My understanding is that a warrant could allow one (let's say owning 5,000 shares) to buy additionnal shares at a "presumably discounted price" (let's say in our case at $0.75) within a certain period of time (let's say during 2006).
If you do, you chip in more and sell right away (increasing offer) if there is demand at a price higher than $0.75 or keep them (averaging down).
However, unless a simultaneous share buyback is announced and executed, you are being diluted.
If by the end of 2006 (in our example) you did not exercise your warrants (buying shares at $0.75) then it dies by Dec.31st.
Not being an expert in the matter, I stand to be corrected.