Mass (say) 1 kilogram. Then we can measure the mass of any other object in the universe by colliding it with the reference object and measuring the accelerations. Additionally, mass relates a body's momentum p to its linear velocity v: and the body's kinetic energy "K" to its velocity: The primary difficulty with Mach's definition of mass is that it fails to take into account the potential energy (or binding energy) needed to bring two masses sufficiently close to one another to perform the measurement of mass. This is most vividly demonstrated by comparing the mass of the proton in the
Dot product representation of a graph Dot product representation of a graph A dot product representation of a simple graph is a method of representing a graph using vector spaces and the dot product from linear algebra. Every graph has a dot product representation. Let "G" be a graph with vertex set "V". Let "F" be a field, and "f" a function from "V" to "F" such that "xy" is an edge of "G" if and only if "f"("x")·"f"("y") ≥ "t". This is the dot product representation of "G". The number "t" is called the dot product threshold, and the smallest possible value of "k" is