machine learning - valid kernel functions for SVM -

i implementing svm following kernel functions:

assume , b scalars:

1. k(a,b) = (a-b)^4

2. k(a,b) = alpha * ab, alpha >=0

3. k(a,b) = (ab+1)^4

are these valid kernels?

thanks help! :)

2 , 3 specific polyonmial kernels k(a,b)=(alpha*<a,b>+c)^p while first 1 not valid scalar product k(a,a)=0 imply each x, phi(x)=0, imply a,b,c,d, k(a,b)=k(c,d) (in other words, kernel constant, not true, contradiction).