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ML/T^2
mass x acceleration |
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ML^2/T^2
mass x velocity^2 |
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| [gravitational field strength] |
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ML^2/T^3
rate of change of energy |
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compactibility graph
(of a junction) |
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| a graph where each flow is represented as a vertex and vertices are joined if the simultaneous flow of both streams does not lead to a crash |
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connected subgraph
(of a graph) |
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| part of the graph such that every vertex in the subgraph is connected to every other vertex in the subgraph |
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| maximal connected subgraph |
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| a connected subgraph where it is not possible to add further vertices and still have a connected subgraph |
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| a set of maximal connected subgraph that contains every vertex |
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| complementary subgraph of S |
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| S (with a bar above it), the subgraph of G containing all the vertices not in S |
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q: number of cars passing a fixed point
cars per hour |
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k: count number of cars per unit length
cars per km |
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| relationship between q, u, k .. |
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| relationship between u, u(o), k, k(jam) |
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| a sharp change in traffic flow at some point |
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| dx/dt in terms of u(1), u(2), k(1), k(2) |
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| dx/dt = {k(1)u(1)-k(2)u(2)}/{k(1)-k(2)} |
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| newton's law of gravitation |
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| terminal velocity formula |
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change in momentum
integrate F dt from t(2) to t(1) to find the impulse of force F |
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| 'simpler' oscillation equation |
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| x(t) = [{x(o)}^2 + {v(o)/w}^2]cos(wt-φ) |
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(i) p(ij)≥0
(ii) Σ p(ij) = 1
from j=1 to n |
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| maximum row sum matrix norm ║A║∞ |
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| ║A║∞=max{1≤i≤n}Σ|a(ij)| from j=1 to n |
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| ║x║∞=max{|x(1)|,...,|x(n)|} |
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| relationship between ║A║∞ and ║x║∞ |
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| relationship between |λ| and ║A║∞ |
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| if P is a stochastic matrix then P^T x>x has .. |
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a 0-1 matrix where G(ij)=1 if there is a link from i to j
G(ij)=0 otherwise |
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| out degree of the ith page |
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| total number of links from that page |
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| a page where the out degree of the page is 0 |
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P = diag({1/d(1),...,1/d(n)}G
where if d(i)=0, 1/d(i)=0 |
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| P with every row of 0s replaced with a row of 1/n |
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| find the pageranks by solving |
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Definition
Pdoublebar^T x = x
and sum{x(1),...,x(n)}=1 |
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Definition
| {x(k)}^T = {x(o)}^T{Pdoublebar}^k |
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Definition
| {x(k+1)}^T = α{x(k)}^T{P} + {α{x(k)}^T{a} + (1-α)}v^T |
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a={a(1),...,a(n)} where
a(i)=1 if page is dangling node
=0 otherwise |
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| number of iterations (k) to reach tolerance level (r) |
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| probability of getting to webpage m in n steps |
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Definition
{v^T}{P^(n-1)}{P(.m)}
v={s(1),...,s(n)} where s(i)=probability of starting at node i
P(.m) is the mth column of P |
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