What is the meaning of the math symbol "$\theta$", as in "$\theta(31\pi-t)\,\theta(t-27\pi)$"?

Question

What would be the meaning of the sign "$\theta$" that looks like a slashed zero?

Thanks in advance.

Answer 1

I have seen it used for a unit step function, which is $1$ if the argument is positive and $0$ if the argument is negative. For most uses you don't care what happens at $0$, but it is often taken to be $\frac 12.$ In your example, the expression would be $0$ outside the interval $[27\pi, 31\pi]$ and the theta functions would multiply to $1$ within that interval and $\frac 12$ at the endpoints.