A method for isochromatic determination in three-fringe photoelasticity is presented. It combines the phaseshifting method with cubic polynomial curve-fitting technology to eliminate the errors caused by color repetit...A method for isochromatic determination in three-fringe photoelasticity is presented. It combines the phaseshifting method with cubic polynomial curve-fitting technology to eliminate the errors caused by color repetition.We perform a demonstration of the method on a circular disc subjected to compressive loading and an injectionmolded cover with residual stresses. The test results compare well with the theoretical results.展开更多
The papcr gives an approach to construct shape preserving piece wise cubic, where twocubic picces are allowed by inscrting at most a new knot in each data subinterval, and these cubicpieees is C2 continuous at each ne...The papcr gives an approach to construct shape preserving piece wise cubic, where twocubic picces are allowed by inscrting at most a new knot in each data subinterval, and these cubicpieees is C2 continuous at each new knot. Two numerical examples show that the method is effec.tive and visually pleasing.展开更多
We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson＇s minimal tori. This provides an alternative proof of the resul...We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson＇s minimal tori. This provides an alternative proof of the result by Perdomo （Characterization of order 3 algebraic immersed minimal surfaces of S3, Geom. Dedicata 129 （2007）, 23 34）.展开更多
A new method for constructing a fitting surface on a triangular grid is presented. Assuming images are obtained by sampling from the original scene. Conventional polynomial interpolation methods generally construct th...A new method for constructing a fitting surface on a triangular grid is presented. Assuming images are obtained by sampling from the original scene. Conventional polynomial interpolation methods generally construct the fitting surface on a square grid. Different from existing methods, the new method constructs the fitting surface on a triangular grid which can divide the original surface more detailed and improve approximation accuracy. As the quality of the image edges plays a key role in visual effects of image, the new method uses image edges as constraints to get a triangle grid. The new method constructs a cubic polynomial patch locally using image data to approximate the original surface. Experimental comparison results of the new method with other methods show that the new method can produce high-quality images and remove the zigzagging artifact.展开更多
Recently, facial-expression recognition (FER)has primarily focused on images in the wild, includingfactors such as face occlusion and image blurring, ratherthan laboratory images. Complex field environmentshave introd...Recently, facial-expression recognition (FER)has primarily focused on images in the wild, includingfactors such as face occlusion and image blurring, ratherthan laboratory images. Complex field environmentshave introduced new challenges to FER. To addressthese challenges, this study proposes a cross-fusion dualattention network. The network comprises three parts:(1) a cross-fusion grouped dual-attention mechanism torefine local features and obtain global information;(2) aproposed C2 activation function construction method,which is a piecewise cubic polynomial with threedegrees of freedom, requiring less computation withimproved flexibility and recognition abilities, whichcan better address slow running speeds and neuroninactivation problems;and (3) a closed-loop operationbetween the self-attention distillation process andresidual connections to suppress redundant informationand improve the generalization ability of the model.The recognition accuracies on the RAF-DB, FERPlus,and AffectNet datasets were 92.78%, 92.02%, and63.58%, respectively. Experiments show that this modelcan provide more effective solutions for FER tasks.展开更多
For the planar Z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessa...For the planar Z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessary and sufficient conditions for the existence of the bi-center are obtained. All possible first integrals are given. Under small Z2-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme （6 II 6） is proved.展开更多
An operator-splitting algorithm for the three-dimensional convection-diffusion equa- tion is presented.The flow region is discretized into tetrahedronal elements which are fixed in time. The transport equation is spli...An operator-splitting algorithm for the three-dimensional convection-diffusion equa- tion is presented.The flow region is discretized into tetrahedronal elements which are fixed in time. The transport equation is split into two successive initial value problems:a pure convection problem and a pure diffusion problem.For the pure convection problem,solutions are found by the method of characteristiCS.The solution algorithm involves tracing the characteristic lines backwards in time from a vertex of an element to an interior point.A cubic polynomial is used to interpolate the concentration and its derivatives within each element.For the diffusion problem,an explicit finite element algorithm is employed.Numerical examples are given which agree well with the analytical solutions.展开更多
Multiobjective trajectory planning is still face challenges due to certain practical requirements and mul-tiple contradicting objectives optimized simultaneously.In this paper,a multiobjective trajectory optimization ...Multiobjective trajectory planning is still face challenges due to certain practical requirements and mul-tiple contradicting objectives optimized simultaneously.In this paper,a multiobjective trajectory optimization approach that sets energy consumption,execution time,and excavation volume as the objective functions is presented for the electro-hydraulic shovel(EHS).The proposed cubic polynomial S-curve is employed to plan the crowd and hoist speed of EHS.Then,a novel hybrid constrained multiobjective evolutionary algorithm based on decomposition is proposed to deal with this constrained multiobjective optimization problem.The normalization of objectives is introduced to minimize the unfavorable effect of orders of magnitude.A novel hybrid constraint handling approach based onε-constraint and the adaptive penalty function method is utilized to discover infeasible solution information and improve population diversity.Finally,the entropy weight technique for order preference by similarity to an ideal solution method is used to select the most satisfied solution from the Pareto optimal set.The performance of the proposed strategy is validated and analyzed by a series of simulation and experimental studies.Results show that the proposed approach can provide the high-quality Pareto optimal solutions and outperforms other trajectory optimization schemes investigated in this article.展开更多
基金supported by the Innovation Fund Project for Graduate Students of Shanghai under Grant No. JWCXSL1301
文摘A method for isochromatic determination in three-fringe photoelasticity is presented. It combines the phaseshifting method with cubic polynomial curve-fitting technology to eliminate the errors caused by color repetition.We perform a demonstration of the method on a circular disc subjected to compressive loading and an injectionmolded cover with residual stresses. The test results compare well with the theoretical results.
文摘The papcr gives an approach to construct shape preserving piece wise cubic, where twocubic picces are allowed by inscrting at most a new knot in each data subinterval, and these cubicpieees is C2 continuous at each new knot. Two numerical examples show that the method is effec.tive and visually pleasing.
文摘We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson＇s minimal tori. This provides an alternative proof of the result by Perdomo （Characterization of order 3 algebraic immersed minimal surfaces of S3, Geom. Dedicata 129 （2007）, 23 34）.
基金Supported by National Natural Science Foundation of China(61572292,61373078,61272430)NSFC Joint Fund with Guangdong under Key Project(U1201258)
文摘A new method for constructing a fitting surface on a triangular grid is presented. Assuming images are obtained by sampling from the original scene. Conventional polynomial interpolation methods generally construct the fitting surface on a square grid. Different from existing methods, the new method constructs the fitting surface on a triangular grid which can divide the original surface more detailed and improve approximation accuracy. As the quality of the image edges plays a key role in visual effects of image, the new method uses image edges as constraints to get a triangle grid. The new method constructs a cubic polynomial patch locally using image data to approximate the original surface. Experimental comparison results of the new method with other methods show that the new method can produce high-quality images and remove the zigzagging artifact.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.62272281 and 62007017the Special Funds for Taishan Scholars Project under Grant No.tsqn202306274Youth Innovation Technology Project of the Higher School in Shandong Province under Grant No.2019KJN042.
文摘Recently, facial-expression recognition (FER)has primarily focused on images in the wild, includingfactors such as face occlusion and image blurring, ratherthan laboratory images. Complex field environmentshave introduced new challenges to FER. To addressthese challenges, this study proposes a cross-fusion dualattention network. The network comprises three parts:(1) a cross-fusion grouped dual-attention mechanism torefine local features and obtain global information;(2) aproposed C2 activation function construction method,which is a piecewise cubic polynomial with threedegrees of freedom, requiring less computation withimproved flexibility and recognition abilities, whichcan better address slow running speeds and neuroninactivation problems;and (3) a closed-loop operationbetween the self-attention distillation process andresidual connections to suppress redundant informationand improve the generalization ability of the model.The recognition accuracies on the RAF-DB, FERPlus,and AffectNet datasets were 92.78%, 92.02%, and63.58%, respectively. Experiments show that this modelcan provide more effective solutions for FER tasks.
基金Supported by National Natural Science Foundation of China （Grant Nos. 10831003 and 10771196）
文摘For the planar Z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessary and sufficient conditions for the existence of the bi-center are obtained. All possible first integrals are given. Under small Z2-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme （6 II 6） is proved.
文摘An operator-splitting algorithm for the three-dimensional convection-diffusion equa- tion is presented.The flow region is discretized into tetrahedronal elements which are fixed in time. The transport equation is split into two successive initial value problems:a pure convection problem and a pure diffusion problem.For the pure convection problem,solutions are found by the method of characteristiCS.The solution algorithm involves tracing the characteristic lines backwards in time from a vertex of an element to an interior point.A cubic polynomial is used to interpolate the concentration and its derivatives within each element.For the diffusion problem,an explicit finite element algorithm is employed.Numerical examples are given which agree well with the analytical solutions.
基金supported by the National Natural Science Foundation of China(Grant No.U1910211).
文摘Multiobjective trajectory planning is still face challenges due to certain practical requirements and mul-tiple contradicting objectives optimized simultaneously.In this paper,a multiobjective trajectory optimization approach that sets energy consumption,execution time,and excavation volume as the objective functions is presented for the electro-hydraulic shovel(EHS).The proposed cubic polynomial S-curve is employed to plan the crowd and hoist speed of EHS.Then,a novel hybrid constrained multiobjective evolutionary algorithm based on decomposition is proposed to deal with this constrained multiobjective optimization problem.The normalization of objectives is introduced to minimize the unfavorable effect of orders of magnitude.A novel hybrid constraint handling approach based onε-constraint and the adaptive penalty function method is utilized to discover infeasible solution information and improve population diversity.Finally,the entropy weight technique for order preference by similarity to an ideal solution method is used to select the most satisfied solution from the Pareto optimal set.The performance of the proposed strategy is validated and analyzed by a series of simulation and experimental studies.Results show that the proposed approach can provide the high-quality Pareto optimal solutions and outperforms other trajectory optimization schemes investigated in this article.
