Topological physics relies on the existence of Hamiltonian’s eigenstate singularities carrying a topological charge, such as quantum vortices, Dirac points, Weyl points and – in non- Hermitian systems – exceptional points (EPs), lines or surfaces 1–3 . They appear only in pairs connected by a Fermi arc and are related to a Hermitian singularity, such as a Dirac point.

结构物理学依赖于汉密尔顿算符特征值奇点的存在，这些奇点带有拓扑电荷，例如量子涡、达拉克点、韦尔点以及非埃尔米特系统中的特例点(EPs)、线或面1–3。它们以一对的形式出现，并且与一个埃尔米特奇点（例如达拉克点）相连接。

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帮我地道的翻译：The differential variational inequalities ((DVIs), for short) are useful for the study of models involving both dynamics and constraints in the form of in￾equalities. They arise in many applications: electrical circuits with ideal diodes, Coulomb friction problems for contacting bodies, economical dynamics, dynamic traffic networks. Pang and Stewart [26], [27] established the existence, unique￾ness, and Lipschitz dependence of solutions subject to boundary conditions for (DVIs) in finite dimensional spaces. Han and Pang investigated a class of dif￾ferential quasi-variational inequalities in [11], and Li, Huang and O’Regan [18] studied a class of differential mixed variational inequalities in finite dimensional Well-Posedness of Differential Mixed Quasi-Variational-Inequalities 137 spaces. Gwinner [8] obtained an equivalence result between (DVIs) and projected dynamical systems. In [9] he also proved a stability property for (DVIs) by using the monotonicity method of Browder and Minty, and Mosco set convergence. Chen and Wang [4] studied dynamic Nash equilibrium problems which have the formulation of differential mixed quasi-variational inequalities. Elastoplastic contact problems can also be incorporated into (DMQVIs) formulation because general dynamic processes in the nonsmooth unilateral contact problems are governed by quasi-variational inequalities. A numerical study for nonsmooth contact problems with Tresca friction can be found in [10], Liu, Loi and Obukhovskii [19] studied the existence and global bifurcation for periodic solutions of a class of (DVIs) by using the topological degree theory for multivalued maps and the method of guiding functions. For more details about (DVIs) we refer to [3], [30], [12], [22]–[21].

差分变分不等式(DVIs)对于研究涉及动力学和不等式约束的模型非常有用。它们出现在许多应用中：带有理想二极管的电路、接触体的库仑摩擦问题、经济动力学、动态交通网络。Pang和Stewart(26,27)在有限维空间中建立了(DVIs)解的存在、唯一性和利普希茨依赖性的边界条件。Han和Pang在(11)中调查了一类差分拟变分不等式，Li、Huang和O'Regan在有限维空间中研究了一类差分混合变分不等式。Gwinner(8)得到了(DVIs)和投影动力系统之间的等价结果。在(9)中，他还通过使用Browder和Minty的单调性方法以及Mosco集收敛法证明了(DVIs)的稳定性性质。Chen和Wang(4)研究了动态Nash均衡问题，其公式为差分混合拟变分不等式。弹塑性接触问题也可以并入(DMQVIs)公式，因为非光滑单向接触问题中的一般动态过程受到拟变分不等式的控制。在(10)中可以找到Tresca摩擦下的非光滑接触问题的数值研究，Liu、Loi和Obukhovskii在(19)中使用多值映射的拓扑度理论和引导函数法研究了一类(DVIs)的周期解的存在和全局分支。关于(DVIs)的更多细节，我们可以参考(3)，(30)，(12)，(22)-(21)。