I have a simple question. I wondered what article I should use to refer to a noun in general. Which one is the right form?   The story of the inventor of a car. The story of the inventor of the car.   And I'm not sure other usages of definite articles in the sentences above were right, either. Thanks in advance
How do I know whether to use the definite (the) or indefinite (a, an) article, and when to omit it altogether?
Install software from packages, or build it from source? This is a  about when to use packaged software and when to build and install it yourself.   When should I install software from packages provided by my OS distribution, instead of building and installing it myself from source?  When is it better to build from source? Find a recurrence relation for the number of $n$-digit binary sequences with no pair of consecutive $1$s Find a recurrence relation for the number of $n$-digit binary sequences with no pair of consecutive $1$s.  I know my base case:$$a_1 = 2$$ for either $1$ or $0$. Normally to construct the recurrent relation I would say fill in $n-1$ spaces then add a $1$ or $0$, which is simply:$$a_n = 2\cdot a_{n-1}$$However, I don't believe this is right, because this doesn't take into account that there can't be any consecutive $1$s.  Even when I use the base case of $2$ digits:$$a_2 = 3$$for either $01$, $10$, or $00$, I still get the recurrence relation of:$$a_n = 3\cdot a_{n-2}$$which also does not account for $01$ and $10$ occurring consecutively.   So how would I express this? What are the correct settings for min-memory and max-memory in this use case?  The server has 8GB ram, dual Intel Xeon processors, running Windows Server 2008 R2 / Sql Server 2008 Standard Edition. It's running several databases ranging from 30GB - 5GB in size.  Originally the memory usage was set to the default settings (min=0 max=2,147,483,647). On these settings most of the memory usage was taken up by sqlservr.exe and the server would eventually need to be restarted every day or two. It would run normally at first but within a day start to timeout on simple operations like looking up a record using the primary key.   I have changed min=4,096 and max=6,144. This results in only 1.4GB memory usage. However now all four cpus are running at 50-60% cpu usage constantly. Tasks are taking roughly 1/3rd longer to execute, although the server is much more stable. In Avatar: The Last Airbender, Aang's eyes glow when he goes into the Avatar State. This seems to be the case with all Avatars, but Aang and the other airbending Avatars tattoos glow too.      Is there any reason for why airbending Avatars tattoos glow as well as their eyes? This has been puzzling me for a few days now, and I asked a graphic designer I knew before trying here and haven't been able to solve it yet. It's quite weird so please bear with me for a bit.  I am using Adobe Illustrator to create a logo, and I have something that can potentially work. I have used only the pen tool with strokes (no fill), but the issue is, when I view the logo at 100%, it looks pixellated! I know vectors should not even be able to appear pixellated, but they are. Here is the screenshot from AI, without exporting to anything:     That was just done using the snipping tool within Windows, and it's at 100% zoom.  I have anti-aliasing turned on from Edit > Preferences > General, and the document resolution is at 300 ppi (I get the same result with 72 ppi).   Could anyone help me with this?   If relevant: Using CS6, and have a 24 inch Dell U2412M at 1920x1200 resolution. I do have a 21.6" Samsung at 1680x1050 and I get the same result there as well. Let me know if you need any other settings, or if you would like the file, I'd be happy to provide it to be able to solve this problem. Does the pilot of a rocket ship experience an asymptotic approach to the speed of light? A question has recently come up that goes beyond my knowledge of special relativity.  Suppose a pilot has his foot on the gas pedal of a rocket ship and keeps it applied to achieve a constant acceleration, and he has a magical engine that can maintain the thrust needed to accomplish such acceleration even as the vehicle acquires mass.  He measures his acceleration at periodic intervals and sums it up as he goes.  Observers perceive the rocket to increase in speed and gradually approach the speed of light (but never reach it). Two possibilities are being debated for what the pilot observes, and my preference is for the first:   Time dilation gives him the impression that the summation of his readings are approaching light speed at a constant rate, but there is an asymptote involved here even in the inertial frame such that he never actually perceives himself to reach, let alone exceed, $c$, because time slows down to a crawl (as seen from the reference frame) before this can happen. Although to observers he is only approaching $c$, it is possible for the summation of the measurements on his accelerometer to indicate that he has surpassed $c$ and is now traveling faster than light.  From the reference frame he is approaching $c$ and his instruments in the inertial frame tell him that he has surpassed it.   I assume (1) is true beyond a doubt?  If so, is there a straightforward explanation for this? Time complexity of nested for-loop I need to calculate the time complexity of the following code:  for (i = 1; i &lt;= n; i++) {   for(j = 1; j &lt;= i; j++)   {    // Some code   } }   Is it O(n^2)? Where can I get flight info for a flight a month ago for an insurance claim? Flight stat sites will only show a weeks worth of data. Is any aspect of the supernatural testable? What level of proof is possible for the supernatural? Duty Free in the USA. Why do I have to be given my purchase as I board the plane? I am not one for buying things in airports but recently my wife asked me to get her an alcoholic beverage while flying from the USA to Ireland (JFK-DUB). I made the purchase in JFK and was surprised to be told I had to collect it when departing for my flight as I board the plane. The sales assistant's English wasn't their best so I may have misheard and my Yorkshire twang may have thrown her, but I was somewhat surprised as to why I couldn't carry the bag myself to the plane.  Is there a law that prevents me from carrying my purchase to the plane or is this an added service I was charged, which I was duped into paying?  When boarding the plane there were several others who had to pick up their sealed duty free bags (why sealed?) so it wasn't just me. No explanation was given. How can you dynamically create variables via a while loop? Holomorphic function has at most countably zeros Let $f$ be holomorphic in a domain $U$, then $f$ has at most countably zeros.  How can I prove this statement? I have seen it in Sheng Gong  explicitly, but without any indications. How to show $ \sin x \geq \frac{2x}{\pi}, x \in [0, \frac{\pi}{2}]$? I have tried the following: $$ f(x) = \sin x-\frac{2x}{\pi} \\ f'(x)= \cos x-\frac{2}{\pi} \\ f''(x) = -\sin x \leq 0 $$ But this doesn't seem to be heading in the right direction as it would appear $f'(x)$ is decreasing and has a zero within the domain, so I'm not sure how this might be used to prove the inequality. Find the Resistance between Two Terminals Let's say R = 49 ohms, and we want to find Req between a and d, how do we do that? Do we have to find Req for the whole circuit? I want to know by an example how prices in stock market changes Let us assume there is a listed company x. Currently it has 100 shares issued to trade in free float market. Current price of stock is let say 10. Now please let me know if I purchase one share of company x at the market price of 10. How it will effect the stock price. And please add and exemplify some other scenarios whichever you find good to explain more. For more information let say promoters of the company holds 100 shares with them like 50% of the company is with promoters and the other half is with people who invest or trade in that company. If I've missed to tell or assume any other vital info. needed please assume it yourself while mentioning it. Thank You I am trying to print a large quantity (several megabytes) of UTF-8 encoded text which consists of Chinese and Latin characters (and maybe a sprinkling of others). I would like to print it in several columns per page, in a very small, condensed font, preferably with control over line spacing. I'd quite like inter-column lines, but I can live without them. The aim is to print to PDF for transfer, as well as to paper.  I have tried enscript and a2ps, but neither of these support Unicode.  I have also tried paps, but this produces bitmapped outputs which cannot be PDF'd effectively, and also look terrible.  Is there a modern way to print UTF-8 text like this without resorting to something like constructing it manually in Python? Compute $\int\limits_{-\infty}^{\infty}\frac{1}{(1+x^2)^{n+1}}dx$ via residue calculus. Let $\Gamma_R$ be the semicircle of radius $R$ in the upper half plane. Then,  \begin{align} \int\limits_{-\infty}^{\infty}\frac{1}{(1+x^2)^{n+1}}dx  &amp;= \lim_{R\to \infty}\int_{\Gamma_R}\frac{1}{(1+z^2)^{n+1}}dz \\ &amp;= 2\pi i \operatorname{Res}\left(\frac{1}{(1+z^2)^{n+1}},i\right) \end{align} The pole of the function at $i$ is of order $n+1$, so the residue is computed by \begin{align} \operatorname{Res}\left(\frac{1}{(1+z^2)^{n+1}},i\right) &amp;= \frac{1}{n!}\lim_{z\to i}\frac{d^n}{dz^n}\left(\frac{1}{(z+i)^{n+1}}\right) \\ &amp;= \frac{1}{n!}\lim_{z\to i}(-1)^n\frac{(n+1)(n+2)\cdots(2n+1)}{(z+i)^{2n+1}} \\ &amp;=\frac{(2n+1)!}{i2^{2n+1}(n!)^2} \end{align} Hence, $$\int_{-\infty}^{\infty}\frac{1}{(1+x^2)^{n+1}}dx = \pi\frac{(2n+1)!}{2^{2n}(n!)^2}$$ The answer provided is $\frac{1\cdot 3\cdot 5\cdots(2n-1)}{2\cdot 4\cdot 6\cdots (2n)}\pi$. How do I manipulate my answer to obtain this answer? Proving the Cauchy-Schwarz inequality by induction I've changed the meta description tag in many of my site pages. Should I select Fetch as Google->Fetch->Add to Index->URL and all linked pages in GWT?  Will Google recrawl the whole site faster than it'd normally?  This option can be used maximum of 10 times in a month. Can there be any side affects when doing this way in case only a few of site pages have changed? Often I see code blocks pasted into questions with no formatting, or terrible formatting.  It's sometimes quite a chore to fix these: you have to either manually space out each line, or paste the code into an IDE, format it there, and paste it back.  Could we have a button/function where you could highlight a code block, and it would turn this:  foreach (var i in stuff) { if (i==1) { Whatever(); } }   into this:  foreach (var i in stuff) {   if (i==1) {     Whatever();   } }   I realise the function would have to work differently based on the language in the code block. Perhaps  it could use the same rules as the prettify code.  Also, it wouldn't be a big deal if it gets the language wrong and breaks the code, since you can always just ctrl+z.