Rituals to be performed during Shiv Ratri and their significance

Question: Shivaratri comes every month and Maha Shivaratri comes once a year. Many people offer prayers to Lord Shiva on that night without sleeping. Are there any specific rituals that one must do while offering prayers during Maha Shivaratri? If yes, what are their significance?
Comment: Some people perform Rudram Yagnas during Maha Shivratri. Chanting Rudram 11 times followed by 1 chamakam (and then repeating that 11 times, and then that 11 times, etc depending on the number of people chanting -- upto a specific limit of namakam it is called Ati Rudram Chanting sir). This is said to improve the welfare of Earth and provide auspicious vibrations through the globe. All the best!! What is the significance? All festivals have only one significance and that is that atleast on this day, the devotees take the name of Ishvara and strive for salvation. Thank you sir!!
Answer: 1. Significance of Shiv Ratri
Attaching a snap from Shiv Purana - Part 1 (VIDYESHWAR SAMHITA) - Chapter 9

Translation in English:
Lord Shiva -

A devotee who fasts on Shivaratri remaining only on fruits, attain virtues equivalent to the worship done for the whole year.
One who has my darshan on this day (Shivaratri) or worships me in my form of linga is dearer to me than Kartikeya.

2. Rituals to be performed during Shiv Ratri
Adding a snap from Shiv Purana - Part 4 (KOTI RUDRA SAMHITA) - Chapter 39

Translation in English:
Lord Shiva-

"Among all the austerities and fastings Mahashivaratri holds a supreme
  place. It falls on the fourteenth day of the dark lunar month of
  Phalgun. On this day the devotee should take a vow to observe a fast
  after awakening in the morning and finishing his daily choirs. He must
  observe a fast for the whole day and night. In the night he should
  worship me either in the temple or in his own home according to his
  convenience. He should worship me with the help of sixteen modes of
  worship (Shodasopachar). He should either chant the mantras of
  Laghurudra or perform 'abhishek' during the course of worship. While
  doing worship he should eulogize me and perform 'artis' in my praise.
  He can perform 'abhishek' with either of the followings - Milk, water,
  sacred water of belonging to a place of pilgrimage, sprinkling water
  with Kusha, Sugarcane juice, Honey and Ghee etc. The devotee should
  engage himself in my devotion for the whole day. In the end he should
  feed the brahmins and make donation to them. A fast observed in this
  way gives infinite virtues to the devotee."

Further Reading

Shiv Purana - Part 4 (KOTI RUDRA SAMHITA) - Chapter 37 to 40

Other Puranas on Shivratri
Vishnu Puran & Bhagavat Puran:

Parashar says: Once on the occasion of Shivaratri, Nand Baba and all other Gopas drove their carts with families and reached Ambikavana on a pilgrimage tour. There they took bath in the river Saraswati and with devotion worshiped lord Shiva and Parvati. They also observed day long fast and decided to pass their night on the bank of Saraswati.

Agni Puran:

The chaturdashi in krishnapaksha that comes between the months of
  Magha and Falguna is known as Shivaratri. Then one has to fast and
  stay awake the whole night. Earlier, there used to be an evil hunter
  named Sundarasena. But because he performed a vrata on Shivaratri, all
  his sins were forgiven.

Skand Puran:

Sage Lomesh eulogizes the virtues of Shivaratri in the following
  words--'The fourteenth day of the dark half of a month is dedicated to
  the worship of Lord Shiva and is famously known as 'Shivaratri'. It
  destroys all the sins committed by a man. Sage Lomesh then narrated a
  tale, which emphasized the greatness of Shivaratri-- Once upon a time
  a brahmin widow developed an illicit relationship with a 'Chandal' (a
  low caste man). Later on she gave birth to a son who was named Dussah.
  Her son had all the bad qualities one can think of-- a gambler, a
  drunker, a thief, a murderer, etc. One day, Dussah went to a Shiva
  temple with the intention of committing robbery. It was the festive
  night of Shivaratri and people had thronged the temple in a large
  number. So, he did not get an opportunity to steal temple property. He
  remained awakened for the whole night waiting for an opportune moment
  but his wishes remained unfulfilled. He spent his time listening to
  the divine tales of Lord Shiva that was being narrated by the temple
  priest. Though he was a sinner yet he took his next birth in a royal
  family on account of his two virtuous deeds--he had remained awakened
  for the whole night of Shivaratri and he had listened to the tales of
  Shiva. In his next birth, he was born to a king named Chitrangad and
  he himself was named Vichitraveerya. Vichitraveerya was a great
  devotee of Lord Shiva. He ultimately united with lord Shiva and
  manifested as Veerabhadra at the time when Lord Shiva had shaken his
  head violently after hearing the sad news of Sati's demise. There are
  numerous instances of people attaining salvation by observing a fast
  on Shivaratri. The names of some great devotees to do so are King
  Bharata, Mandhata, Dhundhumar, Harishchandra etc.

Garud Puran:

During ancient times there lived a hunter named Sundarsen in the
  province of Arbuda. One day, he went deep into the forest in search of
  his prey but unfortunately he found none. He wandered all over the
  place but in vain. When evening came, he climbed up a wood apple
  (Bael) tree to protect himself from the wild animals. Sundarsen was
  worried that his family would have nothing to eat that night.
  Engrossed in his contemplative mood, he kept on plucking leaves from
  the 'Bael' tree and throwing them down. There was a Shivalinga just
  under the tree and the leaves, which Sundarsen threw, fell down on it.
  Next morning while Sundarsen was climbing down the tree, his arrow
  fell down. While picking up his arrow, he touched the Shivalinga.
  Sundarsen was unaware of the fact that it was Shivaratri night and he
  had worshiped Lord Shiva with appropriate rituals albeit
  inadvertently-he had offered Bilva patra to Lord Shiva and had touched
  the Shivalinga. He attained to Shiva loka on account of the virtues
  attained by his inadvertent worship of Lord Shiva.


How often should multiple POV be used?

Question: I'm starting on my second novel, and my two main characters take two paths that give necessary information for the story. I want to begin a chapter using the male's POV, but his POV is unnecessary for the entire book. Am I able to use his POV for only 3-4 chapters throughout the book? Or should I find a way to integrate his information through the female's POV? I'm excited to attempt it, but don't want to waste my time if it's going to confuse the reader.
Comment: Does this answer your question? [Third person multiple pov in a crime mystery](https://writing.stackexchange.com/questions/20709/third-person-multiple-pov-in-a-crime-mystery)
Comment: Hi @Cheyenne Rosenbaum Welcome to Writing SE. We're trying to help reduce duplicate questions on this site. Please have a look at some of the many questions about "multiple pov" in the search results. If you don't find what you're looking for, please say so in a comment, here. Thanks.
Answer: For me, while yes there are possible duplicates, they are not exact duplicates questions
But Cheyenne, do read the Q. In the POV tag for the many ways to deal with multiple povs
In your case I would get confused if it is only for 3-4 chapters that I get a second POV, commit to it or don't, no halfway mesure....
1. Stay with a single character
The information that was to be given by the second character can be in the form of a prelude and the rest found indirectly by the MC.
2. Stay with both characters
Though for that to work they need to have a more even share of the book. Find ways, complications, subplots, to give more room to the male POV.
3. Introduce other characters
If you can't use the male POV for more than 3-4 chapters, consider adding extra POV to balance the MC. If you interlace the MC with 3-4 other povs, I don't think it will be confusing, and always coming "home" to the MC, after each other povs, can help anchor the story.
Answer: Write it the way that works best for your plot.
If you are writing mainly from a single character's point of view and you feel switching to the other POV only a few times during the novel is jarring, you can employ bridges whenever you do, e.g. having your main character think or say something like: I wish I knew (imortant piece of information) just before switching to the other POV when / shortly before that character finds out (important piece of information), or if they started off together, have her wonder what the other person is doing.
There is no need to have both POV for the entire book or to try and write only from one character's point of view if you need to include another POV for a short while. Many authors have written works where they mainly follow one or two characters or groups but include short sections that follow a different character or group. A good example is Tolkien's Lord of the Rings, after the original fellowship is split, not everything experienced by each group gets told from their POV, only those parts that are needed to move the plot along and even after the action is over and they are catching up, only important points where we were kept in suspense during the narrative are cleared up.

How often should multiple POV be used?


Is it OK to post extensive comments as answers?

Question: Here and there, I see answers prefaced by "this is really just a comment that got too long" or the like (and after seeing this a few times I felt comfortable doing it myself, twice in fact). Is that acceptable, or does the fact that it might crowd out the real answers make it very bad? Does it make a difference if the extended comment-answer is also helpful in getting to an answer?
Comment: Observation: these have been allowed in the past if particularly relevant, interesting, and used sparingly.
Comment: Example: http://judaism.stackexchange.com/a/53036/5151
Comment: sort of related http://meta.judaism.stackexchange.com/q/808/759
Comment: @Scimonster another recent example (which was my indications that would be ok): http://judaism.stackexchange.com/a/52900/5083
Answer: From our Help Center's page on "How do I write a good answer?":

Answer the question
Read the question carefully. What, specifically, is the question asking for? Make sure your answer provides that – or a viable alternative. The answer can be "don't do that", but it should also include "try this instead". Any answer that gets the asker going in the right direction is helpful, but do try to mention any limitations, assumptions or simplifications in your answer. Brevity is acceptable, but fuller explanations are better.

Standard Stack Exchange doctrine is that answers need to at least provide information that could be helpful toward getting an answer to the question, preferably explicitly stating how they do so. I don't see any reason why Mi Yodeya should hew to a different standard.
Applying this standard to examples that were brought up in comments to this question:

The question this answer was posted on stipulated to the existence of the "ng" pronunciation in the past and asked if people had heard it in use in the present. So, additional evidence that it has been used in the past will not, presumably, lead to an answer and therefore does not constitute an answer. [Some of] it might be valuable as additions, perhaps in footnotes, to the question post.
The final line of the answer:

"FWIW, I've also heard older community members pronounce Hebrew this way."

does directly address the question, though vaguely. The addition of more information about the location and/or backgrounds of said community members could make it much more valuable.

This answer provides rulings related to the issue in the question that could well suggest approaches to that issue, so I would say that it does constitute an answer. It could be improved a great deal with the addition of explicit analysis of how the cited rulings may relate to the question at hand.
Answer: For what its worth, I checked out those two examples and saw that I had already up-voted those two specific non-answers a few days ago.
I think that if you acknowledge that it is not an actual answer, but you are still bringing valuable material, then you should post it.  Over the long haul, it is better for everyone if valuable material gets posted, even if it might not fit the formal definition of an answer. I would have confidence in the voting and accepting system that users on average will give more votes to real answers than to interesting ancillary material.  That occurred in these two examples, at least.
People might say that it could dilute the quality of the question-answer format, but I think that happens only when the material has little value (rants, jokes, smart-alack remarks). I have posted those occasionally and subsequently deleted them after realizing their inappropriateness. The difference between that crap and what you are providing is that your "extensive comments" do have inherent value.


Standard reference for classical mathematical statistics?

Question: Can anyone recommend some books that are considered to be standard references for classical (frequentist) statistics? IE, fairly comprehensive, and also, been around for a while so that typos and mistakes in formulas had a chance to be checked and corrected
Comment: You could specify whether you need an introduction on applied statistics, or one on (theoretical) statistical inference. I.e., do you want the framework of testing, regression and ANOVA explained or do you want to know what the central limit theorem and the inequality of Chebiyshev have to do with the weak law of large numbers?
Comment: see also question on mathoverflow regarding books on mathematical statistics http://mathoverflow.net/questions/31655/statistics-for-mathematicians
Comment: see also question http://stats.stackexchange.com/questions/414/introduction-to-statistics-for-mathematicians
Comment: Joris: well, internet is already pretty good for explanations, my motivation is having something to check against when I need a statistics related formula. For instance, recently I needed a formula for P(X=x|v'x=a) where X is multivariate gaussian and v is some vector, and none of my statistics books had it
Answer: I have found Statistical Inference by Casella and Berger to be a relatively comprehensive introduction.
Answer: E. L. Lehmann, Theory of Point Estimation, 1983, and its companion book, Testing Statistical Hypotheses.
(NB: The latest edition of TPE, coauthored with George Casella, has not been getting good reviews on Amazon, but the original is still a classic.)
Answer: I'd recommend Theory of Statistics by Mark Schervish.
Comment: +1: i too learned from Lehman (very good reference), but this one is not mentionned nearly enough
Answer: A comprehensive and authoratative reference is Kendall's Advanced Theory of Statistics

Volume 1 Distribution Theory
Volume 2A Classical Inference and Linear Models

There is also a Volume 2B but it is Bayesian Inference.
Other than those, I agree the Casella and Berger is an excellent reference at the graduate level, and suggest Bain and Engelhardt's Introduction to Probability and Mathematical Statistics for upper-level undergraduates.
Comment: Hey, don't get so defensive.  The OP specifically asked for Frequentist.  He was just staying on topic.
Comment: Does the remark "There is also a Volume 2B but it is Bayesian Inference." mean that Volume 2B should not be included in the description "comprehensive and authoratative (sic) reference"? because it does not have one or both of these properties, or it should not be included because it deals with Bayesian Inference rather than with purely frequentist approaches as Volumes 1 and 2A presumably do?
Comment: @Shea, Dilip's query doesn't strike me as defensive. It sounds like a request for clarification. It seems unlikely to receive an answer though, since the answerer hasn't visited the site in several months.
Answer: All of Statistics
Comment: Could you, with the permission of the author, post the error briefly as a comment here? That will be useful to everyone.
Comment: I don't think that's been around for a while, and it's not very comprehensive either...one reason I started this post was because I found an error there, and also couldn't find some things I needed, like density formula for functions of random vectors
Comment: It may be useful if you email the author. Perhaps, it is a misunderstanding and if not it will help in correcting the error in the next edition.
Comment: I have confirmation from author, so it'll probably be corrected in next edition
Comment: Theorem 14.6, Sigma is singular so density isn't defined, this is fixed by instead considering distribution of $\hat{p_i}$ which is $\hat{p}$ with $i$'th component dropped (covariance matrix will be $\Sigma$ with i'th row/column removed)


How can I search for the IP addresses of nodes closest to me?

Question: In order for maximum latency I would like to identify the nodes closest to my location. Is there a way I cant find nearby nodes on a map and create a list of them based on distance?
Comment: *maximum* latency? Really? Most people would prefer to decrease it.
Comment: [Latency](https://en.wikipedia.org/wiki/Latency_(engineering))
Answer: I would:

set up a supernode to get as many peers as possible, this question gives you the command
list peers with a script like below once you have enough peers
Use BatchGeo to display the ips accessible in the json you got in point 2, otherwise you can look at that answer that will enable you to link ips to lat/lng
#!/bin/sh
geth attach << EOF
function getPeers() {
    console.log(JSON.stringify(admin.peers, null, ""))
};
getPeers()
EOF
Answer: First, distance as "physical length" doesn't mean anything on network. You should mind the time needed for the message to go to the peer and come back. This is ping.
if you use the Go client implementation, the p2p part already includes the distance calculation value to select peers. So current Go implementation already does what you aim to do. You can have a look at table.go to start and follow nodesByDistance.
Comment: The OP said "closest", he never said he was talking about physical (IRL) distance. The Go source code you mention uses words like "closest" and "distance", too.
Comment: -1 after reading the source code you mention. I find no trace of a measurement by time (the OP asked for latency), "distance" and "closest" in this source code appears to refer to the closeness of the IDs (which is common in Kademlia).
Comment: OP asked to "find nearby nodes on a map". I don't see why it wouldn't be a physical distance related map. This is the only map that makes sense in this question context.
Comment: In node discovery you'll find that when a node is found, it's "ping" distance is calculated and it's put into the tree in a way to reflect this. So hash distances reveals nodes distances, so searching the closest IDs is the same as searching the closest nodes.
Answer: I am not sure it is a good idea to select the time-closest (minimum latency) peers. Yes, this is what DNS resolvers (to take just an example) do but, in a peer-to-peer network, this would be a security risk: you could take over a node just by having several rogue peers time-close from him. Using peers anywhere in the network protects against targeted attacks.
On my own geth node, I can see that my peers are spread all around the physical globe.


From which exoplanets is our sun the brightest star on the night sky?

Question: The brightest star on the night sky is Sirius, here in the Earth. But are there any exoplanets, where the brightest star on the night sky is our sun?
Comment: My guess would be 'none'. From the distance of the closest exoplanet, Sol would be just another of the brighter stars - no more.
Comment: http://astrobob.areavoices.com/2015/01/31/what-would-the-sky-look-like-if-arcturus-sirius-or-alpha-centauri-were-our-sun/ and/or https://en.wikipedia.org/wiki/Extraterrestrial_skies#Extrasolar_planets may or may not be helpful.
Answer: I wrote https://github.com/barrycarter/bcapps/blob/master/ASTRO/bc-solve-astro-13115.m to solve this with the full results at: https://github.com/barrycarter/bcapps/blob/master/ASTRO/brightest-stars-from-other-stars.txt.bz2
As viewed from RigelKentaurusB, the Sun has magnitude 0.48,
and is the 10th brightest star in the sky. This is the only
star system with known exoplanets where the Sun even makes
the top 10.
From EpsilonEridani, the sun shines at magnitude 2.37,
making it the 79th brightest star in their sky. Things go
rapidly downhill from there:

79 EpsilonEridani Sun 2.36646
207 HIP113020 Sun 3.18865
208 HIP85523 Sun 3.11216
247 HIP106440 Sun 3.29606
396 HIP15510 Sun 3.74083
423 HIP74995 Sun 3.81444
685 Fomalhaut Sun 4.25746
878 HIP64924 Sun 4.48202
949 HIP109388 Sun 4.54456
972 HIP99825 Sun 4.55679

This is based on Mathematica's list of 552 exoplanets
orbiting 464 stars, and a total list of 88,637 stars.
If the naked eye visibility limit is magnitude 5.5, the Sun
would only be visible from 28 of these stars:

10 RigelKentaurusB Sun 0.476137
79 EpsilonEridani Sun 2.36646
208 HIP85523 Sun 3.11216
207 HIP113020 Sun 3.18865
247 HIP106440 Sun 3.29606
396 HIP15510 Sun 3.74083
423 HIP74995 Sun 3.81444
685 Fomalhaut Sun 4.25746
878 HIP64924 Sun 4.48202
949 HIP109388 Sun 4.54456
972 HIP99825 Sun 4.55679
1086 HIP57443 Sun 4.65677
1126 HIP21932 Sun 4.69871
1381 HIP57087 Sun 4.87838
1426 HIP83043 Sun 4.89689
1409 Pollux Sun 4.90049
1617 HIP10138 Sun 5.01833
1649 HIP57050 Sun 5.04143
1676 HIP3093 Sun 5.05658
1716 HIP48331 Sun 5.06528
1831 Gl317 Sun 5.13093
2104 HIP22627 Sun 5.24572
2264 Rho1Cancri Sun 5.31849
2263 HIP40693 Sun 5.32723
2397 HIP27887 Sun 5.36943
2355 HIP80337 Sun 5.37669
2382 GJ1214 Sun 5.3879
2689 UpsilonAndromedae Sun 5.47503

If the limit is magnitude 6.5, 33 more star systems can see the Sun:

2838 Alrai Sun 5.52682
2926 HIP53721 Sun 5.571
3399 HIP79431 Sun 5.69393
3637 MuArae Sun 5.74863
3679 HIP113357 Sun 5.76061
3783 TauBootis Sun 5.7949
3941 HIP98767 Sun 5.83457
4071 HIP85647 Sun 5.86725
4318 HIP71395 Sun 5.92513
4580 HIP6379 Sun 5.95739
4783 IotaHorologii Sun 6.01138
4835 HIP7978 Sun 6.02527
4867 RhoCoronaeBorealis Sun 6.03887
5016 HIP1292 Sun 6.0583
4949 NN3634 Sun 6.08757
4993 HIP55848 Sun 6.10352
5252 HIP49699 Sun 6.11214
5300 HIP83389 Sun 6.11214
5031 HIP65721 Sun 6.11803
5343 HIP79248 Sun 6.12236
5385 PiMensae Sun 6.12986
5453 EpsilonReticulii Sun 6.13303
6158 HIP98505 Sun 6.251
6351 HIP113421 Sun 6.30305
6436 Nu2CanisMajoris Sun 6.31593
6343 HIP99711 Sun 6.32197
6737 Hamal Sun 6.35637
6516 HIP64457 Sun 6.37975
6867 HIP58451 Sun 6.4205
7614 HIP25110 Sun 6.43775
7525 HIP109378 Sun 6.46941
7538 HIP54906 Sun 6.47034
7957 HIP96901 Sun 6.48193

OLD ANSWER FOR REFERENCE (note that Sirius does not have known exoplanets, so the Sirius solution I propose below wouldn't work):
As others have noted, since Sirius is 25 times more luminous than our Sun (though still not luminous as Canopus or Rigel), so it would be the brightest star for most nearby star systems, and all the exoplanets we've found are fairly closeby.
The only possible exception would be an exoplanet orbiting Sirius itself, since Sirius would be considered their sun, and not a star in the night sky.
Unfortunately, Sirius' smaller companion, Sirius B, would be much brighter than our Sun there. I'm also pretty sure Sirius B would be in the night sky (not just in the daytime sky), so it would count.
I'd like to poke around a bit more before declaring this answer complete. I think I can show that any point where the Sun is brighter than Sirius must be less than 4.3 light years (and probably much less) away from our solar system, so, unless we discover an star system MUCH closer than Proxima Centauri, there are no exoplanets where our Sun is the brightest star.
Comment: I just saw this, very nice! 3.5 years later I wonder if the results are any different...
Comment: It would be interesting to do this for all nearby stars, even those w/o exoplanets (or currently undiscovered exoplanets). I've put it on my project list at https://github.com/barrycarter/bcapps/tree/master/README-projects.txt which means I may someday get around to it, but probably not.
Answer: Another way of thinking about the question is, "how close do you need to be for a dim star (our Sun) to outshine a brighter one?"
Consider our Sun, and another star a distance $d$ away that is $m$ times brighter than the Sun (in terms of luminosity or absolute magnitude).  Let's look a location in space that is a distance $x$ from the Sun in the direction of the second star, and a distance $y$ in the perpendicular direction.

The amount of light seen at the location is proportional to the inverse square of the distance.  The relative amount of light from each star is therefore just:
$$
\frac{1}{x^2+y^2} \qquad\qquad \frac{m}{(d-x)^2+y^2}.
$$
We want to know when the first is greater than the second:
$$
\frac{1}{x^2+y^2} > \frac{m}{(d-x)^2+y^2} \\
(d-x)^2+y^2 > m x^2 + m y^2 \\
d^2 - 2dx > (m-1)x^2 + (m-1)y^2 \\
\left(1+\frac{1}{m-1}\right)d^2 > \left(\frac{1}{m-1}\right)d^2 + 2dx + (m-1)\left(x^2 + y^2\right) \\
\left(\frac{m-1+1}{m-1}\right)d^2 > (m-1)\left(\frac{d^2}{(m-1)^2} + 2x\frac{d}{m-1} + x^2 + y^2\right) \\
m\left(\frac{d}{m-1}\right)^2 > \left(\frac{d}{m-1} + x\right)^2 + y^2 \\
$$
This inequality describes a sphere of radius $r=d \sqrt{m}/(m-1)$, centered around the point $x=-d/(m-1),\ y=0$.

Let's take the specific case of Sirius, for which $m=25.4$ and $d=8.60~\text{ly}$.
Applying the above equations, we get $r=1.77~\text{ly}$ and $x=-0.35~\text{ly}$.  Therefore, even at half the distance of the next-closest star Sirius is brighter than the Sun.  This means that the Sun is the brightest star in the sky for exactly eight planets.
Comment: I like this. I was going to use the triangle inequality to show that if you are distance d1 from the Sun, and the Sun is distance d2 from Sirius, you are necessarily less than distance d1+d2 from Sirius, but your approach is better.
Answer: You can use Celestia to get a view of the sun in the night sky from other solar systems, just like this guy did, although the post is a little old.
Comment: This might be better as a comment than an answer (really cool link, though!).
Answer: Dependents. Unless blocked or outshone by a neighboring star Sirius A would continue to be the brightest star visible, Sirius A is bright due to its size and our atmosphere, not because of distance, if the planet had a different atmosphere that broke up wavelengths of light differently than earth other stars may show brighter.
Comment: I object to this answer. Sirius is only about 1.7 times as large as the Sun, weighs only twice as much, and is still bright outside our atmosphere. Sirius is bright because of a combination of its inherent luminosity (ie, brightness) AND its distance. I sort of understand your atmosphere argument (Sirius' peak light wavelength is different from the Sun's), but I think you need to flesh it out a bit.


Is there a proof that a map of the United States requires 4 colors?

Question: The Four color theorem states that no more than four colors are required for any map.  Can it be proved or disproved that 3 colors can be used for United States map?
Comment: Note that 4 colors may not suffice if there are exclaves. I don't know whether this is a problem for the US.
Comment: brute force, that's how the 4 color proof was construced :)
Comment: I think this is a question of geometry.
Comment: @Gilles: [There are](https://en.wikipedia.org/wiki/Kentucky_Bend), but AFAIK none that affect the adjacency graph of the states.
Answer: I started by assuming two adjacent states must be different colors. Therefore, I arbitrarily assigned blue to California and beige to Oregon.

Nevada must therefore be a third color: green.
Arizona must therefore be neither green nor blue: beige.
Utah must therefore neither be green nor beige: blue.

Idaho must therefore be neither beige, green, nor blue - which disproves the ability of the US map to be covered by three colors. Idaho, here highlighted in dark red, must be color number 4.
Comment: If you look at these states as a graph, these states minus Nevada form a cycle of odd length... which itself requires three colors. Add Nevada, which is adjacent to each, and you require a fourth.
Comment: @IQAndreas - The "orange" looks very beige to me.
Comment: I don't see any orange on that map (just a gray Oregon and Arizona); either you or I am colorblind.
Comment: +1. Short, sweet, and to the point.  Also, you included Utah. ;)
Answer: That four colors will suffice may be easily shown by the fact that four-color maps exist.  That three colors will not suffice may readily be shown by pointing out particular places where it is insufficient, but it may be more enlightening to point out a required condition for three-coloring: if a region is encircled by other regions, and at most two of them touch it at any point, then none of those regions may be the same color as the encircled reason, and they must have three different colors unless the number of such regions is either one (in which case one color would obviously suffice for it) or there are an even number (in which case two would suffice).  Many land-locked states other than Colorado, Utah, Arizona, and New Mexico (the only states to meet more than two neighbors at a single point) have an odd number of neighbors; thus, any region of the map containing such a state and its neighbors would require four colors.
Answer: 3 colors are not sufficient for a map of the US.
Take a look at this 4-color US map I found online.

Look at Oklahoma. It has a lot of edges and touches a lot of other states. If you only had 3 colors, there would be no way to color that section. Make Oklahoma color 1, and then start alternating colors for the surrounding states. Kansas is 2, Colorado is 3, New Mexico is 2, Texas is 3, Louisiana is 2, and here's where it breaks down: Arkansas is touching both Texas and Oklahoma. There's no way to color those so that they don't conflict with Oklahoma and Texas.  See this edited version of the map:

Arkansas can't be yellow, green, or pink. So you must have a fourth color.
Comment: Your example is flawed since Louisiana isn't touching Oklahoma. Couldn't then Louisiana be yellow, allowing Arkansas to be pink, and Missouri green?
Comment: It might also be clearer if you use use gray for all state colors that you aren't using in your example. Here is an SVG version of the map of USA on Wikipedia to make it easier: https://commons.wikimedia.org/wiki/File:Map_of_USA_four_colours.svg
Comment: Strictly speaking this coloring is invalid, because Illinois and Michigan share a common border (it's underwater in Lake Michigan) and therefore cannot both be dark blue.  But you can fix it by making Ohio dark blue and Michigan red.
Answer: Another demonstration:
The graph of the US contains a 4-clique: four states which are mutually adjacent.  That is, any two of these four states share a common border (of nonzero length), and therefore cannot receive the same color.  (Obviously one-point borders do not count, so I am not talking about Arizona / Utah / Colorado / New Mexico.)
The states are:

New York, Connecticut, Massachusetts, and Rhode Island.  The border between New York and Rhode Island is underwater, in Block Island Sound between Fishers Island and Napatree Point.

Note that

 this is a special case of supercat's answer, because Connecticut is "encircled" by New York, Massachusetts, and Rhode Island.  You cannot leave Connecticut without passing through one of those states (or its waters).  Thus Connecticut is in some sense "landlocked" despite having a sea coast!

(I tried posing this as a new puzzle, in Four mutually adjacent US states (not the Four Corners), but it was closed as "trivia".)
Comment: I think it's worth noting that although NY and RI share a border, they do not share a _visible edge_ and some mapmakers do assign them the same color. (In fact, even the four-coloring shown on Wikipedia does so.)
Answer: Super cat is the closed to "proofification" in my opinion, maybe lacking in clarity (in my opinion).
Though the other rather decent hand-wavy proofs.
As supercat points out it comes down to one region being landlocked and having an odd number of neighbors.
If we aim for a construction with 3 colors, we can choose colour A to be the central one.
And Color B to ANY adjacent one. Now as we only have 3 colours we are forced to choose a colour for the one clockwise of the B coloured one. This would be C. Which in turn has its clockwise neighbor forced.
This becomes proofy for odd numbers of neighbors as when we reach the spot counterclockwise of the original B colour, it has a minimum of 3 neighbors.

The first of the chain, B coloured.
the middle area, A coloured.
the second to last in the clockwise chain
   In the chain the pattern goes BCBCBC, where the 1st is B and the next is C
Where every odd numbered one must be B, and even numbered C
So the second to last in the chain is C as there are an odd number of neighbours
and it is the second to last so it is an even one.
So as the last in the chain is C, it has A, B, C neighbors. It cannot be A, B, or C: therefore it cannot be three coloured.

If all landlocked US states had an even number of neighbours you could 3 colour it. The reason I specify land locked is ocean adjacent states don't have a complete chain around them. Hope this answer adds some rigour and hopefully enlightenment to general 4 vs 3 Colouredness.
Comment: Your `` tag makes the formatting a mess.  Using such a tag around the list might be excusable (though there are better ways to do the list in Markdown) but it's inappropriate for general paragraph-formatted text.


Sobolev imbedding failure due to a kink in the domain

Question: I'm looking for  a simple example where an inequality of the form $||u||_{L^q} \leq C||u||_{W^{1,p}}$  fails for some  $1 \leq q \leq p^*$ (ie. within the acceptable range for which the bound should hold) on a bounded domain $\Omega$ which must necessarily have a cusp of some sort. I am interested in an example for $1 \leq p < n$ of course. I know how to find examples for the $p > n$ case.
Answer: Hi,
I don't know such an example, but the weaker condition i know is the following
The Weak Cone Condition:
Given $x\in \Omega$, let $R(x)$ consist of all points $y\in \Omega$ such that the line segment from $x$ to $y$ lies in $\Omega$. Let
$$\Gamma(x)=\{y \in R ( x )\hbox { s.t. } \vert y - x \vert < 1\}.$$
We say that $\Omega$ satisfies the weak cone condition if there exists $\delta > 0$ such that
$$ \vert (\Gamma(x))\vert \geq \delta \hbox{ for all } x\in \Omega .$$
You will find a proof in:
Adams, R. A.; Fournier, John
Cone conditions and properties of Sobolev spaces.
J. Math. Anal. Appl. 61 (1977), no. 3, 713--734.


What's the difference between code coverage and test coverage?

Question: At first I though it was the same but with eclemma it seems different. But I can't find anything about it.
Comment: I don't who downvoted this, but the question seems perfectly reasonable.  What a nice way to treat a newbie.  +1 to counteract.
Comment: Upvoted as I agreed with @Ira
Answer: Here is how I use the terms.  Code coverage is a measure of how much code is executed in response to a stimulus (e.g. running a test).  Test coverage is a measure of how much of the feature set was executed as a result of a test.
Others will have other definitions.  When someone uses those terms, if you are not sure what they mean, ask them.
Answer: Test coverage and code coverage as generic terms can mean a broad variety of different measures of what has been covered: lines of code, subconditions of boolean expressions,  accesses to data, calls to API functions, ...
In the common vernacular, and for almost all the tools you can get, "test coverage" and "code coverage" tell you what code executed by whatever testing process you use (whether that is unit test, functional test, informal test, interactive test, ...).
The only widely used variation is MC/DC (test/code) coverage, which tells you which of the boolean subconditions in a logical expression have been exercised in a way that controls the outcome of the boolean expression.  Only a few tools offer this.
I'm sure eclemma provides test/code coverage of the standard type.  Whether it provides anything else... I don't know.
Answer: Here is how I use these terms (although I almost never actually uses these terms).
Code coverage is a measure of how much code is executed during testing.
Test coverage is a measure of how many test cases have been executed during testing.
Your mileage may vary...
Answer: Code Coverage: As a human, we can make mistakes or miss some important issues which lead to errors and defects in a product. Testing thorough makes a product high quality. Performing Unit testing is a good start, but it is sometimes is difficult to measure or improve.
Code Coverage
To begin with, let's learn about code coverage. The main purpose of this metric is to calculate the number of lines covered by the test cases. It reports total number of lines in the code and number of lines executed by tests. Think of it as the degree to which the source code of a program is executed when a test suite runs. The intent is, the higher the code coverage, the lower the chance of having undetected software bugs.
Subtypes
Coverage is split into several subtypes –  condition coverage, branch coverage, loop coverage, function coverage, statement coverage, and parameter value coverage.
Let me define the subtypes for the sake of clarity.
·       If testing cover each function calls in code, function coverage is called to be 100%.
·       Similarly, if all branches in the code, i.e. all if-else conditions have been tested with every possible input, then branch coverage is said to be 100%.
·       If all loop statements in the code are executed then loop coverage and statement coverage would be 100% respectively.
·       In an ideal case, for condition coverage to be 100% every single condition with all feasible combination of condition parameters are perfectly tested. One can check the Parameter value coverage by passing all common values to the criteria in the function call.
Coverage testing tools
These testing tools are obtainable today for each major languages. Note, that mostly are relevant only for unit test and perhaps not for the complete tests performed ( system,  integration, Unit, manual and more).
Now have a look at few of them to understand the code coverage tools scenario.
Cobertura is a Java code coverage reporting tool. It is based on coverage and works on any platform with Java 5 or higher. You can use Cobertura with ant, maven or command-line access. While instrumenting classes, Cobertura generates Cobertura.ser file containing basic information about each class. This file is utilized when instrumenting, running, and creating reports. It also uses ASM when instrumenting. On running testing, it creates a report comprising each package, all class within every package & corresponding branch coverage,  line coverage, and complexity.
For Python, a well-admired tool for code coverage measurement is Coverage.py. It functions in 3 different phases –
·       Execution, where it runs the code and monitors it to see what lines were executed.
·       Analysis, where it examines the code to determine what lines could have run.
·       Reporting is where it combines the results of execution and analysis to produce a coverage number and an indication of missing execution.
This measurement tool extensively used for Go is gocov. This kind of tool provides 4 key commands – test, convert, report & annotate. Making use of these commands, you can generate textual reports with annotations giving coverage information of each function in each go file. A GUI wrapper is also accessible for gocov called as GoCovGUI. It displays the entire report generated by the tool in GUI which is easy to understand. It also has wrappers to generate reports in HTML and XML format.
Test Coverage
Test Coverage aims to measure the effectiveness of testing in a qualitative manner. It evaluates either the test cases are covering whole functional needs. You can believe it as a type of black-box testing when test cases are not written contrary to code but based on user requirements or expected functionality.

Subtypes
The common structure and means used for test coverage measurement are unit testing, functional testing, performance testing, integration or system testing and acceptance testing.
Unit tests are written at a granular level to check if a function/method performs as expected. In functional testing, each functionality mentioned in the requirement document is tested. Performance testing is normally a method to stress test the code for its stability, scalability, and responsiveness at various workloads. Integration testing or system testing is done to test if the completely integrated product works in an expected manner. Acceptance testing is generally done at the end of the development cycle. For acceptance testing, the product is handed over to the stakeholders and tested by them to determine whether the product is in an acceptable state.
Tools
Such test coverage tools aim to measure the test effort in a qualitative way. The idea here is to see if all requirements and functionalities are logically covered via testing. Yet, it is not easy and straightforward to calculate as compared to code coverage. Methodologies such as Test-Driven Development (TDD) are also useful for analyzing test coverage and bring in the discipline for adding testing from the get-go. To measure the impact of such tests, you will need to manually list out requirements and then analyze test case to understand which of those are covered.
Still, you need frameworks to write tests.
Let's see some testing frameworks available for various programming languages.
·       JUnit, the popular Java testing framework serves as a foundation for launching tests on the Java Virtual Machine. With support for assumptions, assertions, default test techniques, and other mechanisms for testing functionality JUnit is a better option to test Java-based software.
·       For Python, a framework called PyUnit is available. As the name indicates it is the JUnit equivalent for Python. However, there are various other test frameworks accessible to assist you as well.
Go also offers a built-in test package for programs allowing you effortlessly write, plan, organize and run testing. This also offers several profiling tools to understand behavior of the software under different loads.
Answer: As the above responses the definition varies. I sometimes say code coverage does not matter to me but test coverage does.
By test coverage I mean in this context that any possible behaviour of a class should be documented by tests (ie. if you look at the tests you should be able to make a safe assumption of the outputs and behaviour of any method of that class, provided any given set of inputs. Which also includes assumptions of invalid inputs.
Lines of code that do not impact behaviour are obviously undesirable, but if they exist that is usually less relevant. For me typical examples of such lines are small best practice approaches that are actually rarely used, so I might not test if I catch an exception if a file is written and I check if it exists before trying to write it. Having that sort of check often is better than not writing or testing this kind of code.
Answer: My 2 cents:
Code Coverage means the ratio of non-test code run by automated tests. Every line of code or instruction that was somehow evaluated and run counts towards this.
Test Coverage means the ratio of logically tested behaviour. "Behaviour" in this case means everything a method is supposed to do according to its description: validate and react to wrong inputs, return the expected result for all correct inputs.
Consider a method add(a, b) which is supposed to add up two numbers and return the sum. Now consider a test that calls the method with two positive numbers, but only looks for errors and does not check the logical outcome. This would probably mean 100% code coverage (whole method was run) but much less test coverage, since the method was tested only against one misbehaviour: erroring out on correct input. Neither the result was tested with different inputs, nor were wrong/unexpected inputs tested.
Answer: Test Coverage is Code Coverage but measured from the perspective of running your tests.
You should aim for 100% test coverage. ;)
There is a 10 minute video here demonstrating the differences using python.
I recommend watching it in double speed so it's only 5 minutes.
https://youtu.be/7BJ_BKeeJyM
Answer: Test coverage and Code coverage metrics are both measurements that can be helpful for assessing the quality of your application code.
Difference between code coverage and test coverage
CODE COVERAGE
•   Code coverage is a measure of how much code is executed during tests &
•   Subtypes- Coverage is split into several subtypes – loop coverage, branch coverage, condition coverage, statement coverage, function coverage, and parameter value coverage.
•   Tools- Cobertura is a Java code coverage reporting tool. It is based on jcoverage and works on any platform with Java 5 or higher. You can make use of Cobertura with maven, ant, or command line access. While instrumenting classes, Cobertura generates cobertura.ser file comrising essential information about each class. This file is used when instrumenting, running, and creating reports.
For Python, the major and most popular tool for code coverage measurement is Coverage.py. It works in three distinct phases –
•   Execution, where it runs the code and checks it to see what lines were executed.
•   Analysis, where it examines the code to determine what lines could have run.
•   Reporting is where it combines the results of execution and analysis to produce a coverage number and an indication of missing execution.

TEST COVERAGE
•   Test coverage is a measure of how many test cases have been executed during tests
•   Subtypes- The common mechanisms used for test coverage measurement are performance testing, functional testing, unit testing, integration or acceptance testing and system testing.
•   Tools- JUnit, the well called as Java testing framework serves as a foundation to launch tests on the Java Virtual Machine. With support for assertions, assumptions, default test methods, and other mechanisms to test functionality JUnit is a very good choice for testing Java-based software.
For Python, a framework called PyUnit is available.
As the name indicates it is the JUnit equivalent for Python. But there are several other testing frameworks available to help you as well.


Who's the oldest?

Question: Albert, Brian and Charles are brothers with different ages.
Albert has twice the age Brian will have when Charles has twice the age Albert has now.
Who's the oldest?
Comment: The brothers are all alive? I.e. some aren't waiting to be born?
Comment: I leave it up to you.
Comment: Isn't it important to mention that "when Charles has twice the age Albert has now." will happen in the future and not in the past ?
Answer: They have A,B,C initially.
P1: Charles will have twice the age Albert has now:

It will be the year Charles will be 2A. Year difference  is 2A-C

P2: Brian will have P1:

Add 2A-C years to Brian's initial age and his age will be 2A+B-C

P3: Albert has twice the age P2

Multiply Brian's age with 2. and Albert's initial age  A = 4A+2B-2C  which means C = (3A+2B)/2 thus Charles is the eldest.
Comment: Beat me to it by 20 seconds! Have an upvote.
Answer: There are 2 points in time:

First, they are $a$, $b$, and $c$ years old
After $n>0$ years, they are $a+n$, $b+n$, and $c+n$ years old

The equations are:

$$a=2(b+n)$$
$$c+n=2a$$

From equation 1 we get $a>b$ because $n>0$.
Equation 2:
$$c+n=a+a$$
Replace first $a$:
$$c+n=2(b+n) +a$$
$$c=2b +a+n$$
We get $c>a$.
Solution:
$$c>a>b$$
Answer: I'll try a different approach which I think is also correct.
Assuming the answer is consistent with every possible age of A, B and C one may take the option in which the "time when Charles will have twice the age Albert has now" is actually now. In that case C is twice the age of A and A is twice the age of B making C the oldest. So for example C = 4, A = 2, B = 1. This does satisfy the condition.
Answer: At every point in time (since the birth of the youngest), the order is the same. What was true will be true.
Thus, instantly: $A>B$, $C>A$.
$C$ is the oldest.
Answer: The other answers have derived the equation
$$c=\frac{3a+2b}{2}$$
Clearly, if $a$ and $b$ are positive, then it is obvious that $c$ is the greatest.
But what if Albert and/or Brian are waiting to be born still?
Let us say that Albert will be born in 2 years, or $a=-2$ and that Brian will be born in 4 years, or $b=-4$. We can then conclude that $$c = \frac{3*(-2) + 2*(-4)}{2} = \frac{-6 + -8}{2} = -7$$. Thus we can say that Albert is the oldest in this scenario. We could just as easily concoct a scenario where Brian is older than Albert and the math shows that, as long as they aren't born yet, we'll be fine.
So if we accept that some of these souls are still waiting to be born, then we can not conclusively say whether or not any of them are the oldest with the information given.
Answer: A=2*(B+(2A-C)
A=2B+4A-2C
A=(2*(C-B))/3
A=C*2/3-B*2/3
Then: C>B (because A>0)
& A<C
Finally: C>B and C>A

Who's the oldest?


How old is Chewbacca?

Question: How old is Chewbacca, anyway? Do Wookiees get gray fur when they are old?
Comment: HHHRRRRAAAAAAGGHHH HHHRRRRAAAAAAGGHHH years old.
Answer: Chewbacca was born 200 BBY (two hundred years before the battle of Yavin)

 and would die 25 ABY (after the battle of Yavin) at the opening Yuuzhan Vong War; at least this was the expected death in the now non-canon Star Wars works. With the opening of episode VII, we learn it is Han that dies, not Chewbacca.

Wookiees in their prime tend to resemble the wooded areas they live in (shades of brown, tan or reddish brown), but are known to change colors as they age. There are recessive genes allowing for albino Wookiees, but those are very rare. Very old Wookiees would lose coloration becoming grey or even white hair in their very old age. Wookiees can live to be upwards of 400 years of age.
Comment: The spoilered part may well be superseded by info in the sequel trilogy, of course, which I'd expect would be set around that time.
Comment: I suspect you may be right, but 25 years is a long time for adventures to take place in before the end...
Answer: According to Disney canon, he was 180 when we see him in Revenge of the Sith:

He was a Wookiee, after all, and he knew passion. His were a proud people, a people who had lived for hundreds of years peacefully on their wooded homeworld of Kashyyyk until the Clone Wars. He had been younger then, just one hundred and eighty, and he had fought the Separatist battle droids. He had witnessed the betrayal of the clones and the beginning of the Empire. He had seen his people, his brothers and sisters, his family, put in chains and sold as slaves throughout the galaxy. He had been put in chains himself, and just the memory of it made a growl rise in his throat.
  -  Star Wars:  Journey to The Force Awakens:  Smuggler's Run - A Han Solo & Chewbacca Adventure

The Battle of Kashyyyk occurs in the year 19 BBY.  The films in the original trilogy are each separated by a period of a year.  The Force Awakens takes place in 33 ABY (30 years after the Battle of Endor).
Thus:

Episode IV:  A New Hope:  Chewbacca is 199 years old.
Episode V:  Empire Strikes Back:  Chewbacca is 200.
Episode VI:  Return of the Jedi:  Chewbacca is 201.
Episode VII:  The Force Awakens:  Chewbacca is 231.

Therefore, assuming that Disney canon maintains the earlier tradition of Wookiees living ~400 years on average, Chewbacca is literally "middle-aged" in the original trilogy.
Answer: According to new information in Solo: A Star Wars Story, Chewbacca was 190 during the events of that film.  As the film takes place in 10 BBY, Chewbacca is 200 years old at the time of the Battle of Yavin.  Empire takes place three years after ANH, Jedi takes place 4 ABY, and the new sequel trilogy takes place in 34 ABY
Chewbacca's age at various points in the series

Episode III: Revenge of the Sith: 181 (RotS takes place nine years before Solo)
Solo: A Star Wars Story: 190.
Episode IV: A New Hope: 200.
Episode V: The Empire Strikes Back: 203
Episode VI: Return of the Jedi: 204
Episode VII: The Force Awakens/Episode VIII: The Last Jedi: 234

How old is Chewbacca?


Would my VM (winxp) perform better if the disk images were stored on a 5.4k drive over SATA, or an external 7.2k SATA drive over USB2?

Question: My laptop has a 5.4k drive - plus i have an external 7.2k drive.  Where to put the vm... hmmm?
Has anyone faced this dilemma?
If not I'll post my results.
Ash
Answer: I'd go with the external drive. Not because it's 7.2k vs. 5.4k, but because it's a different drive than your operating system drive (that is assuming your laptop only has one hard drive, which is the 5.4k in question).
Answer: Almost certainly it'd perform better using the SATA drive. USB has quite a slower latency - 100 microseconds compared to 0.5 for PCI.
The disk speed won't matter so much so if you're reading and writing large files, you're not interested in seek times for small files, the burst time taken to fill an read from the buffers will be more important than the speed of the drive.
Now, if you had an attached 15k SAS RAID array, that's be another story. I'm not sure you'll notice too much of a difference whichever you choose.
Answer: A colleague who is a technical sales person, found on his Dell laptop that getting an SSD as a disk to host VM's for demos, using the CD/DVD drive bay with an adapter (So I assume it is PATA at least, if not SATA, rather than USB, or maybe it is USB?  Don't really know) was a huge performance booster.
The nice thing is that if you get a second drive, a USB enclosure is about $10.  So the experiment is pretty cheap, and if it fails, you can always swap the new drive for you current internal to boost performance overall, and still have a spare USB drive.
I foolishly swapped my internal 100GB 7200 rpm SATA drive for a 300GB 5400 rpm SATA drive and I am currently deeply regretting it.  Performance is very noticeably slower.  If I did not absolutely require the extra space, I would move back to the 7200 drive in a moment!
Answer: Personally I'd go with the 5400 option only for the fact that when using a laptop I do not want to have to plug stuff into it (extra drive = extra weight, usb = more power draw on battery too).
You could swap the 5400 and 7200 drives around as another option.
Answer: If you won't have I/O intensive processes in host system fighting with VM, I recommend going with internal drive (unless external is for convenience/space). USB2 simply can't deliver.

If you want speed, I'd recommend avoiding USB2 - it's slow, sometimes very. If you want to really exploit usage of external hard drive, I recommend getting an eSATA card (or FireWire, especially 800MBit, but it's rare to find SATA bridge for it).
USB is a polled interface and doesn't really support anything like DMA, so I can guarantee that you'll never see those promised 480MBit speeds :)
Long time ago, testing the same, old drive in a dual USB2/FireWire enclosure (a 5400rpm UltraATA133 drive, nothing fancy), I recorded sustained speeds of >30MB/s on FireWire, with USB2 baseline being somewhere around 10~15MB/s (initial speed ~30MB/s, then fast drop).

Lately, similar experience except with modern drive, modern USB2->SATA2 controller vs. eSATA card - do I need to say more? At one point I was sending data from USB2-connected drive, internal drive and DVD and I was still far from maxing out bandwidth - and the target drive was far from "fast" one.


installing package kernel-2.6.36-2.x86_64 needs 52MB on the / filesystem

Question: I am receiving the error:
installing package kernel-2.6.36-2.x86_64 needs 52MB on the / filesystem
how can I safely expand the "/" partition?
Thanks
Comment: More information needed, please. What distribution? Are you using LVM? Do you have other storage available? What all is on / already? (Any other separate partitions?)
Answer: If you're using LVM and you have available free space in your volume group:
<code># lvextend -L +500M /dev/vg0/root
# resize2fs /dev/vg0/root
</code>
(This assumes you're root filesystem is on a LV named root on a VG named vg0.)
If you're not using LVM, you'll need to use a partition editor like parted (http://www.gnu.org/software/parted/manual/parted.html) to resize partitions on your disk to create the necessary space.  When you're finished, use resize2fs to grow the filesystem.  Note that this process, if you're not careful, can result in data loss.
You could also remove some things from your root filesystem.  If /var is on the same filesystem, there may be files in, e.g., /var/cache that can simply be removed (apt and yum, for example, both store packages in subdirectories of /var/cache before installing them).
Answer: Are you sure you can't clear up 52MB on the / partition?  Perhaps removing old kernels ("rpm -qa | grep '^kernel'" for a list of them), perhaps there is space that can be cleared out of /var/tmp, /var/cache, or /tmp?  Perhaps run "du -x / | sort -rn | less" will show you some files or directories that can be cleared out?
Perhaps there's something that you can archive to another system, install the kernel, remove the old kernel and then recover?
Answer: Without knowing what your current configuration is, it's impossible to give a sensible answer. Sean's answer is a good solution - assuming that you've got stuff on / you don't need. But if your whole disk really is full, then you've not got a lot of choices other than adding more storage.
In addition to knowing if you are using LVM, what partitions you've got set up currently and what the usage of these is, we'd need to know what filesystems you've got set up. It may be possible to boot up from a CD/USB and reorganise your partitions using gparted.
OTOH, it may be as simple as dropping down to single user mode and mapping in a spare partition, e.g.
<code>mkfs -t ext4 /dev/sdb5
mkdir /newvar
mount /dev/sdb5 /newvar
mv /var/* /newvar/
umount /newvar
rmdir /newvar
echo '/dev/sdb5   /var  ext4  defaults  1 1' >>/etc/fstab
mount /var
</code>


CiviContribute: customize "find contributions" default view

Question: I'm using CiviCRM 4.7.27 with Wordpress and am trying to figure out how to customize the default results table that is shown when "find contributions" is run. Normally, the search shows a table with the columns: name, amount, type, etc. I would like to customize which columns are shown for the search result but cannot for the life of me figure out how to do this.
I tried to create a profile with the columns I want to view and enabled "Used for: search views". However, when I tried to add a Contributions field to the profile, I got the error "Contribution cannot be used as a result column for profile searches."
Also, supposing I was able to create the profile with the fields that I want, it is not clear how to use it for the search view, since the "find contributions" page does not seem to allow a view to be chosen. Also, the "advanced search" page does not show the profile I created in the "Display Results As Views For Display Contacts" dropdown menu.
Any help would be much appreciated! BTW, this was the reference page I consulted to try to get this feature to work: https://wiki.civicrm.org/confluence/display/CRMDOC/Format+Advanced+Search+Result+Columns
Answer: Through UI there is no such settings to alter the columns of Components Search results such as Contribution, Membership etc. You can achieve this by using Search Column hook.
HTH
Pradeep


User with Mandatory Profile can log in to Windows 7 but not to Windows XP

Question: I have a Windows Server 2008 domain with both WinXP and Win7 PCs. Users are usually fine to log in to either OS, but there is one user who can't login on XP. It fails to create his profile. I believe they are mandatory profiles. How can I allow this user to log in to either Windows 7 or Windows XP?
Answer: Your question doesn't make a whole lot of sense in its current form. From what I can ascertain, you have roaming profiles or mandatory profiles configured and a profile that works on XP doesn't work on Windows 7.
This is because Windows 7 (and Vista and Windows 8 as well) use a new profile structure. You cannot use XP-era profiles with Vista, 7, or 8 clients.
Comment: Absolutely this - the only way is to have a split estate handled with Group Policy or whatever.
Comment: So I need to check the GPO what do I need to check exactly?
Comment: That depends entirely on how you have this set up.
Answer: There is a fair amount of info on this topic on Technet and in the Technet forums. I am not going to replicate it, but here is a forum question with a ton of good info.
What I will say is that you should use this as an excuse, if possible, to eliminate roaming and mandatory profiles.  Use folder redirection instead. With XP clients it requires SP2 or SP3 and the GP Client-side Extensions on each workstation.


Why are there so many stream ciphers out there and even ongoing research?

Question: What make them better than OTP using a CSPRNG initialized
with a secret key?
Comment: How is a CSPRNG different from a stream cipher?
Comment: Many stream ciphers work by transforming a short key (and optionally a nonce) into a long key-stream that's xor-ed into the plaintext to produce the ciphertext, which is exactly the construction you're proposing. Wikipedia calls these [Synchronous stream ciphers](https://en.wikipedia.org/wiki/Stream_cipher#Synchronous_stream_ciphers).
Comment: A CSPRNG transform a key into a stream. A stream cipher transform a clear text stream into a cipher text stream.
Comment: And a stream cipher?
Comment: The API of a DRBG may be different in the sense that it may have methods to add seed information to the state. The stream produced *may* also have additional properties. That's however not of any consequence to the question posed.
Answer: Many stream ciphers work by transforming a short key (and optionally a nonce) into a long key-stream that's xor-ed into the plaintext to produce the ciphertext, which is exactly the construction you're proposing. Wikipedia calls these Synchronous stream ciphers.
Most popular stream ciphers fall into this category, including block ciphers operated in CTR or OFB mode, the venerable RC4 and e-stream finalists like Salsa20 or SOSEMANUK.
So a lot of research into stream ciphers doubles as research into CSPRNGs.
Some stream ciphers don't use this construction. For example:

CFB mode mixes the ciphertext into the cipher. This has the advantage that it "only" leaks the shared prefix and that it can re-synchronize after losing some data.
In practice these advantages are rarely relevant, since you should use a nonce and MAC or a properly misuse resistant cipher. CFB mode is much less popular than CTR mode.
Helix/Phelix or the sponge based NORX also mix the message into the state of the cipher. The goal of these constructions is producing a cheap MAC, reusing the work the cipher has to do to produce the key-stream.
Answer: Using a CSPRNG to generate a pad is a stream cipher. However, that does not mean your question is without merit: if we could kill two birds with one stone by just designing CSPRNGs, that seems like a good idea. So why design dedicated stream ciphers?
One reason is performance. The performance we require from encryption is greater than what most uses require from a CSPRNG. That alone is not a very convincing reason, however, as we would prefer CSPRNGs to be fast as well.
The main reason, as I see it, is the differing requirements:

With a CSPRNG it is considered a useful property that the current state cannot be used to derive any earlier states. That means the CSPRNG must be run sequentially, so using it for encryption is also sequential. Parallelization would require multiple CSPRNGs running in parallel, meaning multiple seeds, more state, more complexity.
With stream ciphers the only requirements are that the output is indistinguishable from random and cannot be used to reveal the key. This allows constructions that are very easily parallelizable and potentially faster even when run sequentially.

Additionally, the other stream cipher constructions that CodesInChaos mentions differ from the random pad model, and have advantages like being able to reuse it for a MAC or some other cryptographic purpose that a CSPRNG might not be able to fulfill.


If I use my custom domain with my Blogger account will this help in SEO of that blog?

Question: Also I want to know that if my custom domain is nothing but one of the keywords and my blog is also about that keyword, so will this help in improving google ranks of my blog after I change from example.blogspot.com to customdomain.com.
Answer: In the long term, your own domain will help.  Having your own domain gives you a lot of power to build a "brand".   Google likes to rank sites that have a brand that people talk about, link to frequently, and generally think highly of.
When your blog is just starting out, your own domain name won't make much of a difference.  In fact, I've seen some evidence to suggest that blogger blogs that use a blogger sub-domain sometimes get ranked higher than they should because they inherit some branding from blogger itself.
I wouldn't worry about this question from an SEO standpoint.  Instead, I'd say that the best reason to get a domain name is the flexibility to move away from blogger if you wanted to.  If you ever wanted to host your own blog or move to a different platform such as WordPress, then having your own domain name makes such a move possible.   At that point you could import the data from blogger and change the domain name to point to a new host.


Is it possible to pay part of a Bitcoin to someone?

Question: Bitcoins are over $800, I need to pay someone about $200. Is it possible to pay someone with a partial bitcoin?
Comment: Related: [What is a 'Satoshi'?](http://bitcoin.stackexchange.com/q/114/5406)
Answer: Yes! To send $200 at a Bitcoin price of $800/BTC, you'd send 0.25 BTC. Bitcoins are highly divisible, up to eight decimals behind the point. The smallest subunit of a bitcoin is currently still less than 1/1000 of a cent.
Many Bitcoin clients will also keep track of the current value of Bitcoin and allow you to enter the amount of a payment either as bitcoins or your preferred national currency.
For example, when I want to send someone $5 from my phone, I could either enter BTC 0.00625, or $5 to set the amount.
As Bitcoin has become so valuable that one bitcoin is worth much more than many things we want to pay for, some people have moved to denominating prices in mBTC, i.e. millibitcoin, which are 1/1000 of a bitcoin.
Comment: Judging by what you have written, I also assume I can buy just .25BTC to send it as a payment without buying the whole coin? If I am right, do you know a place I can buy this small of an amount? it seems like every place I have seen is only selling whole coins, unless I just don't understand their sites.
Comment: Yes, you can definitely buy parts of 'coins! In fact, I've seen sales of a single satoshi on MtGox. The convenience of different exchanges and markets strongly depends on the country that you are located in, but if you are in Europe Bitstamp might be convenient for you, otherwise check out [How do you obtain bitcoins?](http://bitcoin.stackexchange.com/q/91/5406).
Answer: With the current version of the Bitcoin protocol, bitcoins are divisible into 100,000,000 units (0.00000001 bitcoin). This very small amount is called a Satoshi after the creator of Bitcoin.
A Bitcoin transaction may be any amount that is a multiple of 1 Satoshi.


Accidentrally spent from unconfirmed transaction

Question: I accidentally spent btc from an unconfirmed transaction.
Is it likely to confirm at a later date or is it just kinda stuck?
Ive tried searching for answers but I'm seeing conflicting information relating to this.
Comment: I wonder if your tx has been accepted at all - did you get a tx ID? Something that we could look up? If so, when the unconfirmed tx gets confirmed, and your tx is in the mempool, it will also go through. But I'd like to know if there is an tx ID...
Answer: There is nothing wrong with spending unconfirmed outputs.  Bitcoin core will happily spend its own unconfirmed outputs, though it does prefer not to if it has a choice.
Your transaction can't confirm until its parent does, but otherwise it's treated like any other transaction.
If the parent paid a low feerate and will take a while to confirm then you could be waiting a bit, unless your feerate was high enough to make up for it.
If the unconfirmed parent was created by someone else and they successfully double-spend it, then your child transaction will be invalidated. Otherwise, assuming that doesn't happen and the feerates are sensible it'll confirm fine.
Answer: If the transaction still have not been confirmed you can spend your BTC again and maybe send them to an address of your own with an higher fee for making it more likely to be confirmed first
Comment: Your answer sounds a lot like "send it again", which if followed can result in funds loss.


Restricting Enterprise Keyword Suggestions to a Term Set

Question: Does anyone know of a way to lock down a list's built in Enterprise Keyword field to a specific Term Set? I've found on similar solution, but that solution only created a new Site Column that allowed a mult-select Taxonomy field and allowed users to add to the Taxonomy. On the other hand, I'm looking for a way to assist users in selecting keywords while still allowing them to tag enterprise keywords that will not be added to my Managed Metadata. In trying to come up with a proof of concept, I think I created a pretty good example:
public class Feature1EventReceiver : SPFeatureReceiver
{
    private Guid _termSetID = new Guid("4ec3eb26-fb69-49d6-9143-dc41f976443f");
    private Guid _gamesListID = new Guid("d7e1ce12-9523-47df-8ed3-5c4af9e2ee88");
    private Guid _fieldListID = new Guid("23f27201-bee3-471e-b2e7-b64fd8b7ca38");

    public override void FeatureActivated(SPFeatureReceiverProperties properties)
    {
        try
        {
            using(var site = (SPSite)properties.Feature.Parent)
            {
                TaxonomySession session = new TaxonomySession(site);
                TermStore termStore = session.TermStores["Managed Metadata Service"];
                Group group = termStore.Groups["Video Games"];
                TermSet termSet = group.TermSets["Xbox"];

                using(var web = site.RootWeb)
                {
                    SPList list = web.Lists[_gamesListID];
                    TaxonomyField field = (TaxonomyField)list.Fields[_fieldListID];
                    field.TermSetId = _termSetID;
                    //field.TermSetId = termSet.Id;
                    //field.IsKeyword = false;
                    field.CreateValuesInEditForm = true;
                    field.Title = "Xbox Enterprise Keywords";
                    field.Update();
                    list.Update();
                }
            }
        }
        catch (Exception)
        {
            throw;
        }
    }

}

In this case, I could create a list item Halo 4. I may want to mark it Halo and Microsoft Game Studios from my Xbox term set that lives in my Video Games term store. I also would want to create an enterprise keyword for Sequel or 4, but not add those to my Xbox term set, or my Video Games term store at all. However with the way Sharepoint 2010 OOTB works, it's all or nothing. If I type in 'Mar' into my Enterprise Keywords field, I will get an auto suggestion for Mario from my Nintendo term set, which obviously isn't the desired result.
The odd thing is I can run the code no error, but the change doesn't persist.
Answer: the enterprise keywords field cannot be limited to one term set. This can only be done if you have multiple term stores to seperate them. What you need to do is create a new taxonomy field for your list/site collection and set the desired term set to this field like so:
field.SspId = termStore.Id;
field.TermSetId = termSet.Id;
field.PushChangesToLists = true;
field.Update();

Hope this helps you in any way...


Do tennis players go off court for a break before the next set after an even number of games?

Question: Do tennis players go off court for a break before the next set when a set concludes after an even number of games?
Answer: The USTA rule for Changeovers have the following:

90 sec changeover break between odd games
120 sec changeover break between sets (regardless if the set ended even)
A bathroom break can be taken at anytime but it is preferred it during a changeover and the duration is reasonable

For ATP the Rule book has the following for a toilet break (90/120sec rules also apply as above):

VII. THE COMPETITION
O. Toilet Break
1) A player may be permitted to leave the court for a toilet break. A player is entitled
  to one (1) toilet break during a best of three set match and two (2) toilet breaks
  during a best of five set match. Toilet breaks should be taken on a set break and
  can be used for no other purpose

It does come down to the specific organisation running the game but generally the rules are consistent.
Injury is more detailed and depends on its severity, but I would not call that so much as a 'break'
Answer: Leave the court for a break is not expected during tennis matches even if the previous set was very long.
It can happened that a very long match is interrupped by the umpire because of the hours (see Isner-Mahut match details)
Different from what are you asking is the break ask by the tennis player because of a little injury (eg blisters) or to go to the toilet
Answer: Going off court is one thing, having a changeover is another. You can have a changeover even if there's an even number of games. It would be kind of strange not to give players a rest after playing a full set.
Of course, the rules can differ from tournament to tournament and from organizer to organizer. But the standard thing is for the players to have a changeover break at the end of a set, no matter what.
But one thing is for sure: when you do end on an even number at the end of a set, you don't switch sides after you've had a break. That's one thing that will always remain the same no matter in what tournament your playing in.


Quality of Service based on Layer 7 traffic

Question: How can one perform quality of service based on layer 7 traffic? How would you classify the traffic and actively monitor and respond (dynamically prioritizing traffic)? Are there any solutions which provide a kind of weather map?
Comment: you should specify if you want to use new (any) equipment or the OS/Hardware
Answer: I think this depends heavily on the platform on which you want to accomplish this. For example, IOS uses NBAR to classify transit traffic, primarily for QoS and security mechanisms. But as far as I know, NBAR QoS configurations are entirely static.
For centralized monitoring, NetFlow is probably your best bet.
Answer: There are various tools dependant on platform. For example:

Cisco - NBAR
SonicWALL - AppFlow
Juniper - No specific option in JunOS, though can roughly be achieved using class maps.

For monitoring of traffic Netflow & NFSEN is your friend. The bundle simplifies deployment of the NFDUMP capture, dump and analysis tools and gives you a nice frontend to view it all in and make graphs for management.
Answer: You need a proper application aware appliance. Exinda, riverbed, etc.
Cisco and Juniper et al (yes I include WAAS) is a crowbar solution. NBAR is nowhere as accurate esp. with the trickier protcols that use random/dynamic ports. For enterprise use NBAR is fine as you can control the environment but when dealing with the internet you are going to be dealing with a lot of clever tricky protocols and varied situations.
For example the app aware stuff can be tied into dynamic white/blacklists and offer far more granular behaviour e.g. for http, allow burst for first 100M, if the rate is above X (set it above HD youtube lol) then start rate limiting after the first 100M if priority traffic is getting contended. This kind of behaviour gives your users excellent experience and appears transparent to them whilst hitting people downloading large files via http/https like filelockers for example. And critically they deal with a lot more protocols, try getting nbar to spot chinese p2p video streaming like pplive or pps for example.
For basic enterprise use yes you'd rely on nbar/static port definitions then use qos classifications to queue appropriately. Works fine in that scenario.
Answer: If you run linux you could try l7-filter, which is a iptables/netfilter-module. You can then use the usual iptables-magic to do some QOS.
Weathermaps could be created with collectd (writing to RRDs) and then reading from these with http://www.network-weathermap.com or http://weathermap4rrd.tropicalex.net/
I have no tool ready that allows monitoring and dynamic prioritisation — you might have to invest in some soft of tailored linux-distribution or a hardware-firewall of some sort.
Answer: NBAR is the Cisco feature that is capable of classifying traffic at layer-7.
This feature allows the use of the 'match protocol ...' command within your class-map so that you can then take action, such as marking the DSCP value or policing, the matching traffic.
NBAR uses something called a PDLM (Protocol Description Language Module) which is basically the logic for determining is traffic is a match.  For custom applications you need to write your own PDLM.  I have never done this so I cannot comment on how easy or hard this is.  I have personally found the IP addresses and/or ports have worked well for classifying my traffic into my supported traffic categories.
As far as monitoring goes I would agree with Jeremy that NetFlow is the best feature to use.  There are various free and paid tools that can collect and report this data (the router pushes this data to your management station).  Cacti (free) may have support for the "Weather Map" report that you are looking for.
Also for monitoring you may want to look into a reporting tool that uses SNMP to gather the usage and drops from your traffic classes.  It would be advisable that you configure your device with 'snmp mib persist cbqos' if you go that route (this keeps your ifIndex values static across reboots).  Again there are many tool options and Cacti is a good place to start.
Answer: This is way too broad, but here is an effort to answer what I think you are asking.  What follows is more information concerning Jeremy's answer above.
I assume you are asking about prioritizing traffic based on specific aspects of the application layer control protocols (btw, I use TCP/IP terminology rather than OSI ones when discussing TCP/IP because IMO the OSI model does not map to TCP/IP as well as one might think --- for example try to understand how H.323 fits on the model, both as originally designed and when over TCP/IP).
As a simple example, maybe you want to prioritize TFTP requests for PXE booting over other TFTP requests, or perhaps you want to prioritize H.323 signalling of some types over others.
To do this you need either routers or the like which can understand the protocols you wish to shape traffic based on.  These routers then need to be able to inspect the packets deeply at least when required, and then shape the traffic based on what they find.  Needless to say different application protocols will have different requirements and possibilities.
For this reason, it depends on the platform, the protocol, and what you want to accomplish.  As others have noted various vendors have toolkits for this, but to really answer what is involved, we need a lot more information about what traffic you have, what problem you are solving, and what tools you have available to you already.
Answer: If you have a Cisco device use a combination of NBAR and QoS.
NBAR will help classify traffic based on your custom requirements. You can create custom NBAR PDLMs for the protocol/application you need to track. The command is:
ip nbar custom name [offset [format value]] [variable field-name field-length] [source | destination] [tcp | udp ] [range start end | port-number ]
Once this is done create a QoS class for the custom NBAR app and then apply your policies.


How to install Raspbian without an SD card reader

Question: I'm new to the Raspberry Pi platform and I just bought one! I downloaded Raspbian from the download location and then realized that I don't have a card reader to install the ISO. How can I install it without a reader? I've got a desktop computer and all other connectors such as Ethernet cables. Please help me on this.
Comment: You can get a USB SD card reader for $10-20.
Answer: On a B, B+, 2B or 3B you can't do it without something to write the SD card. The only things these models can boot from out of the box is a SD card.
You may well find that you can use a camera or an older smartphone as a card reader (newer smartphones tend to use MTP rather than mass storage, so they are not suitable for this) to write your card.
On a model A,  A+ or Zero I belive you can use an appropriate USB cable (A to A for the A/A+ A to micro B for the Zero) cable along with the flasher utility intended for the compute module. You can find instructions for the compute module flasher utility at https://www.raspberrypi.org/documentation/hardware/computemodule/cm-emmc-flashing.md . If there are already Pi boot files on the SD card then I belive you may have to be careful when you insert it since the Pi A series don't have the special circuitry to suppress the SD card interface that the compute module has.
The Raspberry pi 3B adds USB mass storage and network boot options but unfortunately they need to be enabled by setting a bit in the one time programable memory on the SoC. To set that bit requires a special SD card.
The 3b+ enables the mass storage and network boot options by default.
(note: the above stuff about the A and A+is from memory and I haven't tested it myself, nor could I find the references I remember with a quick google)
Comment: Oh I din't know that with the raspberry. Thank you for your very informative answer.
Comment: See also this documentation page: https://www.raspberrypi.org/documentation/hardware/raspberrypi/bootmodes/msd.md
Answer: You can use your phone as an sd card reader.Just follow below steps:

Insert Your rasberry pi sd card into phones microsd slot.
and connect your phone to laptop via usb.
On your phone select usb options as Mass storage mode (MSC)
You now should be able to see a drive F: on your computer.
Now install a software called Sd card formater from here.
open software and select drive f: and then click on format.
Now install a software called win32disk imager from here
Open software and select drive f: and then browse and select the rasbian image and click on write.
remove ur sdcard from phone and plug it into the pi.
Comment: Pi Card Imager, on Android, is an app dedicated to this (https://www.raspberrypi.org/forums/viewtopic.php?t=170856)
Answer: If you have an Android phone with a microSD card slot, you can burn the image right on the card using Pi SD Card Imager. It's a little buggy, but after a few attempts it did the job for me.
Comment: the only answer that worked for me
Answer: The Pi only boots from the SD card.
You must find a way of writing the image to the SD card.
Are you sure you do not have a PC or laptop with an integral SD card reader?
Comment: I don't have a card reader for my desktop and there was a slot in my lenovo x1 carbon which I thought was a card reader, but it turns out to be a SIM card slot for a reason which have no idea about! so I would have to buy a card reader tomorrow! :( thanks for the headsup!
Answer: There is apparently a method that uses a "bootstrap" technique.
Essentially you only have to get the Pi to boot up which takes 16MB minimum (ie a 128Mbit I2C/SPI chip) and in theory even a regular tape deck if hooked up to a handful of discrete components or LM567's can generate the 4 bits + clock to emulate an SD card.
The catch is that it won't be able to write anything but just getting it to boot is enough for Pi to detect the external pendrive and install Raspbian onto the inserted SD card at the right point during initialization.
Making the special tape needed is left as an exercise for the reader, I suppose you could use a Minidisk or CD-ROM (similar idea, L/R channel) and each channel holds 3 frequencies at non linear harmonics to minimize crosstalk.
Comment: +1 For this crazy workaround which is technically possible, even if it's quite unfeasible.
Answer: I use a USB SD-card reader for writing all my SDs and microSDs. This one is the exact one I use - costs $6 (if you're in the US). There are cheaper ones too ($2-$3) but their quality is not guaranteed (I had one beforte I got the IOGear one that broke after a few months - refused to be recognized by any computer).
Answer: If you dont have a SD card reader, but you have the following

Ethernet Cable
Keyboard
Monitor or TV with hdmi port

then connect it to your raspberry pi and power on. A boot window will show. Press 'shift' key for few seconds and it will install rpi-imager over internet. Then you can choose the os you want and the storage (your SD card).
Thats it. Selected OS will be installed to your SD Card.


Endgame improvement books

Question: I am not playing a bad game, but my endgame is not so good. How can I improve my endgame? Please suggest me some good books for that.
Comment: Do you know your current strength?
Answer: Yasser Seirawan's Winning Chess Endings - Very good book, especially for beginners. Written by one of the best instructional authors out there. This book is written for beginner-intermediate level so it is very easy to understand, but has many lessons that can carry through to advanced levels.
Dvoretsky's Endgame Manual - Very indepth guide. Has just about anything that most players would need until professional level, and even there it has strong value. Can be fairly complicated at times, and assumes at least intermediate level skill from the reader. It can be a good reference manual however, as each topic is clearly outlined. Just be warned that there are many complicated situations that almost never arise in anyone's game, so you should focus your study on more important endgame techniques before conquering specific situations.
Silman's Complete Endgame Course - More like a guide than Dvoretsky's Endgame manual, allowing beginners to pick up the book, and progress through until master level endgame technique (as suggested by the front cover). This is the one I most recommend as it is much simpler for most players with less clutter.
Of course, there are loads more out there! Chess.com has asked this question before, and produced fairly consistent answers from players on the website. In the end, it will largely come down to your skill level, dedication to study and personal preference.
Comment: I like Silman's book too.  Very clear and appropriate material for different levels of player.
Comment: DEM is not for this guy, and it is not even close. It is really aimed at players that are over 2200. My endgame is quite good, and my peak rating was 2298, and I find it mind-boggling.
Answer: If your playing strength is at amateur level (say, 1400-1800 FICS rating) I'd recommend to start with this small brochure:
Yuri Averbakh -- Chess Endings: Essential Knowledge
Answer: If you want to learn more than just endgame theory, but also some strategy, then I can recommend the book Endgame Strategy by Mikhail Shereshevsky. I learned a lot from this book.
Here is a nice review: "Endgame Strategy" by Mikhail Shereshevsky
Answer: 100 endgames you must know by GM De la Villa is a good book to study endgames.

Jesus de la Villa debunks the myth that endgame theory is complex and he teaches you to steer the game into a position you are familiar with. This book contains only those endgames that: show up most frequently are easy to learn contain ideas that are useful in more difficult positions.
Answer: I'd like to add "Endgame Preparation" by Jon Speelman to the lsit of suggested titles.
Answer: You might want to check (pun intended) the internet first:

Queen + King vs. King:

Wikipedia
Explanation on chess.com

Rook + King vs. King:

Wikipedia
Practice

Two bishops + King vs. King

Wikipedia

Bishop + Knight vs. King

Wikipedia

King + Pawn vs. King

Wikipedia
Pawn square rule on chess.com

King + Rook + Pawn vs. King + Rook

Wikipedia
Lucena position
Philidor position

In general, you may want to look at this page on Wikipedia.

Endgame improvement books