The unique continuation on quadratic curves for harmonic functions is dis-cussed in this paper.By using complex extension method,the conditional stability of unique continuation along quadratic curves for harmonic fun...The unique continuation on quadratic curves for harmonic functions is dis-cussed in this paper.By using complex extension method,the conditional stability of unique continuation along quadratic curves for harmonic functions is illustrated.The nu-merical algorithm is provided based on collocation method and Tikhonov regularization.The stability estimates on parabolic and hyperbolic curves for harmonic functions are demonstrated by numerical examples respectively.展开更多
In this paper, we continue to discuss the uniqueness of limit cycle of the quadratic system by using the quadratic curve without contact and several new criteria for the uniqueness have been obtained.
This paper is concerned with a cubic Kolmogorov system with a solution of central quadratic curve which neither contacts with the coordinate axes, nor passes through the origin. The conclusion is that such a system ma...This paper is concerned with a cubic Kolmogorov system with a solution of central quadratic curve which neither contacts with the coordinate axes, nor passes through the origin. The conclusion is that such a system may possess limit cycles.展开更多
Parameterization is one of the key problems in the construction of a curve to interpolate a set of ordered points. We propose a new local parameterization method based on the curvature model in this paper. The new met...Parameterization is one of the key problems in the construction of a curve to interpolate a set of ordered points. We propose a new local parameterization method based on the curvature model in this paper. The new method determines the knots by mi- nimizing the maximum curvature of quadratic curve. When the knots by the new method are used to construct interpolation curve, the constructed curve have good precision. We also give some comparisons of the new method with existing methods, and our method can perform better in interpolation error, and the interpolated curve is more fairing.展开更多
To improve the innovation of agricultural machinery product styling,this paper proposes a shape structure behavior function(SSBF)model suitable for the industrial design field.The feature line evolution method combini...To improve the innovation of agricultural machinery product styling,this paper proposes a shape structure behavior function(SSBF)model suitable for the industrial design field.The feature line evolution method combining shape grammar and genetic algorithm was used for modelling the of the grader,which not only maintains the product style characteristics but also reflects the typical identification characteristics of the bionic prototype and produces a new product modelling scheme.By conducting cognitive and recognition experiments on product styling features,the ranking of product styling features and the contribution of each component to product styling were determined.The method of combining shape grammar and quadratic Bézier curve was used to express and encode feature lines,and genetic algorithm was used to evolve biomimetic forms to form product feature lines with typical biological morphological features;The extracted form bionic elements were integrated into the grader modelling design,and the interaction evaluation was carried out through the genetic algorithm evolution scheme.The basic form elements were extracted and analyzed,and the deduction rules were formulated and reorganized.The derived feature line geometric data considered the product’s image features and the bio-inspired prototype,which can be used for the follow-up guidance of industrial design schemes.展开更多
基金This work was supported by the National Natural Science Foundation of China(No.11971121).
文摘The unique continuation on quadratic curves for harmonic functions is dis-cussed in this paper.By using complex extension method,the conditional stability of unique continuation along quadratic curves for harmonic functions is illustrated.The nu-merical algorithm is provided based on collocation method and Tikhonov regularization.The stability estimates on parabolic and hyperbolic curves for harmonic functions are demonstrated by numerical examples respectively.
文摘In this paper, we continue to discuss the uniqueness of limit cycle of the quadratic system by using the quadratic curve without contact and several new criteria for the uniqueness have been obtained.
基金The NSF of Liaoning provinceFoundation of returned doctors and Foundation of LiaoningEducation Committee.
文摘This paper is concerned with a cubic Kolmogorov system with a solution of central quadratic curve which neither contacts with the coordinate axes, nor passes through the origin. The conclusion is that such a system may possess limit cycles.
基金Supported by National Research Foundation for the Doctoral Program of Higher Education of China(20110131130004)Independent Innovation Foundation of Shandong University,IIFSDU(2012TB013)
文摘Parameterization is one of the key problems in the construction of a curve to interpolate a set of ordered points. We propose a new local parameterization method based on the curvature model in this paper. The new method determines the knots by mi- nimizing the maximum curvature of quadratic curve. When the knots by the new method are used to construct interpolation curve, the constructed curve have good precision. We also give some comparisons of the new method with existing methods, and our method can perform better in interpolation error, and the interpolated curve is more fairing.
基金financially supported by the key research and development project of Shandong Province(Grant No.2021LYXT012)the independent innovation special project of Shandong Province-intelligent laser grader research and industrial demonstration(Grant No.2013CXC90203)。
文摘To improve the innovation of agricultural machinery product styling,this paper proposes a shape structure behavior function(SSBF)model suitable for the industrial design field.The feature line evolution method combining shape grammar and genetic algorithm was used for modelling the of the grader,which not only maintains the product style characteristics but also reflects the typical identification characteristics of the bionic prototype and produces a new product modelling scheme.By conducting cognitive and recognition experiments on product styling features,the ranking of product styling features and the contribution of each component to product styling were determined.The method of combining shape grammar and quadratic Bézier curve was used to express and encode feature lines,and genetic algorithm was used to evolve biomimetic forms to form product feature lines with typical biological morphological features;The extracted form bionic elements were integrated into the grader modelling design,and the interaction evaluation was carried out through the genetic algorithm evolution scheme.The basic form elements were extracted and analyzed,and the deduction rules were formulated and reorganized.The derived feature line geometric data considered the product’s image features and the bio-inspired prototype,which can be used for the follow-up guidance of industrial design schemes.
