I found a writing in an old book which was: "Apple pie à la mode". I was wondering what is the meaning of that?

In American English, à la mode means:   in fashion, up to date. with ice cream. (of beef) braised in wine, typically with vegetables.   While the first meaning matches the French meaning, the other two meanings are different. Why does à la mode have also the last two meanings, in English?


Consider a scenario, a bus is about to pass over a bridge. The bridge is broken in the middle. Now according to ground observer the broken part is bigger than bus (because bus appears smaller to ground observer due to the motion of the bus) and hence bus will fall down the bridge.   Now for observer on the bus sees that the broken part is smaller because, according to him, the bridge is moving and not him and he thinks bus will remain on the bridge.  Whose prediction is right in this situation?

There is a relativistic paradox I was introduced by a friend in Ithaca (Courtenay Footman). It involves a vehicle travelling over a ravine relativistically, so it's in the general family of ladder paradoxes. There are many ways to phrase it, but here's a simple one.   A three-car train with each car of length $L$ is travelling over a bridge across a ravine. (Assume that the couplings between cars are stiff: this train does not bend.) Unfortunately, some evil genius has precisely removed a length $6L$ of the track. The train however is relativistic, travelling at a speed such that $\gamma \approx 12$.  In the reference frame of the ground, the train should appear to be 1/24th the size of the gap, which suggests that it will fall a little and should crash into the bridge opposite. But in the reference frame of the train, each car of the train is at least twice as long as the gap and aside from the very front wheel and the very back wheel, which need to be supported by rigidity, everything is constantly well-supported. This suggests that the train makes it. Who is right?  I vaguely remember that as an undergraduate knowing only a little relativity, I trusted the train's perspective because it's at rest in that perspective, and Courtenay said that this was ultimately correct after a lot of details got resolved. But I do not remember all of these details such that I could work it out for myself. So I'm looking for some discussion that's a little more well-sourced or authoritative.  What is this paradox called, and what literature has addressed the issue?


If my target variable has more 1's (say around 80%) than 0's then how do I handle such imbalanced data for building models using different methods such as GBM, RF, logistic regression, etc. Should I perform under sampling of 1's?

Suppose the event of interest occurs in approximately $10 \%$ of the cases where the number of cases is around $5,000$. Should you use a penalized logistic regression for this or is regular logistic regression okay? In other words, what qualifies something as a rare event?


I tied the following, it seems that there's no difference  import java.math.BigInteger; import java.util.Random; import java.util.Scanner;   public class Main {      /**      * @param args      */      final static int MAXN = 100005;        public static void main(String[] args) {         // TODO Auto-generated method stub         int n = 100;         BigInteger[] a = new BigInteger[n];         BigInteger b[] = new BigInteger[n];         for (int i = 0;i < n;i++){             a[i] = BigInteger.valueOf(i);         }         b = a;         for (int i = 0;i < n;i++){             b[i] = BigInteger.ZERO;         }         if (a == b){             for (int i = 0;i < n;i++){                 System.out.println(a[i]);             }         }     }  }

I have recently been thinking about the difference between the two ways of defining an array:   int[] array int array[]   Is there a difference?


When I type import pygame in Thonny I get an error. I installed pygame with sudo apt-get install python-pygame, but it's not working. Can somebody help?

I had a hard time installing pygame on my ubuntu 16.04 LTS. I use python 3. these are the steps I took to install pygame:  1.first I installed pip:  sudo python3 get-pip.py   this is the output of running pip --version:  pip 10.0.1 from /usr/local/lib/python3.5/dist-packages/pip (python 3.5)    I executed the following commands:   sudo apt-get install python3-dev mercurial  sudo apt-get install libsdl-image1.2-dev libsdl2-dev libsdl-ttf2.0-dev   then I executed the following command:   pip install --user hg+http://bitbucket.org/pygame/pygame  and this is the result in terminal:  Collecting hg+http://bitbucket.org/pygame/pygame   Cloning hg http://bitbucket.org/pygame/pygame to /tmp/pip-req-build-hxy86__i abort: error: Connection reset by peer Command "hg clone --noupdate -q http://bitbucket.org/pygame/pygame /tmp/pip-req-build-hxy86__i" failed with error code 255 in None   and it fails to install pygame. what should I do??


We all know that for a differentiable function $f$ on $\mathbb R$,its derivative function can have only essential or $2$nd kind discontinuity.Now my question is if $X$ be that set of all points of discontinuities of the derivative function,then can we predict the nature of $X$,i.e.can we say anything about the structure of $X\subset \mathbb R$.

There is a well-known result in elementary analysis due to Darboux which says if $f$ is a differentiable function then $f'$ satisfies the intermediate value property.  To my knowledge, not many "highly" discontinuous Darboux functions are known--the only one I am aware of being the Conway base 13 function--and few (none?) of these are derivatives of differentiable functions.  In fact they generally cannot be since an application of Baire's theorem gives that the set of continuity points of the derivative is dense $G_\delta$.  Is it known how sharp that last result is?  Are there known Darboux functions which are derivatives and are discontinuous on "large" sets in some appropriate sense?


I've noticed that there's a line break occurring in the content__date when the browser is in mobile view. I tried to add another container for the content__date but it is not working. Any ideas would be appreciated.~ I am totally new in web development please bear with me.   .content__item {      display: flex;      align-items: center;      justify-content: flex-start;      height: 100vh;      width: 100vw;      color: black;      font-family: sans-serif;      margin: 0; }  .content .p {      margin: 0; }  .content__wrapper {      display: flex;      align-items: flex-start;      justify-content: flex-start;      max-width: 600px; }  .content__date {      display: flex;      transform: rotate(-90deg);      border-bottom: 2px solid black;      padding-left: 3rem; }  .content__category-wrapper {      display: flex;      flex-direction: column;      justify-content: flex-start;      align-items: flex-start;      margin-left: -3.25rem;      margin-top: -3rem; }  .content__category {      padding-bottom: 1rem; }  .content__category-text {      padding-left: 1rem; }  .content__title-line {      border-top: 2px solid black;      margin-left: 0.5rem;      padding-left: 20rem; }  .content__title {      padding-top: 1rem;      padding-left: 20px;      font-size: 18px; }

June 7, 1941

Some text here

Another text here

Is there a word-wrap or any other attribute that stops text from wrapping?  I have a height, and overflow:hidden, and the text still breaks.  Needs to work in all browsers, before CSS3.


I am looking for different ways to pause and resume programmatically a particular process via its process ID under Windows.  Process suspend/resume tool does it with SuspendThread / ResumeThread but warns about multi-threaded programs and deadlock problems.  Or Detect Threads of any process ID.  I need method deadlocks or uses another method?  Prefered languages : C#

How do I suspend a whole process (like the Process Explorer does when I click Suspend) in C#.  I'm starting the Process with Process.Start, and on a certain event, I want to suspend the process to be able to do some investigation on a "snapshot" of it.


In my phone,Google+ app or google play store is an unsupported app. My phone is a Nokia XL. But if I connect to Facebook, will my village be saved?

When I try to connect to Google Play, it would say "download Google play service". After I downloaded it, it says that it is "not supported by your device, please contact the manufacturer".


I am reading about indefinite integrals and I have a question regarding the use of the modulus in integrating $\frac{1}{x}$.   The book I am reading gives me the following explanation -    The book later gives no further explanation, which has left me confused.   I have found no reasonable explanation online, so I would like to ask why this is the case in integration.   What does the book cite as "difficulties that may arise"?

My professor says that writing this is convenient $$\int \frac 1x \mathrm{d}x = \ln|x| + C\tag{1}$$ but wrong, since it should be written as: $$\int \frac 1x \mathrm{d}x = \begin{cases}\ln x + C &x > 0\quad(\star)\\[0.2em] \ln(-x) + C &x < 0\end{cases}$$  I was wondering why is that the case. I thought that the two were equivalent, as one can see by the definition of absolute value. In $(\star)$ the equality sign is dropped because the logarithm is not defined in $0$, but that would be the case with $(1)$ as well.


I would like to allocate certain number of CPU cores to a specific process for performance improvement.  How can I do this?

How to limit process to one cpu core ?  Something similar to ulimit or cpulimit would be nice. (Just to ensure: I do NOT want to limit percentage usage or time of execution. I want to force app (with all it's children, processes (threads)) to use one cpu core (or 'n' cpu cores)).


We know that if $f(x)$ and $g(x)$ are continuous in a domain then $f(x)/g(x)$ is continuous in the domain except for those elements in the domain for which $g(x) = 0$. If I take two functions $f(x) = x$ and $g(x) = 1/x$, then $f(x)$ is continuous for all $R$ and $g(x)$ is continuous for $R-\{0\}$ but if I take $f(x)/g(x)$ which is $x/1/x$ or $x^2$ then it is continuous for all $R$ even when $0$ was not in the domain of $g(x)$. Is this correct?

Let $f(x) = \frac{x}{x}$.  Is it correct to say that $f(x) \ne 1$, since $f(x)$ has a discontinuity at $x=0$?


I have two text files. The first "file1.txt" has content:  Apple Orange Banana   while the second file "file2.txt" has content:  monday tuesday wednesday   I want to combine them into one file and its output is:  Apple monday Orange tuesday Banana wednesday

Standard cat concatenates files line by line (row by row, if you will). I find myself needing a horizontal cat command more and more often recently; i.e. a command that takes a list of files and concatenates them horizontally, column by column. So far I’ve used ad-hoc workarounds but I’d like to know if there exists a good solution for this.  To clarify, consider the following comparison between cat and hcat of two files:  $ cat a.dat 1.dat a b c d 1 2 3 4 $ hcat -s ' ' a.dat 1.dat a b 1 2 c d 3 4   (Unlike for cat we need to specify a separator since by convention UNIX files don’t have a column separator at the end.)


In clang's ActOnIfStmt function, we have:  return Owned(new (Context) IfStmt(Context, IfLoc, ConditionVar, ConditionExpr,     thenStmt, ElseLoc, elseStmt));   I'm under the impression that Context is a pointer type, but it's a class type. How does this work, and what does this code do?

Has anyone here ever used C++'s "placement new"? If so, what for? It looks to me like it would only be useful on memory-mapped hardware.


If I input value: 3.123456789012345e-09  I should get back 3.12345678901235e-09  But it will only round up on .6 to .9  ostringstream os;  double d = 3.123456789012345e-09 ;  os << setprecision( 15 );  os << d;  istringstream is ( os.str() );  is >> setprecision( 15) >> d; std::cout << d << std::endl;   The real bizzare thing is: The rounding behaviour changes depending on the power:  3.123456789012345e-09 = 3.12345678901234e-09  3.123456789012345e-10 = 3.12345678901234e-10  3.123456789012345e-11 = 3.12345678901235e-11  3.123456789012345e-14 = 3.12345678901235e-14  Every 1000th power rounds correctly... I am so confused. I know that rounding is a bit a of a weird subject but I cant make heads or tails of this. on a 64 bit machine btw.

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


I'm trying to model regional implicit bias using multilevel regression with poststratification as described in Hoover, J., & Dehghani, M. (2019). The big, the bad, and the ugly: Geographic estimation with flawed psychological data. Psychological Methods. Advance online publication. .   The authors model Implicit Bias (imp_bias) as a function of six fixed effect county-level (contextual) variables (vote_prop.std + ... + latino_prop.std) and various random effects. Three of these random effects are geographical units: Counties nested within states nested within divisions. Though they are not explicitly specified as nested factors (as (1 | division/state_fips/county_fips) would do), they should be handled as nested factors because every fips-code is unique to the specific geographical unit. The other three are demographic variables: education, sex, & age. In the paper the authors write that the demographic effects were estimated as random intercepts crossed with division and that they did cross them with division because otherwise the model didn't converge.  I am confused as to whether the code they report does achieve this:  iat.imp.mrp.2 <- lmer(imp_bias ~ 1 +                             vote_prop.std +                              ...                             latino_prop.std +                    (1 | county_fips) +                     (1 | state_fips) +                    (1 | division:educ_3lvl) +                    (1 | division:sex:age_4lvl),                    data = iat.estimation.df, verbose=T,                     control=lmerControl(optimizer="bobyqa",                                  optCtrl=list(maxfun=2e5)))   To my understanding (1 | division:educ_3lvl) indicates that education is nested within division rather than crossed with division. And how does this model differ from the following?  iat.imp.mrp.2 <- lmer(imp_bias ~ 1 +                             vote_prop.std +                              ...                             latino_prop.std +                    (1 | county_fips) +                     (1 | state_fips) +                    (1 | division) +                    (1 | educ_3lvl) +                    (1 | sex) +                    (1 | age_4lvl),                    data = iat.estimation.df, verbose=T,                     control=lmerControl(optimizer="bobyqa",                                  optCtrl=list(maxfun=2e5)))   To summarize, I don't really understand what the : does in the authors' code and would like to know how to specify with which of the three levels the demographic variables are crossed. Any help is really much appreciated!

Here is how I have understood nested vs. crossed random effects:    Nested random effects occur when a lower level factor appears only within a particular level of an upper level factor.     For example, pupils within classes at a fixed point in time.   In lme4 I thought that we represent the random effects for nested data in either of two equivalent ways:    (1|class/pupil)  # or   (1|class) + (1|class:pupil)    Crossed random effects means that a given factor appears in more than one level of the upper level factor.     For example, there are pupils within classes measured over several years.   In lme4, we would write:   (1|class) + (1|pupil)    However, when I was looking at a particular nested dataset, I noticed that both model formulas gave identical results (code and output below). However I have seen other datasets where the two formulas produced different results.  So what is going on here?   mydata <- read.csv("https://web.archive.org/web/20160624172041if_/http://www-personal.umich.edu/~bwest/classroom.csv") # (the data is no longer at `http://www-personal.umich.edu/~bwest/classroom.csv` # hence the link to web.archive.org) # Crossed version:  Linear mixed model fit by REML ['lmerMod'] Formula: mathgain ~ (1 | schoolid) + (1 | classid)    Data: mydata  REML criterion at convergence: 11768.8  Scaled residuals:      Min      1Q  Median      3Q     Max  -4.6441 -0.5984 -0.0336  0.5334  5.6335   Random effects:  Groups   Name        Variance Std.Dev.  classid  (Intercept)   99.23   9.961    schoolid (Intercept)   77.49   8.803    Residual             1028.23  32.066   Number of obs: 1190, groups:  classid, 312; schoolid, 107   # Nested version: Formula: mathgain ~ (1 | schoolid/classid)  REML criterion at convergence: 11768.8  Scaled residuals:      Min      1Q  Median      3Q     Max  -4.6441 -0.5984 -0.0336  0.5334  5.6335   Random effects:  Groups           Name        Variance Std.Dev.  classid:schoolid (Intercept)   99.23   9.961    schoolid         (Intercept)   77.49   8.803    Residual                     1028.23  32.066   Number of obs: 1190, groups:  classid:schoolid, 312; schoolid, 107


I tried to write a regular expression using PCRE and regex101 to match a given list of palindromes. Special thanks to @trincot for pointing at the faults I made in earlier versions.   My latest work solves the problems from before though. I wonder if anyone could find a palindrome that isn't matched correctly.   Link to regex:

That was an interview question that I was unable to answer:  How to check that a string is a palindrome using regular expressions?  p.s. There is already a question "" and it gives a lot of answers in different languages, but no answer that uses regular expressions.


Mathematical visualisations (not sure how these should be described, is there a better noun?) are not displaying correctly for me on the stack exchange app.  As you can see in the screenshot, they are being displayed exactly as entered, rather than being parsed and displayed the way the author intended.  This only occurs in comments on all sites. They show fine in questions and answers. They also appear fine in my browser (chrome mobile).  This has been the case for as long as I've used the app, but only just decided to report it here.  The app has no pending updates Device: HTC 10 OS: Android 6.0.1  Is there anything I can do to remedy this or is it a bug?

I'm using the Stack Exchange app for Android. The app displays TeX formulas inside questions and answers as expected, but not in comments. Here it shows only the raw TeX code. I first noticed this issue .


I am interested to know, in which location and format are files stored when we put them in Recycle Bin? And when we delete them, where they go?

What does the Recycle Bin in Windows actually do?  Is it just a glorified folder and a holding place for soon to be deleted files, or does it do something specific?  Specifically, are files that are "moved" to the Recycle Bin actually moved on the hard disc, or are just the pointers to the files moved?  I am a fairly experienced user, I just wanted a more depth explanation of the Recycle Bin.


I'm new to programming so I guess this question is kinda stupid. I want to check if current Text exists in Array of Labels, because I get same name twice sometimes.   for (int i = 0; i < DM.checkedListBox1.CheckedItems.Count; i++) {     labels[i] = new Label();     for (int j = i; j < DM.dataGridView1.Columns.Count; j++)     {         if (DM.dataGridView1.Columns[j].Visible)         {                                     if (labels.Contains(DM.dataGridView1.Columns[j].HeaderText))             {                 labels[i].Text = DM.dataGridView1.Columns[j].HeaderText;                 break;             }         }     } }   Thank you!

What would be the best way to look in a string[] to see if it contains a element. This was my first shot at it. But perhaps there is something that I am overlooking. The array size will be no larger than 200 elements.  bool isStringInArray(string[] strArray, string key) {     for (int i = 0; i <= strArray.Length - 1; i++)         if (strArray[i] == key)             return true;     return false; }


For the purposes of titles, in particular on sites like Sci-Fi & Fantasy, Literature, and Movies & TV, is it possible to allow basic markdown appropriate for titles (italics) in the tag wiki excerpts?  I was recently editing a tag wiki on Movies & TV and realized that the markdown does not work in the excerpts so I'm forced to either leave titles without appropriate text decoration (which is what is generally done on both sites) or to use quotes. Neither of these solutions are "correct".     Is it possible to allow italics specifically on sites that warrant it by having a large volume of book, film, or TV show titles as tags? Or is this something not possible due to how the excerpts work?  This is a very specific request to be only used in very special cases and most likely would not be enabled on all Stack Exchage sites. I understand that, in general, markdown is not popular for tag wiki excerpts but I think that it may be worth making an exception if it is beneficial for clarity.

For example, :   Format like bold or italic are not available , so it leaves ugly text there:  **This tag is *extremely* ambiguous. Consider using other tags instead.**    Does this need to get fixed, or it's not supported and the tag-wiki needs to be format-free?


Let $M$ be a closed connected 3-manifold, and write $H_1(M, \mathbb{Z})$ as $\mathbb{Z^r} \oplus T$ where $T$ is torsion. Show that $H_2(M, \mathbb{Z})$ is $\mathbb{Z^r}$ if $M$ is orientable or $\mathbb{Z^{r-1}} \oplus \mathbb{Z_2}$ if $M$ is not orientable. I tried applying the UCT for Homology but I am not getting any information about $H_2$. On the other hand, when I used UCT for cohomology I am unable to proceed because of the $Ext(*)$. Can anyone help?

I'm trying to solve this problem from Hatcher 3.3.24.  Let $M$ be a closed connected 3-manifold, and write $H_1(M, \mathbb{Z})$ as $\mathbb{Z^r} \oplus T$ where $T$ is torsion. Show that $H_2(M, \mathbb{Z})$ is $\mathbb{Z^r}$ if $M$ is orientable or $\mathbb{Z^{r-1}} \oplus \mathbb{Z_2}$ if $M$ is not orientable. In particular $r \geq 1$ if $M$ is not orientable. Using exercise 6 construct examples showing there are no other restrictions on the homology groups of closed 3-manifolds. (In the nonorientable case consider the manifold $N$ obtained from $S^2 \times I$ by identifying $S^2 \times \{0\}$ with $S^2 \times \{1\}$ via a reflection of $S^2$.)  I think I've solved the first part, here's my proof:   First note the following theorem: If $M$ is a closed connected and orientable n-manifold then $H_n(M, \mathbb{Z}) = \mathbb{Z}$ and $Tors(H_{n-1}(M, \mathbb{Z})) = 0$. If nonorientable, then $H_n(M, \mathbb{Z}) = 0$, $Tors(H_{n-1}(M, \mathbb{Z})) = \mathbb{Z_2}$.  Now note by Poincare duality and UCT we have that $H_2(M) \cong H^1(M) \cong \mathbb{Z^r} \oplus T_0 \cong \mathbb{Z^r}$.   In the nonorientable case consider the exact sequence:  $0 \longrightarrow H_2(M) \longrightarrow H_1(M) \longrightarrow H_0(M) \longrightarrow 0$  But we know $H_1(M) = \mathbb{Z^r} \oplus Z_2$ from the earlier theorem and $H_0(M) = \mathbb{Z}$.   Therefore $H_2(M) \cong ker(\mathbb{Z^r} \oplus Z_2 \rightarrow \mathbb{Z}) \cong \mathbb{Z^{r-1}} \oplus \mathbb{Z_2}$.   For the rest of the question I'm quite lost.


I have a page with an iframe. Inside that iframe I have a javascript function like this:  function putme() {}  How can I call this function on the main page?

Basically, I have an iframe embedded in a page and the iframe has some  routines I need to invoke from the parent page.  Now the opposite is quite simple as you only need to call parent.functionName(), but unfortunately, I need exactly the opposite of that.  Please note that my problem is not changing the source  of the iframe, but invoking a function defined in the iframe.


The Fourier transform of a 1-d "disk" or: f(x) = \begin{cases} 1 & \text{ if } \left | x \right |< \frac{1}{2} \\  0 & \text{ if } \left | x \right |> \frac{1}{2} \\ \end{cases} gives a sinc function, and the Fourier transform of a 2-d disk: f(x,y) = \begin{cases} 1 & \text{ if } \left | \sqrt{x^{2}+y^{2}} \right |< \frac{1}{2} \\  0 & \text{ if } \left | \sqrt{x^{2}+y^{2}} \right |> \frac{1}{2} \\ \end{cases} gives a jinc function. What is the Fourier transform of: f(x,y,z) = \begin{cases} 1 & \text{ if } \left | \sqrt{x^{2}+y^{2}+z^{2}} \right |< \frac{1}{2} \\  0 & \text{ if } \left | \sqrt{x^{2}+y^{2}+z^{2}} \right |> \frac{1}{2} \\ \end{cases} , or for that matter any n-disk?

What is the Fourier transform of the indicator of the unit ball in $\mathbb R^n$? I think it is known as one of special functions, so I would be happy to know which one.


I am 11 years old, and I have made an app I want to post to the App Store. Is there any way to do that, or do I have to use my mom's account? (I have an Apple id because of Family Sharing)

I've seen a lot of questions like this throughout the web but they're mostly from 2 or 3 years ago, so I decided to ask to have some updated answers.   I'm 16 and I want to start publishing and using the benefits that comes with the Developer Program. In the legal agreement says that I should be over 18, and I'm not so, i can't do it. I've contacted the apple developer support and they told me that I should use a account in my father's name. We reside in Brazil. With that, I had some doubts:   Will the name on the App Store be mine or my father's? In the future, when I'm 18, this account can be transferred to my name?   Besides that, if someone has any advice or (legal) workaround I'd appreciate it, thanks


I have some armored cable (AC/MC) that needs to be fastened to the floor joist.  Very limited access.  I could probably reach in and swing a hammer a few inches, but no way to get a drill or screwdriver without busting up the ceiling.  I can use staples meant for NM cable?

I've heard some people say that code requires wiring in the wall to be stapled to framing every so often (how often?), but when you are doing a remodel, is that necessary?  I have a two story house, and would like to remove one standard dome light on the first floor ceiling and replace it with 6 recessed lights.  There is about 12" of empty space between the floors, and it seems easy enough to run the wire from light to light without cutting any drywall except for the 4-5" holes required for the lights. However, there's no way I'd be able to staple the wiring down.  It's just going to be loose in the ceiling, running through a small hole in the I joists every once in a while.  They sell "remodel" light cans that are made specifically so you only have to cut a hole big enough for them to fit in, so this seems like a common job.  What am I missing and how can I do this job in the most correct way?  This is in Dallas, TX, single family residence.


I have configured FTPS in a linux machine but when i am trying to connect through ftps in filezila below error is coming.   Status: Connection attempt failed with "ECONNREFUSED - Connection refused by server". Error:  Could not connect to server

This is a  about Connection Refused    We see a lot of questions to the effect      When I try to connect to a system I get a message      Connection refused      Why is this ?


I'm thinking of buying either a high-end 13'' Air (i7 and 8GB RAM $1,549.00) or 13'' rMBP with an i5 ($1,699.00).  Setting aside portability, display and other differences which I'm still pondering, how does the 1.7GHz Dual-Core Intel Core i7 compare to the 2.6GHz Dual-core Intel Core i5 in terms of performance?  I do some photo editing and programming.

I can see that the 13" version of MacBook Pro and MacBook Air is same $1199, but the Pro is more feature-loaded than Macbook Air. Why would anyone buy MacBook Air? What's the catch in this?    I was thinking of buying a MacBook for development purposes, and worried if there's any problem in the Pro version, because it comes with more features (like more storage).  Edit:    Thanks for the answer guys, I bought a MacBook Pro a week ago and already loving it.


I have a variable which has to be encrypted and after that saved to the database via mysqli prepared statement. I use AES-256-CTR.   $tabvar = openssl_encrypt($final, $encryptionMethod, $secret, OPENSSL_RAW_DATA, $iv);   After the encryption the result looks like this: 5œœ¼Ç=áüû;€é?  This is my php insert code:  $ins = mysqli_prepare($db, "INSERT INTO tab (tid, tabvar) VALUES (?,?)"); mysqli_stmt_bind_param($ins, "ss",$tid,$tabvar); mysqli_stmt_execute($ins);   Because the $tabvar consist of some very strange characters once encrypted, it doesn't get inserted in the database. If I change $tabvar to "i" the row get's inserted, but the entry under tabvar column is 0?  Does anyone have an idea how to solve this?


He_____ (ride) a horse when he was a child. She ______ (sing) in a school choir many years ago.

At the dentist's:     I was on time for my dentist's appointment, but the dentist was still busy with another patient, so I sat in the waiting room and read some of the old magazines lying there. All the while I was wondering whether to leave and come back another day .   Why past simple here and not past continuous? To me both actions are in progress they are not completed


I am creating ArrayList l1 and passing l1 reference to the method foo. As we know that Java doesn't support Pass-By-Reference but here its giving different results.  See the below code  public static void main(String[] args) {     List l1 = new ArrayList(Arrays.asList(4,6,7,8));     System.out.println("Printing list before method calling:"+ l1);     foo(l1);     System.out.println("Printing list after method calling:"+l1); }  public static void foo(List l2) {     l2.add("done"); // adding elements to l2 not l1     l2.add("blah"); }   Output:  Printing list before method calling:[4, 6, 7, 8] Printing list after method calling:[4, 6, 7, 8, done, blah]

I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?


In Latex, I put the following code: \begin{tikzcd} A \arrow[r, "f"] & B \end{tikzcd}  However, the 'f' does not appear over the arrow. How can I solve this?

Why do I get the error Missing \endcsname inserted at line 15?  \documentclass{article}  %\usepackage[strict]{csquotes} %\usepackage[autostyle=true]{csquotes} \usepackage[T2A,T1]{fontenc} \usepackage[russian,main=english]{babel}  \usepackage{tikz-cd}  \begin{document}  \begin{tikzcd}   f \arrow[d, "\partial"] \\   g \end{tikzcd}  \end{document}   Again I get the error if instead of option russian I use:  \usepackage[T1]{fontenc} \usepackage[german,main=english]{babel}   As the commented-out preamble lines show, I tried to invoke package csquotes, in two different ways, to avoid the problem, but that failed, too.  I do not get the error with babel option french however, as in:  \usepackage[T1]{fontenc} \usepackage[french,main=english]{babel}


I have 2 laptops (one of which is my primary PC) and a desktop PC. The desktop run on Vista Home Edition, the secondary laptop also runs on vista and the primary laptop runs on windows 8.  It is possible to link these machines in order to increase the processing power and speed of my primary laptop?

Here are a few questions, I wish you could enlighten me.   Is it possible to combine processing power of 2 computers? How do I do it?


I use  in Arch Linux for installing packages.   The command for installing is pacman -S, The command for a full system upgrade is pacman -Syu and The command for repository update is pacman -Syy.   I want to know what is the equivalent for pacman in Ubuntu and its corresponding command.

How can I install applications like Google Chrome on Ubuntu?  Are there any commands to install an application?    Index of answers:


I have a .ttf file in which I need to add some missing characters. Maybe some of you have faced and overcame this earlier? I would relay appreciate your time spared ;)

I'm trying to find a free tool (on windows ) that would enable me to change some settings on a TrueType font. Specifically, I'm trying to fix the following errors:  E1311 The macStyle bold bit doesn't match the name table's font subfamily string macStyle bold bit is set, but subfamily is Regular  W2000 The subfamily string is inconsistent with the style of the font OS/2.fsSelection bold bit is set, but subfamily string = 'Regular'  I can do that with fontographer, but would prefer to use something free.  Fontforge doesn't seem to work with this font, when saved it corrupts the cyrillic letters in the font.


I understand that this is part of Euclid's Lemma but how do I prove that a must be prime?

I am trying to understand the proof for the following theorem:     Let $R$ be an integral domain. If $x \in R$ is prime, then $x$ is irreducible.   Here is the proof:    I typed this a while ago and I don't understand the part where if $x | bc$, then $x=bc$? Is something wrong at this step?  Also, is the definition of prime elements where $p$ is prime if whenever $p|ab$, then either $p|a$ or $p|b$? Now I don't feel so sure. This could be the reason why I am not understanding the proof...


I'm a beginner programmer I'm working on a website with my friend Alex, we're both beginners actually, I took on the task of designing the landing page to get some practice in. I want to have these divs which contain nothing but text centered horizontally and vertically (or dead center), I've tried some things other people have suggested on other posts on this site but nothing seems to be working. Could one of you gurus please help me? And thanks in advance :D (I should probably mention that I'm using DW with the Bootstrap framework)  Here's the html:  <!DOCTYPE html>               <link href='https://fonts.googleapis.com/css?family=Montserrat:400,700' rel='stylesheet' type='text/css'>     <meta charset="utf-8">     <meta http-equiv="X-UA-Compatible" content="IE=edge">     <meta name="viewport" content="width=device-width, initial-scale=1">     <title>Untitled Document</title>          <link href="css/bootstrap.css" rel="stylesheet">     <link href="css/stylesheet.css" rel="stylesheet" type="text/css">

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TEXT I WANT CENTERED

         TEXT I WANT BELOW CENTERED TEXT
                              Heres the css:  @charset "utf-8"; /* CSS Document */  .background {      background: url(../img/bg1.jpg) no-repeat 50% 50% fixed;      margin: 0 auto;      max-width: 80%;      min-width: 50%;      width: 80%;      height:auto;      background-size: cover;      -webkit-background-size: cover;      -o-background-size: cover;      -moz-background-size: cover;  }       li {      display: inline;      letter-spacing: 2px;      padding-right: 0.5em;      float: right;      font-size: 125%;      font-style:normal;      font-weight: bold;      text-transform: uppercase;      text-decoration:none;      color:#ffffff;      text-shadow: 4px 3px 0px #000000, 9px 8px 0px rgba(0,0,0,0.15);  }   #welcome {     font-family: 'Montserrat', sans-serif;     max-width: 90%;     min-width: 80%;     height: 50%;     font-size: 350%;     font-style:normal;     font-weight: bold;     text-transform:uppercase;     text-decoration:none;     text-align: center;     color:#ffffff;     position: relative;     text-shadow: 4px 3px 0px #000000, 9px 8px 0px rgba(0,0,0,0.15);     z-index: 9998;  }   welcome p {      width: 300px;      height: 100px;      padding: 20px;   }   #best {     font-family: 'Montserrat', sans-serif;     max-width: 100%;     min-width: 70%;     font-size: 200%;     font-style:normal;     font-weight: bold;     text-transform:uppercase;     text-decoration:none;     text-align:center;     color:#ffffff;     position: relative;     text-shadow: 4px 3px 0px #000000, 9px 8px 0px rgba(0,0,0,0.15);  }    p {      text-align:center;   }   a {      color: #FFFFFF;  }   a {      hover: #2a7315;      text-decoration: none;  }

Best way to center a <div> element on a page both vertically and horizontally?  I know that margin-left: auto; margin-right: auto; will center on the horizontal, but what is the best way to do it vertically, too?


I am trying to do SSO with an external website. Is there a way to pass the salesforce object data when doing SSO so that forms on the external website are already prefilled when the page opens up.

I've implemented Single Sign On with Salesforce as Identity Provider scenario using SAML.  I want to pass additional attributes via SAML response to the Service Provider. Out of the box the Connected App allows adding custom attributes based on User/Profile/System objects:    I want to add attributes from other objects.  Is it even possible? Should I implement some interface to have specific fields visible?


I have done it thus far:  $$\lim_{x \to 0}\frac{{(x+1)}^\frac{1}{x}-e}{x} = \bigg[\frac{0}{0}\bigg] = \frac{((x+1)^\frac{1}{x}-e)'}{x'}=({x+1})^\frac{1}{x} \cdot \left(\frac{\ln(x+1)}{x}\right)' = \\({x+1})^\frac{1}{x} \cdot \frac{\left(\frac{x}{x+1}-(\ln(x+1)\right)}{x^2} = ({x+1})^\frac{1}{x} \cdot \left(\frac{\frac{1}{x+1}}{x} - \frac{\ln(x+1)}{x^2}\right) $$  I don't know what to do next.  Also could someone elaborate as to why when I have to find a derivative for $\frac{\ln(x+1)}{x}$ I need to use the quotient rule, but when I first derived the fraction that is given I could derive numerator and denominator separately?

Find the following limit: $$\lim_{x\to 0}\frac{(1+x)^{1/x}-e}{x} \tag{1}$$  The following is my approach, although is full of incorrect assumptions (statements etc).  $$f(x)= \lim_{h\to 0}(1+x+h)^{1/(x+h)}\\$$  From here we can say $f(0) = e$.  $$\ln(f(x)) = \lim_{h\to 0}\frac{1}{x+h}\ln(1+x+h)$$  Near $x=0$, we can use the series of logarithm: $$\ln(f(x)) = \lim_{h\to 0}\frac{1}{x+h}\left(x+h-\frac{(x+h)^2}{2}...\right)$$  Differentiating we get:  $$\frac{f'(x)}{f(x)} = \lim_{h\to 0}-\frac{1}{2} +\frac{x+h}{3}  ... \tag{2}$$  Now we note that $(1)$ is actually $f'(0)$ (?) and so from $(2)$ we get:  $$f'(0) =\frac{-1}{2} f(0) = \frac{-e}{2}$$  While the answer is seemingly correct, the method is absolutely not. It looks like this is fluke than anything else.  I also tried computing taylor series of $(1+x)^{1/x}$ near $x=0$ but couldn't do it.


I've got a subclass of DataGridView that adds all the columns it needs in it's own constructor, but when I use this component in the VS designer it insists on generating code to add the same columns on top of the ones added in the component constructor. How do I force it to not generate code for columns it already finds populated inside a datagridview?

I generate all my columns in a subclassed DataGridView programmatically. However Visual Studio 2008 keeps reading my constructor class (which populates a DataTable with empty content and binds it to the DataGridView) and generates code for the columns in the InitializeComponent method - in the process setting AutoGenerateColumns to false.  This causes errors in design-time compilation which are only solved by manually going into the design code and deleting all references to these autogenerated columns.  How can I stop it doing this?  I have tried:   Making the control 'Frozen' Setting the DataGridView instantiated object protected (suggested in a previous post which referred to )


I am trying to set up an openstack environment, but I am a bit confused due to the different mechanisms to do this.  I have an environment with 8 nodes, and MAAS is installed at one node.( Ubuntu 15.04 with MAAS installation. The other 7 nodes are 14.04 LTS)  Now what ?    Use this procedure  and go for Landscape Autopilot to setup openstack ? There are also other choices in the install procedure Install JUJU and use JUJU GUI to install Openstack ?  Install openstack step by step from shell ?  Openstack-autopilot (? is this the same as landscape-autopilot?)   Other ways ?

How do I install ? Is there an easier way other than official installation instructions?


Failed failed to mount Mount unit for gnome-3-26-1604, revision 98 Failed Failed to mount Mount unit for gnome-3-28-1804, revision 128 Failed Failed to mount Mount unit for gnome-3-28-1804, revision 145 Failed Failed to mount Mount unit for gnome-3-28-1804, revision 60 Failed Failed to mount Mount unit for gnome-3-28-1804, revision 66 Failed Failed to mount Mount unit for gnome-system monitor, revision 145 Failed Failed to mount Mount unit for gnome-system monitor, revision 148 Failed Failed to mount Mount unit for...... Failed Failed to mount Mount unit for.... Failed Failed to mount Mount unit for..... Failed Failed to mount Mount unit for..... Failed Failed to mount Mount unit for......  you are in emergency mode. After logging in, tye "jornalctl -xb" to view system logs,"systemctl reboot" to reboot, "systemctl default" or "exit" to boot into default mode. Pulse enter para mantenimiento (o punse Control -D para continuar)

Yesterday I started the upgrade from 12.10 to 13.04, but I interrupted it because it was taking too long. Now if I restart it, it doesn't proceed.  Is there any possibility to clean the mess it left when I interrupted it and make a clean restart of this update?


The  alternate series $S=\displaystyle \sum_{k=2}^{\infty} \frac{(-1)^n}{\sqrt{n}+(-1)^n}  $ converges?  $S$ is absolutely convergent?

Discuss the convergence of the sum:   $$\sum _{k=2} ^\infty \frac{(-1)^k}{\sqrt{k}+(-1)^k}.$$  My answer so far: It does not converge absolutely since   $$\left | \frac{(-1)^k}{\sqrt{k}+(-1)^k} \right | \geq \frac {1} {\sqrt{k} + 1},$$  the sum of whose terms diverges. Intuitively, I think it should converge conditionally because $ \sum \frac{(-1)^k}{\sqrt{k}}$ does, and the $(-1)^k$ in the denominator should not make a big difference. However, I am having trouble demonstrating its conditional convergence.  Evidently, the problem is that $\frac{1}{\sqrt{k}+(-1)^k}$ is not monotone. Let's call this sequence $a_n$. If we can show that   $$\sum_{k=2}^\infty |a_k - a_{k-1}| < \infty,$$   then we're done by Dirichlet's test. But this seems to be $O(1/k)$.   Any ideas?


So I have been trying to learn how to do motion tracking and I have a good solve error of 0.5507. I thought that after I rendered my object in my video wouldn't experience any irrational moving or sliding but I was wrong. I don't know what I'm doing wrong...      Is it these spikes in my graph that is causing it to slide around? I've read that deleting these spikes will get rid of the sliding, but literally all of my tracks do this so deleting the spike would mean deleting all my tracks.    anyone know how to fix this?  Also here are the files so you can take a look at it all yourself.

Whenever I do camera tracking in Blender the reconstruction is always zooming out or not on the axis. I have a great quality camera, but the end results of the camera tracking always has the model sliding. If you have a solution please tell me.


I'm trying to do some shizzle with SFTP and SSH but it would seem I'm getting hung up on super-simple array declaration.  According to , I should be able to use the following syntaxes to create an array:  [bob in ~] ARRAY=(one two three)  [bob in ~] echo ${ARRAY[*]} one two three  [bob in ~] echo $ARRAY[*] one[*]  [bob in ~] echo ${ARRAY[2]} three  [bob in ~] ARRAY[3]=four  [bob in ~] echo ${ARRAY[*]} one two three four   The part from that for me to focus on is this line:  [bob in ~] ARRAY=(one two three)   I tried replicating in my script:  #!/bin/bash USERS=("user1" "user2" "user3") PASSES=("pass1" "pass2" "pass3")  for i in ${!USERS[@]}; do     echo ${PASSES[i]}; done   Running this (using sh script.sh) outputs:     script.sh: 2: script.sh: Syntax error: "(" unexpected   Why is my array declaration incorrect? Is the guide just wrong?  I know I can use:  declare -a ARRAY   and then append to it, but I like the idea of using a one-liner wherever possible.   Thanks,

Does bash and sh execute a script differently? I executed a shell script with both bash and sh, and got the same output. So what is the difference?  Also, when you just run ./executable, does it use bash or sh?


On my laptop, I had Windows 7 Home Premium preinstalled. A year or so ago, I dual-booted it with Ubuntu 14.04 LTS.   I now want to upgrade Windows 7 to Windows 10 (it's free, so why not?) when it's released.  However, I'm unsure whether this will affect GRUB and stop me from accessing my Ubuntu partition. I need both operating systems and can't afford to lose either.  If this will affect GRUB, how can I restore GRUB so I can access both operating systems?  Thanks in advance.  EDIT: Just to be clear, I already have a dual-boot set up, where Ubuntu was installed alongside a pre-existing Windows installation. I now want to upgrade Windows (from 7 to 10) but am worried it will affect GRUB and my ability to boot into Ubuntu.  UPDATE: I installed Windows 10 and it ended up leaving GRUB alone. Selecting the Windows 7 option booted me into Windows 10.

I installed Windows on my computer, followed by an installation of Ubuntu. However, now I'm unable to boot into my Windows install.  What can I do to fix this?


I am trying to write an app that will trigger an pkg to open so the user can install this. I have the code and it is working well except for the following.  When I try to open the pkg file using open /tmp/mypackage.pkg in most cases it will open the Finder to the users home folder not the package.  I have checked and the package is present within the specified directory and the application is creating the correct command.  The command i am using to do this is in python:  subprocess.Popen(['open', '/tmp/mypackage.pkg']) application.close()

From the command line is it possible to open a package installer window (not install the application).  I understand I could run the application using sudo installer -pkg ..... -target ....... Instead i would like to open the package in a similar way to if I double clicked the package within the Finder.


Let's say I have String type = "Integer" for example, and I have on the other side a public class MyType<T> with a constructor public MyType(){}  How can I use the java reflection newInstance method in order to be able to do something along the lines:  public static MyType<?> create(String type){      return /*new MyType<Integer>() if type was "Integer", etc*/;  }

I read about Java's type erasure .  When does type erasure occur? At compile time or runtime? When the class is loaded? When the class is instantiated?  A lot of sites (including the official tutorial mentioned above) say type erasure occurs at compile time. If the type information is completely removed at compile time, how does the JDK check type compatibility when a method using generics is invoked with no type information or wrong type information?  Consider the following example: Say class A has a method, empty(Box<? extends Number> b). We compile A.java and get the class file A.class.  public class A {     public static void empty(Box<? extends Number> b) {} }     public class Box<T> {}   Now we create another class B which invokes the method empty with a non-parameterized argument (raw type): empty(new Box()). If we compile B.java with A.class in the classpath, javac is smart enough to raise a warning. So A.class has some type information stored in it.  public class B {     public static void invoke() {         // java: unchecked method invocation:         //  method empty in class A is applied to given types         //  required: Box<? extends java.lang.Number>         //  found:    Box         // java: unchecked conversion         //  required: Box<? extends java.lang.Number>         //  found:    Box         A.empty(new Box());     } }   My guess would be that type erasure occurs when the class is loaded, but it is just a guess. So when does it happen?


I understand most of the proof except how it starts with that $p$ and $q$ in $\frac pq$ where $p$ and $q$ are integers and $q$ can’t equal $0$, that $p$ and $q$ must be coprime? Why must they be coprime? I don’t think it’s part of the definition of a rational number.

The proof that shows the square root of 2 is irrational starts by assuming, for a contradiction, that it is rational. It starts with the assumption that it can be written as p/q where p and q have no factors in common.  Why do we start by assuming p and q have no factors in common? If we went on to find that they have factors in common, we could cancel them later on?


I'm trying to export around 20k records from a table in mysql to csv and as expected it crashes my system, is there any alternative to doing this as to avoid crashes?  here's my current export code:  $filename2 = "csv/leads_".date("M-d-Y",time()).".csv";             $fp2 = fopen($filename2, 'w') or die("can't open file");              $sql2 = $sql_getcustomers;             $res2 = mysql_query($sql2);              // fetch a row and write the column names out to the file             $row2 = mysql_fetch_assoc($res2);             $line = "";             $comma = "";             if($row2){                 foreach($row2 as $name => $value) {                     $line .= $comma . '"' . str_replace('"', '""', $name) . '"';                     $comma = ",";                 }                  $line .= ",crm_group";                 $line .= "\n";                 fwrite($fp2, $line);                  // remove the result pointer back to the start                 mysql_data_seek($res2, 0);                  // and loop through the actual data                 while($row2 = mysql_fetch_assoc($res2)) {                           $line = "";                     $comma = "";                     foreach($row2 as $index => $value) {                         $line .= $comma . '"' . str_replace('"', '""', utf8_decode($value)) . '"';                         $comma = ",";                     }                      //** GET THE CRM GROUPS                     $sql_get_group = "SELECT a.crm_group_name, b.* FROM tbl_crm_members b JOIN tbl_crm_groups a ON (a.crm_gid = b.crm_groupid) WHERE crm_uid = ".$row2["uid"];                     $sql_get_groups = mysql_query($sql_get_group);                     $res_get_groups = "";                     while($sgg = mysql_fetch_object($sql_get_groups)) $res_get_groups .= $sgg->crm_group_name.";";                     $line .= ",".trim($res_get_groups, ";");                     $line .= "\n";                     fwrite($fp2, $line);                      }                 fclose($fp2);

Is there an easy way to run a MySQL query from the Linux command line and output the results in  format?  Here's what I'm doing now:  mysql -u uid -ppwd -D dbname << EOQ | sed -e 's/        /,/g' | tee list.csv select id, concat("\"",name,"\"") as name from students EOQ   It gets messy when there are a lot of columns that need to be surrounded by quotes, or if there are quotes in the results that need to be escaped.


I would like to see the labels for every equations in pdf format? this is easier to refere later by looking for the labels in pdf format not in text file.

Working with documents with huge amount of equations it becomes cumbersome to go back and remind yourself what you labeled a certain equation to (I try to name them in a smart way, but there are too many).  Is there a convenient way to have equations print the label along with the tag/number, so that I can easily check the label in the compiled document?  Something like this would be perfect:  x = y               (14.1) eq:my_label


How long can HDD survive without power. I have three Samsung HD103SJ HDDs none of them were powered for few years. I took them from RAID 5 array and all of them were functional. Now I tried to make new RAD 5 array but they are death. All of them.  Im not asking about data retention.  I thought maybe some electrolyte capacitor died or some internal batery that helps actuator arm to get in safe position after sudden power off.

What lifetime can be expected of the typical hard disk? Or are there big differences between different types? And does it make a difference if it is used heavily instead of never being connected to system (for example serving as a backup medium)?


I have been making my first game, I have a number of levels I was thinking of making, around 20-30 but I'm not sure if this is too many. Is there a hard and fast rule for number of levels to include in a game?

One issue I grapple with across many of my games is trying to decide how many levels to put in my game. This is across genres and platforms.  In general, constraints that may decide -- although they are not applicable in my case -- can include:   Pre-determined schedule or release dates Fixed budget The game's story finishes/concludes (PCG games): difficulty becomes "impossible"   These are all great, but not sufficiently constraining as to tell me how many levels to make.   Another constraint that sounds good in theory but is hard to implement is game time -- for example, Mario or Super Meat Boy, I can guesstimate x minutes per level, and target y minutes of intended total gameplay, yielding y/x levels.  But none of these seem quite right to me. It seems like there should be a better way to decide when to add more levels and when to stop.


This is my code. I wonder why it doesn't work when I assign class attribute via javascript, but it works when I assign inline directly in html

How can I change the class of an HTML element in response to an onclick or any other events using JavaScript?


Please note, when we click on copy command on context menu in the file manager the selected file is copying. just like that i want to get the selected file in any folder  to split vedio with ffmpeg command  .  i think you get my request for help  please try to understand, for example i opened a folder and selected a file i want to know the command to store this file"s  name with full path in a  bash script variable

From time to time I come up with ideas of actions I'd like to have available in the context menu of Nautilus. How do I add them there? Is there something like a Thunar UCA plugin for Nautilus?


Apparently, it's not possible to create a nested directory in a single command?  $ sudo mkdir x/y/z mkdir: cannot create directory 'x/y/z': No such file or directory

Is there a linux command that I'm overlooking that makes it possible to do something along the lines of: (pseudo)  $ mkdir -R foo/bar/zoo/andsoforth   Or is there no alternative but to make the directories one at a time?


"The irate customer asked for the chef."  The irate customer asked something. (Noun phrase?)  Since you can fill in something in place of 'for the chef,' does that mean it is a direct object and an adverb at the same time?

An example sentence from the :  [I] He only lived a few days after the accident.  [I] means "intransitive verb". He (subject) + lived (verb) + a few days (noun). What part of speech is a few days? From the :  number 5  way of life[intransitive always + adverb/preposition, transitive] to have a particular type of life, or live in a particular way   used 'transitive verb' like 'She lives a very busy life.' From the ELU question :  She is 16 year old.  '16 years' as acting as an adverb. My questions are:  In "He lived a few days.", is a few days an object (noun) or an adverb? How is it different from "He lived for a few days."? "I walked ten miles." Number + measurement — how can I deal with 'part of speech'?


$$\lim_{x \to 0} \bigg(\frac{\sin x}{x} \bigg)^{\frac{1}{x^2}}$$  The task should be solved by using Maclaurin series so I did some kind of asymptotic simplification  $$\lim_{x \to 0} \bigg(\frac{\sin x}{x} \bigg)^{\frac{1}{x^2}} \approx \lim_{x \to 0} \bigg(\frac{x - \frac{x^3}{6}}{x} \bigg)^{\frac{1}{x^2}} \approx \lim_{x \to 0} \bigg(1 - \frac{x^2}{6} \bigg)^{\frac{1}{x^2}}$$ How can we say answer that is $e$ in the power of $-\frac{1}{6}$. I want some proving of that fact.   Thank you.

I am trying to evaluate the following but without result.  $$\lim_{x\to0}\left(\frac{\sin x}{x}\right)^{{6}/{x^{2}}}$$  Can you please give me some hints? I have tried to put log to both sides but it hasn't lead me somewhere... Thanks a lot


I would like to show a big diagram (full page,  coded as figure with \includegraphics) at the end of a Section (Section 1). Unfortunately, the text of Section 1 does not end at the bottom of a page and I have a big white-space before the diagram. Is there a way to start the text of of the next Section (Section 2) after the text of Section 1 and before the diagram to fill the white-space between Section 1 and the diagram? Thanks for your help!

How to influence the position of float environments like figure and table in LaTeX?   This is a general question and should collect useful answers for all users. I hope we can use this as a reference


Im new to blender, I accidentally dragged what i think is the animation timeline at the bottom of the screen upwards, and now It covers the entire screen. I dont know how to put it back, I tried dragging down from the top but it doesnt work. Please help.

I would like to close some view windows that I opened accidentally.  See the image below:    Edit: another note: I tried searching for the solution, but only found things like "Join Area", which don't seem to work in this situation.


If I am a resident of the United States and I wish to run Google AdSense in my website, how many months old should my website be?

I have a blog which is only 35 days old. What are the requirements for Google AdSense?  How many page views are required and how old does the site have to be?


Since I have some similar question to this one, I'll be happy to understand how to solve it.  $G$ is a group and $A,B\le G$. I need to show that $A \cap B \le G$  (If $A, B,$ are subgroups of $G$, I need to show that $A \cap B$ is a subgroup of $G$, too.)

$P$ and $Q$ are subgroups of a group $G$. How can we prove that $P\cap Q$ is a subgroup of $G$? Is $P \cup Q$ a subgroup of $G$?   Reference: Fraleigh p. 59 Question 5.54 in A First Course in Abstract Algebra.


Just starting out with Python  Could anyone explain the reasoning behind why some built in string functions take arguments within their brackets like this:  length = len("This is a string")   whilst some other functions seem to just be "chained" on to the end of the string that they are operating on for example:  uppercase = "lowercase string".upper()   Probably a silly question but just wondered if there was a reason behind this that I'm unaware of.

I know that python has a len() function that is used to determine the size of a string, but I was wondering why it's not a method of the string object.  Update  Ok, I realized I was embarrassingly mistaken. __len__() is actually a method of a string object. It just seems weird to see object oriented code in Python using the len function on string objects. Furthermore, it's also weird to see __len__ as the name instead of just len.


I have created a 3D animated character in Mixamo and uploaded the .fbx file into Blender. What steps do I need to take to export it as an .mp4 file (Maybe there is a tutorial I could watch?) I'm new to 3D animation and Blender so any help would be much appreciated :)

So I made an intro using animation and it saves it as a .blend and I want it so save as a video like .mp4 or something like that. I've tried changing the codec because I tried opening the intro with windows media instead of blend. I didn't try all the codec's but I tried some of them.


So, one of the spellcasters in my group wants to cast invisibility on the thief to have him scout out a dungeon. The Players Handbook doesn't specifically say the caster must be in sight range of the target and there is a little bit of debate between group members on whether the caster needs to maintain sight range to maintain concentration on the spell, or whether it just works no matter what (checks willing) for an hour.

Does going outside the range of the spell or breaking line of sight between the caster and target break concentration or otherwise affect control over the spell?  For example, a Heat Metal spell has a range of 60 ft. If I cast the Heat Metal spell on a an armored foe, and that foe runs outside the range of the spell (60 ft), or around the corner, does that break concentration and end the spell? Heat Metal also allows you to use a bonus action to cause the 2d8 of damage — would exercising that option be prevented by being out of range or line of sight?


In my header file I want to avoid using #include  but my class will have a vector or a pointer to a vector. I'm content with just a pointer, but I can't figure out how to declare it. Will I have to declare it as a void* and always cast it? That would be lame.  // What do I type here to forward declare vector?  class Counters {     Counters();      void inc(const char* s);      void print();      void clear();  private:     std::vector<int>* Counts;     int total; };   Please note carefully that I only want a POINTER TO a container to be stored in my class, NOT a container. The size of pointers is known without needing to refer to the declaration of the container, so please do not answer that this can't be done because the compiler needs to know the container declaration.

Is it possible to forward declare an standard container in a header file?  For example, take the following code:  #include <vector>  class Foo { private:     std::vector<int> container_;     ... };   I want to be able to do something like this:  namespace std {     template <typename T> class vector; }  class Foo { private:     std::vector<int> container_;     ... };   Can this be done?


If dual of two normed linear space $X$ and $Y$ are isomorphic, then does this implies that these two spaces are also isomorphic?  I encountered this problem while proving that if dual of $X$ is reflexive then it implies that $X$ is also reflexive.  Dual of $X$: All bounded linear functional on $X$  $X$ is reflexive: Dual of Dual of $X$ is isomorphic to $X$, if the natural mapping from $X$ to Dual of Dual of $X$ is onto.

Let $X$, $Y$ be Banach spaces such that the duals $X^\ast$ and $Y^\ast$ are isometrically isomorphic. Are $X$ and $Y$ necessarily isomorphic?    The answer to the question whether $X$ and $Y$ are automatically also isometrically isomorphic is no as the example $c$, $c_0$ which both have dual $\ell^1$ but are not isometrically isomorphic shows.


I am trying to open a TTY by Ctrl+Alt+F1 combination, but instead, I see the Ubuntu login screen, like if I have just logged out.  It is a problem for me as I'd like to run twm instead of Gnome, but I just can't access the tty. SOLVED: Ctrl+Alt+F5 was the combination I needed to access terminal "out of" X.

After upgrading to 17.10 like a true pioneer, I found the old CtrlAltF1 no longer switches between console mode and GUI, and a quick Google search brought up nothing useful. Was this feature removed entirely?


Is it possible for one to triple boot three linux distros or (2 distros together with windows)?

I would love to triple-boot Windows XP Pro, Ubuntu 12.10, and Backtrack 5 R3, but is this safe for my harddrive/other OSs on the computer?


It is said that if we travel at the speed of light,we will go into future,please could you explain how?Is it possible to make a time machine ever? Please give an easy answer, a simple one!

I read somewhere that according to relativity, it is possible - involving black holes and other stuff - to jump into the past. Is it possible for anything to go back in time either continuously or by jumping?


I died in one of my worlds in my house and I respawned in a lava lake. I'm on survival. I'm using Minecraft PC v0.10.2

I landed in lava in Minecraft: pocket edition and died. I keep respawning in that lava. What do I do?


What is the best way to run a JavaScript function when a user reaches a certain point on a web page?

I'm loading elements via AJAX. Some of them are only visible if you scroll down the page. Is there any way I can know if an element is now in the visible part of the page?


When I try to use an image for the world sky material it doesn't show the image in viewport and render, instead it shows the base color and it's black in render view, it is only happening with new .blends , I tried opening other .blends and it works,  as you can see in the picture, the sky is not showing correctly and instead it shows the base color of it which is purple-ish black

I have an object with an hdr for the background. What do I do in Cycles to render the background with my object?  How is this different from an ordinary render in Cycles?  The hdr is a big one, 350MB.


What advantages does Blender Render have? I personally always use Cycles Render, because I think the rendered material looks more realistic and node shaders are easier to use.

How does Cycles work and how is it different from Blender Internal?  Which is better?


What book will teach the most rigorous way the regression analysis? I read as a mathematician myself, and now I have to improve my statistical skills to get a job. I would like to learn what kind of methods there are to measure how to fit model to data and why those methods work. I'm not afraid to work through proofs. Is, for example, "Applied Regression Analysis and Other Multivariable Methods" written by David G. Kleinbaum, Lawrence L. Kupper, Azhar Nizam and Keith E. Muller good for learning the subject rigorously? Are there books similar to "Statistical inference" written by Casella and Berger, but concentrated on regression analysis?

What is a good introduction to statistics for a mathematician who is already well-versed in probability?  I have two distinct motivations for asking, which may well lead to different suggestions:   I'd like to better understand the statistics motivation behind many problems considered by probabilists. I'd like to know how to better interpret the results of Monte Carlo simulations which I sometimes do to form mathematical conjectures.   I'm open to the possibility that the best way to go is not to look for something like "Statistics for Probabilists" and just go to a more introductory source.


It's no longer in the File menu, it seems?

The manual for V. 2.80 says:   "To open the User Preferences editor go To File ‣ User Preferences. "  User Preference does not exist under File.  I want to make paths to folders with filepaths Where do I find it?


I recently came accross the  tag.   It has not tag wiki. Looks like a meta tag for everything that involves characters/letters 0 followers Only 104 questions.   Usages include:   Device letters for Windows as synonym for character specific letters for a language (Greek letters)   I believe it should be burninated.

I don't see any case where the  tag could be useful (or  for that matter).  are always tagged with a programming language, which is much more pertinent.  Should it be Burninated?


I've encountered an elder dragon at level 27 as a Breton. I have no dragon armor, no dragon weapons, no Wabbajack, no horse, no poisons or health based potions and I am over encumbered.   How can I escape alive and/or defeat an elder dragon?  I have a dwarven shield, armor, helmet and gauntlets, blade of woe (unimproved), Nightingale blade and orchish boots and none of them are enchanted. I have one improved item which is Elven bow (superior) and I don't have the dragonrend shout.

I finally got dragonrend and defeated Alduin, but I'm still too weak for fighting ancient dragons. Any certain weapon for killing them.  (I've got lvl 20 one handed weapons and lvl 46 for archery, so the Dragonbane is out of the question)


Here is a very simple question about light. As far as I remember from the school program, each color is merely one of the frequencies of light. I also remember that each color's wave length is different. On the other hand, when talking about the speed of light, I've always heard only one value. Why is it so? Shouldn't it be like the red color's speed must be way higher (or lower) than, say, the purple color's speed? I am quite confused here.    (Sorry if my question is too foolish, but it has bugged me for years and I was quite bad at physics at school and have never touched it since I finished school)

It is well known that a  can "split light" by separating different frequencies of light:    Many sources state that the reason this happens is that the  is different for different frequencies.  This is known as .  My question is about why dispersion exists.  Is frequency dependence for refraction a property fundamental to all waves?  Is the effect the result of some sort of non-linearity in response by the refracting material to electromagnetic fields?  Are there (theoretically) any materials that have an essentially constant, non-unity index of refraction (at least for the visible spectrum)?


Is there any software esp. forensics and such, that allow me to unlock a disabled iPhone from putting in too many wrong attempts. I know the correct PIN but I don't want to reset it since this contains VERY important data. The screen says iPhone is disabled, and connect to iTunes, but before I do that I just wanted to inquire.

A friend asked me to help her with her old iPhone 4 (she has upgraded to a 7). When I turn it on, it says, "iPhone is disabled" and "connect to iTunes."  When I do so, iTunes reports that it is locked with a passcode, and that I need to type that in to continue. However, the iPhone does not display a keypad or allow any sort of input.  Apple suggests the only solution is a wipe, but this will lose all of her photos.  Can photos be retrieved (at a minimum) from a disabled iPhone 4?


Suppose that the joint probability density function of X1 and X2 is given by: $$f(x_1; x_2) = exp(−x_1 − x_2)$$ $x_1 > 0$; $x_2 > 0$ and $0$ $elsewhere$. We define Y1 and Y2 as follows: $$Y_1 = X_1 + X_2$$ and $$Y_2= \frac{X_1}{X_1+X_2}$$  Determine the distribution of Y2.   SOLUTION:  I have used transformation theorem to find the distribution of Y2. Firstly I found that $X_1=Y_2Y_2$ and $X_2=Y_1-Y_2Y_1$  Jacobian determinant yields $J = Y_1$  Finally, I get:  $$f(y_1,y_2) = e^{y_1}\times y_1$$  QUESTION: How are the boundaries for the new joint distribution determined? I always have troubles to determine the boundaries/range in this kind of examples. Is there a technique?  To determine the marginal distribution I "integrate out" the $y_1$ (assimung the boudary is $0<y_1<1$) as follows:  $$ f(y_2) = \int_0^{1} e^{y_1}\times y_1 dy_1 = [(y_1-1)e^{y^1}]_0^1=-1$$  This doesnt seem right. I guess the boundry is where i am making the mistake?

Been crushing my head with this exercise. I know how to get the distribution of a ratio of exponential variables and of the sum of them, but i can't piece everything together.  The exercise goes as this:  If X,Y are independent exponentially distributed with beta = 1 (parameter of the exponential distribution = 1) then what is the distribution of X/(X+Y)  Any ideas?  Thanks a lot.


I want to create an Automator Service that will run an xattr Terminal command on a single or batch of files.  I can do the operation in Terminal (kinda), but I didn't understand how to apply that to Automator.  Basically I was trying to remove Where From extended attributes from an flv or mp4 file. In terminal I'd simply type:  xattr -d com.apple.metadata:kMDItemWhereFroms /Path/To/File   That threw an error, but it still worked.   I'm running macOS 10.11.6, El Cap.    I finally figured it out. It appears I didn't need to be as selective with the xattr command, since I just want to clear all the extended attributes. Here's an image of what appears to work:    I still don't entirely understand the actual Shell Script language. I learned from reading a lot of other posts that unlike Terminal, you have to tell the shell script where xattr (the tool) is.  /usr/bin/xattr   I assume that "$f" is the file(s) that you select in the Finder.  I continue to be confused by the difference between "Get Selected Finder Items" & Get Specified Finder Items." They both seem to pass whatever you choose in the Finder through. I chose the 1st option and it worked.  Apologies if this all seems elementary to you guys, I have zero experience writing scripts. I just usually cut and paste someone else's work, and 9 times out of 10 that's done the job. Just couldn't find this particular explanation anywhere. Hopefully it will help someone else.

I want to create a service using Automator to run a shell script on all files in a folder, say delete all log files. What I have done is    Created a new service in automator. Added a "Run Shell Script" action. I have change this to 'pwd' for now.  Selected "Service receives selected folders". Tried to run it, but get a message. "To test this service within Automator, add the "Get Specified Finder Items" action to the beginning of your workflow. Remove or disable the action before running the workflow outside of Automator. OK. So I add "Get Specified Finder Items". Added a 'test' directory to the list of items.   Now, when I run the script, the results window prints out my home directory.  Elsewhere, I have read that I maybe need to add   cd "$1"   to the beginning of my script. I did that but it still prints my home directory. How do I get this thing to print the directory I have selected in "Get Specified Finder Items?"  Edited to Add  Here is a screen shot of a script that works.    Here is a screen shot os a script that doesn't work.     The usual way I would deal with the "no match found : *.log" error would be to redirect error output to null. Replacing the "rm" line by  find . -name "*.log" -print0 | xargs -0 rm -rf   Does work though. This seems more difficult than it should be.


Say I measure a quantum particle at some place, and then I find it at another place. According to my understanding of wavefunctions  the particle can get from one place to another without traversing the space in between Is this phenomena a consequence of Quantum Mechanics or have i got it wrong?

My question isn't how they receive the energy to jump, but why.  When someone views an element's emission spectrum, we see a line spectrum which proves that they don't exist outside of their orbitals (else we would see a continuous spectrum).  Electrons can be released in the form of beta decay, thus proving that they are capable of traveling outside of orbitals contrary to the statement my teacher said that they stay within orbitals. Then, to add to the confusion, the older model of rings floating around a nucleus has, from what I can tell, been outdated, which would support this model. My teacher's explanation was that the electrons made a quantum jump of some kind. How do electrons move between orbitals or do we know how they jump, excluding the reason that energy causes them to jump, and why are positrons formed sometimes instead of electrons in Beta decay?  When I'm asking "how do electrons jump" I would like to know how an electron can jump between each orbital such as how it moves and how it knows where to jump since it appears to be a jump where the electron doesn't slow into a orbital position. Specifically how they jump what is this Atomic electron transition, I understand that they jump and that they do this through absorbing and releasing energy but what is this Atomic electron transition other than what is already on the wikipedia article .


Show that the number of partitions of a positive integer n where no   summand appears more than twice is equal to the number of partitions   of n where no summand is divisible by 3   So I begin by formulating this problem in terms of generating functions. Let $a(n)$ be the number of partitions of $n$ where no summand appears more than twice and let $b(n)$ be the number of partitions of $n$ where no summand is divisible by $3$.  If I showed that the $a(n)$ and $b(n)$ have the same generating functions then I am done, right ?  Now the generating function for $a(n)$ is $(1+q +q^2)(1 + q^2 + q^4)(1+q^3 + q^6).... = \prod_{i=1}^{\infty} (1 + q^i + q^{2i})$  But now I am stuck here, How can I get the generating function of $b(n)$ ? and how would I show that the generating function of $a(n)$ is the same generating function as $b(n)$ ?

Let $p_\text{odd}(n)$ denote the number of partitions of $n$ into an odd number of parts, and let $p_\text{even}(n)$ denote the number of partitions of $n$ into an even number of parts.  How do I prove that    $|p_\text{even}(n) - p_\text{odd}(n)|$ is equal to the partitions of $n$ into distinct odd parts. Show that the number of partitions of $n$ for which no part appears exactly once is equal to the number of partitions of n for which every part is divisible by 2 or 3. Show that the number of partitions of $n$ for which no part appears more than twice is equal to the number of partitions of $n$ for which no part is divisible by 3.


I am writing a mod for 2ED and really wanted to include something I found in both the 3.0/3.6 Epic Level Handbook and a Pathfinder Bestiary.  I wanted to include a Worm that Walks as the main boss, but am having problems with the conversion to 2ED, as it does not exist in any 2ED books that I am aware of.  Can anyone offer any assistance?

I would like to know if I can convert monsters from 3.x editions  (I already figured out how to convert monsters from the 1ed) into 2ed monsters.


Sometimes, when reviewing certain threads (for example, 'Suggested edits') I notice that there are series of edits from user (usually, low-rep.) with very minor changes. It's obvious that it is an attempt to increase reputation with such kind of edits - and it's not difficult to reject with too minor reason for me.  But I think such edits are not useful for SO (and, as an addition, this causes load to reviewers) - and, therefore, it will be useful to restrict users from suggesting edits for certain period if they have too many rejected edits already (for example, If user has 10 rejected edits today, next edit he would be able to suggest only after 24 hours)  Should we have such functionality? Same is to other review threads, I think. Something similar is discussed  - but it's different in my opinion.  Edit  is very similar discussion - my point is still different, may be - because I think automatic restriction (not only mod. involvement) will be quicker. Or may be such functionality already exists?

I was on the Suggested Edit's review tab today, and noticed that this user (take a look at today's ), was putting in hundreds of edits adding the C# tag to questions that didn't really need it. He got over 275 reputation today.   To me, this looked like spamming the edit system to get reputation. I started rejecting them as too minor, with also a custom message telling him this.   Here's one example:  Another:  Another:    And about 20-30 more. I hit my review cap for the day.  Is this valid editing behavior, and, if not, would a mod please get involved?  UPDATE: I've seen a couple of other meta questions about this in the last day, but it looks like the spike in gaming the system is passed.


I was learning about the relationship between the prime factors of a number and I came across this way to find the number of factors of a number. It goes like this if the prime factorization of a number $x= P_1^{L_1}  P_2^{L_2}  P_3^{L_3} \ldots$ then its number of factors is $(L_1 + 1)(L_2 + 1)(L_3 +1) \ldots$. My question is can someone find a proof of this?

I know that one way to find the number of divisors is to find the prime factors of that number and add one to all of the powers and then multiply them together so for example  $$555 = 3^1 \cdot 5^1 \cdot 37^1$$  therefore the number of divisors = $(1+1)(1+1)(1+1) = 2 \cdot 2 \cdot 2 = 8$  What I do not know (and can't seem to find when I look) is WHY this relationship exists or a formula which shows its proof.  Has anyone seen such a formula?


There came a situation in one game where there was a runner occupying first base (R1) and third base (R3), with one out. The batter then hits a ground ball to the left of the second baseman. He fields the ball and attacks R1, advancing to second base. R1 then stops and back pedals to first base to avoid the tag. The runner the second baseman then throws over to first base to get the battered runner out; with this, R3 advances home, and there is now a hot box between first and second because of R1.   After the runner is tagged at second, the umpire had tried to stop play claiming that because R1 did not just stop but back pedaled to avoid the tag, he is automatically out, and no run scores.  Was the umpire's decision right?

Here's a situation that came up during a back lot league softball game a few weeks ago. (Note: While our league has some of its own rules we try to defer to MLB rules in all causes that aren't specifically addressed.)  There is a runner on second (R2) and a runner on first, with no outs. A ground ball is hit to the third baseman (3B) who cleanly fields the ball away from third base. Seeing that R2 is running toward him, 3B does not go to third and instead waits to tag the incoming R2. R2, in an attempt to buy some time for the other runners, stops advancing to third base. As soon as R2 stops, 3B declares R2 is out (without making a tag) and throws the ball to first to make a play.  During the discussion after the play, the 3B claimed that any player advancing on a force cannot stop moving toward their next bag or they are automatically out (the same way a runner leaving the baseline to avoid a tag is considered out). Our rules don't have a specific clause that addresses this situation and I couldn't find anything in official MLB rules (though it's possible I missed something, as 3B claims it is an MLB rule).  So, is 3B’s claim correct? That if a runner who is forced to advance to their next base stops (in particular to avoid/delay a tag) they are automatically out?


I have deleted the partitions of ubuntu from windows and also wrote the command:  bootrec.exe /fixmbr   from the advanced option which appears after holding the shift key while restarting. But, when I restarted the system, it only showed a Grub terminal mentioning:     Minimal BASH-like line editing is supported. For the first word TAB lists possible command completions. Anywhere else TAB lists possible device or file completions.   Please give some suggestions how can I boot into windows from grub.

I have absolutely no experience with Linux, and I desperately need to get my computer back up and running again with Windows.  How do I remove Ubuntu and reinstall Windows?    Editor's note: many of the answers are about removing Ubuntu from dual-boot but keeping Windows (which is a bit complicated), while other answers are about removing Ubuntu from single-boot (which is easy: basically just format the disk while installing Windows). The question as written is ambiguous between dual-boot or single-boot.


This problem is quite easily solved by using logarithms and derivative and forming the function $f(x,y) = x^y - y^x$, however there are assertions that this problem can be solved without using either of the two. I can not see how one would proceed to solve this problem in the absence of logarithmic manipulation and differentiation. Can anyone shed some light on this?

I've been investigating the Cartesian graph of $x^y=y^x$. Obviously, part of the graph is comprised of the line $y=x$ but there is also a curve that is symmetrical about the line $y=x$. (We can prove this symmetry by noting that the function $x^y=y^x$ is self-inverse; all self-inverse functions are symmetrical about the line $y=x$.) An image of the graph is shown below:  I decided to find the intersection point and arrived at an intriguing result: the intersection point between the two curves is at $(e,e)$. The following is my method: If the gradient of the line $y=x$ is $1$, the gradient of the curve at the intersection point must be $-1$ as it's a normal to the line (as it's symmetrical about the line). This means that at that point $\frac{dy}{dx}=-1$. Now to find $\frac{dy}{dx}$. We have $x^y=y^x$. I then used a very powerful tehnique for differentiating these sorts of functions. We know that eg $$x^y=e^{\ln{x^y}}=e^{y\ln{x}}$$ and $$\frac{d}{dx}e^{f(x)}=f'(x)e^{f(x)}$$ Applying it to our function $x^y=y^x$ and using implicit differentiation and the product rule gives us: $$(\frac{dy}{dx}\times \ln x +\frac{y}{x})x^y=(\ln y +\frac{dy}{dx}\times \frac{x}{y})y^x$$ So $$\frac{dy}{dx}x^y\ln x +yx^{y-1}=\frac{dy}{dx}xy^{x-1}+y^x \ln y$$ Extensively rearranging gives: $$\frac{dy}{dx}=\frac{y^x \ln y -yx^{y-1}}{x^y \ln x -xy^{x-1}}$$ Let $\frac{dy}{dx}=-1$: $$y^x \ln y -yx^{y-1}=xy^{x-1}-x^y\ln x$$ But we know $x=y$ since we are at the intersection point with the line $y=x$: $$x^x \ln x -x^x=x^x-x^x\ln x$$ So $2x^x \ln x -2x^x=0$ $$2x^x(\ln x -1)=0$$ This means either $2x^x=0$ or $\ln x -1=0$ but we know $x^x$ is always greater than $0$ so $\ln x =1$, leaving us with: $$x=y=e$$ So I have my answer, but is there any other method of getting it? I have heard there is. Any help will be very welcome. Thanks in advance


On the request of a publisher, I am trying to change from Chicago style bibliography to APA style. I had this working fine:  \usepackage[backend=biber,authordate]{biblatex-chicago}   I have tried this:  \usepackage[backend=biber,authordate,style=apa]{biblatex}   It fails with   ! Package xkeyval Error: `authordate' undefined in families `blx@opt@pre'.   I remove authordate:  \usepackage[backend=biber,style=apa]{biblatex}   It compiles first, but then after I ran Biber, it fails with  ! Undefined control sequence. <argument> \mkbibdateapalongextra                                 {year}{month}{day}\iffieldundef {endyear}{...   Example:  \documentclass[11pt,a4paper]{article} \usepackage{color} \usepackage{graphicx} \usepackage[hidelinks]{hyperref} \usepackage[UKenglish]{babel} \usepackage[lf]{venturis} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} % \usepackage[backend=biber,authordate]{biblatex-chicago} % works \usepackage[backend=biber,style=apa]{biblatex} % doesn't work  \begin{filecontents*}{foo.bib}  @article{denning2010computation,     AUTHOR      = {Denning, Peter J.},     TITLE       = {What is Computation?},     JOURNAL     = {Ubiquity},     YEAR        = {2010},     DOI         = {10.1145/1880066.1880067} } \end{filecontents*} \addbibresource{foo.bib}  \usepackage{csquotes} \usepackage{tabularx} \usepackage{epigraph} \usepackage[shrink=10, babel=true]{microtype}     \begin{document} foo \autocite{denning2010computation} \printbibliography \end{document}

biblatex-apa gives me this:  ! Undefined control sequence. <argument> \mkbibdateapalongextra                                {labelyear}{labelmonth}{labelday}\iffieldu...   I'm using the default (english) language, and have done the:  \DeclareLanguageMapping{norsk}{norsk-apa} \DeclareLanguageMapping{english}{american-apa}   thing.   Here's a short example:  \documentclass[english]{memoir} \usepackage{babel} \usepackage{roffe} \usepackage[backend=biber,date=short,maxcitenames=2,style=apa]{biblatex}  \DeclareLanguageMapping{norsk}{norsk-apa} \DeclareLanguageMapping{english}{american-apa} \addbibresource{Papers2.bib} \addbibresource{R.bib}  \begin{document} \cite{R-base}  \printbibliography \end{document}   This one replicates the problem.


The union of  $x $ axis and the $y$ axis it's not manifold . It's a hausdorff second countable, but it's not locally euclidean.  I was tryin to prove it by contradiction, but I can't , the issue sopposed to be  with the (0,0).

Consider the subset $X = \{(x, 0) \mid -1 \lt x \lt 1\} \cup \{(0, y) \mid -1 \lt y \lt 1\} \subset \Bbb R^2$. It's just two open segments intersecting at $(0, 0)$.  How do you show that $X$, equipped with the subspace topology of $(\Bbb R^2, \lvert \lvert \cdot \rvert \rvert_2)$, is not locally homeomorphic to an euclidean space because of the point $(0, 0)$ ?


Can someone please guide me through the solving of $\lim \limits_{x \to 0} {\sqrt{x+2}}=2$ using the Epsilon-Delta definition?   I understand how to use $\epsilon-\delta$ in general cases and I know, so far, that: Let $\epsilon > 0,$ $$\left|\sqrt{x+2}-2\right|<\epsilon\ whenever \left|x-0\right|<\delta$$ $$-\epsilon<\sqrt{x+2}-2<\epsilon\ whenever -\delta<x<\delta$$ Let's solve for $-\epsilon<\sqrt{x+2}-2<\epsilon\\2-\epsilon<\sqrt{x+2}<\epsilon+2\\(2-\epsilon)^2<{x+2}<(\epsilon+2)^2\\\epsilon^2-4\epsilon+2<x<\epsilon^2+4\epsilon+2$     And here I'm stuck. Is this even the right way to do it ?

Prove that the function $\sqrt{x}$ is continuous on its domain $[0,\infty)$.  Proof.  Since $\sqrt{0} = 0, $ we consider the function $\sqrt{x}$ on $[a,\infty)$ where $a$ is real number and $s \neq 0.$ Let $\delta=2\sqrt{a}\epsilon.$ Then, $\forall x \in dom,$ and $\left | x-x_0\right | < \delta \Rightarrow \left| \sqrt{x}-\sqrt{x_0}\right| = \left| \frac{x-x_0}{ \sqrt{x}+\sqrt{x_0}} \right| < \left|\frac{\delta}{2\sqrt{a}}\right|=\epsilon.$  Can I do this?


Why is $\displaystyle\sum\limits_{k=0}^{n}(-1)^k\binom{n}{k}^2=(-1)^{n/2}\binom{n}{n/2}$ if $n$ is even ?   The case if $n$ is odd, is clear, since $\displaystyle(-1)^k\binom{n}{k}+(-1)^{n-k}\binom{n}{n-k}=0$ (we have $(n+1)/2$ such pairs.)  but if $n$ is even we have no symmetry, I tried to consider the odd and even terms separately but with no success.   Do you have an idea ? Thanks in advance.

How can I prove the identity:  $$ \sum_{k=0}^n\binom{2n}{2k}^2-\sum_{k=0}^{n-1}\binom{2n}{2k+1}^2=(-1)^n\binom{2n}{n}? $$  Maybe, can we expand $$ f(x)=(1+x)^{2n}? $$  Thank you.


I have used blender before, but h264 is not showing up  any way to get it on?

Even when I start a brand new file in Blender, I only get four video output file options: AVI raw, AVI JPEG, Frame Server, FFMpeg Video.  I am running version 2.78.5 (I'm using the beta so that I can use denoising.  How can I get access to all the other video outputs other people have? Like this:


Are both these sentences correct, do they carry the same meaning? Can I place the adverb now in these positions? If not, why?   Tensions submerged earlier have come to the fore, now Tensions submerged earlier have now come to the fore

Here's my problem:  I've been confused about the placement of adverbs in present/past perfect phrases. For example, which sentence would sound better:     "We had been slowly drifting down the river when a bear attacked."      or      "We had slowly been drifting down the river when a bear attacked."   Personally, I'd go with the former, and this led me to believe that if the sentence contains both "had been" and a verb, the adverb should be placed after "had been"--if the adverb is indeed modifying the verb.  This, however, led to me to think of other uses of the present/past perfect, where another verb isn't present. The is the best example I could formulate:     "He has always been an academic and a charitable person."   See, right there, always--an adverb of frequency--was placed in between has and been.  Does this mean only adverbs of frequency (e.g., always, usually, etc.) should be placed in between such constructs?  A final example to put this topic over the edge is "He had been either sick or exhausted." Now, if you were to move "either" in between "had been," would the sentence be grammatically incorrect? I've noticed that the former is used more frequently, but the sandwiched version doesn't sound wrong either.  Thanks!


I want to verify an element present in screen or not and store result in variable if it is present  I want an output like true or false in a variable and return this variable to flow (Power automate) Please suggest ideas how to do this ?

I have a scenario, in case of the user registration successful, it will display a success message on the next page otherwise an error message shows on the same page. How to automate the test case to return as passed if it is success and failure in case of error message comes up.  Please help me out here.


Can't seem to find clarification on this, it always just directs me to the Mounted Combat rule.  Mounted Combat [...] The initiative of a controlled mount changes to match yours when you mount it. It moves as you direct it, and it has only three action options: Dash, Disengage, and Dodge. A controlled mount can move and act even on the turn that you mount it. [...]  Rules as written, can a rider attack, have the mount take the Disengage action and move, and make another attack on the same turn?

From "Controlling a Mount" on p.198 of the Player's Handbook:     The initiative of a controlled mount changes to match yours when you mount it. It moves as you direct it, and it has only three action options; Dash, Disengage, and Dodge. A controlled mount can move and act even on the turn that you mount it.   Does this mean that the rider and mount share a single turn?


Sometimes when I'm new to a SE site I end up having to come up with some tags for my question that don't really fit into what people normally use on the site. Is there any way we could have the "ask question" page make some suggestions for what tags you might want to use for a particular question based on the question text?

Can we modify "Ask question" to automatically suggests tags based on your question content.   So instead that user needs to type "team-foundation-server" or "TFS" or "TeamFoundationServer" he will see list of tags auto-populated with ajax which he (or she) can then select and it will be associated with the question. So basically only thing we need is code which will cross-match question content with list of known tags while user is typing and display results in some nice ajax-enabled list/cloud/whatever UI control. This should be separate control for tags suggestions so user still has option to use standard tag list input to type-in tags.  In this case, instead of three (or more) tag variations we would have only one tag for Team-Foundation-Server.


I added some paths to Windows environment variables in PATH, but everytime I restart/shutdown my PC it deletes these variables from Windows (My custom paths). I have to add them again. Why is this happening?  For David, I saw the "duplicate" answer but I think he didn't read title. It is still ignoring my path variables even after restart or shutdown. If I apply any of noth, it deletes it.  The question it's different because in my case, it's for restart/shutdown. Duplicate answer is not valid in my question.

I use a command line tools under windows 10. The path to the tool is set in the system PATH variable so that it can be started from the command line.  Whenever a new version of the tool comes out, I store it to a new directory and update the system PATH to point to the new location. Restart the command window and everything is fine, the new version of the tool is used.  After a ahutdown and start however, the PATH reverts back to the old value and the old version of the tool gets used. Opening the envoronment variable editor and clicking OK, without making any changes, solves the problem ... until the next shutdown. I have searched the whole registry, the old PATH value is nowhere found. It must be stored somewhere else.  After some time, (I guess after a windows update gets installed, but I am not sure about this) the problem goes away and the new PATH value is remembered.  In previous windows versions this worked without problems, I see this behaviour only after upgrade to Windows 10.  How can this be fixed? Is there some way to make the effective PATH permanent?


I have read that most research Tokamaks fuse deuterium with tritium to form helium. I had a few questions if someone could kindly answer:  1) I have read that scientists want to harvest helium-3 from the moon for fusion on Earth. Since this will be an expensive endeavour I assume it is a better reaction than deuterium and tritium. Why? 2) More of an opinion from you guys but which method do you think will end up being used in nuclear fusion reactors once we crack the process of fusion -  Tokamaks, laser initiated fusion?

I see that many websites and magazines with physics thematic are pretty excited about mining Helium 3 isotope on the Moon. But this seems to be a very hard-to-get resource. For more than one reason:  There is not too much of it on the moon.  0.007% of the moon soil. Transport to earth would be also very VERY complicated in my opinion.  to take care of the harvesters.  Deuterium can be found in the seas as "heavy water". No spaceships needed. Now even when we get the Helium-3, I have a strong suspicion that it contains less energy than Deuterium but it will require more energy to start the fusion. Why I think it needs more initial energy to start the fusion?  Deuterium contains one proton and one neutron. That makes a +1e core. Helium 3 has 2 protons and one neutron - That's +2 core.  Now the worst problem with fusion reaction is, that once you pull the atoms so close, that the  no longer shield the polarity of the protons they start repelling with electric force. Now if you're trying to pull +1 and +1 together it seems much easier than pulling +2 and +2 together. Just think about the standard equation: $F_e = k*\frac{|Q_1*Q_2|}{r^2}$ where $k$ is the permittivity constant and $Q_{1,2}$ are the proton charges. Repelling force must be 4 times as large.  Why I think it contains less energy? This is even simpler to explain. In the fusion process we merge smaller cores to create larger. We normally start with hydrogen and create helium. Now when we already have Helium fused, it means that we missed one step in the fusion. Why would we do that? Can't actually Helium 3 core be one of cores that are created in Hydrogen fusion?