Authentication information is generated for a group where members within a group are able to communicate with each other, but a non-members is not able to participate in that communication. In one example, during purging of stored fuel vapors, a number of fuel injections to a cylinder during a cylinder cycle are maximized to reduce soot formation. In this manner, a substantially continuous oxide region is formed throughout the plurality of trenches. Furthermore, it is easy to dispose the spent waste water treating material. The collimating lenses are formed in the light pipe.