Based on the triangular lattice two-dimensional photonic crystal(PC), the lattice spacing along the transverse direction to propagation is altered, and a gradient PC(GPC) flat lens is designed. The band structures and...Based on the triangular lattice two-dimensional photonic crystal(PC), the lattice spacing along the transverse direction to propagation is altered, and a gradient PC(GPC) flat lens is designed. The band structures and equal frequency curves of the GPC are calculated;then, the imaging mechanism and feasibility are analyzed. The imaging characteristics of the GPC flat lens are investigated. It is observed that the GPC can achieve multiple types of super-resolution imaging for the point source. This GPC lens is allowed to be applied to imaging and other fields such as filtering and sensing.展开更多
All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as ...All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as an inductive limit of circle algebras, where Lki (ni) are lens spaces. Let Lcd be a cd-homogeneous C*-algebra over whose cd-homogeneous C*-subalgebra restricted to the subspace Tr × T2 is realized as C(Tr) A1/d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lpcd is defined by twisting in by a totally skew multiplier p on Tr+2 × Zm-2. It is shown that is isomorphic to if and only if the set of prime factors of cd is a subset of the set of prime factors of p, and that Lpcd is not stablyisomorphic to if the cd-homogeneous C*-subalgebra of Lpcd restricted to some subspace LkiLki (ni) is realized as the crossed product by the obvious non-trivial action of Zki on a cd/ki-homogeneous C*-algebra over S2ni+1 for ki an integer greater than 1.展开更多
The simplest NMS flow is a polar flow formed by an attractive periodic orbit and a repulsive periodic orbit as limit sets. In this paper we show that the only orientable, simple, compact, 3-dimensional manifolds witho...The simplest NMS flow is a polar flow formed by an attractive periodic orbit and a repulsive periodic orbit as limit sets. In this paper we show that the only orientable, simple, compact, 3-dimensional manifolds without boundary that admit an NMS flow with none or one saddle periodic orbit are lens spaces. We also see that when a fattened round handle is a connected sum of tori, the corresponding flow is also a trivial connected sum of flows.展开更多
基金the National Natural Science Foundation of China(No.61405058)the Natural Science Foundation of Hunan Province(Nos.2017JJ2048 and 2020JJ4161)the Fundamental Research Funds for the Central Universities(No.531118040112).
文摘Based on the triangular lattice two-dimensional photonic crystal(PC), the lattice spacing along the transverse direction to propagation is altered, and a gradient PC(GPC) flat lens is designed. The band structures and equal frequency curves of the GPC are calculated;then, the imaging mechanism and feasibility are analyzed. The imaging characteristics of the GPC flat lens are investigated. It is observed that the GPC can achieve multiple types of super-resolution imaging for the point source. This GPC lens is allowed to be applied to imaging and other fields such as filtering and sensing.
基金The author was supported by grant No. 1999-2-102-001-3 from the interdis- ciplinary research program year of the KOSEF.
文摘All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as an inductive limit of circle algebras, where Lki (ni) are lens spaces. Let Lcd be a cd-homogeneous C*-algebra over whose cd-homogeneous C*-subalgebra restricted to the subspace Tr × T2 is realized as C(Tr) A1/d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lpcd is defined by twisting in by a totally skew multiplier p on Tr+2 × Zm-2. It is shown that is isomorphic to if and only if the set of prime factors of cd is a subset of the set of prime factors of p, and that Lpcd is not stablyisomorphic to if the cd-homogeneous C*-subalgebra of Lpcd restricted to some subspace LkiLki (ni) is realized as the crossed product by the obvious non-trivial action of Zki on a cd/ki-homogeneous C*-algebra over S2ni+1 for ki an integer greater than 1.
基金Partially supported by PB97-0394(DGES)Partially supported by P1B99-09(Convenio Bancaja-Universitat Jaume I)
文摘The simplest NMS flow is a polar flow formed by an attractive periodic orbit and a repulsive periodic orbit as limit sets. In this paper we show that the only orientable, simple, compact, 3-dimensional manifolds without boundary that admit an NMS flow with none or one saddle periodic orbit are lens spaces. We also see that when a fattened round handle is a connected sum of tori, the corresponding flow is also a trivial connected sum of flows.
