# All Questions

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### formula for sequence 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, [migrated]

There is a sequence with the values 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, ... (basically there are always four 0s followed by a 1, then it repeats). Is there a function for this sequence? Here are two ...
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### A conjecture like Cayley–Bacharach theorem

Let six points $A, A', B, B', C, C'$ lie on a conic and a cubic. Let a conic through $B, B', C, C'$ and meets the cubic again at $A_1, A_2$. Let a conic through $C, C', A, A'$ and meets the cubic ...
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### Is an associative division algebra required for this phenomenon?

For which integers $d \geq 1$ can we find real matrices $R_1, \dotsc, R_d$ of size $d \times d$ such that for any unit vector $v \in \mathbb{R}^d$, $$R_1 v, \dotsc, R_d v$$ is an orthonormal basis? ...
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### Maximal ideals of R [x] [on hold]

Let $R$ be a commutative ring with identity. Is there any relation between maximal ideas of $R[x]$ and maximal ideas of $R$?
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### like prime for a ring

Let $R$ be a ring with identity. Is there any characterization for a ring $R$ such that has a decomposition?
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### Algorithm to determine isomorphism of 2 maximal planar graphs

I read on wikipedia that there are efficient algorithms to answer the question whether 2 (maximal) planar graphs F and G are isomorphic. However, after some (IMHO) substantial searching I don't seem ...
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### Most computationally efficient Littlewood-Richardson rule

There are many, many different versions of the Littlewood-Richardson rule: the original characterization via Yamanouchi words, Remmel's version, a description via the Poirier-Reutenauer bialgebra, the ...
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### 2's complement subtraction conversion to decimal for checking [on hold]

I was having some problem when trying to perform a 2's complement subtraction. So the question is: 01110101 - 11010110 ---------- Then I perform the following ...
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### Brownian bridge on a Lie group as a stochastic differential equation

Brownian motion $g_t$ on a compact Lie group satisfies the stochastic differential equation $$dg_t = dB_t \circ g_t$$ where $B_t$ is Brownian motion on the Lie algebra and $\circ$ denotes ...
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### Avoiding the range of a bivariate function or Diophantine function

I have a bivariate integer function where x,y are positive integers in the function $f(x,y)=5+23x+7y+30xy$. The lattice points of this function, or its range, contain a large number of values. I'm ...
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### tangent space of line bundles over projective space

Let a line bundle $$\eta:\mathbb{R}\to E(\eta)\to \mathbb{R}P^m.$$ I want to study the tangent bundle $TE(\eta)$. Question 1. When $n$ is even, $\mathbb{R}P^m$ is non-orientable. Does this imply ...
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### Solution to $(A+x^2)e^x=B$ with Lambert W function

Is it possible to obtain a analytical solution for $(A+x^2)e^x=B$, where we want to solve for $x$ with $A,B$ as constants?
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### Are all transversely oriented, transversely measured foliations given by closed forms?

This paper, "AF-algebras and topology of 3-manifolds" seems to claim on page 5 that a [transversely] oriented measured foliation on a compact surface is given by a closed form. On the other hand, the ...
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### Simultaneous integral equation on $SU(n)$

Consider a smooth curve $U_s:[0,T] \rightarrow SU(4)$ which solves: $\frac{d U_s}{ds} = (a + w(s)b)U_s$ for some given $a,b \in \mathfrak{su}(4)$ (which generate $\mathfrak{su}(n)$) and a smooth ...
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### Almost-Kahler Einstein four manifolds

Are the odd Betti numbers of a compact Almost-Kahler Einstein four manifold necessarily even ?