$g = \Delta v/t$, so $\Delta v = gt$. $v = v_0 + \Delta v$, so $v = v_0 + gt$. So if $\Delta x = vt$, then $\Delta x$ should be $v_0t + gt$. Why the $\tfrac{1}{2}gt^2$? I'm really confused, so this question is also probably very confusing. Sorry and thanks in advance!
I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?
If in a UFD every maximal ideal is principal then it is a PID How can I ensure my Samsung Series 7 is actually using the Radeon switchable graphics? I have a Samsung Series 7 with the Radeon 6750M switchable graphics. The ATI software lets you force programs to use the dedicated card. However, I'm not convinced it is actually ever using it, as the frame rates on some non-taxing games (Portal, TF2) are merely OK. To make matters worse, it looks like the ATI Catalyst Control has vanished from my laptop. To make it even worse, you can't download the driver and ATI CCC from ATI's site, you need to download it from Samsung, and the ZIP they provide is corrupted.   How can I ensure my Samsung Series 7 is actually using the Radeon switchable graphics? What is the probability that $x_1+x_2+...+x_n \le n$? Reference for the subgroup structure of $\rm{PSL}_2(q)$ How to prove that you have significant ties with family in your home country? How can I prove the immigrant officers that I have significant ties in my home country?  Are there any documents that I need? I am aware that, to use a Spell Scroll, you must have the related spell on (at least one of) your spell list(s). Then, if you have the spell slot to cast it, you succeed automatically; else, you must make an ability check in order to cast it (failure resulting in the scroll being wasted).  Consider this example : A Cleric 5 / Wizard 4 finds a Raise Dead Spell Scroll. The spell is on the Cleric List, but is a fifth level spell. Considering that the cleric-wizard has fifth level slots, but can only pick up to third level cleric spells, would he have to make the ability check to successfully cast the Raise Dead in the Spell Scroll, or would he succeed automatically ? shell scripts are still working without #!(sha-bang line) I am new to shell scripts and many books have written that use #!(sha-bang) line in starting of the script to invoke the interpreter .And this will invoke a new shell for script and do the interpretation line by line.But one of my basic script is still running without the magic line.  so my questions are:   from where did my basic script get the interpreter. how did the script manages to locate the interpreter.   now let me tell you about my basic script it just contains the following line:  echo "basic script without the magic lines" Do I have to buy a second wildcard certificate for a subdomain? We already have a wildcard certificate for *.mycompany.com. Our network has hosts that are only reachable internally. All of them belong to the internal.mycompany.com subdomain. There is a private server with the host name server.internal.mycompany.com on which I deployed our wildcard certificate.  When I visit the web server I get a host name mismatch error. Do I really have to get another wildcard certificate for *.internal.mycompany.com or is there another (free!?) way to use our wildcard certificate for all of our subdomains and its subdomains without getting an error in the browser? Does the derivative of a continuous function goes to zero if the function converges to it? Reapplying for a UK Standard Visitor visa after a refusal Default currency symbol In statistical learning, implicitly or explicitly, one always assumes that the training set $\mathcal{D} = \{ \bf {X}, \bf{y} \}$ is composed of $N$ input/response tuples $({\bf{X}}_i,y_i)$ that are independently drawn from the same joint distribution $\mathbb{P}({\bf{X}},y)$ with  $$ p({\bf{X}},y) = p( y \vert {\bf{X}}) p({\bf{X}}) $$  and $p( y \vert {\bf{X}})$ the relationship we are trying to capture through a particular learning algorithm. Mathematically, this i.i.d. assumption writes:  \begin{gather} ({\bf{X}}_i,y_i) \sim \mathbb{P}({\bf{X}},y), \forall i=1,...,N \\ ({\bf{X}}_i,y_i) \text{ independent of } ({\bf{X}}_j,y_j), \forall i \ne j \in \{1,...,N\} \end{gather}  I think we can all agree that this assumption is rarely satisfied in practice, see this related  and the wise comments of @Glen_b and @Luca.  My question is therefore:      Where exactly does the i.i.d. assumption becomes critical in practice?    [Context]   I'm asking this because I can think of many situations where such a stringent assumption is not needed to train a certain model (e.g. linear regression methods), or at least one can work around the i.i.d. assumption and obtain robust results. Actually the results will usually stay the same, it is rather the inferences that one can draw that will change (e.g. heteroskedasticity and autocorrelation consistent HAC estimators in linear regression: the idea is to re-use the good old OLS regression weights but to adapt the finite-sample behaviour of the OLS estimator to account for the violation of the Gauss-Markov assumptions).   My guess is therefore that the i.i.d. assumption is required not to be able to train a particular learning algorithm, but rather to guarantee that techniques such as cross-validation can indeed be used to infer a reliable measure of the model's capability of generalising well, which is the only thing we are interested in at the end of the day in statistical learning because it shows that we can indeed learn from the data. Intuitively, I can indeed understand that using cross-validation on dependent data could be optimistically biased (as illustrated/explained in ).   For me i.i.d. has thus nothing to do with training a particular model but everything to do with that model's generalisability. This seems to agree with a paper I found by Huan Xu et al, see "Robustness and Generalizability for Markovian Samples" .   Would you agree with that?  [Example]   If this can help the discussion, consider the problem of using the LASSO algorithm to perform a smart selection amongst $P$ features given $N$ training samples $({\bf{X}}_i,y_i)$ with $\forall i=1,...,N$ $$ {\bf{X}}_i=[X_{i1},...,X_{iP}] $$ We can further assume that:   The inputs ${\bf{X}}_i$ are dependent hence leading to a violation of the i.i.d. assumption (e.g. for each feature $j=1,..,P$ we observe a $N$ point time series, hence introducing temporal auto-correlation) The conditional responses $y_i \vert {\bf{X}}_i$ are independent. We have $P \gg N$.    In what way(s) does the violation of the i.i.d. assumption can pose problem in that case assuming we plan to determine the LASSO penalisation coefficient $\lambda$ using a cross-validation approach (on the full data set) + use a nested cross-validation to get a feel for the generalisation error of this learning strategy (we can leave the discussion concerning the inherent pros/cons of the LASSO aside, except if it is useful). How did Harry breach the Statute of Secrecy? Something always bothered me with Fudge's accusations:     “Disciplinary hearing of the twelfth of August,” said Fudge in a   ringing voice, and Percy began taking notes at once, “into offences   committed under the Decree for the Reasonable Restriction of Underage   Sorcery and the International Statute of Secrecy by Harry James   Potter, resident at number four, Privet Drive, Little Whinging,   Surrey." - OotP Ch. 8 "The Hearing"   Harry cast the Patronus Charm, so he violated the Decree for Reasonable Restriction of Underage Sorcery alright - extinuating circumstances aside - but how did he breach the Statute of Secrecy?  The only witnesses were Dudley and Mrs. Figg, both of whom already knew that Harry is a wizard. Earlier, even Hermione gets it wrong (don't tell her!):     They haven’t even reported that you broke the International Statute of   Secrecy. We thought they would,... - OotP Ch. 4 "#12"   Yes, Harry does use magic in front of a Muggle, Dudley, but even Dudley is not so thick that the fact that Harry's a wizard would come as a revelation to him. Harry cannot breach the Statute of Secrecy to someone already in the know.  Shouldn't Dumbledore point out that glaring error in the indictment sooner rather than later? Or at least mention it, at all?  Is there maybe a source that mentions the Statute of Secrecy containing a clause, that even the mere possibility of magic being witnessed by an uninitiated muggle is sufficient for its breach?? Cause if so, wouldn't even adult wizards have a really tough time doing anything, ever.  Possibly related: Been trying to find graphic novel for decades - at least I think it's a graphic novel When I was a kid I had a book that I loved, as I think about it I'm pretty sure it would be characterized as a graphic novel although I was unfamiliar with that term at the time. It was a large hardcover comic book but a full-length story, probably a few hundred pages long.  This would have been about 25-30 years ago.  I recall a little about the plot: It starts with a spaceship crashing somewhere, I remember one of the first panels had the phrase that the ship "yawed wildly". I always remembered that because I had to look up the word "yawed".   The rest of the story is told in flashback form, with the rise of an empire, and I'm pretty sure there's a guy who's a slave or otherwise in the lower strata of society who rises to be the ruler of the world or something like that.    I thought that the title had the word "titan" or "empire" in it (Empire of the Titans, or Rise of the Titans, or something similar), but Google searches have been unfruitful. Is there a website with historical temperatures and weather data? I am interested in hiking this fall in France and camping along the way. In order to figure what gear I need to pack to camp (particularly for the sleeping bag), I would like to know what temperatures to expect.  I am interested in historical temperatures to figure the usual temperature and I might look at them for other seasons. If that matters, I am thinking about hiking in the Pays Basque (South West of France), the mountainous part.  Where (ideally online and for free) can I find such data? Are there resources that cover Europe, or even the whole world? How are java.lang.Object's protected methods protected from subclasses? The keyword protected grants access to classes in the same package and subclasses ().  Now, every class has java.lang.Object as superclass ().  Hence I conclude that every class may access java.lang.Object's methods even if they are protected.  Take a look at the following example:   public class Testclass {   public Object getOne() throws CloneNotSupportedException {     return this.clone();   }   public Object getTwo() throws CloneNotSupportedException {     return ((Object) this).clone();   } }   While getOne() compiles fine, getTwo() gives   Testclass.java:6: clone() has protected access in java.lang.Object         return ((Object) this).clone();   I neither understand why getTwo() doesn't compile nor what's the difference (regarding the access of java.lang.Objects members) with getOne(). One frequent aspect of pdflatex output that could be improved is to what extent one can select text output from the generated pdf-file and copy-and-paste it. This is essentially an issue of having the right output encoding. There are at least two important aspects to this:   In the ideal case, Unicode would be the output encoding. Ligature glyphs (such as ﬁ) are ideally de-ligated in the output (here: "fi").   It seems that output encodings are specified through the fontenc package. What is the range of possible output encodings, and most importantly: Is there a way to specify a Unicode output encoding and one that deals with ligatures in the intended way?  (Note: It is important to distinguish output from input encodings. How to use different input encodings in LaTeX has been documented widely. My understanding is that this is best handled by the inputenx package, as it supersedes the inputenc package.)    Quick guide to the solutions: The information in the answers and answer threads is a bit distributed, so here the short summary: one approach is to use \input glyphtounicode together with \pdfgentounicode=1; the other approach is to use cmap/mmap.  Addendum: Sometimes one will need to load the package accsupp and enclose one's macro definition in \BeginAccSupp{method=hex,unicode,ActualText=&lt;codepoint&gt;}[...]\EndAccSupp{} to generate a specific code point. See the caveat about non-BMP code points  and the fix (starting from accsupp version v0.4, 2012/11/18) , which provides the new unichar package option. Installing ArcView 3 on 64-bit Windows? How do I install ArcView 3 on 64bit Windows?   There are numerous threads on the Esri forums for how to accomplish this, but the solutions are scattered, inconsistent and disjointed.   This is a request to post integrated and "cleaned-up" solutions, don't just copy and paste. Please indicate if the method is specific to x64 XP, Vista, or 7 (and post seperately, e.g. win7 method in one answer, vista in another). How do you handle uneven tiles while rendering a tile map? Here is what I want to do with my tile map that I am unsure of. As you can see the top walls are way larger then the bottom and side ones (this is also an issue with my corners which are odd shapes [more like an L then a square] as well as larger then the 40x40px that my current tiles are).    I have also attached the tile sheet I am using for the tiles to show you what the corners and tops look like compared to the rest of the tiles.  What I’m thinking is I might be able to just draw them using the same array I have if I use the tiles width and height instead of a set WxH? I dont know how well this will work, but were the blocks that will have different values will be blocks the player/NPCs can’t step on then it may not be an issue, again I’m not even sure if that is a viable solution.  My code in case you want to see how I'm currently handling it:  (pastebin) (edit:im not handling it, meant how I'm currently doing the map)  tl;dr - how can I take take my 2d looking tile map and change it to have different size tiles? or is there a better way to do what I am trying to do? Is there a name of a method that I should be looking for while googling? In electrostatics, why the electric field inside a conductor is zero? In electromagnetism books, such as Griffiths or the like, when they talk about the properties of conductors in case of electrostatics they say that the electric field inside a conductor is zero.  I have 2 questions:    We know that conductors (metallic) have free electrons which randomly moves in all directions, so how come we can talk about electrostatics which by definition means stationary charges? When the textbooks try to show why the electric field inside a conductor is zero they say let us put our conductor in an electric field. What happens then is that there will be an induced surface charge density which consequently induces an electric field within the conductor such that the total electric field within the conductor will be zero. That is perfectly understood, but my problem is the following: the original claim was that the electric field within a conductor is 0, not the electric field after putting the conductor in an external electric field it became zero. I do not understand the logic!