Velocity is the change in position (x), or distance, over time. If you know the change in position and the amount of time taken to complete the journey, you can determine velocity. Similarly, if you have any two of these variables, you can always solve for the third. The relationship ...
We see that over time, the velocity of our object increases. And we are told this increase happens at a constant rate. Therefore, the object accelerates constantly, and since acceleration in general equals a change in velocity divided by a corresponding change in time, we can write𝑎=𝑣...
If the signed distance function is introduced, the narrow-band transition domain occupied with intermediate material will have a uniform width that equals 2Δ everywhere. Therefore, the level-set function should be properly selected. In fact, the material transition width should be distance-dependent...
If m equals the ‘diameter’ of a network (i.e., the length of the longest geodesic between any pair of vertices), one obtains a reachability index, the number of others that a vertex can reach via paths of any finite length. In Figure 1, vertex F can reach 8 of the other 10 ...
In Euclidean space, the sum of the angles of a triangle equals 180º and squares have all their angles equal to 90º; always. This is something we all take for granted, but this is not true in all spaces. Let's also not confuse Euclidean space with multidimensional spaces. Euclidean...
. . , t}, there exists a codeword [Math Processing Error]yi∈ker(H) such that the restriction of yi to the coordinates in [Math Processing Error]V~′′ equals [Math Processing Error](yi|V~′′)j={1,j=i0,j≠i (28) i.e. on the coordinates [Math Processing Error]V~′′...
In particular, the labeled interleaving distance between merge trees can be computed in polynomial time. In this work, we define the labeled interleaving distance for labeled Reeb graphs. We then prove that the (ordinary) interleaving distance between Reeb graphs equals the minimum of the labeled ...
In particular, if the RF distance equals zero, it means exact topology match between the two trees. All experiments are preformed in an Apple Macbook Pro (Mid-2012 model) running Mac OS 10.10.4 (OS X Yosemite). The machine features a 2.9 GHz dual-core Intel Core i7-3667U processor ...
Distance equals velocity times time, or we could just simply race to the finish line. Art Puns Why did the bald man decide to paint a bunch of rabbits on his head? He thought that they could look like hares from a distance. Rabbit Puns Why did the bald man paint rabbits on his...
As a result, light travel time is now our primary unit of measurement. In other words, a distance of one light-second (the amount of space covered by light in one second) equals 299,792,458.6 metres. In just one second, light travels almost 300 million metres; light travels really ...