A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic w...A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.展开更多
In this paper, the entangled mapping approach (EMA) is applied to obtain variable separation solutions of (1+1)-dimensional and (3+1)-dimensional systems. By analysis, we firstly find that there also exists a ...In this paper, the entangled mapping approach (EMA) is applied to obtain variable separation solutions of (1+1)-dimensional and (3+1)-dimensional systems. By analysis, we firstly find that there also exists a common formula to describe suitable physical fields or potentials for these (1+1)-dimensional models such as coupled integrable dispersionless (CID) and shallow water wave equations. Moreover, we find that the variable separation solution of the (3+1)-dimensional Burgers system satisfies the completely same form as the universal quantity U1 in (2+1)-dimensional systems. The only difference is that the function q is a solution of a constraint equation and p is an arbitrary function of three independent variables.展开更多
Extended mapping approach is introduced to solve (2+1)-dimensional Nizhnik-Novikov Veselov equation. A new type of variable separation solutions is derived with arbitrary functions in the model. Based on this excit...Extended mapping approach is introduced to solve (2+1)-dimensional Nizhnik-Novikov Veselov equation. A new type of variable separation solutions is derived with arbitrary functions in the model. Based on this excitation, rich localized structures such as multi-lump soliton and ring soliton are revealed by selecting the arbitrary function appropriately.展开更多
A theory of (1+1)-dimensional gravity is constructed on the basis of the teleparallel equivalent of general relativity. The fundamental field variables are the tetrad fields ei^μ and the gravity is attributed to t...A theory of (1+1)-dimensional gravity is constructed on the basis of the teleparallel equivalent of general relativity. The fundamental field variables are the tetrad fields ei^μ and the gravity is attributed to the torsion. A dilatonic spherically symmetric exact solution of the gravitational field equations characterized by two parameters M and Q is derived. The energy associated with this solution is calculated using the two-dimensional gravitational energy- momentum formula.展开更多
The purpose of this study was to assess the susceptibility of landslides around the area of Guizhou province based on fuzzy theory.In first instance, slope, elevation, lithology, proximity to tectonic lines, proximity...The purpose of this study was to assess the susceptibility of landslides around the area of Guizhou province based on fuzzy theory.In first instance, slope, elevation, lithology, proximity to tectonic lines, proximity to drainage and annual precipitation were taken as independent, causal factors in this study.A landslide hazard evaluation factor system was established by classifying these factors into more subclasses according to some rules.Secondly, a trapezoidal fuzzy number weighting(TFNW) approach was used to assess the importance of six causal factors to landslides in an ArcGIS environment.Thirdly, a landslide susceptibility map was created based on a weighted linear combination model.According to this susceptibility map, the study area was classified into four categories of landslide susceptibility:low, moderate, high and very high.Finally, in order to verify the results obtained, the susceptibility map and the landslide inventory map were combined in the GIS.In addition, the weighting procedure showed that TFNW is an efficient method for weighting causal landslide factors.展开更多
With the help of an improved mapping approach and a linear-variable-separation approach, a new family of exact solutions with arbitrary functions of the (2+1)-dimensional Nizhnik-Novikov-Veselov system (NNV) is d...With the help of an improved mapping approach and a linear-variable-separation approach, a new family of exact solutions with arbitrary functions of the (2+1)-dimensional Nizhnik-Novikov-Veselov system (NNV) is derived. Based on the derived solutions and using some multi-valued functions, we find a few new folded solitary wave excitations for the (2+1)-dimensional NNV system.展开更多
In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are...In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions (m → 1). This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.展开更多
Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the ...Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the structures are damaged.Aiming at the lightweight structure,fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand.Firstly,the fatigue life is expressed by topology variables and the fatigue life filter function.The continuum fatigue optimization model is established with the independent continuous mapping(ICM)method.Secondly,fatigue life constraints are transformed to distortion energy constraints explicitly by taking advantage of the distortion energy theory.Thirdly,the optimization formulation is solved by the dual sequence quadratic programming(DSQP).And the design scheme of lightweight structure considering the fatigue characteristics is obtained.Finally,numerical examples illustrate the practicality and effectiveness of the fatigue optimization method.This method further expands the theoretical application of the ICM method and provides a novel approach for the fatigue optimization problem.展开更多
An ontology mapping approach based on set & relation theory and OCL is introduced,then an ontology mapping meta-model is established which is composed of ontology related elements,mapping related elements and defi...An ontology mapping approach based on set & relation theory and OCL is introduced,then an ontology mapping meta-model is established which is composed of ontology related elements,mapping related elements and definition rule related elements.This ontology mapping meta-model can be regarded as a unified mechanism to realize different kinds of ontology mappings.The powerful computation capability of set and relation theory and the flexible expressive capability of OCL can be used in the computation of ontology mapping meta-model to realize the unified mapping among different ontology models.Based on the mapping meta-model,a general mapping management framework is developed to provide a common mapping storage mechanism,some mapping APIs and mapping rule APIs.展开更多
With the help of a modified mapping method and a new mapping method, we re-study the (3+1)-dimensional Burgers equation, and derive two families of variable separation solutions. By selecting appropriate functions ...With the help of a modified mapping method and a new mapping method, we re-study the (3+1)-dimensional Burgers equation, and derive two families of variable separation solutions. By selecting appropriate functions in the variable separation solution, we discuss the interaction behaviors among taper-like, plateau-type rings, and rectangle-type embed-solitons in the periodic wave background. All the interaction behaviors are completely elastic, and no phase shift appears after interaction.展开更多
In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the co...In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the conformable fractional derivative. As a result, the singular soliton solutions, kink and anti-kink soliton solutions, periodic function soliton solutions, Jacobi elliptic function solutions and hyperbolic function solutions of (2 + 1)-dimensional time-fractional Zoomeron equation were obtained. Finally, the 3D and 2D graphs of some solutions were drawn by setting the suitable values of parameters with Maple, and analyze the dynamic behaviors of the solutions.展开更多
In this paper, a new method for mobile robot map building based on grey system theory is presented, by which interpretation and integration of sonar readings can be solved robustly and efficiently. The conception of &...In this paper, a new method for mobile robot map building based on grey system theory is presented, by which interpretation and integration of sonar readings can be solved robustly and efficiently. The conception of 'grey number is introduced to model and handle the uncertainty of sonar reading. A new data fusion approach based on grey system theory is proposed to construct environment model. Map building experiments are performed both on a platform of simulation and a real mobile robot. Experimental results show that our method is robust and accurate.展开更多
In this paper we define a fixed point index theory for locally Lip., completely continuous and weakly inward mappings defined on closed convex sets in general Banach spaces where no other artificial conditions are imp...In this paper we define a fixed point index theory for locally Lip., completely continuous and weakly inward mappings defined on closed convex sets in general Banach spaces where no other artificial conditions are imposed. This makes ns to deal with these kinds of mappings more easily. As obvious applications, some results in [3],[5],[7],[9],[10] are deepened and extended.展开更多
With the help of an extended mapping approach and a linear variable separation method,new families ofvariable separation solutions with arbitrary functions for the(3+1)-dimensional Burgers system are derived.Based ont...With the help of an extended mapping approach and a linear variable separation method,new families ofvariable separation solutions with arbitrary functions for the(3+1)-dimensional Burgers system are derived.Based onthe derived exact solutions, some novel and interesting localized coherent excitations such as embed-solitons are revealedby selecting appropriate boundary conditions and/or initial qualifications.The time evolutional properties of the novellocalized excitation are also briefly investigated.展开更多
Starting from the extended mapping approach and a linear variable separation method, we find new families of variable separation solutions with some arbitrary functions for the (3+1)-dimensionM Burgers system. Then...Starting from the extended mapping approach and a linear variable separation method, we find new families of variable separation solutions with some arbitrary functions for the (3+1)-dimensionM Burgers system. Then based on the derived exact solutions, some novel and interesting localized coherent excitations such as embedded-solitons, taper-like soliton, complex wave excitations in the periodic wave background are revealed by introducing appropriate boundary conditions and/or initial qualifications. The evolutional properties of the complex wave excitations are briefly investigated.展开更多
With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the (2+1)-dimensional dispersive long wave equations are constructed by means of a function transfor...With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the (2+1)-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions.展开更多
With an extended mapping approach and a linear variable separation method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions, and rational function solutions) ...With an extended mapping approach and a linear variable separation method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for (3+1)-dimensionai Burgers system is derived. Based on the derived excitations, we obtain some novel localized coherent structures and study the interactions between solitons.展开更多
The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the co...The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the concepts of the limits of multivalued (S) and (S) + type mappings. These kinds of mappings contain many monotone type mappings, such as maximal monotone mapping, bounded pseudo-monotone mapping and bounded generalized pseudo-monotone mapping, as its special cases. In the second part we define the pseudo-degree for (S) type mapping and the degree for (S)+ type mapping. These two kinds of degrees are all the generalizations of the degree defined by Browder[1,2] As applications, we utilize the degree theory presented in part 2 to study the existence of solutions for the multivalued operator equations (see part 3) and to obtain some new fixed point theorems in part 4.展开更多
We propose the generalization of Einstein’s special theory of relativity (STR). In our model, we use the (1 + 4)-dimensional space G, which is the extension of the (1 + 3)-dimensional Minkowski space M. As a fifth ad...We propose the generalization of Einstein’s special theory of relativity (STR). In our model, we use the (1 + 4)-dimensional space G, which is the extension of the (1 + 3)-dimensional Minkowski space M. As a fifth additional coordinate, the interval S is used. This value is constant under the usual Lorentz transformations in M, but it changes when the transformations in the extended space G are used. We call this model the Extended space model (ESM). From a physical point of view, our expansion means that processes in which the rest mass of the particles changes are acceptable now. In the ESM, gravity and electromagnetism are combined in one field. In the ESM, a photon can have a nonzero mass and this mass can be either positive or negative. It is also possible to establish in the frame of ESM connection between mass of a particle and its size.展开更多
文摘A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.
基金The authors express their sincere thanks to the anonymous referees for their constructive suggestions and kind help.
文摘In this paper, the entangled mapping approach (EMA) is applied to obtain variable separation solutions of (1+1)-dimensional and (3+1)-dimensional systems. By analysis, we firstly find that there also exists a common formula to describe suitable physical fields or potentials for these (1+1)-dimensional models such as coupled integrable dispersionless (CID) and shallow water wave equations. Moreover, we find that the variable separation solution of the (3+1)-dimensional Burgers system satisfies the completely same form as the universal quantity U1 in (2+1)-dimensional systems. The only difference is that the function q is a solution of a constraint equation and p is an arbitrary function of three independent variables.
基金The authors would like to thank Profs. Jie-Fang Zhang and Chun-Long Zheng for helpful discussions.
文摘Extended mapping approach is introduced to solve (2+1)-dimensional Nizhnik-Novikov Veselov equation. A new type of variable separation solutions is derived with arbitrary functions in the model. Based on this excitation, rich localized structures such as multi-lump soliton and ring soliton are revealed by selecting the arbitrary function appropriately.
文摘A theory of (1+1)-dimensional gravity is constructed on the basis of the teleparallel equivalent of general relativity. The fundamental field variables are the tetrad fields ei^μ and the gravity is attributed to the torsion. A dilatonic spherically symmetric exact solution of the gravitational field equations characterized by two parameters M and Q is derived. The energy associated with this solution is calculated using the two-dimensional gravitational energy- momentum formula.
基金Project 200331880201 supported by the West Project of the Ministry of Communication of China
文摘The purpose of this study was to assess the susceptibility of landslides around the area of Guizhou province based on fuzzy theory.In first instance, slope, elevation, lithology, proximity to tectonic lines, proximity to drainage and annual precipitation were taken as independent, causal factors in this study.A landslide hazard evaluation factor system was established by classifying these factors into more subclasses according to some rules.Secondly, a trapezoidal fuzzy number weighting(TFNW) approach was used to assess the importance of six causal factors to landslides in an ArcGIS environment.Thirdly, a landslide susceptibility map was created based on a weighted linear combination model.According to this susceptibility map, the study area was classified into four categories of landslide susceptibility:low, moderate, high and very high.Finally, in order to verify the results obtained, the susceptibility map and the landslide inventory map were combined in the GIS.In addition, the weighting procedure showed that TFNW is an efficient method for weighting causal landslide factors.
基金supported by the Natural Science Foundation of Zhejiang Province under Grant No.Y604106the Scientific Research Foundation of Zhejiang Provincial Education Department under Grant No.20070568the Natural Science Foundation of Zhejiang Lishui University under Grant No.KZ08001
文摘With the help of an improved mapping approach and a linear-variable-separation approach, a new family of exact solutions with arbitrary functions of the (2+1)-dimensional Nizhnik-Novikov-Veselov system (NNV) is derived. Based on the derived solutions and using some multi-valued functions, we find a few new folded solitary wave excitations for the (2+1)-dimensional NNV system.
基金Project supported by the Anhui Key Laboratory of Information Materials and Devices (Anhui University),China
文摘In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions (m → 1). This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.
基金This work was supported by the National Natural Science Foundation of China(11872080)Beijing Natural Science Foundation(3192005).
文摘Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the structures are damaged.Aiming at the lightweight structure,fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand.Firstly,the fatigue life is expressed by topology variables and the fatigue life filter function.The continuum fatigue optimization model is established with the independent continuous mapping(ICM)method.Secondly,fatigue life constraints are transformed to distortion energy constraints explicitly by taking advantage of the distortion energy theory.Thirdly,the optimization formulation is solved by the dual sequence quadratic programming(DSQP).And the design scheme of lightweight structure considering the fatigue characteristics is obtained.Finally,numerical examples illustrate the practicality and effectiveness of the fatigue optimization method.This method further expands the theoretical application of the ICM method and provides a novel approach for the fatigue optimization problem.
基金Sponsored by the National High Technology Research and Development Program of China(863)(Grant No.2002AA411420)National Natural Science Foundation(Grant No.60374071)
文摘An ontology mapping approach based on set & relation theory and OCL is introduced,then an ontology mapping meta-model is established which is composed of ontology related elements,mapping related elements and definition rule related elements.This ontology mapping meta-model can be regarded as a unified mechanism to realize different kinds of ontology mappings.The powerful computation capability of set and relation theory and the flexible expressive capability of OCL can be used in the computation of ontology mapping meta-model to realize the unified mapping among different ontology models.Based on the mapping meta-model,a general mapping management framework is developed to provide a common mapping storage mechanism,some mapping APIs and mapping rule APIs.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11005092)the Undergraduate Scientific and Technological Innovation Project of Zhejiang Province of China (Grant No. 2012R412018)the Undergraduate Innovative Base Program of Zhejiang A & F University
文摘With the help of a modified mapping method and a new mapping method, we re-study the (3+1)-dimensional Burgers equation, and derive two families of variable separation solutions. By selecting appropriate functions in the variable separation solution, we discuss the interaction behaviors among taper-like, plateau-type rings, and rectangle-type embed-solitons in the periodic wave background. All the interaction behaviors are completely elastic, and no phase shift appears after interaction.
文摘In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the conformable fractional derivative. As a result, the singular soliton solutions, kink and anti-kink soliton solutions, periodic function soliton solutions, Jacobi elliptic function solutions and hyperbolic function solutions of (2 + 1)-dimensional time-fractional Zoomeron equation were obtained. Finally, the 3D and 2D graphs of some solutions were drawn by setting the suitable values of parameters with Maple, and analyze the dynamic behaviors of the solutions.
基金This project was supported by the National High-Tech Research and Development Plan (2001AA422140) National Science Foundation (69889501, 60105005).
文摘In this paper, a new method for mobile robot map building based on grey system theory is presented, by which interpretation and integration of sonar readings can be solved robustly and efficiently. The conception of 'grey number is introduced to model and handle the uncertainty of sonar reading. A new data fusion approach based on grey system theory is proposed to construct environment model. Map building experiments are performed both on a platform of simulation and a real mobile robot. Experimental results show that our method is robust and accurate.
文摘In this paper we define a fixed point index theory for locally Lip., completely continuous and weakly inward mappings defined on closed convex sets in general Banach spaces where no other artificial conditions are imposed. This makes ns to deal with these kinds of mappings more easily. As obvious applications, some results in [3],[5],[7],[9],[10] are deepened and extended.
基金the Natural Science Foundation of Zhejiang Province under Grant Nos. Y604106 and Y606181the Foundation of New Century "151 Talent Engineering" of Zhejiang Province+1 种基金the Scientific Research Foundation of Key Discipline of Zhejiang Provincethe Natural Science Foundation of Zhejiang Lishui University under Grant No KZ06006
文摘With the help of an extended mapping approach and a linear variable separation method,new families ofvariable separation solutions with arbitrary functions for the(3+1)-dimensional Burgers system are derived.Based onthe derived exact solutions, some novel and interesting localized coherent excitations such as embed-solitons are revealedby selecting appropriate boundary conditions and/or initial qualifications.The time evolutional properties of the novellocalized excitation are also briefly investigated.
基金the Natural Science Foundation of Zhejiang Province under Grant Nos.Y604106 and Y606181the Foundation of New Century"151 Talent Engineering"of Zhejiang Provincethe Scientific Research Foundation of Key Discipline of Zhejiang Province
文摘Starting from the extended mapping approach and a linear variable separation method, we find new families of variable separation solutions with some arbitrary functions for the (3+1)-dimensionM Burgers system. Then based on the derived exact solutions, some novel and interesting localized coherent excitations such as embedded-solitons, taper-like soliton, complex wave excitations in the periodic wave background are revealed by introducing appropriate boundary conditions and/or initial qualifications. The evolutional properties of the complex wave excitations are briefly investigated.
基金supported by the Scientific Research Foundation of Beijing Information Science and Technology UniversityScientific Creative Platform Foundation of Beijing Municipal Commission of Education
文摘With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the (2+1)-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions.
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant Nos.Y606128 and Y604106the Natural Science Foundation of Zhejiang Lishui University under Grant Nos.FC06001 and QN06009
文摘With an extended mapping approach and a linear variable separation method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for (3+1)-dimensionai Burgers system is derived. Based on the derived excitations, we obtain some novel localized coherent structures and study the interactions between solitons.
文摘The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the concepts of the limits of multivalued (S) and (S) + type mappings. These kinds of mappings contain many monotone type mappings, such as maximal monotone mapping, bounded pseudo-monotone mapping and bounded generalized pseudo-monotone mapping, as its special cases. In the second part we define the pseudo-degree for (S) type mapping and the degree for (S)+ type mapping. These two kinds of degrees are all the generalizations of the degree defined by Browder[1,2] As applications, we utilize the degree theory presented in part 2 to study the existence of solutions for the multivalued operator equations (see part 3) and to obtain some new fixed point theorems in part 4.
文摘We propose the generalization of Einstein’s special theory of relativity (STR). In our model, we use the (1 + 4)-dimensional space G, which is the extension of the (1 + 3)-dimensional Minkowski space M. As a fifth additional coordinate, the interval S is used. This value is constant under the usual Lorentz transformations in M, but it changes when the transformations in the extended space G are used. We call this model the Extended space model (ESM). From a physical point of view, our expansion means that processes in which the rest mass of the particles changes are acceptable now. In the ESM, gravity and electromagnetism are combined in one field. In the ESM, a photon can have a nonzero mass and this mass can be either positive or negative. It is also possible to establish in the frame of ESM connection between mass of a particle and its size.