i'm not sure i understand exactly what you meant by pairwise collisions.
if i have 100 particles, each with the same probability distribution of velocities going towards my particle X (assume none of these particles collide with each other but all start at different positions...each position...
so i have a problem which can be formulated in the following way:
assume you have n particles and you know the initial position of each. There is some probability distribution P which contains the probability of having a particular velocity. Now, each particle has this same probability...
so if we take some point P which is not 0, what would P's neighborhood consist of? and what would happen to the neighborhood when we take subsets of RP^n
so first let's take RP^2. I have a little trouble grasping why we can put a subspace topology on it. So RP^2 is the set of all lines through the origin in R^3. So if we take some subset S of RP^2 and the if set of points in R^3 which is the union of these lines in S is open then we can say we...
i want to know if there's any standard symbolic method of solving recurrences often found in the analysis of algorithms. many of these recurrences are readily solved by the master theorem. let's say we don't want to use that (for whatever reason) and we don't want to draw recursion trees...
Homework Statement
A resistor R is connected in series with an inductor L. The battery is connected at time t = 0. How much of this energy after 2 seconds is stored in the magnetic field of the inductor?
Homework Equations
U_{L}=\frac{1}{2}Li^{2}
i(t)=i_{0}(1-e^{\frac{-t}{\tau}})...
Homework Statement
a long hairpin is formed by bending a piece of wire. if the wire carries a current i = 1.15 A.
the figure looks like this:
\subset
point a is at the center of the semicircle part (so that there is a radius r from a to the outside of teh semicircle. i flows...
Homework Statement
Show that, at the bottom of a vertical mine shaft dug to depth D, the measured value of g will be
g = g_{s}\left(1-\frac{D}{R}\right)g_{s} being the surface value. Assume that the Earth is a uniform sphere of radius R.
Homework Equations
F = \frac{GMm}{r^{2}}
V_{S} =...
yeah, i definitely understand what you're saying. But for example, your matrix multiplication, let's say it runs in some time T. and then you partition it. the time it takes for the computation would be less right? (assuming it can be partitioned, you have a large enough matrix, etc), which is...
Let's say I have some algorithm with complexity O(n^k) for some constant k. and let's say it runs in some time T. Now, I want to implement a divide and conquer approach for this algorithm, by dividing the problem in half each recursion. So basically, the first time i run my algorithm it will run...
well...i know it's the feasible region. But let's stick with the economics example...does computing the actual size of that region give anything useful?
basically, let's say i have three linear equations, y1, y2, and y3.
assume y1 = ax+b where a and b are constants
assume y2 = mx+k where m and k are constants
assume y3 = n where n is a constant
also, now assume that they all intersect at y1=y1=y3=n.
would the area between the...
hmm...how about if I have two 1-simplices: [a,b] and [c,d]
If I wanted to compute the product space, would it be two 2-simplices, [a,b,c] and [a,b,d]
or would it be a bunch of 1 simplices: [a,c], [a,d], [b,c], [b,d] ??