In this paper, it is shown that Hardy-Hilbert＇s integral inequality with parameter is improved by means of a sharpening of Hoeder＇s inequality. A new inequality is established as follows：∫^∞α∫^∞α f（x）g（y）...In this paper, it is shown that Hardy-Hilbert＇s integral inequality with parameter is improved by means of a sharpening of Hoeder＇s inequality. A new inequality is established as follows：∫^∞α∫^∞α f（x）g（y）/（x＋y＋2β）dxdy〈π/sin（π/p）{∫^∞α f^p（x）dx}1/p·{∫^∞αgq（x）dx}1/q·（1-R）^m,where R=（Sp （F, h） - Sq （G, h））^2, m= min （1/p, 1/q）. As application; an extension of Hardy-Littlewood＇s inequality is given.展开更多
A series of experiments were performed on three types of closed loop pulsating heat pipes （PHPs）, intending to investigate various kinds of flow patterns, and to develop some improved configurations for the PHPs. Op...A series of experiments were performed on three types of closed loop pulsating heat pipes （PHPs）, intending to investigate various kinds of flow patterns, and to develop some improved configurations for the PHPs. Optical visualization results indicated that there might exist three flow patterns, i.e. bubble-liquid slug flow, semi-annular flow and annular flow, corresponding to different working conditions. For a given geometry and an adequate fill ratio, the PHPs had the self-adjusting characteristic for the flow patterns （from slug flow to semi-annular and then to annular flow） to meet the demands of the increasing heat input. Two special configurations, one with alternately varying channel diameter, the other equipped with one section of thicker tube, were found to be advantageous in establishing and maintaining reliable circulation of the working fluid. The thermal performance of the PHPs was examined over a range of working conditions. Comparing with the normal PHP with uniform diameter, either of the improved PHPs exhibited higher thermal performance.展开更多
文摘In this paper, it is shown that Hardy-Hilbert＇s integral inequality with parameter is improved by means of a sharpening of Hoeder＇s inequality. A new inequality is established as follows：∫^∞α∫^∞α f（x）g（y）/（x＋y＋2β）dxdy〈π/sin（π/p）{∫^∞α f^p（x）dx}1/p·{∫^∞αgq（x）dx}1/q·（1-R）^m,where R=（Sp （F, h） - Sq （G, h））^2, m= min （1/p, 1/q）. As application; an extension of Hardy-Littlewood＇s inequality is given.
基金the National Natural Science Foundation of China under contract 60672151 , 60532020.
文摘A series of experiments were performed on three types of closed loop pulsating heat pipes （PHPs）, intending to investigate various kinds of flow patterns, and to develop some improved configurations for the PHPs. Optical visualization results indicated that there might exist three flow patterns, i.e. bubble-liquid slug flow, semi-annular flow and annular flow, corresponding to different working conditions. For a given geometry and an adequate fill ratio, the PHPs had the self-adjusting characteristic for the flow patterns （from slug flow to semi-annular and then to annular flow） to meet the demands of the increasing heat input. Two special configurations, one with alternately varying channel diameter, the other equipped with one section of thicker tube, were found to be advantageous in establishing and maintaining reliable circulation of the working fluid. The thermal performance of the PHPs was examined over a range of working conditions. Comparing with the normal PHP with uniform diameter, either of the improved PHPs exhibited higher thermal performance.
