In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate con...In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate convexity-preserving in-terpolating transcendental curves;even constructing convexity-preserving interpolating polynomial curves,it is required to solve a system of equations or recur to a complicated iterative process. The method developed in this paper overcomes the above draw-backs. The basic idea is:first to construct a kind of trigonometric polynomial curves with a shape parameter,and interpolating trigonometric polynomial parametric curves with C2(or G1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then,the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter. Performing the method is easy and fast,and the curvature distribution of the resulting interpolating curves is always well-proportioned. Several numerical examples are shown to substantiate that our algorithm is not only correct but also usable.展开更多
This paper reviewed on the green highway definition and green highway terminology to improve knowledge and awareness of green highway for highway construction projects. Moreover, this paper discussed briefly on the ra...This paper reviewed on the green highway definition and green highway terminology to improve knowledge and awareness of green highway for highway construction projects. Moreover, this paper discussed briefly on the rating system for green highway by highlighting various eight rating systems for green highway. This study adopted the secondary data from previous research and findings on green highway construction from all over the world. With regard to published articles on green highways, the outcome of the paper will examine several major issues in green highway which are the definition of green highway, terminology used for green highway aspects, green highway initiatives and green highway rating systems from all over the world.展开更多
Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous.Although a considerable amount of research has been carried ...Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous.Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations,the majority of the results deal with polynomial types.Limited research has been reported regarding such equations of rational type.In this paper we present an adaptation of the(G /G)-expansion method to solve nonlinear rational differential-difference equations.The procedure is demonstrated using two distinct equations.Our approach allows one to construct three types of exact traveling wave solutions(hyperbolic,trigonometric,and rational) by means of the simplified form of the auxiliary equation method with reduced parameters.Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.展开更多
基金Project supported by the National Basic Research Program (973) of China (No. 2004CB719400)the National Natural Science Founda-tion of China (Nos. 60673031 and 60333010) the National Natural Science Foundation for Innovative Research Groups of China (No. 60021201)
文摘In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate convexity-preserving in-terpolating transcendental curves;even constructing convexity-preserving interpolating polynomial curves,it is required to solve a system of equations or recur to a complicated iterative process. The method developed in this paper overcomes the above draw-backs. The basic idea is:first to construct a kind of trigonometric polynomial curves with a shape parameter,and interpolating trigonometric polynomial parametric curves with C2(or G1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then,the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter. Performing the method is easy and fast,and the curvature distribution of the resulting interpolating curves is always well-proportioned. Several numerical examples are shown to substantiate that our algorithm is not only correct but also usable.
文摘This paper reviewed on the green highway definition and green highway terminology to improve knowledge and awareness of green highway for highway construction projects. Moreover, this paper discussed briefly on the rating system for green highway by highlighting various eight rating systems for green highway. This study adopted the secondary data from previous research and findings on green highway construction from all over the world. With regard to published articles on green highways, the outcome of the paper will examine several major issues in green highway which are the definition of green highway, terminology used for green highway aspects, green highway initiatives and green highway rating systems from all over the world.
文摘Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous.Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations,the majority of the results deal with polynomial types.Limited research has been reported regarding such equations of rational type.In this paper we present an adaptation of the(G /G)-expansion method to solve nonlinear rational differential-difference equations.The procedure is demonstrated using two distinct equations.Our approach allows one to construct three types of exact traveling wave solutions(hyperbolic,trigonometric,and rational) by means of the simplified form of the auxiliary equation method with reduced parameters.Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.
