Dear Hai.Caohoang,
I'm not sure I fully understand everything you are saying; however you have to remember that the mass of a particle does not just affect its inertia but is also related to the particle's gravitational field strength. Therefore, if a particle was travelling through a vacuum, i.e. not impacting upon anything, we could still measure its mass by determining its gravitational strength. (If the particle was very small then measuring its gravitational field strength would be difficult, but that does not mean it would not have mass.) Thus the question is whether you define mass from a gravitational or inertial point of view. We note that it has been shown that the gravitational and inertial masses have the same value, but it is not currently understood why this is the case. Hence it would appear to us that to better understand mass, science needs to understand why these masses are the same, i.e. why inertia and gravity are linked.
In this paper, though, we are not dealing with where mass comes from or the link between gravitational and inertial mass. What we are proposing here is that electromagnetic waves can have mass when they are travelling slower than the speed of light in a vacuum. In particular when a wave is travelling at the speed of light in a vacuum it has no mass, but as it speed decreases, its mass increases, such that its maximum mass is portrayed when the "wave's speed is zero". Moreover, the amount of mass a particular wave has for a given speed is also dependent upon the wave's frequency. Thus a gamma ray will have more mass than a radio wave, at a given speed, which is less than the speed of light in a vacuum (at this speed they would both have no mass).
Hopefully this has answered your question, but if not or you have more, then please let me know.
Mark