## All Questions

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### Symmetric sums and Representations of SO(3)

I had tried to help someone on math.StackExchange to prove the identity: $$(1-Tr(A))^2+\sum_{1\le i\le j\le 3}(a_{ij}-a_{ji})^2=4$$ I guess you could argue the left hand side is …
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### Anything special (historical?) about surface $x\cdot y\cdot z\ +\ x+y+z=0$?

QUESTION I wanted to introduce and develop the complex logarithm from scratch. As the result I've arrived a couple of months ago at the following identity after which the road to …
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### When is an ample line bundle on an abelian variety base point free?

So, any line bundle $L$ on an abelian variety $X$ determines a type $(d_1,\ldots,d_g)$ where $d_i|d_{i+1}$. It's well known that if $d_1\geq 3$ then $L$ defines an embedding, that …
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Let $X$ be a smooth and projective variety over a field of characteristic zero. Let $Y$ be a normal variety, with finite quotient singularities (an orbifold!) and let $\pi: Y \to X … 0answers 16 views ### Updated: finding an integer$k$that minimizes$1/(N-k) (1+1/k)$For any positive integer$N$and real number$a > 0$. Define$f(k) = \frac{1}{N-k} (1+\frac{a}{k})$. The problem is to find a positive integer$k$that minimizes$f(k)$. It is qu … 0answers 2 views ### Spectrum gap of large random weighted semiregular bipartite graph Hi I need the bound for the spectrum gap of random semiregular ($\ell$,$r$)-bipartite graph. This paper (http://arxiv.org/abs/1212.5216) gives the bound for$\ell$-regular bipar … 0answers 20 views ### Full$n$-torsion of elliptic curves and the cyclotomic field of order$n$Hi, overflowers. I have a question concerning the torsion of elliptic curves over number fields. Let us consider an elliptic curve$E$defined over${\mathbb Q}$. From the Weil … 0answers 47 views ### finding an integer that minimizes a function For any positive integer$N$and real number$a > 0$. Define$f(k) = \frac{1}{N-k} (1+\frac{a}{k})$. The problem is to find a positive integer$k$that minimizes$f(k)$. It is qu … 2answers 227 views ### strong nilpotent elements An element x in a noncommutative ring R is strongly nilpotent if any chain$x_1=x, x_2, ... $, with$x_{n+1}\in x_n R x_n$terminates at zero. It becomes clear why this is a good d … 0answers 115 views ### mixed Hodge polynomial Let$X$be a smooth projective algebraic variety over a field of characteristic zero. Let$U$be the complement in$X$of a simple normal crossings divisor$D$. For each degree$k$… 0answers 15 views ### Topology of Asymmetric Symmetric Products Let$X_1,...,X_m$be connected, simply-connected CW sub-complexes of a CW complex$X$. Let the symmetric group on$m$letters,$S_m$, act on$P:=X_1\times\cdots\times X_m$in$X^m$… 1answer 43 views ### Asymptotic bounds on$\pi^{-1}(x)$(inverse prime counting function) What are the current best asymptotic bounds on$\pi^{-1}(x)$, where$\pi(x)$denotes the prime counting function (number of primes at most$x$)? In other words, I am curious about … 0answers 49 views ### Composition of spans as a morphism of profunctors Let$\bf C$be a category with pullbacks. Define$Span\colon (A,B)\mapsto \{ (X,f,g)\mid A\xleftarrow{f}X\xrightarrow{g}B\}$and notice that it is a profunctor$s\colon \bf C^\text …
The main radicals of a non-commutative ring (with 1) are the Sum of all nilpotent ideals $\subseteq$ Prime radical $\subseteq$ Nil radical $\subseteq$ Jacobson radical $\subseteq$ …
I came across the following differential equation when considering some direct scattering problems: $$N'_x(x,z)=G(x,z)N(x,z)$$ where $N(x,z)$ is a $2\times2$ complex matrix wit …