Ok guys I can't understand something.  Say that I have this circuit:    Assuming that I apply at the antenna 5V, how can I calculate how much power I will trasmit?  I found on internet that the current that will flow on the antenna radiation resistance, but if for example I go on ebay for try to find antenna no one quote the antenna radiation resistance, so how can I choose my antenna?  Moreover I want to know what  capacitor C1 and C2 do in this circuit.
I made a simple FM transmitter following  and it worked! Now I need some help to understand how.  My coil is made of 1 mm copper wire has 6 turns and 8 mm wire diameter. According to this online calculator:  this means that: L = 3.9e-7 H  I did not have any 5 pF trim capacitor so I used a 3 pF capacitor instead.  Am I correct in assuming that the frequency this will transmit on can be found by looking at the L1 C2 as a LC oscillator and using the frequency formulae:  fR = 1/(2*pi*sqrt(LC))  ?  If so I should get fR = 147 MHz. Which is strange since I received the signal on 91.5 MHz on my radio.  In a LC circuit I understand that the signal decays exponentially over time. That is hopefully not happening here. Why? Because of C4 maybe?  Also what is the purpose of C1?  If I want to increase the range of this FM transmitter somewhat can I do this by simply replacing R2 with a 470 Ohm resistor?  Are there free simulator programs that let me see the resulting spectrum at the antenna?
Successfully connected to a bluetooth speaker, but how do i direct sound there? Upper bound for $\sqrt[n]{n!}$ Sarrus Rule with LaTeX What does $(command) & do? A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$. Is there a good general purpose algorithm (batch of theorems) allowing one to determine the intermediate fields between $\mathbb{Q}(\zeta)$ and $\mathbb{Q}$, where $\zeta$ is some primitive root of unity?  Let $p$ be a prime. Consider the case where $\zeta=\zeta_{p}$ is a primitive $p$-th root of unity. Then the Galois extension is cyclic of order $p-1$ and $1,\zeta,\dots,\zeta^{p-1}$ is a $\mathbb{Q}$-basis for the extension. In this case for any subgroup $H$ of $G=\mathbb{Z}/(p-1)$, by considering the sum $$\alpha_H=\sum_{\sigma\in H}\sigma\zeta,$$ we can observe that $\alpha_H$ lies in the fixed field for $H$, and any automorphism $\tau$ not in $H$ (note automorphisms are identified with subgroups of $\mathbb{Z}/(p-1)$ in the natural way), $\tau$ does not fix $\alpha_H$. Therefore we can conclude that $\mathbb{Q}(\alpha_H)$ is the fixed field of $H$.  In this way we can get all of the intermediate fields of $\zeta_p$ for all odd primes $p$.  We also have a theorem that says if we have $n=p^sq^t$, then $$\text{Gal}(\mathbb{Q}(\zeta_n)/\mathbb{Q})\simeq \text{Gal}(\mathbb{Q}(\zeta_{p^s})/\mathbb{Q})\times\text{Gal}(\mathbb{Q}(\zeta_{q^t})/\mathbb{Q}).$$  So what I have yet to understand is  How can one generally find the intermediate fields between $\mathbb{Q}(\zeta_{p^s})$ and $\mathbb{Q}$ for $s\ge 1$? I would like to also understand the case where $p=2, s&gt;1$ though this might turn out to be a separate case.  EDIT: Even the case $n=pq$ is a little murky to me. Even given the isomorphism given by the Chinese Remainder Theorem I don't see a priori how to get all the "product" subfields. My idea is that you can consider the separate subfields under $\text{Gal}(\mathbb{Q}(\zeta_{p})/\mathbb{Q})$ and $\text{Gal}(\mathbb{Q}(\zeta_{q})/\mathbb{Q})$ separately and then consider the pairwise product of the generators of various subfields to see if you get anything new, but my idea is too inchoate. We all know that speed of gravitational waves (GW) and that of light in space are exactly the same (= $c$).  We also know that space is medium for GW.   Does that mean space is also the medium for light?  Because both of them are waves, and speed of a wave is property of the medium.   Is there any other way to justify the identical speed of the two? LINQ on a LinkedList - iterate over LinkedListNode, not T English equivalent for the Persian proverb "The mountain just gave birth to a mouse" I'm looking for an idiom or expression to describe a well-known person/ organization/ politician/ government  whose achievements in a given situation are smaller than what they had claimed or promised to be.  We Iranians have a proverb that literally means      The (roaring) mountain just gave birth to a mouse!    Its  etymology is like this:  Once a volcanic mountain started roaring, hissing, and bursting bubbles. The people were waiting to see what would happen after all those huge roarings and loud booms. Finally, the volcano activity stopped and the people saw just a tiny mouse came out of there! (rather than a monster that was expected to come). So they said mockingly:     "Heh! After all those huge roarings, the (big) mountain just gave birth to a (tiny) mouse!"    Notes:   The (roaring) mountain -symbol for an apparently big(=important) and strong person-here is figured like a woman who is screaming and shouting while is delivering her baby. We use this proverb for mocking an important person/organization/ government, etc ironically when they have used broad advertisements or have spent much money or resources over doing something noticeable, but the result/ achievement is less noticeable than it was claimed or promised to be.   Is there any equivalent for this Persian proverb?  I just found ; would it convey the same connotation? Efficiently finding two squares which sum to a prime How do I write a mathematical equation for ARIMA (2,1,0) x (0,2,2) period 12 How can I share files over a Windows network? I have a media computer which I recently reformatted to Ubuntu 10.04. I am probably just missing something obvious but I can't figure out how to share folders and files, so that I can browse to them on my Windows computers in order to copy files to/from the computer.  How do I do this? Alright, so the idea of an exponent, $x$, is that you are multiplying its base by itself $x$ number of times. With base $5$ and $x=3$, we have that $5^3$ = $5 \cdot 5 \cdot 5$  I understand that the logarithm with base $a$ of $x = c$,  tells us that  $$a^c = x$$  and for $c =$ positive; values for $x$ are greater than $1$, and for $c =$ negative; values for $x$ are less than $1$,  and for $c = 0$, values for $x$ are...$1$.  So in short, I understand how, by means of observation of the graph of $f(x) = \log x$, we can see that $f(1) = 0$, BUT, I see no other way to understand why $x^0 = 1$, apart from the graph and everything around that very point.  I honestly cannot get my head around the idea, "$5$ times itself $0$ times... is one".  Is it that there is no fundamental answer for this but that we simply know by the graph? Or can I truly understand $x^0 = 1$ on its own? My multiple regression analysis model has a statistically significant F value however all beta values are statistically non-significant.   All the regression assumptions are met. No multicollinearity was found. Correlations among all predictors are all less than 0.60.   What else might be the cause of the insignificant predictors? Missing links to responses to comments on nomination posts In the responses tab in my profile, responses to comments on nomination posts include a working link in the page source, but because there's no title the links are empty and useless.    When listed in the inbox such posts do have a title, though in this case the link is to the post and not directly to the comment. (Actually, the links in responses end up being redirected and also go to the post and not to the comment, but they try to go to the comment.)  In Supercollider:    In Global Profile: How do I delete multiple rows in Entity Framework (without foreach) I have 2 HDD drives in my computer. At the moment second drive is mounted as /media/storage.  How can I move my user data from /home to /media/storage/home?  Can I just move the data over there and then simply symlink it back? ETS() function, how to avoid forecast not in line with historical data? How do I find least cost path over a DEM based on slope magnitude and direction? What sort of algorithms can I use to find a least cost path through a DEM where it costs more to traverse a cell going downhill or uphill than it does to follow the contour of the land?  All the examples I've seen involve creating a least cost surface where the magnitude of the slope is part of the cost - but the direction isn't.    Additionally, the examples assume the cost to travel through a cell does not depend on the direction of travel. Baby Rudin claim: $1+\frac{1}{3}-\frac{1}{2}+\frac{1}{5}+\frac{1}{7}-\frac{1}{4}+\frac{1}{9}+\frac{1}{11}-\frac{1}{6}...$ converges This sequence is a rearrangement of the series $1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}...$. Note that at this point in the text we do not have any theorem about the convergence of rearrangements.  Let $\{s_n\}$ be the sequence of partials sums of the series then for $n \ge 0$  $s_{3(n+1)} = \sum ^n _ {k=0} \frac{1}{4k+1} + \frac{1}{4k+3} - \frac{2}{4k+4}$  We can view it as the sequence(on $n$) of partials sums of  $\sum_0 a_n = \sum_0 \frac{1}{4n+1} + \frac{1}{4n+3} - \frac{2}{4n+4}$  Where $|a_n| = a_n = \frac{1}{4n+4}\{\frac{3}{4n+1}+\frac{1}{4n+3}\} \le \frac{1}{4n^2}$.  By the comparison test $s_{3(n+1)}$ converges to some real $\alpha$.  But $s_{3(n+1)+1} = s_{3(n+1)}+ \frac{1}{4n+5}$ and $s_{3(n+1)+2} = s_{3(n+1)}+ \frac{1}{4n+5}+\frac{1}{4n+7} $hence we have a partition of $\{s_n\}$ into subsequences which tend to $\alpha$ and this implies $s_n \rightarrow \alpha$.  Is my proof correct? Any alternative solutions are appreciated. singlespacing in table with no indent