The first one, I had the vector field $$F=\left( {\frac{{ - 2z}}{{1 + {x^2} + {y^2} + {z^2}}} + \cos y,{e^x},\frac{{2x}}{{1 + {x^2} + {y^2} + {z^2}}}} \right)$$
And I had $M=\{(x,y,z):z=y^2+x^2\;,z\leqslant 4\}$
my first reaction was like: already done that, but reading through this I have only done that the median and altitude in isoceles triangle are the same so I will definitely look into this
@anon That "I know" doesn't necessarily mean he knows that formula I pointed out in the link. On the other hand, maybe my comment didn't help on his specific point (indeed, I see that "numerically"), but in case he didn't know that formula, I'm sure he's glad he knows it now.
@Chris'ssis Again, Chris. You're always telling everybody things like "that is trivial", "that can be computed without pen and paper", "that is easy", "I am awesome and all my questions are awesome".
Hi guys, Suppose $\psi \in C^\infty(\mathbb{R}^d)$ have non empty compact support. I want to show that the family of functions $\psi(x-j)$ where $J\in \mathbb{Z}^d_+$ is bounded in $H_{-d}$. Here, $H_{-d}$ is the L2 sobolev space, ie $f \in H_{-d}$ such that $$||f||_{-d}^2 = \int |\hat{f}(\xi)|^2 (1 + |\xi|^2)^{-d}$$
I also want to show that the family of functions has no convergence subsequence in any $H_s$ ($s\in \mathbb{R})$. I feel like this has to do with Arzella-Ascolli theorem and Rellich's theorem
only a subset of identities fit inside one's field of vision, and only a subset of those can be done penpaperlessly even by those who like those methods, and only a subset of those will be known to people collectively at any given point in time
@anon For instance, with/without paper I'm helpless here. Compute $$\sum_{n=1}^{\infty} \frac{\zeta(2n)}{n(2n+1)2^{2n}}$$ And there are lots of such questions! Why? I know just a tiny bit of math! :-(
I have two triangles and no angle of the first triangle is the same as any angle of the second triangle. Can I deduce that no side of the first triangle will be the same as any side of the second triangle?
Knowing that the lifetime (in hours) of an object has an exponential distribution with parameter 0.001. 6 objects are tested and the time where failures occur is written. What is the probability that any objects fail before 800 hours?
no i was thinking about one thing ,but, maybe it might require a lot of work. Questions about theorems and some exercises , are often related to some book ... if people could seek bookwise about recent questions , it would be a good way to have such a structure
@Danny The problem is that there are A LOT of books and there would be A LOT of tags. If people want to find author X then typing it into search usually gives sufficient results.
i was just suggesting. And having such "special text boxes" where one could write down book title,page, etc (when submitting a question) would give people an incentive to do so. and i people would do it aswell. But once again that was just a taught
@mick When you say "Let $M=[0,\infty)$ be a semiring." you want to say rather something like "Consider $M=[0,\infty)$ endowed with $+$, so $(M,+,\cdot)$ is a semiring"
Knowing that the lifetime (in hours) of an object has an exponential distribution with parameter 0.001. 6 objects are tested and the time where failures occur is written. What is the probability that any objects fail before 800 hours?
