Let SO（n） act in the standard way on C^n and extend this action in the usual way to C^n＋l = C＋ C^n. It is shown that a nonsingular special Lagrangian submanifold L→∪ C^n＋l that is invariant under this SO（n）-...Let SO（n） act in the standard way on C^n and extend this action in the usual way to C^n＋l = C＋ C^n. It is shown that a nonsingular special Lagrangian submanifold L→∪ C^n＋l that is invariant under this SO（n）-action intersects the fixed C→∪ C^n＋1 in a nonsingular real-analytic arc A （which may be empty）. If n 〉 2, then A has no compact component. Conversely, an embedded, noncompact nonsingular real-analytic arc A→∪ C lies in an embedded nonsingular special Lagrangian submanifold that is SO（n）-invariant. The same existence result holds for compact A if n =2. nonsingular SO（n）-invariant special Lagrangian nonsingular SO（n）-invariant special Lagrangian extensions in some open neighborhood of A. If A is connected, there exist n distinct extensions of A such that any embedded extension of A agrees with one of these n The method employed is an analysis of a singular nonlinear PDE and ultimately calls on the work of Gerard and Tahara to prove the existence of the extension.展开更多
An accurate frequency response characterization method for photoreceivers with optical heterodyne technique is presented in this paper.The characterization is implemented with two single-mode tunable lasers operating ...An accurate frequency response characterization method for photoreceivers with optical heterodyne technique is presented in this paper.The characterization is implemented with two single-mode tunable lasers operating near the wavelength of 1.55 μm.The errors introduced by extra fixtures as well as laser output fluctuations are considered and calibrated simultaneously.Compared with previous works,the proposed calibration procedures are more complete.Experimental results indicate that the significant improvement in measurement precision has been achieved with the proposed method in the frequency range from 0 to 30 GHz,which proves the proposed frequency response characterization method to be feasible and reliable.展开更多
基金Project supported by Duke University via a research grant, the NSF via DMS-0103884the Mathematical Sciences Research Institute, and Columbia University.
文摘Let SO（n） act in the standard way on C^n and extend this action in the usual way to C^n＋l = C＋ C^n. It is shown that a nonsingular special Lagrangian submanifold L→∪ C^n＋l that is invariant under this SO（n）-action intersects the fixed C→∪ C^n＋1 in a nonsingular real-analytic arc A （which may be empty）. If n 〉 2, then A has no compact component. Conversely, an embedded, noncompact nonsingular real-analytic arc A→∪ C lies in an embedded nonsingular special Lagrangian submanifold that is SO（n）-invariant. The same existence result holds for compact A if n =2. nonsingular SO（n）-invariant special Lagrangian nonsingular SO（n）-invariant special Lagrangian extensions in some open neighborhood of A. If A is connected, there exist n distinct extensions of A such that any embedded extension of A agrees with one of these n The method employed is an analysis of a singular nonlinear PDE and ultimately calls on the work of Gerard and Tahara to prove the existence of the extension.
文摘An accurate frequency response characterization method for photoreceivers with optical heterodyne technique is presented in this paper.The characterization is implemented with two single-mode tunable lasers operating near the wavelength of 1.55 μm.The errors introduced by extra fixtures as well as laser output fluctuations are considered and calibrated simultaneously.Compared with previous works,the proposed calibration procedures are more complete.Experimental results indicate that the significant improvement in measurement precision has been achieved with the proposed method in the frequency range from 0 to 30 GHz,which proves the proposed frequency response characterization method to be feasible and reliable.
