Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbric...Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbrich theorem for coalgebras C is given.展开更多
We present a novel method for designing transformation optical devices based on electrostatics.An arbi-trary transformation of electrostatic field can lead to a new refractive index distribution,where wave-fronts and ...We present a novel method for designing transformation optical devices based on electrostatics.An arbi-trary transformation of electrostatic field can lead to a new refractive index distribution,where wave-fronts and energy flux lines correspond to equipotential surfaces and electrostatic flux lines,respectively.Owing to scalar wave propagating exactly following an eikonal equation,wave optics and geometric optics share the same solutions in the devices.The method is utilized to design multipole lenses derived from multipoles in electrostatics.The source and drain in optics are considered as corre-sponding to positive charge and negative charge in the static field.By defining winding numbers in vir-tual and physical spaces,we explain the reason for some multipole lenses with illusion effects.Besides,we introduce an equipotential absorber to replace the drain to correspond to a negative charge with a grounded conductor.Therefore,it is a very general platform to design intriguing devices based on the combination of electrostatics and transformation optics.展开更多
文摘Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbrich theorem for coalgebras C is given.
基金the National Natural Science Foundation of China(92050102)the National Key Research and Development Program of China(2020YFA0710100)+1 种基金the National Natural Science Foundation of China(11874311)the FundamentalResearch Funds for the Central Universities(20720200074 and20720190049)。
文摘We present a novel method for designing transformation optical devices based on electrostatics.An arbi-trary transformation of electrostatic field can lead to a new refractive index distribution,where wave-fronts and energy flux lines correspond to equipotential surfaces and electrostatic flux lines,respectively.Owing to scalar wave propagating exactly following an eikonal equation,wave optics and geometric optics share the same solutions in the devices.The method is utilized to design multipole lenses derived from multipoles in electrostatics.The source and drain in optics are considered as corre-sponding to positive charge and negative charge in the static field.By defining winding numbers in vir-tual and physical spaces,we explain the reason for some multipole lenses with illusion effects.Besides,we introduce an equipotential absorber to replace the drain to correspond to a negative charge with a grounded conductor.Therefore,it is a very general platform to design intriguing devices based on the combination of electrostatics and transformation optics.
