【数论系列报告五】：Zeros of quadratic forms in prime coordinates
讲座名称：
【数论系列报告五】：Zeros of quadratic forms in prime coordinates
讲座时间：
2017-06-14
讲座人：
赵立璐
形式：
校区：
兴庆校区
实践学分：
讲座内容：
【数论系列报告五】
讲座题目: Zeros of quadratic forms in prime coordinates
讲座时间: 2017.06.14 (周三) 上午09:00 – 10:30
讲座地点: 理科楼407室
讲座人：赵立璐教授 (山东大学)
讲座摘要:
Let $f(x_1,\ldots,x_n)$ be a nondegenerate indefinite quadratic form. In this talk, we discuss the existence of primes $p_1,\ldots,p_n$ such that $f(p_1,\ldots,p_n)=0$. In particular, we shall establish the local to global principle for the existence of zeors of quadratic forms in prime coordinates.
xist widely in nature and industrial processes, and often involve thin film constructions. Here we represent two experimental realizations in which high-speed video imaging technique is used to accurately measure film profiles, for investigating dominant forces that governing thin film stability, and the fluid dynamics in film evolution. In the first example the stability of a thin film trapped between a rising bubble and a liquid-liquid meniscus interface is studied, to demonstrate the validity of using surface forces to predict film stability, with an emphasis that a short-ranged hydrophobic attraction determines the stability of thin water films. In the second system drop impact onto a solid surface is considered. Owing to viscous lubrication pressure in the intervening air layer, the first contact does not occur at a point but along a ring, leading to the entrapment of a small bubble under drop center. We use high-speed interferometry at 5 million frames per second to reveal the details of this process, including air disc size at first contact, air compression dynamics, as well as the liquid-solid contact mechanism. The effects of surface roughness on the first impact are also investigated.
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