User:Zachgildersleeve

This is a page created for CS6640 Human Computer Interaction at the University of Utah.

About Me

I am a second year masters student at the U of U's School of Computing. Here I am:

File:Zachgildersleeve.jpg

My homepage has more photos and projects (completed and works in progress)

I recently started a blog to organize food recipes of what I eat for dinner. I don’t post every time I eat spaghetti and Bolognese, just the nicer stuff. That’s not to say that spaghetti and Bolognese isn’t nice.

Visit Garlic Is For Heroes

$\mathbf {\gamma } (t)=\sum _{i=0}^{n}\mathbf {P} _{i}\mathbf {\theta } _{i,n}(t),\quad t\in [0,1]$

where

$\mathbf {\theta } _{i,n}(t)={n \choose i}t^{i}(1-t)^{n-i},\quad i=0,\ldots n$

and

${n \choose i}={\frac {n!}{i!(n-i)!}}$

the full expansion takes the form:

$\mathbf {\gamma } (t)=\mathbf {P} _{0}{\frac {n!}{0!(n-0)!}}t^{0}(1-t)^{n-0}+\mathbf {P} _{1}{\frac {n!}{1!(n-1)!}}t^{1}(1-t)^{n-1}+\ldots +\mathbf {P} _{n-1}{\frac {n!}{n-1!(n-n-1)!}}t^{n-1}(1-t)^{n-n-1}+\mathbf {P} _{n}{\frac {n!}{n!(n-n)!}}t^{n}(1-t)^{n-n}$

$\mathbf {\gamma } _{1}(1)=\mathbf {\gamma } _{2}(0)\implies \mathbf {P} _{n}=\mathbf {Q} _{0}$

$\mathbf {\gamma } _{1}^{''}(1)=\mathbf {\gamma } _{2}^{''}(0);$

$\mathbf {\gamma } _{1}^{''}(1)=\mathbf {C} \mathbf {\gamma } _{2}^{'}(0)+k\mathbf {\gamma } _{2}^{''}(0)$

$\mathbf {P} _{n}-\mathbf {P} _{n-1}=k(\mathbf {Q} _{1}-\mathbf {P} _{n})\implies {\frac {1}{k}}\mathbf {P} _{n}-{\frac {1}{k}}\mathbf {P} _{n-1}+\mathbf {P} _{n}=\mathbf {Q} _{1}$

$n(\mathbf {P} _{n}-\mathbf {P} _{n-1})=m(\mathbf {Q} _{1}-\mathbf {P} _{n})\implies {\frac {n}{m}}\mathbf {P} _{n}-{\frac {n}{m}}\mathbf {P} _{n-1}+\mathbf {P} _{n}=\mathbf {Q} _{1}$

$(n-1)(n)(\mathbf {P} _{n}-2\mathbf {P} _{n-1}+\mathbf {P} _{n-2})=(m-1)(m)(\mathbf {Q} _{2}-2\mathbf {Q} _{1}+\mathbf {Q} _{0})$

${\frac {(n-1)(n)}{(m-1)(m)}}(\mathbf {P} _{n}-2\mathbf {P} _{n-1}+\mathbf {P} _{n-2})-\mathbf {P} _{n}+2\mathbf {Q} _{1}=\mathbf {Q} _{2}$