Complex number $i=\sqrt{-1}$
Now i consider $$\frac{1}{i}=\frac{1}{\sqrt{-1}}=\frac{\sqrt{1}}{\sqrt{-1}}=\sqrt{\frac{1}{-1}}=\sqrt{-1}=i$$
so $$i^2=1$$
you just said $\sqrt{}$ takes the principal value, right after asking me if we use both positives and negative square roots to prove $\sqrt{ab}=\sqrt{a}\sqrt{b}$ (I presume you're talking about $a,b>0$)
in which $\sqrt{ab}=\sqrt{a}\sqrt{b}$? sure, as long as $a,b$ are reals and not both negative, for example. or you could specify $a,b$ both have real part $>0$. not sure off the top of my head what the full solution set in $\Bbb C^2$ is.
The reason is that since $f\in L^1$, you can give some large interval outside of which $f$ becomes small, and then stitch some constant function and $|f|$
Well, does it work to just take your starting points and build the sequence to increment each by $1$, so that if you are taking some limit, you'll eventually "outpace" this sequence?
Anonymous
Is there any way to quickly derive the algebraic expressions for cyclic determinants like |{1,a,bc},{1,b,ca},{1,c,ab}|
This happened to us at one point since we were working on his Buck pset, he sorta notices us, is all like "What are you doing here?" and with all this joy, explains something to us that I don't remember offhand. Now, I wasn't quite working with the others since I was dysfunctional after an all nighter and had to work on compsci.
yeah the trouble is I have a galois theory pset and a presentation for neves in a couple days and if I put it off tonight future me is gonna hate current me for it :/
In my lecture there was a Lemma: Any two natural chain maps $C_*(X)\otimes C_*(Y)\to C_*(X)\otimes C_*(Y)$ that are identity in degree zero are chain homotopy equivalent
The proof was not done so I could not guess the definition of natural from the proof
Question : I'd like to formulate a pde for the following minimization problem.
Let $\Omega$ be a convex, closed, compact set in $\mathbb{R}^d$ with a smooth boundary.
Given a data $(x_i,d_i)$, $x_i \in \Omega^{\mathrm{o}} $ ,$d_i \in \mathbb{R}$, $i = 1,2,3...N$, $N>d$ and $\sum\limits_{i=1}^...
so it seems like 'natural chain maps' in the lemma is supposed to mean 'natural constructions for chain maps'. I'm not totally sure I can parse this either but the grammar at least makes more sense ;P
@LeakyNun I can't find anymore what I posted before, but there are 4 input variables, but the vector-valued function is defined only in terms of two variables, that's why you have many zeros
Complex number $i=\sqrt{-1}$
Now i consider $$\frac{1}{i}=\frac{1}{\sqrt{-1}}=\frac{\sqrt{1}}{\sqrt{-1}}=\sqrt{\frac{1}{-1}}=\sqrt{-1}=i$$
so $$i^2=1$$
Question : I'd like to formulate a pde for the following minimization problem.
Let $\Omega$ be a convex, closed, compact set in $\mathbb{R}^d$ with a smooth boundary.
Given a data $(x_i,d_i)$, $x_i \in \Omega^{\mathrm{o}} $ ,$d_i \in \mathbb{R}$, $i = 1,2,3...N$, $N>d$ and $\sum\limits_{i=1}^...
