The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then...The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.展开更多
A kind of stable adaptive fuzzy control of nonlinear system is implemented using variable universe method. First of all, the basic structure of variable universe adaptive fuzzy controllers is briefly introduced. Then ...A kind of stable adaptive fuzzy control of nonlinear system is implemented using variable universe method. First of all, the basic structure of variable universe adaptive fuzzy controllers is briefly introduced. Then the contraction-expansion factor that is a key tool of variable universe method is defined by means of integral regulation idea, and a kind of adaptive fuzzy controllers is designed by using such a contraction-expansion factor. The simulation on first order nonlinear system is done. Secondly, it is proved that the variable universe adaptive fuzzy control is asymptotically stable by use of Lyapunov theory. The simulation on the second order nonlinear system shows that its simulation effect is also quite good. Finally a useful tool, called symbolic factor, is proposed, which may be of universal significance. It can greatly reduce the settling time and enhance the robustness of the system.展开更多
Making use of a new generalized ans?tze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equati...Making use of a new generalized ans?tze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain other new and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profile solitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions.展开更多
In this paper,we present a multiple knowledge representation(MKR)framework and discuss its potential for developing big data artificial intelligence(AI)techniques with possible broader impacts across different AI area...In this paper,we present a multiple knowledge representation(MKR)framework and discuss its potential for developing big data artificial intelligence(AI)techniques with possible broader impacts across different AI areas.Typically,canonical knowledge representations and modern representations each emphasize a particular aspect of trans-forming inputs into symbolic encoding or vectors.For example,knowledge graphs focus on depicting semantic connections among concepts,whereas deep neural networks(DNNs)are more of a tool to perceive raw signal inputs.展开更多
Knowledge of the mechanical properties of structural materials is essential for their practical applications. In the present work,three-hundred and sixty data samples on four mechanical properties of steels—fatigue s...Knowledge of the mechanical properties of structural materials is essential for their practical applications. In the present work,three-hundred and sixty data samples on four mechanical properties of steels—fatigue strength, tensile strength, fracture strength and hardness—were selected from the Japan National Institute of Material Science database, comprising data on carbon steels and low-alloy steels. Five machine learning algorithms were used to predict the mechanical properties of the materials represented by the three-hundred and sixty data samples, and random forest regression showed the best predictive performance.Feature selection conducted by random forest and symbolic regressions revealed the four most important features that most influence the mechanical properties of steels: the tempering temperature of steel, and the alloying elements of carbon, chromium and molybdenum. Mathematical expressions were generated via symbolic regression, and the expressions explicitly predicted how each of the four mechanical properties varied quantitatively with the four most important features. This study demonstrates the great potential of symbolic regression in the discovery of novel advanced materials.展开更多
Abundant exact interaction solutions, including lump-soliton, lump-kink, and lump-periodic solutions, are computed for the Hirota-Satsuma-Ito equation in (2+1)-dimensions, through conducting symbolic computations with...Abundant exact interaction solutions, including lump-soliton, lump-kink, and lump-periodic solutions, are computed for the Hirota-Satsuma-Ito equation in (2+1)-dimensions, through conducting symbolic computations with Maple. The basic starting point is a Hirota bilinear form of the Hirota-Satsuma-Ito equation. A few three-dimensional plots and contour plots of three special presented solutions are made to shed light on the characteristic of interaction solutions.展开更多
A （2 ＋ 1）-dimensional generalized Bogoyavlensky-Konopelchenko equation that possesses a Hirota bilinear form is considered. Starting with its Hirota bilinear form, a class of explicit lump solutions is computed thr...A （2 ＋ 1）-dimensional generalized Bogoyavlensky-Konopelchenko equation that possesses a Hirota bilinear form is considered. Starting with its Hirota bilinear form, a class of explicit lump solutions is computed through conducting symbolic computations with Maple, and a few plots of a specific presented lump solution are made to shed light on the characteristics of lumps. The result provides a new example of （2 ＋ 1）-dimensional nonlinear partial differential equations which possess lump solutions.展开更多
文摘The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 69974006 and 60174013).
文摘A kind of stable adaptive fuzzy control of nonlinear system is implemented using variable universe method. First of all, the basic structure of variable universe adaptive fuzzy controllers is briefly introduced. Then the contraction-expansion factor that is a key tool of variable universe method is defined by means of integral regulation idea, and a kind of adaptive fuzzy controllers is designed by using such a contraction-expansion factor. The simulation on first order nonlinear system is done. Secondly, it is proved that the variable universe adaptive fuzzy control is asymptotically stable by use of Lyapunov theory. The simulation on the second order nonlinear system shows that its simulation effect is also quite good. Finally a useful tool, called symbolic factor, is proposed, which may be of universal significance. It can greatly reduce the settling time and enhance the robustness of the system.
文摘Making use of a new generalized ans?tze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain other new and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profile solitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions.
基金Project supported by the National Key R&D Program of China(No.2020AAA0108800)。
文摘In this paper,we present a multiple knowledge representation(MKR)framework and discuss its potential for developing big data artificial intelligence(AI)techniques with possible broader impacts across different AI areas.Typically,canonical knowledge representations and modern representations each emphasize a particular aspect of trans-forming inputs into symbolic encoding or vectors.For example,knowledge graphs focus on depicting semantic connections among concepts,whereas deep neural networks(DNNs)are more of a tool to perceive raw signal inputs.
基金supported by the National Key Research and Development Program of China (Grant No. 2018YFB0704404)the Hong Kong Polytechnic University (Internal Grant Nos. 1-ZE8R and G-YBDH)the 111Project of the State Administration of Foreign Experts Affairs and the Ministry of Education,China (Grant No. D16002)。
文摘Knowledge of the mechanical properties of structural materials is essential for their practical applications. In the present work,three-hundred and sixty data samples on four mechanical properties of steels—fatigue strength, tensile strength, fracture strength and hardness—were selected from the Japan National Institute of Material Science database, comprising data on carbon steels and low-alloy steels. Five machine learning algorithms were used to predict the mechanical properties of the materials represented by the three-hundred and sixty data samples, and random forest regression showed the best predictive performance.Feature selection conducted by random forest and symbolic regressions revealed the four most important features that most influence the mechanical properties of steels: the tempering temperature of steel, and the alloying elements of carbon, chromium and molybdenum. Mathematical expressions were generated via symbolic regression, and the expressions explicitly predicted how each of the four mechanical properties varied quantitatively with the four most important features. This study demonstrates the great potential of symbolic regression in the discovery of novel advanced materials.
文摘Abundant exact interaction solutions, including lump-soliton, lump-kink, and lump-periodic solutions, are computed for the Hirota-Satsuma-Ito equation in (2+1)-dimensions, through conducting symbolic computations with Maple. The basic starting point is a Hirota bilinear form of the Hirota-Satsuma-Ito equation. A few three-dimensional plots and contour plots of three special presented solutions are made to shed light on the characteristic of interaction solutions.
基金Acknowledgements The work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11301454, 11301331, 11371086, 11571079, 51771083）, the NSF under the grant DMS-1664561, the Jiangsu Qing Lan Project for Excellent Young Teachers in University （2014）, the Six Talent Peaks Project in Jiangsu Province （2016-JY-081）, the Natural Science Foundation for Colleges and Universities in Jiangsu Province （17KJB110020）, the Natural Science Foundation of Jiangsu Province （Grant No. BK20151160）, the Emphasis Foundation of Special Science Research on Subject Frontiers of CUMT under Grant No. 2017XKZDll, and the Distinguished Professorships by Shanghai University of Electric Power and Shanghai Polytechnic University.
文摘A （2 ＋ 1）-dimensional generalized Bogoyavlensky-Konopelchenko equation that possesses a Hirota bilinear form is considered. Starting with its Hirota bilinear form, a class of explicit lump solutions is computed through conducting symbolic computations with Maple, and a few plots of a specific presented lump solution are made to shed light on the characteristics of lumps. The result provides a new example of （2 ＋ 1）-dimensional nonlinear partial differential equations which possess lump solutions.
