C: Define function which takes array of constant strings, returns randomly selected one
How to find the 'sizeof' (a pointer pointing to an array)?
Is $f(a)\!=\!0\!=\!f(b)\Rightarrow (x\!-\!a)(x\!-\!b)\mid f(x)\,$ true if $\,a=b?\ $ [Double Factor Theorem] How do you keep parents of floated elements from collapsing? Why doesn't a fly fall off the wall? Operator Exponential $e^A e^B = e^{A+B}$ This question comes from an exam in my functional analysis class.  Suppose $X$ is a Banach space, and $T \in B(X,X)$ is a bounded linear operator on $X$. For any non-negative integer $n$, let $$S_n=\sum_{k=0}^n \frac{1}{k!} T^k$$ where $T^k$ is the composition of $T$ with itself $k$ times and $T^0=I$.  We can show that for any integer $k&gt;0$, $\Vert T^k \Vert \le \Vert T \Vert ^k$. Then we can show that $S_n \in B(X,X)$ and there is some $S \in B(X,X)$ such that $S_n \to S$. We write $S = e^T$ for this operator.  Finally, We were asked to show that $e^T$ has an inverse, and that it is $e^{-T}$. My thought is to prove the following claim first: if $A,B \in B(X,X)$ and $AB = BA$, then $e^A  e^B = e^{A+B}$. If the claim is true, it follows that $e^T e^{-T}=I$.  The claim can be proven provided that the product series can be computed with the Cauchy rule.  $$e^Ae^B=\sum_{i=0}^{\infty}\frac{A^i}{i!}\sum_{j=0}^{\infty}\frac{B^j}{j!}=\sum_{k=0}^{\infty}\sum_{l=0}^{k}\frac{A^lB^{k-l}}{l!(k-l)!}$$ $$=\sum_{k=0}^{\infty}\frac{1}{k!}\sum_{l=0}^{k}\frac{k!}{l!(k-l)!}A^lB^{k-l}= \sum_{k=0}^{\infty}\frac{1}{k!}(A+B)^k= e^{A+B}$$  But why can the product series be summed in the Cauchy way? I know for real-number series, by Cauchy's theorem, if $\sum_{n=1}^{\infty} a_n$ and $\sum_{n=1}^{\infty} b_n$ are absolutely convergent to $A$ and $B$, respectively, then we can add $a_i b_j$ in any way, and the resulting series will converge to $AB$. Does this proposition still hold for commutable operators? (It would be greatly appreciated if ideas of proof or reference is suggested.) Is there a practical way to change the phone number in Uber app when arriving at a country? Its very easy to prove $p\mid n^p-n$ for p=3,5,7, it fails for p=9 because $$     (n+1)^9-(n+1)= n^9+9n^8+36n^7+84n^6+126n^5+126n^4+84      n^3+36n^2+8n $$ and $84= 2²\times 3\times7$. Is it true for any $p$ prime? I have checked many primes, but have no idea for the general case. I bought a Minecraft account for my little brother for Christmas, and I'd like to play with him on my server every now and then. If I log in while he's on, however, it kicks him off since we have the same username. Is there any way to change my username so that I can play with him, or anything I can do so that we can both play together using this account on my server?  I'm open to anything that could let us play, whether it be username changes, server property changes, etc. I made a character, and its one of my first times texturing, and I saved my character into a new folder, and when I came back to the model ALL the textures were pink, I used to know what to do, but I stopped texturing, how do I bring my textures back? Should I buy a Canon 55-250mm lens or 70-300mm for my Rebel T3i? I have the basic 18-55mm lens that came with my camera but I need a next step up that's not too expensive.   What are the most common types of photos shot with either lenses? Or what is each lens best for? Can you use another material as input to material nodes in cycles? I have two expressions of type Expression&lt;Func&lt;T, bool&gt;&gt; and I want to take to OR, AND or NOT of these and get a new expression of the same type  Expression&lt;Func&lt;T, bool&gt;&gt; expr1; Expression&lt;Func&lt;T, bool&gt;&gt; expr2;  ...  //how to do this (the code below will obviously not work) Expression&lt;Func&lt;T, bool&gt;&gt; andExpression = expr AND expr2 PCIe Bus error severity=Corrected I have a new HP Pavilion Gaming Notebook and a new installation of Ubuntu 16.04. When I press Ctrl + Alt + F1 I go start seeing the errors shown in the following image and it doesn't allow me to interact with the console:    I also see these errors for a while everytime I boot. I need to do Ctrl + Alt + F1 to access a non graphical terminal to install some Nvidia drivers. What's going on?  What's causing the problem seems to be: 00:1c.5 PCI bridge [0604]: Intel Corporation Sunrise Point-H PCI Express Root Port #6 [8086:a115] (rev f1)  jpiabrantes@joao:~$ lspci -nn 00:00.0 Host bridge [0600]: Intel Corporation Sky Lake Host Bridge/DRAM Registers [8086:1910] (rev 07) 00:01.0 PCI bridge [0604]: Intel Corporation Sky Lake PCIe Controller (x16) [8086:1901] (rev 07) 00:02.0 VGA compatible controller [0300]: Intel Corporation Skylake Integrated Graphics [8086:191b] (rev 06) 00:04.0 Signal processing controller [1180]: Intel Corporation Skylake Processor Thermal Subsystem [8086:1903] (rev 07) 00:14.0 USB controller [0c03]: Intel Corporation Sunrise Point-H USB 3.0 xHCI Controller [8086:a12f] (rev 31) 00:14.2 Signal processing controller [1180]: Intel Corporation Sunrise Point-H Thermal subsystem [8086:a131] (rev 31) 00:16.0 Communication controller [0780]: Intel Corporation Sunrise Point-H CSME HECI #1 [8086:a13a] (rev 31) 00:17.0 SATA controller [0106]: Intel Corporation Sunrise Point-H SATA Controller [AHCI mode] [8086:a103] (rev 31) 00:1c.0 PCI bridge [0604]: Intel Corporation Sunrise Point-H PCI Express Root Port #5 [8086:a114] (rev f1) 00:1c.5 PCI bridge [0604]: Intel Corporation Sunrise Point-H PCI Express Root Port #6 [8086:a115] (rev f1) 00:1c.6 PCI bridge [0604]: Intel Corporation Sunrise Point-H PCI Express Root Port #7 [8086:a116] (rev f1) 00:1f.0 ISA bridge [0601]: Intel Corporation Sunrise Point-H LPC Controller [8086:a14e] (rev 31) 00:1f.2 Memory controller [0580]: Intel Corporation Sunrise Point-H PMC [8086:a121] (rev 31) 00:1f.3 Audio device [0403]: Intel Corporation Sunrise Point-H HD Audio [8086:a170] (rev 31) 00:1f.4 SMBus [0c05]: Intel Corporation Sunrise Point-H SMBus [8086:a123] (rev 31) 01:00.0 3D controller [0302]: NVIDIA Corporation GM107M [GeForce GTX 950M] [10de:139a] (rev a2) 07:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. RTS522A PCI Express Card Reader [10ec:522a] (rev 01) 08:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8723BE PCIe Wireless Network Adapter [10ec:b723] 09:00.0 Ethernet controller [0200]: Realtek Semiconductor Co., Ltd. RTL8101/2/6E PCI Express Fast/Gigabit Ethernet controller [10ec:8136] (rev 0a) Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$ I have a dataframe with many observations and many variables. Some of them are categorical (unordered) and the others are numerical.  I'm looking for associations between these variables. I've been able to compute correlation for numerical variables (Spearman's correlation) but :   I don't know how to measure correlation between unordered categorical variables. I don't know how to measure correlation between unordered categorical variables and numerical variables.   Does anyone know how this could be done? If so, are there R functions implementing these methods? How to mount a VirtualBox shared folder at startup? I would like to customize Ubuntu live CD by installing some additional packages. I have followed   but it doesn't seems to work. Can anyone provide clear instructions?   Note: I do not prefer Remastersys, manual way will be appreciated.  Customization  Packages that I want to install:   Thunderbird    Samba    SSH       Changes that I need:   Remove Games menu from the Application menu Firefox shortcut on Desktop Radiance as the default Theme Different default Ubuntu Wallpaper   Configuration file changes   I want the panel to be placed at the bottom I want to paste my Samba configuration file instead of default Samba configuration I have few Firefox shortcuts and folders I would like to show that in Desktop Also it will be nice if you say me how to change the icon sets   Recent Updates   I have customized Ubuntu 10.10 with Firefox shortcuts and few folders on desktops. Everything went smooth. But the installer gets crashes after choosing the timezone. How do i fix this issue? Also setting wallpaper affects the login screen. The wallpaper which i set is displayed on the login screen also. I just want the default one for the login screen. Using the affine linearized polynomial $f(x)=x^p-x-b$ is irreducible over $\mathbb{F}_q$ if and only if $\operatorname{Tr}_{\mathbb{F}_q/\mathbb{F}_p} \neq 0$. But here $\mathbb{F}_3$ is not a field extension of $\mathbb{F}_5$.  Also we have that: Let $a \in \mathbb{F}_q$ and let $p$ be the characteristic of $\mathbb{F}_q$. Then the trinomial $x^P - x - a$ is irreducible in $\mathbb{F}_q[x]$ if and only if it has no root in $\mathbb{F}_q$. Vertical line for the the right margin in Notepad++ Does anyone know if Notepad++ can display a vertical line on the right margin to indicated that the text will or will not fit on a printed page?  I have looked but I cannot find it.  Word wrap does work, but it wraps by my screen width, not by the width of a printed page. I can't seem to access instance members of the surrounding class from inside an enum, as I could from inside an inner class. Does that mean enums are static? Is there any access to the scope of the surrounding class's instance, or do I have to pass the instance into the enum's method where I need it?  public class Universe {     public final int theAnswer;      public enum Planet {         // ...         EARTH(...);         // ...          // ... constructor etc.          public int deepThought() {             // -&gt; "No enclosing instance of type 'Universe' is accessible in this scope"             return Universe.this.theAnswer;         }     }      public Universe(int locallyUniversalAnswer) {         this.theAnswer = locallyUniversalAnswer;     } } HP PSC 1410 all scanner's images are black I have a HP PSC 1410 printer with scanner inside.  I've been scanning documents and images with it for the last couple of years.  Recently my scanner has stopped performing as excepted and i can't scan or copy images\documents.  My problem is that every images\document i'm trying to scan - the result from the printer is a black page.  I've been googling about this issue and couldn't find any helpful stuff beside replacing the whole printer - which is something i'm trying to avoid.  Any ideas ? I've read something about the shipping lock of the scanner but couldn't find any information about how to check it..