What is a $k$-algebra, what is a $k$-algebra morphism?
Intuition behind $k$-algebra, $k$-algebra morphisms?
How can I easily clone my entire system? I am running an Ubuntu 14.04 LTS and I experienced some issues with my hard drive. I bought a new HDD of the same size (1TB), and I intend to move all my data (softs, work, pics, etc.) on the new HDD.  What is the easiest way to do that? SqlServer: can one table's PK be the FK of two table's? I have three tables project, users and proj_user. The PK of proj_user table is the FK of project and users table's pk e.g.(project_id,user_id)  My question is, is it possible if the project_id and user_id's data is different  like project_id = '12345' and user_id = 'abc987'  Please reply  kind regards Vivek Why don't authors include in their publications the duration of the research? Jensen's Inequality implies convexity? Suppose $\phi$ is a real function on $\mathbb{R}$ such that $$\phi \Bigl(\int_0^1f(x)\,dx\Bigr)\leq \int_0^1 \phi(f)\,dx$$ for every real bounded measurable function $f$. Prove that $\phi$ is then convex.    This one is in Rudin's Real and Complex Analysis, page 74, and, to be quite honest, I am unsure what my first step to solve this problem should even be. To help think of a general methodology, I attempted this similar question, from page 71 of the same book:      Assume $\phi$ is a continuous real valued function on $(a,b)$ such that $$\phi\Bigl(\frac{x+y}{2}\Bigr)\leq\frac{\phi(x)+\phi(y)}{2}$$ for all $x, y\in (a,b).$ Prove that $\phi$ is then convex (the conclusion does not follow if continuity is omitted from the hypothesis).   I take it that the latter question is just a special case of the former (assuming $\phi$ is bounded on $(a,b)$), so I attempted to solve the latter problem first. My attempt was to note that \begin{align*} \phi\big(\lambda x + (1-\lambda)y\big) &amp;\leq \phi\Bigl(\frac{2\lambda x + 2(1-\lambda)y}{2}\Bigr) \\ &amp;\leq \frac{1}{2}\Bigl(\phi\bigl(2\lambda x\bigr)+\phi \bigl(2(1-\lambda)y\bigr)\Bigr) \\ &amp; \leq \phi\bigl(\lambda x\bigr)+\phi\bigl((1-\lambda)y\bigr) \end{align*} with the latter inequality justified simply by applying the hypothesis again twice to the previous expression.   From here, however, I am stuck; I cannot justify "popping out" the $\lambda$ and the $(1-\lambda)$ in the last inequality via some bound afforded by the hypothesis and/or the continuity of $\phi$. How do you mock a Sealed class? can be quite a pain.  I currently favor an  to handle this, but something about just keeps feels weird.    So, What is the best way you mock sealed classes?  Java answers are more than welcome.  In fact, I would anticipate that the Java community has been dealing with this longer and has a great deal to offer.  But here are some of the .NET opinions: Interpretation of p-value in Mann-Whitney rank test I am testing Mann-Whitney rank test with two vectors a and b. Vectors are almost similar so I expect a p-value near 0, but the returned p-value is near 1. What is the reason? I read  and also run the code with different parameters, but don't get anything near to what I expect.  from scipy.stats import mannwhitneyu import operator import numpy as np  a = [1000,100,10,1,10,100,1000,10000,1000,100,10,1] b = [999,100,10,1,10,100,1000,10000,1000,100,10,1]  print(mannwhitneyu(a, b))   The output of the code:  MannwhitneyuResult(statistic=73.5, pvalue=0.95291544831453867)   Edit:  Let's formalize the problem to eliminate any misunderstanding (please edit the question if something is wrong):  What I try to prove is that rank distribution of data are approximately equal,   Null hypothesis ($H_0$)= "ranked distribution of a and b are approximately equal"  Alternative hypothesis ($H_a$)= "ranked distribution of a and b are not equal"  significance level (alpha) = 0.05  p-value= 0.95  (p-value > alpha) so there is no sufficient evidence that $H_a$ is correct, but we cannot also conclude that ($H_0$) is true.   Instead if (p-value &lt; alpha) was true, then we would have enough evidence against H0 and Ha can be accepted.  So what happened here is that I could not disprove the null hypothesis. However, it doesn't mean that null hypothesis is false. It is like an investigation to accuse MR X of being guilty:   $H_0$=" MR X guilty" $H_a$=" MR X not guilty"  We guess he is not guilty, but we don't have enough proof against him: (p-value > alpha), but that doesn't mean that ($H_0$) would not be true. If we could obtain enough evidence and state (p-value &lt; alpha), then we disprove $H_0$ and we can conclude that Ha is true and he is not guilty. How to split a file according to a column (including header) and rename the generated files? I have a .txt that can be exemplified like this:  NAME | CODE name1 | 001 name2 | 001 name3 | 002 name4 | 003 name5 | 003 name6 | 003   I need to write a script to split this file according to the CODE column, so in this case I'd get this:  file 1: NAME | CODE name1 | 001 name2 | 001  file 2: NAME | CODE name3 | 002  file 3: NAME | CODE name4 | 003 name5 | 003 name6 | 003   According to some research, using awk would work:  $ awk -F, '{print &gt; $2".txt"}' inputfile   The thing is, I also need to include the header to the first line and I need the file names to be different. Instead of 001.txt, for example, I need the file name to be something like FILE_$FILENAME_IDK.txt. Which is the correct question ("Who has" vs "Who have")? The situation is that:  We've already read three English novels.  Which is the correct question for that situation?   Who has already read three English novels?  Who have already read three English novels?    Or could both be correct? Please also provide the grammatical reasons for your answers. I was trying to solve internet problems, and seem to have made things worse: Now when I start the computer it gets stuck on "Booting system without full network configuration".   Does anyone know how to make it unstuck?   Alternatively: It got messed up when I changed the contents of /etc/network/interfaces, so presumably would work again if I changed it back. How can I edit this file during boot?   I'm using Ubuntu 12.10. Are universal power supplies for laptops worth it? My laptop's cable broke and sadly it seems like I need to buy a new power supply.  What I wonder is, I've found that universal power supplies are much cheaper than the official HP ones. Are they really worth it?  Another question: the original supply has these specs: 65W, 18.5V, 3.5A. However the universal supplies are more powerful (90W, 100W) and come in integer voltages (17V, 18V, 19V, etc). Are they compatible? Should I set them to 18V or 19V? Joining two rigged models I currently trying to join two rigged (and animated) models, which both has separate meshes, separate bones and separate animations. The first mesh is the horse while the second mesh is human:   So I am interested to join human model onto horse model to make a rider:   I think the best way would be to make horse as a parent and human as a child during the join process. In that case I would like that all horse animations (there are 3 of them - idle, walk and run) would remain as they are, while I can lose human animations, as I will need different ones for it. I was also thinking to make human root bone as a child of one horse back bones, that when horse moves up and down it would move entire human mesh together. It would be also good to keep the same weights that human bones would not start deforming horse mesh and vice versa.  I tried to use Ctrl+J by selecting various combinations between bones and meshes in object mode, however, I noticed that it messes up scaling and rotation of the child object. So I was wondering how it would be possible to properly join these models to create a rider? It looks like if I load dynamic content using $.get(), the result is cached in browser.  Adding some random string in QueryString seems to solve this issue (I use new Date().toString()), but this feels like a hack.   Is there any other way to achieve this? Or, if unique string is the only way to achieve this, any suggestions other than new Date()? How can I disable cloud-init? I have a fully-configured instance and an image from that for an autoscaling group. When autoscaling new instances from this image, it calls cloud-init. cloud-init changes the hostname and breaks fstab.  I want to prevent cloud-init from starting on instance launch. Which of the following sentences is correct:        There is a lot of food and fruit in the supermarket.   There are a lot of food and fruit in the supermarket. I am foreign graduate student in USA. I recently completed my undergrad (from USA) and have a bit of money saved up. I know that F1 students cannot work off campus and other business activities such stock trading etc are prohibited as well. I wanted to know if opening an account in an investment management firm like Charles Schwabb or Betterment is allowed. I would not be working but I will still be earning a small interest on my deposits. If that is not allowed, are there any good and legal ways for foreign students to earn a little interest on savings? Prove that $|f''(\xi)|\geqslant\frac{4|f(a)-f(b)|}{(b-a)^2}$ Target='_blank' to show in new window, NOT new tab, possible? Which Answer to Accept: Better Solution or Answer to Actual Question? Possible Duplicate:          I received two answers to a question I asked. One solution suggested I do things in a completely different manner than I have been. Another acknowledged that the first solution was correct but went on to explain how to do what I was asking.  Should I accept the first answer because it provides the better way of doing things or should I accept the second one because it answers the precise question that was asked? I'm currently working on the following question:  "At least one of Plato and Democritus believed in the theory of forms. Plato believed in the theory of forms only if he was not an atomist, and Democritus was an atomist only if he did not believe in the theory of forms. Democritus was an atomist. Prove, using Natural Deduction, that Plato was not an atomist"  I have been working for quite some time to take the information and turn it into a set of literals and statements I can work with.  So far, I have got $P \lor D$,  $P \Rightarrow \lnot a$,  $D \Rightarrow A$,  $D = A$  However, I cannot seem to make these prove the statement using natural deduction, any hints? C++ virtual function from constructor