What is wrong with my terminal? Backspace won't delete everything on the terminal line
Terminal prompt overwrites current line
How to show that Klein four-group is a normal subgroup of the alternating group $A_4$ I want to show that the Klein four-group is a normal subgroup of the alternating group $A_4$.   I am using the information in , that shows explicitly $A_4$, and Klein four-group as a subgroup.  I know that there is the direct way, by definition, but is there a way that does not require actually multiplying so many permutations ? This is what my  looks like when it first loads:    But if we unselect math.SE, we get a y-axis rescaling mess:    I'm using Firefox. I'm in China, so many things involving Google and Imgur are blocked, and I use  to stop the browser attempting to load unloadable Google objects.  I'm hoping other users can check whether or not this issue is localized to my system, and if it's not just me, here's the bug report. A question about causality and Quantum Field Theory from improper Lorentz transformation Related post   In Peskin and Schroeder's QFT p28, the authors tried to show causality is preserved in scalar field theory.  Consider commutator $$ [ \phi(x), \phi(y) ] = D(x-y) - D(y-x) \tag{2.53} $$ where $D(x-y)$ is the two-point correlation function,  $$D(x-y):= \langle 0 | \phi(x) \phi(y) | 0 \rangle  = \int \frac{d^3 p}{ (2\pi)^3} \frac{1}{ 2E_{\mathbf{p}}} e^{-ip(x-y)}\tag{2.50}$$  P&amp;S argued that each term in the right-hand-side of (2.53) is Lorentz invariant, since $$\int \frac{d^3p }{ (2\pi)^3} \frac{1}{2E_{\mathbf{p}}} = \int \frac{ d^4 p }{ (2\pi)^4} (2\pi) \delta(p^2-m^2)|_{p^0&gt;0} \tag{2.40}$$ is Lorentz invariant.  Since there exists a continuous Lorentz transformation in the spacelike interval $(x-y)^2&lt;0 $ such that $(x-y) \rightarrow - (x-y) $ and $D(y-x)=D(x-y)$, (2.53) equals zero in the spacelike interval. In timelike interval, since such continuous Lorentz transformation does not exist, (2.53) is non-zero in general.  My question is, consider a non-continuous Lorentz transmation in the timelike interval, $PT$, namely time reversal times parity transformation. I can also let  $(x-y) \rightarrow - (x-y) $. Why (2.53) in the timelike interval is non-zero?  I guess $PT$ will let (2.40) go to $p^0&lt;0$ branch. But I am not sure if it breaks the Lorentz invariant of (2.40) and (2.50). Can't run my hello world in C How do I serialize a C# anonymous type to a JSON string? I'm attempting to use the following code to serialize an anonymous type to JSON:  var serializer = new DataContractJsonSerializer(thing.GetType()); var ms = new MemoryStream(); serializer.WriteObject(ms, thing); var json = Encoding.Default.GetString(ms.ToArray());    However, I get the following exception when this is executed:     Type   '&lt;>f__AnonymousType1`3[System.Int32,System.Int32,System.Object[]]'   cannot be serialized. Consider marking   it with the DataContractAttribute   attribute, and marking all of its   members you want serialized with the   DataMemberAttribute attribute.  See   the Microsoft .NET Framework   documentation for other supported   types.   I can't apply attributes to an anonymous type (as far as I know).  Is there another way to do this serialization or am I missing something? WAMP Server not working Okay so a continuation from , where you experts intro'd me to , which can basically execute PHP within a Windows XP environment.  So now I've got it installed, but the tray icon forever shows YELLOW, and when I visit any PHP page in my browser, it just shows me the PHP source!  Also, when I visit "" in IE7 it gives me a 404 Not Found, FF3 just shows a blank page.    BTW I've tried "Restart All Services" and restarting my machine, but it still won't work.  Any ideas? Any of you had this problem and solved it? Please help me here, I'm desperate to execute PHP client-side and I'm just reverting to testing on-server for now! Is there a general way to change the font of a particular symbol without switching packages?  For example, suppose I'm using Computer Modern for my entire document, but I want the "subset" operator to look as it does in mathabx.  How can I redefine it to appear in this way? Find and replace text within multiple files Process descendants Placing however at the start of a sentence vs placing it in the middle of a sentence? Basically, what's the difference between this:     However, it didn't mean that I didn't have the potential to become a   rock star.   and this?     It didn't mean, however, that I didn't have the potential to become a   rock star.   Or does it mean exactly the same thing? Cann I use a 19.5V 4.62A laptop charger for 19V 4.74A laptop? I am wondering if my proof is correct? Thank you for whoever willing to take a look at it for me.     Proof $\liminf E_k \subset \limsup E_k $   If $\{E_k\}_{k=1}^\infty$ is a sequence of sets, we define \begin{align*} \limsup E_k &amp; = \bigcap_{j=1}^\infty\left(\bigcup_{k=j}^\infty E_k\right)\\ &amp;= \bigcap_{j=1}^\infty(E_j \cup E_{j+1} \cup \cdots)\\ &amp;= (E_1 \cup E_2 \cup \cdots) \cap (E_2 \cup E_3 \cup \cdots) \cap \cdots. \end{align*}  Therefore, $\limsup E_k$ consists of those points in $\mathbb{R}^n$ which belong to infinitely many $E_k$. \begin{align*} \liminf E_k &amp; = \bigcup_{j=1}^\infty\left(\bigcap_{k=j}^\infty E_k\right)\\ &amp;= \bigcup_{j=1}^\infty(E_j \cap E_{j+1} \cap \cdots)\\ &amp;= (E_1 \cap E_2 \cap \cdots) \cup (E_2 \cap E_3 \cap \cdots) \cup \cdots. \end{align*} Therefore, $\liminf E_k$ consists of those points in $\mathbb{R}^n$ which belong to all $E_k$ for $k \geq k_0$.  Now consider $x \in \liminf E_k$, then $x \in E_1 \cap E_2 \cap \cdots$, or $x \in E_2 \cap E_3 \cap \cdots$ and so on, that is to say, $x \in E_{k_0} \cup E_{k_0+1} \cup \dots$ for some $k_0$. More specifically, $x \in E_k \forall k \geq k_0$. Therefore, $x \in (E_1 \cup E_2 \cup \cdots) \cap (E_2 \cup E_3 \cup \cdots) \cap \cdots$, so we showed $x \in \limsup E_k$. A priori power analysis for generalized linear mixed-effects model Let's say I have a data set (with a binary DV) which I used a generalized linear mixed-effects model on. I am currently trying to run a simulation-based power analysis to determine the sample size I should try to collect for a replication attempt.   I know about the  function for fitted lme4 model objects, which will create simulated responses that follow the size and structure of the actual dataset.  My question is, how can I use this fitted model object to run an a-priori power analysis for my replication?. In other words, is there an easy way to extract the necessary information from the simulate function, vary the sample size, then to simulate responses?  EDIT:  Here is a simple example with ten subjects that should give me a good starting place. The data here are totally fake so the effects are not close to what I have in the pilot data.  The two variables of interest are age in months (between subjects) and whether the stimulus is "similar" or "dissimilar" (within subjects). Each individual is exposed to three items within each similarity group, for a total of six binary responses for each subject. As seen in the model, I am interested in a possible interaction between age and similarity and include a random slope of similarity to do this.   Let me know if I need to modify anything/provide more information to make things easier.   set.seed(28)  fakeData &lt;- data.frame(ID = rep(1:10, each = 6),                        months = rep(round(runif(10, min = 60, max = 80)), each = 18),                        similarity = rep(c("Sim", "Dissim"), each = 3),                        response = sample(c(0, 1), 60, replace = TRUE))  fakeModel &lt;- glmer(response ~ months * similarity + (similarity | ID), family = binomial, data = fakeData) summary(fakeModel) Book a return flight a year in advance Is it possible to buy an airline ticket that has me returning to my country after a year being abroad? I can't seem to book a flight that far in advance online. VAR or VECM for a mix of stationary and nonstationary variables I have 4 time series. One of them is stationary and rest of them are not. I need to find relation between them. I will use AIC to decide lag length.   Should I use VAR or VECM to find relation between them?  Will VAR or VECM give me relation in terms of equation which can be used for forecasting?  Do I need to perform Johansen's test of cointegration?  What good would it do? Geometric proof that a Pythagorean triple has a number divisible by $3$? Can I infer from “If $a,b \in \mathbb{N}$ such that $(a,3)=(b,3)=1$ then $a^2+b^2\neq c^2$ for any $c\in\mathbb{N}$” that any pythagorean triple has a number which is divisible by $3$? If so, how can this relationship be proved geometrically? Does the point at which salt is added to a dish affect how the flavor is changed? I am writing a WP plugin. I have created a button for the user to click in thw WP dashboard. I need to run a function when a user clicks the button, shown with a red arrow. The code snippet for the button is:&lt;p&gt;&lt;button class="button button-primary"&gt;Update Media Titles and ALT Text&lt;/button&gt;&lt;/p&gt;. I have already created the function in my class like so:  public function kh_update_media_seo() {      //update media files title and alt tags here }   I can handle the code that goes in the function alone, I only need help making the button in the WP dashboard fire off this specific function when clicked.  Pardon me if this sounds dump or straight forward. It's my first time doing this.  My plugin is a one file plugin if that helps. Is there an easy way to convert a number to a word in PHP? In PHP, is there an easy way to convert a number to a word? For instance, 27 to twenty-seven. I admin a handful of cloud-based (VPS) servers for the company I work for.   The servers are minimal ubuntu installs that run bits of LAMP stacks / inbound data collection (rsync). The data is large but not personal, financial or anything like that (ie not that interesting)  Clearly on here people are forever asking about configuring  and such like.   I use a bunch of approaches to secure the servers, for example (but not restricted to)   ssh on non standard ports; no password typing, only known ssh keys from known ips for login etc https, and restricted shells (rssh) generally only from known keys/ips servers are minimal, up to date and patched regularly use things like rkhunter, cfengine, lynis denyhosts etc for monitoring   I have extensive experience of unix sys admin. I'm confident I know what I'm doing in my setups. I configure /etc files. I have never felt a compelling need to install stuff like firewalls: iptables etc.  Put aside for a moment the issues of physical security of the VPS.  Q? I can't decide whether I am being naive or the incremental protection a fw might offer is worth the effort of learning / installing and the additional complexity (packages, config files, possible support etc) on the servers.  To date (touch wood) I've never had any problems with security but I am not complacent about it either.