Why $\lim_{z\to 0}\frac{(\bar{z})^2}{z^2}$ doesn't exist?
Does $\lim_{z\rightarrow0}\frac{\bar{z}^2}{z^2}$ exist?
FTP and Apache permission issues Toy Line (Production) Run I am not sure about the meaning of this:          Transformers: Generation 1 (also known as Generation One or G1) was a children's toy line that ran from 1984 to 1991 and was produced by Hasbro.     Would the following rewrite be better?        Transformers: Generation 1 (also known as Generation One or G1) was a children's toy line the production of which ran from 1984 to 1991 and was produced by Hasbro. As a follow-up to :  From what I've seen, this should work as expected:  void greet(){   char c[] = "Hello";   greetWith(c);   return; }   but this will cause undefined behavior:  char *greet(){    char c[] = "Hello";   return c; }   If I'm right, what's the best way to fix the second greet function? In an embedded environment? On a desktop? Understanding shape and calculation of confidence bands in linear regression I am trying to understand the origin of the curved shaped of confidence bands associated with an OLS linear regression and how it relates to the confidence intervals of the regression parameters (slope and intercept), for example (using R):  require(visreg) fit &lt;- lm(Ozone ~ Solar.R,data=airquality) visreg(fit)     It appears that the band is related to the limits of the lines calculated with the 2.5% intercept, and the 97.5% slope, as well as with the 97.5% intercept, and the 2.5% slope (although not quite):  xnew &lt;- seq(0,400) int &lt;- confint(fit) lines(xnew, (int[1,2]+int[2,1]*xnew)) lines(xnew, (int[1,1]+int[2,2]*xnew))     What I don't understand are two things:   What about the combination of 2.5% slope &amp; 2.5% intercept as well as 97.5% slope and 97.5% intercept? These give lines that are clearly outside the band plotted above. Maybe I don't understand the meaning of a confidence interval, but if in 95%  of the cases my estimates are within the confidence interval, these seem like a possible outcome? What determines the minimum distance between the upper and lower limit (i.e. close to the point where the two lines added above intercept)?    I guess both questions arise because I don't know/understand how these bands are actually calculated.   How can I calculate the upper and lower limits using the confidence intervals of the regression parameters (without relying on predict() or a similar function, i.e. by hand)? I tried to decipher the predict.lm function in R, but the coding is beyond me. I'd appreciate any pointers towards relevant literature or explanations suitable for stats beginners.  Thanks. What is the reasoning that leads one to postulate this second form for the relativistic particle action? The action for the free relativistic particle with worldline $\gamma : I\subset \mathbb{R}\to M$ is  $$S[\gamma]=-m\int d\lambda\sqrt{-\dot{\gamma}^a(\lambda)\dot{\gamma}_a(\lambda)}\tag{1} $$  Now, one may postulate a second action  $$S'[\gamma,\eta]=\frac{1}{2}\int d\lambda \bigg(\eta(\lambda)^{-1}\dot{\gamma}^a(\lambda)\dot{\gamma}_a(\lambda)-\eta(\lambda)m^2\bigg).\tag{2}$$  These are classically equivalent actions.  My question is: usually what we have is (1) and we have a problem both with the square root and with the massless limit. Given this, how could we think about postulating (2)? In other words, how can we reach (2)?  Usually some people answer this by saying: "it doesn't matter, actions are postulated, you postulate it, compute the equations, prove it works and its over".  Now I beg to differ. I want to know how could someone reason exactly in order to know what to postulate.   I am perfectly comfortable with computing the equations of motion. I want to know is how given (1) we would have the idea to postulate (2).  Is it some special case of some general procedure that deals with constraints? Cannot change brightness setting using function buttons or using the brightness control bar on HP laptop htaccess subdomain birthday problem - expected number of collisions There are many descriptions of the "birthday problem" on this site — the problem of finding the probability that in a group of $n$ people there will be any (= at least 2) sharing a birthday.  I am wondering how to find instead the expected number of people sharing a birthday in a group of $n$ people. I remember that expectation means the weighted sum of the probabilities of each outcome:  $$E[X]=\sum_{i=0}^{n-1}x_ip_i$$  And here $x$ must mean the number of collisions involving $i+1$ people, which is $n\choose i$. All $n$ people born on different days means no collisions, $i=0$; two people born on the same day means $n$ collisions, $i=1$; all $n$ people born on the same day means $n$ collisions, $i=n-1$.  Since the probabilities of three or more people with the same birthday are vanishingly small compared to two people with the same birthday, and decreases faster than $x$ increases, is it correct to say that this expectation can be approximated by  $$E[X]\approx {n\choose 0}p_{no\ collisions}+{n\choose 1}p_{one\ collision}$$  This doesn't look right to me and I'd appreciate some guidance.    Sorry - edited to change ${n\choose 1}$ to ${n\choose 0}$ in second equation. Sloppy of me. Punctuation with units I remember reading somewhere that if a unit is abbreviated as one character, there must not be a space between the number and the unit (e.g., 5m, 26K). If the unit is abbreviated as two or more Characters, there must be a space between the number and the unit (e.g., "10 km", "USD 5").   Can you please help me find the source again? Is this recommendation correct? After taking a statistics course and then trying to help fellow students, I noticed one subject that inspires much head-desk banging is interpreting the results of statistical hypothesis tests.  It seems that students easily learn how to perform the calculations required by a given test but get hung up on interpreting the results.  Many computerized tools report test results in terms of "p values" or "t values".  How would you explain the following points to college students taking their first course in statistics:   What does a "p-value" mean in relation to the hypothesis being tested?  Are there cases when one should be looking for a high p-value or a low p-value? What is the relationship between a p-value and a t-value? How can I fix "unbalanced brackets" in my data tag? I understand how Insight and Perception can be used passively: for the DM to determine if an enemy Deception or Stealth attempt is successful without alerting the players that someone is deceiving or sneaking.    But the Observant feat in the Player's Handbook states:      [...] You have a +5 bonus to your passive Wisdom (Perception) and passive Intelligence (Investigation) scores.     So in what situation would a DM be rolling something against the player's Investigation without letting them know? I uploaded a pre-print of an article on arXiv 1 year ago. The article was accepted in SCI journal and currently available online. However, I found a typo mistake in one equation and want to add more discussion related one figure (On researchgate I am receiving a lot of queries regarding that figure). Should i upload a new version of pre-print on arXiv? (How citations will work in this case? as arxiv version is more advanced compare to Journal version) OrI may upload a short document on arXiv as an errata/correction with extra discussion?Or I may address errata and discussion in online page of journal? Actually this journal allows the registered users to comment and start discussion related to published article. According to Theorem 8.8 in Time Series A.W. van der Vaart an ARMA process $$\phi (L)X_t=\theta(L)\epsilon_t$$ has a  unique stationary solution $X_t=\psi(L)\epsilon_t$ with $\psi=\theta/\phi$ if $\phi$ has no roots on the complex unit circle. This would imply that the explosive process, with $\rho&gt;1$, is a stationary process $$X_t=\rho X_{t-1}+\epsilon_t$$ with stationary solution $X_t=\sum_{i=1}^\infty \rho^{-i}\epsilon_{t+i}$.  Now indeed $\sum_{i=1}^{\infty} \rho^{-i} &lt; \infty$ so that weak stationarity can be proved by using this representation.   However, here on stackexchange I see a lot of question/answers that suggest that the process above is not stationary (see for example , ). In particular, the accepted answer of the latter question claims that the process is non-stationary by simulating a series and showing it displays explosive trending behaviour.  I think the only way to reconcile the theorem I mention above and the plots in the accepted answer of () is the following: the explosive process is indeed stationary but non-ergodic, that is, we cannot find the statistical properties of $X_t$ such as $\mathbb{E}(X_t)=\mu$ by observing a single infinitely long sample path of the explosive process, mathematically: $$\lim_{t \to \infty}\frac{1}{t}\sum_{t=1}X_t \neq\mathbb{E}X_t$$  Is this reading correct? How can I install .exe files of Windows 7 or more in Ubuntu? I want to run/install .exe files that require Windows 7 or higher in Wine on Ubuntu.   When I try to install a specific .exe file on Wine, it says      Windows version is not supported! You can install it in Windows 7 or higher.   How can I configure which Windows version (XP, Vista, 7, 8, ...) Wine emulates? How to find relevant and new open research topics? Storage order vs Result order This is a spin-off question from .   says this on the subject of storage order (clustered index) and the output order     A lot of people believe that a clustered index guarantees a sort order on output. But that's not what it does; it guarantees a storage order on disk.   See, for example, .   I've read the blog post by Hugo Kornelis and understands that an index doesn't guarantee that the sql server reads the records in a specific order. Yet I have a hard time accepting that I can't assume this for my scenario?  CREATE TABLE [dbo].[SensorValues](   [DeviceId] [int] NOT NULL,   [SensorId] [int] NOT NULL,   [SensorValue] [int] NOT NULL,   [Date] [int] NOT NULL, CONSTRAINT [PK_SensorValues] PRIMARY KEY CLUSTERED  (   [DeviceId] ASC,   [SensorId] ASC,   [Date] DESC ) WITH (     FILLFACTOR=75,     DATA_COMPRESSION = PAGE,     PAD_INDEX = OFF,     STATISTICS_NORECOMPUTE = OFF,     SORT_IN_TEMPDB = OFF,     IGNORE_DUP_KEY = OFF,     ONLINE = OFF,     ALLOW_ROW_LOCKS = ON,     ALLOW_PAGE_LOCKS = ON)   ON [MyPartitioningScheme]([Date])   My original query was this:  SELECT TOP 1 SensorValue   FROM SensorValues   WHERE SensorId = 53     AND DeviceId = 3819     AND Date &lt; 1339225010   ORDER BY Date DESC   But I suggest that I could as well use this one (read below for my explanation):  SELECT TOP 1 SensorValue   FROM SensorValues   WHERE SensorId = 53     AND DeviceId = 3819     AND Date &lt; 1339225010   As you can see, my table rows are small (16bytes) and I've got only one index, a clustered. In my scenario, the table consists of 100.000.000 records at this moment (and this will most likely increase tenfold).  When the database server queries this table it has two ways of finding my rows, either it seeks the primary key and thereby reading and returning my values in desc. order of Date, or it has to do a full table scan. My conclusion is that a full table scan on all those records will be way too slow and the database server will therefore always seek the table via its primary key and thereby returning the values sorted by Date DESC I have a text box that will have a currency string in it that I then need to convert that string to a double to perform some operations on it.   "$1,100.00" → 1100.00  This needs to occur all client side. I have no choice but to leave the currency string as a currency string as input but need to cast/convert it to a double to allow some mathematical operations. What is the term when a word is used consecutively twice, with intentional stress placed on the first word, as a means to alter the severity of the word's meaning?  I am not referring to a  (had had) or a  (that that), but to the slightly sarcastic use as demonstrated in shows like Seinfeld. Sample sentences, with emphasis:  I know we're going out to eat, but I am only going to pick at an appetizer because I'm not hungry hungry. Don't wear something so formal to the party; I don't think you need to be dressed dressed.  Of personal note, some of my relatives decided a few years ago to nick-name the term a &quot;Celaine&quot; (a combination of their names) due to their own frequent use of it. Note: This question explicitly requests the term of art used by linguists and English scholars when discussing this phenomenon. This question is different from a  which requests a historical explanation for the phenomenon described by this term. None of the answers to the suggested duplicate provide the term.  The author of the similar question requests the term for the pattern in a comment, but does not receive an acceptable answer. The only mention of an acceptable term is in a comment made by the author of this question, in response to the author of the similar question, directing back to this very question. I have installed Ubuntu on my laptop and now I want to remove it and the Grub Loader. How I can do it without the Windows installation disk (I cannot use the Recovery Console).