Infinite subset of Denumerable set is denumerable?

Question:
Possible Duplicate:
An infinite subset of a countable set is countable

If $B$ is a denumerable set and $C$ is a subset of $B$ and is infinite, $C$ is denumerable.
Hint or proof please
Comment: Huh? Where does $B$ get into the picture? Did you mean $C\subseteq B$?
Comment: Right It was a typo ;)
Answer: Elements of $B$ can be arranged in a sequence $(x_n)$. Construct a subsequence $(x_{n_k})$ inductively as follows: Let $x_{n_1}$ be the first element of $(x_n)$ which is in $C$. Assuming $x_{n_k}$ has been chosen, consider the least integer $n_{k+1}$ such that $n_{k+1}>n_k$ and that $x_{n_{k+1}}\in C$. Clearly the subsequence $(x_{n_k})$ contains all of $C$, following which $C$ is denumerable.
Answer: Since $B$ is denumerable, there is a bijection $f: B \rightarrow \mathbb{N}$. Put a strict total order $\prec$ on $B$ defined by $x \prec y$ if and only if $f(x) < f(y)$ for $x,y \in B$.
Define now $\prec$ on $C$ via restriction and define a function $g: \mathbb{N} \rightarrow C$ in the natural way ($g(0)$ is the least element of $C$, $g(1)$ is the least element of $C \setminus \{g(0)\}$, and so on).
The function $g$ is injective because $\prec$ is a strict total order and is surjective because $C$ is infinite.


Introduction to jazz theory

Question: I have developed an appreciation of jazz (Coltrane, Ayler, Sanders, etc.). I have no musical education though. I am therefore looking for some sort of lectures or texts for a better (or any at all) understanding of the technical matters (harmonies, modality, etc.). Any I've seen seem to be targeted at students, while what I'm looking should start from the beginning.
Comment: http://music.stackexchange.com/q/6267/1678 might help you out.
Answer: The problem is that John Coltrane's jazz involves extremely advanced concepts in harmony and music theory. If you have no musical education, you are asking to go to post-graduate university before you have attended elementary school (if I may use a figure of speech). I am afraid that you may need to spend a considerable amount of time acquiring an education in the basics of harmony and theory before you can gain an understanding of bebop jazz.
Answer: I went through several levels of a series called Contemporary Music Theory around age 15. While it is targeted at students, it starts pretty basic (more so than "The Jazz Theory Book"), and thus might satisfy your needs.
But, to reiterate Wheat William's answer, you have a long long way to go. This series does not go up to John Coltrane's level, but it's a good start.
Comment: @Karolis: 'The Jazz Theory Book' (by Mark Levine), however, _does_ go up to John Coltrane's level and beyond, should you feel like taking a stab at it. :-)
Answer: I would say your best bet is to take lessons from someone local, take a beginning improvisation class at a community college near you, and then join a combo there.
Answer: Bert Ligon. "Jazz Theory Resources"
Michael Martinez. "Understanding and Implementing Harmony on the Piano"
Jimmy Amadie. The Harmonic Foundation of Jazz and Popular Music.

Introduction to jazz theory


Derived categories of coherent sheaves: suggested references?

Question: I am interested in learning about the derived categories of coherent sheaves, the work of Bondal/Orlov and T. Bridgeland. Can someone suggest a reference for this, very introductory one with least prerequisites. As I was looking through the papers of Bridgeland, I realized that much of the theorems are stated for Projective varieties (not schemes), I've just started learning Scheme theory in my Algebraic Geometry course, my background in schemes is not very good but I am fine with Sheaves. It would be better if you suggest some reference where everything is developed in terms of Projective varieties.
Comment: "Fourier-Mukai transforms in algebraic geometry" by D. Huybrechts
Comment: I disagree with Harry's implicit statement that there is a unique "modern way" to approach derived categories.  Also, I was under the impression that Hovey's book does not say much about coherent sheaves on projective varieties.
Comment: @Scott: Certainly, but I think it's been evident from the beginning that triangulated categories were not the canonical "right" notion.
Comment: If you want to learn about derived categories in the modern way, take a look at M. Hovey's _Model Categories_ chapters 1 and 2 (don't worry, they're pretty short and not too bad a read, although you might want to skip the parts on the small object argument).  After that, there are two ways you can go: The computationally more useful but substantially less natural approach of working with triangulated categories, or by working with simplicial localizations and resolutions.
Comment: Hi,Verma,you might want to take Rosenberg's course now, it is of great help
Answer: Kapustin-Orlov'a survey of derived categories of coherent sheaves is pretty good,

A. N. Kapustin, D. O. Orlov, Lectures on mirror symmetry, derived categories, and D-branes,  Uspehi Mat. Nauk 59  (2004),  no. 5(359), 101--134;  translation in  Russian Math. Surveys 59  (2004), no. 5, 907--940, math.AG/0308173

but more slow/elementary exposition starting with fundamentals of derived categories is in an earlier survey of Orlov

D. O. Orlov, Derived categories of coherent sheaves and equivalences between them, Uspekhi Mat. Nauk, 2003,  Vol. 58,  issue 3(351), pp. 89–172, Russian pdf, English transl. in Russian Mathematical Surveys (2003),58(3):511, doi link, pdf at Orlov's webpage (not on arXiv!)

There are also Orlov's handwritten slides in djvu from a 5-lecture course in Bonn

djvu, but the link is temporary

For derived categories per se, apart from Gelfand-Manin methods book and Weibel's homological algebra remember that a really good expositor is Bernhard Keller. E.g. his text

Bernhard Keller, Introduction to abelian and derived categories, pdf

...and also his Handbook of Algebra entry on derived categories:
pdf
Answer: A good introduction to derived categories of coherent sheaves are Caldaru's notes Derived categories of sheaves: a skimming.
As for Bridgeland's work, I would recommend reading his papers directly, using Huybrecht's book as a reference (as mentioned by Francesco above, "Fourier-Mukai transforms in algebraic geometry"). Specifically for Bridgeland stability conditions, I also have some short notes on
my homepage, but again, you should also read his original papers.
Answer: Let me suggest a perhaps longer program to master derived categories of coherent sheaves. In a comment you said "I don't know much Homological Algebra", so first you have to master the basics of abelian categories and ext and tor of modules. The first chapters of Weibel's "Homological Algebra" may be a useful reference.
This said, I agree with Polizzi's suggestion of Huybrechts' book. The only issue I would point out is that the book concentrates on the bounded derived category of coherent sheaves. It is enough for its application to the classification of non-singular varieties. But if you have varieties with singularities in mind then things may get more complicated. First there is a difference between perfect complexes and bounded complexes of coherent sheaves. Second one sometimes need to use infinite methods, therefore one is forced to consider quasi-coherent sheaves and unbounded derived categories. For this beautiful theory, a good introduction is (as I have suggested here before) the first chapters of Lipman's "Notes on Derived Functors and Grothendieck Duality", (in Foundations of Grothendieck Duality for Diagrams of Schemes, Lecture Notes in Mathematics, no. 1960, Springer, 2009).
This is not a shortest path, but in my experience getting into general methods is that they pay back later. Your mileage may vary.
Comment: Thanks Leo, time is not a constraint for me since I am a first year grad student. Of course I want to learn stuff quickly, but better understanding is my priority.
Answer: Scheme theory won't be that important (as you said, most of the time you are concerned with smooth projective varieties over $\mathbb C$). However, you didn't mention about your experience in homological algebra. Huybrechts' book is a pleasure to read, but it can't serve as a textbook in homological algebra. I would recommend e.g. reading first first few chapters of Weibel's book (1, 2, 3, 5, 10). Gelfand-Manin "Methods of Homological Algebra" is also a good reference here.
Moreover, there is a short introduction by R. P. Thomas "Derived categories for the working mathematician".
Comment: I don't know much Homological Algebra, could you please tell me what topics to look at. I'll highly appreciate if you could outline a roadmap to Bridgeland Stability starting from Projective varieties.Thanks.


how to get IP from DHCP in network in redhat which is installed on VMware

Question: I'm running Red Hat inside a VMware image (on a Windows XP machine). I want to connect the Red Hat VM to our network; do I need to configure something inside VMware or inside Red Hat? I don't have any IPs set to connect to the internet
Answer: Presuming that you have a DHCP server set up on your internal network, all you should need to do is to configure the VMware virtual NIC to be in bridged mode; this tells VMWare to act as a virtual bridge with respect to any packets the virtual machine sends out. When I say a vitrual bridge, I mean a device that just crosses the border between virtual and physical.
Comment: I installed an ubuntu9 on VM, and it worked. unfortunately I don't have access on redhat 4.7
Answer: Red Hat is the name of a company, the last distribution called just Redhat Linux was 9.0 in 2003. Therefore I guess you are in fact running Redhat Enterprise Linux (RHEL).
If you run a recent version, i.e. RHEL 5.x, the network connections are configured using a program called system-config-network. Normally, VMware should give the Linux system network access by means of a virtual network card out of the box, so the process should be self-explaining.
If you need a guide, you can follow generic instructions for getting networking running on RHEL. See, e.g., http://www.cyberciti.biz/faq/rhel-centos-fedoracore-linux-network-card-configuration/


Is it good to strike through visited links?

Question: I've seen in some websites such as http://twomovies.name/watch_movie/Shutter_Island that visited links are striked.
Is this good practice?
Answer: Striking through signifies a revision or marking something as invalid. The established practice for visited link is a change in color, usually a less colorful or less saturated color from the original unvisited link's color.
Using striked through text is a poor choice, as it is ambigious: Is a striked link no longer valid? Is a striked link not recommended? Furthermore, it impacts readability, as it can be hard to figure out the original text once it is striked through.
I understand the need to visually stand out, but striked-through text breaks established patterns and therefore I would personally avoid using this method.
An less severe alternative I have seen is using different types of underlining for links -- i.e. unvisited links are underlined with a solid line, visited links underlined with a dotted or dashed line. While the negative or ambiguous impact is less, dotted underlined words are commonly used for acronyms or other text that shows a tooltip on hover.
Answer: I can see it being useful if you want to the user to get the message "you have been here, and never need to go back"... otherwise, color change is a better, more universal option.
I always find it weird to click on links that are strikethrough, especially if the rollover adds an underline... With two extra horizontal lines, it's a bad case of 1+1=3 and you can hardly read the text underneath.
Answer: Even though a visited link changes in appearance, it generally continues to be a valid link that can be clicked exactly as before to access the url linked to. This is the established convention.
In a slightly different scenario, consider a link that may be valid only once — after which the user cannot or will not click on it ever again. In such a paradigm, it does make sense to show the link in strikethrough font.


How linux kernel (used in Ubuntu) manages concurrent access to the data?

Question: I want to know how linux kernel used in Ubuntu manages concurrent access to shared data?
Answer: Sir, I think you have a misconception about what locking is, and what mutex is for. Also, you have a misconception about what Ubuntu is.
Let's start with the latter: Ubuntu is a Linux-based distribution. Any and all low level system architecture components are done by the Linux kernel. Ubuntu is just a way of putting different software pieces together, configuring, installing and updating them in a robust, uniform and user-friendly fashion. Your question, thus, refers to Linux, and not Ubuntu.
Mutexes are used to make sure that common resources (such as memory) are not by mistake accessed and modified at the same time. Since processes in general do not share such resources as memory (neither in Windows nor in Linux), the problem arises when one uses threads, and not processes. This is done using mutexes, you are right in that; here you will find some more informations about that. Linux uses POSIX threads. However, whether you -- as a programmer -- use mutexes or something else (like spinlocks or critical section), that depends on you, not on the system (see here), be that Windows or Linux.
As for processes, one needs file locking, but that is a different story. And yes, processes are implemented differently in Windows and in Linux (most importantly, in scheduling; see this presentation to shed some light on that).
Comment: Yep, I do know everything. I used Ubuntu instead of linux, because Ubuntu also has its own kernel team. And I'm asking about how does linux manage concurrent access by different processes to the shared data. I'll edit the question.
Answer: Before version 2.6, Linux was a nonpreemptive kernel. Now, it is fully preemptive, so a task can be preempted when it is running in the kernel.
The Linux kernel provides spinlocks and semaphores for locking in the kernel. On SMP machines the fundamental locking mechanism is a spinlock, and the kernel is designed so that the spinlock is held only for short durations.
This is not appropriate for single-processor machines. In single-processor machines, the kernel disables kernel preemption; and rather than releasing the spinlock, it eneables kernel preemption.


What is this purple claw thing (Demon Altar) and what can I do with it?

Question: What are these things?
When I get close to it I take damage, but I can't hurt it.
What does it do and what is it?
Answer: They are Demon Altars which are not monsters - hence you cannot get the tooltip by hovering over them.
You use them to craft some 'boss' summoning materials Slime Crown, Suspicious Looking Eye and Worm Food, as well as creating the stronger pre-hard mode weapon Night's Edge.
Demon Altars can only be destroyed with Pwnhammer or Hamdrax after Wall of Flesh is destroyed. Trying to destroy Demonic Altar before defeating Wall of Flesh, you will take half your current health in damage minus armor, no matter the tool. Pwnhammer is acquired by defeating Wall of Flesh.
Destroying a Demonic Altar will "bless" your world with decreasing amounts of ore, starting with Cobalt, then Mythril, then Adantium and then starting the loop again. This means that it will convert random blocks into whatever ore it is blessing your world with.
It will also place Ebonstone/Pearlstone in random locations underground, allowing Corruption/Hallow to spread faster and from multiple locations.
Source: Terraria Wiki
Comment: StackExchange, now saving lives!
Comment: You actually take half your current health in damage, I believe.
Comment: Thanks for that, I am personally yet to find one (or much interesting), but I did see Coe decide to repeatedly hammer one and take about 30 damage a go.
Comment: I'm so glad I saw this question, I was just about to destroy one.
Comment: No problem, felt like it should be updated to current version since it is currently accepted answer.
Answer: You're looking at a Demon Altar. These act as crafting stations for pre-Hardmode boss summoning items, and the Night's Edge, the most powerful pre-Hardmode sword. They spawn randomly underground when the world was generated and are commonly found in the caverns under corrupted areas.
They cannot be moved (if you try to hit them with a hammer you get damaged with half your health as you discovered), but after you reach Hardmode they can be destroyed using the Pwnhammer to bless the world with Hardmode ores, an important step in progressing further in game.
Answer: That is a Demon Altar, it has various uses. One is that it is a crafting station for certain rare items. The boss summoning items and one strongest pre-hardmode sword.
They are one of the few crafting stations that are not movable. And most of the game they are not even destroyable. Attacking them causes the attacker to lose life.
When the wall of flesh has been defeated, the demon altars can be destroyed using the pwnhammer or the hamdrax.
Each Altar that is destroyed will add new sources of hardmode ores to the game. The first destroyed will add Cobalt, the second Mythril, and the third Adamantite. The fourth adds Cobalt again, but less than the first altar destroyed. Read more about Hardmode, here.
As the Altars are a important crafting station, and they cannot be moved. It can be smart to build your main base near one of the altars. And not destroy this altar, as you want to keep your crafting station.
You can find altars below ground, and they are more common near corruption areas. You can usually find a few near shadow orbs. You can easily find them because they emit a small amount of light.
Answer: Those are not monsters, they are Demon Altars... and awesome find on 3 of em at once :)
Answer: I also would like to add to other answers, that the only way you could destroy/mine/pickup a Demon Altar, is if you have the luck and found the altar on top of a sand block. Destroying the sand block destroys the altar, as it falls down. According to the wiki page it's considered as a bug, but I hope they won't fix it, as it looks good in my house :)
Also, the (currently) strongest weapon, Night's Edge is crafted on a Demon Altar.
Comment: Well, I have it in a house on a multiplayer server, and it's actually possible that it was placed there with a map editor. I assumed that if it can be destroyed it can be picked up from the sand.. I didn't have the luck finding it on sand yet!
Comment: You lie! There is no Demon Altar item; you can't pick it up.


Keeping bugs out of rice

Question: Recently, a sack of whole grain organic rice that we bought became infected with small black bugs. We bought the rice in the bulk bins at the same organic supermarket we always visit, but this time we didn't cook it until a few weeks after buying it. Since, the rice was stored in a sealed plastic bag, it seems like the bugs (or their eggs?) must have been in the rice when we bought it. Is this normal? Should I worry about buying rice there again? Is there a better way I should be storing the rice? It was in a plastic sack with a twist-tie.
Answer: Those bugs are probably weevils.  I would take it back to the store and ask for a refund.  If the rice is the only grain with bugs, chances are the larvae were already in the rice.
The weevils are about 1/4 inch long and they have a little tube sticking out of their head.  The larvae take about 35 days to emerge from inside the kernels.  A farmer can only control a weevil infestation with chemicals, which would preclude the organic label, and there is just so much frogs and birds can eat.
Comment: The question is, what is the lesser of the two weevils?
Comment: Lol, still making people laugh eleven years later @bmargulies
Answer: I have always understood that a certain level of egg incidence is unavoidable (and thus is acceptable under FDA standards). Under the right conditions, they will hatch. I learned to always put a new bag of grain/flour in the freezer for 3 days (I usually forget it for a week or two) after which it keeps for months.
Answer: I occasionally to find bugs in organic bags of unopened rice.  I believe this is normal for organic grains.  I have also found them in organic popcorn. Not often but it happens.  It's  Part of nature & organic natural lifestyle.  If you want to toss it/ return it, understandable, but not necessary.  you can freeze or rinse in colander & remove them.  Then cook as usual.
Answer: I wouldn't be any too pleased. I'd take it back and complain.
My guess is that you could have held this down to 'a bit of extra protein' by freezing the rice, but you shouldn't have to do this. I've bought bulk organic rice from WFM here in Boston for 20 years and never had this problem.
Answer: Line your container at the bottom with salt.  Seal the container.  It will last for years.

Keeping bugs out of rice


Product of positive definite matrices

Question: Let $X,Y,Z$ be positive definite matrices such that $XYZ$ is hermitian . How can we show that $XYZ$ is also a positive definite matrix?
Comment: Somewhat relevant : http://math.stackexchange.com/questions/27656/eigenvalues-of-product-of-matrices
Answer: Since by hypothesis $XYZ$ is Hermitian, then it is enough to show that its eigenvalues are positive. But the product of positive-definite matrices, even though not hermitian in general, always has positive eigenvalues. See a proof in my answer to this question: Product of positve definite matrix and seminegative definite matrix
Answer: Denote $H=XYZ$. Let $X^{1/2}$ be a positive definite square root of $X$ (it always exists -- think unitary diagonalization) and
\begin{align}
y &= X^{1/2}YX^{1/2},\\
z &= X^{-1/2}YX^{-1/2},\\
h &= X^{-1/2}HX^{-1/2} = X^{1/2}YZX^{-1/2} = yz.
\end{align}
Then $y$ and $z$ are positive definite and $h$ is Hermitian. Also, $H$ is positive definite iff $h$ is positive definite. Now, let $y^{1/2}$ be a positive definite square root of $y$. Then $h$ is similar to $y^{-1/2}hy^{1/2}=y^{1/2}zy^{1/2}$, which is positive definite. Therefore $h$ and in turn $H$ are positive definite.

Product of positive definite matrices


What to look for in a fridge to be used for kegging?

Question: I'm sick of the hassle of bottling, so I want to get a fridge and keg setup. Obviously it needs to be able to fit the kegs, but is there any other things I should look for in a fridge? I don't mind spending a bit more money, but I don't want to bring it home to find out it won't work with the other equipment.
Answer: A fridge is fine if you don't plan to use a temp controller with it.  My first keg fridge was a normal standing fridge. Worked great.  But now I use a small chest freezer with a temp controller.
If you were planning on using a temp controller then I'd go with a chest freezer.  Its just a little neater with the lines running around.  I find it easier to connect and disconnect the lines and play with releasing pressure when you have full access to the top of the kegs.  IN a standing fridge I always found myself having to pull a get out to get to it.  And the kegs in the back were always tough to get to.  With a chest freezer you open the top and have full access to any single keg at a time.  Much better IMO.
Answer: In my opinion, not much at all.  Make sure it seals OK, make sure it cools & make sure you have room for all the kegs you want to fit (many fridges have sloped bottoms).
I found a working but nasty-looking fridge to save cash, it lives out of sight but a lick of paint covered up any "beauty spots" it had.  When I got it I cleaned the inside quite thouroughly - I don't think it matters to the sealed keg inside but nobody likes a fridge with gobs of old food stuck to it.
Once you've got the fridge, I recommend investing in a variable thermostat like this or this so you can use the fridge for fermentation as well as getting the perfect temperature for dispensing.  If you're going to grab one of these, you can even put it in a freezer if you find a better size / fit / price.
Answer: For fermenting, I use a 4.x cubit foot "dorm fridge" commonly used by college students or single-room apartment dwellers. No need to buy a new one, just keep your eye on Craigs List or your local equivalent. When a posting appears, take a look at the fridge and make sure you can slide in a carboy or fermenting bucket. Mine has a top "freezer" rack that only comes down a few inches and was used to make ice cubes I guess. I ignore it, but on some models, this freezer space will be too big, and you won't be able to slide the carboy in. Keep in mind that you can cut the shelves out of the door itself if needed.
For kegs, I'd go with a deep chest instead of a fridge. Again, look for used models first, but I ended up buying a new one that was slightly damaged from a big box retail place. You can totally trick out a chest freezer with tap handles and the like, if you are willing to build a wooden "collar" to go on top of the unit.
For a chest freezer, you must weigh the cost of the unit versus how many kegs it will hold. I can't recall the dimensions of mine exactly, but it holds 3 kegs, a 5lb tank, and a secondary fermenter or a No Chill tank just fine. This suits my needs perfectly, and I'm glad I didn't skimp and get a smaller one just to save $50-60. A good suggestion is to make a couple of disks out of cardboard that are the diameter of your kegs. Then, if you are looking at a chest freezer and aren't sure how many kegs it will hold, pull out the disks and position them around to figure out the freezers capacity.
Also, make sure the chest freezer is tall enough to fit kegs with an inch or two extra for the gas/liquid ins/outs. If its not tall enough, then you will have to build a collar, and that's kind of a pain.


Adding images to placemarks multiple times

Question: I have a route that I travel that is saved by coordinates to a .csv file for use in GE.  I have images (pictures) that I would like to add to placemarks I have along the route.  Is there a script or macro I can run that would allow me to add the url of the images to the .csv file so that I could have the images appear inside the placemarks balloon without having to add the images individually to the balloon?
Answer: Perhaps you could use Time Album for that purpose (software and manual)?
It's a small Java program designed to work with Columbus gps loggers and works with data in CSV format. It has a function to link pictures to gps tracks and export as KML. I'm not sure though if CSV data must be supplied in Columbus specified format but perhaps you could reorganize your data to fit into that.
Another option (on Windows machine) would be to use freeware GeoSetter (via Directions Mag)


Mail client locking up?

Question: Is there any way I could lock up my Mail client so that only I can read my emails(which are present locally on the machine)
Answer: I would think a good way of doing this might be to package your ~/Library/Mail folder within an encrypted disk image.  As long as it was allowed to grow to an acceptable size, I think it would work.  You would need to move the Mail folder into the disk image, then create a link from your ~/Library folder, called Mail, to the "real" mail folder on the disk.
In order to get to your mail, (I imagine), firing up Mail.app would follow the link to the disk image, which would prompt for your password, as it needs to mount.
Once you're done with your mail, you would be able to dismount the disk image and voila.
Never having tried this, I have no idea if it would work.
Answer: This question is more or less related.
Some answer will allow you to protect the launch of Mail.app
However, like some people said on the question, it won't fully protect you, since the mail database is accessible on your file system, and it's not password protected.

Mail client locking up?


Including sprite file  for mobile games

Question: I'm making a simple online RPG for Android & IOS using HTML5 & Phonegap and was wondering: should I include sprite file with the game for downloads (because of bandwidth)? What should I do when I modify the sprite file in the future? (i.e. forced update).
Answer: Short Answer: Of course; just include all your assets. Make sure you use proper texture compression and a good file format for your needs and file sizes shouldn't be a problem for a low scale RPG.
Long Answer:
Distribute your app as just a wrapper around your HTML5 game and make life a bit easier that way. You can have your HTTP server and the browser handle the sprite caching, the browser will download new assets for you as required. If there's a major update, you can always order a cache purge to have all users up to date. This way, the updates will be near instant and you won't have to worry about shipping out huge updates.
On startup, it may be a good idea to preload content and tell the user roughly how much data is needed. This prevents confusion and angry players - it has the added bonus of a smoother game experience when completed, too.
Answer: The user will have to download the sprite at some point in order to see it on their device. Whether it's at the initial download or later is a design consideration.
I recommend you use a combination of both. Package the sprite with your game and also have the game check your server to see if there is a newer version of the sprite. Only download from your server if there is a newer version.
Comment: The user is using Phonegap; not the app-market.
Comment: Ah, I didn't know what that was. I'll update my answer.

Including sprite file  for mobile games


Tourism after the Earthquake in Christchurch

Question: I hear that there is still a condemned zone in the heart of Christchurch after their earthquake.  How much impact does that have upon tourist-related activities?  Does it make it difficult to get around the city?
Answer: As someone from Christchurch, this is my cue.
I spent six months back there over summer.  Sure, things have changed.  The CBD is mostly closed off - although that's slowly improving as buildings are demolished and removed.
However, life goes on. Businesses have relocated to other commercial zones. Schools share and build new blocks.  Bars open up in the surburbs.
As a tourist, much of the appeal of Christchurch is the outdoors. Yes, the famous Christchurch Cathedral is coming down, and the Arts Center market is no long accessible.  But the museum is. The Botanical Gardens are as beautiful as ever.  Many pubs and bars are open, and while the number of motel/hostel/hotel rooms are fewer, so are the tourists - just book ahead.  The International Antarctic Center is open (I went over the summer) and is incredible and eye opening. Orana Wildlife Park and Willowbank have the Kiwi bird for you to see the national icon.  Rugby is happening again in Christchurch with an All Blacks test just last week against the Irish. The beaches are open and the golf courses are calling your name.
Outside of Christchurch there are also plenty of day trips - from Hanmer Springs thermal resort, to the small French town of Akaroa, to the mountains if you're planning on skiing at Mount Hutt or Porters Heights.
As far as getting around the city goes, the buses are running, taxis are certainly still going everywhere, and aside from the very center, and some of the harder-hit eastern suburbs, from a tourist point of view it's still very accessible.
If you have any follow-up questions, please feel free to ask.
Comment: @Criggie amazing how plans change. It's being repaired, and the cardboard one is likely to be sold soon
Comment: +1 for banks peninsula/Akaroa. I didn't care for Akaroa itself, but the drive there and the views are really incredible.
Comment: Twelve years later, the Anglican Cathedral is still there although blocked off and isolated.  The Catholic Cathedral is gone completely, and teh temporary Cardboard Cathedral just passed its 10th birthday.   https://en.wikipedia.org/wiki/Cardboard_Cathedral
Answer: Lonely Planet has some recent articles that might be relevant here:
Return to Christchurch
What to do in Christchurch: your post-quake guide
Free download: Lonely Planet's new Christchurch chapter
Answer: Just to clarify something others have said, the museum isn't actually open at the moment; it was closed a couple of months ago for earthquake strengthening.  They are hoping to reopen sometime soon.  Other than that, what people have said is more or less accurate. The visitors I've shown around have found the Lonely Planet page someone mentioned above particularly useful and as long as you get a hire car it's all pretty accessible.  The cordoned area is shrinking all the time and with maps etc it's not too hard to navigate the city.  The best way to know where to avoid is to download the latest red zone map from the CERA website which clearly show what parts are now open.
Comment: No problem. My husband works there so I'm hyper aware of when it's open and closed!
Comment: Crud, [closed as at 16th April](http://www.canterburymuseum.com/).  Thanks for noting that!
Answer: I have not been in Christchurch since April 22nd 2010. however growing up in the surrounding area and with family still living there hopefully I can offer some help.
Christchurch art's centre being inaccessible means the Theatre is no longer operating, the Art Gallery is also closed, there are still some cultural activities on offer, as Mark mentioned the Museum is still open as is the Ferrymead Historic Park.
City Centre the Casino is open 24 hours over the weekend (Friday - Monday) and till 3am the rest of the week, this provides a 24 eating and drinking option in the CBD. To my knowledge there is only one club in the CBD open which is a gay club that is 'accommodating straights' (remember it's their house if you don't like that then don't go).
Christchurch has typically had a 'Car Culture', the bus network while wide reaching is not as regular as similar sized European city's so even before the earth quake I would have recommended hiring a car (not all the roads are in great shape but are passable with some exceptions in the eastern and north eastern suburbs).
Adding to Mark's list of things that are open:
Victoria Park the scene of Peter Jackson's Heavenly Creatures a true story based on the 1954 killing of Honora Parker. Also a good place for short walks in the hill side, mountain biking and picnics with a playground for children.
Godley Heads and WWII defense battery located at the tip of Banks Peninsula there is the remains of the batteries built to defend against a Japanese invasion during WWII.
The best thing about the South Island is its love of adventure activities; Queenstown is well known for it extreme sports, and the surrounding area's has plenty to offer.
Kite sports around the Ferrymead and Sumner area; this is a good way to get into kite-surfing, kite-buggying and kite-skiing.
Paragliding - learn to paraglide or take a tandem ride above Taylor's Mistake. And go surfing afterwards.
Fishing at Lake Coleridge and surrounding lakes(5?) and rivers(3) only a couple of hours drive from Christchurch and accessible in a 2WD car in summer.
If you happen to be interested in fishing / hunting or 4x4 in the South Island let me know and I'll get you more details.
If you have any further questions about the state of various parts of Christchurch let me know; my father operates a taxi in his retirement and would be able to give very detailed advice on most aspects.
EDIT: The Speights Ale House is open on Bealey Ave; there are 'container bars' on the corner of Bealey and Papanui Road and one down Victoria Street as well. The Monday club on Moorhouse Ave down near Madras Street is also an option.
Comment: And to point out, while there may only be one club open downtown, there are several open near the accommodation areas, be that Papanui Ave, Bealey Ave, Lincoln Road or Riccarton Road districts.
Answer: I was there 6 months ago, but from what I have heard on the news not much changed yet, except that they started to demolish the buildings inside the city.
So the city center itself is closed, there is a fence around and you wont be able to get into the city center. The other areas near the city center are pretty depressing, a lot of abandoned businesses and buildings, rubble and weeds growing on the main roads because nobody goes there any more. The other problem was that had to walk for ~1h to find any place that served any food - you see a lot of big signs for Indian, Thai, fish & chips etc on the streets; but after closer inspection it turns out that most of those places went out of business after the quake. Either bring your own food if you don't stay in an all-inclusive hotel, or get something from a gas station until you have time to scout out some better place.
In short, I wouldn't place Christchurch on top of your must-see list right now. Most of the attractions you know from pictures or tourist guides are either destroyed or closed to the public for renovations; except for things outdoors as Mark pointed out.
Comment: One of the Motels on Bealey Ave. The commercial area between Montreal St. and Victoria St. was pretty depressing, and the city center was closed.
Comment: Ah yeah, that was in the rougher hit stretch :( Good memory with the streets!  Had other tourists stay below Moorhouse Ave and it's pretty good that side of the CBD, quite a revival thing going on.
Comment: what area were you staying??? Even in December only a few blocks were still closed off.


Anonymous FTP Risks

Question: If my IIS 6.0 web server is disabled and the only other service running is FTP, what are the security risks of allowing anonymous FTP read/write, considering that a random person couldn't use any sort of php/asp shell to compromise my system?
Answer: Depends on what files/directories you let them read/write.  If there's nothing of value in there (e.g., just benign files) they can't do much to compromise your system assuming your FTP server is fully patched and doesn't have any zero-day vulnerabilities.  However, they still could fill up your disk space (potentially crashing the system or otherwise DoSing it) if quotas aren't in place and its on the same partition as the OS.  Or they could use your system for illegal purposes (sharing copyrighted information/child pornography/etc.).
If you let them read/write important system directories/confidential information, they can do worse things.  I'm not a windows user; but if they know where to look they could get password hashes (the equivalent of /etc/shadow) with read permissions (and use GPUs to attempt to crack offline) or with write permissions possibly insert a hash for a password they know so they can log in as a privileged user.
Comment: @BhubhuHbuhdbus, no, that should not be possible, as long as your IIS webserver is fully patched/updated (and has no unknown vulnerabilities).
Comment: So if I only allowed write to the web server directory no one can upload any sort of shell that could allow them to compromise the system?
Answer: Read access. Enabling anonymous read access to files you intend to be public is relatively low risk. The primary security risks are: (1) misconfiguration: you inadvertently grant access to a file that shouldn't be public, (2) vulnerability: there is some security vulnerability in the IIS code that can be exploited.
Write access. Enabling anonymous write access is riskier. If you let someone upload a file that will then be readable by anyone else, you run the risk of your site being used as for warez (pirated software), as a drop site for credit card numbers and other stuff grabbed by online criminals, or other unsavoury purposes. Enabling write access to a particular directory under the ftp root isn't gonna let the bad guys breach the security of your machine, but you still don't want your machine being used as a distribution point for illegal or unsavoury stuff.
If you need write access enabled, I suggest creating a special directory for uploads which is writeable by everyone but not readable by anonymous users (it is only readable by you, or by other users you authorize).

Anonymous FTP Risks


Protecting an Application with Logins

Question: I am a beginner Java programmer, and have tried searching for a way to set up a login system with my Java application.  The application is a game and I do not want people to just upload it to a website so others can down load and play. I want to use something like MySQL to make the user authenticate in order to use the application. Does anyone have a suggestion?
Comment: Is this a desktop application? Have you looked into any licensing schemes at all?
Answer: In short, don't bother.
A runnable JAR can easily be decompiled back into the Java and the login page would be circumvented rather easily. If the game is in the form of a Java applet, once a person gets past the login page, the applet can be downloaded and distributed with no problem.
Developers have been trying for years to stop people from using their software. To the best of my knowledge, there is no way to stop people from stealing your software. While you can go the route of security through obscurity, this is not in fact security, only a deterrent to the less experienced.
You may be able to stop some people from playing without your permission, but the client will need the code, even if in a binary form, to play the game, and therefore can access and modify it at will.
Answer: One approach to this problem would be the use of a web service which would authenticate the user's credentials before allowing further use of the application or game.  This would mean that the game would have to have internet access, and that you have a server on which you could host the authentication service.
There's a lot to learn to make this work.  First, you'll need to know how to build a web service and how to call one. Presumably, the service would have to send a token back to the game if the credentials are valid--you'd need to use encryption to make sure that the token itself is valid and not a spoof.  That means you probably need to learn something about encryption with public and private keys.  You'll also need to integrate the security checks throughout your application.
In the end, you're still not guaranteed a 100% protected application, but you can limit abuse to the real die-hard hackers.

Protecting an Application with Logins


Answers to the closed questions

Question: I think it's a  bug when a closed question gets an answer. You can see here what I mean. An answer is posted a minute after the question is closed. I understand the idea, that user probably had started writing answer before the question was closed, but I saw a ten-minutes difference. Isn't it possible to notify user that he won't be able to post his answer to a closed question (the same way that he's notified of new answers, or at submission time)?
Comment: On a side note, don't you love when somebody having a reputation of 1 complains about how reputation is hurting the site?
Answer: This has always been by design. The reason has always been stated as making it so the answerer does not lose their work. Even with this in place, people still complain about losing their answers.
However, there is no real reason as you seem to imply that a answerer would want to take back their answer if a question was closed while they were answering. They will likely still get their votes (possibly more if they are right and that is the only answer posted before close). This has long been a 'gaming' method to get easy rep.
Even if the answerer did decide the answer should not be on a closed question, there is always the delete button.
Answer: It does notify anyone mid-compose, and disables the "Post Your Answer" button (at least that's the behaviour I've seen). I believe this works by periodically checking the status of the question - if you time it right, then there will always be the chance of submitting an answer to a question that has been closed. In my opinion, it is better to accept this answer, than throw it away.
Answer: Does it hurt anybody? The question taken as an example has been closed as "belongs on meta". The answer given is a valid answer, and maybe that answer would not have been given on meta as the question might have slipped the answerers attention.
The person now earned +1 rep, but was thrown a downvote as he dared to answer unintentionally a question that is not bad, just on the wrong side. I think this is a little too strict.
Now let's suppose the question gets reopened. Should the person be given these 2 points back?
I do think that the community will have to mature in some aspects of closing, voting etc. and remember the reason for the site: helpful information for programmers.
Comment: most of the questions that get closed don't get reopen.

Answers to the closed questions


Are Halo: Combat Evolved and Minecraft compatible with Ubuntu? How to transfer files from Windows to Ubuntu?

Question: When installing Ubuntu, I got the Install alongside Windows 7 option. Is there a possible way of me being able to transfer a file from my Windows 7 installation to Ubuntu? Also, are Halo: Combat Evolved and Minecraft compatible with Ubuntu?
Comment: It seems like you're asking two things here.
Comment: No.  No they are not.
Comment: I am asking two things but they derived from the same situation.
Answer: Ubuntu can mount your Windows 7 partition, so simply clicking and dragging from the windows partition to the ubuntu partition within ubuntu should allow you to 'transfer' the file.
Minecraft is written in JAVA and thus runs natively in almost every OS, including Ubuntu.
Halo supposedly runs pretty well in WINE.
Answer: Minecraft is java based, so yes. Java is cross platform, and there is a java for Ubuntu.
Halo Combat evolved, well WineHQ claims that it's working with wine.
So yes on both questions.
And with transfering the files, just mount your disk and drag & drop the files.
Answer: In response to your question about moving files, yes you can. Just save the file somewhere on the Windows partition and then from the Ubuntu side, browse to it in Nautilus.
Minecraft is just a Java file. Just search around this site and you'll find instructions to run it.
In order to run games meant for windows, you'll want to use Wine. As for Halo, you can see here that it has a gold rating. Shoot [no pun intended] for versions 1.08 or higher since it doesn't have a CD activation bug.
Answer: In response to Minecraft, the Ubuntu Software Center has a couple applications for launching Minecraft. I've not tried any of them, but you can see them by searching for "Minecraft".
What I found was MC-Launcher ($2.99 USD) and Mini Minecraft Launcher ($4.00 USD)


Which book were the Pegataur Ranger rules in?

Question: I remember from many years ago, I had a pegataur ranger in a DnD campaign. I can't remember which version of D&D it was from, or which book it was from. Any ideas?
I do remember that the book had a brown cover.
Answer: There are no specific rules for playing pegataur rangers in any edition of D&D prior to 3rd edition. (In 3rd edition the pegataur is a playable race simply by virtue of generic monstrous characters rules, and there are no special pegataur/ranger rules.) However, the "brown cover" is a dead giveaway for an AD&D 2nd edition campaign using one of the "Complete" handbooks.
Despite there being no specific rules for pegataur rangers, I think I've figured out what you're remembering. What your DM likely did was use the loose recommendations in the Complete Book of Humanoids (pp. 15-16) to create a playable race from the pegataur monster entry in the Monstrous Compendium, Mystara Appendix (p. 86), and then used the "Wilderness Protector" fighter kit in the Complete Book of Humanoids (p. 72) to create a ranger-equivalent fighter-based class for your character. This kind of ad hoc character-creation rules based on loose recommendations and GM permission was common in AD&D 2nd edition, so it's no stretch at all to figure that this is how your past pegataur PC came to be.
Prior to AD&D, the only appearance of pegataurs a player-character race is in Top Ballista (1989), which describes a flying gnomish city as a campaign setting/expansion in the Mystara world. However, since this is a Basic Dungeons & Dragons book, PC pegataurs advance with a race-as-class paradigm and aren't able to be a separate class like ranger as well.
Answer: The most likely answer is The Complete Book of Humanoids for AD&D's Second Edition. It's brown, and has the rules for centaur characters, which would probably include variants like the pegataur.
Comment: That is definitely the book, the reviews sound spot on!  Thanks!
Comment: Ok, just looked inside, and it appears to not be the right book.   But it's helping me narrow it down.  It's definitely from that series / addition.
Answer: I'm still continuing my research, but what I'm finding is that pegataurs appeared in the following AD&D/2e books...

Module M2: Vengeance of Alphaks by Skip Williams,
AC9: Creature Catalogue
Mystara Monstrous Compendium Appendix.

But that's just the creature.  I imagine that your ranger just focused on them as a monster and there's not a random specifically dedicated class.
Comment: There were rules to make a Pegatuar a PC, and I remember it getting racial bonuses that meshed with a ranger.


Fundamental equations in economics

Question: For the other sciences it´s easy to point to the most important equations that ground the discipline. If I want to explain Economics to a physicist say, what are considered to be the most important equations that underly the subject which I should introduce and attempt to explain?
Comment: I disagree with the "on hold" decision. By characterizing this question as "too broad", we essentially state that the "foundational equations" of Economics are too many and too diverse. Are they really?
Comment: I beg to differ. I think this is an important question for people who would like to get an overview of a field, which can certainly be answered in all the other sciences - and indeed several excellent answers have been posted below. It could be broken up into macro/micro etc., but I think that would miss the point.
Comment: I find this question broad but nevertheless interesting and worth discussing. Proof of that are the very interesting answers.
Comment: @MartinVanderLinden This is a very good question.  But, I would suggest making in more narrow.  What part of economics are these equations coming from? Interest rates? GDP?
Even topics such as "finance" and "international economics" are very broad.
Comment: [What are the foundational equations, inequalities, propositions or concepts of Finance?](http://economics.stackexchange.com/questions/10361)
Answer: Instead of proposing specific equations, I will point to two concepts that lead to specific equations for specific theoretical set ups:
A) Equilibrium
The most fundamental and the most misunderstood concept in Economics. People look around and see constant movement -how more irrelevant can a concept be, than "equilibrium"? So the job here is to convey that Economics models the observation that things most of the time tend to "settle down" -so by characterizing this "fixed point", it gives us an anchor to understand the movements outside and around this equilibrium (which may be changing of course).
It is not the case that "quantity supplied equals quantity demanded" (here is a foundational equation)
$$Q_d = Q_s$$
but it is the case that supply tends to equal demand (of anything) for reasons that any economist should be able to convincingly present to anyone interested in listening (and deep down they all have to do with finite resources).
Also, by determining the conditions for equilibrium, we can understand, when we observe divergence, which conditions were violated.
B) Marginal optimization under constraints
In a static environment, it leads to the equation of marginal quantities/first derivatives of functions.
Goods market: marginal revenue equals marginal cost.
Inputs market: marginal revenue product equals marginal reward (rent, wage).
Etc. (I left "utility maximization" out of the picture on purpose, because, here first one would have to present what this "utility index" is all about, and how crazy we are (not), by trying to model human "enjoyment" through the concept of utility).
Perhaps you could cover it all under the umbrella "marginal benefit equal marginal cost" as other questions suggested:
$$MB = MC$$
Economists live in marginal optimization and most consider it self-evident. But if you try to explain it to an outsider, there is a respectable probability that he will object or remain unconvinced, instead usually proposing "average optimization" as "more realistic", since "people do not calculate derivatives" (we don't argue that they do, only that their thought processes can be modeled as if they were). So one has to get his story straight about marginal optimization, with convincing examples, and a discussion about "why not average optimization".
In an intertemporal setting, it leads to the discounted trade-off between "the present and the future", again "at the margin" -starting with the "Euler equation in consumption", which in its discrete deterministic version reads
$$u'(c_{t})=\beta(1+r_{t+1})u'(c_{t+1})$$
...and one cannot avoid the theme of utility, after all: $u'()$ is marginal utility from consumption, $0<\beta<1$ is a discount rate and $r_{t+1}$ is the interest rate
(don't consult wikipedia article on Euler's equation in consumption, the concept behind it is much more generally applicable and foundational than the specific application that the wikipedia article discusses).
Interestingly, although dynamic economics are more technically demanding, I find this more intuitively appealing since people seem to understand way better "what you save today will determine what you will consume tomorrow", than "your wage rate will be the marginal revenue product of all labor employed".
Comment: @MichaelGreinecker CONTD...-and I understand it as a tendency and not as a situation in which we usually find ourselves. Because if we found ourselves in equilibrium, things wouldn't move -which is the opposite of what we observe... And this is exactly the distinction  I made in my answer. As an aphorism, the world tries to be Walrasian and in attempting so , it ends us being Schumpeterian. And then it tries again to become Walrasian... ad infinitum
Comment: That is exactly the problem with partial equilibrium reasoning. I am of course familiar with the stories one tells econ 101 students about excess demand leads to higher prices and excess supply to lower prices, so that "markets tend to equilibrium". What the story conveniently hides is that in the process, other markets might be upset. And of course Walrasian equilibrium theory is highly idealized- but partial equilibrium models are even more so.
Comment: -1 "for reasons that any economist should be able to convincingly present to anyone interested in listening" Unless of course those economists who actually tried to explain how this dynamics are supposed to work. See for example [this sobering survey](http://economics.mit.edu/files/6988) by Franklin M. Fisher, arguably the leading authority on the subject.
Comment: @MichaelGreinecker I am one of "those economists" and I never have trouble explaining it. Thanks for the link by the way, although this link refers to the "competitive general equilibrium" concept - which is a Platonian ideal that has not much  to do with the concept of "equilibrium" as I understand it... CONTD
Answer: As has already been said, the MOST fundamental equation is surely:
$$\text{MB}=\text{MC}$$
EDIT: This equation is fundamental in terms of the way economists think. As pointed out in the comments below, in terms of fundamental equations of economic models, the most fundamental equations describe equivalences between the uses and supplies of items (money, goods, etc.). These provide the tension of the marginal cost side of this equation.
I would add equations related to comparative statics:

Envelope theorem
$$V^\prime(y)=f_y(x,y)$$
"Delta" analysis, as described in Samuelson's Foundations of Economic Analysis:
$$\Delta p\Delta y-\Delta w\Delta x\geq0$$
(this examines responses of price-taking producers in terms of vectors of production $y$ and uses of inputs $x$, to their prices $p$ and $w$, essentially revealed preference for producers)
Revealed preference

If we can claim game theorists or mathematicians whose equations we use constantly:

Karush-Kuhn-Tucker conditions, especially complementary slackness. There's no single equation for linear programming, but I think econ has a claim to Kantorovich too. \
Stationarity:
$$\nabla f(x^*) = \sum_{i=1}^m \mu_i \nabla g_i(x^*) + \sum_{j=1}^l \lambda_j \nabla h_j(x^*)$$
Primal feasibility:
$$g_i(x^*) \le 0, \mbox{ for all } i = 1, \ldots, m$$
$$h_j(x^*) = 0, \mbox{ for all } j = 1, \ldots, l \,\!$$
Dual feasibility:
$$\mu_i \ge 0, \mbox{ for all } i = 1, \ldots, m$$
Complementary slackness:
$$\mu_i g_i (x^*) = 0, \mbox{for all}\; i = 1,\ldots,m.$$
Nash equilibrium
$$\theta_{i}^\star = \arg \max_{\theta_i} u_i(\theta_i ,\theta_{-i}^\star)$$
Revelation principle: which to be fair isn't so much an equation as a theorem...
Bellman equation
$$V(x)=\max_{c\in\Omega(x)} U(x,z)+\beta\left[V(x^\prime)\right]$$
Comment: I would suggest that there are some inequalities which are even more fundamental than the first equation above. Unlike equations which represent approximations, some of the inequalities represent absolute.  For example, the total quantity of something people will be able to afford cannot exceed the total quantity that will exist.  If the number of people who would like to have something exceeds the quantity that exists, unless more of the thing are produced or some people stop wanting it, not everyone who wants one will get one, period, no matter what else is done.
Comment: That's fair. I suppose budget constraints are also "more fundamental" in that sense.
Comment: If someone proposes a policy which, if successful, would violate one of the normal equations associated with economics, such a person should be called upon to justify the expectation that the equation would not hold in that case, but since most equations don't hold 100% of the time it would be plausible that the policy might work despite the equation suggesting otherwise.  On the other hand, a policy which couldn't achieve its stated aims without violating some fundamental inequalities cannot reasonably be expected to achieve those aims; no wise person could plausibly expect otherwise.
Comment: Does my edit above get at what you're trying to express? I see this as a difference in framing of the term "fundamental". You seem to mean that physical constraints are the most fundamental element of any given *economic model*, with which I agree. But I see $\text{MB}=\text{MC}$ as the most fundamental element in an *economists toolkit* because it combines these constraints with notions of efficient use. I'm especially fond of it because it is a general equation, whereas physical constraints tend to be stated differently for different situations.
Comment: If one imagines the state of an economic system as being a marble rolling over a hilly surface, the equations define grooves in which the marble will tend to roll, but the limiting inequalities define boundaries.  Merely knowing the boundaries in which the marble is constrained without knowing how it will behave within them isn't very useful, but likewise a prediction of the marble's behavior which ignores the existence of a boundary between its present position and expected future position is apt to be very wrong.  In a sense, though, I think the constraints are somewhat more foundational...
Comment: ...since in their absence the natural "solution" would simply be to have everyone get everything they could possibly desire.  It is only the existence of resource limits that makes all the other compromises necessary.  Also, BTW, a concept I've not seen mentioned much is that it's *much* easier to turn \$1 into \$0.95 than \$1.05; if it seems like everyone in some particular field is turning \$1 into \$1.05 with little effort, odds are what's really happening is they're turning \$1 into \$0.95 (or less) but making it *look* like \$1.05.  The fact that the market price of something is \$1.05...
Comment: ...doesn't mean that it will ever be possible to convert a million units of that commodity into \$1,050,000 or even \$1,000,000.  If people too-easily convert \$1,000,000 into 1,000,000 units of something, odds are good that the total liquidation value will end up being noticeably less than \$1,000,000.
Answer: Most of intro econ is intersecting lines. Specifically,
$$MB = MC$$
* Equilibrium is achieved when Marginal Benefit is equal to Marginal Cost*
$$\dfrac{MU_x}{p_x}=\dfrac{MU_y}{p_y}.$$
Marginal Utility per unit cost should always be equal
Economics is about the logic of human behavior, how we make decisions in a world of scarcity. These equations describe constrained optimization under some usual assumptions like continuity, convex preferences, and no corner solutions. I'd also give prominence to consumer theory over producer. Most of undergrad producer theory can be understood with the same tools used in consumer theory.
Comment: I think that philosophically consumer theory is more controversial than producer theory. Even if firms do not behave a perfectly rational optimizing agents, it makes sense that they might want to, or ought to, this can not necessarily be said for consumers. Is there a reason to think of as producer theory using the tools OF consumer theory, or that is just the order in which the tolls are introduced in textbooks?

I think Walras' law is pretty fundamental, should be added to the MB=MC equation to show the result of agents operating in such a way.
Comment: It makes sense to assume that consumers are rational optimizers. That is a toothless statement (complete and transitive preferences). It's just much harder to know what a human's objective is. I think of producer theory as often being a special kind of consumer. They are risk neutral consumers who get utility from dollars.
Answer: I once heard Roger Myerson talk about why he thought Economics has, as a Social Science, been so successful in applying (or has so readily incorporated) mathematics. He suggested that perhaps it was due to some of the fundamental linearities within the world. Two examples would be the flow-balance constraints of scarce goods (commodity constraints) and
no-arbitrage conditions. These are fundamentally linear constraints.

It's important to emphasize the importance of these because we can get a surprising amount out of the two. For example, a lot of people think that the law of demand is a consequence of assuming rationality (specifically, preferences that exhibits a diminishing marginal rate of substitution). A result due to Gary Becker shows that the law of demand (albeit just a slightly weaker version) can be derived from the budget constraint alone. (See Becker 1962, "Irrational Behavior and Economic Theory.") That is, this fundamental economic result can be derived from the reality of scarce resources alone---without assuming rationality.

The no-arbitrage condition is an application of the linear duality theorem (Farkas' lemma). A lot of economics and finance (asset pricing) can be done just by the assumption that in economic equilibrium there is no arbitrage.

Extra Notes:
Gary Becker made a lot of advances in the field by studying the way constraints affect human behavior. One famous quote, taken from his Nobel prize lecture, is the remark that "different constraints are decisive for different situations, but the most fundamental constraint is limited time." (Some discussion here.) Some more resources about how his work in this regard can be found here and here.
Linear duality can be used to describe the no arbitrage condition. More generally, this theorem is typically proved with the Hyperplane Separation Theorem, which is mathematical tool that shows up a lot in economics textbooks.
Also, keep in mind that it's enough just to assume that in economic equilibrium, there
is approximately no arbitrage.
Answer: I think one of the most important equations (at least within macroeconomics) is:
$$E\left[ m R \right] = 1$$
This equation has been used to derive many foundational results.  This equation motivated the Hansen–Jagannathan bound.  It is fundamental for asset pricing as well.
Also, something interesting I saw from once from Tom Sargent.  If you use the stochastic discount factor for a standard model $m = \beta E_t \left[ \frac{u'(c_{t+1})}{u'(c_t)} \right]$ then depending on which piece of the equation you allow to be exogenous you can get some fundamental results of macro:

Permanent Income Hypothesis:  Let $\beta R = 1$ then we get $c_t = E [c_{t+1}]$
Lucas Asset Pricing Model:  Let the process for consumption be a given.  Then the price of an asset can be described by $R_t^{-1} = p_t = E \left[ \frac{u'(c_{t+1})}{u'(c_t)} \right]$
Answer: Although I agree with Jyotirmoy Bhattacharya that the most interesting ideas in economics are not always best expressed through equations, I still want to mention the Slutsky or compensated law of demand from consumer theory
$$ (p' -p) \Big[ x\big(p', p' x(p,w)\big) – x\big(p,w\big)\Big]^T \leq 0,$$
where $p',p \in \mathbb{R}_{++}^n$ are any two price vectors, $w \in \mathbb{R}_+$ is any level of income, and $x(\cdot,\cdot) \in \mathbb{R}^n$ is the demand function.
The underlying relation is a couple of orders of certitude away from fundamental equations in other fields. Also, it does not ground the discipline, in the sense that it is not used all that often.
However, I tend to view it as fundamental because

It is an absolutely non-trivial consequence of three simple and fundamental assumptions in consumer theory, namely,

That the demand function $x(\cdot,\cdot)$ is homogenous of degree zero (no money illusion)
Walras' law (people do not burn money)
The weak axiom of revealed preferences (if you chose A when B is available "today", you will not chose B "tomorrow" if A  remains available)

Therefore testing the inequality is equivalent to testing these three assumptions jointly.
The three assumptions are used in the vast majority (maybe more than 90%?) of the models including consumers in economic theory.
Their validity (at least as approximations) is therefore crucial to the validity of most models in economic theory (at least as approximations).
Although it is not always obvious how to relate the notions of prices, goods and income  to observables, all the element in the equation are observable in principle (as opposed to utility levels for instance) and the validity of the inequality can therefore be tested empirically.
Comment: I'd add that it gets even better: there are _three_ laws of demand, which are equivalent (and boil down to Slutsky negative semidefiniteness) in the infinitesimal case but are distinct in general. After the price change from $p$ to $p'$, you can either (1) adjust wealth such that it can purchase the old bundle, (2) adjust wealth such that utility is constant, or (3) adjust wealth such that the newly chosen bundle could have been purchased yesterday - in all cases you get a law of demand. (These are arguably the laws of overcompensated, compensated, and undercompensated demand, respectively.)
Answer: I don't think there are any economics equations with the same status as, say, Maxwell's equations in physics. In its place we have concepts like the equimarginal principle, competitive equilibrium or Nash equilibrium which are at the core of the "economist's approach". But I think that the real worth of economics is not even in these ideas themselves but in what we know about concrete problems in specific areas of applications: for example what we know about business cycles in macro. In this economics may be more like medicine than physics.
Comment: The acknowledgment that the totality of activities has a scale limit is understandably slow because economic developments are evaluated in the conceptual and quantitative
terms of a system that repudiates the existence of such limits; tough, Maxwell can marginally be introduced to the core of the "economist's approach": [Entropy, limits to growth, and the prospects for weak sustainability](http://www.embl-hamburg.de/aboutus/science_society/discussion/discussion_2006/ref1-13July06.pdf) and the axiomatic base: [Ten Proofs of the Generalized Second Law](http://arxiv.org/pdf/0901.3865v2.pdf)
Answer: A bit late to the game, but I'm surprised no one has named the equation to calculate OLS estimates:
$$
\hat\beta=(X'X)^{-1}X'y
$$
Comment: I don't know if that can be called economics. Or if it can, then what about other results from statistics and mathematics that are widely used in economics?
Answer: Whilst not as foundational as, for example, the Slutsky equation, the condition on the Lerner index that a profit maximising firm with price $p$, cost $c$, and price elasticity of demand $\eta$ has
$$\frac{p-c}{p}=-\frac{1}{\eta}$$
is an important equation in industrial organisation.
This is not only an elegant formulation of the solution of the firm's problem, but it is also practically useful:

A firm that estimates its $\eta$ and knows its $c$ can use this formula to calculate the profit-maximising price.
A regulator that observes a $p$ and estimates $\eta$ can use the formula to calculate $c$—important in many forms of regulation.
Answer: For me, one of the most important ones is the budget constraint. It might seem too obvious but a lot of laypersons (though maybe not physicist) don't get it!
$p⋅x \leq w$
Comment: It's not that foundational if you remember about borrowing.
Answer: It is already written but Euler equation in continous time yields
$$\frac{\dot{C}}{C}=\sigma(r-\rho)$$
where $\sigma$ is intertemporal elasticity of substitution, $r$ interest rate and $\rho$ is the discount rate (impatience level).
Answer: The foundation of intertemporal economics is the net present value equation. That is, the net present value of a future income stream is the yearly incomes divided by an appropriate discount factor, based on the prevailing interest rate, r, taken to the nth power, where n is the number of years.
Comment: I know. What I mean to point out is that, if we think of $E[mR] = 1$ more generally (e.g., drop the equilibrium interpretation), it can encompass NPV as you described it. But it can also do much more. If you write it as $E[m X] = P$ and you treat $X$ as a stream of future cash flows and $m$ as the appropriate discount factor, you can recover your definition of NPV.
Comment: NPV as described in the linked Wikipedia article doesn't seem as general and central to economics as does $E[mR] = 1$, for example.
Comment: @jmbejara: It's the foundation of finance, as it relates to the value of bonds, the mortgage on you house, etc.
Comment: http://en.wikipedia.org/wiki/Stochastic_discount_factor
Answer: Well for microeconomics there are several, however they all follow the same pattern.

Here I'll attempt to teach an entire intermediate microeconomics course in one post.

Most microeconomics problems follow this format:
Though leaving out some minor details, if you do enough microeconomics practice sets the problems end up looking the same after a while. This is what I got to share.
Production/Utility functions
There are three main types of utility/production functions you will be exposed to in an intermediate microeconomics course1. They are:

Cobb Douglas
$$f(x_1,x_2)=x_1^ax_2^b$$
Leontif/ Perfect Complement
$$f(x_1,x_2)=\min\{x_1,x_2\}$$
Perfect substitutes
$$f(x_1,x_2)=x_1+x_2$$

Budget lines and Cost functions
In consumer theory, you have a budget line represented by the formula:
$$m=p_1x_1+p_2x_2$$
In producer theory we call it a cost function.
$$C(x_1,x_2)=w_1x_1+w_2x_2$$
we either want to maximize consumption given a budget/cost function or minimize costs holding your utility/output level constant. To do this we use another equation:
The Lagrangian Multiplier:
Though not exclusive to economics tool per say, its the primary tool of all intermediate microeconomics students.
$$\mathcal{L}=f(x_1,x_2)\pm\lambda(H-g(x_1,x_2))$$
where $H-g(x_1,x_2)$ is either a budget line/cost function or Utility/Production function when its equal to zero.
We use this for calculating utility/profit maximizing consumption bundles/inputs or Minimize Costs holding profit/utility constant.
And thats a wrap!*

*Though there is what to say on marshallian and hicksian demands I'll leave that for others to fill in.

Fundamental equations in economics


Are professional ranks representative for how many stones of handicap players can give each other?

Question: It was mentioned elsewhere that a 9p could not give 7 stones to a 2p. I have no databases available and wondered if this is correct.
Bonus:  If they aren't representative, why not? And is there a historical reason for it developing that way?
Answer: Historically, pro ranks were an indicator of playing strength. It was said that 3 (later: 4) ranks are about a stone difference. To my knowledge, there never was a time when 1 rank difference actually meant 1 stone.
In the 20th century, there was a sudden and increasing change in the strength of new pros. This is generally considered to be a consequence of intensified training in insei schools as well as the advent of the internet and the worldwide communication it enabled.
For instance, earlier, Go schools occasionally developed secret moves - new moves that would stump many opponents who were not familiar with it. Nowadays, such a move would be known by millions right after it is played, and days later, everyone would have studied it already. Modern insei schools make use of this and always present their students with the most up-to-date material and worldwide research, making sure their students are fully aware of the current moves in Go.
Also, there is incredibly fierce competition among the insei. Only a handful of new pros is selected each year, and even the slightest mistake will ruin your chance to become pro. Therefore, everyone is working extremely hard.
This leads to new pros being able to compete on par with previous pros. They already possess the same knowledge as their seniors, and thanks to their young age get less easily exhausted from long, intense games, they are sometimes even said to be stronger than older pros.
In fact, to be successful as a professional Go player, you have to become pro early (around the age 15) and win titles while you still have a slight edge over the competition. In just 10, or 15 max, years, you'll be overwhelmed by the next generation. Very few pros could stay at the top for an extended period of time, one of the most notable being Go Seigen, who dominated the Go world for 30 years. But apart from exceptions like him, modern pros, even huge talents like Lee Sedol, are falling behind very quickly.
This means that rank is basically meaningless. A new 1p may well as strong be as an older 9d. Or the other way around. I asked several pros about this and the reply was always the same: Rank is no longer a useful measurement of playing strength. Personally, I call it an 'experience indicator', but even that is not completely correct.
To compare pros, you need to look at their results in games over time. There are various lists that attempt precisely that, and those lists are a lot more useful than the rank given. Since young pros who do very well get promoted quickly they ensure that the top spots in those lists tend to be occupied by 9 dans, still.
Interestingly, high dan promotions in China and Korea are linked to great performance in title tournaments - both for amateurs and professionals. For instance, a Chinese 6 dan (amateur) is a 5 dan who won a regional tournament. A Chinese 8 dan (amateur) is the current champion of all China (meaning there is only one of them at any time), former champions are 7 dan (*). In a similar fashion, winning an international tournament yields an immediate promotion from 1p to 8p in Korea, while regularly, advancing the ranks is a lot slower. (I'm not 100% up-to-date on details of this topic though.)
Seen this way, ranks of new pros can be seen as a measurement for achievements. Being awarded 9p is indication of outstanding accomplishments. A rank of 1p should not be seen as failure, especially with young pros it simply means their accomplishments will be for later.
Edited to add in 2014:
At times there is a promotion for professionals that specifically promote Go in the West. This is meant to compensate for their lack of tournament experience that is implied by their increased teaching. Since pro rank is an important factor in payment (when teaching), this is an important help for pros working in the West. I am specifically aware of a Korean promotion of Korean professionals from 8p to 9p or from 1p-7p to 8p.
(*) This information about Chinese 6d-8d amateur players appears to be incorrect. I've received multiple explanations as to what the current state actually is, and they all differed, so I'm at a loss here.
Answer: At the professional level, rank differences are very slight. ON AVERAGE, it may take a three or four rank difference in pro rank to equal one stone.
But ranks are largely a matter of achievements; how many games or tournaments you've won. It could be that a gifted "newcomer" (few victories, hence relatively low rank) is actually stronger than a higher ranking person with a longer record (but maybe lower win PERCENTAGE).


Should a "search results" return the number of items found?

Question: Is it recommended to add the number of items found on a search results?
In my opinion it is a useful information that gives a quick idea on what you are going to read.
Could it be omitted?
Answer: The Scent of Search by Tyler Tate includes the following recommendation:

Indicate the number of results. This
  helps users gage the validity of their
  search. Numerous results can act as a
  vote of confidence, while few results
  may raise a red flag.
Answer: Search results should always:

provide the total number of results found
indicate whether the results are ranked in order of relevance (users will often assume that results begin with the most relevant
give clear clues to the user where they are in the results via pagination or a similar mechanism
Answer: Search results should show the number of items found.
As a general rule, the data of complex type (such as a set of database records) should be accompanied by its summary because reading the whole data requires a lot of effort.  While it is difficult to produce a spot-on summary automatically, the number of items is usually easy to generate and pretty useful.  It is usually not sufficient as a summary by itself, but it is better than no summary.
If the search is fuzzy, you may only have the number of "best matches", the number of "good matches", the number of "possible matches" and so on, and there may not be a single "number of items matched".  Even in this case, you should show some meaningful number(s) whenever possible.
Answer: Not only should you include the number of matches, but also include the exact search phrase/criteria that was used, e.g. Your seach for "foo" returned 0 matches..
It is really annoying when you search for something and get no matches, then try with a different search phrase and you have no idea of whether the zero matches result page is a result of your last search or your second last search without rigorously watching the browser to try to detect the expected page reload triggered by your last search.
This is of course less of a problem when there are some matches found, but still always acknowledge the user by in some way saying I searched for .... for you and found .... results.
Answer: If it's cheaply available, of course you should show it. I've built systems however (not based on SQL) where the search results were produced at a rate of about 10-20 per second, and you might get 1000 results. Naturally we didn't wait a minute to show the first result; we showed the first page when it was available.
Now, what should you do with the number of search results? In this case, it made more sense to show pages being added as results came in.
Answer: Yes! If there are too many results, rounding the total is a good idea in my opinion.
Answer: There should be a number but you can do it like Google: display three significant digits, for example:

7
532
7'320
312'000'000
1'180'000'000
Comment: nobody does not check how many records really found, yes?  :)
Answer: It depends on the size of the index being searched. For example, a blog with an index of 100 posts might not need a result count - why clutter the UI if a typical search brings back 3 results, all of which are above the fold? If you are searching a larger index with a wide average range of results returned then you may want to consider adding a result count.
Answer: Sometimes. In a system with a good relevancy ranking, the number of results may not have much meaning.
Answer: Why not? That's one number, it can't create much visual noise, even when not useful. Even as decoration it's acceptable.


How to get out of a Work Out Funk?

Question: Currently I've been working out about 4-5 days a week trying to get in about 6-7 different lifts in per day.  Focusing on a major muscle group each day for example Legs day 1, Arms day 2, chest day 3 etc.  Recently I've been struggling to get through the work outs and getting in only about 4 different lifts.  Is there any suggestions on how to rejuvenate my workouts so that I am able to get back through all my sets.
Comment: Have your eating habits changed? Are you getting less sleep lately? This information would be very helpful for you to get a helpful answer.
Comment: http://fitness.stackexchange.com/q/2999/3778 could also be helpful
Answer: You may have stumbled with your sleep, eating, stress levels, amount of sunlight or socialization, or fallen into overtraining in a million other ways. Maybe your program simply has too much volume for you.
Regardless, it sounds like you're overtrained. Take a day or a week off, and when you start up again, consider doing dramatically less. Five days a week of lifting is often taxing. Sometimes more rest coupled with more intense lifting on the days when you do work out is easier on your recovery in the long term.
Answer: What are your goals?  Do you have any goals?  Goals should be a major part of any workout plan.  Whether you want to be a world class athlete, compete well in a local event, improve stamina, lose some weight or maintain an energy level the lack of a goal can make working out a mental challenge.
If you have an athletic induced goal and you're stuttering to workout, post your goals somewhere to jump start you, be in on the inside of your bedroom door, your desk at work/school or in the car.  If you do not have any try to find additional motivation to work out.
Comment: I've got my daily work out goals set for example I want to do these 7 things at this weight.  I get about half way through and just hit that wall.  Before I could get all 7 in no problem.

How to get out of a Work Out Funk?


how to increase mileage of petrol to match with diesel car

Question: My relatives bought a diesel car and I found out that their gas mileage is better than my petrol gas mileage. Now, the price of petrol is soaring. Can I increase my mileage to match their gas mileage? My engine and tires are well maintained. I stop the engine at the traffic signal but I still lag behind by miles per gallon.
Answer: The simple answer is:
No. You can't.
To expand a little, both diesel and petrol technologies are continually improving, so you can make incremental changes to your engine in terms of engine management, input air flow etc., and also things like use low rolling resistance tyres etc. But you cannot change the basic fact that your engine is less efficient than his - whether or not one is diesel or petrol.
You can learn to drive more efficiently (see hypermiling for an extreme version of this - some of the techniques may reduce your safety, so be careful)
But if you really want to increase your mileage significantly, you will need to change your engine or your car. Newer cars are generally much more efficient than older cars, and diesel technology currently has a mileage advantage.
Answer: Here are a few simple ways to increase gas mileage, but not at par with a diesel:

Operate the vehicle at speeds in the range given in the dash
board as green color and never run the vehicle at red mark indication.
Keep a minimum payload, take out everything you don't need.
Service the engine periodically.
Run the vehicle at proper gearing and proper speeds.
Keep the car in gear when moving.
Keep your spark plugs clean.
Keep your tires properly inflated.
Avoid running the A/C
Avoid heavy braking, and avoid heavy acceleration.
Maintain bearings and moving parts, grease appropriately.
Clean the air filter often.
Before starting the vehicle check the oil and coolant levels.

Any edits or edit suggestions are most welcome.
Comment: No, do not over inflate or under inflate your tyres, keep them at the proper inflation recommended by the manufacturer, do not risk your safety for gas milage.
Comment: More Tyre pressure give you more mileage. But it will make less friction on road. If your Tyre is too old do not put more pressure , it may cause to blast on ride
Answer: No. Because you need more Petrol per combustion stroke than Diesel. The air/fuel mixture for Petrol is about 15:1, whereas Diesel starts off at 18:1 and can go even leaner (more air, less fuel). That means that a 2000cc Diesel engine may burn 5ml of fuel per combustion stroke under operating condition X, whereas a 2000cc petrol engine will burn 6.5ml per stroke under the same operating conditions. That means that the petrol engine uses 30% more fuel than the Diesel engine under the same conditions.
Coupled with that, Diesel engines are also optimised for fuel economy through extremely high compression ratios, low-RPM gearing and mild cam profiling. They can do this because Diesel engines produce lots of torque via the combustion properties of Diesel fuel, and can therefore turn higher gears with ease. That means less RPM's is needed. On the other hand, Petrol engines are usually designed to provide a balance of performance and fuel economy. That's because Petrol does not produce as much torque, and therefore we need higher RPM to produce the same number of kiloWatts.
You'll see that a Diesel engine may produce 250Nm of torque and only 100kW of "work". That's because "work" is calculated by multiplying Torque by RPM. A Petrol engine producing 250Nm would usually do 130 to 150 kiloWatts of "work". So the petrol engine "works" harder than a Diesel engine, hence it needs more fuel.
Answer: Drive smoothly.  Avoid braking (safety first, don't crash to save fuel ;D ).  Braking turns the kinetic energy into heat energy, therefore the fuel you have burnt to propel the vehicle is now being dissipated through the brakes via friction.
As mentioned previously, many people put the vehicle in neutral when coasting.  This is wrong, a modern engine will sense the road turning the engine via the transmission, and therefore supply much less fuel to the cylinders. In neutral fuel will be needed to turn the engine.
Answer: Drive your car always check with your RPM meter and don't accelerate much more when you shifting a gear and while running.


Which amount of side-story is acceptable?

Question: If you grow your writing from short-stories, to longer stories and novels you will have to create more content. Most of it will be more detailed description of settings, people and plot. Also you will add more obstacles to create a longer main-story. But another possibility is to add side-stories. That can be somewhat difficult, as too much side-story might be distracting, the reader not longer knows whats the writing is about. Are there any rules of thumb, how much side-story is acceptable?
Answer: There is no answer.  "3" (if you can actually count them) side-stories can be too much.  Even 1 can... if you want to write (or rather, if the story demands to be) a simple story.
3 can be too many.  But 100 can be just right.  It depends.
Haven't read the Wheel of Time yet, but I've heard it contains lots of side-stories.  Too many?  Some surely think so, but then they're not the audience for it.  Given it is a success, it looks like it didn't contain too many tangents.
So... as I always say: write your story the way it demands.  If it's an intricate, multi-level plot, then there will automatically be "side"-stories (some of them, or even most of them, won't really be tangents, it just won't be obvious how they're all connected for some time, see "Pulp Fiction" for a great (non-linear, too) example)
Comment: Oops.  The "actually count them" is not meant to imply that you cannot count to three. ;-)  It means that "side-plot" as such can be hard to identify.  Is this other thing going on a sub-plot as such, or is it just something going on in the character's life while the main plot happens to unfold?
Comment: wheel of time is closer to an amalgamation of side-stories, than one plot and many side stories.. in any case, the 'main plot' seems to shift between different side stories as they grow and fade in importance
Answer: I'm not sure there is a hard and fast number, but there are other ways you can measure if the side story is acceptable. What does having it in your story achieve. If it's just there to fill out the word count is it worth having it there at all?
On the other hand, if the story story helps move the plot along or helps develop the characters it might be worth having in the story. Sometimes major characters can't be there for all the important events, so having a secondary set to see what's going on can help flesh out the world and increase the tension. It also lets you break up the flow of the main story to help with the placing. And there's always the option of ending a chapter on a cliff hanger then jumping to the side story for a chapter or two.
If you're doing a world spanning epic it might make sense to have dozens of side stories. If you're doing a small story that never leaves the local neighborhood you might only have one or two, or none at all. It really all depends on how much the help the story.
Sometimes side stories are useful to show how bad things are going. Disaster stories and war stories both do this. It allows you to show how bad things are, and if done right you can kill off one of this minor characters after building them up enough that reader will feel the loss.


What could be an alternative for "Share this post with my network!"   in a social application?

Question: What could be an alternative word implying Share this post to my network! for use in a social application ?
Answer: http://sharethis.com/ have used a short catchy phrase 'Share this' and used a really good icon  indicating connected but diverging nodes in a network.
I'd suggest something similar. It depends if there is an intermediate stage between clicking the button and submitting the final share, but Share with, Share to, Share this are all short and to the point.
Of course maybe your social network could have a related 'action', like retweet works well for twitter.
Answer: I've seen "Spread the word" phrase used quite a lot.
Answer: i think there should be some user friendly word like

Hey! let's share it with your friends

OR

Let Your Friends Know about this!
Answer: I would consider shifting the emphasis to the word "post" ...  "Post this to my network."   I know that it might create ambiguity if you have already locked in on some other use of the word Post, but that may not be a problem.
"Syndicate this to my network" would be pretty out there but sure would grab the attention. "wow... I can syndicate something? hmm!!"
Answer: This probably depends on the kind of design you're making. SE itself just uses icons and lets people figure it out because the general audience knows how to share if it needs to.
If you can figure out the general web-savvy of your audience, you could define the right word pretty quickly.
As a rule, if space is not an issue, it's great to be specific: Share this on Facebook/Twitter works best.
Answer: I'd start by looking at other copy in the site and try to find terms that match the voice that's already set there. Is it colloquial, is it formal, is it technical or new age? Driving your search for terms from the brand while ensuring that it's still understandable will help the feature fit with the overall site, and you'll probably feel better about the label you use as well. It's a roundabout way to name something, but the legwork often turns up words you might not otherwise think of.
Answer: How about: 'Infect my friends with this idea' ?
Comment: That's a bit dark. :)


How can I fix my cheap Android 2.2 phone? Should I root it?

Question: I recently purchased a Samsung Intercept for Virgin Mobile. The problem is that it doesn't work very well. There's a delay when doing almost anything on it, even calling or texting. It also has poor battery life. Is there a way I can get it to work decently? Perhaps by removing apps? Would rooting it get it to work better?
Answer: IF you know what you're doing, rooting and flashing a custom rom CAN help. Rooting it will allow you to delete some "system" apps that you don't need, and give you access to more control over your CPU, and some ROMs have ways to help save battery. My sister was forced to get a Droid 2 Global after two faulty replacements of her original Droid 1 which she loved, and she hated the Global. Had problems with battery and the way it was set up and everything. So I rooted it for her and flashed a new rom, and she got an extended battery (VERY USEFUL SUGGESTION), and now she loves it. But as rooting voids your warranty, I wouldn't try it if you don't need to or don't know exactly what you're doing.


How do you attach asset tags to camera equipment?

Question: For all you pros out there, how do you handle asset tags on your equipment?  It seems easy to apply them to computers, notebooks, external hardrives, and even camera bodies, but how do you handle asset tagging lens, memory cards and other fixed assets?
Answer: I don't tend to asset tag any of my camera equipment as it does not lend itself to tagging. I simply enter the serial numbers of the asset into my asset register instead. This is sufficient as the asset register is just a means of tracking fixed assets owned by your company and serial numbers are a valid way to do this.
Answer: If you're handling many items, the serial number, while important to record for warranty and repair purposes, isn't sufficient because you need a fast method of counting/auditing the inventory or booking equipment in and out. That means barcode scanning for speed and accuracy, and a barcode label. Due to limited size of flat surfaces, they can be successfully scanned down to a label of 5mm x 20mm. If the item is too small or complex, such as a lens, then tag the box. After that your're ready to work with asset tracking software but that's a much bigger subject which I'm happy to discuss separately.
Regards, Stephen Laing, ASSETtrac Ltd
Answer: working in IT, we deal with small stuff like SD cards as well. Those aren't tagged, it's just noted how many of which brand and model are released to whom, and when items need to be returned it's expected that same number be returned.


Are there any sample images out there taken with ND filter and the Sigma 8-16mm lens?

Question: I am deciding on getting an ultra-wide lens mostly because a lot of my shots are taken at 17mm and it's often not wide enough.
I narrowed it down to either the Sigma 10-20mm or Sigma 8-16mm. (APS-C)  The problem is that out of the 2 I would prefer the 8-16mm lens except that it has a rounded front element so filters cannot be used and I really like using ND Filters. There are some expensive contraptions that can be used such as the Lee holder with square filters but it my still require taping to prevent light-leaking. (I've read a few things suggesting having to use tape)
The Sigma 8-16 ships with a cylinder like cap onto which the lens cap can be mounted and it also has a 72mm thread for filters. However, according to several articles the vignetting is really bad when filters are used with this cylinder adapter. Some say that at widest angles the cylinder is visible in the photo so cropping is necessary thus rendering the wide end useless. However, I haven't seen any actual photos of this.
Does anyone know of sample photos using this lens with ND filters attached to the cylinder?
Budget is a consideration, the 10-20mm lens can be had for $479 and I can use my existing 77mm filters. Lee holder + square filters (or equivalent) for the 8-16mm can easily be another several hundred dollars on top of the $699 for this lens. The usability of my existing filters might be a deal-breaker here.  (As much as I would love to have the extra 2mm on the wide end.)
Comment: I shoot with the sigma sometimes, it is a sweet lens. I know this doesn't help, but it is nice...
Answer: Read here - they use a Cokin filter set that may be considerably less than the Lee holder..
Sigma 8-16mm, commercial available and D.I.Y filter options.

There is also a sample image at the bottom of that which was taken with a coloured filter on this lens.


Are gold bag locations fixed in Infinity Blade 2?

Question: It's clear that gold bags are MUCH more prevalent in Infinity Blade 2 than they were with the original, not to mention more cleverly hidden. Do they always show up in the same places over multiple playthroughs? Alternatively, is there a fixed set of places that they can show up?
Answer: Like the first game, there are fixed places where gold CAN spawn, but it may or may not appear in a particular location in a given playthrough.
Also, sometimes a larger treasure trove may spawn (a group of three gold bags), and you an also occasionally find keys and health potions in these locations as well.
Comment: Keys in gold bags? Or do they show up as keys on the floor?
Comment: @Nick They show up as keys. It took me a while to realize what they were, and that they were lootable! (The models are kind of funky - you can check them out in the inventory/store screen so you know what you're looking for.)
Answer: What I've noticed is there are times where gold bags only appear when the cinematic is showing. For example after the first fight in the Saranthia wilderness, where you chose to go to the dam or skip it. The cinematic shows you character, and behind you a gold bag (sometimes) appears to the right.
What I do is I tap on the spawn points just in case there is a small key hidden in there.