my daughter's watching a documentary about polar bears and just said "maybe we can go to the arctic someday and see the polar bears." pretty sure there aren't gonna be any.
well technically i could have, but then i'd have had to pay for the book. which would be worse than the pleasure i'd get from destroying it.
one kinda fun thing about our school re-using the same books forever is that sometimes you'd see the name of someone you knew as a previous user of your book. my sister and i used the same 8th grade science book.
they keep a san diego one on a pretty regulated diet with a lot of vegetables so it doesn't build up the fat/fur that it would need in the arctic but would render it miserable in san diego.
hi, i wanted to ask what is the best method of approximating the principal branch lambert w for x < -e^-1 regarding the speed at which it converges to actual value
should the second term $o(h)$ in the answer here math.stackexchange.com/questions/1409167/… read $o(\| h \|_{L^2})$, and if so why is is $\int \|\nabla h\|^2= o(\| h \|_{L^2})$
The Gudermannian function relates a hyperbolic angle measure
ψ
{\textstyle \psi }
to an associated circular angle measure
ϕ
{\textstyle \phi }
. The circular angle measure is called the gudermannian of the hyperbolic rotation, and is denoted
gd
ψ
{\textstyle \operatorname {gd} \psi }
. The Gudermannian function reveals a close relationship between the circular functions and hyperbolic functions. It was introduced in the 1760s by Johann Heinrich Lambert...
On the Gudermannian function, which relates the trig and hyperbolic functions to each other
If $\phi=\operatorname{gd}(\psi)$, then:$$\begin{array}{}\sin\phi=\tanh\psi&\csc\phi=\coth\psi\\ \cos\phi=\operatorname{sech}\psi&\sec\phi=\cosh\psi\\ \tan\phi=\sinh\psi&\cot\phi=\operatorname{csch}\psi\end{array}$$
It's defined by $\operatorname{gd}\psi=2\arctan(\tanh\frac12\psi)=\int_0^\psi\operatorname{sech}t~{\rm d}t$
It's inverse is $\operatorname{gd}^{-1}\phi=2\operatorname{artanh}(\tan\frac12\phi)=\int_0^\phi\sec t~{\rm d}t=\log(\sec x+\tan x)$
(Of course from that table you can also define $\operatorname{gd}\phi=\arcsin\tanh\psi$ etc)
Hello, generally speaking, if we have a mtrix that is in diagonal form, is it true that charpol = minpol? i am thinking of examples like a matrix with zeroes everywhere but a_11 = 2 , a_22 =2 , a_33 = 1 , then the min pol is one degree less than charpol
so i guess its only true, if the matrix is orthogonally diagonalisiable, say every Eigenvalue is different from the other
Is this article (investopedia.com/terms/c/cagr.asp) algebraically illiterate, or is there some ghastly convention in Finance where "$*\ 100$" means "multiply everything to the left by $100$% ignoring order of operations"?
there is a deeper issue there; maintaining consistency between something and a 'model' of something. (not to suggest that mathematics is just a model.)
hey guy any hints on how can i prove this $\lim _{n \rightarrow+\infty}\left(1+\frac{z}{n}\right)^{n}=\mathrm{e}^{z}$ using counting measure and measure theory in general?
Suppose we have an $a\times b\times c$ cuboid, oriented so one vertex is lowest. Then the number of ways to stack cubes in it (following gravity) is$$\prod_{i=1}^a\prod_{j=1}^b\prod_{k=1}^c\frac{i+j+k-1}{i+k+j-2}.$$