AI 中文总结
针对两站点移动目标搜索问题，在MacPhee和Jordan部分证明的基础上，完整证明了Ross猜想在整个正行列式参数区域成立，解决了该猜想的剩余情况。
AI 中文摘要
一个目标根据2×2转移矩阵M的离散时间马尔可夫链在两个站点之间移动。每一轮搜索一个站点需付出正成本，且搜索可能忽略存在的目标。Ross猜想最优策略关于目标在站点1的后验概率是阈值型的。MacPhee和Jordan在非正行列式（det M≤0）区域及部分正行列式（det M>0）区域证明了该猜想，剩余情况未解决。我们在整个正行列式区域证明了阈值最优性，完成了所有参数取值下的Ross猜想。
英文摘要
A target moves between two sites according to a discrete-time Markov chain with a $2\times2$ transition matrix $M$. At each epoch one site is searched at positive cost, and a search may overlook a target that is present. Ross conjectured that an optimal policy is threshold in the posterior probability that the target is at site~1. MacPhee and Jordan proved the conjecture throughout the nonpositive-determinant ($\det M\le0$) regime and for part of the positive-determinant ($\det M>0$) regime, leaving the remaining cases open. We prove threshold optimality throughout the positive-determinant regime, completing Ross's conjecture for all parameter values.
