Scared 2 be lonely beat（当真爱降临）

In this work we tried to prove the lonely runner conjecture also known as the view obstruction problem.

The lonely runner conjecture, now over fifty years old, concerns the following problem. On a unit length circular track, consider $m$ runners starting at the same time and place, each runner having a different constant speed. The conjecture asserts that each runner is lonely at some point in time, meaning distance at least $1/m$ from the others. We formulate a function field analogue, and give a positive answer in some cases in the new setting.

论文为了确定CD法施工中临时横撑的设置对控制地表沉降的效果，结合重庆轨道交通四号线鱼嘴站暗挖隧道下穿既有建筑物工程，通过数值计算模拟了CD法设置临时横撑与未设置临时横撑两种工况，探讨了临时横撑对提高隧道施工期间稳定性、控制地表沉降的作用效果。结果表明，设置临时横撑对提高隧道施工期间稳定性、控制地表沉降效果不显著。

The lonely branching random walks on ${\mathbb Z}^d$ is an interacting particle system where each particle moves as an independent random walk and undergoes critical binary branching when it is alone. We show that if the symmetrized walk is recurrent, lonely branching random walks die out locally. Furthermore, the same result holds if additional branching is allowed when the walk is not alone.