Image float Lyx
Floats appearing in wrong places
In cricket, in UDRS screen, if the ball hits the wicket, then why is not out still given? In cricket, in UDRS screen, if the ball hits the wicket, then why is not out still given?  I saw this situation so many times happened; bowler appealed for UDRS for LBW, in UDRS it shows ball hits the wicket, but still not out is given sometimes. Pull Down Resistors In my quest to understand electrical engineering, I have stumbled across this tutorial:    I have understood the diagrams until I got to switches. I am not sure how switches work on the breadboard or the diagrams. This is the specific one I am thinking of (this is of a pull down resistor):    The implementation is:    Based on the diagram, what I think is happening is: Power goes to the switch, if the button is up then the circuit is not completed. If the button is pressed then the current takes the path of least resistance to pin2 because it has more pull (100ohm &lt; 10kohm).  The way it is described in the tutorial sounds like when the button is up, the circuit is still complete, but the 10k ohm resistor pulls the power to the ground. I am not positive how or why if both the 10k ohm and 100ohm are receiving equal current, the current would get pulled to the ground through a higher resistance than is open to pin 2. Help ending a proof using binomial theorem: $\sum_{k=0}^n {n \choose k}\cdot\frac{(-1)^k}{k+1} = \frac{1}{n+1}$ Why are downloads destructive in the Star Trek universe? There are numerous places in various Star Trek episodes where references are made to the fact that "downloads" are a destructive operation: you download something from one place, and unless you explicitly made a copy beforehand, what you downloaded is gone from its original storage location and instead appears in some other location. Hence was born the term "copy and download".  There are of course out-of-universe, plot reasons for things happening that way which are exploited from time to time. There is also the out-of-universe explanation of how large media companies feel about people downloading copyrighted works, and a possible out-of-universe explanation that at the time, people in general may not have been intimitely familiar with the implications of the term "download", so they added "copy" to help describe what happens to at least portions of their viewership.  But is there a plausible in-universe explanation for why downloads would be destructive by default, and a specific copying operation would have to be made beforehand so as to not delete the data from its original location?  As for specific examples, these are two that I can think of right now (I'm quite sure there are more):   VOY "Twisted" (S2E06), right near the end, stated by Torres: "Our entire database has been copied and downloaded into somebody else's system." VOY "Message In A Bottle" (S4E14), a little more than five minutes into the episode, the EMH is "downloaded into the transceiver array" for transmission across an alien sensor network to the Prometheus when the latter is in the alpha quadrant, and some 20 minutes into the episode it's established that the EMH is not available in the sickbay and will return later. Thermistor control of peltier voltage with Arduino (for DSLR chill box project) I am mildly familiar with electronics, mostly from playing around with electronics kits as a kid. That was a long time ago, though, maybe as much as 20 years ago. I am currently working on a cold or "chill" box for my Canon 5D III, so I can keep it's temperature very low, and very consistent, for doing low noise astrophotography.  I have a general design for the box, and I'm using a single 12v 5.8amp peltier (TEC) attached directly to a copper box for cooling. The box is currently insulated with extruded foam board, and the hot plate of the peltier will be cooled with a water cooler from an old computer kit.   I'm getting more ambitious with my project, however. I want thermal regulation, to maintain a consistent temperature, and I'd eventually like to get into two-stage cooling to achieve a Delta-T of closer to -55-60°C relative to ambient (the chill box will be cooling the camera, so the sensor will be warmer, probably by as much as 10°C, than the temperature of the copper plating in the box itself.) I want to have two primary modes:   Rapid cooling mode, operating the peltier at 12v or higher (max voltage is 15.4v) to quickly cool the box down to the target temperature. Regulated maintenance mode, operating the peltier at lower voltages to maintain a consistent temperature, above the maximum potential cooling the peltier can supply (for headroom as the voltage is adjusted in response to small temperature fluctuations).   I'd like to maintain temperature within 2-3°C if possible. I've looked into Arduino (and I've messed with similar things in the past), and it seems perfectly ideal for the task, with one exception: It doesn't seem to handle the kind of current I need top power a single peltier, and certainly not two.   I've done some research on how I might achieve this, but I'm falling up short on my understanding of the electronics involved. I've found a two-relay "shield" for Arduino Uno that can power two devices with up to 8amps each, and up to 30v each. That can be controlled from the Arduino itself. It seems the design of a relay uses a magnetic coil to actuate a switch that allows an independent power source to be used to power components like a motor, solenoid, or in my case a peltier. I haven't found any way of actually regulating the voltage of the relay with the Arduino, however.  So I kept investigating, and I came across some schematics that showed how to use transistors, specific mosfets to be exact, where the base was connected to an Arduino output, and the collector/emitter were connected to the power loop of whatever needed to be powered at a higher voltage (not sure about current here), and this still allowed control of the voltage.   It's been so long since I messed with any of these components, my memory is extremely rough, and I'm not quite connecting how it all works. I'd be happy with some references to complete examples of powering, and controlling the voltage of, high powered devices via an Arduino, but if anyone here can explain how all this works and why, that would be most ideal. I'd rather understand the concepts, so I can reapply them later, than just have a pattern to follow. Deploy Community Builder audience page assignments with ant migration tool? In Community Builder, if you create audiences and assign them to page variations, you cannot deploy these using change sets, according to .  In fact, Audience doesn't even appear in the list of change set components.  On the other hand, Audience metadata can be deployed using the ant migration tool, so I was hopeful that the audience assignments would also be deployable.  Unfortunately, I haven't had success in deploying any audience assignments, either for entire pages or for components on a page.  Has anyone found a workaround for deploying audience assignments for Community Builder pages?  I should say that I'm using the Build Your Own template.  If it can't be deployed, is there at least a way to get a list of audience assignments so I don't have to open every single page in the Community Builder to check?  Here's what I'm using in my package.xml manifest.  All the community builder page variations and all the audiences are created correctly, but the assignments are not.  &lt;types&gt;     &lt;members&gt;*&lt;/members&gt;     &lt;name&gt;Audience&lt;/name&gt; &lt;/types&gt; &lt;types&gt;     &lt;members&gt;*&lt;/members&gt;     &lt;name&gt;CustomSite&lt;/name&gt; &lt;/types&gt; &lt;types&gt;     &lt;members&gt;*&lt;/members&gt;     &lt;name&gt;SiteDotCom&lt;/name&gt; &lt;/types&gt; How can I find the following limit :$$\lim_{n\to\infty}\left(1-\frac{1}{3}\right)^2\left(1-\frac{1}{6}\right)^2\left(1-\frac{1}{10}\right)^2\cdots\left(1-\frac{1}{\frac{n(n+1)}{2}}\right)^2$$There are four options $(a)\frac1{3}(b)\frac1{9}(c)\frac1{81}(d)0$ Thanks! Configure Postfix to use external MX servers for delivery of local mail if user is unknown I have a following setup:   linux box with postfix configured to be responsible for example.com domain domain's MX servers are configured so that mail sent to example.com is sent to google mail servers several user accounts on linux machine exist (same machine also hosts example.com site)   When someone from the outside attempts to send mail to address ending with @example.com, it gets routed to google mail (and there handled appropriately).  When linux machine tries to send mail to outside world, mail is delivered correctly, as reverse dns and spf records are configured correctly, so linux machine is valid mail sender for example.com domain (along with google mail servers).  However, here's the problem. When php application (hosted at linux box) tries to send mail to someuser@example.com (and someuser doesn't exist on linux box), it fails, since it doesn't even consult google mail servers, but postfix smtp locally concludes that "someuser" is unknown.  So, the question is: how do I tell postfix to relay mails sent to @example.com domain to google mail servers (so, to servers specified in MX records), IF and only if a mailbox is not found locally. parallel thermostat I have a venter room heater in a cabin. It uses a milivo;t thermostat. I am hooking it up to a wifi thermostat using a relay and 24 volt power supply. My concern is that if the power goes off that the thermostat will not power the unit on. I currenty have a digital thermostat that controls the unit and works great. can I wire the current thermostat to the wifi in parallel so if power goes off it will still allow the heater to turn on. If I can how do I wire it? Does going outside of range or line of sight after casting a spell have any effect? Associativity of symmetric difference of sets By $A\oplus B$ we denote the symmectric difference of two sets. The definition is $A\oplus B =(A\setminus B) \cup (B\setminus A)$. Now I hope to show that $A\oplus (B\oplus C) = (A\oplus B)\oplus C$. I remember that there's an elegant proof, but I forget its detail. (The first step is to show $A\oplus (A\oplus B) = B$, and maybe applying this formula, we can obtain associativity.) Expression Versus Statement I'm asking with regards to c#, but I assume its the same in most other languages.  Does anyone have a good definition of expressions and statements and what the differences are? I am trying to grow my C: drive to use the unallocated space on Disk 0. Is it safe to throw away the Recovery Partition (i.e. make it unallocated)? And if so, is GParted an ok tool to do that with? Or do I need to move that, and if so, is the way to do that to reduce the size of the unallocated partition so there is empty space at the end, then move it there? $x^{x^{x^{\dots}}}=2$, what is the value of $x$? I came up with this little simple exercise, stating:  $x^{x^{x^{\dots}}}$ infinite times is equal to $2$, find $x$.   As we're dealing with infinity, we can just separate the first $x$ and get $x^2=2 \implies x=\sqrt2$  But then I thought what if we change $2$ to $4$? Now we get $x^4=4 \implies x=\sqrt[4]4=\sqrt2$  Something went wrong, can someone explain? Can people PLEASE spell out their slang acronyms MathJax half-broken in suggested edit diffs In a suggested edit I just reviewed, about a third of the MathJax renders properly, but the rest doesn't. Note that the delimiters on puzzling are \$, so that doesn't escape it.    Related:  Don't render MathJax when viewing source:   Render MathJax when viewing rendered output: How to justify $\phi(n) \ge \sqrt{n}$ If $\phi(n)$ is the Euler-totient function, how can I show that $\phi(n) \ge \sqrt{n}$? XIV pages in page counts? How to install software or upgrade from an old unsupported release? Recently I have installed an older version of Ubuntu on my old machine. Whenever I try to install any software, I get an error saying it couldn't be found:  $ sudo apt-get install vlc Reading package lists... Done                Building dependency tree        Reading state information... Done     E: Couldn't find package vlc Problems enabling Bitlocker on Surface Pro with Windows 8.1 Using a brand new Surface Pro (first generation) out of the box, installed current updates, then 8.1, and any further recommended updates after 8.1 was installed.   I've installed a two other things that don't seem connected to the issue: the Cisco Anywhere VPN client and Visual Studio 2013.  I'd like to enable Bitlocker, but during the verification step, the following error is displayed, with no options to continue:     This PC deosn't support entering a BitLocker recovery password during startup. Ask your   administrator to configure Windows Recovery Environment so that you can use BitLocker.   The "administrator" in this case is me, and I don't:   ... understand why this has happened ... know how to fix the issue, as if it's really necessary to make this change, what would I do?