MySQL: Add two columns when one or both may be null
Addition with NULL values
How do I create directory if it doesn't exist to create a file? I want to show that for each $n \in \mathbb N$ it holds that $$\sum_{k = 0}^\infty \frac{n^k}{k!} \vert k - n \vert = 2n \frac{n^n}{n!}.$$ But I have absolutely no idea how to do that. I tried to split the series like this:  $$\sum_{k = 0}^\infty \frac{n^k}{k!} \vert k - n \vert = \sum_{k = 0}^{n - 1} \frac{n^k}{k!}(n - k) + \sum_{k = n + 1}^\infty \frac{n^k}{k!} (k - n)$$ Now I want to show that $\sum_{k = 0}^{n - 1} \frac{n^k}{k!}(n - k) = \sum_{k = n + 1}^\infty \frac{n^k}{k!} (k - n) = n \frac{n^n}{n!}$ holds. But I got no idea how to achieve that. I tried to use induction but things became pretty messy and I don't think it will work like that. On the other hand I got the idea that it might have to do with $\exp$ or binomial coefficients but I don't see where I can facilitate that. I would appreciate some hints :) Javascript - Change html tag type ‘So the boy ... the boy must die?’ asked Snape, quite calmly.   ‘And Voldemort himself must do it, Severus. That is essential.’   Deathly Hallows - page 551 - UK Hardcover - chapter 33, The Prince's Tale   Dumbledore tells Snape it is 'essential' that Voldemort be the one to kill Harry, I'm assuming in order for the piece of Voldemort's soul in Harry to be properly killed as well.  But why?   Hermione destroyed the Hufflepuff cup; Ron destroyed the Slytherin locket; Neville killed Nagini; Harry destroyed the diadem and Tom Riddle's diary. So the Horcruxes were not immune to destruction at the hand of someone other than Voldemort. And as it ended up, Harry himself wasn't even a Horcrux, but rather just an unknowing host to a parasitic bit of Voldemort's soul.   Why was it 'essential' that Voldemort be the one to kill Harry in order for the piece of Voldemort's soul to die? Proving that the sequence $F_{n}(x)=\sum\limits_{k=1}^{n} \frac{\sin{kx}}{k}$ is boundedly convergent on $\mathbb{R}$ Here is an exercise, on analysis which i am stuck.    How do I prove that if $F_{n}(x)=\sum\limits_{k=1}^{n} \frac{\sin{kx}}{k}$, then the sequence $\{F_{n}(x)\}$ is boundedly convergent on $\mathbb{R}$? External monitors show blank screen until restart MacBook Pro (15-inch, 2016) with 2 USB-C to HDMI adapters. The setup works great if I start up in that configuration.   If I connect the adapters while the machine is running or simply sleeping, one of the monitors will never get a signal and stay in low power mode. The OS sees the monitor, it shows in the display arrangement settings and I can move the mouse into it, but until I restart, I can't see anything on it.  Once I have restarted I can let the machine sleep or whatever, and the display still works unless I disconnect the adapter. As soon as I do that a restart is required to use it again.   Using MacOS Sierra (10.12.4)  Using this adapter: What is the difference between currying and partial application? I quite often see on the Internet various complaints that other peoples examples of currying are not currying, but are actually just partial application.  I've not found a decent explanation of what partial application is, or how it differs from currying. There seems to be a general confusion, with equivalent examples being described as currying in some places, and partial application in others.  Could someone provide me with a definition of both terms, and details of how they differ? When there are several cottages each with several tariffs (depending on the season), should the plural be "cottage tariffs" or "cottages tariffs"?  For context, this is to be a section title on a website renting out the cottages.  An explanation of the grammatical rules would be helpful. Merging two SQLite databases which both have junction tables Render result is completely blank A scene I made is not rendering, at all. This grey screen stays the same and nothing changes.  Here are my settings:  [ Indicator icons do not appear after upgrade to Ubuntu 17.10 Can I legally downgrade from Win 7 64 bits to Win 7 32 bits? Possible Duplicate:          Tired of the unstable Win 7 64bit I got when I purchased my laptop (it was impossible to find a powerful laptop with Win 7 32 bits).  Can I legally downgrade from Win 7 64 bits to Win 7 32 bits? The key/activation will work?    Details: Everybody comments about the stability of Win 64.  Well, I made a mistake. Is not that Win 64 is unstable (it never crashed). It just works very poor. It feels choppy. Compiling a large program (on an old AMD desktop PC) takes 1.5 seconds on Win 32. The same program compiles on Win 64 in 4-5 seconds in this new and "powerful" laptop. All programs are less responsive. Is Tolkien prejudiced against the East? Solving $x^3-y^3=xy+61$ in integers I'm trying to solve the following equation:  $$x^3-y^3=xy+61$$  I got:  $$(x-y)(x^2+xy+y^2)=xy+61$$  But I can't go any further. I am looking for a solution in integers.  I need some hints to proceed, please! I'd like to do the equivalent of the following in LINQ, but I can't figure out how:  IEnumerable&lt;Item&gt; items = GetItems(); items.ForEach(i =&gt; i.DoStuff());   What is the real syntax? How do I appropriately examine the dimensionality of binary data? I have 72 binary variables and, at a theoretical level, I am trying to identify groups of variables that seem to vary together. In practice, I am struggling with how to analyze this data properly. I am using R and the psych package. Here is what I have tried and what the outcomes were:  Estimated a tetrachoric correlation matrix (ran without problem) Estimated MSA (relatively strong values, ran without problem) Ran parallel analysis to identify how many factors to extract (ran without problem) EFA using fa() to estimate factors (non-positive definite matrix and strangely high RMSEA) Tried different factor counts, smoothing/unsmoothing, estimation methods, rotations methods, and removing variables (problems persisted) Tried to focus instead on eBIC (always returned as NULL in output) EFA using (inappropriately) Pearson correlations (RMSEA behaved)  From looking at other questions and answers on here, I am now aware that tetrachoric matrices can be problematic like this. However, I don't know what to do with that information. Accept the problems as a limitation and move forward? Conduct a different type of analysis? I considered IRT as is recommended, but am unaware of an exploratory way to conduct IRT analyses. I understand that most of my options are imperfect. My goal is to find an analysis that is at least arguably appropriate for binary variables and that will inform the ways in which I group these variables in my theorizing. Given this, my questions are:  Can I trust EFA on a tetrachoric matrix despite problematic output? Can I somehow recover the lost eBIC value and use that? Is exploratory IRT possible/desirable? Are there other analyses, in R, that can be used to examine the dimensionality of binary data?  I appreciate all feedback! I love learning about data analysis and hearing about how I can improve. How do I get list of all tables in a database using TSQL? What is the best way to get the names of all of the tables in a specific database on SQL Server? Question: Suppose that $R$ is a commutative ring without zero-divisors.   Show that the characteristic of $R$ is either $0$ or prime.   I have established that every element in a commutative ring $R$ without zero divisors have the same additive order $n$.   Now, if no such additive order n exists, then the characteristic of $R$ is $0$.  Obviously, if a finite additive order exists, Char of $R$ is finite.  How do I show that Char of $R$ is prime? It probably involves lagrange's theorem and the order of the element in $R$.  Hint is appreciated.  Thanks in advance. I host am ExpressionEngine based website on a single Amazon EC2 instance in the US East (Virginia) region. I use Ubuntu.    The website allows members to post their content, and displays it for other members and for users who are not logged in.   Goal: I need to begin serving the same website across the globe, equally fast to Hong Kong, New York, and Los Angeles.   I considered two solutions:  1.Setting up three separate EC2 instances for three regions: Virginia, Oregon, and Singapore. Use Amazon Rot53 Geo Location to direct traffic to instances based on the browser's IP address.   Pro: the website will load fast for the region.   Contra: these will be essentially three separate websites. Unless I am mistaken?   Setting up one instance in a region equally remote from all three locations: (Ireliand), and boost the server to the highest performance available.    Pro: It will be the same website for all regions.   Contra: it will cost a lot to make it fast enough.   My challenges:   a) I do not know a way to sync server settings, database, and content between multiple Ubuntu instances in real time. If a knowledgeable person could explain to me how to do that, I would be most grateful.   b) I am not thoroughly familiar with all Amazon AWS resources. Does AWS has a built-in method that would allow me to achieve my goal of serving a single PHP / MySQL based membership website across the globe equally fast in all three chosen locations? Story about a utopian city that periodically destroys itself