I thought when a noun followed by "of something" has to be addressed with "the" because it is subject to the following of... However, I found the sentence such as "The age of terror is an age of shocks." Should be it like "The age of terror is the age of shocks"? Please give me some advice.
I can’t for the life of me figure out where to use a and where to use the — and where there is no article at all. Is there a simple rule of thumb to memorize?   The standard rule you always hear:     “If a person knows which item you are talking about then use "the"   . . . doesn’t clear things up for me, as I have no idea whether or not they know.
Can principal component analysis be applied to datasets containing a mix of continuous and categorical variables? I have a dataset that has both continuous and categorical data. I am analyzing by using PCA and am wondering if it is fine to include the categorical variables as a part of the analysis. My understanding is that PCA can only be applied to continuous variables. Is that correct? If it cannot be used for categorical data, what alternatives exist for their analysis? On exactly what criteria is the Electorate badge awarded? There is a badge named Electorate which is going to be awarded on "Voted on 600 questions and 25% or more of total votes are on questions". Can somebody explain this to me?  Voted on 600 Question and 25% are on Question? is this  means   Voted on 600 Posts and 25% are on Question  Can't SO place some easy text or Definitions for average users? (Fitzpatrick Advanced Calculus 2e, Sec. 2.4 #12)  For $c \gt 0$, consider the quadratic equation $x^2 - x - c = 0, x &gt; 0$.  Define the sequence $\{x_n\}$ recursively by fixing $|x_1| \lt c$ and then, if $n$ is an index for which $x_n$ has been defined, defining  $$x_{n+1} = \sqrt{c+x_n}$$  Prove that the sequence $\{x_n\}$ converges monotonically to the solution of the above equation.  Note: The answers below might assume $x_1 \gt 0$, but they still work, as we have $x_3 \gt 0$.    This is being repurposed in an effort to cut down on duplicates, see here: .  and here: . Is there evidence of "think tank" meaning "the brain"? The  Random House Dictionary defines the expression  as:         a research institute or organization employed to solve complex problems or predict or plan future developments, as in military, political, or social areas.      According to  the above connotation  is an extention of an earliar sense  which referred to "the brain":        also think-tank, 1959 as "research institute" (first reference is to Center for Behavioral Sciences, Palo Alto, Calif.); it had been colloquial for "the brain" since 1905.      : shows usage of "think tank" only from the late '50s.  Is there evidence  of earlier usages of "think tank" meaning "the brain"? Despite  its colloquial   usage I assume  the expression was quite widespread before it was adopted by the Stanford University. What is a good KPI for software QA? How can you measure the efficiency of the QA team?   What KPIs would you set up? I am trying to figure out how can I disable/hide the App Name in MacOS X Lion dock. I've also attached an image so you can see what I mean.    Someone has any idea about how can I hide that? Using R, I have fitted a linear model for a single response variable from a mix of continuous and discrete predictors. This is uber-basic, but I'm having trouble grasping how a coefficient for a discrete factor works.   Concept: Obviously, the coefficient of the continuous variable 'x' is applied in the form y = coefx(varx) + intercept but how does that work for a factor z if the factor is non-numeric? y = coefx(varx) + coefz(factorz???) + intercept   Specific: I have fitted a model in R as lm(log(c) ~ log(d) + h + a + f + h:a) where h and f are discrete, non-numeric factors. The coefficients are:  Coefficients:               Estimate  (Intercept)  -0.679695  log(d)        1.791294  h1            0.870735   h2           -0.447570   h3            0.542033    a             0.037362   f1           -0.588362   f2            0.816825  f3            0.534440 h1:a         -0.085658 h2:a         -0.034970  h3:a         -0.040637   How do I use these to create the predictive equation:  log(c) =  1.791294(log(d)) + 0.037362(a) + h??? + f???? + h:a???? + -0.679695   Or am I doing it wrong?   I THINK that that concept is if the subject falls in category h1 and f2, the equation becomes:   log(c) =  1.791294(log(d)) + 0.037362(a) +  0.870735  + 0.816825  + h:a???? + -0.679695   But I'm really not clear on how the h:a interactive term gets parsed. Thanks for going easy on me. In Euclidean geometry texts, it is always mentioned that point is undefined, it can only be described. Consider the following definition: "A point is a mathematical object with no shape and size." I do not understand what is the problem with this definition. Please give the detailed reasons. Thanks in advance! Bias of maximum likelihood estimators for logistic regression Polynomials, prove exercise question about question There is a polynomial P with integer coefficients and with pairwise different integers $a,b,c$ . Prove that it is not possible for $P(a) = b$, $P(b)=c$, $P(c) = a$  First off I don't understand "pairwise different" part - what does it mean ,can you show me this as an equation? After that I'd like to get a hint in case I don't make it. + I'd prefer to have hints/answers written more algebraically without $\sum$ etc. (It helps me get better understanding what's going on under the hood) How do electromagnetic waves travel in a vacuum? This is perhaps a total newbie question, and I will try to formulate it the best I can, so here it goes. How does an electromagnetic wave travel through for example, the vacuum of space?   I usually see that waves are explained using analogies with water, pieces of rope, the strings of a guitar, etc, but it seems to me that all those waves need a medium to propagate. In fact, from my point of view, in those examples the wave as a "thing" does not exist, it's just the medium that moves (involuntary reference to The Matrix, sorry).   But in space there is no medium, so how does a wave travel? Are there free particles of some sort in this "vacuum" or something? I believe , so supposedly there isn't a medium for the wave to travel through.   Moreover, I've seen other answers that describe light as a perturbation of the electromagnetic field, but isn't the existence of the field, potential until disturbed? How can it travel through something it does not exist until it's disturbed by the traveling light in the first place? (this last sentence is probably a big misconception by me). In evaluating integral $\int\sin^{3}x dx $ I am pretty sure we need to use substitution $e^x=t$, but can't go  next step. The main effect will be non-significant if the interaction is significant? Lost supplementary user groups for GUI login session Ubuntu 16.04.5  Very weird situation - after Xorg crash, now every time when I login into Unity, my user account doesn't have it's system groups like adm, sudo, plugdev, fuse etc. But when I login on virtual console (Alt+F1) or over SSH - all my additional groups are there, as reported by id command.  Neither of /etc/group* or /etc/gshadow* files have changed, my user is still listed there in many system groups.  It looks like some systemd session parameters for GUI logins or lightdm cache files got screwed. But I have no idea where to start looking..  A lightdm log:  $ journalctl -au lightdm  -- Reboot -- systemd[1]: Starting Light Display Manager... systemd[1]: Started Light Display Manager. lightdm[3223]: pam_kwallet5(lightdm-greeter:setcred): (null): pam_sm_setcred lightdm[3223]: pam_unix(lightdm-greeter:session): session opened for user lightdm by (uid=0) lightdm[3345]: pam_succeed_if(lightdm:auth): requirement "user ingroup nopasswdlogin" not met by user "chm" lightdm[4867]: pam_ecryptfs: Passphrase file wrapped lightdm[3345]: pam_kwallet5(lightdm:auth): (null): pam_sm_authenticate lightdm[3345]: pam_kwallet5(lightdm:setcred): pam_kwallet5: pam_sm_setcred lightdm[3345]: pam_unix(lightdm:session): session opened for user chm by (uid=0) lightdm[3046]: Error writing to daemon: Bad file descriptor lightdm[3046]: Error writing to daemon: Bad file descriptor lightdm[3046]: Error writing to daemon: Bad file descriptor lightdm[3046]: Failed to write utmpx: Permission denied URL line breaks with biblatex How do I allow long URLs to have line breaks at any point. This is in the bibliography not the main text. I am trying to save space so don't want extra spaces to be added to make it only break at slashes, for example, as it does by default.  I am using biblatex+biber. Why wasn't Sauron invisible when he wore the Ring? When Sauron is shown killing Elendil and then being destroyed by Isildur he is clearly not invisible and he is wearing the Ring.  But any time Bilbo or Frodo put on the Ring they went invisible without fail.  Did the Ring change after Sauron was destroyed or is Sauron capable of controlling the rings power unlike anyone else? Stop suggesting Microsoft Edge browser in start menu when typing "internet" I use Chrome as my primary browser but must use Internet Explorer to be able to remote in to my work via Remote Desktop web client (since it uses ActiveX plugins). To start an app, I would often type out the name from the start menu unless I had a pinned link or shortcut handy. But if I type &quot;internet&quot; as if I were trying to start Internet Explorer, I will always be recommended Edge and have it highlighted by default.  I will never be able to use Edge here so stop recommending it... can this behavior be disabled somehow? Not even pinning the Internet Explorer link to the start menu prevents this. If I had any other shortcuts that started with the word &quot;internet,&quot; it still offers Edge and is preselected. At least if I type in &quot;chrome,&quot; Chrome is selected first. Windows 10 Pro 1909 (18363.900) Reproducible LaTeX builds - compile to a file which always hashes to the same value Determine the Set of a Sum of Numbers I want to determine the set of natural numbers that can be expressed as the sum of some non-negative number of 3s and 5s.  $$S=\{3k+5j∣k,j∈\mathbb{N}∪\{0\}\}$$  I want to check whether that would be: 0,3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, and so on.  Meaning that it would include 0, 3, 5, 8. Then from 9 and on, every Natural Number. But how would I explain it as a set? or prove that these are the numbers in the set? Top Bar background does not persist when scrolling horizontally Update  A month Several months later, a new top bar, and the bug still exists. An answer has already been posted that would fix the bug, so is this something that the dev team plans on fixing?  There are also a host of other problems caused by this, especially on the  and . Again, this would be fixed with  html{min-width:1000px;}   There is a slight bug with small windows on both the new meta and main site(s)?, shown here. The problem is that the top bar coloring doesn't stretch across when you resize and scroll left or right.        On Meta, when a horizontal scroll bar is needed, the black background will only be as wide as the width of the viewport, but when you scroll the coloring will not shift.  To reproduce:   Make screen as large as possible, or wait until the menu bar starts expanding Make it smaller and smaller until horizontal scrollbar appears, then scroll left and right.