Recent content by s3a

I know how to solve each of those problems. For the set one, I look at the output of the S and try to match it with the input of T and then take the pair (input_of_S, output_of_T), and I do that for each pair. As for the formula one, I just plug in x = g(y). My confusion lies in trying to...

All right, thank you. :) (And, sorry for the delay!)

Actually, the sub-sequence examples I mentioned are not valid because of the third or fourth sentences (□[p → O q] or □[q → O p]), depending on whether it's p or q that's the last element of the sub-sequence, and not because it is generally the case that all moments in time need to be "occupied"...

Also, is my (latest, corrected) diagram correct? It seems correct to me (since it seems to graphically represent both structures 1 and 2), but I'm asking just in case. And, is it correct to say that each of the subsequences I mentioned are each not sufficient to show that the set of sentences...

So, there are an infinite number of sequences but only two structures (where if even an infinite amount of sequences can be expressed as part of one formula, it's one structure)? And, I see, thanks. :)

"The second formula in your diagram is not consistent with the problem statement, containing a rogue additional 'not' sign." Oops! For what it's worth, here is the corrected version.: "Not necessarily true. For instance if both t1 and t2 are always active then statement 1 fails. You need to...

Consider the following set of sentences that represent the requirements of a multi-threaded system for two threads t1 and t2: □¬[(t1 active) ∧ (t2 active)]. □[(t1 active) ⊕ (t2 active)]. □[(t1 active) → O(t2 active)]. □[(t2 active) → O(t1 active)]. (Pretend the O letters are the circles...

Thanks for your input, Babadag, but I still don't fully understand how to compute the connection of the two "sub-circuits". I also don't understand why multiplying the two transfer functions isn't good enough. Could you please elaborate on those? Having said that, I figured out how to do the...

In the context of control systems, if I have a vibratory second-order system, (ω_n)^2 / [s^2 + 2ζ(ω_n) + (ω_n)^2], I know how to get the natural frequency ω_n. So, if I have something like 2 / (3s^2+5s+2), I know how to get the natural frequency ω_n. However, if I instead have something like...

Basically, take a look at the "expanded form" of this (...

Actually, is the going from (s^5 + 3s^4 + 2s^3 + 4s^2 + 5s + 2) C(s) = (s^4 + 2s^3 + 5s^2 + s + 1) R(s) to ##c^(5) + 3c^(4) + 2c^(3) + 4c^(2) + 5 c^(1) + 2c^(0) = r^(4) + 2r^(3) + 5r^(2) + r^(1) + r^(0)## from the L{f^(n) (t)} = ##s^n F(s) – s^{n-1} f(0) – s^{n-2} f'(0) - . . . – s f^(n-2)(0)...

Maybe the solution is wrong? Since no one else answered, @Ssnow, could you please explain to me what you've done just in case you are in fact correct?

I'm not sure of anything ( ;P ), but that ( ##r(t) = t^3 · u(t)## ) is technically what the solution says.

I have the solution to the problem, and I mechanically, but not theoretically (basically, why do the C(s) and R(s) disappear?), understand how we go from ##(s^5 + 3s^4 + 2s^3 + 4s^2 + 5s + 2) C(s) = (s^4 + 2s^3 + 5s^2 + s + 1) R(s)## to ##c^{(5)}(t) + 3c^{(4)}(t) + 2c^{(3)}(t) + 4c^{(2)}(t) +...

OFFICIAL SOLUTION: d=e^(-1) mod 160=107 mp= c^(d) mod p=7 mq:=c^(d) mod q=7 MY THOUGHTS: I understand how d = 107, but I got that by using m = (17-1)(11-1) = 160. What I don't understand is the next two lines (from the official solution). I am aware of the P = C^d mod n (decryption) formula...