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THE INTEGRAL FORMULA FOR CALCULATINGTHE HAUSDORFF MEASURE OF SOME FRACTAL SETS
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作者 Lu Shipan (Jimei University, China) Su Weiyi (Nanjing University, China) 《Analysis in Theory and Applications》 2001年第1期70-75,共6页
It is important to calculate the Hausdorff dimension and the Hausdorff mesure respect to this dimension for some fractal sets. By using the usual method of “Mass Distribution”, we can only calculate the Hausdorff di... It is important to calculate the Hausdorff dimension and the Hausdorff mesure respect to this dimension for some fractal sets. By using the usual method of “Mass Distribution”, we can only calculate the Hausdorff dimension. In this paper, we will construct an integral formula by using lower inverse s-density and then use it to calculate the Hausdorff measures for some fractional dimensional sets. 展开更多
关键词 THE INTEGRAL formula FOR CALCULATINGTHE HAUSDORFF MEASURE OF SOME FRACTAL SETS
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INFLUENCE OF CAPILLARITY ON NANO-LITER FLOWRATE MEASUREMET WITH DISPLACEMET METHOD 被引量:2
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作者 GUO Qiang CHENG Rui SILBER-LI Zhan-hua 《Journal of Hydrodynamics》 SCIE EI CSCD 2007年第5期594-600,共7页
Nanoqiter flowrate measurements in micro-tubes with displacement method were performed and the effect of capillarity force on the accuracy was investigated through lab experiments and theoretical analysis in this arti... Nanoqiter flowrate measurements in micro-tubes with displacement method were performed and the effect of capillarity force on the accuracy was investigated through lab experiments and theoretical analysis in this article. The experiments were conducted under the pressure drops ranging from 1 kPa to 10 kPa in a circular pipe with a diameter of 50 pm, to give the pressure-flowrate (P-Q) relation and verify the applicability of the classical Hagen-Poiseuille (HP) formula. The experimental results showed that there existed a discrepancy between the experimental data and the theoretical values predicted by the HP formula if the capillary effect was not considered, which exceeded obviously the limit of the system error. And hence a modified formula for the relation, taking the capillary effect into account, was presented through theoretical deduction, and after the HP formula had been modified the error was proved to be less than 3%, which was permitted in comparison with the system error. It was also concluded that only by eliminating the effect of the capillary force in experiments could the original HP formula be employed to predict the pressure-flowrate relation in the Hagen-Poiseuille flow in the micro-tube. 展开更多
关键词 nano-liter flowrate measurement Hagen-Poiseuille (HP) formula displacement method capillarity force
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