http://arxiv.org/pdf/0807.1310v5.pdf
Equation 4.6 strikes me as wrong. The integral is \int_{0}^{\infty} B \mathrm{d}B
The limits of the integral seem to be values of z, but the integral seems to be wrt B. If the limits were values of B, the answer would be ∞. It's clearly not, but I don't...
This is now solved. It can be solved by extending the left triangle to a right-angled triangle, with a base of V+k (hence where the single V comes from). Then \cos{\delta}=V+k
k is given by x \cos{(\pi-(\theta + \beta))}=-x \cos({\theta + \beta}).
Using the cosine sum rule I stated above...
Homework Statement
Given the following two triangles:
Show that v \cos{\delta} = V(1-\cos{\beta})+u\cos(\alpha - \beta)
The Attempt at a Solution
Using the cosine law I've got:
v^{2}=x^{2}+V^{2}-2xV\cos{(\theta + \beta)}
and u^{2}=x^{2}+V^{2}-2xV\cos{(\theta)}
I figured maybe using the...
But because the joint PMF is a multiplication of the individual PMFs, the term becomes \lambda_{1}^{n_{1}}\lambda_{2}^{n_{2}}\lambda_{3}^{n_{3}}... which means the term \sum_{i=1}^k N_i = n doesn't appear in the joint PMF (although it would if the \lambda_{i} were equal), so I don't understand...
I don't understand how the \sum_{i=1}^k N_i = n term constrains the joint distribution, given that each \lambda_{i} can be distinct.
Also, to evaluate P(\sum_{i=1}^k N_i = n), wouldn't this be the joint distribution, evaluated at N_{1}=n-\sum_{i=2}^{k}N_{i} and then...
Homework Statement
The Attempt at a Solution
I have that the joint probability mass function would be
\Pi_{i=1}^{k} \frac{\lambda_{i}^{n_{i}}}{n_{i}!} e^{-\lambda_{i}}
How would I go about applying the conditional to get the conditional distribution?
Homework Statement
Question (specifically part b):
Solution:
The Attempt at a Solution
My issue is that I don't agree with \Gamma^{0}_{3} and \Gamma^{1}_{3}, surely if they're given by [S][n] they should be given by \mp(0,0,\rho g x_{3}). The answers they have don't make sense, because...
Isn't \nabla \cdot v \otimes n = (n_{1}(\frac{dv_{1}}{dx_{1}}+\frac{dv_{2}}{dx_{2}}+\frac{dv_{3}}{dx_{3}}), n_{2}(\frac{dv_{1}}{dx_{1}}+\frac{dv_{2}}{dx_{2}}+\frac{dv_{3}}{dx_{3}}), n_{3}(\frac{dv_{1}}{dx_{1}}+\frac{dv_{2}}{dx_{2}}+\frac{dv_{3}}{dx_{3}}))
Which is n \cdot \nabla v?
This would...
Homework Statement
Homework Equations
So I have that v \otimes n = \left( \begin{array}{ccc}
v_{1}n_{1} & v_{1}n_{2} & v_{1}n_{3} \\
v_{2}n_{1} & v_{2}n_{2} & v_{2}n_{3} \\
v_{3}n_{1} & v_{3}n_{2} & v_{3}n_{3} \end{array} \right)
The Attempt at a Solution
I've tried applying the...
Homework Statement
Suppose v is a vector satisfying:
\alpha v + ( a \times v ) = b
For \alpha a scalar and a, b fixed vectors. Use dot and cross product operations to solve the above for v.
Homework Equations
The unique solutions should be:
v=\frac{\alpha^{2}b- \alpha (b \times a) + (b...
Ah, I see.
So instead I use \hat{n}=\frac{1}{\sqrt{6}}(1i-2j+1k)
and that gives Pv=\frac{1}{6}(25i+10j-5k).
And Tv=\frac{1}{6}(32i-4j+2k).
Is that right now?
Makes sense, thanks for the quick response.
I get 10i-10k+5k which, when dotted with n obviously gives 0.
Correcting the sign error for the second yields 17i-24j+12k.
Thanks for your help
Homework Statement
Given a plane \Pi with normal n=i-2j+k and a vector v=3i+4j-2k calculate the projection of v onto \Pi and the reflection of v with respect to \Pi.
The Attempt at a Solution
I need to check that I'm doing this is right.
I think I need v - (v \cdot n)n =...
Homework Statement
A simple dynamical model for the price P (in £) of shares in a single stock or commodity traded in a stock market describes the behaviour of all the traders in the market with the same simple rule. All traders buy or sell shares at each "tick" (or time step \Delta t. To...
Homework Statement
Prove that their are infinitely many primes such that \left(\frac{14}{p}\right)=1
Homework Equations
The bracketed symbol is the legendre symbol (i.e. there are infinitely many primes such that 14 is a square modulo p)
The Attempt at a Solution
Well by...