In this paper,we prove the extreme values of L-functions at the central point for almost prime quadratic twists of an elliptic curve.As an application,we get the extreme values for the Tate-Shafarevich groups in the q...In this paper,we prove the extreme values of L-functions at the central point for almost prime quadratic twists of an elliptic curve.As an application,we get the extreme values for the Tate-Shafarevich groups in the quadratic twist family of an elliptic curve under the Birch and Swinnerton-Dyer conjecture.展开更多
In order to study the pressure characteristics of slug flow in horizontal curved tubes,two kinds of curved tubes with central angle 45° and 90° respectively are studied,of which are with 0. 5m circumference ...In order to study the pressure characteristics of slug flow in horizontal curved tubes,two kinds of curved tubes with central angle 45° and 90° respectively are studied,of which are with 0. 5m circumference and 26 mm inner diameter are used. When the superficial liquid velocity or the superficial gas velocity is constant,the pressure fluctuations and the probability distribution of the average velocity of slug flow are clear for all of the five experimental conditions. The results of experiment show that the pressure characteristics of slug flow in curved tubes have periodic fluctuations. With the rise of central angle,the period of pressure fluctuation is more obvious. The system pressure of the slug flow increases with the increasing of superficial liquid/gas velocity. Meanwhile,the probability distribution of pressure signal shows regularity,such as unimodal,bimodal or multimodal.展开更多
基金supported by the National Key R&D Program of China (Grant No. 2021YFA1000700)National Natural Science Foundation of China (Grant Nos. 12001314 and 12031008)。
文摘In this paper,we prove the extreme values of L-functions at the central point for almost prime quadratic twists of an elliptic curve.As an application,we get the extreme values for the Tate-Shafarevich groups in the quadratic twist family of an elliptic curve under the Birch and Swinnerton-Dyer conjecture.
基金Supported by the National Natural Science Foundation of China(No.5130416)
文摘In order to study the pressure characteristics of slug flow in horizontal curved tubes,two kinds of curved tubes with central angle 45° and 90° respectively are studied,of which are with 0. 5m circumference and 26 mm inner diameter are used. When the superficial liquid velocity or the superficial gas velocity is constant,the pressure fluctuations and the probability distribution of the average velocity of slug flow are clear for all of the five experimental conditions. The results of experiment show that the pressure characteristics of slug flow in curved tubes have periodic fluctuations. With the rise of central angle,the period of pressure fluctuation is more obvious. The system pressure of the slug flow increases with the increasing of superficial liquid/gas velocity. Meanwhile,the probability distribution of pressure signal shows regularity,such as unimodal,bimodal or multimodal.
