In the present paper, we study the limit sets of the almost periodic functions $f(x)$. It is interesting that the values $r=\inf|f(x)|$ and $R=\sup|f(x)|$ may be expressed in the exact form. We show that the ring $r\leq |z|\leq R$ is the limit set of the almost periodic function $f(x)$ (under some natural conditions on $f$). The exact expression for $r$ coincides with the well known partition problem formula and gives a new analytical method of solving the corresponding partition problem. Several interesting examples are considered. For instance, in the case of the five numbers, the well-known Karmarkar--Karp algorithm gives the value $m=2$ as the solution of the partition problem in our example, and our method gives the correct answer $m=0.$ The figures presented in Appendix illustrate our results.

翻译：在本文件中,我们研究了几乎定期函数的上限(f(x)美元)。有趣的是,美元和美元(s)+(x) 美元和美元(sup) +(x) 美元可以以精确的形式表示。我们显示,美元和美元(x)是几乎定期函数的上限(f(x)美元(在某种自然条件下,以美元计,以美元计,以美元计,以美元计)。美元的确切表示与众所周知的分区问题公式相吻合,并提供了解决相应的分区问题的新的分析方法。我们考虑了几个有趣的例子。例如,在五个数字中,众所周知的Karmarkar-Karp算法提供了价值=2美元,作为我们例子中分割问题的解决方案,我们的方法给出了正确的答案(x)美元=0美元。附录中的数字说明了我们的结果。