what does this symbol mean: [] but without the top bars?

Question

What does the highlighted symbol mean? What are the details of this method?

Answer 1

The symbol $\lfloor\cdot\rfloor$ usually denotes the floor function. $\lfloor x\rfloor$ is the largest integer not greater than $x$, i.e. $$ \lfloor x \rfloor=\max\, \{m\in\mathbb{Z}\mid m\le x\} $$ for each $x\in\mathbb R$.

Answer 2

This answer relates only to the first question.

$\lfloor x \rfloor$ is the floor function, which rounds down $x$ to nearest integer.

Answer 3

It's the floor function. It's shorthand for the largest integer not greater than $T_w$.

Answer 4

Tangentially, if you want to reproduce a symbol here and you don't know its Latex code, I encourage you to try detexify, which is as fun as it is powerful.