calculating the mean for each subj in r
calculate the mean of trials for each subject in R
Removing OS from Dual Boot computer, and recovering HD space. I have a computer that dual boots Linux Mint, and Ubuntu, I am wondering what the best way would be to remove Linux Mint, then recovering the hard drive space that is resides in so that Ubuntu will be able to access it. Accessing Reduce from DSolve Proof of the First Isomorphism Theorem for Groups Why Do Glueballs Have Mass, When Individual Gluons Are Massless? Good abstract algebra books for self study Last semester I picked up an algebra course at my university, which unfortunately was scheduled during my exams of my major (I'm a computer science major). So I had to self study the material, however, the self written syllabus was not self study friendly (good syllabus overall though).  The course was split up into 3 parts, group theory, ring theory and field theory. As a computer science major we only had to study the first 2.  Now that I passed the exam for this course I want to study the field theory part ( which covers Galois theory, etc).  So, now I want to ask whether any of you know any good books on abstract algebra, which lift off at basic ring theory and continue to more advanced ring theory and to finite fields, Galois theory, ...  Please keep in mind that I am not a math major, and that I would like books which are suited for self study (thus a lot of examples and intuition).  Thanks in advance! Prove that an infinite ring with finite quotient rings is an integral domain How can we show that if $R$ is an infinite commutative ring and $R/I$ is finite for every nonzero $I \unlhd R$, then $R$ is an integral domain?   I tried proceeding by contradiction: assume $a$,$b$ $\in R \backslash \{0\}$ and $ab=0$; then $R/(a)$ and $R/(b)$ must be finite, say $R/(a)=\{k_i + (a) : 1 \leq i \leq m\}$ and $R/(b)=\{l_j + (b) : 1 \leq j \leq n\}$. Does this mean $R$ must be finite? Or what about using the fact that $R/(a,b)$ finite?  Thanks for any help with this! Why does as.factor return a character when used inside apply? I've often wondered why Stack Exchange has opted to keep the upvote/downvote buttons available for clicking on question/answers posted by the user. For instance:    Even though these buttons have no use for the user, why are they still placed on the post's left hand column? Moreover, the comments have no controls for flagging/+1'ing the user's own comment. What is the reason for this discrepancy? What benefit do the +1/-1 buttons provide to the user, even though they can't be used for anything? I seem to remember from first year physics that we can calculate the RMS speed of a stationary, ideal gas with $v=\sqrt{\frac{3RT}{M}}$. Does a similar equation exist for liquids? For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$ I was reading a text book and came across the following:  Important Results (This comes immediately after LCM:) If 2 [integers] $a$ and $b$ are given, and their $LCM$ and $HCF$ are $L$ and $H$ respectively, then $L \times H = a \times b$  Can some please help me understand why the above result is true? Thanks in advance. Suppose that $X_1,X_2,\ldots,X_n$ is a random sample from a distribution with probability function:  $$p_X(x)=\begin{cases} 1/2 &amp;x=-1,1 \\ 0 &amp; \text{otherwise} \end{cases}$$  Now if we define the average   $\bar{X}= \frac{1}{n} \sum X_i$, I need to show that that for an odd $n$ the probability function for $\bar{X}$ is:  $$p_{\bar{X}} (x)= \frac{\binom{n}{\frac{n}{2} (x+1)}}{2^n}$$ for $x=\pm 1/n,\pm 3/n,\ldots,\pm 1$, $0$ otherwise.    Since $P[\sum X_i=k] =P [\bar{X}=k/n ]$, I thought it would be easier to first derive the probability function for the sum. Since they are still $2^n$ n-tuples and each one is equilikely, I need to count the ones whose sum is $k$ for:  $k=\pm 1,\pm 3,\ldots \pm n-2,\pm n$ (since even numbers are not a feasible combination)  The problem here though is that I do not immediately recognize how I could count all these tuples. Could you please help me with this? If it is easier to proceed another way, I am of course all ears. Does Calculate Value (Model Only Tool) work correctly in tools run in Batch? Am I correct that if my model has a model-only tool (Calculate Value), and then I run the model as a batched process, it will not run the Calculate Value expression?   I wrote a model to upload, define, project (and clip) XY data from excel files. I had thought to use iterate tables, but it wasn't working. (I assume due to having to choose which worksheet within xlxs). So I thought to do a batch, but this seems to leave that annoying $ that arc appends to table names (and is an invalid character in most tools...)  My guess is that the Calculate value that removes my $ is not being run in the batch. Ideas? Confirmations? I'm looking for a simple, easy to understand algorithm to alphabetically sort an array of characters in C. How to Sort a 2D array? I read this sentence in a book:     I just took part in a study over in the Psychology Department.   Why do we add over in front of in the here? I have set of temp files created in my folder with .bak extensions. How can I make them hide by default in Ubuntu?  I tried adding a .hidden file with *.bak as entry in the file, but that is not working. Any help is very appreciated... Troubleshooting for biber I'm trying to switch from BibTeX to biber and ran into the problem that biber does not produce any output file. I noticed several questions about problems with biber e.g.,            ,                       But none of them helped me in my particular situation (which was actually just an old version of biber somewhere in the path of my OS). Since I also noticed that several questions regarding problems with biber were closed as too localized since the underlying problem was due to formatting of a bib resource or similar simple issues, I would rather like to ask for a general troubleshooting guideline for using biber (since I saw many hints like "check/delete the cache", "check versions of this and that" etc.).  What steps are to be taken and what things (in particular files) to be checked if biber does not produce an output file (and its output on the command line does not directly give you the advice what to do)? Find weak form of linear transport equation I am stuck on the following problem that says:       a) Find a weak formulation for the partial differential equation $${\partial u\over\partial t\ }+ c{\partial u \over \partial x\ }=0$$    b) Show that $u=f(x-ct)$ is a generalized solution of $${\partial u\over\partial t\ }+ c{\partial u \over \partial x\ }=0$$ for any distribution $f$    My Attempt:   I know that in order to find a weak form of a pde, we need to multiply it by a test function, then integrate it. Also, to find a generalized solution, we need to find a weak solution and just multiply it by the Heaviside function.  Let's take any test function $\phi $, then we have (integrating by parts second part of the integral) $$\int_{\Omega } ( {\partial u\over\partial t\ }+ c{\partial u \over \partial x\ })*\phi(x) dx= \int_{\Omega } {\partial u\over \partial t}\phi(x) dx - c\int_{\Omega } u(x,t)\phi'(x)dx$$ where $\phi $ vanishes at boundaries. So, is it the final form or can we proceed further? And how am I supposed to find a generalized solution?  Can someone help me out? Thanks in advance for your time. Change multiple filenames by replacing a character I have multiple files named like that : screenshot 13:25.png Windows struggle to open these files probably because of the ":".  How can I replace it? How can I stop using beta iOS on my iPhone? I'm currently on the beta program on my iPhone. How can I stop using the beta versions and go back to the newest version of iOS (non-beta)?