For a (molecular) graph G, the first and the second entire Zagreb indices are defined by the formulas M1εG=∑x∈VG∪EGdx2 and M2εG=∑xiseitheradjacentorincidenttoydxdy in which dx represents the degree of a vertex or an edge x. In the current manuscript, we establish some lower bounds on the first and the second entire Zagreb indices and determine the extremal trees which achieve these bounds.

Micro-metal products have recently enjoyed high demand. In addition, metal microforming has drawn increasing attention due to its net-forming capability, batch manufacturing potential, high product quality, and relatively low equipment cost. Micro-hydromechanical deep drawing (MHDD), a typical microforming method, has been developed to take advantage of hydraulic force. With reduced dimensions, the hydraulic pressure development changes; accordingly, the lubrication condition changes from the macroscale to the microscale. A Voronoi-based finite element model is proposed in this paper to consider the change in lubrication in MHDD according to open and closed lubricant pocket theory. Simulation results agree with experimental results concerning drawing force. Changes in friction significantly affect the drawing process and the drawn cups. Moreover, defined wrinkle indexes have been shown to have a complex relationship with hydraulic pressure. High hydraulic pressure can increase the maximum drawing ratio (drawn cup height), whereas the surface finish represented by the wear is not linearly dependent on the hydraulic pressure due to the wrinkles.

Turn-Milling Combined NC machine tool is different from traditional machine tools in structure and process realization. As an important means in the design stage, the analysis method of geometric accuracy error is also different from the traditional method. The actual errors and the error compensation values are a pair of "symmetry" data sets which are connected by the movement of machine tools. The authors try to make them more consistent through this work. The geometric error terms were firstly determined by topological structure analysis, then based on homogeneous coordinate transformation and multibody system theory, the geometric error model was established. With the interval theory, the function rule of sensitivity of geometric error sources to spatial errors was analyzed in detail, and the global maximum interval sensitivity of nine geometric error sources was extracted, providing a theoretical basis for error compensation and precision distribution. The geometric error sensitivity analysis method proposed in this paper can accurately evaluate the influence weights of each error term on the machining accuracy, and identify the important sensitive error terms with great influence on the machining accuracy from many error terms.

In the process of human–robot collaborative assembly, robots need to recognize and predict human behaviors accurately, and then perform autonomous control and work route planning in real-time. To support the judgment of human intervention behaviors and meet the need of real-time human–robot collaboration, the Fast Spatial–Temporal Transformer Network (FST-Trans), an accurate prediction method of human assembly actions, is proposed. We tried to maximize the symmetry between the prediction results and the actual action while meeting the real-time requirement. With concise and efficient structural design, FST-Trans can learn about the spatial–temporal interactions of human joints during assembly in the same latent space and capture more complex motion dynamics. Considering the inconsistent assembly rates of different individuals, the network is forced to learn more motion variations by introducing velocity–acceleration loss, realizing accurate prediction of assembly actions. An assembly dataset was collected and constructed for detailed comparative experiments and ablation studies, and the experimental results demonstrate the effectiveness of the proposed method.

Li, P.Z.; Zheng, Y.B., and Luo, L., 2020. An ANN based optimization algorithm for diffracted laser beam shaping. In: Guido Aldana, P.A. and Kantamaneni, K. (eds.), Advances in Water Resources, Coastal Management, and Marine Science Technology. Journal of Coastal Research, Special Issue No. 104, pp. 255–260. Coconut Creek (Florida), ISSN 0749-0208.To overcome the lack of flexibility in laser beam shaping in current industrial applications, a new improved artificial neural network algorithm for diffracted laser beam shaping is proposed. Aiming at the existing problems in laser beam shaping, the Unet neural network algorithm is improved from the label image and convolution operation. By clarifying its training and application steps, the improved neural network algorithm is pre-trained firstly and then formally trained (full training). The result shows that the UNet neural network algorithm can gradually realize the laser beam shaping with the spatial light modulator and find the mapping relationship between the input image (phase diagram) and the output image (laser contour diagram).