All-optical analog-to-digital conversion (ADC) has been extensively researched to break through the inherently limited operating speed of electronic devices. In this paper, we use the photonic crystal fiber (PCF) for ...All-optical analog-to-digital conversion (ADC) has been extensively researched to break through the inherently limited operating speed of electronic devices. In this paper, we use the photonic crystal fiber (PCF) for time-stretch (TS) analog-to-digital (A/D) conversion system through generating low noise, linear chirp distribution and flat super-continuum (SC). Based on the radio frequency (RF) analog signal modulated to the linearly chirped super-continuum, the large-dispersion photonic crystal fiber is used for time-domain stretching.展开更多
This paper considers the pointwise estimate of the solutions to Cauchy problem for quasilin-ear hyperbolic systems, which bases on the existence of the solutions by using the fundamental solutions. It gives a sharp po...This paper considers the pointwise estimate of the solutions to Cauchy problem for quasilin-ear hyperbolic systems, which bases on the existence of the solutions by using the fundamental solutions. It gives a sharp pointwise estimates of the solutions on domam under consideration. Specially, the estimate is precise near each characteristic direction.展开更多
This paper concerns a system of nonlinear wave equations describing the vibra- tions of a 3-dimensional network of elastic strings. The authors derive the equations and appropriate nodal conditions, determine equilibr...This paper concerns a system of nonlinear wave equations describing the vibra- tions of a 3-dimensional network of elastic strings. The authors derive the equations and appropriate nodal conditions, determine equilibrium solutions, and, by using the methods of quasilinear hyperbolic systems, prove that for tree networks the natural initial, boundary value problem has classical solutions existing in neighborhoods of the ＂stretched＂ equilibrium solutions. Then the local controllability of such networks near such equilib- rium configurations in a certain specified time interval is proved. Finally, it is proved that, given two different equilibrium states satisfying certain conditions, it is possible to control the network from states in a small enough neighborhood of one equilibrium to any state in a suitable neighborhood of the second equilibrium over a sufficiently large time interval.展开更多
Modeling genetic regulatory networks is an important research topic in genomic research and computationM systems biology. This paper considers the problem of constructing a genetic regula- tory network （GRN） using t...Modeling genetic regulatory networks is an important research topic in genomic research and computationM systems biology. This paper considers the problem of constructing a genetic regula- tory network （GRN） using the discrete dynamic system （DDS） model approach. Although considerable research has been devoted to building GRNs, many of the works did not consider the time-delay effect. Here, the authors propose a time-delay DDS model composed of linear difference equations to represent temporal interactions among significantly expressed genes. The authors also introduce interpolation scheme and re-sampling method for equalizing the non-uniformity of sampling time points. Statistical significance plays an active role in obtaining the optimal interaction matrix of GRNs. The constructed genetic network using linear multiple regression matches with the original data very well. Simulation results are given to demonstrate the effectiveness of the proposed method and model.展开更多
For first-order quasilinear hyperbolic systems with zero eigenvaiues, the author establishes the local exact controllability in a shorter time-period by means of internal controls acting on suitable domains. In partic...For first-order quasilinear hyperbolic systems with zero eigenvaiues, the author establishes the local exact controllability in a shorter time-period by means of internal controls acting on suitable domains. In particular, under certain special but reasonable hypotheses, the local exact controllability can be realized only by internal controls, and the control time can be arbitrarily small.展开更多
基金supported by the Doctoral Program of Higher Education Research Fund (No.1101.01.001.672)
文摘All-optical analog-to-digital conversion (ADC) has been extensively researched to break through the inherently limited operating speed of electronic devices. In this paper, we use the photonic crystal fiber (PCF) for time-stretch (TS) analog-to-digital (A/D) conversion system through generating low noise, linear chirp distribution and flat super-continuum (SC). Based on the radio frequency (RF) analog signal modulated to the linearly chirped super-continuum, the large-dispersion photonic crystal fiber is used for time-domain stretching.
基金the National Natural Science Foundation of China(No.10131050).
文摘This paper considers the pointwise estimate of the solutions to Cauchy problem for quasilin-ear hyperbolic systems, which bases on the existence of the solutions by using the fundamental solutions. It gives a sharp pointwise estimates of the solutions on domam under consideration. Specially, the estimate is precise near each characteristic direction.
基金supported by the DFG SPP1253:Optimization with PDE-Constaintsthe DFG-CE315 Cluster of Excellence:Engineering of Advanced Materials
文摘This paper concerns a system of nonlinear wave equations describing the vibra- tions of a 3-dimensional network of elastic strings. The authors derive the equations and appropriate nodal conditions, determine equilibrium solutions, and, by using the methods of quasilinear hyperbolic systems, prove that for tree networks the natural initial, boundary value problem has classical solutions existing in neighborhoods of the ＂stretched＂ equilibrium solutions. Then the local controllability of such networks near such equilib- rium configurations in a certain specified time interval is proved. Finally, it is proved that, given two different equilibrium states satisfying certain conditions, it is possible to control the network from states in a small enough neighborhood of one equilibrium to any state in a suitable neighborhood of the second equilibrium over a sufficiently large time interval.
基金supported in part by HKRGC GrantHKU Strategic Theme Grant on Computational SciencesNational Natural Science Foundation of China under Grant Nos.10971075 and 11271144
文摘Modeling genetic regulatory networks is an important research topic in genomic research and computationM systems biology. This paper considers the problem of constructing a genetic regula- tory network （GRN） using the discrete dynamic system （DDS） model approach. Although considerable research has been devoted to building GRNs, many of the works did not consider the time-delay effect. Here, the authors propose a time-delay DDS model composed of linear difference equations to represent temporal interactions among significantly expressed genes. The authors also introduce interpolation scheme and re-sampling method for equalizing the non-uniformity of sampling time points. Statistical significance plays an active role in obtaining the optimal interaction matrix of GRNs. The constructed genetic network using linear multiple regression matches with the original data very well. Simulation results are given to demonstrate the effectiveness of the proposed method and model.
文摘For first-order quasilinear hyperbolic systems with zero eigenvaiues, the author establishes the local exact controllability in a shorter time-period by means of internal controls acting on suitable domains. In particular, under certain special but reasonable hypotheses, the local exact controllability can be realized only by internal controls, and the control time can be arbitrarily small.
