(ZIBs)以其低成本、高安全性和环境友好的优点受到了研究者的广泛关注,成为大规模电化学储能系统的理想选择之一。然而锌金属负极在应用时面临着锌枝晶生长、腐蚀反应和副反应等难以克服的障碍,严重制约了水系锌离子电池的发展。探索可替代锌金属的储锌负极是应对上述问题的有效策略,因此研究者围绕过渡金属氧化物、硫化物和导电聚合物开展了深入研究。以TiX_(2)(X=S,Se)为代表的二维过渡金属硫族化合物(TMDs)具有较大的层间距和快速的离子传输通道,可作为锌离子电池的负极,但其储锌反应机制尚未得到完整的揭示。在本文中,我们使用密度泛函理论(DFT)计算方法系统地研究锌离子在TiX_(2)中的嵌入反应。首先我们采用群论去描述嵌锌TiX_(2)的稳定层间构型的特点,定义了一个依赖于超胞并且只涉及平移旋转两种对称操作的群,其子群可以用来描述层间构型的对称性,而且用来描述最稳定构型的子群总是倾向于有最大的阶数。基于该计算得到的一系列对应于不同放电深度的TiX_(2)的稳定结构,我们发现TiS_(2)和TiSe_(2)两种材料在锌嵌入/脱出过程中的开路电压(OCV)均低于0.5V。态密度(DOS)的计算结果表明TiX_(2)具有很好的电子导电性,而分波态密度(PDOS)的结果显示随着锌的嵌入闭壳层的Ti^(4+)还原成开壳层的Ti^(3+),并且伴随着Zn―X键的生成。Bader电荷分析的结果表明随着X的嵌入,X相比Ti得到了更多的负电荷,意味着X也参与了TiX_(2)的氧化还原过程。爬坡弹性带方法(CINEB)计算的结果证实了Zn^(2+)在TiX_(2)中具有较低的扩散能垒(对于TiS_(2)是0.333 e V,对于TiSe_(2)是0.338e V)。本文的研究结果不仅从本质上证明了TiX_(2)适合作为锌离子电池的嵌锌负极材料,而且为其他高性能TMDs电池材料的DFT研究提供了新的见解。
基金Supported by National Natural Science Foundation of China (Grant Nos.51525504,51475431)Zhejiang Provincial Natural Science Foundation of China (Grant No.LZ14E050005)Science Foundation of Zhejiang Sci-Tech University,China (Grant No.16022091-Y)
文摘Parallel mechanisms(PMs) having the same motion characteristic with a UP kinematic chain(U denotes a universal joint, and P denotes a prismatic joint) are called UP-equivalent PMs. They can be used in many applications, such as machining and milling. However, the existing UP-equivalent PMs suffer from the disadvantages of strict assembly requirements and limited rotational capability. Type synthesis of UP-equivalent PMs with high rotational capability is presented.The special 2 R1 T motion is briefly discussed and the fact that the parallel module of the Exechon robot is not a UP-equivalent PM is disclosed. Using the Lie group theory, the kinematic bonds of limb chains and their mechanical generators are presented. Structural conditions for constructing such UP-equivalent PMs are proposed,which results in numerous new architectures of UP-equivalent PMs. The high rotational capability of the synthesized mechanisms is illustrated by an example. The advantages of no strict assembly requirements and high rotational capability of the newly developed PMs will facilitate their applications in the manufacturing industry.
文摘苯(C 6 H 6)作为大气和室内环境中的主要污染物,具有强烈致癌性,是大气环境主要监测的内容之一。基于群论方法分析建立一种苯分子的泛频跃迁谱线计算方法,利用苯分子简正振动模式与光谱活性,获得30个振动模式的振动频率及其不可约表示。基于D 6点群乘法规则,给出苯分子泛频跃迁的振动模式、光谱活性与谱线位置,为后续精确测量近红外区域苯分子未知谱线跃迁提供了数据与理论支撑。
