-1
votes
0answers
151 views
+50

On even almost perfect numbers other than the powers of two, as compared to odd perfect numbers given in Eulerian form

This question has been cross-posted from MSE. Let $\sigma(x)$ be the sum of the divisors of $x$. We say that $X$ is almost perfect if $\sigma(X) = 2X - 1$. Antalan and Tagle (in a 2004 preprint ...
18
votes
0answers
979 views
+50

Is formula valid for relating $\pi$ with ALL of its OEIS A002485(n)/A002486(n) convergents?

Could anyone try to prove that the below conjectured formula is valid for relating $\pi$ with ALL of its convergents - those, which are described in OEIS via A002485(n)/A002486(n) ? $$(-1)^n\cdot(\pi ...
7
votes
1answer
251 views
+50

When is a general sheaf (on the projective plane) globally generated?

Let $v$ be a chern character on $\mathbb P^2$ so that the moduli of sheaves of chern character $v$ is non-empty of the expected dimension. When is it true that the general sheaf in moduli is globally ...
17
votes
0answers
287 views
+50

Is the Flajolet-Martin constant irrational? Is it transcendental?

Facebook has a new tool to estimate the average path length between you and any other person on Facebook. An interesting aspect of their method is the use of the Flajolet-Martin algorithm. In the ...
10
votes
1answer
291 views
+50

Obstructed automorphisms of schemes

Let $X$ be a smooth projective scheme over a field $\mathbf{k}$ of characteristic zero such that $\mathrm{H}^0(X, \mathrm{T}X)$ vanishes, and let $f$ be an automorphism of $X$. I would like to have an ...
4
votes
0answers
122 views
+50

Complexity of approximating the size of the range of a matrix

Given an $m$ by $n$ matrix $M$ with $m \leq n$ and elements from $\{-1,1\}$, let us define: $$S_M = |\{Mx : x \in \{-1,1\}^n\}.$$ It is NP-hard to compute $S_M$ exactly I believe by applying the ...
11
votes
0answers
343 views
+200

Unifying (& “justifying”) the various definitions for differential operators

Reading about differential operators in different sources I've picked up several definitions which are not obviously equivalent (to me). Here they are: Definition 1 ("naive"): Let $X$ be a (real) ...
-2
votes
0answers
53 views
+50

How one can use a real math function on transaction in Hybrid Petri Net fundamental equation?

Say we have a simple HPN with 2 continuous places $A$ and $B$ and one transition. We want a transition not only add and substract $N$ marks from $A$ and add $M$ to $B$ but use mathematical function ...
10
votes
0answers
248 views
+100

What is Koszul dual of a curve?

Let $X$ be a curve embedded into a projective space $\mathbb P$ such that it is cut out (scheme-theoretically or ideal-theoretically) by quadrics. What is known about the Koszul dual of the ...
5
votes
1answer
165 views
+50

Analytic continuation of the double sum $\sum_{n,m\ge0}x^ny^mt^{nm}$

Define function $f(x,y,t)$ as the analytic continuation of the series $$f(x,y,t)=\sum_{n,m\ge0}x^ny^mt^{nm}$$ This series definitely converges when all the arguments are small enough. I would like to ...