Recent content by dba

Homework Statement Two teams A and B play at most 2n-1 games. For any match there is a constant probability p that A wins and a constant probability q=1-p that B wins. P(i,j) is the probability that A wins; A needs i more wins to win and b needs j more wins to win. At the begin the...

Homework Statement I try to order given functions and I am stuck with evaluating the following: f(n)= (n+1)! and g(n)=n^{logn} Homework Equations \lim_{n\to\infty}\frac{f(n)}{g(n)} = 0 then g(n) is faster growing. \lim_{n\to\infty}\frac{f(n)}{g(n)} = \infty then f(n) is...

Thank you very much. I understand this now :smile:

Homework Statement I have trouble with the summation notation. \sum_{i=0}^{k}\binom{k}{i}f_{n+i} How do I write this as a sequence based on the definition of Fibonacci sequence? Homework Equations Definition: f(0)=0 f(1)=1 f(n)=f(n-1) + f(n-2) for n>=2 Example: f(2) = f(1) +...

Homework Statement \sum_{i=0}^{k} {k \choose i}f_{n+i} = f_{n+2k} Homework Equations Definition: f(0)=0 ; f(1)=1 f(n)=f_{n-1} + f_{n-2} for n>=2 The Attempt at a Solution I searched a basis for which the statement is true: n=2 and k=1 \sum_{i=0}^{1} {1 \choose i}f_{2+i} =...

Yes, I see it. i did write is good on my paper. soory about that. How would I express a referal to the first part with f and g reversed. Something like: since f(n)=O(g(n)) implies that g(n)=Ω(f(n)) we can say that g(n)=O(f(n)) implies that f(n)=Ω(g(n)) ? Thank you very much for your help!

Is this proof correct? f(n)=O(g(n)) \Leftrightarrow g(n)=Ω(f(n)) LHS → f(n)=O(g(n))→ f(n) ≤ c*g(n) → (1/c)*f(n) ≤ g(n) → g(n) ≥ (1/c)f(n) where d=1/c → g(n) = Ω(g(n)) → RHS RHS → g(n)= Ω (f(n))→ g(n) ≥ d*f(n) →(1/d)*g(n) ≥ f(n) → f(n) ≤ (1/d)g(n) where c=1/d → f(n) = O (f(n)) → LHS...

Thank you. Your explanation makes it much easier to understand. I will try to proof what you said and see what I get. :-)

mmmh. Ok the problem states: prove that the notation is symmetric: for any function f,g,h:N→R>=0 if f(n)=θ(g(n)) then g(n) = θ(f(n)) So, I looked at the definition of Big Theta which is if d*f(n) <= t(n) <= c*f(n) then t(n)=θ(f(n)) Thus, both conditions need to be true: t(n) <=...

Homework Statement proof if f(n) = O(g(n)) then g(n) = O(f(n)) = stands for element of c is some constant Homework Equations if f(n) <= c*g(n) then f(n) = O(g(n)) if g(n) <= c*f(n) then g(n) = O(f(n)) The Attempt at a Solution I tried to go from the left-hand-side(LHS) to the...

Homework Statement I had a Physics lab with the following setting: A signal generator is connected to a speaker which is located on one end of a tube. This creates the sound wave. The tube is open on both ends. A micro is movable along the tube and it is connected to an occsilator which...

Homework Statement Reduce, x(w+y'+z') + (w+x)y'z + wx'yz + wxy Homework Equations + stands for OR * (multiplication) stands for AND ' NOT The Attempt at a Solution I tried to combine some terms but I cannot find a good start... x(w+y'+z') + (w+x)y'z + wx'yz + wxy = xw + xy'+...

Homework Statement I need to simplify the boolean expression by algebraic manipulation as much as possible. (a+b+c)*(a'+c)*(a'+b') Homework Equations + stands for OR * stands for AND (or no operator between variables) ' Stands for NOT The Attempt at a Solution I tried but I do not...

That is exactly what I do not understand. I do not know how to imagine a direction of a change. As I mentioned in the beginning, I would assume if my B goes to zero, then the flus will be zero and the current will be zero. therefore there would't be a direction.

Can you explain a little better what you mean by the direction of the change in the flux? For the problem, there are no numbers. There is a vertical loop and the direction of the field is to the right. The flux is the integral of B*A since B and da are parallel and A is pi*r^2. Thanks!.