… Collatz function”, we treat mainly the bijectivity of the Collatz … computations of the values of
the Collatz function. In the third … recursive calls) of the Collatz function. A comparison between … …Collatz 函数“，我们主要处理 Collatz 的双射性 ...计算 Collatz 函数。在第三...递归调用）。比较 ...

… for possibly proving Collatz Conjecture (CC). We propose Reduced Collatz Conjecture (RCC…
For proving RCC, we propose exploring laws of Reduced Collatz Dynamics (RCD), ie, from … …可能证明 Collatz猜想 （CC）。我们提出了简化 Collatz猜想 （RCC... 为了证明 RCC，我们建议探索约化 Collatz 动力学 （RCD） 定律，即，从......

… the proof of the Collatz conjecture for many types of sets … Collatz conjecture is an unsolved
problem in mathematics as it has been for more than 60 years. It is named after Lothar Collatz … …许多类型集合的 Collatz猜想的证明......Collatz猜想是一个未解之谜 60 多年来一直是数学问题。它以 Lothar Collatz 的名字命名......

… We explore the Collatz conjecture and its variants through … the iterated application of the
Collatz function on strings … system is equivalent to the Collatz conjecture. To show the feasibility … …我们通过以下方式探索 Collatz猜想及其变体......Collatz 函数在字符串上的迭代应用程序 ...系统等同于 Collatz猜想。为了显示可行性 ...

… This is actually the area that the “creator” of the problem, Lothar Collatz, was working on.
Although his examples are different from what is now known as the Collatz Conjecture (CC), … …这实际上是问题的“创造者”Lothar Collatz 正在研究的领域。 尽管他的例子与现在所谓的 Collatz猜想 （CC） 不同，但......

… , mathematical phenomenon related to the conjecture may be of … Collatz conjecture; this
section is broken up into two sections with the first focusing on determining the number of Collatz … ...，与猜想相关的数学现象可能是......Collatz猜想;这 部分分为两个部分，第一个部分侧重于确定 Collatz 的数量......

… The purpose of this study is to prove the Collatz conjecture … by 2 is performed in the Collatz
operation. Then, the star … same meaning as the Collatz conjecture. Theorem proving support … …本研究的目的是证明 Collatz猜想......by 2 在 Collatz 中执行 操作。然后，星星......与 Collatz猜想的含义相同。定理证明支持 ...

… allowed me to prove new theorems, formulate new conjectures and strengthened my faith
that someday we will be able to prove that the Collatz Conjecture is true. Therefore, I feel as … …让我证明新的定理，提出新的猜想，并增强我的信仰 总有一天，我们将能够证明 Collatz猜想是正确的。因此，我觉得......

… This paper proposes a new hashing function based on the modified Collatz conjecture,
Chaos theory and sine infinity as discussed in Section 2.2. The mathematical description of the … …本文基于修正的 Collatz猜想，提出了一种新的哈希函数， 混沌理论和正弦无穷大，如 2.2 节所述。数学描述 ...

… famous open problems in mathematics, namely the Collatz conjecture. The first part of the
paper is … The second part is dedicated to the visualization of behaviors of the Collatz iteration … …数学中著名的开放问题，即 Collatz猜想。第一部分 纸张是 ...第二部分专门介绍 Collatz 迭代行为的可视化......