F-rough law and the discovery of rough law

By using function one direction S-rough sets （function one direction singular rough sets）, this article presents the concepts of F-law, F-rough law, and the relation metric of rough law; by using these concepts, this article puts forward the theorem of F-law relation metric, two orders theorem of F-rough law relation metric, the attribute theorem of F-rough law band, the extremum theorem of F-rough law relation metric, the discovery principle of F-rough law and the application of F-rough law.

Thermal properties of Lense-Thirring spacetime in tetrad theory of gravity

Using the divergence term appearing in the Lagrangian of the teleparallel equivalent of general relativity （TEGR）, we calculate the thermodynamic quantities of four tetrads＇ spacetime reproducing Lense-Thirring （LT） metric. We also investigate the first law of thermodynamics and the quantum statistical relation.

Field and current driven versions of Brandt method for calculating transport ac loss of superconducting cylinder and strip

As an elegant and fast numerical tool for solving time‐dependent electromagnetic field problems in hard superconductors,Brandt’s method has played an important role in understading the magnetic behavior of superconducting strips,discs,bars and cylinders in various aspect ratios.However,the application of this convenient method was mainly in magnetization processes.Traditionally,the solution of current transport problem needs to introduce a driving electric field E_(a),which requires a low efficiency iterative process and E_(a) itself was not clearly explained.In this work,three integral algorithms based on the Brandt’s method are developed to deal with current transport problems,which directly adopt the applied current as a boundary condition.Namely the current(I)‐driven version and two current‐field‐driven versions A and B.Moreover,the arbitrary applied magnetic field can also be included in the I‐driven version.The derivation with all necessary formulas for the methods are given in this work.As an example,the new methods,as well as the traditional method are used for calculating transport ac loss Q of a superconducting cylinder or strip obeying a power‐law relation of E∝J^(n)as a function of a given I(t).Derived from the Ampère law and the differential rather than the integral expression of the Faraday law,the current‐driven version can be used for more accurate and much quicker computation.Being an intermediate quantity,E_(a)(t) in the two current‐field‐driven versions is accurately calculated under the given I(t),but version B is much quicker than A.Problems relating to E_(a)(t) and Q stabilization process are discussed.