SHAPE PRESERVING INTERPOLATION USING PIECEWISE CUBIC

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.

DEGREE 3 ALGEBRAIC MINIMAL SURFACES IN THE 3-SPHERE

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）.

Cubic polynomial curve-guided method for isochromatic determination in three-fringe photoelasticity

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.

Image interpolation algorithm on a triangular grid

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.

Complete Study on a Bi-Center Problem for the Z2-Equivariant Cubic Vector Fields

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.

CF-DAN: Facial-expression recognition based on cross-fusion dual-attention network

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.

AN OPERATOR-SPLITTING ALGORITHM FOR THREE-DIMEN-SIONAL CONVECTION-DIFFUSION PROBLEMS

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.

Multiobjective trajectory optimization of intelligent electro-hydraulic shovel

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.