diff --git a/math.tex b/math.tex
index 0931a73..2181517 100644
--- a/math.tex
+++ b/math.tex
@@ -40,9 +40,12 @@
 
 \newcommand{\sbk}[1]{\left( #1 \right)}
 \newcommand{\sqbk}[1]{\left[ #1 \right]}
+\newcommand{\ssbk}[1]{\left< #1 \right>}
 \newcommand{\detb}[1]{\det\sqbk{#1}}
 \newcommand{\cosb}[1]{\cos\sbk{#1}}
 \newcommand{\sinb}[1]{\sin\sbk{#1}}
+\newcommand{\arcsinb}[1]{\arcsin\sbk{#1}}
+\newcommand{\bigOb}[1]{\bigO\sbk{#1}}
 
 
 \newcommand{\levicivita}[1]{\varepsilon_{#1}}