To solve the fuzzy and unstable tactile similarity relationship between some sample points in the perception experiment,an improved non-metric multidimensional scaling(INMDS)is proposed in this paper.In view of the in...To solve the fuzzy and unstable tactile similarity relationship between some sample points in the perception experiment,an improved non-metric multidimensional scaling(INMDS)is proposed in this paper.In view of the inconsistency of each sample s contribution,the maximum marginal decision when constructing the perception space to describe the tactile perception characteristics is also proposed.The corresponding constraints are set according to the degree of similarity,and controlling the relaxation variable factor is proposed to optimize the perception dimension and coordinate measurement.The effectiveness of the INMDS algorithm is verified by two perception experiments.The results show that compared with the metric multidimensional scaling(MDS)and non-metric multidimensional scaling(NMDS)algorithms,the perceptual space constructed by INMDS can more accurately reflect the difference relationship between different leather sample points perceived by people.Moreover,the relative position of sample points in the perceptual space is more consistent with subjective perception results.展开更多
In this paper, the investigation is focused on a （3＋1）-dimensional variable-coefficient Kadomtsev- Petviashvili （vcKP） equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plas...In this paper, the investigation is focused on a （3＋1）-dimensional variable-coefficient Kadomtsev- Petviashvili （vcKP） equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plasma in three spatial dimensions. In order to study the integrability property of such an equation, the Painlevé analysis is performed on it. And then, based on the truncated Painlevé expansion, the bilinear form of the （3＋1）-dimensionaJ vcKP equation is obtained under certain coefficients constraint, and its solution in the Wronskian determinant form is constructed and verified by virtue of the Wronskian technique. Besides the Wronskian determinant solution, it is shown that the （3＋1）-dimensional vcKP equation also possesses a solution in the form of the Grammian determinant.展开更多
基金The National Key R&D Program of China(No.2018AAA0103001)the National Natural Science Foundation of China(No.62073073)。
文摘To solve the fuzzy and unstable tactile similarity relationship between some sample points in the perception experiment,an improved non-metric multidimensional scaling(INMDS)is proposed in this paper.In view of the inconsistency of each sample s contribution,the maximum marginal decision when constructing the perception space to describe the tactile perception characteristics is also proposed.The corresponding constraints are set according to the degree of similarity,and controlling the relaxation variable factor is proposed to optimize the perception dimension and coordinate measurement.The effectiveness of the INMDS algorithm is verified by two perception experiments.The results show that compared with the metric multidimensional scaling(MDS)and non-metric multidimensional scaling(NMDS)algorithms,the perceptual space constructed by INMDS can more accurately reflect the difference relationship between different leather sample points perceived by people.Moreover,the relative position of sample points in the perceptual space is more consistent with subjective perception results.
基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant Nos. 20060006024 and 20080013006Chinese Ministry of Education, by the National Natural Science Foundation of China under Grant No. 60772023+2 种基金by the Open Fund of the State Key Laboratory of Software Development Environment under Grant No. SKLSDE-07-001Beijing University of Aeronautics and Astronauticsby the National Basic Research Program of China (973 Program) under Grant No. 2005CB321901
文摘In this paper, the investigation is focused on a （3＋1）-dimensional variable-coefficient Kadomtsev- Petviashvili （vcKP） equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plasma in three spatial dimensions. In order to study the integrability property of such an equation, the Painlevé analysis is performed on it. And then, based on the truncated Painlevé expansion, the bilinear form of the （3＋1）-dimensionaJ vcKP equation is obtained under certain coefficients constraint, and its solution in the Wronskian determinant form is constructed and verified by virtue of the Wronskian technique. Besides the Wronskian determinant solution, it is shown that the （3＋1）-dimensional vcKP equation also possesses a solution in the form of the Grammian determinant.
