English equivalent of *refrán*, which is less formal than a proverb

Spanish makes a subtle distinction between proverbio [proverb] and refrán [?].  This distinction was described well .  I'll attempt to translate informally from that answer.     Although the two words can be considered synonymous, the connotations   are different:         refrán: a colloquial, folksy saying or piece of advice.  It needn't be about something weighty.  It often features a rhyme, making   it catchy and easy to remember.   proverbio: a bit more serioius than refrán.  Generally speaking, it doesn't provide advice about banal matters, but has more of a   moral, ethics tone.         For example:           Marzo ventoso y abril lluvioso sacan a mayo florido y hermoso. [Loosely: April showers bring May flowers; literally: Windy March and     rainy April bring out a flowering and beautiful May.]         The subject matter of this refrán is the weather.      A proverb, on the other hand, is more formal, has a more serious subject matter and attempts to teach something.   Here's an example of a proverb:     No es oro todo lo que reluce. | All that glitters is not gold.   My German spouse informs me that refrán seems to be similar to Bauernregel (guidance for farmers), but with a particular focus on the weather.  For example     Der April macht was er will. | April does whatever it wants to.   My question is what is the closest equivalent to refrán in English?    Edit after question was closed as a duplicate of a question that was closed because a sample sentence wasn't provided:  Sample sentence:     Spanish has a charming refrán that's relevant to your situation: [....]   An additional thought: I'd like ideally to find something as graceful as, for example, "turn of speech."  But that won't work because a turn of speech is a fragment, not necessarily a whole sentence.


Why we only use L1 and L2 in penalized regression

I understand we do not want to go lower than 1 because the problem is no longer convex. But why not use L3 for example? Is there any reason why L2 is so popular but not higher norm?


How do I deal with wrong or irrelevant edits made to my posts?

So... from a while back, I posted a question dealing with implementing a certain feature within an iPad app (no specifics, see  for question), and I noticed that there was an approved edit by a user named Zephyer who posted something about Windows 7.  After a face-palm, I re-edited my question to bring it back in line with my query.  So, my question then is: What the heck do we do with the occasional stupid/irrelevant edit?  I know it doesn't happen often, but there's got to be something other than just re-editing I can do!    EDIT: Excellent suggestions.  To clarify two things though:   This post is quite old.  I was a new user at the time, unaware of the rollback feature if it even existed at the time of it's posting. I just wanted to know if there was some way to get the attention of the editor.  It doesn't need to be a downvote or a flag, just a message, or an indication.


Splitting a repository using filter-repo

This is so simple to describe, but being new to GIT I haven't been able to find a gif-filter-repo solution.  I have a repository 'old' with two directories 'part1' and 'part2'.  I want to create two new repositories, 'new1' which will contain everything from 'part1' directory (except the part1 directory itself) and 'new2' which will contain everything from 'part2'.  Can someone show me how to accomplish this? I have: old   .gif   /part1     /A     /B   /part2     /C     /D  and I want to extract the subdirectories and build new repositories: new1   .gif   /A   /B  new2   .gif   /C   /D


What happens if I make more than $100k with the free Unity license?

If an indie game developer makes more than $100,000 using the free version of Unity, what happens to the money that goes over $100k? How will Unity people come to know how much money they are making?  What precautions should I take just in case a game is a great success?


Userscript to strip a portion of a pages title

IMDb's reference view was recently changed to include "- Reference View - IMDb" after the page title that only used to have Movie (year)  New...  <title>Movie Title (2018) - Reference View - IMDb</title>   Old...  <title>Movie Title (2018)</title>   How do i strip the stuff they added to the reference pages so I just have Title (year)?  // ==UserScript== // @name        IMDb - strip garbage from reference view page titles // @match       *://www.imdb.com/title/tt*/reference   Code makes my head spin and the above is all I can manage.


Samsung galaxy S4 Blacked out Screen need to retreive files

Anyone know how to get photos/files from a galaxy 4 that has a broken / blacked out screen - Ive tried every method possible ive read online and im getting no-were and ready to scream ...I cant seem to unlock the screen to allow a computer to extract files - Ive pluged the phone into multiple computers it wont read the phone...ive tried the Kies Program...the Samsung recovery system - can I plug the phone into something and see the screen separate from the phone?


How can I pad an int with leading zeros when using cout << operator?

I want cout to output an int with leading zeros, so the value 1 would be printed as 001 and the value 25 printed as 025. How can I do this?


When applying for an Indian Passport, how do I know if I'm in the ECR or non-ECR category?

I'm applying for a fresh Passport from India but I don't know what "ECR" & "NON-ECR" mean:     "Is applicant eligible for Non-ECR category?"      [Yes] [No]   I've already Graduated from University. I don't know whether to choose "YES" or "NO"?. I'm Indian by birth.


Inbox Messages aren't loading on Android App when opening app through notification

Seems to be a reincarnation of this  issue from early last year: .  I'm on Android 5.1.1 and my Stack Exchange app is version 1.0.73.  If I open the application through a notification it opens with the inbox sidebar open, but there is no content inside. The loading graphic doesn't display, either, as if to suggest that loading never gets kicked off. To view the notification properly I then have to close the sidebar and reopen it:


Removing the gaps between two vector layers and merge them seamlessly

I have multiple vector files  needed to merge them without any error, but there is gap between one layer and another layer as shown in image 1 respectively. How can I rectify this error?  I merged the layer files but I can see the gap in the layer as shown in Image-2.  PS: All the operations are carried out in QGIS. How can I resolve this issue?


I made an account on Stack Exchange but I can't edit my network profile.  How can I edit this?


Negative Sign in Potential Energy Expression

The potential energy can be mathematically expressed as: $$U=-\int \vec F \cdot d\vec x$$ I do understand the negative sign is basically to adjust in the relation $$K_1+U_1=K_2+U_2$$ What is the physical significance of the negative sign.


I am struggling to understand the derivation of the expected prediction error per below (ESL), especially on the derivation of 2.11 and 2.12 (conditioning, the step towards point-wise minimum). Any pointers or links much appreciated.   Below I am reporting the excerpt from ESL pg. 18. The first two equations are, in order, equation 2.11 and 2.12.    Let $X \in \mathbb{R}^p$ denote a real valued random input vector, and $Y \in \mathbb{R}$ a real valued random output variable, with joint distribution $\text{Pr}(X,Y)$. We seek a function $f(X)$ for predicting $Y$ given values of the input $X$. This theory requires a loss function $L(Y,f(X))$ for penalizing errors in prediction, and by far the most common and convenient is squared error loss: $L(Y,f(X))=(Y-f(X))^2$. This leads us to a criterion for choosing $f$,  $$ \begin{split} \text{EPE}(f) &= \text{E}(Y - f(X))^2\\ & = \int [y - f(x)]^2 \text{Pr}(dx, dy) \end{split} $$  the expected (squared) prediction error. By conditioning on $X$, we can write EPE as  $$ \text{EPE}(f) = \text{E}_X \text{E}_{Y|X}([Y-f(X)]^2|X) $$  and we see that it suffices to minimize EPE point-wise:  $$ f(x) = \text{argmin}_c \text{E}_{Y|X}([Y-c]^2|X) $$  The solution is  $$ f(x) = \text{E}(Y|X=x) $$  the conditional expectation, also known as the regression function.


Axis with trigonometric labels in PGFPlots

How do I make the axis labels use multiples of \pi in PGFPlots?


Constructing a continuous function whose graph seems 'special'

I've been reading through Zorich's "Analysis I" book recently, and I came across this nice little exercise.  Let $f: [0,1]\to \mathbb R$ be a continuous function such that $f(0)=f(1)$. Show that    for any $n\in \mathbb N$ there exists a horizontal closed interval of length $\frac 1n$ with endpoints on the graph of this function; if the number $\ell$ is not of the form $\frac 1n$ there exists a function of this form on whose graph one cannot inscribe a horizontal chord of length $\ell$.   The first part can be proven like this: Consider $g: [0,(n-1)/n] \to \mathbb R$ given by $g(x) = f(x) - f(x+1/n)$. Then   $$\sum_{k=0}^{n-1} g(k/n) = 0$$  and therefore either all of these points are zero or there exists both a point where $g$ is positive and a point where $g$ is negative. By continuity, there must then also be a point where $g = 0$. So we are done.  Now, the second statement seemed rather counterintuitive, and I have given it some time now, but don't see a counterexample for $\ell < 1/2$.  (For $\ell > 1/2$ the function $f(x) = \sin(2\pi x)$ will do.)  Can anyone help me out?  Cheers,


I want to copy a live production database into my local development database.  Is there a way to do this without locking the production database?  I'm currently using:  mysqldump -u root --password=xxx -h xxx my_db1 | mysql -u root --password=xxx -h localhost my_db1   But it's locking each table as it runs.


Can I travel to a Schengen Country on Multiple Entry C-type Visa issued by a different country?

I have a multiple entry C-type Visa issued by Switzerland, valid until 2020, and period of stay 90 days. I've already been to Switzerland with that visa before, and stayed for around 20 days. Now I need to go for a short visit to Germany for 3 days. Can I use the same visa or I need to apply a new one?


About supported devices under ubuntu touch

I am a fan of ubuntu operating system. I have been using ubuntu as my pc OS from a last few years. I had heard that ubuntu had also launched the Os for mobile phones named ubuntu touch. I have a mobile phone named Micromax Canvas Doodle 3. But when I installed ubPorts installer , I did not find its name. Can you please tell , If there is other way of installing it on my phone. Do Ubuntu Touch is made only made for a fixed a number of mobile phones ?of which my phone is not a part of.


Loading scripts only if a particular shortcode or widget is present

I needed a way to filter a page/posts content before it was loaded so I could add scripts to the header if a specific shortcode was present. After much searching I came across this on    function has_my_shortcode($posts) {     if ( empty($posts) )         return $posts;      $found = false;      foreach ($posts as $post) {         if ( stripos($post->post_content, '[my_shortcode') )             $found = true;             break;         }      if ($found){         $urljs = get_bloginfo( 'template_directory' ).IMP_JS;      wp_register_script('my_script', $urljs.'myscript.js' );      wp_print_scripts('my_script'); }     return $posts; } add_action('the_posts', 'has_my_shortcode');   which is absolutely brilliant and did exactly what I needed.   Now I need to extend it a bit further and do the same for sidebars. It can be by a particular widget type, shortcode, code snippet or anything else that would work to identify when the script needs to be loaded.  The problem is I can't figure out how to access the sidebars content before the sidebar is loaded (the theme in question will have several sidebars)


Show that $f$ is uniformly continuous if limit exists

Let $f(x)$ be continuous on $(0,1]$. Show that $f$ is uniformly continuous IFF $\displaystyle \lim_{x\to0^+} f(x)$ exists.    Thoughts:  Backward Proof:  Let another function $\overline f(x)$ be continuous on $[0,1]$ which is equal to $f(x)$ plus the limit point. Thus the limit exists and it is uniformly continuous. So, as $f(x)$.  Forward Proof: I Don't really have any idea...??  Please help guys


Clarification about domains of inverse trigonometric functions

Hy friends!  Is there any special reason for the definition ot inverse trigonometric functions domains? It is clear thar we have many possibilities of resriction in the domains that still keep the funcitions bijectives (in order to garantee the existence of their inverses). But always than possible, we choose domains that contains or are close to zero, where the functions are monotonous and that garantee a continuous function after the restriction. If we choose another domain, some calculations as strenght of a curve could be wrong? (for example, when we determine a definite integral)Thanks a lot for the clarification.


Files Upload is not Working for Community Profiles

I have created one file upload component page and using that page in the community portal but when I'm uploading a file a file its not working.  If I'm doing the same with a console app, then it is working. So I think some permission issues I have because its working for system admin profile but not for community profile.  Can Anyone have some Idea on this? what I need to do to fix this.


I'd like to fetch a webpage and save the content as a string? Is there a library to do that? I want to use the string for some a program I am building. It's for websites, that don't necessarily provide rss feed.


Euler's Constant: The asymptotic behavior of $\left(\sum\limits_{j=1}^{N} \frac{1}{j}\right) - \log(N)$

I want to show that there exists a constant $\gamma\in\mathbb{R}$ such that   $$ \sum_{j=1}^N \frac1{j} = \log(N)+\gamma+O(1/N). $$  I know how to prove that the Euler-Mascheroni constant exists (which I believe $\gamma$ to be), but I am having trouble with the big-$O$ notation and the subsequent bounding. I've considered   $$ \left|\left(\sum_{j=1}^N \frac1{j}\right) - \log(N)-\gamma\right|\le |K/N| $$ for some $K$, and I was approaching this by trying to show the that the left side of the inequality decays faster, but so far am stuck. Any advice for this type of problem, or analogous ones, would be appreciated.  Thanks!


How to show there is no real valued function whose limit approaches to infinity at every real number.

Question: Show that there is no function from $\mathbb{R}$ to $\mathbb{R}$ such that for every real number a, $f(x)$ approaches infinity as $x$ approaches $a$.  We know that, limit of function $f$ as $x$ approaches to $a$ is infinity if for all $N>0$ there exist $\delta>0$  such that $f(x)>N$ whenever $|x-a|<\delta$.   then by above we get $f(x)>m$ for every $m\in \mathbb{R}$ and hence such real valued function $f$ does not exist.  is this proof is correct? If not Please explain me what details are missing and what mistakes I had done in proof. Thank you.


Did Jordan base the Aiel on Herbert's Fremen?

Were the Wheel of Time's  based on Dune's ?   Did Robert Jordan acknowledge or otherwise address this connection?


Proof that the inverse of a square matrix is unique

From my textbook     ... if a 2×2 matrix $A$ is invertible then its inverse is unique.   I wonder, how can one prove this? Also can one extend this proof to larger square matrices of order $n$? Thanks


Creating Metes and Bounds text from a polygon in ArcGIS

Lots of questions about turning metes and bounds into a polygon, but how about going in reverse? Are there any existing tools or do I need to look at building a script myself?  Ultimately I'd like to generate points with x/y and at all the vertices and line segments with distance and direction as attributes (so I can label them).   This for submission to our local government as part of their legal requirements.


Moment generating function of the inner product of two gaussian random vectors

Can anybody please suggest how I can compute the moment generating function of the inner product of two Gaussian random vectors, each distributed as $\mathcal N(0,\sigma^2)$, independent of each other? Is there some standard result available for this? Any pointer is highly appreciated.


The Setup: Let's say we want to study a Euclidean $\mathrm{CFT}_2$ on $\mathbb R^2$ with coordinates $\sigma^1$ and $\sigma^2$ and metric   $ds^2 = (d\sigma^1)^2+(d\sigma^2)^2$.    It seems to me that in the usual discussion (e.g. di Francesco, Ginsparg, Polchinski), one proceeds to consider an analytic continuation of the CFT to $\mathbb C^2$ with coordinates $z^1, z^2$ and complex metric  $ds^2 = (dz^1)^2+(dz^2)^2$  and then, one performs the coordinate transformation $z = z^1+iz^2$ and $\bar z = z^1-iz^2$.  In this way the coordinates $z$ and $\bar z$ can be considered "independent" because they are coordinates on a complex two-dimensional manifold.  Also, in these coordinates the metric becomes  $ds^2 = dz\,d\bar z$  and it becomes clear that conformal mappings consist of mappings: $(z, \bar z)\to (f(z), g(\bar z))$.  My confusion is this: Since our original theory was on $\mathbb R^2$, books say that when we do calculations, we should consider the physical theory as living on the copy of $\mathbb R^2$ embedded in $\mathbb C^2$ given by the condition $\bar z = z^*$.  But consider the mapping $(z, \bar z)\to (z^2, \bar z)$.  This is a conformal mapping on $\mathbb C^2$, but it does not map the surface $\bar z = z^*$ to itself; for example the point $(z, \bar z)=(2,2)$ gets mapped to the point $(z^2, \bar z) =(4,2)$ and $2$ is clearly not equal to $4^*$.  In particular, it seems to me that analytic continuation to a CFT on $\mathbb C^2$ enlarges the set of mappings one can have, so what relevance does it really have to the original CFT on $\mathbb R^2$?


Can anyone recommend video lectures on all subjects of physics for a masters student?

I am a student of Physics doing masters in it and I am looking forward to study on my own. By own I mean with video lectures, books etc. It would be really kind of you all if you could recommend me some good books and video lectures on each subjects I will come across.


align environment: set position of & manually

In the following code, the alignment position for & is computed automatically:  \begin{align*} x^2 + y^2 &= 1 \\ y &= \sqrt{1 - x^2}. \end{align*}   Now, I'd like to have all my equality signs (over many equations/aligns in many sections and subsections) aligned at the same position, preferably by just manually giving a position. Is this possible, and how?


One-boxed content is blank in the Android app

See the accepted answer in this question:   There is a YouTube link at the end of the post which doesn't appear (neither the link or onebox).


Why did Itachi say that he needs to get someone's MS to get EMS while Sasuke only had a normal Sharingan?

In the fight between Sasuke and Itachi, Itachi said that to get Eternal Mangekyou Sharingan (EMS), he must transplant his brother's eyes that have to be Mangekyou Sharingan (MS). However, Sasuke didn't have MS yet.  So, even if Sasuke did get his normal Sharingan eyes, how could he get the EMS?


I open the fridge - do I let the heat in or the cold out?

Conventionally, heat flows from hot to cold. How legitimate is it to redefine things in terms of "cold" rather than "heat" eg Cold flows from cold to hot?


How to take self portraits without a remote?

How can I take a self-portrait without using a remote?  My camera is a Canon Powershot SX210 IS. I do not have a remote, but I do have a tripod.


How to weight down older data in an OLS fit

I am doing a ordinary least squares fit. I have data which was recorded at different times. The fit could depend on time so I want to trust my older data less. The obvious way to do this is to weight the data based on how old each data point is and use a weighted least squares fit.   For example, suppose I am trying to fit a linear relationship to estimate the number of people inside McDonald's based on the number of cars in the parking lot. I have [people,cars] data points from many location for the last year recorded a sporadic times. The most recent data should be more useful to predict this relationship as it may change over time but I do not want to throw out older at some arbitrary age.   Is there a standard for this sort of issue or do I need to make some assumption about how the quality of my data ages? Is there a better way to conceptualize this problem?  EDIT: It is quite possible that there is a trend in the dependant variable as the age changes. In fact the error of each measurement should not change. It might be a better idea to fit that dimension as well and take it out after. In the above example this would be to fit the number of customers inside as a function of cars outside and how long ago the measurement was taken. Then use the current time for predictions.


I live with my mom here in the Philippines. She owns a sari sari store and shes a pensioner. She pays me monthly. And I don't have a bank account as a proof of my financial status.My sister and her husband want me to visit them in the UK since she's going to have a baby and she really needs someone to be with her since my brother in law is working. My brother in law would like to sponsor my trip. What documents will I comply since I don't have a proof of employment?    And what to do to prove that I'm going to the Philippines after my visit for 6 months in the UK.   Surely, I have to return home since my 74 mom needs me. Will making a letter help to prove that I will go back home after my visit to the UK?


Searching for a short story about people being stuck together

I have been trying to find a short story I read many years ago. I think it was a 60s/70s story. Something happens on Earth, and whenever people touch they become stuck together. These blobs of people exist and create nest for themselves.   There are still some individual people but they live in fear, I think, of being joined with the rest.  Any ideas?


is there a shortcut for toggle between default screen layout and composit screen layout?

i click a lot on the two screen layouts , composite and default.  every click that i do often,  i try to find a shortcut for it.  but i doubt there is a shortcut for screen layouts ? i have not seen a Phyton code showing up at these places. or am i missing something ? is there a way to get this shortcut ? in the worst case i will just keep on clicking each time.   but i prefer the shortcut. i hope anyone has an answer, thanks.


How to derive the asymptotic distribution of the test statistic of a large sample test for equality of two binomial populations?

Let $X_1, \ldots, X_{n_X}$ and $Y_1, \ldots, Y_{n_Y}$ be $n_x$ and $n_Y$ iid observations from two independent Bernoulli populations with probabilities of success $p_X$ and $p_Y$. Define the statistics $T_X = \sum_{i=1}^{n_X}X_i$ and $T_Y = \sum_{i=1}^{n_Y}Y_i$. I am testing the hypothesis:  $$ H_0 : p_X = p_Y \ \ \ \text{and} \ \ \ H_1 : p_X \neq p_Y $$  Consider the test statistic:  $$ T = \dfrac{\hat{p}_X-\hat{p}_Y}{\sqrt{\hat{p}(1-\hat{p})\left(\frac{1}{n_X}+\frac{1}{n_Y}\right)}} $$  where $\hat{p}_X = \frac{T_X}{n_X}$ and $\hat{p}_Y = \frac{T_Y}{n_Y}$, and $\hat{p} = \frac{T_X+T_Y}{n_X+n_Y}$.   I would like to derive the asymptotic distribution of $T$ under $H_0$ as both $n_X$ and $n_Y$ go to infinity. My works is as follows: By the asymptotic properties of the MLE:  $$ \sqrt{n_X}(\hat{p}_X-p_X) \to_{D}N(0,p_X(1-p_X)) $$  and  $$ \sqrt{n_Y}(\hat{p}_Y-p_Y) \to_{D}N(0,p_Y(1-p_Y)) $$  I would like to find the distribution of $\hat{p}_X-\hat{p}_Y$, but am not sure how. In general two "in distribution" results are not additive. That is, it is genreally NOT the case that $X_n+Y_n \to_{D} X+Y$. Does anyone have any ideas?  I know in general that under the null:  $$ T = \dfrac{\hat{p}_X-\hat{p}_Y}{\sqrt{\hat{p}(1-\hat{p})\left(\frac{1}{n_X}+\frac{1}{n_Y}\right)}} \to_D N(0,1) $$


My computer has an SD card slot. When I put a working SD card into the slot, nothing happens. When I put a CD or DVD in, or plug in a USB drive, the medium is mounted and available. Is there something special I need to do for SD cards?  Hardware specifics  I am running 11.10 on a Dell XPS L502X. The card slot is marked "SDXC/MMC - MS/Pro" (which Wikipedia tells me are various SD card types).


I'm having a small issue with visible seams on normal maps. The map was painted on Substance Painter and has no weirdness around seams. When I plug it into a Normal Map node set to Tangent Space this happens:   (it's a horse underside)  When I set the map to Blender Object Space the seams become nearly invisible, as they should be, but the shadows also looks awful.    What can be done to minimize the issue? I need to be able to use maps on tangent space. Moving the seams or hiding them under other stuff isn't always feasible.


Why couldn't the Jedi detect Senator Palpatine as having powers?

In Return of the Jedi, when trying to sneak into the base on a shuttle, Luke said he senses Darth Vader's presence and said he shouldn't have come lest he jeopardize the mission. Darth Vader also sensed Luke, but let him in anyways. Also, Yoda and Obi-Wan could detect the Force in young Anakin.  So if Jedi and Sith can detect each other, why couldn't they detect Senator Palpatine to begin with? It seems like a giant plot hole.


Prove that $\det(A)=p_1p_2-ba={bf(a)-af(b)\over b-a}$

Let $f(x)=(p_1-x)\cdots (p_n-x)$ $p_1,\ldots, p_n\in \mathbb R$ and let $a,b\in \mathbb R$ such that $a\neq b$  Prove that $\det A={bf(a)-af(b)\over b-a}$ where $A$ is the matrix:  $$\begin{pmatrix}p_1 & a & a & \cdots & a \\ b & p_2 & a & \cdots & a \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ b & b & b & \cdots & p_n \end{pmatrix}$$  that is the entries $k_{ij}=a$ if $i<j$, $k_{ij}=p_i$ if $i=j$ and $k_{ij}=b$ if $i>j$  I tried to do it by induction over $n$. The base case for $n=2$ is easy $\det(A)=p_1p_2-ba={bf(a)-af(b)\over b-a}$  The induction step is where I don´t know what to do. I tried to solve the dterminant by brute force(applying my induction hypothesis for n and prove it for n+1) but I don´t know how to reduce it. It gets horrible.  I would really appreciate if you can help me with this problem. Any comments, suggestions or hints would be highly appreciated


Use sed on a string variable rather than a file

I have been told it was possible, but without a single working example, that sed can read from a string variable without need for an input file. I have yet to get it to work.  For general safety, I’m writing the $PATH variable to another variable, as I mess with this, because I don’t need other problems to arise until I know exactly how to do this.  Consider the following:  ~$x=$PATH ~$sed -i 's/:/ /g' $x   this fails with: No such file or directory.  Here are some others I have tried:  ~$ sed -i 's/:/ /g' | (read x)  sed: no input files ~$ sed -i 's/:/ /g' | (read $x)  bash: read: `/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games': not a valid identifier sed: no input files ~$ sed -i 's/:/ /g' | $(read x)  sed: no input files ~$ sed -i 's/:/ /g' | $(read $x)  bash: read: `/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games': not a valid identifier sed: no input files ~$ sed -i 's/:/ /g' < $(read $x)  bash: read: `/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games': not a valid identifier bash: $(read $x): ambiguous redirect ~$ sed -i 's/:/ /g' < read $x  bash: read: No such file or directory ~$ sed -i 's/:/ /g' < (read x)  bash: syntax error near unexpected token `(' ~$ sed -i 's/:/ /g' < $((read x))  bash: /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games: syntax error: operand expected (error token is "/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games") ~$ sed -i 's/:/ /g' < $((read $x))  bash: read /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games: division by 0 (error token is "usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games") ~$ sed -i 's/:/ /g' << $((read $x))  > ;^C ~$ sed -i 's/:/ /g' << $(read $x) > ;^C ~$ sed -i 's/:/ /g' $x sed: can't read /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games: No such file or directory ~$ sed -i 's/:/ /g' < $x bash: /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games: No such file or directory ~$ sed -i 's/:/ /g' < echo $x bash: echo: No such file or directory ~$ sed -i 's/:/ /g' |  echo $x /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games sed: no input files   Can this even work? I would prefer not to need to write files I don't need just so I can use sed. For this particular example, if ~$x=$PATH ~$sed -i 's/:/ /g' $x actually worked the way I would have hoped, I would get:   /usr/local/sbin /usr/local/bin /usr/sbin /usr/bin /sbin /bin /usr/games /usr/local/games   which I could then assign to a variable, and use in future commands, like ls $x


I have script return JSON like this   {"a":"something","b":"something"} {"a":"something1","b":"something1"}   It's NDJSON response! Now i am trying to retrieve it from android but i get null on jsonResult. This is the code I use after fetching:  JSONObject jsonResponse = new JSONObject(jsonResult); JSONArray jsonMainNode = new JSONArray(jsonResponse);   I get null pointer exception on first line because jsonResult is null. What is wrong?  This is how i fetch:  HttpClient httpclient = new DefaultHttpClient(); HttpGet httpget = new HttpGet(url);  HttpResponse response = httpclient.execute(httpget); jsonResult = inputStreamToString( response.getEntity().getContent()).toString();


How are groups with the same Lie Algebra inequivalent?

I thought that groups with the same Lie Algebra are automatically equivalent, but there appear to be some exceptions to this?   What sort of exceptions are there and why?


Why were many users suddenly awarded the Generalist badge?

Lots of users were just awarded the  badge 30 minutes ago. What changed?


Replacing (not upgrading) Ubuntu 12.04.5 with 14.04

I have a new laptop. I have dual booted it with Windows 8.1 and Ubuntu by installing Ubuntu 12.04.5. I don't have any data on the Ubuntu side and can format it. I want to uninstall Ubuntu 12.04.5 completely and recreate a dual boot by installing Ubuntu 14.04. I do NOT want to upgrade; rather, I want to freshly install Ubuntu 14.04.  Is this possible? If so, how?


How to align text to the right in math mode?

I have a table of formulas, some have a description next to them, I want the equations to appear left flush and the text between parentheses right flush. I was writing it in the following way.  \documentclass[letterpaper,10 pt,twocolumn,fleqn]{article} \setlength{\columnsep}{2.5cm} \usepackage[inner=2.5cm,outer=2.5cm,bottom=2.5cm,top=2.5cm,landscape]{geometry} \usepackage{nopageno,array,graphicx,amsbsy,amsfonts}  \usepackage{amsmath}  \begin{document}        \[{\bf P} = \int_{t_i}^{t_f}{\bf F}\,dt = \Delta{\bf p}\mbox{\hspace{7mm} (Impulse) }\] \[\frac{dA}{dt} = \frac{l}{2\mu}=cte \mbox{\hspace{7mm} (Kepler's Second Law) }\] \end{document}   but the alignment is different for each equation.


Why is ray travelling through pole passes undeviated?( not changing any direction) ( this was asked in kvpy interview)


When I restart httpd, I get the following error.  What am I missing?  [root@localhost ~]# service httpd restart Stopping httpd:                                            [  OK  ] Starting httpd: Syntax error on line 22 of /etc/httpd/conf.d/sites.conf: Invalid command 'SSLEngine', perhaps misspelled or defined by a module not included in the server configuration   I have installed mod_ssl using yum install mod_ssl openssh  Package 1:mod_ssl-2.2.15-15.el6.centos.x86_64 already installed and latest version Package openssh-5.3p1-70.el6_2.2.x86_64 already installed and latest version   My sites.conf looks like this  <VirtualHost *:80> #    ServerName shop.itmanx.com     ServerAdmin webmaster@itmanx.com      DocumentRoot /var/www/html/magento     <Directory /var/www/html>         Options -Indexes         AllowOverride All     </Directory>      ErrorLog logs/shop-error.log     CustomLog logs/shop-access.log </VirtualHost>  <VirtualHost *:443>     ServerName secure.itmanx.com     ServerAdmin webmaster@itmanx.com      SSLEngine on     SSLCertificateFile /etc/httpd/ssl/secure.itmanx.com/server.crt     SSLCertificateKeyFile /etc/httpd/ssl/secure.itmanx.com/server.key     SSLCertificateChainFile /etc/httpd/ssl/secure.itmanx.com/chain.crt      DocumentRoot /var/www/html/magento     <Directory /var/www/html>         Options -Indexes         AllowOverride All     </Directory>      ErrorLog logs/shop-ssl-error.log     CustomLog logs/shop-ssl-access.log     </VirtualHost>


How to find out the default file manager in the terminal?

I'm working on different Linux distributions.  In my .bashrc I'd like to set up an alias that opens a window of the default file manager (e.g. nautilus, nemo, pacman, ...).  Is there a way find out what the file-manager of a session is? (It does also depends on the session, doesn't it?)


Lenovo laptop keyboard acts as if key is stuck

For the past year or so, my Lenovo W530 laptop has intermittently decided that I'm holding down the 'z' key. The key was never physically stuck; indeed, I could double the rate at which it typed z's by holding down the key! I always had to reboot to fix it, but the problem didn't crop up too frequently.  As of this evening, however, it has been constantly malfunctioning. It starts spamming z's within seconds of logging in - there is a bit of a delay before the horde of z begins.  In Windows 7, I can temporarily stop it by switching users, but it begins again before long. The issue also occurs in Ubuntu Trusty and a live-booted copy of Debian, so it's probably not caused by malware or something similar.  The issue does not occur in the BIOS menu.  I've combed through forum posts about stuck keys and whatnot, but I still haven't the foggiest idea about what's going on. Does anyone know what might be causing this?


can you explain me the working of this circuit in detail?

this circuit is a occupancy light circuit i want to know the working of the transistor regarding base,collector and emitter in the transitor


I've seen the cat command come up in some online stuff and I was curious as to what cat did and what it's for in the context of someone who is just doing some simple command line stuff.


Find the highest power of $2$ which divides the numerator of $H_{k}=1+\frac{1}{3}+\frac{1}{5}+\cdots+\frac{1}{2k-1}$

Question:     Let $k$ be give the postive integers,Find the highest power of $2$ which divides the numerator of   $$H_{k}=1+\dfrac{1}{3}+\dfrac{1}{5}+\cdots+\dfrac{1}{2k-1}$$   I found some case when $k=2$,then $$H_{2}=1+\dfrac{1}{3}=\dfrac{4}{3}$$,because the numerator $4$ havethe highest power of is $2$  when $k=3$,then $$H_{3}=1+\dfrac{1}{3}+\dfrac{1}{5}=\dfrac{23}{15}$$because the numerator $23$have the highest power of is $0$  when $k=4$,then $$H_{4}=1+\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{7}=\dfrac{176}{105}$$because the numerator $144$ have the highest power of is $4$  So I conjecture this problem answer is $2V_{2}(k)$.then How to prove？


Find a string in a file and replace the whole line

I am Recently quite new to python and am trying to write a script. What would be the easiest way to search for a string in a file and replace the whole line. I have found that re.sub can achieve this, but nothing is specific enough that I can do it.    For example:      #configuration file     Stuff that configures a file   to      #configuration file     Port 22   by searching for configures  Also does this command have different functions such as searching for a string   in the middle of a line and replacing everything after it.


Java: Constructor, initialization using new : Why this code doesn't print 512 in the last sentence?

I suppose this code prints 512, but it prints 100. I think  f = new Foo(512); change the reference of f from new Foo(100) to new Foo(512); then int num should be initialized as 512. But it doesn't. Is there any my misunderstanding regarding this code?  class Foo{   private int num;   public Foo(int n){     num =n;   }   public void setNum(int n){     num = n;   }   public int getNum(){     return num;   } } public class Bar{   static void changeFoo(Foo f){     f = new Foo(512);   }   public static void main(String[] args){     Foo f = new Foo(100);     changeFoo(f);     System.out.println("f is " + f.getNum());   } }


How to change the default views of quad view in blender 2.8?

I have the same question as  but for Blender 2.8 where you can not press N to display the View Properties. I would like to have a 3ds max view and change the viewports accordingly.


I'm having a problem with Blender after a recent GPU crash. While rendering a moderately intense scene in Cycles, my computer locked up and I had to do a hard shut-down. Ever since, Blender's LookDev mode has only shown me a grey screen. I can 'see' the edges of my plane, but no other details, no textures or materials. Lighting does not work at all for me in this mode. Eevee also does the same thing in either LookDev or Render modes, with even more broken results sometimes in the form of reflective artifacts. I have tried importing my scene into a new file. I updated to a newer version of Blender, and I also re-installed my graphics drivers. None of these gave any improvements. I am at a loss and a bit of a wall, as I am having a hard time working on my file without LookDev mode. Any and all help is appriciated. Scene shown in Solid View mode with random colors.  Scene shown in LookDev mode, grey screen with some edges barely visible.


trigonometrical inequality $\tan{A} + \tan{B} + \tan{C} = \tan{A}\tan{B}\tan{C}$, Hint to prove $S2\neq 1$?

I was studying conditional identities for triangle in trigonometry where I had to prove that $\tan{A} + \tan{B} + \tan{C} = \tan{A}\tan{B}\tan{C}$ So I started with $\tan({A+B+C)}=\frac{S1-S3}{1-S2}$ where $S1=\sum_{cyc}\tan A$,  $S2=\sum_{cyc}\tan A.\tan B$ and  $S3=\prod_{cyc}\tan A$ Now since $A+B+C=\pi$ and since $\tan\pi=0$, therefore $\frac{S1-S3}{1-S2}=0$ and hence $S1=S3$ but I got stuck when I realized that another condition, $1-S2\neq0$ should also be true. Now I can't prove this. I'm not having any idea how to start to prove $S2\neq1$ for a triangle. please give me a hint.


What evidence exists for string theory viability?

I know that string theory is still under heavy development, and as such it still can't make predictions (or not that many predictions anyways).  On the other hand, it is clear from the number of years this theory has been under development and from the large number of theoretical physicists studying it, that it is considered a good and viable candidate as a quantum gravity theory.     So, what is the evidence that this is true? Why is it considered such a good candidate as the correct quantum gravity theory?   Without wanting to sound inflammatory in the least, it has been under heavy development for a very long time and it's still not able to make predictions, for example, or still makes outlandish statements (like extra dimensions) that would require a high amount of experimental evidence to be accepted. So - if so many people believe it is the way to go, there have to be good reasons, right? What are they?


what are path and environment variables, and how I set or use them?

I have tried to set the environment variables through command prompt and through control panel. but when i run the echo command its not showing the added path. Please help me to add the path.


Landsat 8 cloud/cloud shadow/snow masking in Google Earth Engine

I am a new Google Earth Engine user and I am trying to understand basic procedures/functions. More specifically, I want to remove clouds, cloud shadows and snow pixels form a Landsat 8 collection and then, calculate the NDVI. I have found the following sample code but I can not understand how to remove apart from the clouds, the cloud shadows and the snow. I think the Fmask might be he way to do this but I can not understand this.  Example code from :    // This function masks clouds in Landsat 8 imagery. var maskClouds = function(image) {   var scored = ee.Algorithms.Landsat.simpleCloudScore(image);   return image.updateMask(scored.select(['cloud']).lt(20)); };  // This function masks clouds and adds quality bands to Landsat 8 images. var addQualityBands = function(image) {   return maskClouds(image)     // NDVI     .addBands(image.normalizedDifference(['B5', 'B4']))     // time in days     .addBands(image.metadata('system:time_start')); };  // Load a 2014 Landsat 8 ImageCollection. // Map the cloud masking and quality band function over the collection. var collection = ee.ImageCollection('LANDSAT/LC08/C01/T1_TOA')   .filterDate('2014-06-01', '2014-12-31')   .map(addQualityBands);  // Create a cloud-free, most recent value composite. var recentValueComposite = collection.qualityMosaic('system:time_start');  // Create a greenest pixel composite. var greenestPixelComposite = collection.qualityMosaic('nd');  // Display the results. Map.setCenter(-122.374, 37.8239, 12); // San Francisco Bay var vizParams = {bands: ['B5', 'B4', 'B3'], min: 0, max: 0.4}; Map.addLayer(recentValueComposite, vizParams, 'recent value composite'); Map.addLayer(greenestPixelComposite, vizParams, 'greenest pixel composite');


Compare files that are in directory 1 but not directory 2?

I'm having trouble with a bash script I want to make  I know ls will list files that are in a directory but I want it to list directories that are in directory1 but NOT in directory2, and then list files in directory2 that are NOT in directory1.  In a feeble attempt, I tried:  ls -al | diff directory1 directory2   Quickly I realized why it didn't work. Can anyone help out a total bash nerd out?


Looping through a file with two columns and reading those two columns

I have a txt files with all the file names I need to analyze. I have this file (inputFile.txt) :  /path/file1a  path/file1b  /path/file2a  path/file2b   i have a code which needs two two input files in order to run.   ./Analyzethis /path/file1a /path/file1b   i am trying to create a bash loop to go through my txt files, read through each row and run my code.  I had  #!/bin/bash IFS=$'\n'; for FILE1 in `cat inputFile.txt`; do ./Analyzethis $FILE1; done   but, it doesnt work. How can i loop through each row and use the columns with the bash loop?


so I'm trying to make a game menu, but both buttons that switch to totally different scenes lead to the same one.There are two planes, and one is connected to one scene, while the other is to another scene. but when i play the game, both scenes go to the same one. help.


How to dynamically prepare sql statement which also dynamically include the fields name

How to prepare fields name dynamically in sql statement.   Here is my query but it return 500 error. Im guessing this is because I'm preparing names dynamically.   Is there any way to prepare fields name dynamically in sql statement.   if (!($update_stmt = $mysqli_scs->prepare("UPDATE `signs_sgn` SET ? = ? , ?=? WHERE (`signcode_sgn`= ?) LIMIT 1;"))) {                 echo "Prepare failed: (" . $mysqli_scs->errno . ") " . $mysqli_scs->error;             }   Many Thanks


Using PostGIS relationships (M:N) in QGIS without loading all related tables in layertree

I am working with a PostgreSQL/PostGIS (version 12.3/3.0.1) database and I am using QGIS (version 3.10) to visualize and work with my data. In the database I have two schemas:  schema for spatial data tables, e. g. gebaeude schema for documents, e. g. dokument, dok_gebaeude (without spatial information)  I set a m:n relation between gebaeude and dokument using the table dok_gebaeude. My tables are:  dokument: id, bezeichnung, dateityp, pfad  dok_gebaeude: id, fk_dokument, fk_gebaeude --> fk_dokument references dokument(id) and fk_gebaeude references gebaeude(id)  gebaeude: id, geom, nummer, nutzung   In QGIS I loaded the relationship with the project properties>relation manager and I can use it to connect documents (stored in table dokument) with gebaeude-objects. All work fine. BUT... In QGIS I only need the table gebaeude and I don´t want to load the tables dokument and dok_gebaeude in my layers (the latter are only technical tables). Unfortunately it is neccessary to load all three tables (dokument, gebaeude and dok_gebaeude) in my layers in QGIS, otherwise I am not able to add the relationship in my project properties>relations. Is there any possibility to hide or remove or not even load tables (dokument and dok_gebaeude) in my layertree without losing the relationsships?


Calling generic method with a type argument known only at execution time

Edit:  Of course my real code doesn't look exactly like this. I tried to write semi-pseudo code to make it more clear of whay I wanted to do.  Looks like it just messed things up instead.  So, what I actually would like to do is this:  Method<Interface1>(); Method<Interface2>(); Method<Interface3>(); ...   Well ... I thought that maybe I could turn it into a loop using reflection. So the question is: How how do I do it. I have very shallow knowledge of reflection. So code examples would be great.  The scenario looks like this:  public void Method<T>() where T : class {} public void AnotherMethod() {     Assembly assembly = Assembly.GetExecutingAssembly();      var interfaces = from i in assembly.GetTypes()     where i.Namespace == "MyNamespace.Interface" // only interfaces stored here     select i;      foreach(var i in interfaces)     {         Method<i>(); // Get compile error here!     }       Original post:  Hi!  I'm trying to loop through all interfaces in a namespace and send them as arguments to a generic method like this:  public void Method<T>() where T : class {} public void AnotherMethod() {     Assembly assembly = Assembly.GetExecutingAssembly();      var interfaces = from i in assembly.GetTypes()     where i.Namespace == "MyNamespace.Interface" // only interfaces stored here     select i;      foreach(var interface in interfaces)     {         Method<interface>(); // Get compile error here!     } }   The error I get is "Type name expected, but local variable name found". If I try  ...     foreach(var interface in interfaces)     {         Method<interface.MakeGenericType()>(); // Still get compile error here!     } }   I get "Cannot apply operator '<' to operands of type 'method group' and 'System.Type'" Any idea on how to get around this problem?


Convergence of the Cauchy product of series

Determine whether the following series is convergent or not  $$2\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n+1}\sum_{k=1}^{n}\frac{1}{k}$$  My trial : Since I was stuck in this problem, I drew the sequence in computer so that I was convinced it converges to zero. So, In order to use alternating series test, I tried to show $\frac{\sum_{k=1}^{n}\frac{1}{k}}{n+1}$ is decreasing and converge to zero. I can identify the series is decreasing, but I was stuck in showing it converges to zero. Could you give me a few hint to proceed the next step..?


How can I execute a script that needs sudo permission in the background?

Since my Asus VivoBook keyboard shortcut to change de keyboard lightning level is not working, I made a bash script and configured it to be activated when I press a combination of keys. This is my script:  level=$(cat /sys/class/leds/asus\:\:kbd_backlight/brightness)  [[ $level = 3 ]] && echo 0 | sudo tee /sys/class/leds/asus\:\:kbd_backlight/brightness || echo $(($level+1)) | sudo tee /sys/class/leds/asus\:\:kbd_backlight/brightness   The script is working when I run it on terminal, but when I press the keys, it doesn't, I think because of the sudo permission that requires a password. Is there any way I can change the script permissions so that when I run it in the background it doesn't request for the password?


With the plane added delete 1 edge and bevel the side corner and with the bevel circle i have bevel it. Problem it bevel but the center part is flat and the both end are rounded like a tube. I have set the radius 1 yet to cant find the result to be fully tube.


In what sense is the kernel of a group homomorphism a universal?

Question: In what sense is "the kernel of a group homomorphism a universal"?  Do we here mean that a group homomorphism is a universal arrow in some comma category? If so, what comma category?  Attempt: If we let $K$ be a normal subgroup of $G$ and $i: K \rightarrow G$ being the inclusion homomorphism, then for any other normal subgroup $T$ of $K$ with $k : T \rightarrow K$ being another inclusion homomorphism and likewise with $j : T \rightarrow G$, then we have that $j = i \circ k$.  Now let $C$ be the category of the subgroups of $G$ with inclusion homomorphisms as morphisms. Let $S: C \rightarrow C$ be the identity functor on $C$.  Then do we not here have that $(K, i)$ is a universal arrow in $(C \downarrow G)$? And if so, is this the sense in which "the kernel of a group homomorphism is a universal"?  EDIT: Answers in another thread on this site have confused me in the sense that they don't discuss explicitly about universal arrows and comma categories.


How can I get a specific line from a file?

I want to extract an exact line from a very big file. For example, line 8000 would be gotten like this:  command -line 8000 > output_line_8000.txt


Which ISO should I use for the cleanest image?

Assume the case of a Canon 6D Mark II. Its lowest ISO is regulary 100. If expanded, I can set it to L, which is ISO 50.  Until now, I was always under the impression the lower the ISO the cleaner the image, so whenever possible I've been using ISO 50. Now I came across this chart from :    And that leaves me completely confused. According to this chart, I have a lower noise at ISO 100. ISO 50 seems to have a higher noise than ISO 300 too. Is that anywhere near correct? As long as I would not be clipping highlights, couldn't I just use ISO 160, 300 or 600 instead of lets say 50, 200 and 400 (depending on my needed exposure) and later drop down the exposure in post to get a cleaner image?  I've seen  question about ISO 50 but the two top answers are kinda contradicting:     Since your camera offers this 'expanded ISO" that provides for 80 ISO, you can assume that this ISO is sub-optimal, and could exhibit more noise or a loss of dynamic range than the 'native' ISO. [...]  Some suggest Canon cameras are 'native' for ISO 100, and full stop ISO are best (100,200,400 etc.).   Vs.:     You can use it and it gives excellent dynamic-range and very low image noise but really barely any different from the ISO 100 setting.   The chart above would suggest the first answer is right, but that definitely doesn't hold true for the latter part of the quote, as ISO 160, 300 and 600 seem to be the best choices.  Can someone tell me if I interpret the chart correctly, and if ISO 160, later darkened in post, will really give me cleaner, less noisy images in the end than using ISO 50 (assuming that would be the perfect exposure) in the camera right away?


I can not open softwer boutique ,or pacage manager

the error message was: 'Error: Opening the cache(E:Malformed entry 52 in list file/etc/apt/sources could not be read.)


I am a beginner in Quantum Mechanics so i am pretty new to the EPR paradox although i have heard about it a long time ago but finally studying in detail. And came across a doubt: Why the hidden characteristics in any particle as predicted by Einstein can not exist? If anyone can provide an  elaborated explanation !


Can I get the sum() using entity framework

I want to calculate the sum of a column note that:column result showed as column in a table produced by calling stored proc with entity framework and AJAX  The code below show Web method that call the stored proc called divideTypes   if (ddlTer == "0")     {          var sp = db.divideTypes(dateFrom, dateTo, ddlType).ToList();         foreach (var u in sp)         {             result += "
";             result += "" + u.custid + "	";             result += "" + u.custname + "	";             result += "" + u.depno + "	";             result += "" + u.Terr + "	";             result += "" + u.deidate + "	";             result += "" + u.gooddesc + "	";             result += "" + u.custdec + "	";             result += "" + u.pkg + "	";             result += "" + u.wt + "	";             result += "" + u.vwt + "	";             result += "" + u.lcamt+ "	";             result += "" + u.invno + "	";             result += "" + u.invamt + "	";             result += "
";         }      }   Note: I used to call stored proc because there's many join statement in SQL command so I cannot deal with it.   My question is how to get the sum of u.invmat column? (In any way)


resource to learn group theory like Brilliant.org provide

I was thinking to self study Group theory as my university was closed. I choose Abstract Algebra by I.N. Herstein to understand group theory because I have to cover Abstract Algebra also in the future course. But the main problem is I can't visualize or fully grasp those concepts. After spent some time on internet I found , and realized that the way they drive into this subject is much interesting. But I can't afford their premium membership that's why just complete the Introduction part.  I've had some work with proofs and I have also taken classes at university such as real analysis(Understanding Analysis by Stephen Abbott), linear algebra, and differential equations.  Is there any resource which also drive into group theory like they do or I can visualize while reading?  I heartily thank if anyone helps me to understand this subject.


How to do something to each file in a directory with a batch script

How do you iterate over each file in a directory with a .bat or .cmd file?  For simplicity please provide an answer that just echoes the filename or file path.


Thas the effect of Spirit Shield of the Path of the Ancestral Guardian can happens after the effcts of Ancestral Protectors?

this question is something that has been in my head for some time. is says that with Ancestral Protectors of some one gets hit they half the damage, so can you use Spirit Shield after the effect of Ancestral Protectors to reduce even more damage, that if you thit the effect of Spirit Shield bifore the damage is half¡?


Clicking "answered" or "modified" when answers are paginated should go to the answer anyway

A high-traffic question ( ) showed up at the top of the questions list today with a new answer from a low-rep user.    Because I knew that question had a lot of answers, I clicked on the word answered to go straight to the answer. Instead I just found myself at the top of the question page. This is what happens on sites where I have a lower rep and can't see deleted posts; if I click answered for a deleted answer I just see the question. But I can see deleted posts on meta.  I found the answer eventually towards the bottom of page 2 of the 3 pages of answers. While questions whose answers need to paginate are a bit of an edge case, they are one of the times we need this feature the most. Please make it work.


Let $G$ a group with normal subgroups $M,N$ such that $M\cap N=\{e\}$. Show that if $G$ is generated by $M\cup N$ then $G\cong M \times N$.

Let $G$ a group with normal subgroups $M,N$ such that $M\cap N=\{e\}$.   i) Show that for every $m\in M$ and for every $n\in N$, $mn=nm$.   ii) If $G$ is generated by $M\cup N$ then $G\cong M \times N$.   This is an homework question for abstract algebra. I think I can prove $i)$. But I have no idea how to prove $ii)$. Can anybody give me a hint for this one ?    Here my proof for i): Let $n \in N$ and let $m\in M$. Let $x=mnm^{-1}n^{-1}$. As $N$ is normal subgroup, $mnm^{-1} \in N$. Therefore $x \in N$.  As $M$ is normal subgroup , $nmn^{-1} \in M$. Since $m\in M$, then $x=m(nm^{-1}n^{-1})\in M$. This implies that $c\in M \cap N$, then $c\in \{e\}$, then $c=e$, and we get $mn=nm$.


What do I do when no rules cover what players improvise, and I don't know from real life?

I'm a fairly new DM running my first campaign. What do I do when players try something, but there are no rules for it, and my real-world knowledge doesn't help me figure out what would happen?  For example, in our last session one of my players wanted to start a fire in front of a cave to drive the inhibitants out. There are no printed guidelines for this, and I don't know how or whether that would actually work — I've never done anything remotely like lighting a fire to smoke something out of a cave before. I didn't know what would or should happen (How long does the fire have to burn for the plan to work? How deep into the cave would the smoke go?), but more importantly I didn't know how to deal with this and move the game forward, which is the DM's job. Luckily the other players talked him into a different plan, but I don't know what I would have done.  When a situation comes up in the game where there are no direct rules and one doesn't have the expertise to know what should happen, what is a DM to do?


Get to Schiphol early in the day/sleep at airport?

I will depart from Schiphol on a Sunday at 10:00, and return on some other day at 05:00. What options do I have to travel to/from Schiphol Airport?   I'd prefer the train, but if I am not mistaken, the first connection from Heerlen will arrive on 09:56, so this is no option. I could take the car, parking for two weeks is 100€. But I will have to drive back after a night in the plane, possibly without sleep. So, no option either, I guess. Third option is to try to get a hotel room. Best rates I found are 150€ per night. Any tips on that? The last night train arrives 04:00. Since I will travel with my sleeping bag could I just take a nap somewhere near/at the airport?


I have a CSV file  that has following form.      I read the CSV using CSV reader. It outputs the objects in following form instead of the string.  Output  [Ljava.lang.String;@138617da  **  This is my code. What is wrong with code?     public  void readFeatures () throws IOException{             File(classLoader.getResource(filename).getFile());      CSVReader reader = new CSVReader(new FileReader(file));     List myEntries = reader.readAll();      for( int i = 0; i< myEntries.size(); i ++){         System.out.println(myEntries.get(i).toString());     }  }


Proving a combinatoric proof using the result of $\sum_{k=0}^n \binom nk\ (-1)^k = 0$

so I am supposed to solve a proof which seems fairly easy, but the negative exponents in $$\sum_{k=0}^n \binom nk\ (\frac{(-1)^k}{k+1})= \frac{1}{n+1}$$ are making this question very difficult for me. I have tried using binomial theorem on the right side with $(n+1)^{-1}$ but I understand that operation does not make sense. I can also tell that the only difference between the two proofs is that the left side has an additional $(k+1)^{-1}$ and the right side has an additional $(n+1)^{-1}$, but I am still having difficulty solving this question. Hints appreciated.


Understanding the definition of manifolds with boundary

One example of a manifold with boundary is said to be the $n$-dimensional disk, so $M:=\{x\in\mathbb{R}^n:||x||\le 1\}$. In order to show this, one has to show there are charts $h_i:U_i\to U_i^\prime\subseteq\mathbb{R}^n_-=\{(x_1,...,x_n)\in\mathbb{R}^n:x_1\le 0\}$ with the properties of an atlas for normal manifolds. So basically the charts have to homeomorphically map the manifold to open sets in the "half-plane". To verify the example of the disk, can't I just take the translation $h:M\to M-(1,0,...,0)\subseteq \mathbb{R}^n_-$ as an atlas consisting of just a single chart? Moreover for any bounded set in $\mathbb{R}^n$, can't I just translate it into $\mathbb{R}^n_-$ and get a manifold with boundary?


Show there exists $g:(0,1)\to\mathbb{R}^2$ such that $h\circ g$ constant, $g$ continuously differentiable and $g$ injective

Let $h\in C^1(\mathbb{R}^2,\mathbb{R})$. Show:   There exists $g:(0,1)\to\mathbb{R}^2$ such that $h\circ g$ constant, $g$ continuously differentiable and $g$ injective.   Dini's theorem:  Let $\Omega \subseteq \mathbb{R}^2$ open, $f \in C^1(\Omega, \mathbb{R})$ and $p \in \Omega$ with $f(p) = 0$.  If $\frac{\partial f}{\partial y}(p) \neq 0$, then there exist open intervals $V_1, V_2$ with $p \in V_1 \times V_2 \in \Omega$ and $g \in C^1(V, \mathbb{R})$ with $$\{(x,y) \in V_1 \times V_2 \mid f(x,y) = 0 \} = \{(x,g(x) \mid x \in V_1\}$$ and $g$ furthermore satisfies $$g' = -\left(\frac{\partial f}{\partial y}(x, g(x))\right)^{-1}\frac{\partial f}{\partial x}(x, g(x)).$$  Proof of existance of $g$:  Let without loss of generality $\frac{\partial f}{\partial y}(p) \gt 0$.  Then there exists $\epsilon \gt 0$ with $\overline{B_\epsilon(p)} \subseteq \Omega$ and $\frac{\partial f}{\partial y} \gt 0$ on $\overline{B_\epsilon(p)}$.  Let $y^- = p - \frac{\epsilon}{2}$ and $y^+ = p + \frac{\epsilon}{2}$. Then there exists $\delta \in (0, \epsilon)$ with $f(x, y^-) \lt 0 \lt f(x, y^+)$ for $x \in (p - \frac{\delta}{2}, p + \frac{\delta}{2}) =: V_1$ and $(y^-, y^+) =: V_2$.  For $x \in V_1$ there exists exactly one $y \in V_2$ with $f(x,y) = 0$ (mean value theorem). Set $y(x) := g$ and the claim follows.


Finding some points with which one can calculate the integral of multiplication of two functions

Let $f,g:[a,b]\to\mathbb{R}$ be two Riemann integrable functions. For each partition $P=\{t_0,...,t_n\}$ of $[a,b]$ take some points in two different ways, that is by choosing two points $\eta_i$ and $\xi_i$ belonging to each $[t_{i-},t_i]$.      show that $$\lim_{|p|\to 0}\Sigma_{i=1}^{n}f(\xi_i)g(\eta_i)(t_i-t_{i-1})=\int_{a}^{b}f(x)g(x)dx.$$   I tried to use the definition of upper and lower integral and as $fg$ is integrable we have equality instead of nonequality. However I got nowhere.   Thanks in advance.


Are better SSL certificates (better type or better encryption) better for SEO?

I was looking at the different types of SSL certificates and providers. I came across a website that states this:     We believe Extended and Business Verification SSL certificates gets more top rankings instead of Domain verification certs, but that is minor changes in Google algorithm   I searched Google but could not find any mention that the way a certificate is validated affects SEO (specifically with Google). I saw some websites suggest using a high key size for the certificate but I'm thinking that's for security?  Questions: Does Organization Validation (OV) and Extended Validation (EV) certificates get a better rank than Domain Validation (DV) certificates? What about the (RSA) key size?


I removed /bin on my Mac, How can I restore it?

I removed the /bin instead of ~/bin :(  My laptop no longer boots up! It has no DVD or CD drive!  How can I restore the OS X?  It is MacBook Pro OS X 10.8, SSD 128GB.


shell script edited on windows displays unexpected error message

I am having some trouble running a script to ssh to a remote server. If I simply ssh from the command line I have no trouble reaching the server, but when I run a script to do this I get an error, "Name or service not knownname". I have added the IP address and host name to /etc/hosts and that did not help.   My script is simply:   #!/bin/bash  ssh username@hostname   Am I doing something wrong? Obviously I don't need a script just for this, but I'm going to add commands to execute once I get this working.


Prove the Trigonometric Identity: $\frac{\sin x}{1-\cos x} = \frac{1+\cos x}{\sin x}$

I'm doing some math exercises but I got stuck on this problem.  In the book of Bogoslavov Vene it says to prove that:  $$\frac{\sin x}{1-\cos x} = \frac{1+\cos x}{\sin x}.$$  It is easy if we do it like this: $\sin^2 x = (1-\cos x)(1+\cos x)=1-\cos^2 x$. But how to prove it just by going from the left part or from the right  Can anybody help me?  Thank you!


Why do we only see $L_1$ and $L_2$ regularization but not other norms?

I am just curious why there are usually only $L_1$ and $L_2$ norms regularization. Are there proofs of why these are better?


Compare two unordered lists in Excel and return differences

I have two Excel files, with customer data. I need to compare the two.   I have copied the username column from both into a new sheet. Now I want to go through, and if the username is in the first column and the second, ignore that record. So I have a list of only the unique usernames.  The lists are not in any order, so I cannot just compare each column depending on row, I need to compare one cell, to all the cells in the other column, all the way through.  Is this even possible? I have never used Excel before.


figures and text do not appear in the right order

That's my code  \subsection{Here is the subsection}  Here is the text\\  \begin{figure}[htbp]      \centerline{\resizebox{\width}{5cm}{\includegraphics[scale=0.5]{r1.png}}}      \caption{Here goes the caption.}  \end{figure}  More text\\  \begin{figure}[htbp]      \centerline{\resizebox{\width}{5cm}{\includegraphics[scale=0.5]{e1.png}}}      \caption{Here goes the caption.}  \end{figure}  More text\\  \begin{figure}[htbp]     \centerline{\includegraphics[scale=0.35]{r_e1.png}}     \caption{Here goes the caption.}  \end{figure}   The order in which they appear on the pdf is:  1.Text all together at the beginning of the subsection  2.all figures.  Before I added the captions I think there was no such problem. Any clue?


How to build large demultiplexers using SystemVerilog?

Note: This question about demultiplexers is similar to but not identical to  which is about multiplexers. I want to build a fully parameterisable demultiplexer in SystemVerilog. So far, I know how to build demultiplexers of variable widths like this: module scale_mux #(parameter WIDTH = 1) (   input logic sel_a,         logic [WIDTH-1:0] in,   output logic [WIDTH-1:0] out_a, out_b);    always_comb     unique case (sel_a)       1'b1 : out_a = in;       1'b0 : out_b = in;     default: out = 1'bx;     endcase  endmodule   I also know how to extend this for 1:4 and 1:8 demultiplexers. But the number of case statements for large demultiplexers will be a lot. I'd like to build a demultiplexer in which the number of inputs is variable. I'm not sure how I can extend the case statement for the n input case, do you have any ideas?


Digging a hole in the moon across its diameter

What will occur if one digs a hole in some moon/dead-planet without an atmosphere (and without a Lava Core), such that this hole shall have a 1 meter diameter and will be so deep that shall go through its core and appear on the other side of the moon?  Then one shall jump (or drop a ball) into that hole.  Will the object simply reach the other side of the planet/moon at speed of 0? Thus a harmonic motion from side to side of the planet?  Addition: Differences from :   This is vacuum (no atmosphere) I drop an object and do not jump inside the hole


How to Authenticate when Accessing Custom Apex REST Web Service

I thought this would be a simple thing to find, but all the documentation deals specifically with either creating an Apex web service, or accessing the SF REST API in some general way - but what about accessing a custom Apex web service?   To be more clear, when a developer creates a post request to an Apex web service, what do they include in the headers or body of that post request so that they are able to access the Salesforce endpoint?  For example, one might make a request to a custom SF web service like this:  HttpRequest request = new HttpRequest();      request.setEndpoint('https://yay.my.salesforce.com/services/apexrest/CreateDOService/v1'));      request.setMethod('POST');      request.setHeader('Content-Type', 'application/json;charset=UTF-8');      request.setHeader(Does some token go here? How do I get it?);      request.setBody('{"Event":"Thing Returned"}'); HttpResponse response = http.send(request);   What else needs to be included?  I see references to OAuth 2.0, SessionIDs, and connected apps in the documentation below, but I can't find any actual examples of code that uses these things. Once I create a connected app for an external application, how do I tell the developer of that application to use the connected app? What kind of code do they need to write?       Many thanks for any code examples you could provide.


Cosmology: Is there any experimental evidence for the redshift scale-factor relation?

Modern cosmology relies heavily on the redshift scale-factor relation $$a=\frac{1}{1+z}$$ But what is the experimental evidence for it? It's derived in textbooks from General Relativity, but for all other predictions of GR there have been stringent tests.  The bending of light by stars, precession of the perihelion of Mercury, the equivalence principle, time dilation, etc... have all been subject to high precision tests.  Even if GR is correct, it's possible that the derivations misinterpret something... Have any tests been done, or are any planned, that that look for direct experimental evidence of the relation?  The question is different to this one  as it asks specifically about attempts to experimentally verify the redshift scale-factor relation.


I just came across on lyrics of Eminem's "survival" which confused me. Here is piece of song which confused me.     Throw me to them wolves and close the gate up on me.   I thought that correct phrase is their wolves instead them wolves. Am I right?


Cannot enable shopt extglob from bash command string argument? (temporarily set shopt extglob)

I'm using bash version:  $ bash --version GNU bash, version 4.4.23(1)-release (x86_64-pc-msys)   So, say I have these files:  $ ls a.txt  aa  b.txt  bb  README   Say, I want to list anything but aa; (EDIT: but I do not want to enable extglob permanently - just want to enable it for a single command run!) if I do this:  $ bash  $ shopt -s extglob  $ ls -x ./!(aa) ./a.txt  ./b.txt  ./README  ./bb: bb.txt  $ exit   ... then it seems shopt works fine; but if I try it as a one-liner, inside a command string:  $ bash -c 'shopt -s extglob ; ls -x ./!(aa)' bash: -c: line 0: syntax error near unexpected token `(' bash: -c: line 0: `shopt -s extglob ; ls -x ./!(aa)'   ... although, this (running in subshell with parentheses) works (although, it seems it changes the shopt also for the parent shell? and actually, for all open shells under MSYS2 ?!??):  $ echo $(shopt -s extglob; ls -x ./!(aa)) ./a.txt ./b.txt ./README ./bb: bb.txt   Why does this happen - why can't the shopt -s extglob be enabled/executed when running as part of a bash command that is specified from the command line (via the command line argument -c)?


Theory behind partial least squares regression

Can anyone recommend a good exposition of the theory behind partial least squares regression (available online) for someone who understands SVD and PCA?  I have looked at many sources online and have not found anything that had the right combination of rigor and accessibility.    I have looked into The Elements of Statistical Learning, which was suggested in a comment on a question asked on Cross Validated, , but I don't think that this reference does the topic justice (it's too brief to do so, and doesn't provide much theory on the subject).  From what I've read, PLS exploits linear combinations of the predictor variables, $z_i=X \varphi_i$ that maximize the covariance $ y^Tz_i $ subject to the constraints $\|\varphi_i\|=1$ and $z_i^Tz_j=0$ if $i \neq j$, where the $\varphi_i$ are chosen iteratively, in the order in which they maximize the covariance.  But even after all I've read, I'm still uncertain whether that is true, and if so, how the method is executed.


How to enter a string from a variable into a textarea?  When i use the  it brings in the value fine. but need to have a textarea as the text would be quite long. I've got the textarea appearing but no content within it
Description:<input type="text" name="description" value="<?php echo $description; ?>" readonly>
Description:<textarea name="description" value="<?php echo $description; ?>" readonly></textarea>


I was checking  that was posted on Twitter where everyone seemed to be so enthusiastic about, so I had a short check on it. Here is the first line:  Post-Cartesian frameworks, including developments within the embodied and enactive cognitive sciences, complex systems science, and dialogical approaches to cognition, strongly emphasize the inherently indeterminable nature of the person and the inextricably entangled relationship between person, other, and technology.  And it goes on with:  Automation, on the one hand, is something that is achieved once a given process is complete, that is, it is understood, and discrete such that it can be implemented from a set beginning to a set finish reliably. People and social systems, on the other hand, are partially-open, always becoming, and inherently unfinalizable (Bakhtin, 1984). Automation as complete understanding, therefore, stands at odds with human behaviour, which is inherently incomplete, making machine classification and prediction futile.  Is it me, or is this paper obscurely written? And why didn't anyone seemingly notice it, given that it was both peer-reviewed and published? Why were people so enthusiastic about it, instead of admitting they just didn't have a clue of what it is about (or at least to understand the arguments presented in the paper)? Why is there still so much academic gibberish? Related link:  Edit: My mistake! It might not be peer reviewed. But I'm still wondering if this is very common in academia, or if it is dependent from field to field?


Why do dead bodies only reanimate beyond the Wall?

Why do dead bodies beyond the Wall reanimate but those south of the Wall do not?                                  We only see dead bodies reanimate in Castle Black, but further south the dead do not come back to life.  Is there a reason for this? Or is this just something that happens in that region?


"The" and "A" at the beginning of explanation

I am little bit confused about the usage of the article "The" and "A". For example, following pages start their description from "A".  Starts with "A"       A laptop (also laptop computer), often called a notebook, is ...        A dictionary is a listing of words in one or more specific languages ...   On the other hand, following pages start with "The".  Starts with "The"       The electron is a subatomic particle, symbol ...        The pipe organ is a musical instrument that ...   Each word is countable noun and they do not have any context because all of them are first line of the explanation.  Even the purpose looks same for me. I mean, all of them explain abstract nature of the noun.  What is the difference "The" and "A" in such the case ?


I've been trying to install steam all day and I've been encountering all kinds of problems, but I'd like a little bit of help with this specific one:  Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  steam:i386 : Depends: libgl1-mesa-glx:i386 E: Unable to correct problems, you have held broken packages


Is the population parameter more likely to occur closer to the sample statistic?

When we use the sample statistic to find a confidence interval, is there any reason to using the sample statistic after that, when we can instead refer to the confidence interval? For example, let's say I have a sample mean of 50 and have determined a +- 5 interval with 95% confidence. I could say "The population average is 50, plus-or-minus 5, with 95% confidence" I could also say "The population average is between 45 and 55, with 95% confidence" Is the probability of the population parameter occurring uniform across the confidence interval, or, would it be more likely to occur closer to the sample statistic? The reason I ask, is, it seems to me that if the population parameter is more likely to occur closer to the sample statistic then it's useful to say "50, plus-or-minus 5", while if it's uniform then "between 45 and 55" is simpler.


How do I add myself back as a sudo user?

I clean-installed Ubuntu 11.10 today, and then installed VirtualBox.  This required me to add myself to the vboxusers group, and since 11.10 seems to no longer have a graphical app to add users to a group, I ran the following command:  sudo usermod -G vboxusers stephane   This is a problem.  I now see what I should have run instead is:  sudo usermod -aG vboxusers stephane   The end result is I'm no longer in the groups I should be in.  Including whatever group is required to run "sudo".  When I run any command as sudo now, I get the following:  $ sudo ls [sudo] password for stephane:  stephane is not in the sudoers file.  This incident will be reported.   Is there a way to fix this, or do I need to re-install from scratch again?


Segmentation fault (core dumped) in C, The C Programming Language by K&R Exercise 2.5

I am writing a code for squeeze(s1,s2) that deletes each character in string s1 that matches any character in string s2 and I get "Segmentation fault (core dumped)" when I try to run the program. I believe the error comes from in how i call the function inside the main(). I am a beginner and I don't know how to call functions. Please help!  #include<stdio.h> void squeezer(char s[], char c[]);  main() {     squeezer("abcdefgabcdefgabcdefg", "abcd"); } void squeezer(char s[], char c[]) {     int i,j,k,z;     for(k=0; c[k] != '\0'; k++) {         for(i=j=0;s[i] != '\0';i++) {             if (s[i] != c[k]) {                 s[j++] = s[i];             }         s[j] = '\0';         }     }       for(z=0; z < j; z++)         printf("%c",s[z]); }


Does a reference have a storage location?

Does a reference have a storage location or is it just an alias for another location? Does this differ by C++ revision or is it consistent with all versions of C++? And if a reference has a storage location, does it then just allow value semantics on a pointer like type?  How would a reference work when you use it as such:  struct aStruct{    int aVariable;    aClass& aReferencetoaClass; };   Does it take up space or is it an alias?


I read the summary of deniable encryption on wikipedia:   Then I read a question, by doom123 on security.SE:   But I had a subtly different problem which can be stated as follows:   Alice wants to send Bob the book "Mocking Jay" which is banned in Bob's country.  Alice encrypts "Mocking Jay" to data MJ with the password P1. Using another book of similar size (or by trimming a larger book), say the "The Hobbit", she processes the data MJ and computes password P2.   The solution to this problem will allow Bob to claim that he maintains a copy of "The Hobbit" (assuming that "The Hobbit" is not banned of course), while being able to read  "Mocking Jay". The solution, in theory, should also allow Bob to plausibly deny that there's any other copy hidden in the data "MJ" other than "The Hobbit"; or like the aforementioned security.SE question, should allow "MJ" to hold any number of copies (and thus any number of passwords), providing Bob the excuse of acknowledging only one copy that he has the knowledge of.  The  provided by the user lynks to the question posed by doom123 solves the problem for storing data on a hard-disk. Is there a general solution to this problem?  UPDATE 1 With regards to the answer provided by fgrieu I am slightly modifying the question. Is it possible to add a third layer (and an arbitrary number of further layers) of such encryption? What I mean is, with Mocking Jay, The Hobbit, and Silmarillion (assuming that the books are roughly the same in size) as inputs, is it possible to create an encrypted output say MJTHSI? I am alright with the passwords being the output as well. Decrypting with password P1 will reveal Mocking Jay. If rubber-hose is used password P2 can also be given up revealing The Hobbit (with the intention of ultimately protecting Silmarillion which can be revealed using P3).


Misunderstanding in Spivak's Proof of the Intermediate Value Theorem

I am a student who has taken the basic calculus courses but I am working through Calculus (the fourth edition) by Spivak in my spare time in order to both review the material and to gain a more rigorous understanding of the concepts. I am currently in Chapter 8 where he supplies a proof of the basis of the Intermediate Value Theorem, Theorem 7-1 (pp. 135-136 of the fourth edition). It seems mostly straightforward but I think there is some nuance of it that I don't grasp.  I am including in this post the statement Theorem 6-3 since he references it in the proof of Theorem 7-1 as well as part of Theorem 7-1 itself.     Theorem 6-3 Suppose $f$ is continuous at $a$, and $f(a) > 0$. Then $f(x) > 0$ for all $x$ in some interval containing $a$; more precisely, there is a number $\delta > 0$ such that $f(x) > 0$ for all $x$ satisfying $|x-a| < \delta$. Similarly, if $f(a) < 0$, then there is a number $\delta > 0$ such that $f(x) < 0$ for all $x$ satisfying $|x-a| < \delta$.     Problem 6-16 is also referenced. However,it is the same thing as Theorem 6-3 for one-sided limits. The following proof is the Theorem 7-1 up through the paragraph which I don't fully understand.     Theorem 7-1: If $f$ is continuous on $[a,b]$ and $f(a) < 0 < f(b)$, then there is some number $z$ in $[a,b]$ such that $f(x) = 0$.  Proof: Define the set $A$ as follows:  $$A = \{x : a \le x\le b, \mbox{ and } f \mbox{ is negative on the interval } [a,x] \}.$$       Clearly $A \ne \emptyset$, since $a$ is in $A$; in fact, there is some $\delta > 0$ such that $A$ contains all points $x$ satisfying $a \le x < a + \delta$; this follows from Problem 6-16, since $f$ is continuous on $[a,b]$ and $f(a)<0$. Similarly, $b$ is an upper bound for $A$ and, in fact, there is a $\delta > 0$ such that all points $x$ satisfying $b-\delta < x \le b$ are upper bounds for $A$; this also follows from Problem 6-16, since $f(b) > 0$.       From these remarks it follows that $A$ has a least upper bound $\alpha$ and that $a < \alpha < b$. We now wish to show that $f(\alpha) = 0$, by eliminating the possibilities $f(\alpha) < 0$ and $f(\alpha) > 0$.       Suppose first that $f(\alpha) < 0$. By Theorem 6-3, there is a $\delta > 0$ such that $f(x) < 0$ for $\alpha - \delta < x < \alpha + \delta$. Now there is some number $x_0$ in $A$ which satisfies $\alpha - \delta < x_0 < \alpha$ (because otherwise $\alpha$ would not be the least upper bound of $A$). This means that $f$ is negative on the whole interval $[a,x_0]$. But if $x_1$ is a number between $\alpha$ and $\alpha+\delta$, then $f$ is also negative on the whole interval $[x_0,x_1]$. Therefore $f$ is negative on the interval $[a,x_1]$, so $x_1$ is in $A$. But this contradicts the fact that $\alpha$ is an upper bound for $A$; our original assumption that $f(\alpha) < 0$ must be false.    The point I don't understand is in the final paragraph of the excerpt. Why does Spivak split the interval $[a,b]$ up into the subintervals $\lbrack a,x_0 \rbrack$ and $[x_0,x_1]$? Isn't it true that, because $\alpha$ is a least upper bound of $A$ and $f$ is continuous on $[a,b]$, it must be true that if $a \le x < \alpha$ then $f(x)<0$? I understand the need to pick out the $x_1$ but not the $x_0$. Especially perplexing is the statement "there is some number $x_0$ in $A$ which satisfies $\alpha - \delta < x_0 < \alpha$ (because otherwise $\alpha$ would not be the least upper bound of $A$." Wouldn't it be true that if there were some $x_0$ such that $a \le x_0 < \alpha$ and $f(x_0) \ge 0$ that $x_0$ would be an upper bound for $A$, contradicting that $\alpha$ is the least upper bound of $A$?  Thanks for any help.


Limit of the sum of the funtion and its derivative

Let $f$ be a continous differentiable function on $\mathbb R$. Suppose that    $$L = \lim_{x \to \infty} ( f(x) + f'(x) )$$    exists. If $ 0 < L < \infty$, then which of the following statments is / are true ?    if $\lim_{ x \to \infty} f'(x)$ exists, then it is $0$. if $\lim_{ x \to \infty} f(x)$ exists, then it is L. if $\lim_{ x \to \infty} f'(x)$ exists, then $ \lim _{x \to \infty} f(x) = 0$ . if $\lim_{ x \to \infty} f(x)$ exists, then $ \lim _{x \to \infty} f'(x) = L$   Any help would be appreciated. Thank you


biblatex: make title hyperlink to DOIs, URL or ISBN

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What is the origin of the phrase "wrapped around her little finger" come from

I know what "wrapped around her little finger" means, but I cant get straight on where it originates. Thanks


$\lim x_n = a \in \mathbb{R}$, $\lim y_n = b \in \mathbb{R}$. Prove that $\lim \frac{x_1y_n + x_2y_{n-1} + \cdots + x_ny_1}{n} = ab$

So, here we have two converging sequences. It is obvious that from certain point our $x_n$ will be extremely close to $a$ and $y_n$ will be extremely close to $b$. Hence, we have infinite number of their reversed products which are extremely close to $ab$, there are only finite number of products for fixed $\epsilon$ which are not in $(ab - \epsilon, ab + \epsilon)$. Okay, these are intuitive assumptions, but how to prove it formally?


Lubuntu Raring Ringtail. I want to be able to execute my scripts with ./  I start my python script with #!/usr/bin/python and it says  bash : ./myscript.py: /usr/bin/python^M: bad interpreter: No such file or directory   If I use #!/usr/bin/env python it gives a similar error:  : No such file or directory   What am I doing wrong?  I absolutely have python installed, and can run the scripts as normal with python myscript.py


The precise meaning of "may/might and/or may/might not"?

She may/might be honest.   This sentence already has the meaning that      She may/might not be honest.   1. Why do we sometimes say:     She might and/or might not be honest.   2. Which conjunction is (more) correct: "and" or "or"?  So, the question is not on when to use "might" and when to use "may", it is about why each comes along with its negation, and what difference that usage makes to the meaning. Is it just about emphasis?  The second question is about the conjunction that should be used between them: "and" or "or"? Both versions  are used frequently on the web.


Steam isn't displaying after running [Kubuntu]

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Why is it wrong to serial voteup someone you like his answers?  Sometimes I just came to stackoverflow to read certain people answers(there are 4 guys currently) I have their profile bookmarked in my browser and in my free time at office I go to their profile and read their answers and learn a lot from them, but because I'm afraid to be a serial voter, I dont voteup them.   I think there is nothing wrong with that, if there is, please let me know.


Workflow rule to be fired when lookup field is updated?

I have a lookup field X and I want to make a workflow rule to fire when that lookup field is updated or the record is created. How can I do this because I keep getting an error like "Function ischanged cannot be used in this type of field."


Why does len() built-in method in python take object as an argument instead of being called using the object with dot operator?

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Name of book that includes giant space creatures, resembling manta rays, that eat solar fuel and kill stars

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Is it possible to give items with a custom max durability?

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Forgot password on Pokemon go how do I get it back

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I want to quick paste some different strings using hotkeys. For example if I press Alt+L in any input form it works like if I pasted loremipsum. Or it  may be some abbreviation, for example I enter li, press Tab and get loremipsum.  I'm using Linux Mint with KDE desktop.  In Windows I could do it using AutoHotkey


Windows applications not restoring on restart

Summary When I restart, applications that should reopen automatically afterwards do not do so.  I've checked all of the relevant steps that I can find, however none have any effect.  Basic information on this issue can be found in .    System Details Windows 10 Enterprise, version 1903, build 18362.267.  This is a fresh install (not an upgrade) of Windows 10 on a desktop that used to run Windows 7.  It's not connected to an Active Directory.    Problem Specifics When I restart, no applications reopen, although many should.  Examples include browsers (e.g. Chrome, Firefox, Edge) and Microsoft Office programs (e.g. Outlook).  As discussed in the comments below, the online documentation on this can be confusing since this feature in Windows has evolved over time, as have the applications that support it, but I am contrasting this problematic desktop with observed behavior on two other laptops, both of which received a clean Windows 10 Enterprise install.  On both of these laptops, applications reopen both when Windows performs an automatic update + restart and when I initiate the restart, .    In terms of problem diagnosis, I have run through a host of means of enabling/disabling this feature, however none have any effect on whether it occurs.     I have verified that the requisite setting is enabled (see ).   I have verified that the requisite registry key is set (see Option 2 ).   I have verified that the local computer policy is set to "Not configured" (see Option 3 in last link).     In all cases, toggling these has no effect on restart behavior, though the option in the Settings menu does disappear (as it should) when it is disabled by other methods.  Lastly, note that folders do reopen on restart of the misbehaving computer, which, as also noted in  mentioned at the start of this post, is a separate option from application restoring.    Down the Road For future readers, there is also some discussion in  about further evolution of this feature in future releases (starting in build 18963) about modification to the behavior.  Although this is a later build than mine, out of an abundance of caution, I did try adding the registry key described  (the setting doesn't appear in the Settings menu in my build, as it shouldn't), but this had no effect.


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I have had my new Nikon for around 2 months and am learning about settings and modes. I have lost the exposure indicator in the information display. What did I do to cause this? Thanks


On an existence of a real-valued measurable function on a non-atomic probability measure space

Suppose that $(X,E,μ)$ is a non-atomic probability  measure space.  Let $\xi :X \to \mathbb{R}$ be a random variable. A Borel measure $\mu_{\xi}$ in $\mathbb{R}$ defined by $\mu_{\xi}(X)=\mu(\xi^{-1}(X))$ for $X \in B(\mathbb{R})$ is called a Borel probability measure on $\mathbb{R}$ defined by $\xi$.  Question: Does there exists a measurable function $\xi :X \to \mathbb{R}$ such that a Borel probability measure $\mu_{\xi}$ is non-atomic?


Teenagers find an ancient lizard creature in stasis and accompany him on adventures to an undersea city

When I was a kid, I read a book (likely from the '60s) about a pair of kids who find an ancient lizard/fish man inside a cave. The cave has been recently exposed by an earthquake and the creature is inside a super technologically advanced stasis chamber. I think this creature's name is something like "Sslaa". He takes the kids on a quest to find his lost underwater city.  They end up finding the city, which is still populated by creatures like himself and protected from the ocean above by an immense diamond dome. Eventually, Sslaa has to drive an advanced mining vehicle deep into the crust of the earth, presumably to prevent his city's destruction by an impeding magma flow or other seismic event.  For extra obscurity bonus points, I could swear I managed to find this book on Google several years ago, and was shocked to learn that it had originally been written in German, and then translated to English.  Does anyone out there recognize this one?


Suppose $A \subseteq \mathbb{R} $, $m(A) > 0 $. Then for almost all $x \in A $ we have $$ \lim_{\epsilon \to 0^+ } \frac{ m(A \cap (x - \epsilon, x + \epsilon))}{2 \epsilon} = 1.$$  Can someone help me with this problem? $m$ is the Lebesgue measure  thanks


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