Tag Archives: Mathematics

Question: Do you think I’m able to pass the drug test?

I use to smoke maybe 4 days out the week, no more than 6-8 puffs (it don’t take many puffs to get me high). I stopped for 2 months, and ended up smoking again for my bday with only 4 puffs, stopped for maybe 2 weeks and ended up smoking again with only 4 puffs.… Read More »

Can I calculate the product over the primes efficiently and with high precision?

I want to calculate the following product : $$prod_{p prime , ple 10^{10}} 1-frac{1}{p}$$ I know the approximation formula $$frac{e^{-gamma}}{ln(10^{10})}$$ where $gamma$ is the Euler-Mascheroni-constant. The result should be good to $12$ decimal digits. Is there an efficient way (not brute force by determining all primes, which takes long with PARI/GP) to calculate this product… Read More »

How can I plot this nonlinear system using MATLAB

I am trying to plot this servomechanism system in MATLAB. The system is shown in figure. $V$(voltage) is input of the system and $theta_L$ is output of the system. How can I plot $V(t)$ and $theta_L(t)$ ? Equations of the system is shown below. $$dot{omega}_L=-512θ_L-25θ_M-10omega_L$$ $$dot{omega}_M=V-10omega_M-128θ_L-6θ_M $$ $$$$ So, $$ theta_L”=-512theta_L+25theta_M-10theta_L’ $$ $$theta”_M=V-10theta’_M+128theta_L-6theta_M $$ So… Read More »

Does $max_{ile n} big|Z_ibig|=frac 1 n sum_{ile n} big|Z_ibig|$ as $n to infty$? (Convergence of R.V.s sequence $Z_1,Z_2,Z_3,…$)

$Z_1,Z_2,Z_3,…$ are integrable R.V.s that are independent and identically distributed. Show that the following expression converges to zero in probability: $frac 1 n max_limits{ile n} left|Z_iright|$. What does $max_limits{ile n} big|Z_ibig|$ mean? Is it the biggest $Z_i$ for $ile n$? If so, the law of large numbers state that $frac 1 n sum_limits{ile n} big|Z_ibig|… Read More »