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comment A name for the property $ \| x \star y \| = \| x \| \| y \| $.
I'm actually working with base $\mathbb {Z} $ so perhaps a norm is not what I'm looking for. Maybe a valuation.. ?
1d
comment Is there an object in reality that is proven to be uncountable?
you could travel around the Earth countably infinite number of times, with certain unrealistic assumptions. That doesn't really answer your question but may be helpful to a layperson to understand you can pair off each circumnavigation with the natural numbers...
1d
comment $\int _{ 0 }^{ 1 }{ \frac { { x }^{ t }-1 }{ \ln { x } } dx } $
What is $t$? An integer, rational, real, complex, ... Also, what have you tried so far?
May
19
comment Curious formula for minimum?
Thanks. I knew that must be true since they are clearly equal.
May
18
comment A name for the property $ \| x \star y \| = \| x \| \| y \| $.
@tampis of course I should have remembered that from Number Theory !
May
18
comment A name for the property $ \| x \star y \| = \| x \| \| y \| $.
Thanks both, wasn't sure about terminology. I will take a look into algebras!
May
18
comment Curious formula for minimum?
@Andre I wasn't aware of the softmax function. Seems then that softmax can be transformed into the usual max by adding $-\log(1+e^{|x-y|})$ to it. Interesting.
May
13
comment Is there a good book on Circulant Matrices?
Yes, that's what I gathered. My eyes just don't like the block print for some reason.
May
11
comment Notation for a vector with constant equal components of arbitrary dimension
Thanks. I also saw this article mathoverflow.net/questions/9898/…
May
11
comment Notation for a vector with constant equal components of arbitrary dimension
Is this standard?
May
11
comment Notation for replacing a matrix column with a vector
Thank you, that's good too. I will have a think about this with respect to my work :-)
May
10
comment Notation for replacing a matrix column with a vector
Thank you that's great. Nice notation !
May
10
comment Notation for replacing a matrix column with a vector
Thanks, I was looking for something similar to this. I was going to use $A_j[v]$ before you answered my question.
Apr
13
comment Calculate $\int_\Gamma ze^{z}dz$ where $\Gamma$ is line from point $z_1=0$ to point $z_2=\frac{\pi i}{2}$
@user227317 yes. See my answer for full details, but you got the answer! You can also use Blatter's approach too.
Apr
12
comment Calculate $\int_\Gamma ze^{z}dz$ where $\Gamma$ is line from point $z_1=0$ to point $z_2=\frac{\pi i}{2}$
@user227317 no, as I said use the substitution $z=it$. Also @ JessicaK's solution will also work. See also @ ChrisrianBlatter's answer.
Apr
12
comment Calculate $\int_\Gamma ze^{z}dz$ where $\Gamma$ is line from point $z_1=0$ to point $z_2=\frac{\pi i}{2}$
You need to parametrize the curve $\Gamma$, e.g. let $z(t)=it$ where $t\in[0,\pi/2]$. Looks like integration by parts may be helpful too.
Apr
8
comment $F(x)+G(y)= e^{x+y}?$
Yes, the way it is written confused me for a moment. However, on expanding the middle equality now I clearly see it does equal $F(1)-F(0)$. I was looking at what you had written from a different perspective - I was trying to construct the middle equality from the first by rearranging the original equation. Sorted now I see clearly what's happing - that "old trick" of adding something and then taking it away, so yes maybe best read right to left. +1 for your answer!
Apr
8
comment $F(x)+G(y)= e^{x+y}?$
I could be wrong, but shouldn't the middle equality be $-G(y)+e^{1+y}-(-G(y)+e^y)$ ? Maybe it's equivalent...
Apr
8
comment How to deduce that $1\cdot 1 + 2\cdot 1 + 2\cdot 2 + 3\cdot 1+3\cdot 2+3\cdot 3 +…+(n\cdot n) = n(n+1)(n+2)(3n+1)/24$
Try proof by induction ?
Mar
30
comment Question on branches and $\iff$.
Thank you. So if I restrict my attention to the principal branch (and I will also assume $f$ and $g$ are continuous) then $f+ig=0\iff e^{f(x)}\cos(g(x))+ie^{f(x)}\sin(g(x))=1$ ?