In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated...In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated module over a principal ideal domain.展开更多
The Generalized Falk Method(GFM)for coordinate transformation,together with two model-reduction strategies based on this method,are presented for efficient coupled field-circuit simulations.Each model-reduction strate...The Generalized Falk Method(GFM)for coordinate transformation,together with two model-reduction strategies based on this method,are presented for efficient coupled field-circuit simulations.Each model-reduction strategy is based on a decision to retain specific linearly-independent vectors,called trial vectors,to construct a vector basis for coordinate transformation.The reduced-order models are guaranteed to be stable and passive since the GFM is a congruence transformation of originally symmetric positive definite systems.We also show that,unlike the Pade-via-Lanczos(PVL)method,the GFM does not generate unstable positive poles while reducing the order´of circuit problems.Further,the proposed GFM is also faster when compared to methods of the type Lanczos(or Krylov)that are already widely used in circuit simulations for electrothermal and electromagnetic problems.The concept of response participation factors is introduced for the selection of the trial vectors in the proposed model-reduction methods.Further,we present methods to develop simple equivalent circuit networks for the field component of the overall field-circuit system.The implementation of these equivalent circuit networks in circuit simulators is discussed.With the proposed model-reduction strategies,significant improvement on the efficiency of the generalized Falk method is illustrated for coupled field-circuit problems.展开更多
Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C ...Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C R regular ring,and the relations between C R regular ring and C R FP injective module.展开更多
An approach for full duty frequency-doubled triangle shape lightwave generation is proposed and demonstrated.It requires a dual-parallel Mach–Zehnder modulator（DP-MZM） driven by a sinusoidal signal. A stop band fil...An approach for full duty frequency-doubled triangle shape lightwave generation is proposed and demonstrated.It requires a dual-parallel Mach–Zehnder modulator（DP-MZM） driven by a sinusoidal signal. A stop band filter is coupled to filter out two undesired sidebands. By tuning the bias voltage applied to the DP-MZM, the output optical intensity with a full duty cycle triangle shape profile can be obtained. It is found that the required modulation index is no longer a fixed one. It can vary within a range, without degrading the target waveform. The principle is analyzed by theory and evaluated by simulation. A proof-of-concept experiment is also conducted.Good agreements between theoretical prediction and experimental results have been found. This approach might be attractive due to the feature of a variable modulation index, which insures simple operation in practice.展开更多
We theoretically analyze and experimentally demonstrate a method of generating equal-amplitude optical comb exploiting multi-frequency phase modulation. The theoretical analysis shows that 4n-1 equalamplitude spectral...We theoretically analyze and experimentally demonstrate a method of generating equal-amplitude optical comb exploiting multi-frequency phase modulation. The theoretical analysis shows that 4n-1 equalamplitude spectral lines can be obtained when the modulation signal comprises n frequency components including the fundamental frequency and the odd harmonic frequencies, and 2n＋1 equal-amplitude spectral lines can be obtained when the modulation signal comprises n frequency components including the fundamental frequency and the even harmonic frequencies. Then, we numerically simulate the spectra of 5, 7, 9, and 11 equal-amplitude spectral lines, respectively, which are also obtained in experiments with frequency separation of 30 MHz and flatness of better than 0.3 dB.展开更多
An optical modulation format generation scheme based on spectral filtering and frequency-to-time mapping is experimentally demonstrated. Many modulation formats with continuously adjustable duty radio and bit rate can...An optical modulation format generation scheme based on spectral filtering and frequency-to-time mapping is experimentally demonstrated. Many modulation formats with continuously adjustable duty radio and bit rate can be formed by changing the dispersion of dispersion element and the bandwidth of shaped spectrum in this scheme. In the experiment, non-return-to-zero(NRZ) signal with bit rate of 29.41 Gbit/s and 1/2 duty ratio return-to-zero(RZ) signal with bit rate of 13.51 Gbit/s are obtained. The maximum bit rate of modulation format signal is also analyzed.展开更多
Let R, S be rings, U a flat right .R-rnodule and V a flat right S-module. We show in this paper that (N, (U, V))-lc.dim(R(?) S) = sup((N, U)-lc.dimR, (N, V)-lc.dimS).
In this article,we introduce and study the concept of countably generated dimension,which is a Krull-like dimension extension of the concept of DCC on countably generated submodules.We show that some of the basic resu...In this article,we introduce and study the concept of countably generated dimension,which is a Krull-like dimension extension of the concept of DCC on countably generated submodules.We show that some of the basic results of Krull dimension are true for countably generated dimension.It is shown that an jR-module M has Krull dimension if and only if it has countably generated dimension,and its Krull dimension and countably generated dimension coincide.展开更多
A method to evaluate the influence of the laser linewidth on the linearly frequency-modulated(LFM)signals generated by heterodyning two free-running laser diodes(LDs)is proposed.The Pearson correlation coefficient bet...A method to evaluate the influence of the laser linewidth on the linearly frequency-modulated(LFM)signals generated by heterodyning two free-running laser diodes(LDs)is proposed.The Pearson correlation coefficient between the instantaneous frequency of the generated LFM signal and that of an ideal LFM signal is introduced to quantify the quality of the generated LFM signal.The closed-form solution of the correlation coefficient is given,which shows that the correlation coefficient is determined by the ratio of the LFM signal bandwidth to the square root of the total linewidth of the two LDs when the observation interval is fixed.Simulation results are also given,which proves the correctness of the theoretical results.展开更多
This paper presents an introduction to the researches in microwave photonics based packages and its application, a 973 project （No. 2012CB315600）, which focuses on addressing new requirements for millimeter wave （...This paper presents an introduction to the researches in microwave photonics based packages and its application, a 973 project （No. 2012CB315600）, which focuses on addressing new requirements for millimeter wave （MMW） system to work with higher frequency, wider bandwidth, larger dynamic range and longer distance of signal distribution. Its key scientific problems, main research contents and objectives are briefed, and some latest achievements by the project team, including generation of linear frequency modulation wave （LFMW）, tunable optoelectronic oscillator （OEO） with lower phase noise, reconfigurable filter with higher Q value, time delay line with wider frequency range, down conversion with gain, and local oscillator （LO） transmission with stable phase, are introduced briefly.展开更多
文摘In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated module over a principal ideal domain.
文摘The Generalized Falk Method(GFM)for coordinate transformation,together with two model-reduction strategies based on this method,are presented for efficient coupled field-circuit simulations.Each model-reduction strategy is based on a decision to retain specific linearly-independent vectors,called trial vectors,to construct a vector basis for coordinate transformation.The reduced-order models are guaranteed to be stable and passive since the GFM is a congruence transformation of originally symmetric positive definite systems.We also show that,unlike the Pade-via-Lanczos(PVL)method,the GFM does not generate unstable positive poles while reducing the order´of circuit problems.Further,the proposed GFM is also faster when compared to methods of the type Lanczos(or Krylov)that are already widely used in circuit simulations for electrothermal and electromagnetic problems.The concept of response participation factors is introduced for the selection of the trial vectors in the proposed model-reduction methods.Further,we present methods to develop simple equivalent circuit networks for the field component of the overall field-circuit system.The implementation of these equivalent circuit networks in circuit simulators is discussed.With the proposed model-reduction strategies,significant improvement on the efficiency of the generalized Falk method is illustrated for coupled field-circuit problems.
文摘Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C R regular ring,and the relations between C R regular ring and C R FP injective module.
基金supported in part by the National Natural Science Foundation of China under Grant No.61405007
文摘An approach for full duty frequency-doubled triangle shape lightwave generation is proposed and demonstrated.It requires a dual-parallel Mach–Zehnder modulator（DP-MZM） driven by a sinusoidal signal. A stop band filter is coupled to filter out two undesired sidebands. By tuning the bias voltage applied to the DP-MZM, the output optical intensity with a full duty cycle triangle shape profile can be obtained. It is found that the required modulation index is no longer a fixed one. It can vary within a range, without degrading the target waveform. The principle is analyzed by theory and evaluated by simulation. A proof-of-concept experiment is also conducted.Good agreements between theoretical prediction and experimental results have been found. This approach might be attractive due to the feature of a variable modulation index, which insures simple operation in practice.
基金supported by the China Postdoctoral Science Foundation(No.20060400230)the Foundation for Innovation Talents by the Technology Ministry of Harbin(No.2006RFQXG025)
文摘We theoretically analyze and experimentally demonstrate a method of generating equal-amplitude optical comb exploiting multi-frequency phase modulation. The theoretical analysis shows that 4n-1 equalamplitude spectral lines can be obtained when the modulation signal comprises n frequency components including the fundamental frequency and the odd harmonic frequencies, and 2n＋1 equal-amplitude spectral lines can be obtained when the modulation signal comprises n frequency components including the fundamental frequency and the even harmonic frequencies. Then, we numerically simulate the spectra of 5, 7, 9, and 11 equal-amplitude spectral lines, respectively, which are also obtained in experiments with frequency separation of 30 MHz and flatness of better than 0.3 dB.
基金supported by the National Natural Science Foundation of China(No.61377075)the Tianjin Natural Science Foundation(No.17JCYBJC16600)
文摘An optical modulation format generation scheme based on spectral filtering and frequency-to-time mapping is experimentally demonstrated. Many modulation formats with continuously adjustable duty radio and bit rate can be formed by changing the dispersion of dispersion element and the bandwidth of shaped spectrum in this scheme. In the experiment, non-return-to-zero(NRZ) signal with bit rate of 29.41 Gbit/s and 1/2 duty ratio return-to-zero(RZ) signal with bit rate of 13.51 Gbit/s are obtained. The maximum bit rate of modulation format signal is also analyzed.
基金National Natural Science Foundation of China(10171082)by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE.
文摘Let R, S be rings, U a flat right .R-rnodule and V a flat right S-module. We show in this paper that (N, (U, V))-lc.dim(R(?) S) = sup((N, U)-lc.dimR, (N, V)-lc.dimS).
基金The author is grateful to the Research Council of Shahid Chamran University of Ahvaz for financial support(SCU.MM99.192).
文摘In this article,we introduce and study the concept of countably generated dimension,which is a Krull-like dimension extension of the concept of DCC on countably generated submodules.We show that some of the basic results of Krull dimension are true for countably generated dimension.It is shown that an jR-module M has Krull dimension if and only if it has countably generated dimension,and its Krull dimension and countably generated dimension coincide.
基金supported by the National Key R&D Program of China(No.2017YFE0121500)the National Natural Science Foundation of China(Nos.61971193 and 61601297)+1 种基金the Open Fund of State Key Laboratory of Advanced Optical Communication Systems and Networks,Peking University,China(No.2020GZKF005)the Fundamental Research Funds for the Central Universities。
文摘A method to evaluate the influence of the laser linewidth on the linearly frequency-modulated(LFM)signals generated by heterodyning two free-running laser diodes(LDs)is proposed.The Pearson correlation coefficient between the instantaneous frequency of the generated LFM signal and that of an ideal LFM signal is introduced to quantify the quality of the generated LFM signal.The closed-form solution of the correlation coefficient is given,which shows that the correlation coefficient is determined by the ratio of the LFM signal bandwidth to the square root of the total linewidth of the two LDs when the observation interval is fixed.Simulation results are also given,which proves the correctness of the theoretical results.
文摘This paper presents an introduction to the researches in microwave photonics based packages and its application, a 973 project （No. 2012CB315600）, which focuses on addressing new requirements for millimeter wave （MMW） system to work with higher frequency, wider bandwidth, larger dynamic range and longer distance of signal distribution. Its key scientific problems, main research contents and objectives are briefed, and some latest achievements by the project team, including generation of linear frequency modulation wave （LFMW）, tunable optoelectronic oscillator （OEO） with lower phase noise, reconfigurable filter with higher Q value, time delay line with wider frequency range, down conversion with gain, and local oscillator （LO） transmission with stable phase, are introduced briefly.
