When I was a kid I had this large (coffee table-ish) hard cover illustrated book, which was basically a travel-companion guide for people going on this intergalactic cruise.  The whole thing was spun (basically) as a brochure for all these different exotic destinations that the cruise would visit.  It was (as I recall) incredibly well crafted, with a lot of very clever detail and gorgeous art.
I remember reading a sci-fi story where astronauts visit a planet, which is covered in stationary aliens with mile long necks that filter feed from the atmosphere.  It was published between 1960 and 2000.    It was in English and involved a pair of astronauts that went from planet to planet on a tour or something, though I don't know details of any other planets they visited.
Find asymptotic of recurrence sequence Given a sequence $x_1=\frac{1}{2}$, $x_{n+1}=x_n-x_n^2$. It's easy to see that it limits to $0$.  The question is: is there exists an $\alpha$ such, that $\lim\limits_{n\to\infty}n^\alpha x_n\neq0$.  I tried to find explicit formula for $x_n$, but did not succeed. I stucked at that point: if $a_1=(\frac{1}{4})^2$, $a_n=(a_{n-1}+\frac{1}{4})^2$, then $x_n=-a_{n-2}+\frac{1}{4}$ for $n\ge3$.   Thanks for any ideas and help. Let $z_1,z_2,\ldots,z_n$ be complex number such that $|z_i|&lt;1$ for all $i=1,2,\ldots,n$. Show that we can choose $a_i \in\{-1,1\}$, $i=1,2,\ldots,n$ such that $$\left|\sum_{i=1}^n a_iz_i\right|&lt;\sqrt3.$$ How come if $\ i\ $ not of the following form, then $12i + 5$ must be prime? I know if $\ i\ $  of the following form $\ 3x^2 + (6y-3)x - y\ $ or $\ 3x^2 + (6y-3)x + y - 1, \ \ x,y \in \mathbb{Z}^{+},i \in \mathbb Z_{\ge 0}$,  then $\ 12i + 5\ $ must be composite number, because:  $12(3x^2 + (6y-3)x + y - 1) + 5 = 36x^2 + (72y - 36)x + (12y - 7) = (6x + 12y - 7)(6x  + 1)$  How come if $\ i\ $ not of the following form $\ 3x^2 + (6y-3)x - y\ $ and $\ 3x^2 + (6y-3)x + y - 1\ $,  then $12i + 5$ must be prime? $\ x,y \in \mathbb{Z}^{+},i \in \mathbb Z_{\ge 0}$.  For example: $\ 5 = \ 3*1^2 + (6*1-3)*1 - 1\ $ ,when $\ x = y = 1\ $, as proved before,$\ 5*12+5\ $ must be composite number;  $\ 0, \ 1. \ 2.\ 3.\ 4\ $ can't of the following form $\ 3x^2 + (6y-3)x - y\ $ and $\ 3x^2 + (6y-3)x + y - 1\ $,  $\ 12*0 + 5 = 5\ $, $\ 5 $ is prime,$\ 12*1 + 5 = 17\ $, $\ 17 $ is prime, and so on, My daughter asked me to cosign on a car loan.  Somehow I ended up as the borrower and she a the cosigner.  Is that legal? How to get speech output from entered text by using command-line?  Also facility to change speech rate, pitch, volume etc using simple command. I am trying to write a condition into a SQL WHERE clause that forces the column comparison to a variable to be compared in lowercase. However the addExpression function isn't accomplishing this (since that is putting the expression in the field selection, not the where clause.  Here is what I have tried:  $category = 'mobile wifi'; $query = db_select('taxonomy_term_data', 'ttd')     -&gt;fields('ttd', array('tid')); $query-&gt;innerJoin('taxonomy_vocabulary', 'tv', 'ttd.vid = tv.vid'); $query-&gt;addExpression("LOWER(ttd.name) = $category"); $result = $query-&gt;condition('machine_name', 'images_cat', '=')     -&gt;execute()     -&gt;fetchAssoc();   And this:  $category = 'mobile wifi'; $query = db_select('taxonomy_term_data', 'ttd')     -&gt;fields('ttd', array('tid')); $query-&gt;innerJoin('taxonomy_vocabulary', 'tv', 'ttd.vid = tv.vid'); $result = $query-&gt;condition('machine_name', 'images_cat', '=')     -&gt;condition('LOWER(ttd.name)', $category, '=')     -&gt;execute()     -&gt;fetchAssoc();   The second one becomes invalid and the first one causes the problem I mentioned above. Any thoughts or suggestions?  Thanks, Patrick Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$ For all $a, m, n \in \mathbb{Z}^+$,   $$\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$$ Appendix without letter in TOC let $x,y,z,w&gt;0$,show that $$(x+y)^3+(y+z)^3+(z+w)^3+(w+x)^3\ge 8(x^2y+y^2z+z^2w+w^2x)$$  it seem use AM-GM inequality to solve it,But I can't it,Thanks I am going to shoot a wedding this weekend, and I want to do my best for my friend's big day.    What can I do to prepare for the day in order to minimize failures and mistakes? How do I avoid missing important shots? What backup plan should I have?   I have been shooting for 6 years or so, and I know wedding is one of the hardest thing to do. I have told my friend what I end up producing will be of no match with the work of dedicated wedding photographers, not even the ones that are about to fall out of business.  They are on a tight budget, they said some photos are still better than none, they really must minimize the cost as much as they can. I exaggerated again that my photos will be worse off than the cheapest wedding photographer you can find.  She has been a close friends for years, I want to do everything I can to help her.  Their wedding is at 12:30pm coming Sunday, I have visited the venue last Sunday at 12:30pm to check traffic condition and also the lighting.  The setup is mainly outdoor (no church), the indoor area will not have a good ceiling for bounce. Being at the middle of the day, this can mean some tricky fill flash. I have jot down a list of must-have shots. I am also asking for the seating plan and the event run-down.  Gear:   Canon EOS 60D , EF-S 15-85mm f/3.5-5.6 IS USM Canon EOS 450D (or I can borrow a 550D), EF 50mm f/1.4 Speedlite 580 EXII Speedlite 270 EXII Yongnuo 460 (a cheap but powerful manual flash as backup) Samsung EX-1 f/1.8 point and shoot (backup of a backup...?)   Other lenses that I have but I don't think will be useful:   50mm f/1.8 EF-S 50-250mm f/4.0-5.6 IS II EF-S 18-135mm f/3.5-5.6 IS (I have the better 15-85 on 60D, should I put this on the 450D as a backup allrounder?) EF-S 60mm f/2.8 Macro (should I replace 50mm f/1.4 with this for added macro? You can hardly use f/1.4 under direct sunlight if you want to have fill-flash)   I have two batteries for all cameras (60D 450D and EX1). I have like in total 64GB SD card (I am really inclined to get more, or bring a laptop for on-the-fly backup, or do both). I recently repaired my 580EXII, it has a brand new flash head so the recycle time is as good as it can be, I just need a tonne of batteries. No I don't have external power pack or battery grip for my cameras.  I have a great monopod, but a cheap tripod.  I am happy to bring everything, just putting them in the boot of my car. The carpark is on-site, walking from venue to my car is under 1 minute.  I will have my girlfriend carry the 450D and shoot details / non-portraits.  One concern that I have is fill flash, I really do not have a large surface to bounce off  from. I have shot events before but they are not as dynamic/critical as a wedding.  How do I prepare for differing weather conditions?  If its sunny, fill flash is probably going to be in every single shot. If its cloudy, I probably will turn off the flash. If it rains, my 60D should be fine I have used it in slight rain before, but I really don't know their plan and if they have extendable shelters etc.  What else should I prepare for? Having no experience I want to be as prepared as I can be. Maybe I have overlooked something, maybe there is something else I can do to ensure the shooting will go smoothly. Your help is greatly appreciated! How to reverse the pagination numbers of an archive? I have archive pages that each contain titles and excerpts from 10 blog entries. Both entries and archive pages are in reverse chronological order:   when a new blog entry is written its title and excerpt go to the top of the front page; when you are on one page and you click through to "Next page", you get the titles and excerpts for the 10 previous blog entries.   This is pretty standard for blogs.  But the archive pages are numbered by default in the same order. Thus Page 1 contains excerpts from the most recent 10 entries, Page 2 contains excerpts from the next 10 most recent, etc.  To be clear: at the moment, "Next page" refers to the page with the next higher number. Thus the front page, which contains excerpts from the most recent entry and the nine next most recent entries, is labelled Page 1, and the 10 entries posted before those 10 entries are on Page 2.  I need the page-numbering the other way round, namely in direct chronological order, so that for example if there are 97 entries then   entries 28-37 would be excerpted on Page 4, and the PREVIOUS page from there, containing excerpts from entries 18-27, would be called page 3.   How can I achieve this, whether by amending functions.php in the child theme (preferably), by writing a "Snippet" (next most preferred), or by amending archive.php in the Astra parent theme directly (least preferred, because of possible update problems)?  Edit  The following isn't a solution but it may be part of one. This re-numbers pages into direct chronological order, but unfortunately it also reverses the order in which they are shown (from reverse chronological to direct chronological). So it causes the front archive paget to contain excerpts from the earliest posts rather than the latest ones!  &lt;?php  add_filter('pre_get_posts', 'posts_by_forward_date');  function posts_by_forward_date($query) {   if(is_archive() || is_home()) {     $query-&gt;set('order', 'ASC');   } } ?&gt; How many numbers of 6 digits, that can be formed with digits 2,3,9. And also divided by 3? How many numbers of 6 digits, that can be formed with digits 2,3,9. And also divided by 3?  $$$$ I was trying to to add 2^6 (when there is no 2)+ C(6,2)2^2 (when 2 can be in two places)+C(6,3)2^3 (when 2 can be in three places)... I know that Wubi is slower in disk IO, but I can't find anything about it online other than vague statements such as "slightly slower disk seeks".  Has anyone done any benchmarks to quantify the speed difference? In TeX, how is computing zero sign written with slanted vertical line on it? How to change user in WinSCP? I'm using WinSCP to access Unix computers. How can I change user after I have logged into a Unix server using WinSCP?  E.g. I have personal account in Unix computer A. I can log into this computer using PuTTY and then change user to root user  $sudo /usr/bin/su - rootuser   How can I do the same thing using WinSCP? I don't know the password for rootuser. How to open recovered files in word? My computer restarted while I was asleep because of system updates (need to turn that off), and when I opened up Word the first time after it restarted, it gave me a pane on the left hand side that showed me all the documents I had opened.  I chose one of the documents but I want to open them all, how can I bring that pane back?    Update:  I forgot to mention I'm on Word 2007.  I've found that if you go to      C:\Users*YOURUSER*\AppData\Roaming\Microsoft\Word   you can see the autorecovery files.  Mine are still in there, but I don't want to touch them, I'd rather bring back that pane and do it right just in case they disappear as soon as I double click haha... A Banach space is reflexive if and only if its dual is reflexive How to show that a Banach space $X$ is reflexive if and only if its dual $X'$ is reflexive? Assuming I have an ArrayList  ArrayList&lt;MyClass&gt; myList;   And I want to call toArray, is there a performance reason to use  MyClass[] arr = myList.toArray(new MyClass[myList.size()]);   over  MyClass[] arr = myList.toArray(new MyClass[0]);   ?  I prefer the second style, since it's less verbose, and I assumed that the compiler will make sure the empty array doesn't really get created, but I've been wondering if that's true.  Of course, in 99% of the cases it doesn't make a difference one way or the other, but I'd like to keep a consistent style between my normal code and my optimized inner loops... How to get pixel data from a UIImage (Cocoa Touch) or CGImage (Core Graphics)? As I understand, the different voltage between two object is caused by the total different charged between two object. Thus, the higher extra electron between two opposite charged object, the higher voltage between them, isn't it? So if i have two battery or capacitor connect in parallel, the negative connect to negative, the positive connect to the positive. Caused the charge from each plate to be double. So that's as my expected, it must be double voltage, but ironically why it's out of my expected and the reality is vice-versa?