Can decimals/fractions be odd or even?
Can decimal numbers be considered "even" or "odd"?
Ring and Subring with different Identities With 5 images I have to create a video of 60 seconds in ffmpeg, each image has to display for 15 seconds. after  15 seconds, first image has to fade out and 2nd image has to fade in, after that 2nd image has to fade out, 3rd image has to fade in..etc. Please guide me how can I achieve this using ffmpeg commands. Why does my iPad keep asking for my iCloud password? I keep receiving an iCloud pop-up message to insert my iCloud password every time i switch on my iPad and I'm unable to do anything on it, inserting the password doesn't help. What should I do? Is this true?  If $A$ and $B$ are sets, then $A=\emptyset $ if and only if $B = A \bigtriangleup B$.  If $A=\emptyset$ then $B=\emptyset$ too?  Could someone help me please? Export cycles material to unity I have been experiencing an issue that once I have a material created and looking the way I want it, I cannot seem to export it correctly with the textures mixed.  I don't know the correct words to use, but in blender I have the material created using the nodes editor, and I have placed two textures inside of there (one for the rock texture and one for moss, my object is a rock). When I export this model and import to Unity (the game engine I am using), I find a materials folder but the material inside of it does not have the textures assigned, it's just a plain white material?  How can I export my material from blender in a way that it will allow me to import it WITH TEXTURES into Unity? Accessing raster attribute table in QGIS? I have some Python code that makes Raster Attribute Tables for GeoTiffs using GDAL.    In ArcGIS I can see these attribute tables fine and they behave how I like (as classifications) but in QGIS the whole concept of an attribute table seems to be missing.    Is there any way to access a RAT in QGIS? How To quickly do derivatives with respect to matrices Whats a quick way to work the below (and problems similar) out?   For me to take this derivative it involves a lot of time and boring calculation, there has to be a better way.    This is taken from the solutions to Chris Bishop's Pattern Recognition and Machine learning: Prove $\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$ I am trying to prove  $$\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$$  This problem is a classic, but I seem to be missing one step or the understanding of two steps which I will outline below.   $$I_n := \int\cos^n x \ dx = \int\cos^{n-1} x \cos x \ dx \tag{1}$$  First question: why rewrite the original instead of immediately integrating by parts of $\int \cos^n x \ dx$?  Integrate by parts with $$u = \cos^{n-1} x, dv = \cos x \ dx \implies du = (n-1)\cos^{n-2} x \cdot -\sin x, v = \sin x$$  which leads to  $$I_n = \sin x \ \cos^{n-1} x +\int\sin^2 x (n-1) \ \cos^{n-2} x \ dx \tag{2}$$  Since $(n-1)$ is a constant, we can throw it out front of the integral:  $$I_n = \sin x \ \cos^{n-1} x +(n-1)\int\sin^2 x \ \cos^{n-2} x \ dx\tag{3}$$  I can transform the integral a bit because $\sin^2 x + cos^2 x = 1 \implies \sin^2 x = 1-\cos^2 x$  $$I_n = \sin x \ \cos^{n-1} x + (n-1)\int(1-\cos^2 x) \ \cos^{n-2} x \ dx \tag{4}$$  According to Wikipedia as noted , this simplifies to:  $$I_n = \sin x \ \cos^{n-1} x + (n-1) \int \cos^{n-2} x \ dx - (n-1)\int(\cos^n x) \ dx \tag{5}$$  Question 2: How did they simplify the integral of $\int(1-\cos^2 x) \ dx$ to $\int(\cos^n x) \ dx$?  Assuming knowledge of equation 5, I see how to rewrite it as  $$I_n = \sin x \ \cos^{n-1} x + (n-1) I_{n-2} x  - (n-1) I_{n} \tag{6}$$  and solve for $I_n$. I had tried exploiting the fact that  $$\cos^2 x = \frac{1}{2} \cos(2x) + \frac{1}{2} $$  and trying to deal with $\int 1 \ dx - \int \frac{1}{2} \cos (2x) + \frac{1}{2} \ dx$  which left me with $\frac{x}{2} - \frac{1}{4} \sin(2x)$ after integrating those pieces. Putting it all together I have:  $$I_n = \sin x \ \cos^{n-1} x + (n-1) I_{n-2} x \left(-(n-1) (\frac{x}{2} - \frac{1}{4} \sin 2x) \right) \tag{7}$$  but I'm unsure how to write the last few terms as an expression of $I_{something}$ to get it to match the usual reduction formula of   $$\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$$ I'm using Rules 7.x-2.6 and the way it works has changed a bit since I last saw.  I have a rule as follows:  EVENT A node has been flagged, under "Report content"  CONDITIONS None  ACTIONS Send mail to [site:mail]   However, I'd like to, instead of sending directly to [site:mail], send an email to all users flagged with an "admin" role.   Now I know that I'll need to provide a loop do so, but my sticking point is generating the list of users to pass to the loop. So far, I have attempted to add a new action:   "Fetch entity by property" Entity type: User Property: User roles Value: admin   But this doesn't seem to give me what I want in data selection, when passing it to the loop. Can someone recommend what they would set here? Okay I have the following fitch proof almost figured out, from here I know I have to move forth in conlcuding but I don't know what I am missing  (2 premises)  S → (R ∨ P)  P → (¬R → Q)   my work below  new scope assume S   Rule: > elim  R ∨ P  New scope assume R  Q∨R     Rule: V intro  End scope – (new scope assume P)  ¬R → Q         Rule: > Elim  my confusion comes where I go from here  Q∨R            rule Taut Con ??  Goal:├ S → (Q ∨ R) The current is maximum through those segments of a circuit that offer the least resistance. But how do electrons know beforehand that which path will resist their drift the least? On an upcoming trip, I will be taking a desktop computer and monitor as checked luggage (on a United/Continental flight). What should I be aware of when doing this? What needs to be done to properly protect all the components? Are there any airline policies I should be aware of? I am facing this issue on Ubuntu 12.04, which is for my Wimax modem with beceem chipset.    If I replug the device Ubuntu goes in hang state. Its happens very often. If I plug the USB and restart it works most of the time. But it is very annoying to restart every time it hangs. The modem works smoothly in Windows 7. And it used to work OK in  Ubuntu 11.10.   Jun 13 19:25:54 iftekhar-HP-520-Notebook-PC dbus[1102]: [system] Activating service name='org.freedesktop.UDisks' (using servicehelper) Jun 13 19:25:54 iftekhar-HP-520-Notebook-PC dbus[1102]: [system] Successfully activated service 'org.freedesktop.UDisks' Jun 13 19:26:00 iftekhar-HP-520-Notebook-PC goa[2168]: goa-daemon version 3.4.0 starting [main.c:112, main()] Jun 13 19:26:47 iftekhar-HP-520-Notebook-PC udevd[432]: timeout 'cdrom_id --lock-media /dev/sr1' Jun 13 19:26:48 iftekhar-HP-520-Notebook-PC udevd[432]: timeout: killing 'cdrom_id --lock-media /dev/sr1' [1072] Jun 13 19:26:49 iftekhar-HP-520-Notebook-PC kernel: [   85.820162] sr 2:0:0:0: Device offlined - not ready after error recovery Jun 13 19:26:49 iftekhar-HP-520-Notebook-PC udevd[432]: timeout: killing 'cdrom_id --lock-media /dev/sr1' [1072] Jun 13 19:27:20  udevd[432]: last message repeated 31 times Jun 13 19:27:25  udevd[432]: last message repeated 4 times    What can I do to avoid this hangs and restarts? How can I make a directory on the desktop?  I tried cd /desktop command but it gives an error  no such file or directory.  What's the correct command? My question is not about (pseudo) philosophical debate; it concerns mathematical operations and experimental facts.  What is an observer? What are the conditions required to be qualified of observer, both mathematically and experimentally? How to to resize an ext4 partition from the command line? What's the easiest way to resize an ext4 partition (or any type partition depending on the method) from the command line (potentially with the fewest commands, but also the easiest to understand)?  Using a tool like Gparted is obviously easy in a GUI, but what about in the command line? I guess text-based GUIs can count for the answer too since it's technically still in the command line. It just needs to be easy.  By partition I mean a simple partition on a single disk of a personal computer (e.g. on a laptop). For example, I want to resize /dev/sda4. There's no RAIDs, there's not more than one disk drive, there's not anything complicated here. Just a simple partition on a single disk (/dev/sdaX on /dev/sda). Looking for a book series about a girl and her friends captured and sold as slaves Automatic pyqgis categorized renderer classification I have some layers in my project and I would like to alter their styles, since ranges of values for underlying columns have changed.  Normally it would require to enter each layer style settings separately and trigger "Remove All", and "Classify" button, however I would like to execute it from the code.   I found such method for graduated symbol:  renderer.updateClasses(layer,0,bins)   ,however I'm having trouble to find corresponding method for categorized symbol class  Is there any way to do this from pyqgis without the need to specify the layer style from the scratch (create category, label etc.) ? Some equivalent of "Classify" button from below screenshot: com.mysql.jdbc.exceptions.jdbc4.CommunicationsException: Communications link failure Why can't I use Stack Exchange if I'm under 13 years old, or if I'm under 16 years old and from the EU?