This study introduces a novel single-layer meshless method,the space-time collocation method based on multiquadric-radial basis functions(MQ-RBF),for solving the Benjamin-Bona-Mahony-Burgers(BBMB)equation.By reconstru...This study introduces a novel single-layer meshless method,the space-time collocation method based on multiquadric-radial basis functions(MQ-RBF),for solving the Benjamin-Bona-Mahony-Burgers(BBMB)equation.By reconstructing the time variable as a space variable,this method establishes a combined space-time structure that can eliminate the two-step computational process required in traditional grid methods.By introducing shape parameteroptimized MQ-RBF,high-precision discretization of the nonlinear,dispersive,and dissipative terms in the BBMB equation is achieved.The numerical experiment section validates the effectiveness of the proposed method through three benchmark examples.This method shows significant advantages in computational efficiency,providing a new numerical tool for engineering applications in fields such as shallow water wave dynamics.展开更多
In this paper,a simple direct space-time semi-analytical meshless scheme is proposed for the numerical approximation of the coupled Burgers'equations.During the whole solution procedure,two different schemes are c...In this paper,a simple direct space-time semi-analytical meshless scheme is proposed for the numerical approximation of the coupled Burgers'equations.During the whole solution procedure,two different schemes are considered in terms of radial and non-radial basis functions.The time-dependent variable in the first radial scheme is directly considered as the normal space variables to formulate an"isotropic"space-time radial basis function.The second non-radial scheme considered relationship between time-dependent and spacedependent variables.Under such circumstance,we can get a one-step space-time meshless scheme.The numerical findings demonstrate that the proposed meshless schemes are precise,user-friendly,and effective in solving the coupled Burgers'equations.展开更多
Currently, mere are many onune review weo sites where consumers can freely write comments about different kinds of products and services. These comments are quite useful for other potential consumers. However, the num...Currently, mere are many onune review weo sites where consumers can freely write comments about different kinds of products and services. These comments are quite useful for other potential consumers. However, the number of online comments is often large and the number continues to grow as more and more consumers contribute. In addition, one comment may mention more than one product and con- tain opinions about different products, mentioning something good and something bad. However, they share only a single overall score, Therefore, it is not easy to know the quality of an individual product from these comments. This paper presents a novel approach to generate review summaries including scores and description snippets with re- spect to each individual product. From the large number of comments, we first extract the context （snippet） that includes a description of the products and choose those snippets that express consumer opinions on them. We then propose several methods to predict the rating （from 1 to 5 stars） of the snip- pets. Finally, we derive a generic framework for generating summaries from the snippets. We design a new snippet selec- tion algorithm to ensure that the returned results preserve the opinion-aspect statistical properties and attribute-aspect cov- erage based on a standard seat allocation algorithm. Through experiments we demonstrate empirically that our methods are effective. We also quantitatively evaluate each step of our ap- proach.展开更多
基金supported by the Horizontal Scientific Research Funds in Huaibei Normal University(No.2024340603000006)the Science and Technology General Project of Jiangxi Provincial Department of Education(Nos.GJJ2203203,GJJ2203213)。
文摘This study introduces a novel single-layer meshless method,the space-time collocation method based on multiquadric-radial basis functions(MQ-RBF),for solving the Benjamin-Bona-Mahony-Burgers(BBMB)equation.By reconstructing the time variable as a space variable,this method establishes a combined space-time structure that can eliminate the two-step computational process required in traditional grid methods.By introducing shape parameteroptimized MQ-RBF,high-precision discretization of the nonlinear,dispersive,and dissipative terms in the BBMB equation is achieved.The numerical experiment section validates the effectiveness of the proposed method through three benchmark examples.This method shows significant advantages in computational efficiency,providing a new numerical tool for engineering applications in fields such as shallow water wave dynamics.
基金the Science and Technology Research Project of Henan Province (242102231052)the Key Scientific Research Plan of Colleges and Universities in Henan Province (23B140006)the Natural Science Foundation of Jiangxi Province (20224BAB201018)。
文摘In this paper,a simple direct space-time semi-analytical meshless scheme is proposed for the numerical approximation of the coupled Burgers'equations.During the whole solution procedure,two different schemes are considered in terms of radial and non-radial basis functions.The time-dependent variable in the first radial scheme is directly considered as the normal space variables to formulate an"isotropic"space-time radial basis function.The second non-radial scheme considered relationship between time-dependent and spacedependent variables.Under such circumstance,we can get a one-step space-time meshless scheme.The numerical findings demonstrate that the proposed meshless schemes are precise,user-friendly,and effective in solving the coupled Burgers'equations.
基金This work was partially supported by the National Science Foundation of China （Grant Nos. 61103039, 61232002, 61472345）, National Basic Research Program of China （2010CB731402） and Wuhan Key Lab Research Foundation （SKLSE2012-09-16）.
文摘Currently, mere are many onune review weo sites where consumers can freely write comments about different kinds of products and services. These comments are quite useful for other potential consumers. However, the number of online comments is often large and the number continues to grow as more and more consumers contribute. In addition, one comment may mention more than one product and con- tain opinions about different products, mentioning something good and something bad. However, they share only a single overall score, Therefore, it is not easy to know the quality of an individual product from these comments. This paper presents a novel approach to generate review summaries including scores and description snippets with re- spect to each individual product. From the large number of comments, we first extract the context （snippet） that includes a description of the products and choose those snippets that express consumer opinions on them. We then propose several methods to predict the rating （from 1 to 5 stars） of the snip- pets. Finally, we derive a generic framework for generating summaries from the snippets. We design a new snippet selec- tion algorithm to ensure that the returned results preserve the opinion-aspect statistical properties and attribute-aspect cov- erage based on a standard seat allocation algorithm. Through experiments we demonstrate empirically that our methods are effective. We also quantitatively evaluate each step of our ap- proach.
