Electrical measurement was employed to investigate the early hydration characteristics of cement pastes with different dosages of superplasticizer in the same W/C ratio. The hyperbolic method was applied to analyze th...Electrical measurement was employed to investigate the early hydration characteristics of cement pastes with different dosages of superplasticizer in the same W/C ratio. The hyperbolic method was applied to analyze the electrical resistivity development. The peak point （Ph） on the hyperbolic curve could be easily read. The time （th） to reach the point Ph had strong relations with the setting time. th was delayed with the increment of the dosage of superplasticizer. The time th was used to plot the relationship between the initial setting time and final setting time. The hyperbolic equation was established to predict the ultimate resistivity. The retardation effect of the superplasticizer was confirmed in the same W/C ratio by setting time and isothermal heat evolution.展开更多
This paper presents the application of a new method for obtaining new exact solutions of some well-known nonlinear partial differential equations.The Rational Hyperbolic method is used for handling the Zhiber-Shabat e...This paper presents the application of a new method for obtaining new exact solutions of some well-known nonlinear partial differential equations.The Rational Hyperbolic method is used for handling the Zhiber-Shabat equation and the related equations such as Liouville,Sinh-Gordon,Dodd-Bullough-Mikhailov and Tzitzeica-Dodd-Bullough equations.We show power of the Rational Hyperbolic method that is simple and effective for solving nonlinear partial differential equations.展开更多
A convergence theorem for the method of artificial viscosity applied to the nonstrictly hyperbolic system u(t)+1/2(3u2+v2)x=0, v(t)+(uv)x=0 is established. Convergence of a subsequence in the strong topology is proved...A convergence theorem for the method of artificial viscosity applied to the nonstrictly hyperbolic system u(t)+1/2(3u2+v2)x=0, v(t)+(uv)x=0 is established. Convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves.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
A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators, in which the perturbation proce- dure is improved for those systems whose exact homoclin...A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators, in which the perturbation proce- dure is improved for those systems whose exact homoclinic generating solutions cannot be explicitly derived. The generalized hyperbolic functions are employed as the basis functions in the present procedure to extend the validity of the hyperbolic perturbation method. Several strongly nonlinear oscillators with quadratic, cubic, and quartic nonlinearity are studied in detail to illustrate the efficiency and accuracy of the present method.展开更多
A bilogarithmic hyperbolic cosine method for the evaluation of overlapping formation constants at varying (or fixed) ionic strength is devised in this paper and applied to data reported in the analytical literature, i...A bilogarithmic hyperbolic cosine method for the evaluation of overlapping formation constants at varying (or fixed) ionic strength is devised in this paper and applied to data reported in the analytical literature, i.e. succinic acid system, Cu(II)-glycine system and Ag(I)-aminobutan-1-ol system. The method is based on the linearization of the formation function ? = f(pH) or ? = f(pL) data. A theoretical slope of unity should be obtained thus proving the correctness of the assumed equilibria. An additional advantage of the bilogarithmic method proposed is that it provides a closed scale representation of Y and X unlike other plots. This paper forms part of an investigation into the uses of bilogarithmic methods and hyperbolic functions in parameter estimation. Methods based on the application of spectrophotometric measurements have been the subject of recent studies.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
The evolution of solitons in Bose-Einstein condensates （BECs） with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we success...The evolution of solitons in Bose-Einstein condensates （BECs） with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we successfully obtain the bright and dark soliton solutions. In addition, some new soliton solutions in this model are found. The results in this paper include some in the literature （Phys. Rev. Lett. 94（2005）050402 and Chin. Phys. Lett. 22（2005） 1855）.展开更多
Effects of oblique collisions of the dust acoustic(DA)waves in dusty plasma are studied by considering unmagnetized fully ionized plasma.The plasma consists of inertial warm negatively charged massive dusts,positively...Effects of oblique collisions of the dust acoustic(DA)waves in dusty plasma are studied by considering unmagnetized fully ionized plasma.The plasma consists of inertial warm negatively charged massive dusts,positively charged dusts,superthermal kappa distributed electrons,and isothermal ions.The extended Poincaré–Lighthill–Kuo(e PLK)method is employed for the drivation of two-sided Korteweg–de Vries(KdV)equations(KdVEs).The Kd V soliton solutions are derived by using the hyperbolic secant method.The effects of superthermality index of electrons,temperature ratio of isothermal ion to electron,and the density ratio of isothermal ions to negatively charged massive dusts on nonlinear coefficients are investigated.The effects of oblique collision on amplitude,phase shift,and potential profile of right traveling solitons of DA waves are also studied.The study reveals that the new nonlinear wave structures are produced in the colliding region due to head-on collision of the two counter propagating DA waves.The nonlinearity is found to decrease with the increasing density ratio of ion to negative dust in the critical region.The phase shifts decrease(increase)with increasing the temperature ratio of ion to electron(κe).The hump(compressive,κe<κec)and dipshaped(rarefactive,κe>κec)solitons are produced depending on the angle(θ)of oblique collision between the two waves.展开更多
The so-called extended hyperbolic complex （EHC） function method is used to study further the stationary axisymmetric Einstein Maxwell theory with p Abelian gauge fields （EM-p theory, for short）, Two EHC structural...The so-called extended hyperbolic complex （EHC） function method is used to study further the stationary axisymmetric Einstein Maxwell theory with p Abelian gauge fields （EM-p theory, for short）, Two EHC structural Riemann- Hilbert （RH） transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-p theory. This symmetry group is verified to have the structure of semidirect product of Kac-Moody group SU（p ＋ 1, 1） and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author＇s paper by a different scheme, This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.展开更多
Combining difference method and boundary integral equation method,we propose a new numerical method for solving initial-boundary value problem of second order hyperbolic partial differential equations defined on a bou...Combining difference method and boundary integral equation method,we propose a new numerical method for solving initial-boundary value problem of second order hyperbolic partial differential equations defined on a bounded or unbounded domain in R~3 and obtain the error estimates of the approximate solution in energy norm and local maximum norm.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
The hyperbolic function method for nonlinear wave equations ispresented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. ...The hyperbolic function method for nonlinear wave equations ispresented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. The method is based on the fact that the solitary wave solutions are essentially of a localized nature. Writing the solitary wave solutions of a nonlinear wave equation as the polynomials of hyperbolic functions, the nonlinear wave equation can be changed into a nonlinear system of algebraic equations. The system can be solved via Wu Elimination or Grbner base method. The exact solitary wave solutions of the nonlinear wave equation are obtained including many new exact solitary wave solutions.展开更多
基金the National Natural Science Foundation of China(No.50778078)
文摘Electrical measurement was employed to investigate the early hydration characteristics of cement pastes with different dosages of superplasticizer in the same W/C ratio. The hyperbolic method was applied to analyze the electrical resistivity development. The peak point （Ph） on the hyperbolic curve could be easily read. The time （th） to reach the point Ph had strong relations with the setting time. th was delayed with the increment of the dosage of superplasticizer. The time th was used to plot the relationship between the initial setting time and final setting time. The hyperbolic equation was established to predict the ultimate resistivity. The retardation effect of the superplasticizer was confirmed in the same W/C ratio by setting time and isothermal heat evolution.
文摘This paper presents the application of a new method for obtaining new exact solutions of some well-known nonlinear partial differential equations.The Rational Hyperbolic method is used for handling the Zhiber-Shabat equation and the related equations such as Liouville,Sinh-Gordon,Dodd-Bullough-Mikhailov and Tzitzeica-Dodd-Bullough equations.We show power of the Rational Hyperbolic method that is simple and effective for solving nonlinear partial differential equations.
文摘A convergence theorem for the method of artificial viscosity applied to the nonstrictly hyperbolic system u(t)+1/2(3u2+v2)x=0, v(t)+(uv)x=0 is established. Convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves.
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Project supported by the National Natural Science Foundation of China (Nos. 10972240 and 11102045)the Natural Science Foundation of Guangdong Province of China (No. S20110400040)+2 种基金the Foundation of Guangdong Education Department of China (No. LYM10108)the Foundation of Guangzhou Education Bureau of China (No. 10A024)the Research Grant Council of Hong Kong of China (No. GRF-HKU-7173-09E)
文摘A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators, in which the perturbation proce- dure is improved for those systems whose exact homoclinic generating solutions cannot be explicitly derived. The generalized hyperbolic functions are employed as the basis functions in the present procedure to extend the validity of the hyperbolic perturbation method. Several strongly nonlinear oscillators with quadratic, cubic, and quartic nonlinearity are studied in detail to illustrate the efficiency and accuracy of the present method.
文摘A bilogarithmic hyperbolic cosine method for the evaluation of overlapping formation constants at varying (or fixed) ionic strength is devised in this paper and applied to data reported in the analytical literature, i.e. succinic acid system, Cu(II)-glycine system and Ag(I)-aminobutan-1-ol system. The method is based on the linearization of the formation function ? = f(pH) or ? = f(pL) data. A theoretical slope of unity should be obtained thus proving the correctness of the assumed equilibria. An additional advantage of the bilogarithmic method proposed is that it provides a closed scale representation of Y and X unlike other plots. This paper forms part of an investigation into the uses of bilogarithmic methods and hyperbolic functions in parameter estimation. Methods based on the application of spectrophotometric measurements have been the subject of recent studies.
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.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 1057508 and 10302018）, the Natural Science Foundation of Zhejiang Province, China （Grant No Y605056）.
文摘The evolution of solitons in Bose-Einstein condensates （BECs） with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the extended hyperbolic function method, we successfully obtain the bright and dark soliton solutions. In addition, some new soliton solutions in this model are found. The results in this paper include some in the literature （Phys. Rev. Lett. 94（2005）050402 and Chin. Phys. Lett. 22（2005） 1855）.
文摘Effects of oblique collisions of the dust acoustic(DA)waves in dusty plasma are studied by considering unmagnetized fully ionized plasma.The plasma consists of inertial warm negatively charged massive dusts,positively charged dusts,superthermal kappa distributed electrons,and isothermal ions.The extended Poincaré–Lighthill–Kuo(e PLK)method is employed for the drivation of two-sided Korteweg–de Vries(KdV)equations(KdVEs).The Kd V soliton solutions are derived by using the hyperbolic secant method.The effects of superthermality index of electrons,temperature ratio of isothermal ion to electron,and the density ratio of isothermal ions to negatively charged massive dusts on nonlinear coefficients are investigated.The effects of oblique collision on amplitude,phase shift,and potential profile of right traveling solitons of DA waves are also studied.The study reveals that the new nonlinear wave structures are produced in the colliding region due to head-on collision of the two counter propagating DA waves.The nonlinearity is found to decrease with the increasing density ratio of ion to negative dust in the critical region.The phase shifts decrease(increase)with increasing the temperature ratio of ion to electron(κe).The hump(compressive,κe<κec)and dipshaped(rarefactive,κe>κec)solitons are produced depending on the angle(θ)of oblique collision between the two waves.
基金Project supported by the Science Foundation from Education Department of Liaoning Province, China （Grant No 202142036） and the National Natural Science Foundation of China （Grant No 10475036）.
文摘The so-called extended hyperbolic complex （EHC） function method is used to study further the stationary axisymmetric Einstein Maxwell theory with p Abelian gauge fields （EM-p theory, for short）, Two EHC structural Riemann- Hilbert （RH） transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-p theory. This symmetry group is verified to have the structure of semidirect product of Kac-Moody group SU（p ＋ 1, 1） and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author＇s paper by a different scheme, This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.
基金China State Major Key Project for Basic Researches
文摘Combining difference method and boundary integral equation method,we propose a new numerical method for solving initial-boundary value problem of second order hyperbolic partial differential equations defined on a bounded or unbounded domain in R~3 and obtain the error estimates of the approximate solution in energy norm and local maximum norm.
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This work was supported by the National 973 Project (Grant No. G1998030600) Post-doctoral Foundation .
文摘The hyperbolic function method for nonlinear wave equations ispresented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. The method is based on the fact that the solitary wave solutions are essentially of a localized nature. Writing the solitary wave solutions of a nonlinear wave equation as the polynomials of hyperbolic functions, the nonlinear wave equation can be changed into a nonlinear system of algebraic equations. The system can be solved via Wu Elimination or Grbner base method. The exact solitary wave solutions of the nonlinear wave equation are obtained including many new exact solitary wave solutions.
