# All Questions

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### Mixed PDE/finite difference equation

I have the following mixed pde/finite-difference equation for $f(t,x,y)$: $a x^2 f_{xx} + bxf_x + f_t - bxy + c\sinh(d\delta) = 0$ subject to $f(T,x,y)=0$, $x>0,\ t\geq 0,\ y\in\mathbb Z$, ...
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### What are the indecomposable $U_q\mathfrak g$-modules?

Let $\mathfrak g=\mathfrak{sl}(2)$. Let $\zeta$ be a primitive root of unity of even order. Say $\zeta=e^{2\pi i/6}$, for concreteness. Let $U_q\mathfrak g$ be Lusztig's integral form of the ...
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### projectivity with assumption of big and semi-amplness

Let $X$ be a compact Kaehler manifold with $D$ be an effective divisor on $X$ such that $K_X+D$ is semi-ample and big then $X$ is projective?
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### Floquet solution to Mathieu equation in terms of Mathieu sin and cos [on hold]

In wikipedia https://en.wikipedia.org/wiki/Mathieu_function#Floquet_solution I want to know how the Floquet solution is plotted. One way I am thinking is to write Floquet solution in terms of the ...
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### Choi type matrix condition for completely positivity on a certain operator system spanned by some unitaries

Let $B_1$ and $B_2$ be $C^*$-algebras. Let $U_1, \ldots, U_n$ be some unitaries in $B_1.$ We consider the operator system $S$ spanned by $U_iU_j^*.$ Let $\phi: S \rightarrow B_2.$ Given that the ...
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### Does the Turaev-Viro theory for the generalized $E_6$ subfactor for $\mathbb{Z}/7$ distinguish $L(7,1)$ and $L(7,2)$?

In the paper Sato-Wajui "COMPUTATIONS OF TURAEV-VIRO-OCNEANU INVARIANTS OF 3-MANIFOLDS FROM SUBFACTORS" they compute certain Turaev-Viro-Ocneanu invariants of certain lens spaces. One of the results ...
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### Density of prime divisors of $a^n + b$

Suppose $a > 1, b \neq 0$ be two rational numbers. Is it known in general that the set of prime divisors of (the numerator of) $a^n + b$ has a positive relative density?
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### which is the relationship between infinite set and the orbits of their points? [on hold]

I have been studying the proof of the following theorem: Theorem: Let's suppose that $X$ is some metric space and $X$ is a infinite set. If $f:X\to X$ is transitive and has dense periodic points the ...
If $G$ is a finite, connected simple graph then is there an expression for the average geodesic length? That is suppose I know two nodes $n_1$ and $n_2$, the number of edges in my graph and at those ...