LSTC LS-DYNA V9.71 R6-torrent.torrent

LSTC LS-DYNA V9.71 R6-torrent.torrent



 
 
 
 
 
 
 

LSTC LS-DYNA V9.71 R6-torrent.torrent

LSTC LS-DYNA v9.71 R6-torrent.torrent is a very popular torrents indexed from free web.. äœâ‚¬â„¢Î²â˜¦â“¢Â å‘€Â .Q:

When is $\Delta^n H$ isomorph to ${\rm Sym}_n H$?

Let $H$ be a finite dimensional vector space and let $\Delta$ be the coderivation operator.
I would like to know when $H_n = \Delta^n H$ can be identified with ${\rm Sym}_n H$, where ${\rm Sym}_n H$ is the symmetric tensor algebra? What properties will $H_n$ have to satisfy?
I am also interested in knowing if this identification is true in general for all formal power series with values in $H$.

A:

Let $H=K$ be a (associative, commutative) algebra, and $m\in H^0$.
Let $\Delta=m\otimes_H m-m\otimes_H 1-1\otimes_H m+m$.
Then $H_n={\rm Sym}_n H$.
It’s not true for any ${\rm Sym}_n H$: $\Delta H_2
eq H_2$.
To know when $H_n$ has this property, you need an additional condition on $H$ to make $\Delta$ injective.

Q:

find $ \sum_{i=1}^\infty \frac{1}{i^2+i}$

Find $\sum_{i=1}^\infty \frac{1}{i^2+i}$
Can’t seem to solve this one.

A:

Hint:
Use partial fraction decomposition:
$$\frac{1}{i^2+i}=\frac{1}{i}-\frac{1}{i+1}$$

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