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您的检索式：作者名="GU David XianFeng"
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| 1 | From a projective invariant to some new properties of algebraic hypersurfaces显示文摘Projective invariants are not only important objects in mathematics especially in geometry,but also widely used in many practical applications such as in computer vision and object recognition. In this work,we show a projective invariant named as characteristic number,from which we obtain an intrinsic property of an algebraic hypersurface involving the intersections of the hypersurface and some lines that constitute a closed loop. From this property,two high-dimensional generalizations of Pascal's theorem are given,one establishing the connection of hypersurfaces of distinct degrees,and the other concerned with the intersections of a hypersurface and a simplex. | LUO ZhongXuan ZHOU XinChen GU David XianFeng | 2014 | Science China Mathematics2014，57，11： | 8 |
| 2 | Concurrent optimization of structural topology and infill properties with a CBF-based level set method显示文摘In this paper,a parametric level-set-based topology optimization framework is proposed to concurrently optimize the structural topology at the macroscale and the effective infill properties at the micro/meso scale.The concurrent optimization is achieved by a computational framework combining a new parametric level set approach with mathematical programming.Within the proposed framework,both the structural boundary evolution and the effective infill property optimization can be driven by mathematical programming,which is more advantageous compared with the conventional partial differential equatiodriven level set approach.Moreover,the proposed approach will be more efficient in handling nonlinear problems with multiple constraints.Instead of using radial basis functions(RBF),in this paper,we propose to construct a new type of cardinal basis functions(CBF)for the level set function parameterization.The proposed CBF parameterization ensures an explicit impose of the lower and upper bounds of the design variables.This overcomes the intrinsic disadvantage of the conventional RBF-based parametric level set method,where the lower and upper bounds of the design variables oftentimes have to be set by trial and error;A variational distance regularization method is utilized in this research to regularize the level set function to be a desired distanceregularized shape.With the distance information embedded in the level set model,the wrapping boundary layer and the interior infill region can be naturally defined.The isotropic infill achieved via the mesoscale topology optimization is conformally fit into the wrapping boundary layer using the shape-preserving conformal mapping method,which leads to a hierarchical physical structure with optimized overall topology and effective infill properties.The proposed method is expected to provide a timely solution to the increasing demand for multiscale and multifunctional structure design. | Long JIANG Yang GUO Shikui CHEN Peng WEI Na LEI Xianfeng David GU | 2019 | Frontiers of Mechanical Engineering2019，14，2： | 3 |
| 3 | Characteristic Class of Isotopy for Surfaces显示文摘It is an important problem in topology to verify whether two embeddings are isotopic.This work proposes an algorithm for computing Haefliger-Wu invariants for isotopy based on algebraic topological methods.Given a simplicial complex embedded in the Euclidean space,the deleted product of it is the direct product with diagonal removed.The Gauss map transforms the deleted product to the unit sphere.The pull-back of the generator of the cohomology group of the sphere defines characteristic class of the isotopy of the embedding.By using Mayer Vietoris sequence and Ku¨nneth theorem,the computational algorithm can be greatly simplified.The authors prove the ranks of homology groups of the deleted product of a closed surface and give explicit construction of the generators of the homology groups of the deleted product.Numerical experimental results show the efficiency and efficacy of the proposed method. | REN Yuxue WEN Chengfeng ZHEN Shengxian LEI Na LUO Feng GU David Xianfeng | 2020 | Journal of Systems Science & Complexity2020，33，6： | 0 |
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