There is an apple and an orange on the table.    There are an apple and an orange on the table.      Which is grammatical?
Which one is correct?     There is an apple and an orange..   or     There are an apple and an orange?"
LWJGL Eclipse Resource Deployment I'm still experimenting with some OpenGL in LWJGL, and as I get to know more and more about OpenGL, I start to do more complicated things like multi texturing, shadowmapping and more. Now, right now I'm using the src folder (src/res) for my resources, and use src/resourcename in my code. When I export it, this won't work on another location as the relative path is ofcourse incorrect. What would be the best way of deploying your game with all the resources in one file? Maybe put the files in the jar?  I would like to hear from a few people how they store and deploy their project with resources, thanks! Describing integral closure of quadratic number fields I'm facing the following problem.      Let $p$ be a prime and $ K=\mathbb{Q}(\sqrt{p}) $. I'm trying to find the integral closure of $ \mathbb{Z} $ in $ K $.   I don't really know where to start. I've managed to prove that $ \mathbb{Z}[\sqrt{p}] $ is in the integral closure and I'm almost sure $ \mathbb{Q} $ is not.   I can't think of a systematic way to approach this. I would appreciate any help. indefinite article before proper names Kafka, discovered in the 1920s by the Expressionists, damned by the Nazis in the 1930s and by the Marxists at more or less the same time, was reinvented after World War II by the French Existentialists. They saw in him the father of Angst and the Angst for the father: an Albert Camus before his time.   Can you tell me what the purpose of using the indefinite article before the proper name is in the sentence above. What it be a mistake to write just "Albert Camus" without the article? build argument lists containing whitespace What's a word like "disregard" or "bypass" that means "hides"? exponentiation of cardinal number Hidden fields though inheritance My question is from Apostol's Vol. 1 One-variable calculus with introduction to linear algebra textbook.  Page 57. Exercise 12. Show that the following are polynomials by converting them to the form $\sum_{k=0}^{m}a_kx^k$ for a suitable $m$. In each case $n$ is a positive integer. $a)$ $(1+x)^{2n}.$ $b)$ $\frac{1-x^{n+1}}{1-x}, x\not=1.$ $c)$ $\prod_{k=0}^{n}(1+x^{2^k}).$  The attempt at a solution: a) part of the problem is pretty easy I guess, it is example of binomial theorem, so the answer would be $(1+x)^{2n}=\sum_{k=0}^{2n}(^{2n}_{k})x^k.$ Answer to part b) would be the following: $$\frac{1-x^{n+1}}{1-x}=\frac{(1-x)(1+x+x^2+\cdots+x^n)}{1-x}=1+x+x^2+\cdots+x^n=‌​\sum_{k=0}^{n}x^k.$$thanks to @DiegoMath's hint. As for part c), we have $$\prod_{k=0}^{n}(1+x^{2^k})=(1+x)(1+x^2)(1+x^4)(1+x^8)\cdots(1+x^{2^n})$$ and I have trouble &quot;converting&quot; this to sum which would be of a form of polynomial. QuickStart basic layout/template for web development? I'm looking for a quick start or template, or something, to get a web site's basic layout done quickly and looking fairly professional, and then let me do the coding.  I don't want a CMS, as this is for a highly customised reporting application, but I need something like frame header and two columns and frame footer.  I can design the pretty reports for the wide right hand column myself, as the left hand column menu. Elastic net penalty I have a question about the elastic net penalty as implemented in glmnet in R compared to the original paper by Zou and Hastie (2005). In glmnet the penalty is listed as   $$ (1-\alpha)/2||\beta||_2^2+α||\beta||_1. $$  but in the paper it is  $$(1-\alpha)||\beta||_1 + \alpha||\beta||_2^2.  $$  Does anyone know where the factor $\frac12$ some from? (Never mind the fact that the $\alpha$'s were swapped between the two parameterisations.) In both cases the penalties are multiplied by $\lambda$, but what are the mathematical/technical arguments for not using a simple convex combination of the lasso and ridge penalties? I think that  is pretty good prima-facia evidence that  is just facilitating the deposition of crap. I have Google Chrome Version 70.0.3538.77 (Official Build) (64-bit).  Today, after running sudo apt update and sudo apt full-upgrade, I saw:  E: Repository 'http://dl.google.com/linux/chrome/deb stable Release' changed its 'Origin' value from 'Google, Inc.' to 'Google LLC' N: This must be accepted explicitly before updates for this repository can be applied. See apt-secure(8) manpage for details.   I looked at the man page for apt-secure but it's pretty technical and difficult, at least for me, to follow.  So how do I fix this issue?    Edit: for now, I've removed the existing Google Chrome ppa from Software Sources and then ran sudo apt update and sudo apt full-upgrade successfully with the following being installed/upgraded successfully:  The following NEW packages will be installed:   python3-netifaces The following packages will be upgraded:   netplan.io nplan ppp 3 upgraded, 1 newly installed, 0 to remove and 0 not upgraded. In Minecraft, there are a lot of cool sounds. I decided to find there location and move them to my desktop. I have Ubuntu, and if when I remove them from that folder will Minecraft be unable to play them or is it smart enough to figure out that they are gone and download them again. Before minecraft was installed, it had to download the files. I even moved my favorite song (creative 6) from the sounds. The sounds are not labeled and have seemingly random names like b0b12118a97ddd733a50e9382e91a21652568641 and how will I know what to call them that will be recognized without digging through the index if Minecraft fails to download them? Or do I not have to worry because it will download them again upon launch?  Note: Why does it not label them and call them random names? My question is pretty simple.  Since $n! \gt n!!$, it's clear by the comparison test that $\sum_{n=0}^\infty \frac {1}{n!!}$ converges.      But what value does the sum converge to? How does one go about determining its value (if possible)? "Heard me [infinitive]" vs. "heard me [present participle]" Is it true that the Fibonacci sequence has the remainders when divided by 3 repeating? Correlating filename with package Say, I'm given a filename like libasound.so.2. Is there a way to query the package manager to correlate the filename with its corresponding package?  I'm interested to get answers for any package manager, but my primary focus is on apt and yum. I have the following file:  ---------- 1 Steve Steve 341 2017-12-21 01:51 myFile.txt   I switched the user to root in the terminal, and I have noticed the following behaviors:   I can read this file and write to it. I can't execute this file. If I set the x bit in the user permissions (---x------) or the group permissions (------x---) or the others permissions (---------x) of the file, then I would be able to execute this file.   Can anyone explain to me or point me to a tutorial that explains all of the rules that apply when the root user is dealing with files and directories? Mobile chat "you have been suspended" notification is too ambiguous Earlier today, I was suspended from chat due to an inappropriate message (I totally deserved it, but that's not the point). I looked at my phone, and this is all that it told me:    ...which confused me because chat was still moving as normal. I didn't realize that I had been suspended until I checked on my computer to see what the heck was going on.  To me, "This room is read-only" sounds like some sort of database lockup or something related specifically to the room, not the user. It doesn't give any feedback to indicate that the room will be "read-only" for 30 minutes, and doesn't mention that all other rooms are also "read-only". Even a message saying just "You have been suspended from chat" would be more helpful. Choosing between LM and GLM for a log-transformed response variable I'm trying to understand the philosophy behind using a Generalized Linear Model (GLM) vs a Linear Model (LM). I've created an example data set below where:  $$\log(y) = x + \varepsilon $$   The example does not have the error $\varepsilon$ as a function of the magnitude of $y$, so I would assume that a linear model of the log-transformed y would be the best. In the example below, this is indeed the case (I think) - since the AIC of the LM on the log-transformed data is lowest. The AIC of the Gamma distribution GLM with a log-link function has a lower sum of squares (SS), but the additional degrees of freedom result in a slightly higher AIC. I was surprised that the Gaussian distribution AIC is so much higher (even though the SS is the lowest of the models).   I am hoping to get some advice on when one should approach GLM models - i.e. is there something I should look for in my LM model fit residuals to tell me that another distribution is more appropriate? Also, how should one proceed in selecting an appropriate distribution family.   Many thanks in advance for your help.  [EDIT]: I have now adjusted the summary statistics so that the SS of the log-transformed linear model is comparable to the GLM models with the log-link function. A graph of the statistics is now shown.  Example  set.seed(1111) n &lt;- 1000 y &lt;- rnorm(n, mean=0, sd=1) y &lt;- exp(y) hist(y, n=20) hist(log(y), n=20)  x &lt;- log(y) - rnorm(n, mean=0, sd=1) hist(x, n=20)  df  &lt;- data.frame(y=y, x=x) df2 &lt;- data.frame(x=seq(from=min(df$x), to=max(df$x),,100))   #models mod.name &lt;- "LM" assign(mod.name, lm(y ~ x, df)) summary(get(mod.name)) plot(y ~ x, df) lines(predict(get(mod.name), newdata=df2) ~ df2$x, col=2)  mod.name &lt;- "LOG.LM" assign(mod.name, lm(log(y) ~ x, df)) summary(get(mod.name)) plot(y ~ x, df) lines(exp(predict(get(mod.name), newdata=df2)) ~ df2$x, col=2)  mod.name &lt;- "LOG.GAUSS.GLM" assign(mod.name, glm(y ~ x, df, family=gaussian(link="log"))) summary(get(mod.name)) plot(y ~ x, df) lines(predict(get(mod.name), newdata=df2, type="response") ~ df2$x, col=2)  mod.name &lt;- "LOG.GAMMA.GLM" assign(mod.name, glm(y ~ x, df, family=Gamma(link="log"))) summary(get(mod.name)) plot(y ~ x, df) lines(predict(get(mod.name), newdata=df2, type="response") ~ df2$x, col=2)  #Results model.names &lt;- list("LM", "LOG.LM", "LOG.GAUSS.GLM", "LOG.GAMMA.GLM")  plot(y ~ x, df, log="y", pch=".", cex=3, col=8) lines(predict(LM, newdata=df2) ~ df2$x, col=1, lwd=2) lines(exp(predict(LOG.LM, newdata=df2)) ~ df2$x, col=2, lwd=2) lines(predict(LOG.GAUSS.GLM, newdata=df2, type="response") ~ df2$x, col=3, lwd=2) lines(predict(LOG.GAMMA.GLM, newdata=df2, type="response") ~ df2$x, col=4, lwd=2) legend("topleft", legend=model.names, col=1:4, lwd=2, bty="n")   res.AIC &lt;- as.matrix(     data.frame(         LM=AIC(LM),         LOG.LM=AIC(LOG.LM),         LOG.GAUSS.GLM=AIC(LOG.GAUSS.GLM),         LOG.GAMMA.GLM=AIC(LOG.GAMMA.GLM)     ) )  res.SS &lt;- as.matrix(     data.frame(         LM=sum((predict(LM)-y)^2),         LOG.LM=sum((exp(predict(LOG.LM))-y)^2),         LOG.GAUSS.GLM=sum((predict(LOG.GAUSS.GLM, type="response")-y)^2),         LOG.GAMMA.GLM=sum((predict(LOG.GAMMA.GLM, type="response")-y)^2)     ) )  res.RMS &lt;- as.matrix(     data.frame(         LM=sqrt(mean((predict(LM)-y)^2)),         LOG.LM=sqrt(mean((exp(predict(LOG.LM))-y)^2)),         LOG.GAUSS.GLM=sqrt(mean((predict(LOG.GAUSS.GLM, type="response")-y)^2)),         LOG.GAMMA.GLM=sqrt(mean((predict(LOG.GAMMA.GLM, type="response")-y)^2))     ) )  png("stats.png", height=7, width=10, units="in", res=300) #x11(height=7, width=10) par(mar=c(10,5,2,1), mfcol=c(1,3), cex=1, ps=12) barplot(res.AIC, main="AIC", las=2) barplot(res.SS, main="SS", las=2) barplot(res.RMS, main="RMS", las=2) dev.off()