Recent content by boombaby

I guess it should be |det(A)|=1, rather than det(A)=+/-1.

These are some easy functions you might want to check out first, in order to understand your own questions. to your first question: sin(x)+sin(pi*x) 's period=? . by the way, f is period iff f(x)=f(x+T) for some T. to your second: sin(x)/cos(x)=tan(x)'s period=? to your third: the...

yea, I'm reading it. cool. Thanks guys!

anyone?...

Homework Statement Let f\in C^{1} on [0,1], and f(0)=f(1)=0, prove that \int_{0}^{1}(f(x))^{2}dx \leq \frac{1}{4} \int_{0}^{1} (f'(x))^{2}dx Homework Equations The Attempt at a Solution what is the trick to produce a 1/4 there? and how to make use of f(0)=f(1)=0? well I know that...

Thanks! the ideas are great, especially the last one, clear and efficient... well my space-filling-curve thought was...nasty... Thanks a lot!

Oh, this is what I know about measure: a set A has measure zero means there is a countable collection of open/or closed rectangle that covers A that the sum of the volumn of each rectangle is less than an arbitrary given epsilon. my original goal is to construct the subset S of Q, then \chi_{S}...

thank you. I don't find an example in textbooks yet but your idea sounds workable, in which f seems to be unbounded, and I'll try to figure it out... well, I forgot to tell that f is supposed to be bounded in my original question. Anyway it's helpful and thanks a lot.

Homework Statement Let Q=I\times I (I=[0,1]) be a rectangle in R^2. Find a real function f:Q\to R such that the iterated integrals \int_{x\in I} \int_{y\in I} f(x,y) \; and \int_{y\in I} \int_{x\in I} f(x,y) exists, but f is not integrable over Q. Edit: f is bounded Homework...

use the definition. note that |(a1+a2+...+an)/n-L| = |((a1-L)+...+(an-L))/n|, and I guess you know something about the behavior of |a_n-L| when n goes to infinity :) hope this helps u

hi, could you please explain a little about how to write it as an Riemann-Stieljes integral? I learned something about Riemann-Stieljes integral in principle of mathematics but havn't met any concrete examples. Thanks

...I think it is necessary to know the graph of cos(x), which may help a lot. so, find one. edit (:shy: trying not to be ambiguous) ...I think it is necessary for one to know the graph of cos(x), which may also help a lot. (regardless of this particular problem)... "periodic" is really the...

I will prefer the domain to be [0,infinity]...for x is not defined at -1/n, which makes it a bit complicated.

Many things beyond my knowledge:( I'll come back to this problem when I am ready for it. Anyway, thanks very much! I'll keep an eye on Jordan's curve theorem and Brouwer's theorem.

sorry for reply late...last night I was unable to open this forum... I havn't learned Brouwer's theorem and I've no idea what causes the differences between unequal dimensions and equal dimensions of domain and range (guess it needs a lot of preliminary knowledge that I havn't learned). but...