JavaFX primaryStage remove windows borders?
JavaFX: Undecorated Window
$SU(3)$ irreducible representations with tensor method I am dealing with the tensor product representation of $SU(3)$ and I have some problems in understanding some decomposition.  1) Let's find the irreducible representation of $3\otimes\bar{3}$  we have that this representation trasforms like   $${T^\prime}^i_j=U^i_k {U^{\dagger}}^l_j T^k_l $$  hence I observe that  $$Tr(T)=\delta^j_iT^i_j$$ is an invariant and so  $$T^i_j=\left(T^i_j-\frac{1}{3}\delta^j_iT^i_j\right)+\frac{1}{3}\delta^j_iT^i_j$$  allows me to write $$3\otimes\bar{3}=8\oplus1$$ Here comes my questions: I have heard that this $8$ representation is an "$8_{MA}$" where MA is for "mixed-antisymmetric". The meaning of "mixed-antisymmetric" shold be: "the tensor $\left(T^i_j-\frac{1}{3}\delta^j_iT^i_j\right)$ should be antisymmetric for an exchange of 2 particular indexes but not for a general exchange of 3 indexes". What does this mean? I see only 2 index in that tensor.  2) Consider this representation: $$3\otimes3\otimes3=3\otimes(6\oplus\bar{3})=3\otimes6_S\oplus3\otimes\bar{3}=3\otimes 6_S\oplus8_{MA}\oplus1$$  and now on my notes I have $$3\otimes6_S=10_S\oplus8_{MS}$$  Where "MS" is for "mixed symmetric": symmetric for an exchange of 2 particular indexes but not for a general exchange of 3 indexes.  I could not demonstrate this last decomposition using tensor method. I started noticeing that: $$3\otimes6_S=q^iS^{k,l}$$ where $S^{k,l}$ is a symmetric tensor But then I am not able to proceed in demonstrating the above decomposition (note: I would like to demonstrate this decomposition using only tensor properties, not Young tableaux). I tried to look on Georgi, Hamermesh, Zee and somewhere online but I have not found any good reference which explains well this representatin decomposition...  EDIT: the demonstration should not include the use of Young diagrams...my professor started the demonstration by writing $\epsilon_{\rho,i,k}q^i S^{k,l}=T'^l_\rho=8_{MS}$ and then stopped the demonstration. Why do people not upvote, or accept answers that worked for them? I am regular Stack Exchange user, especially at Stack Overflow.  One of the things I really dislike about new and sometimes veteran users is that:   Either they do not accept an answer that works for them, Or they accept the answer but do not vote it up   I mean they can really both accept the answer and vote it up but somehow they wouldn't =(.  How many of you feel the same way? Like the title says, can a matrix in $\mathbb{R}$ have a minimal polynomial that has coefficients in $\mathbb{C}$?  I have a feeling the answer is yes because the characteristic polynomial can have coefficients in $\mathbb{C}$ and so I don't see any reason why not, I was merely asking in case there was some sneaky proof that proves that this cannot happen. How would one format an Excel sheet so numeric fields are set to numeric field types when importing to ArcGIS 10.2? What is the difference between CentOS "DVD" vs "Everything" ISOs How to power a button's LED within a guitar? I'm working on a guitar, and the plan is to use three latching push buttons so that each pickup can be turned on and off individually. I'm fairly confident that the following diagram should work for that (Feel free to correct me)   The buttons I want to use are , which have a built-in LED when turns on when the button is pressed.   Which brings me to my question: Is there a way to power the LED? If I introduce a 9volt into the wiring, wouldn't that cause problems with the guitar's standard electronics? How to apply for a Schengen visa when the travel dates are uncertain My husband has a Chinese passport and I am a U.S. citizen; I don't need a visa to travel to Schengen countries. I am helping him to apply for a visa.  Our plans are to go to Paris, Italy and Spain, but we haven't nailed down definite dates; the approximate dates are August 18 to September 11. We made an appointment with Spain consulate to apply for the visa. We need to show air flight reservations, I could book it online without any problems.    Since we don't have definite dates, what dates should he put down on the application?  I know that, once they approve you, they give you 90 days, so does it matter what dates I put down on the visa application?   Our appointment at the Spanish Consulate is in a few days. I wrote a script to create a big number of heat maps for a given scenario. I would like to save the result of every heat map as an PNG image. I have figured it out doing it with simple Map Rendering but the quality of the result is too low. Furthermore I would like to export to OpenLayers using the same code, which does not seem to be possible with simple rendering.   Now I am trying to do it with QgsComposition instead. Manually in the Map Composer you can just set the paper color to transparent and disable the background of the map canvas.   This is the code that I have so far. I just cannot figure out why it is not working. The result png-file always has a white opaque background.   My OS is Windows 7 and I'm using QGIS 2.6 Brighton.  I hope someone can help me out here.  # PARAMETERS mainPath = 'path/to/folder/' filename = 'filename' imageType = "png" imageWidth_mm = 400 imageHeight_mm = 160 dpi = 300  mapRenderer = iface.mapCanvas().mapRenderer()  c = QgsComposition(mapRenderer) c.setPlotStyle(QgsComposition.Print)  c.setPaperSize(400, 160)  x, y = 0, 0 w, h = c.paperWidth(), c.paperHeight() composerMap = QgsComposerMap(c, x ,y, w, h) c.addItem(composerMap)  # get all items and disable the backgrounds itemList = c.items() c.removeItem(itemList[2]) c.removeItem(itemList[2]) itemList[2].setBackgroundEnabled(False) itemList[3].setBackgroundEnabled(False) # add them to the composition c.addItem(itemList[2]) c.addItem(itemList[3])  c.refreshItems() c.refreshDataDefinedProperty(QgsComposerObject.AllProperties)  c.setPrintResolution(dpi) dpmm = dpi / 25.4 width = int(dpmm * c.paperWidth()) height = int(dpmm * c.paperHeight())  # create output image and initialize it # image = QImage(QSize(width, height), QImage.Format_ARGB32) image = QImage(QSize(width, height), QImage.Format_ARGB32_Premultiplied) image.setDotsPerMeterX(dpmm * 1000) image.setDotsPerMeterY(dpmm * 1000) #image.fill(0)  imagePainter = QPainter(image)  # This part does not seem to have any effect #brush = QBrush(Qt.BrushStyle(0)) # transparent brush # #imagePainter.setBackgroundMode(0) #c.setBackgroundBrush(brush)  c.renderPage( imagePainter, 0 ) imagePainter.end()   imageFilename =  mainPath + filename + '.' + imageType image.save(imageFilename, imageType) print 'image saved' print 'done' How do I move child windows without moving or minimizing parent in GNOME 3? I have Ubuntu 17.10 with GNOME 3.  What happens: I have (for example) LibreOffice Calc open, with some data columns in it.  I highlight the columns I want to chart, then I select INSERT > CHART.  The chart child window dialog pops up on top of my data, so I want to move it to the side.  When I grab the top bar and move it, the parent (spreadsheet) window minimizes (I think it actually disappears).  Continuing the above example, if I click FINISH on the chart window, I can then see the minimized spreadsheet application, which is the window title bar plus the menu bar just below it.  This seems like really odd behaviour and certainly falls under the category of "not being useful to the user", since the whole idea of moving the child window in the first place was just to be able to better see the spreadsheet!  In other applications, for example the PDF viewer, a slightly different problem occurs.  When I try to move the child window (for example the print dialog) the parent does not minimize but instead follows the child window around.  This is less surprising than having the parent disappear entirely but equally useless in terms of allowing the user to see the information present in the parent window.  Update 2017/11/06  Pomsky's answer below fixes the problem, but leaves me wondering why the window manager is making the decision that all child windows have modal behaviour (or don't), and not the applications themselves; and further, why modal behaviour prevents moving the child screen around when it obscures useful info on the parent screen.  Neither of these seem like good design to me... What MySQL query will do a text search and replace in one particular field in a table?  I.e. search for foo and replace with bar so a record with a field with the value hello foo becomes hello bar. Coupon collector's problem: mean and variance in number of coupons to be collected to complete a set (unequal probabilities) There are $n$ coupons in a collection. A collector has the ability to purchase a coupon, but can't choose the coupon he purchases. Instead, the coupon is revealed to be coupon $i$ with probability $p_i=\frac 1 n$. Let $N$ be the number of coupons he'll need to collect before he has at least one coupon of each type. Find the expected value and variance of $N$. Bonus: generalize to the case where the probability of collecting the $j$th coupon is $p_j$ with $\sum\limits_{j=1}^n p_j=1$  I recently came across this problem and came up with/ unearthed various methods to solve it. I'm intending this page as a wiki with various solutions. I'll be posting all the solutions I'm aware of (4 so far) over time.    EDIT: As mentioned in the comments, this question is different from the one people are saying it is a duplicate of since (for one thing) it includes an expression for the variance and it covers the general case where all coupons have unequal probabilities. The case of calculating the variance for the general case of coupons having unequal probabilities has not been covered anywhere on the site apart from , which this one intends to consolidate along with other approaches to solve this problem.    EDIT: Paper on the solutions on this page submitted to ArXiv: Limit of function of hyperbolic How can I - without using derivatives - find the limit of the function  $f(x)=\frac{1}{\cosh(x)}+\log \left(\frac{\cosh(x)}{1+\cosh(x)} \right)$  as $x \to \infty$ and as $x \to -\infty$?  We know that $\cosh(x) \to \infty$ as $x \to \pm \infty$ thus $\frac{1}{\cosh(x)} \to 0$ as $x \to \pm \infty$.  And I imagine that $\frac{\cosh(x)}{1+\cosh(x)} \to 1$ as $x \to \pm \infty$ thus $\log\left(\frac{\cosh(x)}{1+\cosh(x)}\right) \to 0$ as $x \to \pm \infty$.  Is this approach sufficiently formal?  Any help is appreciated. C++ Redefinition Header Files (winsock2.h) Compression API on the iPhone Here’s something that sucks:   Plug in external monitor to laptop (Mac OS X Leopard in my case). Arrange your windows to have the IDE on one screen and browser on another. (Etc etc.  Resize, rearrange, fuss, fuss, fuss.) Unplug monitor to run to a meeting, or whatever. Goto 1.   I’d like to replace step 2 with “computer remembers exactly how I had it and just puts it back that way”.  (I personally only need a solution for Mac but collecting solutions for other systems here might be useful to others.  I’m sure it’s a common problem.) Can you use an external 301 redirect for a blog post hosted on wordpress.com? Can I pack a cardboard box as checked luggage? As mentioned in , I'm planning on traveling with a desktop computer as checked baggage. After considering the options, I've decided to take it in its original cardboard box (used for shipping), making sure to pad everything inside very well.  What should I do to securely prepare the box before checking it in? Some suggestions others have given me so far:   Spray paint the box black so it's not obvious there's a computer inside. Wrap the entire box with duct tape to reinforce it. Use tape to seal the "hand holes" on either side used for carrying the box. Run packing tape around all the edges to reinforce the box. Why can't variables be declared in a switch statement? I've always wondered this - why can't you declare variables after a case label in a switch statement?  In C++ you can declare variables pretty much anywhere (and declaring them close to first use is obviously a good thing) but the following still won't work:  switch (val)   {   case VAL:     // This won't work   int newVal = 42;     break; case ANOTHER_VAL:     ...   break; }     The above gives me the following error (MSC):     initialization of 'newVal' is skipped by 'case' label   This seems to be a limitation in other languages too.  Why is this such a problem? What does it mean if a professor does not answer your email in time? I recently joined a research group as a postdoc. I wrote the professor an email to ask quick but important questions including asking him when when he wanted me to start. It's been over a week and I haven't received get an answer. Other emails I've sent previously have also gone unanswered for long periods as well.   With that background, my question is: do professors sometimes (intentionally or otherwise) not respond to emails in a timely manner? The following code receives seg fault on line 2:  char *str = "string"; str[0] = 'z';  // could be also written as *str = 'z' printf("%s\n", str);   While this works perfectly well:  char str[] = "string"; str[0] = 'z'; printf("%s\n", str);   Tested with MSVC and GCC.