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Is it possible to take shallow depth of field photos with point-and-shoot cameras?

When I shoot portraits with my brother's Nikon D90, this is quite easy to fade out the background. But with my Fuji HS10, super-zoom camera, I haven't been able to take such photos yet. I choose a large aperture for my camera but it still doesn't work. I know that standing further and zooming will result in a smaller depth of field. Why DSLR cameras are so much better in this area? Why zooming make the depth of field smaller? What are the general recommendations to do the job using a super-zoom?