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$$f(x,y)~=~ (a\,x)^2 +(b\,y)^2-\cos c\,x \,\cos d\,y$$$$f(x,y)~=~ \frac{-1}{1+ x^2 + y^2}-\cos (a\,x) \,\cos (b\,y)\,e^{-\frac{x^2 + y^2}{c^2}}$$ for $a,b,c,d\in \mathbb{R}$$a,b,c \in \mathbb{R}^+$, where $a,b$ are$c $ is sufficiently smalllarge.
$$f(x,y)~=~ (a\,x)^2 +(b\,y)^2-\cos c\,x \,\cos d\,y$$ for $a,b,c,d\in \mathbb{R}$, where $a,b$ are sufficiently small.
$$f(x,y)~=~ \frac{-1}{1+ x^2 + y^2}-\cos (a\,x) \,\cos (b\,y)\,e^{-\frac{x^2 + y^2}{c^2}}$$ for $a,b,c \in \mathbb{R}^+$, where $c $ is sufficiently large.
