In this paper, an extended functional transformation is given to solve some nonlinear evolution equations. This function, in fact, is a solution of the famous KdV equation, so this transformation gives a transformatio...In this paper, an extended functional transformation is given to solve some nonlinear evolution equations. This function, in fact, is a solution of the famous KdV equation, so this transformation gives a transformation between KdV equation and other soliton equations. Then many new exact solutions can be given by virtue of the solutions of KdV equation.展开更多
In a recent article [Physics Letters A 372 （2008） 417], Wang et al. proposed a method, which is called the （G′/G）-expansion method, to look for travelling wave solutions of nonlinear evolution equations. The trav...In a recent article [Physics Letters A 372 （2008） 417], Wang et al. proposed a method, which is called the （G′/G）-expansion method, to look for travelling wave solutions of nonlinear evolution equations. The travelling wave solutions involving parameters of the KdV equation, the mKdV equation, the variant Boussinesq equations, and the Hirota-Satsuma equations are obtained by using this method. They think the （G′/G）-expansion method is a new method and more travelling wave solutions of many nonlinear evolution equations can be obtained. In this paper, we will show that the （G′/G）-expansion method is equivalent to the extended tanh function method.展开更多
System of systems architecture（SoSA） has received increasing emphasis by scholars since Zachman ignited its flame in 1987. Given its complexity and abstractness, it is critical to validate and evaluate SoSA to ensur...System of systems architecture（SoSA） has received increasing emphasis by scholars since Zachman ignited its flame in 1987. Given its complexity and abstractness, it is critical to validate and evaluate SoSA to ensure requirements have been met.Multiple qualities are discussed in the literature of SoSA evaluation, while research on functionality is scarce. In order to assess SoSA functionality, an extended influence diagram（EID） is developed in this paper. Meanwhile, a simulation method is proposed to elicit the conditional probabilities in EID through designing and executing SoSA. An illustrative anti-missile architecture case is introduced for EID development, architecture design, and simulation.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
The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is intr...The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.展开更多
The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct m...The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schrodinger equation. When the modulous m → 1or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.展开更多
In this paper, an extended Jacobi elliptic function rational expansion method is proposed for constructing new forms of exact Jacobi elliptic function solutions to nonlinear partial differential equations by means of ...In this paper, an extended Jacobi elliptic function rational expansion method is proposed for constructing new forms of exact Jacobi elliptic function solutions to nonlinear partial differential equations by means of making a more general transformation. For illustration, we apply the method to the （2＋1）-dimensional dispersive long wave equation and successfully obtain many new doubly periodic solutions, which degenerate as soliton solutions when the modulus m approximates 1. The method can also be applied to other nonlinear partial differential equations.展开更多
In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its app...In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the system of shallow water wave equations and modified Liouville equation which play an important role in mathematical physics.展开更多
A micro-extended-analog-computer （uEAC） is developed on the basis of Rubel＇ s extended analog computer（EAC） model. Through the uEAC mathematical model, the resistance properties of the conductive sheet, several f...A micro-extended-analog-computer （uEAC） is developed on the basis of Rubel＇ s extended analog computer（EAC） model. Through the uEAC mathematical model, the resistance properties of the conductive sheet, several feedback uEAC models, and a more flexible uEAC cell structure with a multi-level hierarchy are discussed. Futhermore, for the dynamic uEAC array with a linear Lukasiewicz function, a nonlinear differential equation description is presented, and then a sufficient global asymptotic stability condition is derived by utilizing a Lyapunov function and a Lipchitz function. Finally, comparative simulations for a cam servo mechanism system are conducted to verify the capability of the uEAC array as an adaptive controller.展开更多
In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its app...In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to Dynamical system in a new Double-Chain Model of DNA and a diffusive predator-prey system which play an important role in biology.展开更多
CAD model retrieval based on functional semantics is more significant than content-based 3D model retrieval during the mechanical conceptual design phase. However, relevant research is still not fully discussed. There...CAD model retrieval based on functional semantics is more significant than content-based 3D model retrieval during the mechanical conceptual design phase. However, relevant research is still not fully discussed. Therefore, a functional semantic-based CAD model annotation and retrieval method is proposed to support mechanical conceptual design and design reuse, inspire designer creativity through existing CAD models, shorten design cycle, and reduce costs. Firstly, the CAD model functional semantic ontology is constructed to formally represent the functional semantics of CAD models and describe the mechanical conceptual design space comprehensively and consistently. Secondly, an approach to represent CAD models as attributed adjacency graphs（AAG） is proposed. In this method, the geometry and topology data are extracted from STEP models. On the basis of AAG, the functional semantics of CAD models are annotated semi-automatically by matching CAD models that contain the partial features of which functional semantics have been annotated manually, thereby constructing CAD Model Repository that supports model retrieval based on functional semantics. Thirdly, a CAD model retrieval algorithm that supports multi-function extended retrieval is proposed to explore more potential creative design knowledge in the semantic level. Finally, a prototype system, called Functional Semantic-based CAD Model Annotation and Retrieval System（FSMARS）, is implemented. A case demonstrates that FSMARS can successfully botain multiple potential CAD models that conform to the desired function. The proposed research addresses actual needs and presents a new way to acquire CAD models in the mechanical conceptual design phase.展开更多
We examined the characteristic feature and predictability of low frequency variability (LFV) of the atmosphere in the Northern Hemisphere winter (January and February) by using the empirical orthogonal functions (EOFs...We examined the characteristic feature and predictability of low frequency variability (LFV) of the atmosphere in the Northern Hemisphere winter (January and February) by using the empirical orthogonal functions (EOFs) of the geopotential height at 500 hPa. In the discussion, we used the EOFs for geostrophic zonal wind (Uznl) and the height deviation from the zonal mean (Zeddy). The set of EOFs for Uznl and Zeddy was denoted as Uznl-1, Uznl-2, ..., Zeddy-1, Zeddy-2, ..., respectively. We used the data samples of 396 pentads derived from 33 years of NMC, ECMWF and JMA analyses, from January 1963 to 1995. From the calculated scores for Uznl-1, Uznl-2, Zeddy-1, Zeddy-2 and so on we found that Uznl-1 and Zeddy-1 were statistically stable and their scores were more persistent than those of the other EOFs. A close relationship existed between the scores of Uznl-1 and those of Zeddy-1. 30-day forecast experiments were carried out with the medium resolution version of JMA global spectral model for 20 cases in January and February for the period of 1984-1992. Results showed that Zeddy-1 was more predictable than the other EOFs for Zeddy. Considering these results, we argued that prediction of the Zeddy-1 was to be one of the main target of extended-range forecasting.展开更多
In this paper,we give four characteristic theorems of the natural Tchebysheff splint functionassociated with multiple knots.These theorems possess specific form,that arc convenient forapplicaton;In the case of with si...In this paper,we give four characteristic theorems of the natural Tchebysheff splint functionassociated with multiple knots.These theorems possess specific form,that arc convenient forapplicaton;In the case of with simple knots or polynomial splint,the corollaries of this paper’s the-orems give corresponding results.展开更多
In numerical analysis, it is significant to approximate the linear functional Ef=sum from i=0 to m-1([integral from a to b(a<sub>1</sub>（x）f<sup>1</sup>（x）dx+ sum from f=0 to i<sub>1&...In numerical analysis, it is significant to approximate the linear functional Ef=sum from i=0 to m-1([integral from a to b(a<sub>1</sub>（x）f<sup>1</sup>（x）dx+ sum from f=0 to i<sub>1</sub>(b<sub>1</sub>f<sup>1</sup>（x<sub>1</sub>）)]) by a simpler linear functional Lf=sum from i=1 to m（a<sub>1</sub>f（x<sub>1</sub>）） In this paper, making use of natural Tchebysheff spline function, we give existence theorem and uniqueness theorem of L that is exact for the degree m to F; we also give three sufficient and necessary conditions in which L is the Sard best approximation to F.展开更多
In this paper, we have successfully extended the Jacobian elliptic function expansion approach to nonlinear differential-difference equations. The Hybrid lattice equation is chosen to illustrate this approach. As a co...In this paper, we have successfully extended the Jacobian elliptic function expansion approach to nonlinear differential-difference equations. The Hybrid lattice equation is chosen to illustrate this approach. As a consequence, twelve families of Jacobian elliptic function solutions with different parameters of the Hybrid lattice equation are obtained. When the modulus m → 1 or O, doubly-periodic solutions degenerate to solitonic solutions and trigonometric function solutions, respectively.展开更多
Ionospheric delay error is considered to be one of the most prominent factors impacting the Global Navigation Satellite Systems(GNSS) positioning and navigation accuracies. Due to dispersive nature and anisotropic of ...Ionospheric delay error is considered to be one of the most prominent factors impacting the Global Navigation Satellite Systems(GNSS) positioning and navigation accuracies. Due to dispersive nature and anisotropic of the ionosphere above certain regions, the positioning accuracy is seriously affected when using a precision-limited model. In this paper, an attempt has been taken to estimate ionosphere-delays based on Planar Fit(PF) and Spherical Harmonic Function(SHF) models by applying the commonly used single layer Model(SLM) and an extended single layer model(ESLM) which has been explored sparsely over the region. The results show that ESLM of PF and SHF techniques performed better in estimating ionospheric delay compared to the existing SLM model. Although the performance of the ESLM approach is almost comparable to the SLM results during the quiet ionospheric conditions, the ESLM-PF and ESLMSHF models led to respective improvements of 4.66% and 7.14% over the classically used SLM model under the disturbed ionospheric conditions. In view of the uneven variability of equatorial/low latitude ionosphere above the Indian subcontinental region, the suitability of ESLM-PF and ESLM-SHF models has been emphasized and suggested for assessing its completeness and reliableness across other parts of the globe. The output of this work may be useful for high precession GNSS positioning through mitigating the ionospheric delays under quiet as well as varied ionospheric conditions across the low/equatorial latitude regions.展开更多
文摘In this paper, an extended functional transformation is given to solve some nonlinear evolution equations. This function, in fact, is a solution of the famous KdV equation, so this transformation gives a transformation between KdV equation and other soliton equations. Then many new exact solutions can be given by virtue of the solutions of KdV equation.
基金Supported by National Natural Science Foundation of China under Grant No. 10671172
文摘In a recent article [Physics Letters A 372 （2008） 417], Wang et al. proposed a method, which is called the （G′/G）-expansion method, to look for travelling wave solutions of nonlinear evolution equations. The travelling wave solutions involving parameters of the KdV equation, the mKdV equation, the variant Boussinesq equations, and the Hirota-Satsuma equations are obtained by using this method. They think the （G′/G）-expansion method is a new method and more travelling wave solutions of many nonlinear evolution equations can be obtained. In this paper, we will show that the （G′/G）-expansion method is equivalent to the extended tanh function method.
基金supported by the National Natural Science Foundation of China(71571189)
文摘System of systems architecture（SoSA） has received increasing emphasis by scholars since Zachman ignited its flame in 1987. Given its complexity and abstractness, it is critical to validate and evaluate SoSA to ensure requirements have been met.Multiple qualities are discussed in the literature of SoSA evaluation, while research on functionality is scarce. In order to assess SoSA functionality, an extended influence diagram（EID） is developed in this paper. Meanwhile, a simulation method is proposed to elicit the conditional probabilities in EID through designing and executing SoSA. An illustrative anti-missile architecture case is introduced for EID development, architecture design, and simulation.
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.
文摘The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.
文摘The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schrodinger equation. When the modulous m → 1or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.
文摘In this paper, an extended Jacobi elliptic function rational expansion method is proposed for constructing new forms of exact Jacobi elliptic function solutions to nonlinear partial differential equations by means of making a more general transformation. For illustration, we apply the method to the （2＋1）-dimensional dispersive long wave equation and successfully obtain many new doubly periodic solutions, which degenerate as soliton solutions when the modulus m approximates 1. The method can also be applied to other nonlinear partial differential equations.
文摘In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the system of shallow water wave equations and modified Liouville equation which play an important role in mathematical physics.
基金Supported by the National Natural Science Foundation of China(61433003,61273150)Beijing Higher Education Young Elite Teacher Project
文摘A micro-extended-analog-computer （uEAC） is developed on the basis of Rubel＇ s extended analog computer（EAC） model. Through the uEAC mathematical model, the resistance properties of the conductive sheet, several feedback uEAC models, and a more flexible uEAC cell structure with a multi-level hierarchy are discussed. Futhermore, for the dynamic uEAC array with a linear Lukasiewicz function, a nonlinear differential equation description is presented, and then a sufficient global asymptotic stability condition is derived by utilizing a Lyapunov function and a Lipchitz function. Finally, comparative simulations for a cam servo mechanism system are conducted to verify the capability of the uEAC array as an adaptive controller.
文摘In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to Dynamical system in a new Double-Chain Model of DNA and a diffusive predator-prey system which play an important role in biology.
基金Supported by National Natural Science Foundation of China (Grant No.51175287)National Science and Technology Major Project of China (Grant No.2011ZX02403)
文摘CAD model retrieval based on functional semantics is more significant than content-based 3D model retrieval during the mechanical conceptual design phase. However, relevant research is still not fully discussed. Therefore, a functional semantic-based CAD model annotation and retrieval method is proposed to support mechanical conceptual design and design reuse, inspire designer creativity through existing CAD models, shorten design cycle, and reduce costs. Firstly, the CAD model functional semantic ontology is constructed to formally represent the functional semantics of CAD models and describe the mechanical conceptual design space comprehensively and consistently. Secondly, an approach to represent CAD models as attributed adjacency graphs（AAG） is proposed. In this method, the geometry and topology data are extracted from STEP models. On the basis of AAG, the functional semantics of CAD models are annotated semi-automatically by matching CAD models that contain the partial features of which functional semantics have been annotated manually, thereby constructing CAD Model Repository that supports model retrieval based on functional semantics. Thirdly, a CAD model retrieval algorithm that supports multi-function extended retrieval is proposed to explore more potential creative design knowledge in the semantic level. Finally, a prototype system, called Functional Semantic-based CAD Model Annotation and Retrieval System（FSMARS）, is implemented. A case demonstrates that FSMARS can successfully botain multiple potential CAD models that conform to the desired function. The proposed research addresses actual needs and presents a new way to acquire CAD models in the mechanical conceptual design phase.
文摘We examined the characteristic feature and predictability of low frequency variability (LFV) of the atmosphere in the Northern Hemisphere winter (January and February) by using the empirical orthogonal functions (EOFs) of the geopotential height at 500 hPa. In the discussion, we used the EOFs for geostrophic zonal wind (Uznl) and the height deviation from the zonal mean (Zeddy). The set of EOFs for Uznl and Zeddy was denoted as Uznl-1, Uznl-2, ..., Zeddy-1, Zeddy-2, ..., respectively. We used the data samples of 396 pentads derived from 33 years of NMC, ECMWF and JMA analyses, from January 1963 to 1995. From the calculated scores for Uznl-1, Uznl-2, Zeddy-1, Zeddy-2 and so on we found that Uznl-1 and Zeddy-1 were statistically stable and their scores were more persistent than those of the other EOFs. A close relationship existed between the scores of Uznl-1 and those of Zeddy-1. 30-day forecast experiments were carried out with the medium resolution version of JMA global spectral model for 20 cases in January and February for the period of 1984-1992. Results showed that Zeddy-1 was more predictable than the other EOFs for Zeddy. Considering these results, we argued that prediction of the Zeddy-1 was to be one of the main target of extended-range forecasting.
文摘In this paper,we give four characteristic theorems of the natural Tchebysheff splint functionassociated with multiple knots.These theorems possess specific form,that arc convenient forapplicaton;In the case of with simple knots or polynomial splint,the corollaries of this paper’s the-orems give corresponding results.
文摘In numerical analysis, it is significant to approximate the linear functional Ef=sum from i=0 to m-1([integral from a to b(a<sub>1</sub>（x）f<sup>1</sup>（x）dx+ sum from f=0 to i<sub>1</sub>(b<sub>1</sub>f<sup>1</sup>（x<sub>1</sub>）)]) by a simpler linear functional Lf=sum from i=1 to m（a<sub>1</sub>f（x<sub>1</sub>）） In this paper, making use of natural Tchebysheff spline function, we give existence theorem and uniqueness theorem of L that is exact for the degree m to F; we also give three sufficient and necessary conditions in which L is the Sard best approximation to F.
文摘In this paper, we have successfully extended the Jacobian elliptic function expansion approach to nonlinear differential-difference equations. The Hybrid lattice equation is chosen to illustrate this approach. As a consequence, twelve families of Jacobian elliptic function solutions with different parameters of the Hybrid lattice equation are obtained. When the modulus m → 1 or O, doubly-periodic solutions degenerate to solitonic solutions and trigonometric function solutions, respectively.
文摘Ionospheric delay error is considered to be one of the most prominent factors impacting the Global Navigation Satellite Systems(GNSS) positioning and navigation accuracies. Due to dispersive nature and anisotropic of the ionosphere above certain regions, the positioning accuracy is seriously affected when using a precision-limited model. In this paper, an attempt has been taken to estimate ionosphere-delays based on Planar Fit(PF) and Spherical Harmonic Function(SHF) models by applying the commonly used single layer Model(SLM) and an extended single layer model(ESLM) which has been explored sparsely over the region. The results show that ESLM of PF and SHF techniques performed better in estimating ionospheric delay compared to the existing SLM model. Although the performance of the ESLM approach is almost comparable to the SLM results during the quiet ionospheric conditions, the ESLM-PF and ESLMSHF models led to respective improvements of 4.66% and 7.14% over the classically used SLM model under the disturbed ionospheric conditions. In view of the uneven variability of equatorial/low latitude ionosphere above the Indian subcontinental region, the suitability of ESLM-PF and ESLM-SHF models has been emphasized and suggested for assessing its completeness and reliableness across other parts of the globe. The output of this work may be useful for high precession GNSS positioning through mitigating the ionospheric delays under quiet as well as varied ionospheric conditions across the low/equatorial latitude regions.
