I am an Indian citizen currently in NZ and I need to travel to India really fast.   The cheapest flight I could find was a China Airlines that will be stopping at Sydney for a refuel. I know that Indian passports need Transit Visa when travelling through  Aus but, do you still need it if you don't have to deboard the plane and it's only stopping for a 2 min refuel?
Indian passport holder. Do I need transit visa in Sydney?
Save entire process for continuation after reboot Ways to update Ubuntu (debian-based distros) offline What is the easiest way to update/upgrade an offline Ubuntu machine with the help of a Windows machine that has internet access?  This question also applies to installing new packages offline and not only updates/upgrades.  The Linux system shall remain completely cut off from the Windows machine, meaning there should be no ethernet connection or the likes between the two computers.  Update:  Please have patience, since I haven't updated this since two weeks. There are some complications getting apt-offline to work properly on Lubuntu and all other methods seem to be too old and deprecated:  AptOff - last update 2006 AptMedium - last update 2007 Keryx - last update 2011, looks like this project was discontinued  I hope I will be able to somehow update the offline machine, finally.  While I was still not able to update/upgrade the offline system due to authentication errors, I accepted an answer, because it's taking too long. What's the easiest way to install a missing Perl module? I get this error:  Can't locate Foo.pm in @INC  Is there an easier way to install it than downloading, untarring, making, etc? If a stock doesn't pay dividends, then why is the stock worth anything? I read somewhere that companies are not required to pay dividends to shareholders (this is correct, yes?).   If so, then if company A never pays dividends to its shareholders, then what is the point of owning company A's stock? Surely the right to one vote for company A's Board can't be that valuable.   What is it that I'm missing? Show that the LU decomposition of matrices of the form $\left[\begin{smallmatrix}0& x\\0 & y\end{smallmatrix}\right]$ is not unique How can I show that every matrix of the form $\begin{bmatrix}0&amp; x\\0 &amp; y\end{bmatrix}$ has an $LU$ factorization and that even if $L$ is unit lower triangular there is not a unique factorization?  I am completely stuck. Any ideas would be greatly appreciated I'm trying to write a shell script that, when run, will set some environment variables that will stay set in the caller's shell.  setenv FOO foo   in csh/tcsh, or  export FOO=foo   in sh/bash only set it during the script's execution.  I already know that   source myscript   will run the commands of the script rather than launching a new shell, and that can result in setting the "caller's" environment.  But here's the rub:  I want this script to be callable from either bash or csh.  In other words, I want users of either shell to be able to run my script and have their shell's environment changed.  So 'source' won't work for me, since a user running csh can't source a bash script, and a user running bash can't source a csh script.  Is there any reasonable solution that doesn't involve having to write and maintain TWO versions on the script? What measures can/should I take to make sure that security around my SSH server is absolutely impermeable?  This will be community wiki from the start, so lets see what people do to secure their servers. In the radio series, how did Zaphod get into the artificial universe? In the book The Restaurant at the End of the Universe, it's very clearly explained how Zaphod gets into the simulated universe; he's in it from the moment he enters Zarniwop's office, and a big deal is made of him leaving via the window rather than the door so that he stays in it.  In the radio series, however, this doesn't happen. At the end of Fit the Seventh, Zaphod asks "How do we get to this universe, then?" and Roosta replies "I'm afraid it looks like we don't...", pointing out that the building is splitting down the middle, preventing them reaching the office.  Later, in Fit the Twelfth, Zaphod finally meets Zarniwoop in the lounge of the slightly-delayed spaceliner and reacts with astonishment at learning he's been in the artificial universe all this time. "How did we get into it? I mean like where, when?"  Zarniwoop only replies enigmatically: "You didn't notice? Well, I'll let you work it out for yourself."  So, how did he get in? As noted, he never actually entered Zarniwoop's office. My only thought is that it happened during the "body debit" incident with the disco, but there's no particular indication that that should be the case. Is there any other possibility? A murder of crows? I love the subset of collective nouns known as the terms of venery. These are collective nouns specific to a particular group of animals. Some of the more inventive examples are: a murder of crows, a crash of rhinos, a mischief of mice, and a puddling of ducks (specifically swimming ducks).  Is there a standard for these group names and is there a central reference for them as with other zoological taxonomy?  I can see in the Wikipedia articles that the practice has its origins in Medieval Hunting tradition, but the Kangaroo (Mob), for instance would have been unknown at that time, so how do new collections come into being? The question is $$\text{If }\, p, \ q\in \mathbb{N}, \;1-\frac12+\frac13-\frac14-\dotsb-\frac{1}{1318}+\frac{1}{1319}=\frac{p}{q}.\qquad \text{Prove that } 1979\mid p.$$ So my solution went like this:  $$S=1-\frac12+\frac13-\frac14-\dotsb-\frac{1}{1318}+\frac{1}{1319}\Rightarrow S=\sum_{k=1}^{1319}\frac{1}{k}-2\sum_{k=1}^{659}\frac{1}{2k}=\sum_{k=660}^{1319}\frac{1}{k}$$ Now this is equivalent to finding the sum of the roots of the equation $$\left(x-\frac{1}{660}\right)\left(x-\frac{1}{661}\right)\dots \left(x-\frac{1}{1319}\right)=0$$. Rewriting this equation, we get $(660x-1)(661x-1)\dotsc(1319x-1)=0$ (we can discard the $\displaystyle \frac{1319!}{659!}$ since $1979$ is a prime). Calculating the sum of the roots, we get the required value to be equal to $(1320+659)\times 330$ which is obviously divisible by $1979$ (again discarding the coeffecient of $x^{660}$).  Now my question is: Using the same method of converting the problem into finding the sum of roots of a polynomial, we get from the original equation something like this: $$(x-1)\left(x+\frac{1}{2}\right)\dots \left(x-\frac{1}{1319}\right)=0 \Rightarrow (x-1)(2x+1)\dotsc(1319x-1)=0$$ So, the sum of roots would be $-1+2-3+4-\dotsc+1318-1319=-660$ But this is not divisible by $1979$. Why does the former solution work while the latter doesn't? Is there a flaw in my reasoning? Note: I know that the question can be solved by some other methods. Please only explain my given doubts and don't instead give another solution  I realised my mistake after some hours of pondering over it. (In the 1st equation) To get the required sum I would need to take calculate $\displaystyle -\frac{\text{coeffecient of }x^{659}\,}{\text{coeffecient of }x^{660}}$. However what I've done is calculate this:  $\displaystyle -\frac{\text{ coeffecient of }x}{\text{coeffecient of }x^{660}}$ which is actually equal to $\text{sum of roots taken }659 \text{ at a time} $. It was just a coincidence that the value I calculated was divisible by $1979$. The correct way, indeed, would be through the link supplied Given two positive integers $a$ and $b$, prove that  $\sum_{k=0}^{n} {k \choose a} {n-k \choose b} = {n+1\choose a+b+1}$  I think there should be a good combinatorial proof for this, given the simplicity of the right-hand side... my hunch is to form all possible subsets of size $a+b+1$ by dividing the set into $k$ and $n-k$ elements, then choosing $a$ from the first, $b$ from the second, iterating over all values of $k$.  I can't quite make this work, so I've also been trying to rewrite ${n+1 \choose a+b+1}$ to make it clear.  Open to any proof method, all help appreciated. today I installed Ubuntu 64-bit on a netbook. When the netbook boots this, error report appeared. I think there is a problem with the partitions.  Gave up waiting for root device. Common problems:   — Boot args (cat /proc/cmdline)     — Check rootdelay= (did the system wait long enough?)     — Check root= (did the system wait for the right device?)   — Missing modules (cat /proc/modules; ls /dev) ALERT! /dev/mapper/ubuntu--vg-root does not exist. Dropping to a shell!   BusyBox v.1.21.1 (Ubuntu 1:1.21.1-1ubuntu1) built-in shell (ash)    Enter 'help' for list of built-in commands.    (initramfs)   Output of lsblk as requested:  $ lsblk NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT sda      8:0    0 232.9G  0 disk  ├─sda1   8:1    0   231G  0 part  ├─sda2   8:2    0     1K  0 part  └─sda5   8:5    0     2G  0 part [SWAP] sr0     11:0    1   1.2G  0 rom  /cdrom loop0    7:0    0   1.1G  1 loop /rofs Database design for products with bundles of products I am building a database system for my retail business. I have set some tables which are:   Product Purchase Sales Balance   All are connected one another and are able to show my inventory level.  The problem I am having is I also sell bundles of products - that have different prices than their individual prices. Example: I sell an orange for $1, an apple for $1.2; I sell fruit package 1 (2 oranges and 2 apples) for $3.8, package 2 (4 oranges and 4 apples) for $7.  Is there a right way how to create relationship for these product bundles?  PS: I am using FileMaker Pro creating this. How do I install the latest version of node.js? How do I install the latest  on Ubuntu? I've been looking around, and I can't find anything. Is there a Ubuntu package for node.js, or do I have to compile it myself? GBM vs XGBOOST? Key differences? I am trying to understand the key differences between GBM and XGBOOST. I tried to google it, but could not find any good answers explaining the differences between the two algorithms and why xgboost almost always performs better than GBM. What makes XGBOOST so fast? Integrate : $\int \frac{x^2}{(x\cos x -\sin x)(x\sin x +\cos x)}dx$ $$\int \frac{x^2}{(x\cos x -\sin x)(x\sin x +\cos x)}\ dx$$   My approach :   Dividing the denominator by $\cos^2x$ we get $\dfrac{x^2\sec^2x }{(x -\tan x)(x\tan x +1)}$ then  $$\int \frac{x^2\sec^2x}{x^2\tan x -x\tan^2x+x-\tan x}\ dx=\int \frac{x^2(1+\tan^2x)}{x^2\tan x -x\tan^2x+x-\tan x}dx$$  But I am not getting any relation between numerator and denominator so that I will take any substitution and solve further please suggest whether it is correct and how to proceed in this. Thanks. How can I group numerical data into naturally forming "brackets"? (e.g. income) The following describes what I'm trying to accomplish, but it's possible an alternative problem statement can describe my goal:  I want to    divide the following numbers into groups where the variances of the numbers within each group are not too large, and the differences between the averages of groups are not too small  compare the distribution obtained in the end with the "perfect" ones and see how "different" it is from being perfect.     Layman's explanation of goal  , and determine the "income brackets" each population is in.  The income bracket is supposed to be self-adjusting based on the input data.  My goal is to ultimately measure or calculate the difference between the income brackets.  I assume there will be many brackets, and want to see how far "apart" each tier is.  Here is a sample of hourly income for a sample set of a population of 20, and a total income of 3587:  Population= 10                   pop=2   population=5              population =3 10, 11,13,14,14,14,14,14,15,20,  40,50  ,90,91,92,93,94      999,999,900    How can I use mathematical concepts to group, sort and analyze data that acts like income distribution over a given population?  At the end of the calculation, I want to determine tiered income distribution, where a perfect distribution would look (something) like this   (each person makes $10 more per hour than the previous; total is 3587) 89, 99, 109, 119, 129, 139, 149, 159, 169, 179, 189, 199, 209, 219, 229, 239, 249, 259, 269, 279   or this:   (evenly distributed groups of people make the same per hour)  (gaps between income groups is consistent and not "too far") (income total is 3587) 99 99 99   129 129 129   159 159 159   199 199 199  229 229 229  269 269 269    Question  How should I analyze the population groups, and measure the gap in a way that will tell me how much is needed to make it more like the last two model sets listed above? Can you use two "and"s in a sentence? For example,      I like chocolate, vanilla, and lemon and orange ice cream.    Indicating "lemon and orange" is a combined flavor, as an item in the list needing an initial and. $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function. Assume that $\lim_{x \rightarrow \pm \infty} f(x)$ exist and are finite. Prove that $f$ is bounded.  So to show that $f$ is bounded, I must show that $\exists M \in \mathbb{R}$ such that $|f(x)| \leq M$ for all $x \in Dom(f)$. Assuming that $f(x)$'s limit exist, then I know that $\forall \epsilon  &gt; 0$, $\exists N$ such that for $n &gt; N$, $|f(n) - L| &lt; \epsilon$. But I am having trouble with figuring out how to connect the two ideas together. How to control Windows 7 snap feature with two monitors? There is an  feature in Windows 7. However, it seems to not work when dragging a window to the edge that is adjoined to the second monitor. How to make it work properly? Maybe some regedit modification or something?