I'm working my way through an introduction to lambda calculus, and it seems to start from the premise that TRUE and FALSE (as well as everything else) can be encoded as functions. From this, they define these two functions as: \begin{align} T & = \lambda a b.a\\ F & = \lambda a b.b \end{align} Now, I'm not a genius, but it seems like this looks less like 'booleans' and more like 'first' and 'second' (or left and right, if looking at the equation). Is this just an agreed-upon convention or how is that allowed? For example, what if I had a function that passed the value of 0 or False (or low-voltage or whatever represents zero in the physical world), some examples being: \begin{align} & False=0 \\ & True=1 \\ & T(False)(False) \\ & T(0)(0) \\ & T(50)(12)  \end{align} Or even passing more than two values to the function, how could one tell where it is True or False? $$T(2)(3)(4)(5)(6)(7)$$ Maybe I'm missing the boat, but basically I'm curious why what seems to me like such an arbitrary definition of booleans would be allowed in lambda calculus, other than as a convenience where nothing else exists.

Good afternoon,  I'm trying to learn lambda calculus, and I do understand the notation (it's not hard, $f=\lambda a_1.\cdots\lambda a_n.x=\lambda a_1\cdots a_n.x\Leftrightarrow f(a_1;\cdots;a_n)=x$), but not what is defined by it. For an example of something I don't understand, take the Church numerals:  $$ 0=\lambda f.\lambda x.x\\ 1=\lambda fx.f\ x\\ 2=\lambda fx.f(f(x))\\ \cdots\\ n=\lambda nfx.f^n\ x $$ (where $f^n$ is $f$ composed with itself $n$ times)  I see $0$'s definition is to not apply a function (apply it zero times), and $1$'s to apply it once, and $n$'s to apply it $n$ times. This kind of makes sense; however, what I don't get is how, formally, can a function be turned into a number. Shouldn't $\lambda f.\lambda x\ x$ be a function with two arguments, one of which is a function? Is it a function or is it a number? Wouldn't one have to pass values of to $f$ and $x$ to it for it to be a value? Is it a representation of the number? How does that really work?  Also, with true ($\lambda xy.x$) and false's ($\lambda xy.y$) definitions? How are those boolean values? They seem two argument functions that yield the first and second argument, respectively. Again, are they values or are they functions? Please help me out here, it's just so confusing to me. I've   like , but I'm still clueless. I know some programming, so any working program showing this would be most welcome.


Let $A,B$ disjoint closed subsets of a normal topological space $(X,\Gamma)$. Show that there exist a continuous function $f:X\to [0,1]$ such that $f^{-1}(\{0\})=A$ and $f(B)=\{1\}$ if and only if $A$ is a $G_{\delta}$ on $(X,\Gamma)$.  Recall that $A$ is a $G_{\delta}$ set in  $X$, if $A$ is the intersection of a countable collection of open sets of $X$.  Let $A,B$ disjoint closed subsets of a normal topological space $(X,\Gamma)$, and suppose there exist a continuous function $f:X\to [0,1]$ such that $f^{-1}(\{0\})=A$ and $f(B)=\{1\}$, but note that $$\{0\}=\bigcap_{n=1}^{\infty}{\left[0,\dfrac{1}{n}\right)}$$  $$A=f^{-1}(\{0\})=f^{-1}\left(\bigcap_{n=1}^{\infty}{\left[0,\dfrac{1}{n}\right)}\right)=\bigcap_{n=1}^{\infty}{f^{-1}\left[0,\dfrac{1}{n}\right)}$$  Thus, $f^{-1}\left[0,\dfrac{1}{n}\right)$ is in $\Gamma$ for all $n\in\mathbb{N}^{+}$, so $A$ is a $G_{\delta}$ in $(X,\Gamma)$.  But, I really need help with the other part of the proof. Thanks!!

Let $A$ be closed in $X$ , where $X$ is a normal space, and $A$ is also a countable intersection of open sets. Prove that there exist a continuous function such that $$ \eqalign{   & f\left( x \right) = 0\,\,\text{ if }\,x\, \in A  \cr    & f\left( x \right) > 0\,\,\text{ if }\,x \notin A \cr}  $$ EDITED: I mean intersection, sorry


I just took a midterm for a Discrete Mathematics class. On couple of questions, it says "Show why this is true". For example, a sample question might have said "Show that five consecutive numbers is divisible by 120"  My question is, is there a difference between "show" and "proof"?

In many mathematics problems you see the phrase "prove that..." or "show that..." something is. What's the difference between these two phrases? Is "showing" something different from "proving" something in mathematics?  Thanks.


I have to sort a large list (more than 10,000 elements). On adding an element I have to insert it on the right place. I saw that an ArrayList will shift all the element that are after the insertion point.   How do all the different implementation of the List interface behave in such a case? And what are the pros and the cons when choosing one implementation over the other?

I've always been one to simply use:  List<String> names = new ArrayList<>();   I use the interface as the type name for portability, so that when I ask questions such as these I can rework my code.    When should  be used over  and vice-versa?


If $0 \rightarrow M' \rightarrow M \xrightarrow[]{f} M'' \rightarrow 0$ is exact then $M$ is Noetherian iff $M',M''$ are.   For an infinite chain $M_i$ in $M$ we have chains $M'_i = M_i \cap M'$ and $ M''_i = f(M_i)$ in $M',M''$, respectively.   If both $M', M''$ are Noetherian then eventually both induced chains will halt; then w.l.o.g. $M'_i, M''_i$ are constant. If $x_i \in M_i \setminus M_{i-1}$ intersects $M'$ then $M'_i \supsetneq M'_{i-1}$, a contradiction...  That's as far as I've gotten. It's not explained in detail in Atiyah-MacDonald.

Let $0 \to M' \xrightarrow{\alpha} M \xrightarrow{\beta} M'' \to 0$ be an exact sequence of $A$-modules. Then $M$ is Noetherian is equivalent to $M'$ and $M''$ are Noetherian.  For the ''$\Leftarrow$'' case:  I guess if we let $(L_n)_{n\geq 1}$ be an ascending chain of submodules of $M$, then $(\alpha ^{-1}(L_n))_{n\geq 1}$ is a chain in $M'$, and $(\beta(L_n))_{n\geq 1}$ is a chain in  $M''$. For large $n$ both these chains are stationary. Then why we know the chain $(L_n)$ is stationary?   Thanks!


I had an idea/feature suggest to make for Ubuntu. But, as I found out, the site is dead. See: .  Question: Where can i make a feature suggest/idea now that brainstorm.ubuntu is no more.

Where can I send feature requests? Both for Ubuntu as a whole and individual (supported) apps?


Since 's introduction in JDK 1.0, Java introduced 9 more versions.  Yet, despite its clear , it is still available, even in JDK 10.  Oracle itself states in :     The finalize() Method      The Object class provides a callback method, finalize(), that may be   invoked on an object when it becomes garbage. Object's implementation   of finalize() does nothing—you can override finalize() to do cleanup,   such as freeing resources.      The finalize() method may be called automatically by the system, but   when it is called, or even if it is called, is uncertain. Therefore,   you should not rely on this method to do your cleanup for you. For   example, if you don't close file descriptors in your code after   performing I/O and you expect finalize() to close them for you, you   may run out of file descriptors.   Which begs the question: Are there any known proper uses of this method?

I've been reading through a lot of the rookie Java questions on finalize() and find it kind of bewildering that no one has really made it plain that finalize() is an unreliable way to clean up resources.  I saw someone comment that they use it to clean up Connections, which is really scary since the only way to come as close to a guarantee that a Connection is closed is to implement try (catch) finally.    I was not schooled in CS, but I have been programming in Java professionally for close to a decade now and I have never seen anyone implement finalize() in a production system ever.  This still doesn't mean that it doesn't have its uses, or that people I've worked with have been doing it right.  So my question is, what use cases are there for implementing finalize() that cannot be handled more reliably via another process or syntax within the language?    Please provide specific scenarios or your experience, simply repeating a Java text book, or finalize's intended use is not enough, as is not the intent of this question.


Let $f: [0, \infty) \to [0,\infty)$ be concave, meaning;  $$ f(tx + (1-t)y) \ge tf(x) + (1-t)f(y)$$  for $t \in [0,1]$. Also, assume $f(0) = 0$. I trying to show $f(x+y) \le f(x) + f(y)$ but I fail. Is there any advise you can give me for help? I appreciate.

Well If I've got a nice understanding, this proof involves the use of Rolle's and/or Mean Value Theorems. But I don't even an idea of how to start. We already know that  $$f\text{ concave}\Rightarrow f''<0$$ but, then...


I understand that this issue in C++ can be a matter of . I also understand that optimization comes into play and can make this a non issue in most, if not all cases. My question is whether or not current compilers make this a complete non-issue or there are still some occasions to consider a difference.

Is there a performance difference between i++ and ++i if the resulting value is not used?


When listing a numerical hyphenation...,for example "2- or 4-person", does the first number have a unconnected hyphen? What is the general rule?

In my native language, Norwegian, one uses hyphens when stating two or more copulated compound words that has common parts (words). In a thesis I'm working on, should I write     test specimens, test setups and test results   or could I write (like in Norwegian)     test specimens, -setups and -results?


I have this code  query = request.GET.get("q")     if query:         if query == "song" or query == "songs":             return render(request, 'music/cloud.html', {                 'songs': song_results,                 'generic_songs': song_results_generic,             })   The thing is, I want the "if" statement to ignor uppercases. For example, when the user search by "SoNg" or "SonG" or.. it will be converted to "song" before testing

How can I do case insensitive string comparison in Python?  I would like to encapsulate comparison of a regular strings to a repository string using in a very simple and Pythonic way. I also would like to have ability to look up values in a dict hashed by strings using regular python strings.


$K$ is a compact subset of $\Bbb R^n$ and $f:K\rightarrow K $ satisfies :  $$\|f(x)-f(y)\|\geq \|x-y\|$$  Show that $f$ is bijective, and that : $$\|f(x)-f(y)\| = \|x-y\| $$  It's easy to show that $f$ is injective. But I can't think of a way to prove surjectivity.

A prelim problem asked to prove that if $X$ is a compact metric space, and $f:X \to X$ is an isometry (distance-preserving map) then $f$ is surjective. The official proof given used sequences/convergent subsequences and didn't appeal to my intuition. When I saw the problem, my immediate instinct was that an isometry should be "volume-preserving" as well, so the volume of $f(X)$ should be equal to the volume of $X$, which should mean surjectivity if $X$ is compact. The notion of "volume" I came up with was the minimum number of $\epsilon$-balls needed to cover $X$ for given $\epsilon > 0$. If $f$ were not surjective, then because $f$ is continuous this means there must be a point $y \in X$ and $\delta > 0$ so that the ball $B_\delta(y)$ is disjoint from $f(X)$. I wanted to choose $\epsilon$ in terms of $\delta$ and use the fact that an isometry carries $\epsilon$-balls to $\epsilon$-balls, and show that given a minimum-size cover of $X$ with $\epsilon$ balls, that a cover of $X$ with $\epsilon$-balls could be found with one fewer ball if $f(X) \cap B_\delta(y) = \emptyset$, giving a contradiction. Can someone see a way to make this intuition work?


I have a game called 'Shapes Dodge' which is still in development. I figured out the name back in February when I began developing it. Since then I've been checking monthly the Google Play Store for games with similar titles and today I saw my worst nightmare coming true - there are a few games with a similar name:   I am worried about the first two games which both have the name 'Shape Dodge'. So will I get sued if I publish my game with the name 'Shapes Dodge' ('shapes' with 'S' at its end) on the Google Play Store?  I want to emphasize that the content of my game is very different from these games' (different controlls, gameplay, graphics, music, etc), only the title is similar.  Please answer me as simple as possible because I am not very familiar with legislation, laws, copyright, trademark and so on.  Thank you! :)  Edit  So after serios consideration and brainstorming I figured out a new name for my app: 'Dodgy Shapes'. Obvously the amount of similarity with the other apps which contain these keywords () is much less. But do you think it is enough difference so that I won't have any problems in the future?  Again, thanks to all who responded. :)

I published my game  the other day. I checked there was no game on Google Play with the same name. But today I searched for "eyeroller" on Google (Yes, I should have done it a long time ago) and realized there is a game named . They are completely different games, as you can see.  What are the legal implications of this? Can things like trademarks and copyrights be a problem? Should I change my game's name?


I've been studying descriptive statistics and am having a hard time understanding the actual intuition behind standard deviation. I'm trying to get a practical feeling for it and so I'm trying to draw conclusions from it using a distribution of 20 numbers, from 1 to 20. I know the mean is 10.5 and the absolute average deviation is 5, which is pretty intuitive.   Now when taking the standard deviation I get the value 5.77 which still makes some sense if I think about it as the average euclidean deviation from the mean. So I imagine adding orthogonal distances and then averaging them $\frac{\sum(x_i-\bar x)^2}{n}$ and taking the square root of that at the end to get the actual average distance. The formula makes sense from an euclidean perspective. So all that being said, my questions:  1) Why would an euclidean average distance be more accurate than an absolute deviation from the mean? I actually think absolute average deviation is more accurate since it doesn't infer any direction of the values. When taking the euclidean distance, I'm pretty much saying every value is placed at a 90° angle from each other. That does not sound right. So why the Euclidean distance? (I'm aware of this article but If someone could actually explain what efficiency is that would be very helpful: )  2) If The advantage of using SD is because of all the math we have developed around normal distribution shapes (68%, 95%, 99,7%...) wouldn't it be better to just rewrite that model with the new average deviation?  3) Ill probably post another question in the future about this, but when calculating standard error, this standard deviation seems to get even worse, since we need corrections for finite populations. Does this make any sense?

In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute value of the difference instead and get the expected value (mean) of those, and wouldn't that also show the variation of the data? The number is going to be different from square method (the absolute-value method will be smaller), but it should still show the spread of data. Anybody know why we take this square approach as a standard?  The definition of standard deviation:  $\sigma = \sqrt{E\left[\left(X - \mu\right)^2\right]}.$   Can't we just take the absolute value instead and still be a good measurement?  $\sigma = E\left[|X - \mu|\right]$


I was proposing an idea on a , and I noticed that you cannot use bullet points inside a blockquote. To show what I mean, here are some images:  Part of the original post I was trying to quote   My post on MA.meta   Notice that the bullet points are outside the blockquote. This is frustrating, because I don't want to have to change the quote at all, then it's not really a quote. Should blockquotes have closing tags as well or have a different markup symbol? Even when I use

 bullet points aren't recognized; they turn out like this:   This is an issue, because   A. It looks bad  B. It's technically not a quote anymore  C. It takes away the entire emphatic purpose of bullet points in the first place

I have an answer that I want to use a block quote to cite and outside reference. That reference is a bulleted list.   Pretty sure I have seen this before but I cannot find anyone using it.  How can I use a numbered or bulleted list inside block quotes?


I was browsing the HNQs (Hot network questions) when I saw that some of the gravatars had different usernames, but the same gravatar. When investigating further, I found that in fact, they all belong to different users, and those users have profile pictures that are not the same as those displayed on the HNQ page. Here is an example from page 1 (around UTC 1900)  And another example from page 3 (around 19:05)  However, when I click on the profiles of the generic green Gravatar icon for any of the below users, such as  on Worldbuilding SE, it takes me to their profile page on that site... with a completely different profile picture. As this is a recurring bug (the same happened for all the other ones I clicked on) is this a problem with my device/browser/operating system (I'm using Windows 10 on a PC on Chrome) or is this a larger, site-wide bug? Edit: Just checked for the other Gravatars; they seem to work fine as the bug only occurs with the teal/white generic one.

Same gravatar is displayed for different users in the stackexchange.com , under the Top Network Askers in the right side bar.   The red circled image's source (<img src=) are from   https://www.gravatar.com/avatar/?s=18&d=identicon&r=PG&s=30                                ^   Seems the gravatar id is missing here in the image source.  For an example from the list, the user  gravatar id should be    https://www.gravatar.com/avatar/66c66c4d97a7bc3859a85253f003e1fb?s=18&d=identicon&r=PG&s=30   but it is mapped with   https://www.gravatar.com/avatar/?s=18&d=identicon&r=PG&s=30   which caused the display issue.


In a graph i associate a node to a quantity : quantities could be redundant and nodes can't, so in order to sort according to ascending quantities i put nodes as keys and quantities as values of a LinkedHashMap and sort it as follows :  LinkedHashMap<Node, Integer> orderedResult = mapNameToSize.entrySet()                 .stream()                 .sorted(Map.Entry.comparingByValue())                 .collect(Collectors.toMap(                         Map.Entry::getKey,                         Map.Entry::getValue,                         (oldValue, newValue) -> oldValue, LinkedHashMap::new));  But my question is how to get the keys sorted accordingly into a ArrayList?

I am relatively new to Java, and often find that I need to sort a Map<Key, Value> on the values.  Since the values are not unique, I find myself converting the keySet into an array, and sorting that array through array sort with a custom comparator that sorts on the value associated with the key.  Is there an easier way?


I've pretty much got the terminal colour scheme I want, however the user@host colours stick out like a sore thumb, and really don't fit in with the scheme. See screenshot in link:    How do I go about changing the user@host colours (currently green)? Also, is it possible to change the archive colours (currently red)?

Is it possible to change the colors in the command prompt for the user@computer, as well as the the current directory and command parts of the prompt display?   I've already seen something like this done by OSX users, but I don't know how to do the same thing in gnome terminal (I can only change foreground and background colors).   It'd be very useful when, for example, trying to compile programs that have errors, since long, unformatted messages make it hard to distinguish which lines are commands and which are output.


I have three tables  1.  Ordertable 2.  Bill  3.  Customers  In Ordertable I have following columns   (*) represents Primary key here  | Customer ID*c| Customer Name | Address | Contact Number   | Email|  In Order table I have following columns  | Order ID* | Order Status | Delivery Date | Manager ID | Customer ID| Salesmanager ID| Where Order_status can Containt ‘pending’ for pending order  And ‘completed ’ for for completed order  In bill table I have these columns   | Bill ID*| Order ID | Date | Amount |  Now I want to create Query that display completed Order  data with inner join on these three as these rules   Order_ID as OID from order table Order_Status as Status from order table Delivery_Date as Date from order table Customer_name as Name from customer table Amount as Bill Amount from Bill table What I tries is this Query   select order_status Status,Order_ID OID,Delivery_date Date from ordertable inner join bill ON ordertable.order_id = bill.Order_id   and I got this error Msg 209, Level 16, State 1, Line 1 Ambiguous column name 'Order_ID'.    I know that order_id is in both tables but how I can solve this  And also when I remove it error gone but in the result I see only two columns for Status and Date   but not OID and any data from bill  how I can do this ?

I am getting an error with the following query that uses a right join.  My table has a column named 'id'.  SELECT TOP 6 id FROM   dbo.tbldata        RIGHT JOIN tblimg                ON tbldata.id = tblimg.newsid ORDER  BY createdDate DESC    The error is:     Ambiguous column name 'id'


I'm pretty far along in the game, and I still haven't caught wind of a key for the last house in the village. Is there actually any way to get into the last house, or does is remain locked for the entire game?

I've 'completed' the game, but didn't find the key for the first house. (I got the one for the arcade machine house). Where can I find it?


("" refers to spacing between equation environments within a subequations environment. This question refers to spacing between two different subequations environments.)  I am using fleqn so that a number of sets of subequations are all aligned on the left side. The space that exists above and below each set of subequations is bigger than I need it to be. And when two sets appear back to back (picture below), this results in a very large vertical space in between.  Is there any (simple) solution to reduce this vertical space before/after every subequations (+align) environment?  \documentclass[11pt]{book} \usepackage[fleqn]{amsmath} \usepackage[utf8]{inputenc} \begin{document}  \begin{subequations}\begin{align} x = & r_M\cos\beta\cos\alpha        \\ y = & r_M\cos\beta\sin\alpha    \\ z = & r_M\sin\beta \end{align}\end{subequations} \begin{subequations}\begin{align} v_{p_x} = & -v_M\sin\gamma\sin\beta\cos\alpha - v_M\cos\gamma\sin\alpha \\ v_{p_y} = & -v_M\sin\gamma\sin\beta\sin\alpha + v_M\cos\gamma\cos\alpha \\ v_{p_z} = & v_M\cos\beta\sin\gamma \end{align}\end{subequations}  \end{document}

How can I reduce Spacing of the following subequations:  $ \begin{subequations} \begin{equation} x_{n+1}= x_n + v_n \Delta t + \frac{1}{2} a_n \Delta t^2 \end{equation}     \begin{equation}  v\left(t_n+\Delta t/2\right)= v_n + \frac{1}{2}a_n \Delta t \end{equation} \begin{equation} a_{n+1}=\frac{1}{m} F(x_{x+1},t_{n+1}) \end{equation} \begin{equation} v_{n+1}=v(t_n+\Delta t/2) + \frac{1}{2}a_{n+1}\Delta t \end{equation} \end{subequations} $   I do not know how to embed the code here correctly.


I am learning the Ridge Regression. And I found that Ridge Regression is better than LASSO to analyze multicollinear? I wonder the reason?

I have a set of 150 features, and many of them are highly correlated with each other. My goal is to predict the value of a discrete variable, whose range is 1-8. My sample size is 550, and I am using 10-fold cross-validation.   AFAIK, among the regularization methods (Lasso, ElasticNet, and Ridge), Ridge is more rigorous to correlation among the features.  That is why I expected that with Ridge, I should obtain a more accurate prediction.  However, my results show that the mean absolute error of Lasso or Elastic is around 0.61 whereas this score is 0.97 for the ridge regression. I wonder what would be an explanation for this.  Is this because I have many features, and Lasso performs better because it makes a sort of feature selection, getting rid of the redundant features?


This is a recent problem that is making me punch holes through walls. Two points up front -   My connection speed is fine. Using the various speedtest tools out there, it is consistently over 1mbps, 6mbps+ on a good day. My download speeds and file transfers (P2P, torrents, ftp etc.) are similarly fine.   My browser performance (whether FF, Chrome or Opera) however is decidedly NOT fine. Over the last few weeks it has been in the toilet. HTTP is bad and HTTPS is worse.  I used curl as described at -    to try and see what the problems may be. These are the outputs -  bob@beelzebubba:~/curl$ curl -w "@curl-timing.cfg" -o /dev/null -s http://www.google.com/    DNS lookup                          :  0.162   Connect to server (TCP)             :  0.442   Connect to server (HTTP/S)          :  0.000   Time from start until transfer began:  0.442   Time for redirection (if any)       :  0.000   Total time before transfer started  :  0.752           Total time                   :  0.752          Size of download (bytes)     :  260          Average d/l speed (bytes/s)  :  345.000  bob@beelzebubba:~/curl$ curl -w "@curl-timing.cfg" -o /dev/null -s https://www.facebook.com/    DNS lookup                          :  0.230   Connect to server (TCP)             :  0.729   Connect to server (HTTP/S)          :  1.620   Time from start until transfer began:  1.620   Time for redirection (if any)       :  0.000   Total time before transfer started  :  2.079           Total time                   :  2.080          Size of download (bytes)     :  0          Average d/l speed (bytes/s)  :  0.000  bob@beelzebubba:~/curl$ curl -w "@curl-timing.cfg" -o /dev/null -s https://www.google.com/    DNS lookup                          :  0.118   Connect to server (TCP)             :  0.435   Connect to server (HTTP/S)          :  1.375   Time from start until transfer began:  1.375   Time for redirection (if any)       :  0.000   Total time before transfer started  :  1.825           Total time                   :  1.825          Size of download (bytes)     :  263          Average d/l speed (bytes/s)  :  144.000   Generally terrible. My questions are -   What could cause this out of the blue? How can I fix it? There is very little of help googling.   Yes I've cleared caches, nuked cookies, started browsers in safe mode etc.

Ubuntu 12.10 I'll explain the first problem. Sometimes when I load a webpage it never finishes loading and it says cannot reach server or something like that. When I ping that website, the terminal says it cannot resolve the hostname. So I then tried Google's DNS servers but had no luck there. It's weird because I've never had this problem in Windows 7. I used cat /etc/resolv.conf  and it came up with this: # Dynamic resolv.conf(5) file for glibc resolver(3) generated by resolvconf(8) #DO NOT EDIT THIS FILE BY HAND -- YOUR CHANGES WILL BE OVERWRITTEN nameserver 127.0.1.1 search hsd1.or.comcast.net  Why would it use 127.0.1.1? Does that mean it's trying to resolve addresses locally? When I ping the comcast search server I get a timeout error.


In the last 10 seconds of the video,the guy says that the rotation is unstable, the the moment of inertia is intermediate, why is this so? Is it as rotation from the other axes also contribute?

We have the Euler equations for a rotating body as follows  $$I_1\dot\omega_1+\omega_2\omega_3(I_3-I_2)=0\\ I_2\dot\omega_2+\omega_1\omega_3(I_1-I_3)=0\\ I_3\dot\omega_3+\omega_2\omega_1(I_2-I_1)=0$$ Where $I_i$ are the moments of inertia about the $x_i$ axis, and $\omega_i$ is the angular velocity about this axis.  It can be shown (*) that if $I_1>I_2>I_3$, then objects with angular velocity very close to $\vec\omega=(0,1,0)$ are unstable. Why is this and how can I try to picture it?   I tried to picture this using a ball, but realised this is probably not a good way to visualise it, since a ball is spherically symmetric, so the moments of inertia are not distinct. Is there any visualisation or animation that could allow me to see this rotation, and possibly understand why it is unstable?     (*) In response to @SRS's comment:  I am not sure about any references, but I know how to do it: Let $\omega_1=\eta_1,\omega_3=\eta_3$ where $\eta$ is a small perturbation, and suppose $\omega_2=1+\eta_2$. Then the Euler eqns become$$I_1\dot\eta_1=(I_2-I_3)\eta_3+O(\eta^2)\tag1$$$$I_2\dot\eta_2=O(\eta^2)\tag2$$$$I_3\dot\eta_3=(I_1-I_2)\eta_1+O(\eta^2)\tag3$$Differentiate $(1)$ and sub in $(3)$ to the resulting expression$$\ddot\eta_1=\frac{(I_2-I_3)(I_1-I_2)}{I_3I_1}\eta_1$$If $I_1>I_2>I_3$, then the constant on the right hand side is positive, so the solution to this equation is an exponential (if it was any other order, then the solution would be a $\sin/\cos$). Therefore it is unstable.    Edit:  To clarify, I posted this question to see other more visual ways of understanding this effect rather than solving the equations as I did above, and to see how this effect comes into play in real life. So I don't think it is a duplicate of the other questions, since they don't have answers that fit this.


Iam from India. My name is RAJUCHAMBANNA VEERABHADRAPPA YARADAL and I have a valid indian passport. My wife's passport is her maiden name even after marriage as PRATIBHA KHODANAPUR.  Now I have a Child passport wherein the mothers name is PRATIBHA RAJUCHAMBANNA YARADAL which does not match with her passport. Because the birth certificate shows name of mother as PRATIBHA RAJUCHAMBANNA YARADAL.  Can I get the passport with short name of mother as PRATIBHA in Child passport and keeping her name is passport as PRATIBHA KHODANAPUR? Hope there should not be any problem in this arrangement. Please suggest the best possible solution to have uniformity in all documents.

Assume a child (aged 15) has a different surname from their mother. They live with their mother and father, but the mother did not take the father's name on marriage. All three are UK citizens, have UK passports in their own name, are UK residents, and the father and mother are married. The only thing mildly unusual (and hardly remarkable in the 21st century) is the mother did not take the surname of the father on marriage, and the child has the surname of the father (which is different from that of the mother).  A few weeks ago, the mother and child travelled by plane to an EU destination, without the father.   On flying out of the UK, this presented no problem. On returning to the UK (from the EU), a long dialog with the immigration officer ensued where he threatened to not permit re-entry because the child had a different surname to the parent traveling, and "The Children's Act" (sic - there are several) requires that the child also carries a birth certificate. Eventually (30 minutes later, and after interrogation as to what the child's middle names are etc), common sense prevails.   There were no other factors likely to interest the immigration officer. The child's passport had been issued a month previously and the photograph was thus a good likeness. The child concerned had no difficulty travelling with school to another EU country without a birth certificate or any letters from either parent.  This seems completely bizarre to me, given:   I can find no legal requirement that anyone needs to carry a birth certificate. The child could simply have gained entry as a UK citizen if the mother was not there at all. The risk one would have thought needed addressing was one parent absconding with a child after separation. In this case, should the check not be being made on departure? Returning to where all parties are resident seems unproblematic. The fact that the mother and child have different surnames is not indicative of marital break-up (consider e.g. unmarried parents); indeed when a married couple break up it is likely (if they changed name on marriage) that they will still have the same surname (at least on their passport) for a while.   So, to my questions:   Is there a requirement that children traveling with a parent with a different surname carry their birth certificate? If so, where is the legal origin of such a requirement?   Note: I am not asking this in order to assist in the parent concerned raising a complaint against a particular immigration officer. I am asking so I can tell the parent concerned what the requirements are should she wish to travel with her children unimpeded in future.


I am not really sure if it is correct. My idea is:  Let $ab=x^3 $ and $(a, b) = 1$ and $a, b, x$ are some elements in an arbitrary ring $R$.  Then $a|x^3 $ and $b|x^3$ which means there exists some elements $c,d \in R$ that satisfies $ac = x^3$ and $bd = x^3$. We then know that $a|d$ because $a, b$ are coprime and $a\space|\space x^3 = bd$.   For example: Consider the ring $R=Z[i]$   I want to  find all solutions $x,y \in \mathbb{Z}$ with $y^2=x^3-1$  Now the factored form in $R$ is $$x^3=(y+i)(y-i) $$  I would like to know why the factors have to be cubes .

I'm trying to do the following exercise from Neukirch's Algebraic Number Theory (exercise 2, $\S 1$, chapter 1):  Show that, in the ring $\mathbb{Z}[i]$, the relation $\alpha\beta=\varepsilon\gamma^n$, for $\alpha,\beta$ relatively prime numbers and $\varepsilon$ a unit, implies $\alpha=\varepsilon^{\prime}\xi^n$ and $\beta=\varepsilon^{\prime\prime}\eta^n$, with $\varepsilon^{\prime},\varepsilon^{\prime\prime}$ units.  My attempt: once $\alpha$ and $\beta$ are relatively prime, $\alpha\nmid\beta$ and $\beta\nmid\alpha$. Therefore $N(\alpha)$ and $N(\beta)$ are relatively prime too (where $N(a+ib)=a^2+b^2$). Therefore,  $$N(\alpha\beta)=N(\alpha)N(\beta)=N(\varepsilon)N(\gamma^n)=N(\gamma)^n=(p_1\cdot\ldots\cdot p_r)^n=p_1^n\cdot\ldots\cdot p_r^n$$  And once $N(\alpha)$ and $N(\beta)$ are relatively prime, we have (if necessary, we reorder the $p_i$'s):  $$N(\alpha)=p_1^n\cdot\ldots\cdot p_k^n=(p_1\cdot\ldots\cdot p_k)^n=N(\xi)^n=N(\xi^n)$$ and $$N(\beta)=p_{k+1}^n\cdot\ldots\cdot p_r^n=(p_{k+1}\cdot\ldots\cdot p_r)^n=N(\eta)^n=N(\eta^n)$$  And the result follows.  But I'm not sure about one step. It is $\alpha$ and $\beta$ relatively prime $\Rightarrow$ $N(\alpha)$ and $N(\beta)$ relatively prime. I know that if $\alpha|\beta$ then $N(\alpha)|N(\beta)$, but the previous assertion is not necesseraly true, and if it is, and don't know how to prove it. If it is true, the result follows, unless I made something wrong in the rest of the proof.  That's it. If you know another way of doing the exercise, please show me.


I have this code and I want to show the price_final var with comma and currency  Here is my code:  $(document).ready(function() {   var prices = $('span.product_weight').text()   $("input").change(function() {     var price = '';     var quantity = parseInt($('input[name=quantity]').val());     console.log(quantity)     var price = prices.replace(/[^\d-]/g, '');     var price_final = price * quantity;     $('span.product_weight').html(price_final);   }); });

I would like to format a price in JavaScript. I'd like a function which takes a float as an argument and returns a string formatted like this: "$ 2,500.00"  What's the best way to do this?


MacBook Air version 6,2  System using 70%  Is there a way to fix this? Been trying for hours

Typically, my kernel_task process uses 1-4% CPU and 100-700MB of memory. However, sometimes when I have the power adapter plugged in, the CPU usage jumps to around 500% (8 cores) and stays there until I unplug the power adapter. I can plug it back in and everything is fine for a few seconds or a few days, then it eventually happens again. How can I stop this from happening?


What is the best way, if indeed there is a way, to get the X and Y position of any element embedded deep inside another element (called root for convenience) with respect to the root element itself. The embedded element may have layers of other containers with different position CSS (e.g. relative, absolute, etc.). I prefer JQuery but a pure JS solution would be even better.  For example:

 <other elements....>
 <other elements...>

   I want to know the absolute X and Y positions of input field with id "id1" with respect to div with id "root".   EDIT: "root" is always set to position:relative

I want to know how to get the X and Y position of HTML elements such as img and div in JavaScript relative to the browser window.


I was recently observing the way bubbles move as they pop and disappear. I noticed that when bubbles destabilize and pop, the remaining bubbles immediately surrounding it will move to fill its place. I was wondering what the driving cause is here.   At first, I figured that stickiness was the cause. But, I don't think this would be a driving force unless perhaps the bubbles are clustered (i.e. they share at least 1 membrane).  I've also noticed this behavior in groups of individual, non-clustered bubbles. As an introductory physics student, I'm curious: what causes this phenomenon?

Two identical bubbles floating on water surface will form clumps, according to the "cheerio effect". But what's the detail about the force? It's necessary to calculate the shape of water surface, in order to find the force?


print(model.predict(image)) print(model.predict_proba(image)) print(model.predict_classes(image))   Using the above different predict methods I always get predictions like     [[ 1.  0.  0.  0.]]   but I want the probabilities of each classes something like this     [[ 0.8  0.05  0.05  0.1]]   This is the model  model = Sequential([     Conv2D(32, (3, 3), input_shape=input_shape, padding='same',activation='relu'),     Conv2D(32, (3, 3), activation='relu', padding='same'),     MaxPooling2D(pool_size=(2, 2), strides=(2, 2)),     Conv2D(64, (3, 3), activation='relu', padding='same', ),     Conv2D(64, (3, 3), activation='relu', padding='same', ),     MaxPooling2D(pool_size=(2, 2), strides=(2, 2)),     Conv2D(128, (3, 3), activation='relu', padding='same', ),     Conv2D(128, (3, 3), activation='relu', padding='same', ),     MaxPooling2D(pool_size=(2, 2), strides=(2, 2)),     Conv2D(256, (3, 3), activation='relu', padding='same', ),     Conv2D(256, (3, 3), activation='relu', padding='same', ),     MaxPooling2D(pool_size=(2, 2), strides=(2, 2)),     Conv2D(512, (3, 3), activation='relu', padding='same', ),     Conv2D(512, (3, 3), activation='relu', padding='same', ),     MaxPooling2D(pool_size=(2, 2), strides=(2, 2)),     Flatten(),     Dense(512, activation='relu'),     Dense(num_classes, activation='softmax') ])   Compiled as   sgd = SGD(lr=0.0001,momentum=0.9) model.compile(loss = "categorical_crossentropy", optimizer =sgd,metrics=['accuracy'])   Not sure if this has any effects, but this is how I loaded the data     train_datagen = ImageDataGenerator(       rescale=1./255,   )      train_generator = train_datagen.flow_from_directory(folder+'apex/train',                                                       target_size=(200, 400),                                                       batch_size=batch_size,                                                       class_mode='categorical')

I have built the following model:  def create_model(conv_kernels = 32, dense_nodes = 512):      model_input=Input(shape=(img_channels, img_rows, img_cols))     x = Convolution2D(conv_kernels, (3, 3), padding ='same', kernel_initializer='he_normal')(model_input)     x = Activation('relu')(x)     x = MaxPooling2D(pool_size=(2, 2))(x)     x = Convolution2D(conv_kernels, (3, 3), kernel_initializer='he_normal')(x)     x = Activation('relu')(x)     x = MaxPooling2D(pool_size=(2, 2))(x)     x = Dropout(0.25)(x)     x = Flatten()(x)      conv_out = (Dense(dense_nodes, activation='relu', kernel_constraint=maxnorm(3)))(x)      x1 = Dense(nb_classes, activation='softmax')(conv_out)     x2 = Dense(nb_classes, activation='softmax')(conv_out)     x3 = Dense(nb_classes, activation='softmax')(conv_out)     x4 = Dense(nb_classes, activation='softmax')(conv_out)      lst = [x1, x2, x3, x4]      model = Model(inputs=model_input, outputs=lst)     sgd = SGD(lr=lrate, momentum=0.9, decay=lrate/nb_epoch, nesterov=False)     model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])      return model   When I do a prediction:  model.predict(X_test)   it works properly. However, when I want to get prediction probability like this:  model.predict_proba(X_test)   my model has no predict_proba function. Why not? Is it because of the multiple-output nature of the model?


Is it possible to find the present index in an enhanced for loop? If so how?  I am aware we can check it with an extra variable. But is there any other way.  public boolean cancelTicket(Flight f, Customer c) {     List<BookingDetails> l = c.getBooking();     if (l.size() < 0) {         return false;     } else {         for (BookingDetails bd : l) {             if(bd.getFlight()==f){                 l.remove()  // Index here..             }         }     } }

Is there a way in Java's for-each loop  for(String s : stringArray) {   doSomethingWith(s); }   to find out how often the loop has already been processed?  Aside from using the old and well-known for(int i=0; i < boundary; i++) - loop, is the construct  int i = 0; for(String s : stringArray) {   doSomethingWith(s);   i++; }   the only way to have such a counter available in a for-each loop?


I originally removed the default camera, but now when I wanted to add a new camera, it won't show up. There's only this weird yellow rectangle.  I suppose this rectangle somehow represents the camera, but it's difficult to move it, because if I grab or rotate it, it disappears completely. If I open a new Blender project, then it opens with the normal default cube and camera all working as they should. So, what's going on and how do I fix the camera in this current project? Thanks for assistance!

I am new to Blender. The camera widget in my viewport only displays as a dot and yellow rectangle, while in the tutorials it has a pyramid shaped bounding box and arrow indicating which way is up. How do I correct this?


Here I mention only hiding from hard-science SE websites : maths, phsycis, chemistry, earth science, etc. And I explained why with a simple and verifiable argument : religions are considered anti-scientific (the opposite of science) by so many professional scientists recall that many of those websites are mainly used by professionnal researchers, the same people who answered to those famous surveys on religions.  Given that religions are considered anti-scientific (the opposite of science) by so many professional scientists, wouldn't it be a good idea to hide from the "hot-network-questions" the  discussions originating from ,  or  when we are on one of those  ? And isn't there a huge bias in favour of downvotes here ? Even if you don't agree, the question isn't "stupid" nor "crazy".

I have deep issues with the 'Hot Network Questions' containing questions from the religion sub-sites. This is not because I dislike questions about religion, nor because I think these sites have no place on the network in theory - they do. The reason I am annoyed by these Q&A's is that the quality of highly upvoted questions is often extremely low, and questions that are out of scope (since they are about reality) are not deleted.  Obligatory examples: All answers have been upvoted and are popular, I did not rotten-cherry pick:   Q    A +0 accepted   Q    A +10   Q    A +36     Q    A +4   Q    A +8   Q    A +9     I imagine questions, and answers such as these would be deleted on any other StackExchange site. Would I not be told 'reality' was not in scope if I asked a question on scifi.stackexchange.com like .   The level of answers at the sub-sites specifically for religion is very low, especially the answers that turn up in the 'Hot Network Questions' list. I propose removal of these sites from the network, as they do not fit the quality standards for SE. Alternatively, I would like to filter out these sites from the 'Hot Network Questions' list.  Addendum There is a related question under , a denied feature request for personalizing a filter for hot network questions. While that would have solved my issue, the fact that it wasn't implemented means my issue is unsolved, and my wish for a resolution to jarring questions on the Hot Network Question list remains (and in this case it's not just the low-quality floating up as usual, but actually especially jarring for the non-'experts' of religion.SE).


Hi I'm pretty new to using C. My teacher told me to code a function to sort characters in a string alphabetically by using array & the fact that when a scanf() a string, the first character is called and the rest are saved in the buffer. (I haven't learnt about pointers yet.)  For example, if I type in badf and space(signalling "an end", or the sentinel value for end of string), the function should return abdf.  I'm stuck here. It's my first ever stackoverflow question! Please help. Thanks.  #include <stdio.h> #include <string.h>  int main() {     char arr[100];     char front_char, first_char;     // set the variables     int i, j, k, l;      printf("Enter a string and press space to end\n");      // get the input using scanf, which will just get the first character and save the rest in buffer     scanf("%c", &first_char);     // assign the first_character in arr[0] for initialization     arr[0] = first_char;      // 32 is "space" in ascii code. Space is used as a sentinel value. User is supposed to press space at the end of the String     while(front_char != 32) {         // get the "second" character from buffer and ass. repeat this until the next character in buffer is 32, or "space"         scanf("%c" , &front_char);          // load character from buffer, and check if its assigned number in ascii code is smaller than characters in array         for(i = 1; front_char != 32; i++) {             for(j = 0; j < i; j++) {                 // go through the previously aligned array to compare the ascii number of the loaded character from buffer                 if(arr[j] <= front_char) {                     continue;                 } else {                     // run through the previously aligned array, and if a character with bigger ascii number comes up,                     for(k = i-1; k >= j; k--) {                         // assign/push the values in array to the next index(i don't know how to describe this, but I hope you see what I mean..)                         arr[k+1] = arr[k];                     }                 }                 // assign the loaded character according its ascii number size                 arr[j] = front_char;             }         }          // print the result         for(l = 0 ; l < i ; l++){             printf("%c", arr[l]);         }     }      return 0; }

I'm looking for a simple, easy to understand algorithm to alphabetically sort an array of characters in C.


I am trying to generate a space (6pt) between the boxed figure and its caption. Since I am using tikz code \includegraphics did not work. Also I tried \setlength{\abovecaptionskip}{6pt}, \captionsetup[figure]{skip=6pt}. However they did not work. How to handle this problem?    \documentclass[a4paper,12pt]{article} \usepackage[margin=10pt,font=small,justification=centering]{caption} \usepackage{tikz} \usepackage{floatrow} \usepackage{float,lipsum} \floatstyle{boxed} \restylefloat{figure} \usepackage{wrapfig} \usepackage{caption} \usepackage{subcaption} \usepackage{amsmath}  \begin{document} \begin{figure}[ht] \begin{center} \begin{tikzpicture}[thick,scale=1] \filldraw[black] (0,0) circle (2pt) (1,1) circle (2pt) (1,-1) circle (2pt) (3,1) circle (2pt) (3,-1) circle (2pt) (4,0) circle (2pt); \draw (0,0) -- (1,1) -- (1,-1) -- (0,0); \draw (1,1) -- (3,1) -- (4,0) -- (3,-1) -- (3,1); \draw (3,-1) -- (1,-1)--(1,1); \draw (3,1)-- (3,-1); \draw (4,0) -- (0,0); \node[above] at (1,1) {$v_1$}; \node[left] at (0,0) {$v_0$}; \node[below] at (1,-1) {$v_5$}; \node[below] at (3,-1) {$v_4$}; \node[right] at (4,0) {$v_3$}; \node[above] at (3,1) {$v_2$}; \end{tikzpicture} \caption{$G$.} \label{factorex} \end{center}  \end{figure}   \end{document}

After reading this question , I want to know the answer of the following.  When should we use \begin{center} instead of \centering?  For example, should we use this one?  {% \centering <other contents> }   or this one?  \begin{center} <other contents> \end{center}


I studied the definition of limits today, and I think I mostly understood it, but I have a little doubt. In the definition:  $f(x)$ is defined on some open interval containing $a$, except at possibly $a$. So, $\lim_{x\to a} f(x) = L $ if and only if for every number $\varepsilon>0$, there exists a corresponding number $\delta>0$ such that:  $$\text{If   } 0<|x-a|<\delta \text{ then } |f(x)-L|<\varepsilon$$  First of all, if you see any mistake in my definition or understanding, please tell. So my question is, why can't we write $0<|x-a|\leq\delta$ and $|f(x)-L|\leq\varepsilon$ in the last line? What kinds of problems can arise from this? If the definitions are equivalent, can you explain/prove me why?

Definition (As written in Michael Spivak's Calculus)     The function $f$ approaches a limit $l$ near $a$ means: for every $\epsilon >0$ there is some $\delta > 0$ such that, for all $x$, if $0<|x-a|<\delta$, then $|f(x)-l|<\epsilon$.   my question is: why can't it be: $$0<|x-a|\leq \delta,|f(x)-l|\leq \epsilon$$ After looking at limits of functions for a long time just to grasp it's meaning and using the definition quite a lot solving homework I realized I keep writing the same inequality without really understanding why.  The only explanation given in Spivak's book for this part of the definition goes over it without explaining the inequality. I tried looking for an explanation myself but wasn't really able to find anything wrong with it. Is it also possible to write the definition like that or is there a problem with that?   (first non-homework related question :p)


I recently installed Ubuntu 14.04 on the same partition (C:/) in which I had Windows 7 installed. After installation of ubuntu, I see Ubuntu boot options in the grub, along with FreeDOS (FreeDOS shows up for my other 2 partitions, D:/ and E:/, my PC had initially come with FreeDOS and I had installed Windows7 to it) and there is no Windows 7 option.   However my Windows data of C: drive is still visible in Ubuntu as "140 GB Volume" with all the previous data present.  Is there a way in which I can recover the Windows 7?  I am providing the procedure I used in installing Ubuntu, and believe the problem would have happened due to the partitioning option   I selected "Do something else" and not "Install Ubuntu along with Windows" Selected the same partition in which there was Windows (C:/) Gave it 40 GB of space, there was 70 GB free space in the partition. No other step I performed which I feel could have caused the problem. Please help me out.    I also performed sudo update-grub, but it still lists only linux and freedos systems, and no Windows updates.  Thanks :)

I installed Windows 7, which ate Ubuntu's boot file. When starting up the computer, it now goes straight to Windows, without giving me the option of booting Ubuntu.   How can I get Ubuntu back?


I am wondering if there is any difference between order of convergence and rate of convergence.  If the questions asks me to determine the rate of convergence, What exactly do I have to find?   For instance, $\lim_{n \rightarrow \infty}\frac{n-1}{n^3+2}=0.$  What is the corresponding rate of convergence?

What is the difference between rate of convergence and order of convergence? Have they any relationship to each other? For example could i have two sequences with the same rates of convergence but different orders of convergence, and vice versa?


Is there a HTML tag that does the opposite of <noscript>? That is, displays some content only if JavaScript is enabled? For example:  <ifscript> <h1> Click on the big fancy Javascript widget below</h1>     <ifscript>   Of course <ifscript> doesn't actually exist. I know I could achieve the same result by adding <h1> to the DOM using JavaScript, but if I'd prefer to do this with (X)HTML if possible.  Thanks, Donal

Is there a tag in HTML that will only display its content if JavaScript is enabled? I know <noscript> works the opposite way around, displaying its HTML content when JavaScript is turned off. But I would like to only display a form on a site if JavaScript is available, telling them why they can't use the form if they don't have it.  The only way I know how to do this is with the document.write(); method in a script tag, and it seems a bit messy for large amounts of HTML.


I am Indian national, with students one year Visa studying in France.  For two months vacation, I have booked a round trip flight ticket from Paris to Delhi with transit in London Heathrow airport and vice versa(same) I arrive in London Heathrow airport at 10.20 P.M and my departing flight to Delhi is on next day 10.00 A.M.. I arrive and depart from the same terminal!  I have been told that I need to get transit Visa here in France! My questions are-  1. Is the direct transit Visa that I get is applicable for the full round trip, or should I get one while going to India and again another while coming from India?  2. If I apply for direct transit Visa online, should I get separate appointment for biometric registration or just by applying for direct transit Visa I will be called for biometric registration !

Is there a website or some other way to find out if I need a transit visa for a short stop in the UK on my way somewhere else? Ideally this should give me the answer for all nationalities, and take into account any other visas I may have.


I was wandering if there is a way i could possibly due to factory reset Linux? If someone could help that would be great.

I have Ubuntu 10.04 on my computer, with Windows 7 next to it. Instead of upgrading to 10.10, I feel like doing a clean install. However, I don't want to erase my Windows, even though I barely ever use it. My question is: how would I remove Ubuntu 10.04 from my drive and install Ubuntu 10.10 in place, without losing any space or anything, or losing Windows 7?


I'm writing a small Perl script that depends on some modules that might be available, so during the installation I would have to check if everythings there.  I could just write use some::module and see if an error comes up, but a short message like "You need to install some::module" would be more helpful for endusers.  I also could just search every directory in @INC, but as it's Perl, there has to be an easier way.

I have Perl code which relies on Term::ReadKey to get the terminal width. My installation is missing this module, so I want to provide a default if the module isn't present rather than throw an exception. How can I conditionally use an optional module, without knowing ahead of time whether it is available. # but only if the module is installed and exists use Term::ReadKey; ...  How can I accomplish this?


Reading the proof of exponential derivatives I understand this: To show that $(2^x)'=\ln 2 \cdot 2^x$ in the proof is used the limit: $$\lim_{x \to 0} \frac{2^x-1}{x}$$ My question is: ¿How do I prove that this limit exist? I don't care about its value. If I were going to prove that this limit is equal to $\ln 2$, I would need the number $e$, and again, this number is defined as the number $a$ such that: $$\lim_{x \to 0} \frac{a^x-1}{x} = 1$$ In another words if I know that for some constant value $a$ the limit: $$\lim_{x \to 0} \frac{a^x-1}{x} $$ exists, let's say it's a number $L$ then I could find all the limits like these in function of $L$, But what makes obvious that this limit exist?

In my calculus class, $e$ was defined to be the number such that $\frac{d}{dx}e^x = e^x$.  From the definition of the derivative, we have  \begin{align*} \frac{d}{dx}a^x &= \lim_{h \to 0} \frac{a^{x+h} - a^x}{h}\\ &= a^x \lim_{h \to 0} \frac{a^h - 1}{h} \end{align*}  Thus $e$ is the number such that  $$ \lim_{h \to 0} \frac{e^h - 1}{h} = 1 $$  But how is it proven that there exists such number?


There was a great sci-fi book series that I read about experiments with clones (Pratwa?). The lab produced sets of 2 clones that were linked mentally. When they meditated and merged consciousnesses they became a higher being, 2 minds became 1 new different personality. They all had different weapons... the first attack was done by smiler/slasher clones. There was a scientist/researcher clone for tech. When merged the sets of clones (5?) merged they met as Ash Oak. The security team revived an old Pratwa hunter... he later turned out to be a Pratwa who's twin had been killed. Does anyone know the name of book series?

This was a trilogy about a future earth where double clones were made to fight wars and they nearly destroyed the earth. They were good fighters because they were mentally linked. All were supposedly destroyed but a few were found by this reporter type.  I believe the USA version were called Jeeks.  In the second book a space ship containing a bunch of them returned.  In the final book one clone of a command 3 person clone fought them (the other 2 in the triad were killed and somehow this one did not go insane).  I have looked for this book for 30 years.


I am looking for the most common way how people in US/Canada spell something like this, preferably in accordance with Chicago Manual of Style. What is the right way to spell the title "Diana and Tom's Grill" or "Diana's and Tom's Grill"?

If I was to label something      The Poets and Painters' Distillery    do I only apply the possessive apostrophe after 'Painters' as in the text written above, or do I also need to apply one to 'Poets' so that it becomes      The Poets' and Painters' Distillery ?    I'm thinking the former is correct, but cannot be too sure.


I just baked this bread using sour dough. Everything looks fine until I take it out of the owen. Pre-oven it looks like the first picture, but when I take it out it got a "tail" (see red circle in second picuture). The texture seems to be fine. What am I doing wrong?  Before owen:   After owen:   Sliced:

Instead of swelling as a whole loaf, my loaf will often expand in the oven off to the side or the bottom - looking 'blown out', a big tear.  This results in a loaf that leans to one side, doesn't rise well, or generally doesn't look good.    Why is this happening and what can I do about it?


Like - trying to catch a disease on purpose.

Is there a single word to describe an object or idea that is so desirable that everyone wants to attain it but once they have it they are immediately cursed?  The idea is often used in literature—some examples:   In Lord of the Rings, the 'one ring' is a perfect example of this. In Guy de Maupassant's story , the necklace might be considered to be this. There are many stories of people making deals with the devil (see question: ), or being granted three wishes by a Djinn or fairy, which inevitably turn out bad. In the Twilight Zone episode , Bemis's desire to be left alone with his books would be an example of this word.   'Bane' covers the cursed part, but no one desires it.  Is there a single word to describe a most highly desired treasure that (knowingly or unknowingly) comes with a curse?


I have been searching for ages and ages. But can’t find anything, so does anyone remember a show on Cartoon Network (I think it was, but I’m not sure) where there were 3 main characters and they used cards or something to get powers? One of them was a girl with blue hair and another, I think, was a boy with blonde hair. But the other boy (I think his hair was brown) was like the leader of the trio. And there was this villain that was the blue-haired girl's father. I think her name was like Nya or Mia Idek. But it was around the same time period as the 2004 Ben 10 and I thought I remembered the name, but there is no trace of it.

Looking for a show about a group of three kids/teens who, using cards to change into monsters, fight and recover relics. I believe there are two or three other groups of three also trying to get the relics.  In the main group there are two boys and a girl. The boys were both white, one is from a farm and I don't know where the other is from. The girl was dark skinned and either black or blue hair. The three travelled around the world using a red plane.  I think they only use one monster primarily. The girl uses a monster created from gas and at one point is green. One of the boys uses a metal robot most of the time and at one point is given another better version of that card to use. I believe the episode for this was called something like green with envy.  All I'm getting from the internet is that it may be Chaotic, but that isn't the right show.  I also believe the girl's name was Mai and one of the boys were Ky, but I may be wrong.


As there is heated discussion as to where some edge case questions should end up, there is similar confusion on my part as to where I should search for answers to particular problems.   Is there any thought being put to have an integrated search that will pull results from whichever one of the trilogy the question has been asked?   This may also be useful to drive knowledge of the various strands of SuperStackFault to people that don't follow the place that closely.

There should be an easy way to search Server Fault from Stack Overflow (and the others)  The easiest thing would be to add a "Try searching Server Fault" link next to the "Alternately, try your search in Google:" on the no-results page, but this wouldn't help with overlapping searches..  For example, searching for [sql] error 1234 might have better results of ServerFault, but a programmer might only searching SO for such a problem (a reasonable thing to do)  Maybe there could be a SO/SF/SU/Meta buttons at the top of the search results, which jump you between sites?  Since the user may not be logged into ServerFault, I guess it'd be best to display the results on the current site (with the different colour scheme maybe?), obviously all the links would go to the correct site (http://serverfault.com/questions/... in the example image)  A good example of such a feature is Google.


Thanks for the help everyone. All problems sorted!

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


My ubuntu has not internet connection. Because I cant connect my modem there. Can anyone give me a good idea so that I can downlod the all media codec (ubuntu_restricted_extras.dev) for ubuntu 14.04 32 bit from my mobile and install it to my Laptop (ubuntu 14.04 LTS)

I have a friend who has got a computer that is not connected to the Internet. Is there any way to install software offline easily?


I want to remove the underline of the header "NOT FOR DISTRIBUTION" in the following document:  \documentclass[conference,letterpaper]{IEEEtran}  \setlength{\headheight}{12pt} \setlength{\headsep}{5mm}  \usepackage{fancyhdr} \usepackage{lipsum}% just to generate text for the example  \pagestyle{fancy} \fancyhf{} \fancyhead[C]{NOT FOR DISTRIBUTION} \makeatletter \let\ps@IEEEtitlepagestyle\ps@fancy \makeatother  \begin{document} \title{The Title} \author{Michael Shell \and Homer Simpson}  \maketitle  \lipsum[1-20]  \end{document}   Any suggestions on how to fix this?

When using fancyhdr, how do you remove the top horizontal rule?  I do not want a header at all, just a footer.  This is what I do now:  \documentclass{article} \usepackage{fancyhdr} \pagestyle{fancy}  \lfoot{text} \cfoot{text 2} \rfoot{text 3}  \begin{document} Foo Bar \end{document}


My Windows 7 is on an SSD disk, and I have HDD disk from old Windows XP divided into several partitions. When I try to create a file on one of those partitions H:, it gives me an error:     0x80070522 A required privilege is not held by the client.   Creating files works fine if I go inside any folder. I'm using an administrator account, and I have tried setting an owner and changing privileges, but nothing works.

One of our customers has just found a problem when trying to create a file on the root of the C Drive (C:\), on a Windows 7 Professional PC.  I know they shouldn't be keeping files here, but there is a valid reason in this case, so I've relaxed the security on C:\ by giving the users group users modify permissions.  Before I relaxed the security, the user was receiving access denied, but now they are receiving the message:     An unexpected error is keeping you from creating the file. If you continue to recieve this error, you can use the error code to search for help with this problem. Error 0x80070522: A required priviledge is not held by the client.    for this suggests that it is caused by UAC, but how can I get around this when the user doesn't have admin rights on their PC?


Is there a way to monitor number of attempted Skype connections on a specified port and dynamically firewall off the offending IPs if they break a certain threshhold within a specific time limit - in Windows 7?  On a Linux box, though it's a bit crude, I know I could use wireshark or nstat and output to a file, then cron a job to grep through and then parse the data for number of attempted connections to a specified port, add a firewall rule to iptables, then truncate the log file for the next iteration, and I'm all set. I'm a bit lost on how to go about this or something similar on a Windows 7 box.  The situation I'm trying to solve is that I have several users that need Skype access. Resolving a skype username to IP is fairly simple and this has resulted in their machines being DDOS'd on occasion. While I know I could do this upstream on a full-fledged ASA or similar device, for various networking reasons I'm trying to find a solution that can be implemented on the users computer. White-listing and blocking everybody else is not an option.  Thanks for any input or ideas on this.

This is a  about DoS and DDoS mitigation.   I found a massive traffic spike on a website that I host today; I am getting thousands of connections a second and I see I'm using all 100Mbps of my available bandwidth.  Nobody can access my site because all the requests time out, and I can't even log into the server because SSH times out too!  This has happened a couple times before, and each time it's lasted a couple hours and gone away on its own.  Occasionally, my website has another distinct but related problem: my server's load average (which is usually around .25) rockets up to 20 or more and nobody can access my site just the same as the other case.  It also goes away after a few hours.  Restarting my server doesn't help; what can I do to make my site accessible again, and what is happening?  Relatedly, I found once that for a day or two, every time I started my service, it got a connection from a particular IP address and then crashed.  As soon as I started it up again, this happened again and it crashed again.  How is that similar, and what can I do about it?


The urn contains $N$ balls including $b$ white balls. We pick without replacement $n$ balls $(n \leq N)$. Define random variable $X$ as a number of white balls picked. Find expected value and variance of $X$.  I found that  $$P(X=k)=\frac{\binom{b}{k}\binom{N-b}{n-k}}{\binom{N}{k}},$$ so the expected value will be $$EX=\sum_{k=0}^n \frac{\binom{b}{k}\binom{N-b}{n-k}}{\binom{N}{k}} k.$$ My questions are, how can this expression be simplified, and how do I calculate the variance?

I need clarified and detailed derivation of mean and variance of a hyper-geometric distribution.   If a box contains $N$ balls, $a$ of them are black and $N-a$ are white, and $n$ number of balls are drawn at random without replacement , then the probability of getting $x$ black balls (and obviously $n-x$ white balls) is given by the following p.m.f.  The p.m.f is $$f(x) =\frac{(_{a}C_x) \cdot (_{N-a}C_{n-x})}{_{N}C_n}  $$  The mean is given by: $$ \mu = E(x) = np = na/N$$ and, variance $$ \sigma^2 = E(x^2)+E(x)^2 = \frac{na(N-a)(N-n)}{N^2(N^2-1)} = npq \left[\frac{N-n}{N-1}\right] $$  where $$ q = 1-p = (N-a)/N$$  I want the step by step procedure to derive the mean and variance. Thank you.


Here is my code: System.out.println("Enter Username: "); String unm=System.console().readLine();  System.out.println("Enter Password: "); char[] pwd=System.console().readPassword();  System.out.println("Welcome: " + "" + " Your password is " + new String(pwd));  Why am I getting this error?  Enter Username:   Exception in thread "main" java.lang.NullPointerException at Cons.main(Cons.java:13)

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I have an object with a single mesh, and it has a subdivision surface modifier on it. I'm using BGE, and I cannot figure out, how to render both the wireframe (let's say in white) and the faces (let's say in red) of this object at the same time.

I want it to look like the top image when I press P, so it has those lines around each face.    Like this:    Not like this:


I am using Ubuntu 14.04. I think the mutt command is not available with this version of Ubuntu. Then how can I mail an attachment using terminal commands?


Physicists often assign a finite value to a divergent series $\sum_{n=0}^\infty a_n$ via the following regularization scheme: they find a sequence of analytic functions $f_n(z)$ such that $f_n(0) = a_n$ and $g(z) := \sum_{n=0}^\infty f_n(z)$ converges for $z$ in some open set $U$ (which does not contain 0, or else $\sum_{n=0}^\infty a_n$ would converge), then analytically continue $g(z)$ to $z=0$ and assign $\sum_{n=0}^\infty a_n$ the value $g(0)$.  Does this prescription always yield a unique finite answer, or do there exist two different sets of regularization functions $f_n(z)$ and $h_n(z)$ that agree at $z=0$, such that applying the analytic continuation procedure above to $f_n(z)$ and to $h_n(z)$ yields two different, finite values?

Does the regularization of a divergent infinite sum yield a unique value?  I.e. do different regularization schemes acting on the same infinite sum produce the same exact value independent of the regulator?  What, exactly, do these values mean?  Or what are they?  My understanding is that they are not "convergent" values.  (Sorry in advance for being a physicist.


I'm trying to run the JAAS code sample. lc = new LoginContext("JaasSample", new TextCallbackHandler());  To register the configuration file I try the command: java -Djava.security.auth.login.config=jaas.config JaasAcn  And gets the error:  Error: Could not find or load main class .security.auth.login.config=jaas.config Caused by: java.lang.ClassNotFoundException: /security/auth/login/config=jaas/config

I am getting a NoClassDefFoundError when I run my Java application.  What is typically the cause of this?


I know that lightsabers consist of a plasma blade, powered by a kyber crystal, but do the Blasters in Star Wars work by shooting out plasma rays, too?

Since they aren't just light energy (move too slowly), they are probably some kind of matter or semi-matter. It has been speculated that starship fire is of a different nature from rifle fire (different movement speeds, based on movie physics analysis), so is it possible that is also the case for blaster fire vs lightsaber blades?  Reason being, if the two are the same, then why is cortosis specifically just lightsaber resistant?


I am trying to add a sidebar to a Java application that will have a news feed from a website, most likely computerweekly.com, and will display the most recent stories with a link from the title to the online article.  I am pretty sure I need to somehow use an RSS feed, at least that's what seems to me would be the easiest way. But I'm exactly sure how I would do this.  Let's say I wanted the articles from this RSS feed:  to show up on the side panel of a project, could someone tell me how I would get started in doing so?   If I didn't explain that well enough, I'd be happy to try again, thanks all!

I'm using Java, and need to generate a simple, standards-compliant RSS feed. How can I go about this?


I wanted to reuse older Window XP Dell Latitude D610 machine with Pentium M 1.8GHz processor with 512 RAM. Please advice which Linux OS would be best on this machine.

For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements?


I know the statistics of several subgroups. For example,  Mean, variance, standard deviation, and number of group A Mean, variance, standard deviation, and number of group B  Group C = Group A + Group B With this information, can you find the mean, variance, standard deviation, and number of group C? Assuming that the values of each group are unknown

I'm calculating the covariance of a distribution in parallel and I need to combine the distributed results into on singular Gaussian. How do I combine the two?  Linearly interpolating between the two almost works, if they are similarly distributed and sized.   provides a forumla at the bottom for combination but it doesn't seem right; two identically distributed distributions should have the same covariance, but the formula at the bottom of the page doubles the covariance.  Is there a way to combine two matrices?


I am Indian who will study in France from Jan 16 on a Long Stay Student Visa.  In Dec 15, I intend to travel to Italy.  Should I apply for a separate Visa to go to Italy?  If the answer to the preceding question is NO, is it mandatory for me to enter France first and only then travel to Italy?  If the answer to the preceding question is Yes, how quickly can I leave to Italy after arriving in France? Are there bureaucratic procedures to be completed in France before departing to Italy and if yes, how long are they likely to take?

I have requested for a French long term (Type D) student visa from a consulate in India. It's a national Type D visa and not a Schengen visa. My question is that can we still go to other Schengen countries on this visa? If not then can we get a Schengen visa from a consulate in France?


If $p_n$ is the nth prime  number does $\frac{p_{n+1}}{p_n}$ approach any particular number when $n$ is large? What about $\frac{p_n}{p_{n+1}}$? Is it possible to prove that the limits converge or diverge with elementary methods?

I have recently read an article about the prime number theorem, in which Mathematicians Erdos and Selberg had claimed that proving $\lim \frac{p_n}{p_{n+1}}=1$, where $p_k$ is the $k$th prime, is a very helpful step towards proving the prime number theorem, although I don't know how, primarily because I have not gone through the proof of the theorem even once.  Anyway, I was trying to prove the result $\lim \frac{p_n}{p_{n+1}}=1$ by really elementary methods, as is always my habit, and quite recently I learned of a theorem that the sum of the reciprocals of the primes diverges (I am only a beginner). The idea that suddenly struck me is that this theorem implies $\limsup\frac{p_n}{p_{n+1}}=1$, by a simple application of the ratio test and the fact that $\frac{p_n}{p_{n+1}} < 1$ for all $n$. So, is there any simple way to show that $\liminf\frac{p_n}{p_{n+1}}=1$ or at least $\ge1$, so that the result is proved?  Another beautiful result that came to me, follows from the theorem on divergence of $\sum\frac{1}{p}$, that given any $h > 1$ there are infinitely many $n$ such that $p_n < h^n$. Are there any other results with really simple proofs (easy to understand even for beginners like me) having deep consequences in the theory of the distribution of primes? I'd really like to hear them!


I have to compile a long article with the following structure:  -Abstract  -Contents  -Preface  -1 article_A (saved in separate folder)   -1 Introduction (intro.tex in folder of A) -2 Model (model.tex in folder of A) -3 Result (result.tex in folder of A) -4 Reference (BibTeX in folder of A)   -2 article_B (saved in separate folder)    (similar structure as A)    -3 article C (save in separate folder)    (similar structure as A)    -Conclusion  Actually, new each article can be compiled individually within their own main.tex. But I want to compile them together without modify internal order but taking into account the modification of page numbers.  What I need: Not modify the content of files of A, B, and C; numbers within each article remain the same, don't follow the numbering of articles; table of content shows this structure; at the end of each article there is its own reference (I have BibTeX file in each folder).  I have checked a lot of existing documents online, import or subfiles packages, or input+include didn't work. Could anyone please help me?

I have a collection of articles written in latex, and I would like to "merge" them into a larger thesis document, in which each article will be a chapter. I have been looking at include and input, which are great if you start with the meta-document in mind. However in my articles I have sometimes a bit exotic dependencies, such as dot2texi, and using the naive approach fails rather abysmally with all kinds of broken paths.  So I was wondering, do you recommend any "best practices" for merging non-trivial documents -- which packages to look at, or to avoid at all cost, etc.  Thanks


Here's the question:     Let $f(x)=\sin \left( \frac{1}{x} \right)$ for $x\ne 0$ and let   $f(0)=0$. Show that $f$ is discontinuous on $\mathbb{R}$ and still has   the intermediate value property on $\mathbb{R}$.   It's easy to show that $f$ is discontinuous at $x=0$. Now, I go on to prove that $f$ has the intermediate value property. Let $a,b \in \mathbb{R}$ with $a<b$. Assume that $y$ be some real such that $f(a) < y < f(b)$. If $y=0$ we are done for $f(0)=y$. If $y\ne 0$, I was hoping to use the continuity of sine on $\mathbb{R}$ but nothing seems work out.  Hints would be appreciated. I do not need full solution.

Let $$f(x)=\begin{cases} \sin \tfrac 1 x &\text{if $x\ne 0$}\\ 0 & \text{if $x = 0$.}\end{cases}$$ I have to show that $f$ has the intermediate value property. That is, for any $a < b$, if $y$ is any real number such that $f(a) < y< f(b)$ or $f(a)>y> f(b)$, then there exists a $c \in (a,b)$ such that $f(c)=y$.  I feel like I kind of know how to go about completing this. I just am curious as to if I have to create a bound such as letting $a = -1$ and $b = 1$, or keep $a$ and $b$ both arbitrary.


I would like to ask something. Is it possible to change my android phone to ubuntu??? like to change the rom or anythink it needs to be full ubuntu.  I have galaxy s4 gt-i9505.

With the announcement of the Ubuntu Phone OS I'd like to know what phone (and tablet) models are supported at this time.  Note from foss & Oli: We are making this the master question for all future "Will this work on <insert random tablet/phone/device here>?!" questions


I like Ubuntu 20.04 (most times) and i like macintosh keyboards. At my keyboard I choosed swiss german macintosh. Everything else is correct, but § and < are interchanged. Of course ° and > are interchanged too. I tried some hours to help myself. I have two computes with the same problem. Perhaps someone could help me.

I am running Ubuntu 16.10 on a MacbookPro and keys 49 and 94 are inverted... I resolved this problem with xmodmap, but this won't apply permanently. After some research I found xmodmap is no longuer use by Ubuntu but xkb instead. So I searched in the configuration of xkb and I found in the config file /usr/share/X11/xkb/keycodes/macintosh this lines :   xkb_keycodes "badmap" {     <TLDE> =  94;     <LSGT> =  49; };  xkb_keycodes "goodmap" {     <TLDE> =  49;     <LSGT> =  94; };   This is exactly my problem, this two keys are inverted. So I wondering if I can't change my layout configuration with the param badmap.    The ouput of setxkbmap -query -v 10  Setting verbose level to 10 locale is C Trying to load rules file ./rules/evdev... Trying to load rules file /usr/share/X11/xkb/rules/evdev... Success. Applied rules from evdev: rules:      evdev model:      pc105 layout:     fr,fr,us variant:    mac,oss, Trying to build keymap using the following components: keycodes:   evdev+aliases(azerty) types:      complete compat:     complete symbols:    pc+fr(mac)+fr(oss):2+us:3+inet(evdev) geometry:   pc(pc105) rules:      evdev model:      pc105 layout:     fr,fr,us variant:    mac,oss,


Do they both mean the same thing with former having 'disappointed'  as a noun while the latter, as a verb.Or the latter may refer seeing a person becoming disappointed and the former, a person already in a disappointed state.  There's another statement:     He seemed to becoming disappointed.   But I believe this's incorrect.

The baby seems happy/comfortable. The baby seems to be happy/comfortable.   Are these both correct? If both are correct, what are the differences between them?


Assume $A$ is diagonalizable. Show that $A$ is similar to $A^T$  Any help would be very appreciated. I know for a matrix to be diagonalizable it has to be a square matrix so the # of rows and columns stay the same for $A^T$.

Mariano mentioned somewhere that everyone should prove once in their life that every matrix is conjugate to its transpose.  I spent quite a bit of time on it now, and still could not prove it. At the risk of devaluing myself, might I ask someone else to show me a proof?


I could use some help with a shell script to rename files using portions of the directory tree and existing file name.  Background: The file naming convention is from an Amcrest security camera that cannot be modified. The camera creates a new folder for every minute and every hour of the day.   The jpeg files are created using the seconds past the minute.  Current naming structure:    AMC0103W_93Sxxx/2017-02-07/001/jpg.14/02/29[M][0@0][0].jpg   where 14 is the hour, 02 is the minute, and 29 is the seconds.    Here's the format that I'd like to have:    AMC0103W_93Sxxx/2017-02-07/140229.jpg   My goal is to set a crontab job that runs hourly to rename these into a new directory then deletes the old directory and files.

Given the following structure:  source/   dir1/    file1.ext1    file2.ext2   dir2/    file3.ext3     dir3/      file4.ext4   I want to achieve the following:  destination/  dir1file1.ext1  dir1file2.ext2  dir2file3.ext3  dir3file4.ext4   In other words, I want to move all the files, recursively, from source to destination, appending the original subdirectory name to the file name.


I currently have 13.10 Saucy Salamander installed, and I'm following this guide in order to update:   I got as far as step 6, click the Check button for new updates. There is no Check button, only Settings, Remind Me Later, and Install Now. When I click Install Now, a box comes up saying "To install or remove software, you need to authenticate". I type in my password and hit enter. Another box comes up saying:  Software Updater Requires installation of untrusted packages This requires installing packages from unauthenticated sources.   with the options Settings and OK. I click OK and the box just...goes away. Nothing else happens. Nothing is downloaded, the Software Updater doesn't come back, nothing. When I open Software Updater again, the whole process has to be started again.  What am I doing wrong here?    Command Line Method  sudo apt-get update   returns a bunch of lines of code but ends with this:  E: Unable to fetch some archives, maybe run apt-get update or try with --fix-missing?   I ran:  sudo apt-get update --fix-missing    that also returns a bunch of lines of code but ends with this:  E: Some index files failed to download. They have been ignored, or old ones used instead.   Finally, sudo apt-get upgrade returns the same error as sudo apt-get update:  E: Unable to fetch some archives, maybe run apt-get update or try with --fix-missing?

Recently I have installed an older version of Ubuntu on my old machine. Whenever I try to install any software, I get an error saying it couldn't be found:  $ sudo apt-get install vlc Reading package lists... Done                Building dependency tree        Reading state information... Done     E: Couldn't find package vlc


I have been working on a html file on my mac os 10.10 via Texedit for about a week. When I started my computer today the file appeared on my machine as an rtf, and when I opened it I saw my page as rich text with no javascript of html tags. I then tried to restore it but all the versions were rtf. I then choose to view the page a plain text and restore again and now all the versions were plain text. Again no javascript or html tags. How can I restore my file as a html file?

When I try to save a new file in TextEdit, I always get a popup saying I can't save with ".txt" at the end of the file name.  I want to save a plaintext file, but TextEdit insists on saving as .rtf instead. It also lists .doc, .odt, .html, and some others.  How can I save a TextEdit document as plain text?


I will be a single parent in future, and I will have a 8 hour job (7:30 AM to 3:30 PM) always.  Assuming the school bus drops the kid at the colony gate, at what age can I expect the child to come home and stay at home alone for 6 hours safely, after coming from school?  The child should be able to take out food from fridge, heat it on gas stove, and feed herself.  The child should not open the door even if the stranger pleads to death.  At what age will I be able to leave the child alone at home for long intervals?

I'm curious what kind of criteria others are using to decide when a child can be left at home unattended for a period of time.  I realize that the answer is going to depend on a few factors: The child's safety awareness and knowledge of what to do in a particular situation; their age; their maturity level; how long you intend to be gone; how far you're going; etc.  For a more concrete example: My daughter is 7-1/2, knows right from wrong, how to use a phone, our phone numbers, 911 (US emergency services number), not to answer the door unless we ask her to, not to mess with the stove, etc.  Is it conceivable that she's old enough to stay home alone for relatively short intervals?  We'd have to start with very short (5-10 minutes) intervals until both our and her confidence were built up, but I think she should be able to gain the confidence to be left home for longer than that.  I don't think she's old (or mature) enough to be left in charge of her younger siblings yet, but she could entertain herself and stay out of trouble.  Edit:  This is about children taking early steps towards independence at home.  I know that when I was a teenager, my parents left me at home alone while they went shopping (which can be an all-day event with my mother :-) ) or even spent a weekend away.  They trusted that both the house and I would be in one piece when they came home.  But those weren't my first times being left at home alone -- this question is about the first steps one takes towards that level of independence.  When is the right time to start?  What are you looking for in your children that makes you think: "They're ready to begin this particular journey?"


I am new to Blender even to the world of animation.  I have 4 cameras and I have bind them with markers in the timeline. When I animate they change fine. When I open the Render view from the button side to the Object Mode button it shows perfect Camera view.  But when I Render it as png all the images are black, they are like a view from a camera just pointed towards ground but there is no other camera I have checked the Outliner list also.  I have also tried selecting the Border option in Render tab but when I click on Render or Animate, I get a message that border is not allowed for sequencer.  I have searched on google and all the solutions I am being told are not working.  Someone Please help me out. Thanks a lot in advance.

This is meant to solve this problem once and for all. What is every reason an object isn't showing up in a render or viewport in when using the cycles render engine?


I'm pretty new to python and curious why my function prints out each character from a new line. Any suggestions on how to correct it? Any other implementations of that would be helpful as well.   This how my function looks like  def reverse(word):     len_word = len(word)     x = 0     while x < len_word:         x += 1         index = len_word - x          print(word[index]) reverse("123abcd")    What I get is the input with each character on a new line.  What I want to get: dcba321

I'd like to do it in Python. What I'd like to do in this example in C: #include <stdio.h>  int main() {     int i;     for (i=0; i<10; i++) printf(".");     return 0; }  Output: ..........  In Python: >>> for i in range(10): print('.') . . . . . . . . . . >>> print('.', '.', '.', '.', '.', '.', '.', '.', '.', '.') . . . . . . . . . .  In Python print will add a \n or space, how can I avoid that? Now, it's just an example, don't tell me I can first build a string then print it. I'd like to know how to "append" strings to stdout.


Ubuntu 17.04 introduces a swap file to replace swap partitions.  However, I would prefer not to have any disk-based swap space at all, so I would like to know how to turn the swap file off.  Clarification: I need a way to turn the swap file off permanently.  AFAIK, the swapoff command only disables it temporarily.  Clarification 2: I do not want swapping disabled completely, as I am using zram as my swap.  I only want the swap file disabled.  My question specifically deals with the swap file, while the answers to the other questions deal with either turning off the swap partition, or they deal with turning off all swap.  I do not want either, I just want the swap file turned off.

I have some sensitive data in RAM that I prefer not to be on disk. How do I disable swap?  I have more than enough RAM. If RAM consumption gets too high I have no problems with processes being terminated. How do I disable swap?  Note: I do not have a swap partition and this is running in a VM ()


In my code I wrote :   $\therefore$ There is a total of 21,168 ways that we can choose 2 chemists and 3 physicists.    However, I am getting the undefined control sequence error. I have used packages amsfonts and amsmath, but that doesn't seem to fix the problem.  Thank you.

I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out?


From what I understand I can use the  Euler-Lagrange equation to find the function ( Let us call L. ) where L can be the function as stated in the action formula.  But how difficult is it to actually derive the stationary action formula itself or is it the case that once I have he function I can always construct the action formula from first principles ?

We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's principle) and even General Relativity (we get Einstein's equation from the Einstein-Hilbert action). However, how do we explain this very principle, i.e., more mathematically, I want to ask the following:      If I am given a set of generalized positions and velocities, say, $\{q_{i}, \dot{q}_{i}\}$, which describes a classical system with known dynamics (equations of motion), then, how do I rigorously show that there always exists an action functional $A$, where    $$A ~=~ \int L(q_{i}, \dot{q}_{i})dt,$$    such that $\delta A = 0$ gives the correct equations of motion and trajectory of the system?    I presume historically, the motivation came from Optics: i.e., light rays travel along a path where $S = \int_{A}^{B} n ds$ is minimized (or at least stationary). (Here, $ds$ is the differential element along the path). I don't mind some symplectic geometry talk if that is needed at all.


I have NEVER in my life stayed in a hotel where it said visitors are not welcome. I am going to NYC, and my friend wanted to visit me, not spend the night. We have done this before at another hotel, but that one was all booked up.  So I made sure I read the policies for the hotel that I booked. It said nothing about visitors or anything at all really, but in two reviews of the hotel they said visitors weren't allowed. I am trying to contact the manager, but apparently the staff have pretty poor English. Can they charge me for my friend visiting? Or not allow him in at all?  I am not asking for anyone to spend the night only for a Visitor.

We are going to an event and because of this event all hotels are fully booked. Now a friend wants to join us, but can't find accommodation. We are okay with him crashing in our hotel room, either on the couch or on a self-inflatable mattress. We have done this in the past where we secretly sneaked the "guest" in.   It is not that we don't want to pay the tourist tax, it is that when ask and the hotel says no, we can't sneak him in, because we drew attention to ourself. In many hotels you can just order another bed, but there are also a lot that don't have that service.   I don't have any ethical problems with my behavior of secretly hosting a guest. I did pay for the room. I don't like being sneaky about it, since again I do pay for the hotel room. Also if I have to choose between sneaking someone in the room to crash on the couch or let him/her sleep on bench in the park. I opt for the first.   Am I just worrying to much and will being honest about it in the end be acceptable to most if not all hotels?


I want to show that each of the ideals $I_k=\langle x_1,...,x_k\rangle$ in $F[x_1,...,x_n]$ for $1\leq k \leq n$ are prime, and that each of their powers is primary, where $F$ is a field.  I have been able to show that each $I_k$ is prime, by considering the map $F[x_1,...,x_n] \rightarrow F[x_{k+1},...,x_n]$ given by $f(x_1,...,x_n)\mapsto f(0,...,0,x_{k+1},...,x_n)$ and using the first isomorphism theorem to show that $F[x_1,...,x_n]/I_k \cong F[x_{k+1},...,x_n]$ is a domain.  The part where I'm struggling is showing that each power of the $I_k$ is primary. I managed to prove that when $n=3$, $I_2^2$ is primary using brute force, but I'm unable to generalise this approach to either $n>3$ or higher powers of the ideal. Any help would be appreciated!

Let $K$ be a field. Then how to show that all powers of the prime ideals $p_i=(x_1,\ldots,x_i)$ $(i=1,\ldots,n)$ are primary ideals in $K[x_1, \ldots,x_n]$ ?   It is easy when $i=n,$ but if $i<n$ how can I approach ? Any help will be appreciated. Thanks.


I have a file which has the following content:  BWA='/software/bwa/bwa-0.7.12/bwa' SAMTOOLS='/software/samtools/samtools-1.3.1/samtools'   The above tools are on my computer:   which bwa => /work/waterhouse_team/miniconda2/envs/arima/bin/bwa and pwd/hic-fq => /scratch/waterhouse_team/benth/dbg2olc-40x/hic-fq   Next, I used those two sed commands:  sed -i.bak 's|/software/bwa/bwa-0.7.12/bwa|$(which bwa)|g' mapping_arima.sh sed -i.bak 's|/software/samtools/samtools-1.3.1/samtools|$(which samtools)|g' mapping_arima.sh   Unfortunately, as output I received:   BWA='$(which bwa)' IN_DIR='$(`pwd`)/hic-fq'   How do I have to change the sed commands to get:   BWA='/work/waterhouse_team/miniconda2/envs/arima/bin/bwa' and  IN_DIR=/scratch/waterhouse_team/benth/dbg2olc-40x/hic-fq   Thank you in advance

I want to do:  cat update_via_sed.sh | sed 's/old_name/new_name/' > new_update_via_sed.sh   in my program.  But I want to use variables, e.g.  old_run='old_name_952' new_run='old_name_953'   I have tried using them but the substitution doesn't happen (no error). I have tried:  cat update_via_sed.sh | sed 's/old_run/new_run/' cat update_via_sed.sh | sed 's/$old_run/$new_run/' cat update_via_sed.sh | sed 's/${old_run}/${new_run}/'


I've heard this phrase mainly in old movies. From the context, I inferred that it was a mild form of swearing and not considered terribly offensive.  However, I'm not sure what the 'it' in 'beat it' referred to. Going by colloquial expressions such as 'beat the meat', I can only think of one logical answer to that. If it means what I think it means, it's a lot less mild than it sounds.  I feel that the usage of the phrase has declined drastically, as one hears it a lot less often currently. So it's difficult to correctly gauge the usage pattern now.  If someone could please shed some light on the historic context, meaning and current usage status of the phrase, that would be great. How offended should I be when someone tells me to 'beat it'?

I would like to know what does this phrase means:     "Why don't you just beat it?"   My dictionary says only that: beat it: get lost Can you beat it? : Do you get it?


I have two URLs: http://ent.example.com and http://www.example.com/ent/. Both of them are mapped to my server path /www/ent.   I am very confused, how would this affect my SEO as far as Google is concerned? If two URLs are pointing to the same path, would Google consider this cheating?

This is a general, community wiki question regarding duplicate content.  If your question was closed as a duplicate of this question and you feel that the information provided here does not provide a sufficient answer, please open a discussion on .     What does Google consider to be duplicate content? Will the way I am presenting my content result in a duplicate content penalty? How can I avoid having my site's content treated as duplicate content?