This paper is concerned with the connection between the Volterra series and the regular perturbation method in nonlinear systems analyses. It is revealed for the first time that, for a forced polynomial nonlinear syst...This paper is concerned with the connection between the Volterra series and the regular perturbation method in nonlinear systems analyses. It is revealed for the first time that, for a forced polynomial nonlinear system, if its derived linear system is a damped dissipative system, the steady response obtained through the regular perturbation method is exactly identical to the response given by the Volterra series. On the other hand, if the derived linear system is an undamped conservative system, then the Volterra series is incapable of modeling the forced polynomial nonlinear system. Numerical examples are further presented to illustrate these points. The results provide a new criterion for quickly judging whether the Volterra series is applicable for modeling a given polynomial nonlinear system.展开更多
We construct analytical self-similar solutions for the generalized (3+1)-dimensional nonlinear Schrdinger equation with polynomial nonlinearity of arbitrary order. As an example, we list self-similar solutions of quin...We construct analytical self-similar solutions for the generalized (3+1)-dimensional nonlinear Schrdinger equation with polynomial nonlinearity of arbitrary order. As an example, we list self-similar solutions of quintic nonlinear Schrdinger equation with distributed dispersion and distributed linear gain, including bright similariton solution, fractional and combined Jacobian elliptic function solutions. Moreover, we discuss self-similar evolutional dynamic behaviors of these solutions in the dispersion decreasing fiber and the periodic distributed amplification system.展开更多
Comprehensive studies on CO_(2)breakthrough times and flooding effects are crucial for optimizing CO_(2)flooding strategies.This study utilized numerical simulations to investigate the effects of hydraulic fractures,p...Comprehensive studies on CO_(2)breakthrough times and flooding effects are crucial for optimizing CO_(2)flooding strategies.This study utilized numerical simulations to investigate the effects of hydraulic fractures,permeability,and CO_(2)injection rates on CO_(2)breakthrough times and cumulative oil production.Nonlinear relationships among the respective variables were established,with Sobol method analysis delineating the dominant control factors.The key findings indicate that although hydraulic fracturing shortens CO_(2)breakthrough time,it concurrently enhances cumulative oil production.The orientation of hydraulic fractures emerged as a pivotal factor influencing flooding effectiveness.Furthermore,lower permeability corresponds to lower initial oil production,while higher permeability corresponds to higher initial daily oil production.When reservoir permeability is 1 mD,oil production declines at 1000 days,and at 2 mD,it declines at 700 days.At a surface CO_(2)injection rate of 10,000 m^(3)/d,the daily oil production of a single well is approximately 7.5 m^(3),and this value remains relatively stable over time.The hierarchical order of influence on CO_(2)breakthrough and rapid rise times,from highest to lowest,is permeability,well spacing,CO_(2)injection rate,porosity,and hydraulic fracture conductivity.Similarly,the order of influence on cumulative oil production,from highest to lowest,is well spacing,porosity,permeability,CO_(2)injection rate,and hydraulic fracture conductivity.This paper analyzed the impact of geological and engineering parameters on CO_(2)flooding and oil production and provided insights to optimize CO_(2)injection strategies for enhanced oil recovery.展开更多
The semilinear wave equation with logarithmic and polynomial nonlinearities is considered in this paper.By adjusting and using potential well method,we attain the global-in-time existence and infinite time blowup solu...The semilinear wave equation with logarithmic and polynomial nonlinearities is considered in this paper.By adjusting and using potential well method,we attain the global-in-time existence and infinite time blowup solutions at subcritical initial energy level E(0)0.展开更多
The application of optimization methods to prediction issues is a continually exploring field.In line with this,this paper investigates the connectedness between the infected cases of COVID-19 and US fear index from a...The application of optimization methods to prediction issues is a continually exploring field.In line with this,this paper investigates the connectedness between the infected cases of COVID-19 and US fear index from a forecasting perspective.The complex characteristics of implied volatility risk index such as non-linearity structure,time-varying and nonstationarity motivate us to apply a nonlinear polynomial Hammerstein model with known structure and unknown parameters.We use the Hybrid Particle Swarm Optimization(HPSO)tool to identify the model parameters of nonlinear polynomial Hammerstein model.Findings indicate that,following a nonlinear polynomial behaviour cascaded to an autoregressive with exogenous input(ARX)behaviour,the fear index in US financial market is significantly affected by COVID-19-infected cases in the US,COVID-19-infected cases in the world and COVID-19-infected cases in China,respectively.Statistical performance indicators provided by the developed models show that COVID-19-infected cases in the US are particularly powerful in predicting the Cboe volatility index compared to COVID-19-infected cases in the world and China(MAPE(2.1013%);R2(91.78%)and RMSE(0.6363 percentage points)).The proposed approaches have also shown good convergence characteristics and accurate fits of the data.展开更多
This paper gives a full classification of Dembowski-Ostrom polynomials derived from the compositions of reversed Dickson polynomials and monomials over finite fields of characteristic 2.The authors also classify almos...This paper gives a full classification of Dembowski-Ostrom polynomials derived from the compositions of reversed Dickson polynomials and monomials over finite fields of characteristic 2.The authors also classify almost perfect nonlinear functions among all such Dembowski-Ostrom polynomials based on a general result describing when the composition of an arbitrary linearized polynomial and a monomial of the form x^(2+2^α) is almost perfect nonlinear.It turns out that almost perfect nonlinear functions derived from reversed Dickson polynomials are all extended affine equivalent to the well-known Gold functions.展开更多
基金supported by the National Science Fund for Distinguished Young Scholars(11125209)the National Natural Science Foundation of China(51121063 and 10702039)
文摘This paper is concerned with the connection between the Volterra series and the regular perturbation method in nonlinear systems analyses. It is revealed for the first time that, for a forced polynomial nonlinear system, if its derived linear system is a damped dissipative system, the steady response obtained through the regular perturbation method is exactly identical to the response given by the Volterra series. On the other hand, if the derived linear system is an undamped conservative system, then the Volterra series is incapable of modeling the forced polynomial nonlinear system. Numerical examples are further presented to illustrate these points. The results provide a new criterion for quickly judging whether the Volterra series is applicable for modeling a given polynomial nonlinear system.
基金Supported by the Applied Nonlinear Science and Technology from the Most Important Among all the Top Priority Disciplines of Zhejiang Province
文摘We construct analytical self-similar solutions for the generalized (3+1)-dimensional nonlinear Schrdinger equation with polynomial nonlinearity of arbitrary order. As an example, we list self-similar solutions of quintic nonlinear Schrdinger equation with distributed dispersion and distributed linear gain, including bright similariton solution, fractional and combined Jacobian elliptic function solutions. Moreover, we discuss self-similar evolutional dynamic behaviors of these solutions in the dispersion decreasing fiber and the periodic distributed amplification system.
基金supported by the China Postdoctoral Science Foundation(No.2024M752803)the National Natural Science Foundation of China(No.52179112)+1 种基金the Open Fund of National Key Laboratory of Oil and Gas Reservoir Geology and Exploitation,Southwest Petroleum University,China(No.PLN2023-02)the Open Fund of Key Laboratory of Deep Geothermal Resources,Ministry of Natural Resources of the People's Republic of China(No.KLDGR2024B01).
文摘Comprehensive studies on CO_(2)breakthrough times and flooding effects are crucial for optimizing CO_(2)flooding strategies.This study utilized numerical simulations to investigate the effects of hydraulic fractures,permeability,and CO_(2)injection rates on CO_(2)breakthrough times and cumulative oil production.Nonlinear relationships among the respective variables were established,with Sobol method analysis delineating the dominant control factors.The key findings indicate that although hydraulic fracturing shortens CO_(2)breakthrough time,it concurrently enhances cumulative oil production.The orientation of hydraulic fractures emerged as a pivotal factor influencing flooding effectiveness.Furthermore,lower permeability corresponds to lower initial oil production,while higher permeability corresponds to higher initial daily oil production.When reservoir permeability is 1 mD,oil production declines at 1000 days,and at 2 mD,it declines at 700 days.At a surface CO_(2)injection rate of 10,000 m^(3)/d,the daily oil production of a single well is approximately 7.5 m^(3),and this value remains relatively stable over time.The hierarchical order of influence on CO_(2)breakthrough and rapid rise times,from highest to lowest,is permeability,well spacing,CO_(2)injection rate,porosity,and hydraulic fracture conductivity.Similarly,the order of influence on cumulative oil production,from highest to lowest,is well spacing,porosity,permeability,CO_(2)injection rate,and hydraulic fracture conductivity.This paper analyzed the impact of geological and engineering parameters on CO_(2)flooding and oil production and provided insights to optimize CO_(2)injection strategies for enhanced oil recovery.
文摘The semilinear wave equation with logarithmic and polynomial nonlinearities is considered in this paper.By adjusting and using potential well method,we attain the global-in-time existence and infinite time blowup solutions at subcritical initial energy level E(0)0.
基金This research has been funded by Scientific Research Deanship at University of Ha’il,Saudi Arabia through Project number RG-20210.
文摘The application of optimization methods to prediction issues is a continually exploring field.In line with this,this paper investigates the connectedness between the infected cases of COVID-19 and US fear index from a forecasting perspective.The complex characteristics of implied volatility risk index such as non-linearity structure,time-varying and nonstationarity motivate us to apply a nonlinear polynomial Hammerstein model with known structure and unknown parameters.We use the Hybrid Particle Swarm Optimization(HPSO)tool to identify the model parameters of nonlinear polynomial Hammerstein model.Findings indicate that,following a nonlinear polynomial behaviour cascaded to an autoregressive with exogenous input(ARX)behaviour,the fear index in US financial market is significantly affected by COVID-19-infected cases in the US,COVID-19-infected cases in the world and COVID-19-infected cases in China,respectively.Statistical performance indicators provided by the developed models show that COVID-19-infected cases in the US are particularly powerful in predicting the Cboe volatility index compared to COVID-19-infected cases in the world and China(MAPE(2.1013%);R2(91.78%)and RMSE(0.6363 percentage points)).The proposed approaches have also shown good convergence characteristics and accurate fits of the data.
基金supported by the National Basic Research Program of China under Grant No.2011CB302400
文摘This paper gives a full classification of Dembowski-Ostrom polynomials derived from the compositions of reversed Dickson polynomials and monomials over finite fields of characteristic 2.The authors also classify almost perfect nonlinear functions among all such Dembowski-Ostrom polynomials based on a general result describing when the composition of an arbitrary linearized polynomial and a monomial of the form x^(2+2^α) is almost perfect nonlinear.It turns out that almost perfect nonlinear functions derived from reversed Dickson polynomials are all extended affine equivalent to the well-known Gold functions.
