The issue I'm currently struggling with is: What is the mathematical relationship between power dissipation and temperature in a resistor?    The project I'm working on is a controller card for a [supercapacitor w/ resistive precharge] in a box.         &ndash; Schematic created using   The resistance and capacitance are known parameters of the system and the voltages are measured.  With this information I can calculate the amount of energy I'm getting ready to dump into the resistors and then decide if I have the thermal overhead to complete that charge cycle:     if(Predicted_Energy &lt; MAX_ENERGY - Current_Energy)   {      charge=1;      Current_Energy += Predicted_Energy;   }     Once I finish charging and switch to RUN mode, those resistors are cut out of the circuit.  Now they're just sitting there cooling off... dissipating energy.  How can I take this cooling over time into account with my Current_Energy value?  Is it possible to estimate or assume how much energy is lost given time only? Or would I need to monitor the temperature of the resistor to determine this?
I want to model the transfer function of a resistor mathematically, and am after some resources / tips on if it's possible to do so.  For example, if I put 1V into a 1 Ohm resistor, I want to know how long and how (shape) it will take to reach a steady state temperature, given 25 deg C ambient.  I.e.   $$ \frac{T(s)}{V(s)} = ??? $$  Where T(s) is the laplace transform of temperature T(t), measured in say Kelvin.  I understand there are a lot of factors which will affect this model (material, size, shape, ambient (?)), but I'm not sure where to even start. A  shows the heat rise at a certain load, but not really how it gets there. I can't find a time-domain function for the temperature rise either.
Do the 46 human chromosomes form a single unbroken DNA helix?  Or is it rather that a human's genome consists of 46 disconnected helices?    If it is the former, does the common numbering scheme for the chromosomes have any correlation to their actual ordering in the one large strand?  If is the latter, is there a convention on how the chromosomes are ordered in genomic datasets?  Also, is there a clear understanding of how sister chromosomes "find" each other in Meiosis I?  Generally, during periods when Mitosis/Meiosis are not occurring,  what's a good physical picture for how the chromosomes are physically arranged (e.g. a bowl of 46 spaghetti noodles, or maybe the sister chromosomes always stay close together, etc)  thanks! Solution for PHP / MySQL website loading fast in multiple regions What are the blue dots next to App names in iOS and macOS? They disappear once you open the apps and then return to the home screen, but I can't tell what they indicate.  Are they apps that haven't been opened since an app update? Or that it thinks have never been opened (not accurate in my case, but that could be a function of a "restore" confusing the phone). Placement of varistor with respect to fuse My design includes a pretty standard AC/DC converter powered by mains for intended use at home. For overvoltage and overcurrent protection, I am planning to use a combination of varistor and fuse placed before the power converter.  I understand it is good practice to put the fuse before the varistor - in an overvoltage event, the varistor will draw a large current that may blow the fuse, protecting the rest of the circuit and even the upstream circuitry.  However, due to extremely tight layout, it is very hard to put the fuse before the varistor.  What risk am I running if I put the varistor before the fuse?  What if I put a second fuse in series with the varistor? Does it negate the varistor's protection of the downstream circuit? Post Feedback link is broken I first noticed this a while back. But it has yet to resolve itself.  When I click on the  in the 10k tools, it hangs for a while.Then it gives me an error message: How to directly prove that $M$ is maximal ideal of $A$ iff $A/M$ is a field? An ideal $M$ of a commutative ring $A$ (with unity) is maximal iff $A/M$ is a field.  This is easy with the correspondence of ideals of $A/I$ with ideals of $A$ containing $I$, but how can you prove it directly?  Take $x + M \in A/M$.  How can you construct $y + M \in A/M$ such that $xy - 1 \in M$?  All I can deduce from the maximality of $M$ is that $(M,x) = A$. Qualcomm Atheros QCA6174 802.11ac Wireless Network Adapter [168c:003e] (rev 32) can't enable wi-fi Fixed Field of $\sigma, \tau$ Let $k$ be a field and let $K=k(x)$ be the rational function field in one variable over $k$. Let $\DeclareMathOperator{\aut}{Aut}\sigma, \tau \in \aut(K)$ s.t. $$\sigma\left(\frac {f(x)}{ g(x)}\right)=\frac {f(1/x)}{g(1/x)}\qquad \&amp;\qquad \tau\left(\frac {f(x)}{ g(x)}\right)=\frac {f(1-x)}{g(1-x)}.$$ Find the fixed field $F$ of $&lt;\sigma, \tau&gt;$. Determine $\DeclareMathOperator{\gal}{Gal}\gal(k/F)$. Find an $h \in F$ so that $F=k(h)$.   Now for the first automorphism $\sigma$, I think if I concentrate on $k[x]$ it will give me some idea. Now, if $f(x)=a_0+a_1x+a_2x^2+ \cdots + a_nx^n \in k[x]$ then if $x^n \sigma(f(x))=f(x)$ the case will be $a_i=a_{n-i}$ $\forall i=0(1)[n/2]$. So all the funtions in $K$ which will be fixed by $\sigma$ are of the form $\frac {f(x)}{ g(x)}$ where $f(x)=a_0+a_1x+a_2x^2+ \cdots + a_nx^n$ and $g(x)=b_0+b_1x+b_2x^2+ \cdots + b_nx^n$ such that $a_i=a_{n-i}$ $\forall i=0(1)[n/2]$ and $b_i=b_{n-i}$ $\forall i=0(1)[n/2]$.   Please check whether am I right or not?  And any ideas for the rest of the part? Make it cost more to downvote without comment; make it hurt to leave a crap comment Possible Duplicate:    In the spirit of &quot;encouraging&quot; people to leave comments on downvoting, I would propose that if someone downvotes without a comment, I propose a heavy point tax, say 3x the current point cost for a downvote. If he or she downvotes and leaves a comment, then it costs the current amount. If someone leaves a crap comment (to avoid the &quot;charge&quot;) they get a painful spank (100 points gone or whatever the community decides) if and only if:  The comment is flagged Three (five? whatever) moderators agree it is crap  Common complaints Or, why my proposal is different.  &quot;  a &quot;   No it isn't. I specifically address the issue of leaving garbage comments to avoid the downvote tax, unlike the other proposals.   &quot;Some people want to leave anonymous (down)votes.&quot;  I understand that some might be fearful of retaliation. Is retaliation a real problem or a &quot;what if&quot; conjecture? (Where's the data?) What if we try it for 3-6 months and then circle back to see how well it works?  If a user starts retaliating against another user, they will be dealt with as are all other problem users. Nothing else is anonymous - asking questions, answering questions, editing questions, leaving comments, etc. and there is a clear benefit. What is the benefit to the community for having anonymous voting? I would argue &quot;none.&quot; Even though some people might want to leave anonymous questions, answer anonymously or anonymously edit a question, it is not allowed, because it is not good for the community.   &quot;But this will discourage downvoting&quot;  I agree, and I think that's a good thing, which goes to the philosophy of the site: promote good questions and answers. If a question or answer is poor, few will up-vote it. If is is really poor, it will get flagged and . If someone really wants to downvote, no one is stopping him or her. Just as we want quality questions and answers, we need quality voting.   It will require too much work to implement  Maybe. Let's ask if it is worth the effort. What benefit does anonymous, no-comment downvoting add to the site? It certainly doesn't allow the author to improve. What benefit would owned, commented downvoting add? It would hopefully allow authors to improve and discourage drive-by downvoting. Would me (or someone else) submitting a patch alleviate this complaint?   Jeff (or Joel) thinks this is a stupid feature, and you're stupid for suggesting it.  &quot;&quot; Is this a true statement?    Thanks for reading. What is the best Java email address validation method? What are the good email address validation libraries for Java?  Are there any alternatives to ? How do I solve this limit: $\lim _{x \to 0} \left(\frac{ \sin x}{x}\right)^{1/x}$? $$\lim _{x \rightarrow 0} \left(\frac{ \sin x}{x}\right)^{1/x}$$  I have spent an hour on the above limit and have no work to show. I tried using L'Hopital's Rule, but just kept going around in circles. Any help would be appreciated. Thank you. Living potato clock? Can a shell script set environment variables of the calling shell? I'm trying to write a shell script that, when run, will set some environment variables that will stay set in the caller's shell.  setenv FOO foo   in csh/tcsh, or  export FOO=foo   in sh/bash only set it during the script's execution.  I already know that   source myscript   will run the commands of the script rather than launching a new shell, and that can result in setting the "caller's" environment.  But here's the rub:  I want this script to be callable from either bash or csh.  In other words, I want users of either shell to be able to run my script and have their shell's environment changed.  So 'source' won't work for me, since a user running csh can't source a bash script, and a user running bash can't source a csh script.  Is there any reasonable solution that doesn't involve having to write and maintain TWO versions on the script? Circle-Rectangle collision detection (intersection) How can I tell whether a circle and a rectangle intersect in 2D Euclidean space? (i.e. classic 2D geometry) I'm sure this is a newbie question, but I can't figure this out. I have tried to follow the advice here:  and here:   But I can not seem to be able to generate any font change. I either get no change or error messages.  Here is the output of one failed attempt to change the font to Times using this command:  \rmfamily \renewcommand{\rmdefault}{ptm}     Apparently I either don't have a correct package installed or...  The output says " Metric (TFM) file not found." but I am not sure where to go from there. When it comes to getting a tenure-track position where one has both a lot of resources and academic freedom to do what one wants to do (so having a tenure-track position in a top university might be more useful because one may get more resources at a top university).   Or in short, when one wants to maximize one's chances of becoming a "top scientist".  There are obviously numerous factors, and "rank/prestige" should not be considered as a factor in itself. That said, the period after one gets a PhD is an extremely important time for building up connections, and those are easier to get at a top university. How do I go about tracking down IO usage in Linux and other *nix OS'? Occasionally, something on my system starts hammering the disk. I would like to log data that would let me know about I/O usage per process, then I could go back to it later and see what keeps doing this. How should I go about solving this problem? Bonus points for solving this for arbitrary block devices. Limits, find a limit that exist in absolute value but not outside the absolute value. Let I be an open interval that contains the point c and let f be a function that is defined on I except possibly at the point c. Suppose that lim |f(x)| as x->c exists. Give an example to show that lim f(x) as x->c may not exist.   Not really sure of an example for this? My table is:     id home datetime player resource     1 10 04/03/2009 john 399   2 11 04/03/2009 juliet 244   5 12 04/03/2009 borat 555   3 10 03/03/2009 john 300   4 11 03/03/2009 juliet 200   6 12 03/03/2009 borat 500   7 13 24/12/2008 borat 600   8 13 01/01/2009 borat 700     I need to select each distinct home holding the maximum value of datetime. Result would be:     id home datetime player resource     1 10 04/03/2009 john 399   2 11 04/03/2009 juliet 244   5 12 04/03/2009 borat 555   8 13 01/01/2009 borat 700     I have tried: -- 1 ..by the MySQL manual:   SELECT DISTINCT   home,   id,   datetime AS dt,   player,   resource FROM topten t1 WHERE datetime = (SELECT   MAX(t2.datetime) FROM topten t2 GROUP BY home) GROUP BY datetime ORDER BY datetime DESC  Doesn't work. Result-set has 130 rows although database holds 187. Result includes some duplicates of home. -- 2 ..join  SELECT   s1.id,   s1.home,   s1.datetime,   s1.player,   s1.resource FROM topten s1 JOIN (SELECT   id,   MAX(datetime) AS dt FROM topten GROUP BY id) AS s2   ON s1.id = s2.id ORDER BY datetime   Nope. Gives all the records. -- 3 ..something exotic:   With various results. Can I charge computers by inducing 5-volt into their USB connectors? Is this possible? I noticed that when my EeePC 900 is off but plugged in charger, there is power coming out of the USB port. Can this be a sustainable way of charging a PC, or a flaw in design?