NVIDIA SHIELD tablet, how do I return to 4.4 KitKat from Lollipop?
Downgrade nVidia Shield to Android 4.4 KitKat
Arrow with plus/minus sign on top Below you can see an arrow with a plus and a minus sign on top of it. How is this achievable in latex? Further possibilities: arrow with only plus and arrow with only minus sign on top. How can I do this? Typesetting 144...4 with "n times" under the 4's is easy, but what about \sqrt{144...4}? I applied for a B1 visa to attend a conference in the USA in 2013. I had another nationality (Non- VWP) at the time and my B1 application rejected under section 306 of border security. I now can apply for ESTA under my new nationality. Can my ESTA application get approved? If not and I need to apply for visa is it every time I need to travel to stated or is it just the first time? I want to know is there a way to render Shadows only in Blender's new EEVEE Render Engine. I want my objects in a separate collection and a ground plane on a separate collection(to receive shadows from the objects collection).I want to render the shadows only and not the objects. Probability Problem with $n$ keys A woman has $n$ keys, one of which will open a door. a)If she tries the keys at random, discarding those that do not work, what is the probability that she will open the door on her $k^{\mathrm{th}}$ try?  Attempt: On her first try, she will have the correct key with probability $\frac1n$. If this does not work, she will throw it away and on her second attempt, she will have the correct key with probability $\frac1{(n-1)}$. So on her $k^{\mathrm{th}}$ try, the probability is $\frac1{(n-(k-1))}$ This does not agree with my solutions.   b)The same as above but this time she does not discard the keys if they do not work.  Attempt: We want the probability on her $k^{\mathrm{th}}$ try. So we want to consider the probability that she must fail on her $k-1$ attempts. Since she keeps all her keys, the correct one is chosen with probability $\frac1n$ for each trial. So the desired probability is $(1-\frac{1}{n})^{k-1} (\frac1n)^k$. Again, does not agree with solutions.  I can't really see any mistake in my logic. Can anyone offer any advice? Many thanks Is liquid cooling necessary for high CPU performance over extended periods? I'm planning on building a system for high CPU and memory performance.  Graphics performance is not a major concern, as I do not plan to use it for gaming.  I noticed that liquid cooling seems to have become common since my last build, and I am wondering if it is needed in my case.  I do not plan to overclock any of the components.  The intended use for the system is primarily development and occasional compute-intensive tasks that will run on all cores continuously for several days to a week.  The system will not normally be in continuous usage like this, but it needs to be capable of occasional extended periods of continuous use at full capacity.  I have included the main components below.  CPU: i7-5960X  Memory: 64GB DDR4  Graphics card: Nvidia GeForce GT 730 2GB  Drive 1: 1TB SSD  Drive 2: 4TB 7200RPM HDD  Power supply: 700W  Is liquid cooling needed for the above build?  If not, is there any advantage in using it?  I have read reviews that mentioned liquid cooling unit failures that resulted in leaks, so I would rather not use it if it is not necessary.  Thanks! DDL Trigger in MySQL? How can I find all files I can not write to?  Would be good if it takes standard permissions and acls into account.  Is there an "easy" way or do I have to parse the permissions myself? Sum of the series $\frac{1}{2\cdot 4}+\frac{1\cdot3}{2\cdot4\cdot6}+\dots$ I am recently struck upon this question that asks to find the sum until infinite terms $$\frac{1}{2\cdot 4}+\frac{1\cdot3}{2\cdot4\cdot6}+\frac{1\cdot3\cdot5}{2\cdot4\cdot6\cdot8}+.....∞$$ I tried my best to get something telescoping or something useful, but I failed. I even made a recurrence as $t_n=t_{n-1}\frac{2n-1}{2n+2}$, but this question was expected to be done with simple logic of series (Also that the recurrence on solving gives a higher order charasteristic polynomial, which might be difficult to solve without calculator). So, thus I ended up being confused with this question. So, can anyone prode a small solution to this (might be easy) problem  . Xcode free space requirement I am trying to update Xcode to 8.0. My OS is 10.11.6 El Capitan. However I am getting:     We could not complete your update   There is not enough disk space available to install the product.   I have got 14.22 GB free space. How much do I need?  UPDATE: I do not know the exact figure, though I did manage to update with 17.21 GB free space later on. Recursive matching with regular expressions in Javascript How to create & execute a script file Is there a way to create and execute a script file in Ubuntu 14.04?  Perhaps something like Windows batch files.  Specifically, I mean the default scripting language of the Ubuntu terminal (Bash).  How do you make a text file containing bash commands which will be run by the Ubuntu terminal from the top of the file to the bottom. Now the cubs are growing, fed on mom's milk, but mom herself hasn't eaten in five months, and is getting thinner by the day.   What does in mean here, and how would the meaning of that piece change if for were used? I am looking for a good source on group theory aimed at physicists. I'd prefer one with a good general introduction to group theory, not just focusing on Lie groups or crystal groups but one that covers "all" the basics, and then, in addition, talks about the specific subjects of group theory relevant to physicists, i.e. also some stuff on representations etc.  Is Wigner's text a good way to start? I guess it's a "classic", but I fear that its notation might be a bit outdated? Prove by induction that for all $n \ge 0$:  $${n \choose 0} + {n \choose 1} + ... + {n \choose n} = 2^n.$$  In the inductive step, use Pascal’s identity, which is:  $${n+1 \choose k} = {n \choose k-1} + {n \choose k}.$$  I can only prove it using the binomial theorem, not induction. How to execute a script just by double clicking like .EXE files in Windows? How can I make a bash script executable by double clicking just like .exe files in Windows? I tried , but there are two consequences:   the terminal twinkles, disappears, and nothing is done. you must specify to run in terminal in order to work.   I have a script that installs tomcat on an offline PC, including all dependencies of tomcat in the script. I need to make the script work on double clicking like windows since most who use the script will not be familiar with Ubuntu.  Forget the above explanation. I want to make a script that can be run by double-clicking on it, without using the terminal. Anybody knows how? Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$ Let $G$ be a finite abelian group and let $\phi: G \rightarrow G$ be a group homomorphism. I am trying to show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$.  I know that since $G$ is abelian we have that $\ker(\phi^{k})$ and $\phi^{k}(G)$ are normal subgroups of $G$ for any $k$  I also suspect we have the following towers which stabilize at $m$ and $m'$  $$\phi(G) \unrhd \phi^{2}(G) \unrhd \cdots \unrhd \phi^{m}(G)=\phi^{m+1}(G)=\cdots$$  $$\ker(\phi) \unlhd \ker^{2}(\phi) \unlhd \cdots \unlhd \ker^{m'}(\phi)=\ker^{m'+1}(\phi)=\cdots$$  I know that if given a group of the form $HK$ where $H$ and $K$ are normal subgroups of $HK$ and $H\cap K=1$ then $H \times K \cong HK$. I want to apply this to this situation but I am unable to show how write $G$ as a product $HK$  Resolution One of the comments directed me to the following article:  The last part of which answers the question. Below is what is says:  Choose $n=\max(m,m')$, then we have for $x \in \ker^{n}(\phi) \cap \phi^{n}(x)$, this means that $x=\phi^{n}(y)$ for some $y \in G$. This gives:  $0=\phi^{n}(x)=\phi^{2n}(y)$ which means that $y \in \ker^{2n}\phi=\ker^{n}{\phi}$. and then we have that $0=x=\phi^{n}(y)$.  The answer below kindly points out that every element $x$ is contained in one of the cosets of $G/\ker^{n}(\phi)$, this means that $x=k+g$ for some $k \in \ker^{n}(\phi)$ and $g \in G$. We also have that $g=\phi^{n}(h)$ for some $h \in G$. Writing $x=k+\phi^{n}(h)$ essentially shows that $G=\ker(\phi^{n}) + \phi^{n}(G)$. Using the fact above, the claim follows. Youths can teleport, they are chased by the government What is the quantum mechanical explanation of the octet rule? What is the quantum mechanical explanation of the ? In other words, what makes the octet rule be true from a quantum mechanical view? How we explain  what makes some atoms don't follow the octet rule using QM? Is there a reason the British omit the article when they "go to hospital"?