Based on the superiority of adaptive filtering algorithms designed with hyperbolic function-like objective functions,this paper proposes generalized spline adaptive filtering(SAF)algorithms designed with hyperbolic fu...Based on the superiority of adaptive filtering algorithms designed with hyperbolic function-like objective functions,this paper proposes generalized spline adaptive filtering(SAF)algorithms designed with hyperbolic function-like objective functions.Specifically,a series of generalized new SAF algorithms are proposed by introducing the q-deformed hyperbolic function as the cost function,named SAF-qDHSI,SAF-qDHCO,SAFqDHTA&SAF-qDHSE algorithms,respectively.Then,the proposed algorithm is theoretically demonstrated with detailed mean convergence and computational complexity analysis;secondly,the effect of different q values on the performance of the new algorithm is verified through data simulation;the new algorithm still has better performance under the interference of Gaussian noise and non-Gaussian noise even when facing the system mutation;finally,the new algorithm is verified through the measured engineering data,and the results show that the new algorithm has better convergence and robustness compared with the existing algorithm.In conclusion,the generalized algorithm based on the new cost function proposed in this paper is more effective in nonlinear system identification.展开更多
Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f i...Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f is subordinated by q_(λ).We establish inclusion and radii results for the class S^(*)(q_(λ))for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S^(*)(q_(λ)).We also find a sharp bound for the third Hankel determinant for the caseλ=1/2.展开更多
Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference...Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.展开更多
By using the extended hyperbolic function method, we have studied a quintic discrete nonlinear Schrodinger equation and obtained new exact localized solutions, including the discrete bright soliton solution, dark soli...By using the extended hyperbolic function method, we have studied a quintic discrete nonlinear Schrodinger equation and obtained new exact localized solutions, including the discrete bright soliton solution, dark soliton solution, bright and dark soliton solution, alternating phase bright soliton solution, alternating phase dark soliton solution, and alternating phase bright and dark soliton solution, if a special relation is bound on the coefficients of the equation.展开更多
Rotating Space Slender Flexible Structures(RSSFS)are extensively utilized in space operations because of their light weight,mobility,and low energy consumption.To realize the accurate space operation of the RSSFS,it i...Rotating Space Slender Flexible Structures(RSSFS)are extensively utilized in space operations because of their light weight,mobility,and low energy consumption.To realize the accurate space operation of the RSSFS,it is necessary to establish a precise mechanical model and develop a control algorithm with high precision.However,with the application of traditional control strategies,the RSSFS often suffers from the chattering phenomenon,which will aggravate structure vibration.In this paper,novel deformation description is put forward to balance modeling accuracy and computational efficiency of the RSSFS,which is better appropriate for real-time control.Besides,the Neural Network Sliding Mode Control(NNSMC)strategy modified by the hyperbolic tangent(tanh)function is put forward to compensate for modeling errors and reduce the chattering phenomenon,thereby improving the trajectory tracking accuracy of the RSSFS.Firstly,a mathematical model for the RSSFS is developed according to the novel deformation description and the vibration theory of flexible structure.Comparison of the deformation accuracy between different models proves that the novel modeling method proposed has high modeling accuracy.Next,the universal approximation property of the Radial Basis Function(RBF)neural network is put forward to determine and compensate for modeling errors,which consist of higher-order modes and the uncertainties of external disturbances.In addition,the tanh function is proposed as the reaching law in the conventional NNSMC strategy to suppress driving torque oscillation.The control law of modified NNSMC strategy and the adaptive law of weight coefficients are developed according to the Lyapunov theorem to guarantee the RSSFS stability.Finally,the simulation and physical experimental tests of the RSSFS with different control strategies are conducted.Experimental results show that the control law according to the novel deformation description and the modified NNSMC strategy can obtain accurate tracking of the rotation and reduce the vibration of the RSSFS simultaneously.展开更多
With the aid of Maple, the extended hyperbolic function rational expansion method is used to construct explicit and exact travelling solutions for the discrete mKdV lattice. As a result, many solutions are obained whi...With the aid of Maple, the extended hyperbolic function rational expansion method is used to construct explicit and exact travelling solutions for the discrete mKdV lattice. As a result, many solutions are obained which include kink-shaped solitary wave solutions, bell-shaped solitary wave solutions and singular solitary wave solutions.展开更多
In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tan- gent activation function. Firstly, an equat...In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tan- gent activation function. Firstly, an equation of partitions of unity for the hyperbolic tangent function is given. Then, two kinds of quasi-interpolation type neural network operators are con- structed to approximate univariate and bivariate functions, respectively. Also, the errors of the approximation are estimated by means of the modulus of continuity of function. Moreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated.展开更多
Addition formulas exist in trigonometric functions.Double-angle and half-angle formulas can be derived from these formulas.Moreover,the relation equation between the trigonometric function and the hyperbolic function ...Addition formulas exist in trigonometric functions.Double-angle and half-angle formulas can be derived from these formulas.Moreover,the relation equation between the trigonometric function and the hyperbolic function can be derived using an imaginary number.The inverse hyperbolic function arsinher(r)■ro 1/√1+t^(2)dt p1tt2 dt is similar to the inverse trigonometric function arcsiner(r)■ro 1/√1+t^(2)dt p1t2 dt,such as the second degree of a polynomial and the constant term 1,except for the sign−and+.Such an analogy holds not only when the degree of the polynomial is 2,but also for higher degrees.As such,a function exists with respect to the leaf function through the imaginary number i,such that the hyperbolic function exists with respect to the trigonometric function through this imaginary number.In this study,we refer to this function as the hyperbolic leaf function.By making such a definition,the relation equation between the leaf function and the hyperbolic leaf function makes it possible to easily derive various formulas,such as addition formulas of hyperbolic leaf functions based on the addition formulas of leaf functions.Using the addition formulas,we can also derive the double-angle and half-angle formulas.We then verify the consistency of these formulas by constructing graphs and numerical data.展开更多
In this paper, a new spline adaptive filter using a convex combination of exponential hyperbolic sinusoidal is presented. the algorithm convexly combines an exponential hyperbolic sinusoidal Hammerstein spline adaptiv...In this paper, a new spline adaptive filter using a convex combination of exponential hyperbolic sinusoidal is presented. the algorithm convexly combines an exponential hyperbolic sinusoidal Hammerstein spline adaptive filter and a Wiener-type spline adaptive filter to maintain the robustness in non-Gaussian noise environments when dealing with both the Hammerstein nonlinear system and the Wiener nonlinear system. The convergence analyses and simulation experiments are carried out on the proposed algorithm. The experimental results show the superiority of the proposed algorithm to other algorithms.展开更多
A hyperbolic Lindstedt-Poincare method is presented to determine the homoclinic solutions of a kind of nonlinear oscillators, in which critical value of the homoclinic bifurcation parameter can be determined. The gene...A hyperbolic Lindstedt-Poincare method is presented to determine the homoclinic solutions of a kind of nonlinear oscillators, in which critical value of the homoclinic bifurcation parameter can be determined. The generalized Lienard oscillator is studied in detail, and the present method＇s predictions are compared with those of Runge-Kutta method to illustrate its accuracy.展开更多
In this paper, by using symbolic and algebra computation, Chen and Wang＇s multiple R/ccati equations rational expansion method was further extended. Many double soliton-like and other novel combined forms of exact so...In this paper, by using symbolic and algebra computation, Chen and Wang＇s multiple R/ccati equations rational expansion method was further extended. Many double soliton-like and other novel combined forms of exact solutions of the （2＋1）-dimensional Breaking soliton equation are derived by using the extended multiple Riccatl equations expansion method.展开更多
Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagati...Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.展开更多
An approximate solution of the Dirac equation for a spin-1/2 particle under the influence of q-deformed hyperbolic P ¨oschl–Teller potential combined with trigonometric Scarf II non-central potential is studied ...An approximate solution of the Dirac equation for a spin-1/2 particle under the influence of q-deformed hyperbolic P ¨oschl–Teller potential combined with trigonometric Scarf II non-central potential is studied analytically. It is assumed that the scalar potential equals the vector potential in order to obtain analytical solutions. Both radial and angular parts of the Dirac equation are solved using the Nikiforov–Uvarov method. A relativistic energy spectrum and the relation between quantum numbers can be obtained using this method. Several quantum wave functions corresponding to several states are also presented in terms of the Jacobi Polynomials.展开更多
In a recent article [Commun. Theor. Phys. （Beijing, China） 47 （2007） 270], Cao et al. gave some nontrivial solutions of a Riccati equation by using symbolic and algebra computation. They took these solutions, whic...In a recent article [Commun. Theor. Phys. （Beijing, China） 47 （2007） 270], Cao et al. gave some nontrivial solutions of a Riccati equation by using symbolic and algebra computation. They took these solutions, which are in the form of q-deformed hyperbolic and triangular functions as new solutions. In this comment, we will show that these solutions are just the special cases of some known solutions of the Riccati equation and thus they are not new solutions.展开更多
A hyperbolic function is introduced to reflect the attenuation effect of one firm＇s default to its partner. If two firms are competitors （copartners）, the default intensity of one firm will decrease （increase） ab...A hyperbolic function is introduced to reflect the attenuation effect of one firm＇s default to its partner. If two firms are competitors （copartners）, the default intensity of one firm will decrease （increase） abruptly when the other firm defaults. As time goes on, the impact will decrease gradually until extinct. In this model, the joint distribution and marginal distributions of default times are derived by employing the change of measure, and the fair swap premium of a credit default swap （CDS） can be valued.展开更多
In the realm of nonlinear physics, it is crucial to establish precise traveling wave solutions and solitary wave solutions for a variety of nonlinear models, as this aids our exploration of these fields. In this paper...In the realm of nonlinear physics, it is crucial to establish precise traveling wave solutions and solitary wave solutions for a variety of nonlinear models, as this aids our exploration of these fields. In this paper, we propose a new method to construct precise solitary wave solutions if nonlinear equation with complex structure. As an application, we employ this method to solve the Burgers-Fisher equation, yielding a multitude of new solitary wave solutions. This approach demonstrates a broader applicability in addressing nonlinear evolution equations (NLEEs).展开更多
The objective of this study was to achieve a better control effect of the controller on the liquid level of the liquefied natural gas(LNG)carrier and to achieve the goal of energy saving and carbon reduction.This pape...The objective of this study was to achieve a better control effect of the controller on the liquid level of the liquefied natural gas(LNG)carrier and to achieve the goal of energy saving and carbon reduction.This paper took the loaded square tank of an S175 highspeed container ship as the research plant,combined with the closed-loop gain-shaping algorithm(CGSA)and nonlinear modification technology to further optimize the controller.We initially employed a third-order CGSA approach in formulating the foundation of our linear controller.Subsequently,we introduced a non-linear modification to this controller by harnessing the power of the hyperbolic tangent function,and the control effect is verified by the MATLAB simulation experiment.Based on the outcomes of MATLAB simulations,by integrating the third-order CGSA technique and introducing non-linear modification through the hyperbolic tangent function,we observed a significant enhancement in the controller’s performance.Specifically,it outperformed the traditional PID controller by a substantial margin,demonstrating a remarkable 19%boost in control efficacy.Additionally,it provides better energy savings than the non-linear controller.The controller designed in this paper has a better control effect on the liquid tank-level control of LNG ships,the control process is more energy-saving and the purpose of carbon reduction is realized.展开更多
This paper presents a new and efficient approach for constructing exact solutions to nonlinear differential-difference equations （NLDDEs） and lattice equation. By using this method via symbolic computation system MA...This paper presents a new and efficient approach for constructing exact solutions to nonlinear differential-difference equations （NLDDEs） and lattice equation. By using this method via symbolic computation system MAPLE, we obtained abundant soliton-like and/or period-form solutions to the （2＋1）-dimensional Toda equation. It seems that solitary wave solutions are merely special cases in one family. Furthermore, the method can also be applied to other nonlinear differential-difference equations.展开更多
To date no analytical solution of the pile ultimate lateral capacity for the general c–φ soil has been obtained. In the present study, a new dimensionless embedded ratio was proposed and the analytical solutions of ...To date no analytical solution of the pile ultimate lateral capacity for the general c–φ soil has been obtained. In the present study, a new dimensionless embedded ratio was proposed and the analytical solutions of ultimate lateral capacity and rotation center of rigid pile in c–φ soils were obtained. The results showed that both the dimensionless ultimate lateral capacity and dimensionless rotation center were the univariate functions of the embedded ratio. Also,the ultimate lateral capacity in the c–φ soil was the combination of the ultimate lateral capacity（f;） in the clay, and the ultimate lateral capacity（f;） in the sand. Therefore, the Broms chart for clay, solution for clay（φ=0） put forward by Poulos and Davis, solution for sand（c=0） obtained by Petrasovits and Awad, and Kondner’s ultimate bending moment were all proven to be the special cases of the general solution in the present study. A comparison of the field and laboratory tests in 93 cases showed that the average ratios of the theoretical values to the experimental value ranged from 0.85 to 1.15. Also, the theoretical values displayed a good agreement with the test values.展开更多
基金financially supported by the National Natural Science Foundation of China (8225041038)the Sichuan Science and Technology Program (23NSFSC2916)the Fundamental Research Funds for the Central Universities, Southwest Minzu University (ZYN2024077)
文摘Based on the superiority of adaptive filtering algorithms designed with hyperbolic function-like objective functions,this paper proposes generalized spline adaptive filtering(SAF)algorithms designed with hyperbolic function-like objective functions.Specifically,a series of generalized new SAF algorithms are proposed by introducing the q-deformed hyperbolic function as the cost function,named SAF-qDHSI,SAF-qDHCO,SAFqDHTA&SAF-qDHSE algorithms,respectively.Then,the proposed algorithm is theoretically demonstrated with detailed mean convergence and computational complexity analysis;secondly,the effect of different q values on the performance of the new algorithm is verified through data simulation;the new algorithm still has better performance under the interference of Gaussian noise and non-Gaussian noise even when facing the system mutation;finally,the new algorithm is verified through the measured engineering data,and the results show that the new algorithm has better convergence and robustness compared with the existing algorithm.In conclusion,the generalized algorithm based on the new cost function proposed in this paper is more effective in nonlinear system identification.
基金supported by the Grant No.20-16367/NRPU/RD/HEC/20212021。
文摘Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f is subordinated by q_(λ).We establish inclusion and radii results for the class S^(*)(q_(λ))for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S^(*)(q_(λ)).We also find a sharp bound for the third Hankel determinant for the caseλ=1/2.
基金Project supported by the National Natural Science Foundation of China （Grant No 10461006）, the Natural Science Foundation （Grant No 200408020103）, the High Education Science Research Program （Grant No NJ02035） of Inner Mongolia, China and the Youth Foundation （Grant No QN004024） of Inner Mongolia Normal University, China.
文摘Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.
基金The project supported by National Natural Science Foundation of China, the Natural Science Foundation of Shandong Province of China, and the Natural Scienoe Foundation of Liaocheng University
文摘By using the extended hyperbolic function method, we have studied a quintic discrete nonlinear Schrodinger equation and obtained new exact localized solutions, including the discrete bright soliton solution, dark soliton solution, bright and dark soliton solution, alternating phase bright soliton solution, alternating phase dark soliton solution, and alternating phase bright and dark soliton solution, if a special relation is bound on the coefficients of the equation.
基金Supported by the Applied Basic Research Program of Liaoning Province,China(No.2023JH2/101300159)the National Natural Science Foundation of China(No.52275090).
文摘Rotating Space Slender Flexible Structures(RSSFS)are extensively utilized in space operations because of their light weight,mobility,and low energy consumption.To realize the accurate space operation of the RSSFS,it is necessary to establish a precise mechanical model and develop a control algorithm with high precision.However,with the application of traditional control strategies,the RSSFS often suffers from the chattering phenomenon,which will aggravate structure vibration.In this paper,novel deformation description is put forward to balance modeling accuracy and computational efficiency of the RSSFS,which is better appropriate for real-time control.Besides,the Neural Network Sliding Mode Control(NNSMC)strategy modified by the hyperbolic tangent(tanh)function is put forward to compensate for modeling errors and reduce the chattering phenomenon,thereby improving the trajectory tracking accuracy of the RSSFS.Firstly,a mathematical model for the RSSFS is developed according to the novel deformation description and the vibration theory of flexible structure.Comparison of the deformation accuracy between different models proves that the novel modeling method proposed has high modeling accuracy.Next,the universal approximation property of the Radial Basis Function(RBF)neural network is put forward to determine and compensate for modeling errors,which consist of higher-order modes and the uncertainties of external disturbances.In addition,the tanh function is proposed as the reaching law in the conventional NNSMC strategy to suppress driving torque oscillation.The control law of modified NNSMC strategy and the adaptive law of weight coefficients are developed according to the Lyapunov theorem to guarantee the RSSFS stability.Finally,the simulation and physical experimental tests of the RSSFS with different control strategies are conducted.Experimental results show that the control law according to the novel deformation description and the modified NNSMC strategy can obtain accurate tracking of the rotation and reduce the vibration of the RSSFS simultaneously.
基金the National Natural Science Foundation of China (No.10771118)
文摘With the aid of Maple, the extended hyperbolic function rational expansion method is used to construct explicit and exact travelling solutions for the discrete mKdV lattice. As a result, many solutions are obained which include kink-shaped solitary wave solutions, bell-shaped solitary wave solutions and singular solitary wave solutions.
基金Supported by the National Natural Science Foundation of China(61179041,61272023,and 11401388)
文摘In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tan- gent activation function. Firstly, an equation of partitions of unity for the hyperbolic tangent function is given. Then, two kinds of quasi-interpolation type neural network operators are con- structed to approximate univariate and bivariate functions, respectively. Also, the errors of the approximation are estimated by means of the modulus of continuity of function. Moreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated.
文摘Addition formulas exist in trigonometric functions.Double-angle and half-angle formulas can be derived from these formulas.Moreover,the relation equation between the trigonometric function and the hyperbolic function can be derived using an imaginary number.The inverse hyperbolic function arsinher(r)■ro 1/√1+t^(2)dt p1tt2 dt is similar to the inverse trigonometric function arcsiner(r)■ro 1/√1+t^(2)dt p1t2 dt,such as the second degree of a polynomial and the constant term 1,except for the sign−and+.Such an analogy holds not only when the degree of the polynomial is 2,but also for higher degrees.As such,a function exists with respect to the leaf function through the imaginary number i,such that the hyperbolic function exists with respect to the trigonometric function through this imaginary number.In this study,we refer to this function as the hyperbolic leaf function.By making such a definition,the relation equation between the leaf function and the hyperbolic leaf function makes it possible to easily derive various formulas,such as addition formulas of hyperbolic leaf functions based on the addition formulas of leaf functions.Using the addition formulas,we can also derive the double-angle and half-angle formulas.We then verify the consistency of these formulas by constructing graphs and numerical data.
基金supported by the National Natural Science Foundation of China (Grant No. 62371242, Grant No. 61871230)。
文摘In this paper, a new spline adaptive filter using a convex combination of exponential hyperbolic sinusoidal is presented. the algorithm convexly combines an exponential hyperbolic sinusoidal Hammerstein spline adaptive filter and a Wiener-type spline adaptive filter to maintain the robustness in non-Gaussian noise environments when dealing with both the Hammerstein nonlinear system and the Wiener nonlinear system. The convergence analyses and simulation experiments are carried out on the proposed algorithm. The experimental results show the superiority of the proposed algorithm to other algorithms.
基金supported by the National Natural Science Foundation of China (10672193)Sun Yat-sen University (Fu Lan Scholarship)the University of Hong Kong (CRGC grant).
文摘A hyperbolic Lindstedt-Poincare method is presented to determine the homoclinic solutions of a kind of nonlinear oscillators, in which critical value of the homoclinic bifurcation parameter can be determined. The generalized Lienard oscillator is studied in detail, and the present method＇s predictions are compared with those of Runge-Kutta method to illustrate its accuracy.
基金The project partially supported by National Natural Science Foundation of China under Grant No. 10471143 and the State 973 Project under Grant No. 2004CB318001 The authors are very grateful to Prof. Hong-Bo Li, Yong Chen, Zhen-Ya Yan, and Zhuo-Sheng Lii for their kind help and valuable suggestions. They also thank Prof. En-Gui Fan and Prof. Chun-Ping Liu for their constructive suggestions about the solutions of Riccati equation.
文摘In this paper, by using symbolic and algebra computation, Chen and Wang＇s multiple R/ccati equations rational expansion method was further extended. Many double soliton-like and other novel combined forms of exact solutions of the （2＋1）-dimensional Breaking soliton equation are derived by using the extended multiple Riccatl equations expansion method.
文摘Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.
文摘An approximate solution of the Dirac equation for a spin-1/2 particle under the influence of q-deformed hyperbolic P ¨oschl–Teller potential combined with trigonometric Scarf II non-central potential is studied analytically. It is assumed that the scalar potential equals the vector potential in order to obtain analytical solutions. Both radial and angular parts of the Dirac equation are solved using the Nikiforov–Uvarov method. A relativistic energy spectrum and the relation between quantum numbers can be obtained using this method. Several quantum wave functions corresponding to several states are also presented in terms of the Jacobi Polynomials.
基金supported by National Natural Science Foundation of China under Grant No.10671172the Natural Science Foundation of Jiangsu Province under Grant No.BK2006064
文摘In a recent article [Commun. Theor. Phys. （Beijing, China） 47 （2007） 270], Cao et al. gave some nontrivial solutions of a Riccati equation by using symbolic and algebra computation. They took these solutions, which are in the form of q-deformed hyperbolic and triangular functions as new solutions. In this comment, we will show that these solutions are just the special cases of some known solutions of the Riccati equation and thus they are not new solutions.
基金the National Basic Research Program of China(973 Program)(No.2007CB814903)the National Natural Science Foundation of China(No.70671069)
文摘A hyperbolic function is introduced to reflect the attenuation effect of one firm＇s default to its partner. If two firms are competitors （copartners）, the default intensity of one firm will decrease （increase） abruptly when the other firm defaults. As time goes on, the impact will decrease gradually until extinct. In this model, the joint distribution and marginal distributions of default times are derived by employing the change of measure, and the fair swap premium of a credit default swap （CDS） can be valued.
文摘In the realm of nonlinear physics, it is crucial to establish precise traveling wave solutions and solitary wave solutions for a variety of nonlinear models, as this aids our exploration of these fields. In this paper, we propose a new method to construct precise solitary wave solutions if nonlinear equation with complex structure. As an application, we employ this method to solve the Burgers-Fisher equation, yielding a multitude of new solitary wave solutions. This approach demonstrates a broader applicability in addressing nonlinear evolution equations (NLEEs).
基金supported by the National Science Foundation of China(Grant No.51679024)Dalian Innovation Team Support Plan in the Key Research Field(Grant No.2020RT08)+1 种基金Doctoral Research Initial Fund Project of Liaoning Province(Grant No.2021-BS-078)Dalian Maritime University University-level Team"Open Ranking"Project(Grant No.3132023502).
文摘The objective of this study was to achieve a better control effect of the controller on the liquid level of the liquefied natural gas(LNG)carrier and to achieve the goal of energy saving and carbon reduction.This paper took the loaded square tank of an S175 highspeed container ship as the research plant,combined with the closed-loop gain-shaping algorithm(CGSA)and nonlinear modification technology to further optimize the controller.We initially employed a third-order CGSA approach in formulating the foundation of our linear controller.Subsequently,we introduced a non-linear modification to this controller by harnessing the power of the hyperbolic tangent function,and the control effect is verified by the MATLAB simulation experiment.Based on the outcomes of MATLAB simulations,by integrating the third-order CGSA technique and introducing non-linear modification through the hyperbolic tangent function,we observed a significant enhancement in the controller’s performance.Specifically,it outperformed the traditional PID controller by a substantial margin,demonstrating a remarkable 19%boost in control efficacy.Additionally,it provides better energy savings than the non-linear controller.The controller designed in this paper has a better control effect on the liquid tank-level control of LNG ships,the control process is more energy-saving and the purpose of carbon reduction is realized.
基金supported by the National Natural Science Foundation of Chinathe Natural Science Foundation of Shandong Province in China (Grant No Y2007G64)
文摘This paper presents a new and efficient approach for constructing exact solutions to nonlinear differential-difference equations （NLDDEs） and lattice equation. By using this method via symbolic computation system MAPLE, we obtained abundant soliton-like and/or period-form solutions to the （2＋1）-dimensional Toda equation. It seems that solitary wave solutions are merely special cases in one family. Furthermore, the method can also be applied to other nonlinear differential-difference equations.
基金financially supported by the National Natural Science Foundation of China(Grant No.51379132)
文摘To date no analytical solution of the pile ultimate lateral capacity for the general c–φ soil has been obtained. In the present study, a new dimensionless embedded ratio was proposed and the analytical solutions of ultimate lateral capacity and rotation center of rigid pile in c–φ soils were obtained. The results showed that both the dimensionless ultimate lateral capacity and dimensionless rotation center were the univariate functions of the embedded ratio. Also,the ultimate lateral capacity in the c–φ soil was the combination of the ultimate lateral capacity（f;） in the clay, and the ultimate lateral capacity（f;） in the sand. Therefore, the Broms chart for clay, solution for clay（φ=0） put forward by Poulos and Davis, solution for sand（c=0） obtained by Petrasovits and Awad, and Kondner’s ultimate bending moment were all proven to be the special cases of the general solution in the present study. A comparison of the field and laboratory tests in 93 cases showed that the average ratios of the theoretical values to the experimental value ranged from 0.85 to 1.15. Also, the theoretical values displayed a good agreement with the test values.
