Discrete-time sequence with labels for individual samples
plotting discrete signals
I have a ext4 partition and I've set the group owner for all subdirectors to mygroup:  # chgrp -R mygroup /mount/abc # chmod -R g+swrx /mount/abc   My user is part of that group. Inside that partition is a folder who is owned by user 'nobody' and now by the group 'mygroup'. My user is part of 'mygroup'. Here's an ls -l:  myuser@host:/mount/abc/folder$ ls -l drwxr-sr-x 2 nobody      mygroup      4096 Apr 25 12:08 ./ drwxrwsrwx 6 nobody      mygroup      4096 Apr 24 07:57 ../ -rw-r-xr-- 1 otheruser   mygroup    159539 Apr 23 23:44 test.png*  myuser@host:/mount/abc/folder$ groups myuser myuser : mygroup {... a list of other groups also...}   myuser@host:/mount/abc/folder$ rm test.png  rm: remove write-protected regular file ‘test.png’? y rm: cannot remove ‘test.png’: Permission denied  myuser@host:/mount/abc/folder$ touch test.txt touch: cannot touch ‘test.txt’: Permission denied   Note that I cannot delete nor create a file that is owned by a group that my user is a part of.  I guess I don't fully understand how groups work. I thought if you were part of a group then you inherit the permissions of that group. Am I doing something wrong?  Thanks In Spivak's Calculus 3rd Edition, there is an exercise to prove the following:  $$x^n - y^n = (x-y)(x^{n-1} + x^{n-2} y + ... + x y^{n-2} + y^{n-1})$$  I can't seem to get the answer. Either I've gone wrong somewhere, I'm overlooking something, or both. Here's my (non) proof:  $$\begin{align*} x^n - y^n &amp;= (x - y)(x^{n-1} + x^{n-2}y +\cdots+ xy^{n-2} + y^{n-1}) \\           &amp;= x \cdot x^{n-1} + x \cdot x^{n-2} \cdot y + \cdots + x \cdot x \cdot y^{n-2} + x \cdot y^{n-1}\\ &amp;\qquad + (-y) \cdot x^{n-1} + (-y) \cdot x^{n-2} \cdot y + \cdots + (-y) \cdot x \cdot y^{n-2} + (-y) \cdot y^{n-1}\\           &amp;= x^n + x^{n-1} y + \cdots + x^2 y^{n-2} + x y^{n-1} - x^{n-1}y - y^2 x^{n-2}  - \cdots- x y^{n-1} - y^n \\           &amp;= x^n + x^2 y^{n-2} - x^{n-2} y^2 - y^n  \\           &amp;\neq x^n - y^n \end{align*}$$  Is there something I can do with $x^n + x^2 y^{n-2} - x^{n-2} y^2 - y^n$ that I'm not seeing, or did I make a mistake early on?  EDIT:  I should have pointed out that this exercise is meant to be done using nine of the twelve basic properties of numbers that Spivak outlines in his book:     Associate law for addition   Existence of an additive identity   Existence of additive inverses   Commutative law for additions   Associative law for multiplication   Existence of a multiplicative identity   Existence of multiplicative inverses   Commutative law for multiplication   Distibutive law If ${n \choose 3} + {n+3-1 \choose 3} = (n)_3$, compute $n$.  Just making sure I am on the right track...  Do I expand each piece out and solve algebraically? Should I disconnect my MacBook Pro's power cord when the battery is fully charged? My friend told me that I need to disconnect the power cord when the battery is fully charged. Otherwise, I will shorten the life of the battery.  Other people say you should drain it once a month or point out that for long term storage, you should charge it to 50% and then periodically (3 to 6 months) bring it back to 50% and store it again.  I am going to use my laptop at home 90% of the time. So, I plan to have the power cord connected all the time.  I'd prefer to just plugging in my MacBook Pro and letting it be on charge long term and occasionally taking it away from the charger when I'm not at home or my desk.  Are these specific recommendations worth the inconvenience? $M /K \land L /K$ algebraic $\implies ML/K$ algebraic? How can I verify a Google authentication access token?  I need to somehow query Google and ask: Is [given access token] valid for the [example@example.com] Google account?  Short version: It's clear how an access token supplied through the  can be used to then request data from a range of Google services. It is not clear how to check if a given access token is valid for a given Google account. I'd like to know how.  Long version: I'm developing an API that uses token-based authentication. A token will be returned upon provision of a valid username+password or upon provision of a third-party token from any one of N verifiable services.  One of the third-party services will be Google, allowing a user to authenticate against my service using their Google account. This will later be extended to include Yahoo accounts, trusted OpenID providers and so on.  Schematic example of Google-based access:    The 'API' entity is under my full control. The 'public interface' entity is any web- or desktop-based app. Some public interfaces are under my control, others will not be and others still I may never even know about.  Therefore I cannot trust the token supplied to the API in step 3. This will be supplied along with the corresponding Google account email address.  I need to somehow query Google and ask: Is this access token valid for example@example.com?  In this case, example@example.com is the Google account unique identifier - the email address someone uses to log in to their Google account. This cannot be assumed to be a Gmail address - someone can have a Google account without having a Gmail account.  The Google documentation clearly states how, with an access token, data can be retrieved from a number of Google services. Nothing seems to state how you can check if a given access token is valid in the first place.  Update The token is valid for N Google services. I can't try a token against a Google service as means of verifying it as I won't know which subset of all Google's services a given user actually uses.  Furthermore, I'll never be using the Google authentication access token to access any Google services, merely as a means of verifying a supposed Google user actually is who they say they are. If there is another way of doing this I'm happy to try. Proof that a formula $\theta$ is valid if and only if $\forall x \theta$ is valid I need to prove for first-order logic that $\vDash\theta$ if and only if $\vDash\forall x \theta$. The proof for the forward direction seems simple enough:  Suppose $\theta$ is valid. Let $\mathfrak{A}$ be an arbitrary structure and let $s:V\to |\mathfrak{A}|$ be an arbitrary function assigning values of the universe of $\mathfrak{A}$ to variables. Then we know by assumption that $\vDash_\mathfrak{A}\theta[s]$.  But since $s$ is arbitrary, it follows that $\vDash_\mathfrak{A}\theta[s(x|c)]$, for all $c\in|\mathfrak{A}$. But this means that $\vDash_\mathfrak{A}\forall x\theta[s]$. Since $\mathfrak{A}$ and the function assigning elements of the structure to variables are arbitrary, it follows that $\vDash\forall x\theta$.   Now we have to show that if $\vDash\forall x\theta$, then $\vDash\theta$, and this is where I'm stuck. I understand why it makes sense that this should be true, I'm just having a hard time writing it rigorously. Any suggestions would be greatly appreciated. I have removed the mentioned libraries. Then my system disconnected from NIS service and many packages are being removed. The problem is I am not even able to login in my system. When i restarted it is showing "low graphics mode error". I do not know what to do Please help me. I am a beginner to Ubuntu. My processor is an Intel Core 2 Duo P8600 (2.40GHz). As far as I know that's a 64-bit processor - I'm a bit confused as the architecture is called AMD 64, is this a generic name given to 64-bit architectures? I've heard of x64 but can't see a release labelled with this. Just need help understanding this question, as I don't really understand what a continuous random vector is. My limited understanding is that a continuous random vector must be completely continuous (so for continuous X and Y this is satisfied) and that to get the probability of the random vector occurring, we double integrate over the supports (of X and Y obviously). My guess is then, that the c.r.v (X,Y) IS a continuous random vector.  Also, what of the converse? If (X,Y) is a continuous random vector, then are X and Y continuous random variables? I also think this is correct, as the continuity of the vector MUST imply the continuity of X and Y, although I'm honestly not sure.  Thanks How do I get horizontal lines to the left and right of a heading in Microsoft word? In Word 2007 I want to put a heading in the center of a line with a horizontal line to the left and to the right of the text.  The line must not cross through the text. I have tried using autoshapes and lines - but then the lines move each time I press Enter or &larr; Backspace and I have to put them in place again manually.  At Borders and Shading there is an "Insert horizontal line" option, but this gives me a solid line from the left to the right of the page and I cannot insert text anywhere on it or in it.    The final product should look something like this:     -------------------------  Heading ------------------------- Gnome Panel becomes fully transparent when window is not maximised! How do I change a close vote to a duplicate? Voted to close a question based on "lack of minimal understanding".  Later realized the question was a duplicate.  How to I change vote to mark as duplicate instead? How do I pronounce "ratio 1:1"? How do I pronounce "ratio 1:1"?  Should I pronounce it "ratio 1 to 1"? Are user accounts on data.stackexchange.com and Stack Exchange two different entities? I tried to search for similar questions, as I always do, but was not able to find one. I just created a new  on Data.Stack Exchange with my existing Google OpenID and it seems to be not associated with my regular Stack Exchange account. Is this by design? and if so, why? Difference between generalized linear models & generalized linear mixed models I am wondering what the differences are between mixed and unmixed GLMs. For instance, in SPSS the drop down menu allows users to fit either:   analyze-&gt; generalized linear models-&gt; generalized linear models &amp; analyze-&gt; mixed models-&gt; generalized linear     Do they deal with missing values differently?    My dependent variable is binary and I have several categorical and continuous independent variables. Get all categories and posts in those categories I am looking for a solution that allows me to print the following:  Cat 1        Cat 2        Cat 3  Post 1       Post 1       Post 1  Post 2       Post 2       Post 2  Post 3                    Post 3                            Post 4   EDIT  I am looking for something that will only require one database query! So if you have a foreach in your code followed by a new WP_Query then that is not what I am looking for (I am planning to put this onto my website's homepage). Android app - can I see interesting questions? On the website the default list of questions displays interesting tab (which I believe has questions based on my highest scoring tabs). That's very convenient and allows me to check new questions that are relevant for me easily.   Can the same view be added to the mobile app? Determine Which of the following Sets is a Vector Space Determine which of the following sets is a vector space.  $V$ is the line $y=x$, in the $xy$-plane: $V =\{[x,y]: \; y=x\}$  $W$ is the union of the first and second quadrants in the $xy$-plane: $W=\{[x,y]: \; y\geq0\}$  $U$ is the line $y = x+1$ in the $xy$-plane: $U=\{[x,y]: \; y=x+1\}$    I know that the answer is that "$V$" is the only vector space. However how do I come up with a quick proof to show that $V $is a vector space and that the other $2$ aren't? Intuition behind the Definition of Conditional Probability (for 2 Events)