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Setting a custom RGB background color in beamer I believe I've correctly followed the manual in defining a custom background color in the example below.     But as the example shows, the background color is black rather than an extremely pale beige.    Could anybody advise what I'm doing wrong please?  \documentclass{beamer} \definecolor{MyBackground}{RGB}{1.0000    0.9451    0.6549} \setbeamercolor{background canvas}{bg=MyBackground} \begin{document} \begin{frame} Hullo world \end{frame} \end{document} Fibonacci addition law $F_{n+m} = F_{n-1}F_m + F_n F_{m+1}$ Question: Let $F_n$ the sequence of Fibonacci numbers, given by $F_0 = 0, F_1 = 1$ and $F_n = F_{n-1} + F_{n-2}$ for $n \geq 2$. Show for $n, m \in \mathbb{N}$: $$F_{n+m} = F_{n-1}F_m + F_n F_{m+1}$$   My (very limited) attempt so far: after creating a small list of the values $F_0=0, F_1=1, F_2=1, F_3=2, F_4=3, F_5=5, F_6=8, F_7=13, F_8=21, F_9=34, F_{10}=55$ i can see that yes it does seem to work for instance $F_{6+3}=F_5 F_3 +F_6 F_4 = 10 +24 = 34 = F_9$. However, I really don't know where to begin as showing that this must hold in general terms. Should I be looking to use limits? Or perhaps induction? What is the best way to solve this? What is the capacity of this circuit? I simply can't figure out what the capacity of this circuit is.  I can do the math myself, I just need a hint how to create an equivalent circuit where it is obvious what is parallel and what is in series... How can I download this flash game for offline play? is one of the best flash games ever.    Is there some way to download it, so that I can play it offline? If someone who is otherwise healthy decided to drink fairly heavily and consistently over a long period of time, what is the healthiest way to do so?  Example: Stay extra hydrated by drinking more water, take a multivitamin, get more sleep, etc.  Obviously the best solution would be to cease drinking, but IF that person is stubborn and won't quit - what's the best way to go about it? I was trying to solve a question of an entrance exam. I am completely stuck in the problem. I am not able to find idea how to proceed. Please help me.     Let $A$ be the set of twice continuously differentiable functions on the interval $[0, 1]$ and let $B = \{f \in A : f(0) = f(1) = 0, f'(0) = 2\}$. Find the value of $$\text{min}_{f\in B} \displaystyle \int_0^1 (f''(x))^2dx.$$    I am really sorry for not showing some effort from my side but I can not find ant way to proceed.  Please help me. Thnx in advance. If there is a wizard that, by some means, has acquired proficiency in the use of shields, can said wizard use his shield in one hand and his arcane focus quarterstaff in the other and still cast somatic component spells?  Since the quarterstaff has been crafted to also be an arcane focus, and the Sage Advice Compendium states that you can provide the somatic components of spells with the same hand wielding the arcane focus, in this case an arcane focus quarterstaff, could that wizard still be able to perform somatic component spells while using a shield in the other?  I understand War Caster is the feat that allows you to cast somatic component spells even while using a shield and weapon or two weapons in each hand, but is this a simple way around those rules seeing as this "weapon" is your arcane focus? I would like to believe it is not, but I'm not fully fluent in the ways of spellcasting. Process Unicode files with BOM correctly with POSIX tools Trying to use grep today, I ran into the  of the  in a Unicode file (UTF-8, in this case). Specifically, I was trying to find a file beginning with XYZ with the pattern grep '^XYZ', but of course grep treated the BOM as three separate characters and did not match the first line of the file if the first line started with XYZ. I even tried to update the regular expression to ignore spaces ('^[[:space:]]*XYZ'), but to no avail.  Other questions have dealt with  or , but I want to know if POSIX tools have a general option to handle Unicode files correctly. If grep handled the Unicode file correctly, it would consider the file contents to start after the BOM and match XYZ on the first line just like any other line. NSString question - rangeOfString method What is $P(X > 0 \mid X + Y > 0)$ given that $X, Y$ are i.i.d standard normal? Find all $x$ such that $x^6 = (x+1)^6$. How to read a csv file and use the values as x and y points in blender? How can i use the value in column 'lon' and 'lat' as the position of my uv_sphere? For example,read the values from line 4, (116.4559081, 39.9139083), and make these 2 numbers as my uv_sphere x and y position in blender? and gives different colors for different mode, for example i have 4 modes in the csv , i want to make the uv sphere that represents the bus mode to be red, and subway to be green , rail to be blue and tram to be yellow., and use the row ['from'] and ['to'] to connect the nodes with a cylinder with x scale 0.5 , y scale 0.5 and the z scale with the value in ['length'] value. Which $n$ can be expressed as $x^2 − y^2$? Which $n$ can be expressed as $x^2 − y^2$?  Attempt: Any number which is odd or or which is a multiple of 4. Combining the first and second law of thermodynamics we can get the following equation  $$TdS=dU-P_{ext}dV$$  First question: Is this equation applicable for irreversible processes such that that $dS≠\dfrac{dQ}{T}$?  Second question:If the system temperature $T_{sys}$ is smaller than the surrounding temperature $T_{sur}$, which temperature should we put in the equation?   I have this question because sometimes people use $T_{sur}$ instead of $T_{sys}$ (e.g. , ) but the equation is supposed to describe changes in the system. What posts should be escalated to staff using [status-review], and how do I escalate them? We currently have some indexes where ALLOW_PAGELOCKS is set to off. This presumably was done in order to reduce deadlocks. However I doubt that it would really had an effect back then.   Now I am trying to understand WHEN SQL Server actually chooses to start locking pages rather than keys in a clustered index. I asked Jonathan Keyhaisas recently and he told me that this could happen if I am touching rows on several subsequent pages. However I didn't manage to get any exclusive page locks by updating rows in a clustered index with a sample query.   Could you help me understand page locks better with a sample query and table? I am running SQL Server 2008 SP4.  Thanks in advance  Martin Is it possible to transfer Minecraft PE worlds to Minecraft PC? Proving a limit of a trigonometric function: $\lim_{x \to 2/\pi}\lfloor \sin \frac{1}{x} \rfloor=0$ Why is "glide symmetry" its own type? Artin's Algebra pages 155 &amp; 156 list the types of symmetry of a plane figure as:   Reflective Rotational Translational Glide   He then goes on to say "Figures such as wallpaper patterns may have two talk about other figures having combinations of independent" symmetries. EDIT: He says "... having combinations of independent translational symmetries". See Joriki's answer.  Why doesn't glide symmetry count as having two independent (reflection + translation) symmetries? If we're going to count combinations, why not have rotation + translation etc. as their own types too? Windows 7 / 8 tool for amplifying sound / equivalent to pavucontrol? I'm watching live streamed videos, but the volume sometimes is barely loud enough.  With Windows, I can only turn the system volume and the flash volume up to maximum, and then bad luck if that's still not loud enough.  On Linux, on the same notebook, I have the same problem, but I can use pavucontrol (pulseaudio volume control) to amplify the sound volume beyond 100%.  Unfortunately, I can't always work on Linux, since Visual Studio and SQL-Server only run on Windows.  Is there any tool or way to amplify volume on Windows 7 / 8 , without having to resort to run Linux in a virtual machine?