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obladi
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Joined: October 16th, 2004, 4:05 am

partial derivatives

February 4th, 2006, 5:52 am

Hello,I have the following expressiongCan I have the expression equivalent to the above one, perhapsor of the form??If I can have those forms, in what condition?Thanks a lot.
 
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vplanas
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partial derivatives

February 4th, 2006, 7:30 am

The square of an operator is the operator acting twice on the function and by symmetry of the second derivatives (if they exists) you arrive to your first expression.victor
 
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ppauper
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Joined: November 15th, 2001, 1:29 pm

partial derivatives

February 4th, 2006, 1:17 pm

in addition to vplanas's form,you could also "diagonalize" it by changing coordinates to lose the cross term
 
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obladi
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Joined: October 16th, 2004, 4:05 am

partial derivatives

February 4th, 2006, 3:30 pm

In fact, I wanted to use argument that( A + B )^2 >=0 In this case, can I use this kind of argument?Perhaps, I can not.