\frac { \dot { \Delta P } _ { N } } { P _ { 0 } } \sim \gamma ^ { 2 } \frac { P _ { 0 } P _ { N } } { \alpha ^ { 2 } } \int _ { W } d \omega _ { 1 } \int _ { W } d \omega _ { 2 } \int _ { W } d \omega _ { 3 } \int _ { W } d \omega _ { 3 } \int _ { W } d \omega S [ \omega _ { 1 } , \omega _ { 2 } \rightarrow \omega _ { 3 } , \omega
I converted the mathematical image to latex and my latex is "<pre>\frac { \dot { \Delta P } _ { N } } { P _ { 0 } } \sim \gamma ^ { 2 } \frac { P _ { 0 } P _ { N } } { \alpha ^ { 2 } } \int _ { W } d \omega _ { 1 } \int _ { W } d \omega _ { 2 } \int _ { W } d \omega _ { 3 } \int _ { W } d \omega _ { 3 } \int _ { W } d \omega S [ \omega _ { 1 } , \omega _ { 2 } \rightarrow \omega _ { 3 } , \omega
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