Quantum coherence has wide-ranging applications from quantum thermodynamics to metrology, channel discrimination and even biology. Thus, detecting quantifying are two fundamental problems in resource theory. Here, we introduce feasible methods detect estimate the by constructing witnesses for any finite-dimensional states. Our coherent states testing whether expectation value of witness is nega...

Given a finite subgroup G of the mapping class group surface S, Nielsen realization problem asks whether can be realized as homeomorphisms S. In 1983, Kerckhoff showed that for S finite-type surface, any may isometries some hyperbolic metric on We extend Kerckhoff's result to orientable, infinite-type surfaces. As applications, we classify torsion elements in plane minus Cantor set, and also sh...

Primitive harmonic maps of finite type from a Riemann surface M into a k-symmetric space G/H are obtained by integrating a pair of commuting Hamiltonian vector fields on certain finite-dimensional subspaces of loop algebras. We will clarify and generalize Ohnita and Udagawa’s results concerning homogeneous projections p : G/H →G/K , with H ⊂ K , preserving finite-type property for primitive har...

Let S be a connected orientable surface of finite topological type. We prove that there is an exhaustion of the curve complex C(S) by a sequence of finite rigid sets.

In this paper, a general elastoplastic-damage constitutive model considering the effect of strain rate has been developed. The derivation of this model has been cast into the irreversible thermodynamics with internal variables within the fundamentals of Continuum Damage Mechanics (CDM). The rate effect has been involved as an additional term into the plastic yield surface (dynamic plastic yield...