Recent content by Lament

Increase your stop time to say 50 secs. Initially, during transient time none of the values will be stable. Secondly, don't you also need to include field winding voltage and current for input power calculation? Thirdly, since you are input and/or output signals are chopped, you need to do an...

This is the first time I have seen this. Can you give me some idea behind why such an erroneous result happens while we use approximations @fresh_42? Is it because the derivative at those crossings of the arc with the diameter is not continuous as ##n\to\infty##? I think @Antarres already did...

@Infrared as per your suggestions I have reworded my claim 2. Is it airtight now? Or did I miss something? Claim 2: Since ##f(x)## is continuous bijection in the domain ##[0,1]##, so ##f(x)## is either strictly increasing or strictly decreasing within the interval. Proof: WLOG, let us...

True, I overlooked that. I took a stationary point for defining the extrema. It is supposed to be IVT (typographical error on my part). What I meant to do was to take an interval around the extrema, if it exists. And then prove that since any horizontal line in between the range of the interval...

Edited after comments from @fresh_42

The question confines itself to ##f:[0,1]\to [0,1]## such that ##f(f(f(x)))=x## for all ##x\in [0,1] \Rightarrow f(x)=x##. However, it can be proved for the general case,i.e. when ##f :\mathfrak {R}\rightarrow \mathfrak {R} ## such that ##f(f(f(x)))=x## for all ##x\in \mathfrak {R}##...

Yes, I think there is no reason to use concavity here. Here, I modified the Claim 2 according to your suggestion. Claim 2: Since ##f(x)## is continuous bijection in the domain ##[0,1]##, so ##f(x)## is either strictly increasing or strictly decreasing within the interval. Proof: WLOG, let us...

Question 9 : Claim 1: ##f(x)## is one - one., i.e., ##f(x)=f(y)\Rightarrow x=y## Proof: $$f(x)=f(y)$$ $$\Rightarrow f(f(x))=f(f(y))$$ $$\Rightarrow f(f(f(x)))=f(f(f(y)))$$ $$\Rightarrow x=y$$ So, ##f(x)## is one - one. Claim 2: Since ##f(x)## is continuous in the domain...