Utilizing the tool of beam propagation method (BPM) to calculate the zeroth order diffraction beam intensity, we find SVHG displays notched diffraction response as a function of the readout wavelength. Using the metho...Utilizing the tool of beam propagation method (BPM) to calculate the zeroth order diffraction beam intensity, we find SVHG displays notched diffraction response as a function of the readout wavelength. Using the method of SA and considering the variance of refractive index as the readout wavelength changes, a practiced notch filter can be designed and the period of the filter is discussed.展开更多
In this paper, a unified method based on the strong approximation(SA) of renewal process(RP) is developed for the law of the iterated logarithm(LIL) and the functional LIL(FLIL), which quantify the magnitude of the as...In this paper, a unified method based on the strong approximation(SA) of renewal process(RP) is developed for the law of the iterated logarithm(LIL) and the functional LIL(FLIL), which quantify the magnitude of the asymptotic rate of the increasing variability around the mean value of the RP in numerical and functional forms respectively. For the GI/G/1 queue, the method provides a complete analysis for both the LIL and the FLIL limits for four performance functions: The queue length, workload, busy time and idle time processes, covering three regimes divided by the traffic intensity.展开更多
In this paper, the complex short pulse equation and the coupled complex short pulse equations that can describe the ultra-short pulse propagation in optical fibers are investigated. The two complex nonlinear models ar...In this paper, the complex short pulse equation and the coupled complex short pulse equations that can describe the ultra-short pulse propagation in optical fibers are investigated. The two complex nonlinear models are turned into multi-component real models by proper transformations. Lie symmetries are obtained via the classical Lie group method, and the results for the coupled complex short pulse equations contain the existing results as particular cases.Based on the linearizing operator and adjoint linearizing operator for the two real systems,adjoint symmetries can be obtained. Explicit conservation laws are constructed using the symmetry/adjoint symmetry pair(SA) method. Relationships between the nonlinear selfadjointness method and the SA method are investigated.展开更多
基金Supported by the National Natural Science Foundation of China!696 07005)
文摘Utilizing the tool of beam propagation method (BPM) to calculate the zeroth order diffraction beam intensity, we find SVHG displays notched diffraction response as a function of the readout wavelength. Using the method of SA and considering the variance of refractive index as the readout wavelength changes, a practiced notch filter can be designed and the period of the filter is discussed.
基金supported by the National Natural Science Foundation of China under Grant No.11471053
文摘In this paper, a unified method based on the strong approximation(SA) of renewal process(RP) is developed for the law of the iterated logarithm(LIL) and the functional LIL(FLIL), which quantify the magnitude of the asymptotic rate of the increasing variability around the mean value of the RP in numerical and functional forms respectively. For the GI/G/1 queue, the method provides a complete analysis for both the LIL and the FLIL limits for four performance functions: The queue length, workload, busy time and idle time processes, covering three regimes divided by the traffic intensity.
基金funded by the National Natural Science Foundation of China(No.12105073)Science and Technology Program of Colleges and Universities in Hebei Province(No.QN2020144)+2 种基金Science and Technology Plan Project(Special Program for Soft Science)in Hebei Province(No.20556201D)Scientific Research and Development Program Fund Project of Hebei University of Economics and Business(Nos.2020YB15,2020YB12 and 2021ZD07)Youth Team Support Program of Hebei University of Economics and Business。
文摘In this paper, the complex short pulse equation and the coupled complex short pulse equations that can describe the ultra-short pulse propagation in optical fibers are investigated. The two complex nonlinear models are turned into multi-component real models by proper transformations. Lie symmetries are obtained via the classical Lie group method, and the results for the coupled complex short pulse equations contain the existing results as particular cases.Based on the linearizing operator and adjoint linearizing operator for the two real systems,adjoint symmetries can be obtained. Explicit conservation laws are constructed using the symmetry/adjoint symmetry pair(SA) method. Relationships between the nonlinear selfadjointness method and the SA method are investigated.
