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D.H. Bailey 《Journal of Symbolic Computation》2011,46(7):741-754
One of the most fruitful advances in the field of experimental mathematics has been the development of practical methods for very high-precision numerical integration, a quest initiated by Keith Geddes and other researchers in the 1980s and 1990s. These techniques, when coupled with equally powerful integer relation detection methods, have resulted in the analytic evaluation of many integrals that previously were beyond the realm of symbolic techniques. This paper presents a survey of the current state-of-the-art in this area (including results by the present authors and others), mentions some new results, and then sketches what challenges lie ahead. 相似文献
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Precision position control using combined piezo-VCM actuators 总被引:2,自引:0,他引:2
This paper presents the control performance of a high-precision positioning table using the hybrid actuators composed of the piezoelectric (PZT) actuators and voice-coil motors (VCMs). The combined piezo-VCM actuator features two main characteristics, i.e., a large operation range due to the long stroke of VCM, and a high precision and heavy load positioning ability due to the actuation of PZT impact force. In this paper, a one-degree-of-freedom (1-DOF) experimental setup was configured to examine the control performance and the parametric identification for the VCM was performed based on the recursive-least-square (RLS) method. The control performance was effectively demonstrated by using a switching controller configured by an integral variable structure controller (IVSC) for the VCM to conduct rough position control and an impact force controller (IFC) for the PZT actuator to conduct fine position control. The experimental results showed that the positioning table having mass 881 g was successfully positioned within the positioning accuracy of 10 nm by both the forward and backward positioning processes. In the forward control, it totally took 1.253 s for the sliding table to reach the target position of 450 μm; in the backward control, it took 1.387 s for the sliding table moving from the position of 450 μm to the target position of 200 μm. 相似文献
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Since conventional mechanical punching technology for Flexible Printed Circuit Board (FPCB) drilling has restricted via-hole size and depth control for multi-layer circuit boards, CO2 and Ultra Violet (UV) laser drilling technologies have been developed. However, the FPCBs for mobile phones and Personal Digital Assistants (PDAs) require smaller via-hole diameters, since the development of thinner and higher circuit density devices is demanded. Currently, UV laser systems are widely used for FPCB drilling of 75–105 μm diameter via-holes and inspectors performs quality test manually using microscopes. We developed a high-precision UV laser microfabrication system for next-generation FPCB drilling of 15 μm diameter via-holes. The degrees of the precision of the microfabricated via-holes of 15, 35, 50 and 85 μm were mean absolute error rate of 4.4, 2.2, 2.3, and 2.2 which was fully satisfied with industrial inspection specification ±10%. The drilling speed of the system of 2800 via-holes per second at stationary state was achieved. In addition, we applied modified Greedy 2-opt algorithm to find out optimal drilling path which reduced the total time of via-hole fabrication. We successfully reduced the production time by 25% compared with the result obtained in the normal Greedy 2-opt algorithm. Moreover, we designed very accurate inspection method using Canny edge detection and geometric pattern matching algorithms and successfully applied it to the Automated Optical Inspection (AOI) module for the inspections of 15 μm diameter via-hole which was required for the fabrication of high density FPCB. 相似文献
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Fabrication of arrays of line with a nanoscale width less than 150 nm and length over 1500 μm on SU8 resist was proposed when using SEM-converted exposure system with high-precision positioning stage. Investigating the effect of the stage movement and the local-aperture contamination on stitching errors, we found that changing the deflector gain factors and the cleaning aperture after each exposure made it possible to improve stitching accuracy. Overlapping length 200 nm of line arrays was obtained with increase of 0.35% in x direction and 0.16% in y direction for deflection gain factors. 相似文献
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In laser beam welding, when the width of weld seam is less than 0.1?mm, present vision sensor-based measurements can barely obtain the seam width and seam position stably and reliably. A seam measuring method based on narrow depth of field (NDOF) is proposed in this article, which aims to detect this kind of narrow and small weld seam with great accuracy. This measurement system consists of a multiple optical magnifier, a Charge-Coupled Device/Complementary Metal Oxide Semiconductors (CCD/CMOS) camera, and an external light-emitting diode lighting unit. First, the principle of the NDOF method is explained. Second, key features of weld seam are extracted by image-processing algorithm. Lastly, the result of experiment reveals that the NDOF method can meet the demanded detection precision. Measurement accuracy for the seam width and seam position is 6 and 8?μm, respectively. 相似文献
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CCD图象的解调测量法可以实现图象边缘点的高分辨率检测,达到高精度尺寸测量的目的。采用这种方法测量数据的产生速率由高频电子细分频率决定,数据量上被测量 图象中需检测的边缘点的多少决定。本文介绍了测量图象边缘间距或中心距CCD图象解调测量法的数据采集、存贮和与微机接口方法。实现高精度、高速度、多边级点大数据量数据的实时有效采集及存贮,并可以和微机系统接口。 相似文献
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