Subset $A_1,..A_m$ of $\{1,2,...n\}$ where $|A_i|$ is even $\forall i$ and $|A_i \cap A_j|$ is odd when $i \neq j$, prove $m \leq n$
A Variation of the even-town odd-town problem
It looks as if the 10k-tools flagged post list is b0rken.  Next to the review link in the toolbar there is a flag counter showing there are 10 flags to be reviewed:    Clicking on that flag counter leads to an empty page:        The moment I visit that page (through clicking on the flags counter, or by going to the review queue first then clicking on Tools, selecting the flags tab if not already selected), the flags counter disappears from the toolbar:    but after a while (half an hour, an hour?) the flag count re-appears in the toolbar.  Either the counter is wrong (presumably taken from a Redis cache somewhere) or the 10k flag review page is falling over every time someone tries to load it.  This at first appeared to happen only on Meta, on Stack Overflow the flags page has plenty to review. However, there are now  on Stack Overflow. looks like someone got happy with the CSS - you can now no longer tell what tab is active, e.g. answer tabs:        Even if you hover over an option - it wont show you what tab is currently selected - it only shows you what tab you are currently hovering over: Add new item in existing array in c#.net How to add new item in existing string array in C#.net?  I need to preserve the existing data. Find a plane that passes through a point and is perpendicular to 2 planes Find an equation of a plane that passes through $p(1,5,1)$ and is perpendicular to planes $2x+y-2z = 2$ and $x+3z=4$.  I basically need the 2 other points to make the vector and perform the cross product.  Since $ax+by+cz+d=0$ is the form of a plane. Can I obtain the points as $(a,b,c)$ of the 2 planes given? Also, how can I set them up to obtain the points? How do I define custom web.config sections with potential child elements and attributes for the properties? The web applications I develop often require co-dependent configuration settings and there are also settings that have to change as we move between each of our environments. All our settings are currently simple key-value pairs but it would be useful to create custom config sections so that it is obvious when two values need to change together or when the settings need to change for an environment. What's the best way to create custom config sections and are there any special considerations to make when retrieving the values? Examples in which the light maximizes the optical path length I posted a similar  about geodesics on Math.SE. Many sources ( for instance) claim that the light could maximize the optical path length in some cases. But I don't think it's actually true since between two points I can always imagine a path with arbitrary length. Therefore, or the light minimizes the optical length or it's stationary (neither maximum nor minimum). My question is: is the trajectory in red in the figure below a local minimum or a stationary curve?   If I'm wrong, please provide some examples which the light propagates in trajectory of maximum length. $\lim_{h\to 0}\int \frac{f(x+h)-f(x)}{h}\,\mathrm{d}x = f(b)-f(a)$ Let $f:[a,b]\to  R$ be integrable and continuous on $(a,b)$. Prove that: $$\lim_{h\to 0} \int_a^b\frac{f(x+h)-f(x)}{h} \,\mathrm{d}x = f(b)-f(a).$$  What I've tried so far: make a change of variables, which didn't help. I also thought of using the intermediate value theorem inside the integral, but the function being differentiable is not specified. Any help, tips? Thanks in advance! I'm trying to create a join/relate in QGIS where I have a shapefile of buildings and to that I would like to join a non-spatial table (.csv-file) containing people who work in each building. So I have multiple records in my table that I would like to be able to join to my single features in my shapefile. I can only run a join in QGIS where the first record is joined to the shapefile feature (ie building) but subsequent records get removed. Could someone let me know how to complete this join/relate in QGIS? I have been trying to achieve a true mesh displacement on meshes for quite some time, without ever getting it to work.  If I understand it correctly, this experimental feature would allow me to easily displace the vertices of a mesh - or to create new mesh vertexes where needed - to get a displaced mesh in the result, based off an image, but without using a bump map (simpler, faster?).   This all sounds very exciting in theory, but I am having a really hard time finding examples or tutorials that are both recent and whose links function. So I think there is the need for a question here which will call upon detailed and recent answers to bridge that gap.  I'll start with a simple ico sphere:    Then, , I will change the Feature Set to the Experimental one:    I then add a pink granite image to the mesh:    Mark Seams, Unwrap, add image in the UV Editor:      and finally, in the Object Data panel, change the Displacement method from Bump to True as explained :    no result yet:    if I click "Use Subdivision" this is what I get (so I won't click it right now):    Looking into the Node Editor, nothing seems to have changed with the Displacement of the mesh:    so I tried to replicate the node setup seen in  of  (Linear isn't an option, Clip, Single and Repeat are):    ... but the result is a white ICO Sphere, similar to Image 1.  So, can the "Experimental Feature Set" be used to create actual displacement, and modify a mesh?  This is what I'm trying to obtain - but with the image of the texture actually displaying on the mesh (image from ):    .blend file: How to restrict some websites in Ubuntu 14.04 I would like to restrict some websites to be surfed. I mean I want to prevent access to some websites. Please guide me on how to do the same in Ubuntu 14.04 LTS. I want to install lubuntu on my current (pre-existing) Ubuntu Install because of it's light-weight footprint.   Can I preserve currently installed apps after installation? 80/90s UK children's drama series about an "alien" boy with radio weapon I've been trying to track down a live-action children's TV series (or short story perhaps) from the 1980s or 1990s, probably on CBBC or CITV.  A few people I've spoken to IRL have suggested The Boy from Space or Sky, but I'm pretty sure it's neither as a lot of the details don't seem to match.  The story was set on Earth (possibly England or Wales) and was about an "alien" boy who was being pursued by a group of people, though I don't remember who they were.  Somehow he encountered siblings, a girl and a boy, and made friends with them. I think they lived on a farm with their parents, as I remember quite a large barn or other building, and they hid(?) the boy in a car which was inside or next to this building. He also slept in this car with a dog (which might have been a German shepherd).  The "alien" boy had a portable "radio" (all silver, very 1980s) that repelled his pursuers by emitting a high-pitched sound when he turned a dial on it, and he used it when out and about with the other children whenever they encountered a pursuer. I seem to remember lots of hills and valleys, lots of green.  In the end it turned out he wasn’t really an alien, but a human from the far future. He was pretending to be an alien as he was from 20000 years into the future and humans' appearance had changed by then, but he had the ability to make himself look like current-day humans. When he was in his car/bed he reverted to his normal appearance, so he would hide under the blankets until he was able to assume current-day human appearance.  In the finale, it was revealed that he was never in any danger – the pursuers were testing him as part of a kind of coming-of-age thing. I remember a scene on a spaceship or something where his elders/parents where shown telling him that he was safe all along and that he "passed".  I also seem to remember them referring to "ancestors" and making sure they didn't find out, so the either the girl or boy could well have been a direct ancestor. Search for text files where two different words exist (any order, any line) I'm looking for a way to search files where two word instances exist in the same file.  I've been using the following to perform my searches up to this point:  find . -exec grep -l "FIND ME" {} \;   The problem I'm running into is that if there isn't exactly one space that between "FIND" and "ME", the search result does not yield the file.  How do I adapt the former search string where both words "FIND" and "ME exist in a file as opposed to "FIND ME"?  I'm using AIX. Badges with long names overflow on the profile page So far, I understand that I have to look at each Jordan block. How do I prove that for a Jordan block with a value of x, $J_n(x)$, the Jordan decomposition of $(J_n(x))^2$ is $J_n(x^2)$ ? I have a feeling this will lead me to the solution. Thanks for your time. Single Variable Calculus Reference Recommendations This question is a  of the common question asking for calculus references. It is here to  away the repetition, and give a canonical resource for calculus references.      I'm looking for a resources to learn single-variable calculus. If I click to open achievements from a question when I click the X to close the achievements view I end up on the answers tab of the question, I assume because the X is over the tab and it's tapping through.    It appears if I hit the X it's ok, but if I tap anywhere else in the top row (where the X is) then I can switch to the question or answer tab. My SoulSeek client Nicotine+ checks my open ports during initial configuration and promts that the one port number it needs is closed, cutting me off frmo about 50% of the users. Is there anyway I can open that particular port for the application to use?  RUnning ubuntu desktop 13.04. I have not manually installed any firewalls, but not sure if its included in the default installation. My 8 year old son won't fall asleep We put him to bed at 9pm and he stays up til 1am or later. When I go to check on him he is always playing with his hands and sometimes talking. I ask him why he is awake and not trying to sleep and he says it's because he just wants to play. He never comes to tell us that he is having a hard time sleeping or that there is anything wrong. The weird thing is that he used to be the first one to fall asleep out of 3 boys and the staying up started a few months ago. He does this every night and on top of keeping us awake, he is now waking up his brothers.   About a month or so ago, we decided to punish him by grounding him from video games. He doesn't want to be grounded, but he still keeps doing it. Nothing we do seems to be helping and it seems to be getting worse. I have talked to him about why it is so important to get enough sleep and why it's even more important for kids. He also gets plenty of exercise and time to play during the day.   I'm really starting to wonder if he is doing it just to be defiant. If anyone has any suggestions I would greatly appreciate it.  The problem is that he is being disruptive to everyone in the house and it has been EVERY night for the last 3 months.   He is tired and emotional during the day, and it is causing his brothers to be tired during the day while they are at school.   Because he is tired during the day he doesn't really want to be as active as he used to be. However, I do still encourage him to be active. We have always had a bedtime routine. We have asked him many different times if he is just having trouble sleeping, if he is uncomfortable, and if there is something wrong. He always tells us that he just wants to play.   At the beginning of all this he told me that he wants to be the one to decide when he goes to sleep and when he wakes up. Which is why I would even ask if it was out of defiance.   We really didn't want to get to the point of punishing him, but nothing else seemed to help and it was only after he started keeping his brothers awake.   It's not like we haven't asked him what he thinks would help or what would help him sleep better. He ALWAYS says that he just WANTS to stay up and play because it is fun. We know it is important for him to get enough sleep, and I'm worried because I don't think he is (and he's preventing the rest of us from getting enough, too). Incorrect plot using pgfplots (trigonometric functions like cos, sin and tan) I'm trying to plot a function with pgfplots for LaTeX. Unfortunately, pgfplots plots the function incorrectly.  Here is the LaTeX code I use:  \begin{figure}[H] \centering \begin{tikzpicture}     \begin{axis}[xlabel=Gameplays,ylabel=Rating]         \addplot+[gray,domain=1:30]         {0.5 + 0.5 * ((atan(x) * 2 / pi)^11.79)};     \end{axis} \end{tikzpicture} \caption{Omzetten van aantal gameplays tot impliciete rating} \label{fig:omzetten_impliciete_ratings} \end{figure}   Here is how the function should look like:     This is how it is plotted:    Does anyone know what I do wrong?  Thanks in advance!