A nonlinear transformation of the Whitham-Broer-Kaup (WBK) model equations in the shallow water small-amplitude regime is derived by using a simplified homogeneous balance method. The WBK model equations are linearize...A nonlinear transformation of the Whitham-Broer-Kaup (WBK) model equations in the shallow water small-amplitude regime is derived by using a simplified homogeneous balance method. The WBK model equations are linearized under the nonlinear transformation. Various exact solutions of the WBK model equations are obtained via the nonlinear transformation with the aid of solutions for the linear equation.展开更多
Wave transmission and overtopping around nearshore breakwaters can have significant influence on the transmitted wave parameters,which affects wave conditions and sediment transportation and becomes the focus of desig...Wave transmission and overtopping around nearshore breakwaters can have significant influence on the transmitted wave parameters,which affects wave conditions and sediment transportation and becomes the focus of design in engineering.The objective of this paper is to present a simplified model to estimate these important wave parameters.This paper describes the incorporation of wave transmission and overtopping module into a wave model for multi-directional random wave transformation based on energy balance equation with the consideration of wave shoaling,refraction,diffraction,reflection and breaking.Wen's frequency spectrum and non-linear dispersion relation are also included in this model.The influence of wave parameters of transmitted waves through a smooth submerged breakwater has been considered in this model with an improved description of the transmitted wave spectrum of van der Meer et al.(2000) by Carevic et al.(2013).This improved wave model has been validated through available laboratory experiments.Then the verified model is applied to investigate the effect of wave transmission and overtopping on wave heights behind low-crested breakwaters in a project for nearshore area.Numerical calculations are carried out with and without consideration of the wave transmission and overtopping,and comparison of them indicates that there is a considerable difference in wave height and thus it is important to include wave transmission and overtopping in modelling nearshore wave field with the presence of low-crested breakwaters.Therefore,this model can provide a general estimate of the desired wave field parameters,which is adequate for engineers at the preliminary design stage of low-crested breakwaters.展开更多
Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and...Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan's, Xie's and Yan's results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.展开更多
Due to low parameter sensitivity for balanced realiza- tions, balanced structure becomes a good candidate for an statespace adaptive infinite impluse response （IIR） filter. Here, using coefficients of the transfer f...Due to low parameter sensitivity for balanced realiza- tions, balanced structure becomes a good candidate for an statespace adaptive infinite impluse response （IIR） filter. Here, using coefficients of the transfer function as the adaptive filtering parameters, a balanced adaptive IIR filtering algorithm is proposed for output-error minimization. The algorithm in the internally balanced realization guarantees that the adaptive IIR filter always minimizes the ratio of maximum-to-minimum eigenvalue of the Grammian matrices at the each iteration. Simulation results are provided to corroborate the proposed algorithm.展开更多
Using available data and necessary estimations, this paper provides a tentative picture of the balance sheet of China＇s sovereign account between 2000 and 2010. The main findings indicate that the net worth of China...Using available data and necessary estimations, this paper provides a tentative picture of the balance sheet of China＇s sovereign account between 2000 and 2010. The main findings indicate that the net worth of China＇s sovereign assets had been positive and increasing during the period under review. This implies that the Chinese government has sufficient sovereign assets to cover its sovereign liabilities, therefore the likelihood of a sovereign debt crisis in China is extremely low in the near term. Moreover, although China＇s leverage ratio （total liabilities/GDP） is far lower compared to advanced economies, it seems higher than that of other major emerging economies such as Brazil, Russia, and India （BRIC）. In fact, the leverage ratio has been increasing rapidly over recent years and requires special attention. In particular, according to sector-specific analysis, high corporate liability ratios （percentage to GDP） constitute a major concern of China＇s national balance sheet. In 2010, this liability ratio exceeded l OO percent, which exceeds the 90 percent level observed in OECD countries. Lastly, this paper concludes that a sustainable economic growth and structural transformation of growth model are the fundamental means to taming China＇s balance sheet risks.展开更多
In conventional polarization sensitive optical coherence tomography(PS-OCT),phase retar-dation is obtained by the amplitude of P and S polarization only,and the fast axis angle is obtained by the phase difference in P...In conventional polarization sensitive optical coherence tomography(PS-OCT),phase retar-dation is obtained by the amplitude of P and S polarization only,and the fast axis angle is obtained by the phase difference in P and S polarizations via Hilbert transformation.In this paper,we proposed a modifed PS OCT setup in which the phase retardation and fast axis angle are simply expressed as the function of the amplitude ofP and S polarization and their differential signal.Due to the common-path feature between the two channels ofP and S polarization,the fuctuation in the measurement of phase retardation and fast axis angle caused by excess noise and phase noise from the laser source can be reduced by the differential signal of P and S polarization via a modified balance detector.Thus,the signal of phase retardation and fast angle axis in the deep layer of a porcine sample can be improved.展开更多
Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers e...Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers equation with variable coefficients by white noise W（t）=Bt, where Bt is a Brown motion. The auto-Baecklund transformation and stochastic soliton solutions of the Wick-type stochastic Burgers equation are shown by the homogeneous balance and Hermite transform. The generalization of the Wick-type stochastic Burgers equation is also studied.展开更多
文摘A nonlinear transformation of the Whitham-Broer-Kaup (WBK) model equations in the shallow water small-amplitude regime is derived by using a simplified homogeneous balance method. The WBK model equations are linearized under the nonlinear transformation. Various exact solutions of the WBK model equations are obtained via the nonlinear transformation with the aid of solutions for the linear equation.
基金supported by the NSFC-Shandong Joint Fund Project(No.U1706226)Research Award Fund for Outstanding Young and Middle-aged Scientists of Shandong Province(No.ZR2016EEB06)the Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents
文摘Wave transmission and overtopping around nearshore breakwaters can have significant influence on the transmitted wave parameters,which affects wave conditions and sediment transportation and becomes the focus of design in engineering.The objective of this paper is to present a simplified model to estimate these important wave parameters.This paper describes the incorporation of wave transmission and overtopping module into a wave model for multi-directional random wave transformation based on energy balance equation with the consideration of wave shoaling,refraction,diffraction,reflection and breaking.Wen's frequency spectrum and non-linear dispersion relation are also included in this model.The influence of wave parameters of transmitted waves through a smooth submerged breakwater has been considered in this model with an improved description of the transmitted wave spectrum of van der Meer et al.(2000) by Carevic et al.(2013).This improved wave model has been validated through available laboratory experiments.Then the verified model is applied to investigate the effect of wave transmission and overtopping on wave heights behind low-crested breakwaters in a project for nearshore area.Numerical calculations are carried out with and without consideration of the wave transmission and overtopping,and comparison of them indicates that there is a considerable difference in wave height and thus it is important to include wave transmission and overtopping in modelling nearshore wave field with the presence of low-crested breakwaters.Therefore,this model can provide a general estimate of the desired wave field parameters,which is adequate for engineers at the preliminary design stage of low-crested breakwaters.
基金Supported by the National Nature Science Foundation of China(10371070)Supported by the Nature Science Foundation of Educational Committee of Liaoning Province(2021401157)
文摘Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan's, Xie's and Yan's results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.
基金supported by the National Natural Science Foundation of China(61201321)the Basic Research Foundation of Northwestern Polytechnical University(JC20100217)
文摘Due to low parameter sensitivity for balanced realiza- tions, balanced structure becomes a good candidate for an statespace adaptive infinite impluse response （IIR） filter. Here, using coefficients of the transfer function as the adaptive filtering parameters, a balanced adaptive IIR filtering algorithm is proposed for output-error minimization. The algorithm in the internally balanced realization guarantees that the adaptive IIR filter always minimizes the ratio of maximum-to-minimum eigenvalue of the Grammian matrices at the each iteration. Simulation results are provided to corroborate the proposed algorithm.
文摘Using available data and necessary estimations, this paper provides a tentative picture of the balance sheet of China＇s sovereign account between 2000 and 2010. The main findings indicate that the net worth of China＇s sovereign assets had been positive and increasing during the period under review. This implies that the Chinese government has sufficient sovereign assets to cover its sovereign liabilities, therefore the likelihood of a sovereign debt crisis in China is extremely low in the near term. Moreover, although China＇s leverage ratio （total liabilities/GDP） is far lower compared to advanced economies, it seems higher than that of other major emerging economies such as Brazil, Russia, and India （BRIC）. In fact, the leverage ratio has been increasing rapidly over recent years and requires special attention. In particular, according to sector-specific analysis, high corporate liability ratios （percentage to GDP） constitute a major concern of China＇s national balance sheet. In 2010, this liability ratio exceeded l OO percent, which exceeds the 90 percent level observed in OECD countries. Lastly, this paper concludes that a sustainable economic growth and structural transformation of growth model are the fundamental means to taming China＇s balance sheet risks.
基金supported by National Science Council of Taiwan through Grant#NSC95-2221-E-010-015-MY3.
文摘In conventional polarization sensitive optical coherence tomography(PS-OCT),phase retar-dation is obtained by the amplitude of P and S polarization only,and the fast axis angle is obtained by the phase difference in P and S polarizations via Hilbert transformation.In this paper,we proposed a modifed PS OCT setup in which the phase retardation and fast axis angle are simply expressed as the function of the amplitude ofP and S polarization and their differential signal.Due to the common-path feature between the two channels ofP and S polarization,the fuctuation in the measurement of phase retardation and fast axis angle caused by excess noise and phase noise from the laser source can be reduced by the differential signal of P and S polarization via a modified balance detector.Thus,the signal of phase retardation and fast angle axis in the deep layer of a porcine sample can be improved.
文摘Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers equation with variable coefficients by white noise W（t）=Bt, where Bt is a Brown motion. The auto-Baecklund transformation and stochastic soliton solutions of the Wick-type stochastic Burgers equation are shown by the homogeneous balance and Hermite transform. The generalization of the Wick-type stochastic Burgers equation is also studied.
