Show that splitting an edge in a flow network yields an equivalent network. More formally, suppose that flow network G contains edge .u; /, and we create a new flow network G0 by creating a new vertex x and replacing .u; / by new edges .u; x/ and .x; / with c. u; x/ D c. x; / D c. u; /. Show that a maximum flow in G0 has the same value as a maximum flow in G.

Mariah was working on a multimedia presentation that included both video and audio files. the file was huge, and she wanted to send it to her coworker in another office. she needed to reduce the size of the file so that it could be transmitted faster. the utility she used to do this was

Answer the following questions regarding your system by using the commands listed in this chapter. for each question, write the command you used to obtain the answer. a. what are the total number of inodes in the root filesystem? how many are currently utilized? how many are available for use? b. what filesystems are currently mounted on your system? c. what filesystems are available to be mounted on your system? d. what filesystems will be automatically mounted at boot time?

In which part of a professional email should you try to be brief, but highly descriptive?