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Ring theory: Prove if $g \in \mathcal{B}$, then $g=f_1 h_1+...+f_nh_n$ for some elements $h_1,...,h_n$ in $A$.
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Write $S=Rf_1+...+Rf_n$. Let $\phi \in P$, then $\phi(0)=\sum_1^n \lambda_ia_i$ where $\lambda_i \in R$ and $\phi-\sum_1^n \lambda_if_i \in P \cap (t)$. So $\phi-\sum_1^n \lambda_if_i=t\psi$ with $\...

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Telephone calls arrive at an office according to a Poisson process on the average of two every 3 minutes.
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Given that the call is on average of two every 3 minutes. the expected number of calls $\lambda$ would be $\frac{2}{3}$ per minute. Given the formula $f(x)$=$\frac{1}{\theta}$$e^\frac{x}{\theta}$ ...

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existence of a PDE problem
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We first solve the IVP $$u''+u'=f(x),\qquad u(0)=u'(0)=0\ .$$ The auxiliary function $v(x):=e^x u'(x)$ satisfies $$v'(x)=e^x f(x),\qquad v(0)=0\ .$$ It follows that $$v(x)=\int_0^x e^\tau f(\tau)\>...

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