This paper deals with embedding theorems on Campanato-Marrey spaces formed by degenerate vector fields, which include Honnander and Grushin type of vector fields. These embedding theorems are somewhat different from t...This paper deals with embedding theorems on Campanato-Marrey spaces formed by degenerate vector fields, which include Honnander and Grushin type of vector fields. These embedding theorems are somewhat different from the known Poincare estimates. The main ingredients of the proofs rely on the fractional maximal functions. These results evidently have applications to the regularity of subelliptic PDE.展开更多
In this paper we first summarize our results published in recent years and their sketch proofs on local integrability,which are on the characterization of local integrability and on the existence of analytic normaliza...In this paper we first summarize our results published in recent years and their sketch proofs on local integrability,which are on the characterization of local integrability and on the existence of analytic normalization of analytically integrable differential systems. Then we present a new result on the equivalent characterization of the existence of the first integrals of an analytic differential systems near a nonhyperbolic singularity. Finally we pose some open problems on this subject.展开更多
Six high-index cores are embedded around the central solid core of the photonic crystal fiber to form a fiber embedded photonic crystal fiber （FEPCF）, which is investigated based on the beam propagation method. In t...Six high-index cores are embedded around the central solid core of the photonic crystal fiber to form a fiber embedded photonic crystal fiber （FEPCF）, which is investigated based on the beam propagation method. In this structure, the Gaussian mode could be transferred to the ring mode. So FEPCF could used as a mode convertor.展开更多
We present an exact solution to the problem of electromagnetic scattering by nanosphere clusters embedded in a liquid crystal cell, based on the Mie theory. The dependence of the scattering property on the structure p...We present an exact solution to the problem of electromagnetic scattering by nanosphere clusters embedded in a liquid crystal cell, based on the Mie theory. The dependence of the scattering property on the structure parameters is investigated in detail. It is shown that strong transverse light currents at the optical frequency can be obtained from these complex structures. Furthermore, we find that sign reversal of the transverse light current can be realized by changing frequency and voltage. The physical origins of these phenomena have been analyzed.The transverse light current for subwavelength nanoscale dimensions is of practical significance. Thus, the application of these phenomena to optical devices is展开更多
In this paper we first survey the results on the embedding flow problem of dif-feomorphisms in higher dimensional spaces. Next we present some new results on the characterization of semi-unipotent diffeomorphisms in R...In this paper we first survey the results on the embedding flow problem of dif-feomorphisms in higher dimensional spaces. Next we present some new results on the characterization of semi-unipotent diffeomorphisms in R3, which have a formal embedding flows.展开更多
基金Research supported in part by he National Sience Foundation Grant # DMS93-15963
文摘This paper deals with embedding theorems on Campanato-Marrey spaces formed by degenerate vector fields, which include Honnander and Grushin type of vector fields. These embedding theorems are somewhat different from the known Poincare estimates. The main ingredients of the proofs rely on the fractional maximal functions. These results evidently have applications to the regularity of subelliptic PDE.
基金supported by the NNSF of China Grant 11271252the RFDP of Higher Education of China grant 20110073110054the FP7-PEOPLE-2012-IRSES-316338 of Europe
文摘In this paper we first summarize our results published in recent years and their sketch proofs on local integrability,which are on the characterization of local integrability and on the existence of analytic normalization of analytically integrable differential systems. Then we present a new result on the equivalent characterization of the existence of the first integrals of an analytic differential systems near a nonhyperbolic singularity. Finally we pose some open problems on this subject.
基金suopported by the Heilongjiang Grant for Young Leading Teachers (No.1151G071)the Harbin Technology Foundation for Oversee Returnee (No.2007RFLXG007)
文摘Six high-index cores are embedded around the central solid core of the photonic crystal fiber to form a fiber embedded photonic crystal fiber （FEPCF）, which is investigated based on the beam propagation method. In this structure, the Gaussian mode could be transferred to the ring mode. So FEPCF could used as a mode convertor.
基金National Key R&D Program of China(2017YFA0303800)National Natural Science Foundation of China(NSFC)(11574031,61421001)
文摘We present an exact solution to the problem of electromagnetic scattering by nanosphere clusters embedded in a liquid crystal cell, based on the Mie theory. The dependence of the scattering property on the structure parameters is investigated in detail. It is shown that strong transverse light currents at the optical frequency can be obtained from these complex structures. Furthermore, we find that sign reversal of the transverse light current can be realized by changing frequency and voltage. The physical origins of these phenomena have been analyzed.The transverse light current for subwavelength nanoscale dimensions is of practical significance. Thus, the application of these phenomena to optical devices is
基金supported by NNSF of China grant 11271252by RFDP of Higher Education of China grant 20110073110054by FP7-PEOPLE-2012-IRSES-316338 of Europe
文摘In this paper we first survey the results on the embedding flow problem of dif-feomorphisms in higher dimensional spaces. Next we present some new results on the characterization of semi-unipotent diffeomorphisms in R3, which have a formal embedding flows.
