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Suppose I have problem like this:
\begin{equation*}
\min_x\left\{f^Tx:\sum^n_{i=1}\left\lvert x_i-x^0_i\right\rvert^{3/2} \le t\right\},
\end{equation*}
How can I recast it into SOCP? I have some useful lemma such as
$z^{3/2}\le t \iff \exists w: wt\ge z^2, z\ge w^2$, and
$wt\ge z^2\iff \left\lV...
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Here goes the theorem:
Suppose $\phi$ is a strictly increasing continuous function that maps
an interval $[A,B]$ onto $[a,b]$. Suppose $\alpha$ is monotonically
increasing on $[a,b]$, and let $f:[a,b]\to\mathbb{R}$ be a function
such that $f\in\mathfrak{R}(\alpha)$ on $[a,b]$. Define $\...1
I'm thinking about doing my Master's Thesis on the subject of Arithmetic Topology: the relation between knots and primes, 3-manifolds and number fields, and other connections between topology and number theory (based on the works of B. Mazur, M. Morishita et al.).
I've talked about it with my to...
Arithmetic topology is an area of mathematics that is a combination of algebraic number theory and topology. It establishes an analogy between number fields and closed, orientable 3-manifolds.
== Analogies ==
The following are some of the analogies used by mathematicians between number fields and 3-manifolds:
A number field corresponds to a closed, orientable 3-manifold
Ideals in the ring of integers correspond to links, and prime ideals correspond to knots.
The field Q of rational numbers corresponds to the 3-sphere.
Expanding on the last two examples, there is an analogy between knots and prime...
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On math.SE a tag called (arithmetic--topology) has been created a few days ago. (It was created on Jun 9 at 10:19 according to the list of new tags.) The two hyphens in the tag name are probably a typo an the tag name is going to be corrected eventually. But still this revealed interesting tag.
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