Will it hit my ranking if I have the same URLs where / on the end is the only difference?   Those URLs return the same content and one redirects to another or they both redirects to some 3rd URL.  These URLs are all in canonical tags on the page.  Do I need to have both www.example.com/asdf and www.example.com/asdf/ in the canonical, can that situation hit my ranking?
Does it make any difference to SEO ratings what-so-ever if your url has a trailing slash:  http://www.example.com/some/slug/paths/   as opposed to one that does not:  http://www.example.com/some/slug/paths
Import a module from a relative path Suppose that $y_1(x)$ and $y_2(x)$ are solutions of the differential equation $y''+py'+qy=0$ on $I$. How can I show that if $y_1$ and $y_2$ vanish at the same point then they are not linearly independent?   Here is my attempt to prove the problem. Since $y_1(x)$ and $y_2(x)$ are solutions of the differential equation $y''+py'+qy=0$ on $I$, it is enough for me to show that the Wronskian of $y_1$ and $y_2$ denoted by $W(y_1,y_2)$ is zero. Now since $y_1$ and $y_2$ vanish at the same point say $p$ we have $y_1(p)=0$ and also $y_2(p)=0$.   Solving for $W(y_1,y_2)(p)$ we have: $y_1(p)y_2'(p)-y_2(p)y_1'(p)=0$ since $y_1(p)=0$ and also $y_2(p)=0$.   Am I correct? Thanks Assume I have a dataset for a supervised statistical classification task, e.g., via a Bayes' classifier. This dataset consists of 20 features and I want to boil it down to 2 features via dimensionality reduction techniques such as Principal Component Analysis (PCA) and/or Linear Discriminant Analysis (LDA).  Both techniques are projecting the data onto a smaller feature subspace: with PCA, I would find the directions (components) that maximize the variance in the dataset (without considering the class labels), and with LDA I would have the components that maximize the between-class separation.  Now, I am wondering if, how, and why these techniques can be combined and if it makes sense.  For example:   transforming the dataset via PCA and projecting it onto a new 2D subspace transforming (the already PCA-transformed) dataset via LDA for max. in-class separation   or    skipping the PCA step and using the top 2 components from a LDA.   or any other combination that makes sense. Order discrete x scale by frequency/value Parsing XML, JSON, and newer data file formats in UNIX using command line utilities The Unix environment has some excellent tools for parsing text in various forms. However, of late, the data is not in the traditional (historical) formats (CSV, TSV, record-based or some other delimiter-based) it used to be before. Data these days is exchanged in structured formats like XML/JSON.  I know there are some good tools like sed, awk and Perl which can chew down nearly any form of data out there. However, to work with this sort of structured data, often one has to write a complete program, and, given the little time available to extract information, one has to sit down and figure out the whole logic of what one wants to query and put it down programmatically. Sometimes this is not OK – basically because the information extracted from those files acts as inputs for further work; also because of the time it takes to search for the appropriate solution and code it up. A command line tool is needed with sufficient switches to find, query and dump data.  I'm looking for tools that take a XML/JSON or other forms of structured data and dump it into other formats like csv, etc., so that from there one could use other commands to get any information out of it.  Are there any command line utilities you know of which do this kind of a job? Are there already awk/Perl scripts available to this? The normal JOIN ... ON ... syntax is well known. But it is also possible to position the ON clause separately from the JOIN that it corresponds to. This is something that is rarely seen in practice, not found in tutorials and I have not found any web resource that even mentions that this is possible.  Here is a script to play around with:  SELECT * INTO #widgets1 FROM (VALUES (1), (2), (3)) x(WidgetID)   SELECT * INTO #widgets2 FROM (VALUES (1, 'SomeValue1'), (2, 'SomeValue2'), (3, 'SomeValue3')) x(WidgetID, SomeValue)  SELECT * INTO #widgetProperties FROM (VALUES     (1, 'a'), (1, 'b'),     (2, 'a'), (2, 'b')) x(WidgetID, PropertyName)   --q1 SELECT w1.WidgetID, w2.SomeValue, wp.PropertyName FROM #widgets1 w1 LEFT JOIN #widgets2 w2 ON w2.WidgetID = w1.WidgetID LEFT JOIN #widgetProperties wp ON w2.WidgetID = wp.WidgetID AND wp.PropertyName = 'b' ORDER BY w1.WidgetID   --q2 SELECT w1.WidgetID, w2.SomeValue, wp.PropertyName FROM #widgets1 w1 LEFT JOIN #widgets2 w2 --no ON clause here JOIN #widgetProperties wp  ON w2.WidgetID = wp.WidgetID AND wp.PropertyName = 'b'  ON w2.WidgetID = w1.WidgetID ORDER BY w1.WidgetID   --q3 SELECT w1.WidgetID, w2.SomeValue, wp.PropertyName FROM #widgets1 w1 LEFT JOIN (     #widgets2 w2 --no SELECT or FROM here     JOIN #widgetProperties wp     ON w2.WidgetID = wp.WidgetID AND wp.PropertyName = 'b') ON w2.WidgetID = w1.WidgetID ORDER BY w1.WidgetID   q1 looks normal. q2 and q3 have these unusual positionings of the ON clause.  This script does not necessarily make much sense. It was hard for me to contrive a meaningful scenario.  So what do these unusual syntax patterns mean? How is this defined? I noticed that not all positions and orderings for the two ON clauses are allowed. What are the rules governing this?  Also is it ever a good idea to write queries like this? Why is integration the inverse of differentiation Why is integration the inverse of differentiation, I mean why do I get the same function when I integrate and then differentiate the result? When you send a group text message in iOS, it appears as if you automatically opt in to receive any and all replies to that message. Is there a way to avoid being included in group replies? Is there a way to remove oneself from a group chat? Graph theory: Tree holds two sub-tree with an amount of vertices Not every open set in $\mathbb{R}^n$, for $n\geq2$, is a disjoint union of countable open balls. I know that every open set in $\mathbb{R}$ can be decomposed as the union of countably many disjoint open intervals and I'm trying to show that this property no longer holds in higher dimensions. For this I'm trying to show that there is no countable, pairwise disjoint open balls whose union is the open square $(0, 1)^2 ⊂ \mathbb{R}^2$. I know that it is because of the corners, but I don't know how to write this in mathematical terms. Thanks for any help. Proving the total number of subsets of S is equal to $2^n$ Student here! Just reading Liebecks Introduction to pure mathematics for fun and I made an attempt at proving the total number of subsets of S is equal to $2^n$.   I realized that the total number of subsets of S is just:  $ \binom{n}{1} + \binom{n}{2} + \cdots + \binom{n}{n} + 1$  And so I put together the cool looking formula  $ \displaystyle \sum_{r=1}^n \frac{n!}{r!(n-r)!} = 2^n - 1$  But I have no clue how to approach proving this formula analytically. Any help?    So if I try a proof by induction:  $\displaystyle \sum_{r=1}^n \frac{n!}{r!(n-r)!} = 2^n - 1$  $\displaystyle \sum_{r=0}^n \frac{n!}{r!(n-r)!} = 2^n$  obviously true for $n = 1$:  $1 + \frac{1}{1!0!} = 2 = 2$  assume true for $n$, I could multiply both sides by $2$?  $\displaystyle 2\sum_{r=0}^n \frac{n!}{r!(n-r)!} = 2^{n+1}$  How could I go about proving that  $\displaystyle 2\sum_{r=0}^n \frac{n!}{r!(n-r)!}  = \sum_{r=0}^{n+1} \frac{(n+1)!}{r!((n+1) - r)!}$ Does anyone know the major differences between the Java and .Net garbage collectors? A web search has not revealed much, and it was a question that came up in a test. I have used the websites of SO a lot the past few months because I am busy with a large scale web project. I feel I get better answers here on SO than when I just do a Google search, maybe because I can be more specific here with my problem, and the responses are really fast.  Occasionally when I am not working I try to answer some questions, but the question almost always has an answer which is 'as good as' or 'better' than the answer I would supply.  So my question/answer ratio is about 20/1 something, if not more. When I look at my profile page I see a bucket-load of questions and almost nothing I answered myself.  Is this considered bad behaviour? I can see that this looks a little egoistic.  : One devoted to one's own interests and advancement. I would like to ask for some simple examples showing the uses of &lt;div&gt; and &lt;span&gt;.   I've seen them both used to mark a section of a page with an id or class, but I'm interested in knowing if there are times when one is preferred over the other. I read this book series in middle school. I believe that it would be classified as young adult fiction/fantasy. A girl has magical powers, and with her growing powers comes runes/tattoos in her arms. This is shown on every book cover. I know that one cover is blue. This one shows the girl in a black tank top and black pants. One is a yellow cover, with her in a dress (I think).  The girl has a friend/mentor, who she develops feelings for. The girl is the key to stopping a war between multiple factions/people. Each side is trying to use her to their advantage. I think the series was written in the early 2000s. I installed Ubuntu 14.04.1 on one of my laptops and now I want distribute that exact installation to a few of my friends. I tried making an iso with Gparted on a live session but it makes a 500 GB file (I've only used around 8 GB) .   Thanks in Advance ! Getting Started With Java EE I am about to start a web project and have been working almost exclusively with a LAMP stack for the past 5 years.  I would like to build something larger and more scalable and hence have been looking into Java EE.  The division of logic between JSP and EJB seems ideal for what I want to do.  Can anyone recommend resources for getting familiar with Java EE?  And perhaps if anyone knows of technologies that are more scalable than PHP that I should consider as well, I'm all ears.  Thanks a lot! Trying to Remember a Book that explored evolution of Dinosaurs to intelligence and then encountering humans Many, many years ago, I read a book where dinosaurs were assumed to have suvived the K-T event (or it never happened), and they evolved to intelligent species that used not only language (which combined sound, posture, and colour changes on their skin) but also used technology.  In the series, a human is captured or somehow gets integrated with one of the evolved dinosaur groups.  Again, from a very faint memory, the dinosaurs had a level of technology that would be about middle ages, and the humans were much more analogous to American Indian.  That's really all I can recall about the book, and I am trying to find it for my daughter to read.  Can anyone help me out? Is it possible to switch a certain Stack Exchange site's interface (as a personal preference) to the theme used by beta sites?  Some sites have flashy decorations or unreadable fonts (I prefer to disable antialiasing on fonts). It would be nice to have an option to see a site with the "beta" theme.  If there's a solution using custom styles, I would accept that as an answer. Photoshop CS6 Resize Rectangle with Rounded Corners This question is about Photoshop CS6. Hopefully the feature was added in this version. Before posting I looked up Google and  and  but didn't find an answer for CS6.  So the question is: Is there a feature within CS6 or a script that allows to resize a vector element with rounded corners without using the Direct Selection Tool (white arrow tool) and not changing the border radius? What would be great would be something like simply using the transform tool or something like a grid resize tool.