How would increase labor productivity lead to improved living standards of people in an economy?

Question: I would like to know more about the mechanisms through which higher labor productivity would translate into higher living standards for a population in a given economy.
Answer: In economics we measure living standards by the amounts of goods and services people can consume. Increasing labor productivity allows us to produce more goods and services and thus also consume more goods and services, hence it improves the living standards.
For example consider classic Cobb-Douglas production function:
$$ Y = K^{\alpha} (AL)^{1-\alpha}$$
in this production function $A$ can be viewed as a productivity of labor (or technology that makes labor more effective). In the equation above $Y$ is income or output (i.e. amount of goods and services) $K$ capital and $L$ labor supply.
Even if everything stays constant (meaning economy does not have more capital or people dont work more hours and so L is also constant), but the labor productivity increases ($A$ goes up) the output of economy goes up as well. Higher output means that there are more goods and services for people to enjoy and in economics we would count that as an increase in (material) living standards.
Comment: Thanks. You say that "higher output means that there are more goods and services for people to enjoy", but isn't this only true if certain conditions are met? It's not clear to me how the purchasing power of consumers would increase thanks to increases in productivity. For example, what if companies keep salaries the same and charge the same price as before the productivity boost for the goods and services it sells..despite the increases in productivity?
Comment: @StatsScared in equilibrium in competitive markets people are paid their marginal product. Also, my answer above gave you the mechanism because that was your question. This being said empirically of course this does not hold perfectly. You can have years when there is clearly increase in productivity but wages stagnate. However, when you look at empirical studies of this over long periods of time wages and output are moving more or less close together. Of course, in real life any relationship due to random chance and other influences outside the model (regulation taxes etc) won't be perfect
Comment: Just to add to my previous comment. In long run in competitive industries firms can't really choose any wages or prices they want. They have a choice in a sense that the owner of company could set any price or wage she or he wants, but it's choice as choosing whether to eat or not eat... in the end in long run in competitive markets if you dont pay wage at least equal to marginal product other firms will lure all workers away from you. Same if you try to charge above equilibrium prices. Even in non-competitive labor market you can't set any wage you want and marginal product will affect wage


What is the difference in meaning between "husband and wife" 夫婦【ふうふ】 and 夫妻【ふさい】?

Question: I see that those two compounds mean husband and wife, as a married couple. But is there a difference in usage or context?
Answer: 夫妻 is the more formal of the two, and shouldn't be used when talking about yourself or people from your inner circle. As a general rule of thumb, use 夫婦 for such close relations or for general comments about married couples, and 夫妻 when talking about people outside your group.
Comment: Actually people do say ご夫婦 but ご夫妻 is "proper" keigo.
Answer: They mean the same thing but 夫妻【fusai】is more polite.
For example, you can use 夫婦【fuufu】to refer to yourselves (私たち夫婦), you can use for others and use it formally (ご夫婦). But you can't use 夫妻【fusai】to refer to yourselves (私たち夫妻 = NG).
Also when speaking formally, ご夫妻 is better than ご夫婦.
Answer: As the other two answers say, 夫妻 'husband and wife' is a more proper way to say. That is probably because 夫婦 'huband and woman' is not politically correct. Interestingly, it goes the opposite of the phrase used in Western wedding ceremony: 'man and wife', but the idea is the same; both phrases are based on sexual discrimination.
However, since the word 夫婦 is more established, it appears in many compound nouns, where it cannot be replaced with 夫妻, even in legal terms:

夫婦漫才 (but not 夫妻漫才)
夫唱婦随 (but not 夫唱妻随)
夫婦喧嘩 (but not 夫妻喧嘩)
夫婦財産制 (but not 夫妻財産制)
夫婦別姓 (but not 夫妻別姓)

And 夫妻 cannot be used alone as a word. It needs to be used as a part of a word. I.e., ご夫妻.


Booting Problem with ubuntu 13.04

Question: I installed Ubuntu 13.04 via DVD and everytime i restart, theres just a black screen bith the blinking cursor. I tried updating my video driver, but that did not help. i tried it with ubuntu 12.something, too but there was the same problem. I searched 3 hours straight and tried everzthing i found but nothing yet helped. I have the NVIDIA GeForce GTX 260 along with an asus M5A78L - M LX mainboard and the AMD FX-6100.
Answer: Without more information, this sounds like a boot problem rather than a particular graphics card issue.
Try using:
http://www.ubuntugeek.com/boot-repair-simple-tool-to-repair-frequent-boot-problems.html
to resolve the issue, this will also generate a pastebin link which you can paste here and someone will be able to point you in the right direction.

Booting Problem with ubuntu 13.04


No sound on Rakarrack 6.0.1

Question: I just installed Rakarrack and get no audio. I'm using Ubuntu 12.04 LTS. Help is appreciated.
Comment: more info is required
Answer: Like many professional audio tools Rakarrack needs Jack audio server. In order to get audio outputs working you may have to configure Jack (see the Jack Wiki for details).
This configuration depends very much on your individual set up. A generally valid answer can therefore hardly be given. One thing you may want to set up however is pulseaudio integration for applications that don't work with Jack (but read also this).

No sound on Rakarrack 6.0.1


$A \wedge A \wedge A$ in Chern-Simons

Question: I am confused with the wedging operations of Lie algebra valued differential forms.  Especially, for instance, I have some problems with the Chern-Simons 3-form
$$A \wedge dA + \frac{2}{3}A \wedge A \wedge A,$$
where $A$ is a Lie algebra valued 1-form.  My question is "how is the last term $A \wedge A \wedge A$ defined?"
As far as I know, a lot of sources (e.g. Wedge Product of Lie Algebra Valued One-Form, http://en.wikipedia.org/wiki/Lie_algebra-valued_differential_form) define the wedge of Lie algebra valued 1-forms as follows.
$$[\omega \wedge \eta](X_1,\dots,X_{p+q}) := \text{(coefficient)}\times \sum_{\sigma \in S_{p+q}} \text{sgn}(\sigma) [\omega(X_{\sigma(1)},\dots,X_{\sigma(p)}),\eta(X_{\sigma(p+1)},\dots,X_{\sigma(p+q)})],$$
where $\omega$ and $\eta$ are Lie algebra valued $p$-form and $q$-form, respectively. The coefficient differs by authors.  Other people utilises local description (e.g.  https://math.stackexchange.com/questions/315235/reference-for-lie-algebra-valued-differential-forms, and also in the Wikipedia)
$$[\omega \wedge \eta] = [\omega^a \otimes T^a, \eta^b\otimes T^b] := \omega^a \wedge \eta^b \otimes [T^a,T^b],$$
where $T^c (c=1,\dots,\dim \mathfrak{g})$ are generators of the Lie algebra $\mathfrak{g}$, and the implicit sums understood.
These definitions, as the notations suggest, force you to take Lie bracket explicitly.  Therefore it is obvious that wedged one $[\omega\wedge\eta]$ is Lie algebra valued $(p+q)$-form.
Then what about wedged ones without brackets, such as $A\wedge A, A\wedge A \wedge A$?
I can show that $A \wedge A$ is equivalent to $[A \wedge A]$ up to coefficient, using either matrix representation, considering $\mathfrak{g}=\mathfrak{gl}(n)$, or universal enveloping algebra.  The basic idea is
$$A \wedge A = (A^a \otimes T^a) \wedge (A^b \otimes T^b) = (A^a \wedge A^b) T^a T^b.$$
This time, by graded commutation relation, the multiplication of generators can be converted to commutators.  This seems ok.  Then what about $A\wedge A \wedge A$?  I could not convert it to an expression only using commutators of generators...
So, what I did was calculating $[A \wedge [A \wedge A]]$, which gave zero.  I am totally confused at this stage.  Could you point out some pieces that I possibly keep missing??
Answer: Option (1) Use the definition $(\omega \otimes S) \wedge (\eta \otimes S) = (\omega \wedge \eta) \otimes (S\otimes T)$ of the wedge product for Lie algebra valued forms. Define Lie bracket and Killing form as bilinear maps $[S\otimes T] = [S,T]$ and $\langle S \otimes T \rangle = \langle S, T\rangle$. Then the formula that you want is $$\langle A \wedge [A \wedge A] \rangle,$$ where the commutator and Killing form apply only to the Lie algebra factors, ignoring the differential form factors.
Option (2) Use the definition $(\omega \otimes S) \wedge (\eta \otimes S) = (\omega \wedge \eta) \otimes ST$ of the wedge product of forms valued in a particular matrix representation of a Lie algebra. Then the formula that you want is $$\operatorname{tr} (A \wedge A \wedge A),$$ where again the trace applies only to the matrix factors ignoring the differential form factors.
The two formulas agree up to a constant factor, as long as your Lie algebra is simple.
Answer: For Lie algebras of matrices (which is what you really care about in Chern-Simons theory) think of $A$ as a form with matrix coefficients
$$ A=\sum_i A_i dx^i, $$
where $A_i$ are $r\times r$ matrices.With this convention, use  the usual wedge product
$$\left(\sum_i A_i dx^i\right)\wedge \left(\sum_j A_j dx^j\right)\wedge \left(\sum_k A_k dx^k\right) = \sum_{i,j,k} A_iA_jA_k dx^i\wedge dx^j\wedge dx^k, $$
where you need to recall that   the product of matrices is not commutative.
Comment: When the notation is ambiguous, you have to be more precise about the context. If you want a formula for the Lagrangian density of the Chern-Simon's theory, then it cannot be Lie algebra valued.
Comment: Liviu, just want to note that your formula gives a matrix-valued 3-form. One still needs to take the trace of the matrix coefficients to get an ordinary 3-form that one could use as a Lagrangian density.
Comment: So, do you think that $A\wedge A \wedge A$ does not have to be Lie algebra valued 3-form?  Perhaps this is the point that I cannot understand.
Answer: This is not a direct answer to my question, but I think it is worth noting.
  The reason why $A \wedge A \wedge A$ without trace should not be a Lie algebra valued 3-form is as follows.
Suppose $A \wedge A \wedge A$ be a well-defined Lie algebra valued 3-form in some sense.  Then it must have such  a local expression
$$C_{\mu\nu\rho}^a T^a \otimes dx_{\mu}\wedge dx_{\nu} \wedge dx_{\rho}.$$
To make this Chern-Simons Lagrangian density, you have to take trace of it, which gives zero unless the Lie algebra $\mathfrak{g}$ in consideration is abelian.
On the other hand, if the algebra were abelian, the expression $A \wedge A \wedge A$ must vanish (due to antisymmetry).  This would make the theory useless.  Thus the expression should never be a Lie algebra valued form.
P.S.  I did not come up this story when I asked my question.  But the discussion here uncovered my poor understanding on the subject and enlightened how I should proceed.  Thank you everyone!

$A \wedge A \wedge A$ in Chern-Simons


In a right triangle, can $a+b=c?$

Question: I understand that due to the Pythagorean Theorem, $a^2+b^2=c^2$, given that $a$ and $b$ are legs of a right triangle and $c$ is the hypotenuse of the same right triangle. However, most of the time, $a+b\neq c$. What I have been wondering is, is there any set of values for $a$, $b$, and $c$ that make the statement $a+b=c$ true?
Comment: Try to draw it, $a+b=c$ makes a very flat triangle ...
Comment: Since nobody apparently brought it up: look up the triangle inequality.
Answer:
(Addendum: As noted as well by others, this should highlight that your question has little to do with right triangles, as this is in fact a property of triangles in general)
Comment: this is a beautiful explanation. I'm wondering if it is possible to do such an illustrative drawing to prove that $a^2+b^2=c^2$ if and only if the triangle is right.
Comment: @Surb I suspect there is; you should ask this as a new question.
Answer: Your question has nothing to do with right triangles. If $c=a+b$ in any triangle, then the vertex $C$ must lie on the segment $AB$, and this is called a "degenerate" triangle.
Comment: @OldBunny2800: Exactly. It depends on you whether you still want to call such a thing "a triangle".
Comment: Does have relevance the question with right triangles: it corresponds to a leg equal to zero. In contrast, when simply $a+b=c$ the triangle is degenerated and  $a$ and $b$ can be nonzero.
Comment: As in a triangle that looks exactly like a plain line segment? Makes sense.
Comment: In computer science this is called a corner case.  You modeled a triangle and tried to capture every possible case and ended up capturing some cases you never imagined.  It happens.  It's why we have the number zero in the first place.  It's why 0! = 1.  A surprising number of things are degenerative cases of other things.
Answer: From the pythagorean theorem, $a^2+b^2=c^2$.
Suppose $a+b=c$, then
$$
a^2+b^2=(c)^2\iff a^2+b^2=(a+b)^2
$$
Can you take it from here?
Comment: @Lii either a or b, but not necessarily both.
Comment: @Lii Well, the question was "is there any set that makes this true"? The answer is yes. Take any of the legs to have $0$ length (not necessarily both, though). If you want to call that a triangle or not depends on you.
Comment: *a* = *b* = 0. But that's not a triangle any more...
Comment: @Lii and if it isn't a legitimate triangle what does that tell you about whether a right triangle can have a+b=c? (Hint:  if you ask a yes/no question the answer can be no.)
Answer: Substituting $c = a + b$ into $a^2+b^2=c^2$ gives us $a^2+b^2=(a+b)^2$. Multiplying that out gives us $a^2+b^2=a^2+2ab+b^2$ which means $2ab=0$
So to satisfy both $c = a + b$ and $a^2+b^2=c^2$ either $a=0$ or $b=0$.
The question then becomes a bit more philosophical. We have a result that satisfies the Pythagorean equation but can we really consider it a right angle triangle? Is a "side" of length zero really a side at all?
Comment: that's funny, so a line of length 5cm can be either an unspectacular triangle with side lengths of, say, 5cm, 2cm and 3cm or it could be rectangular, but only if a=0cm, b=c=5cm. And this is the only case I can think of where the hypotenuse is one of the two equally long sides in an isosceles triangle. So which is the hypotenuse then, b or c? Or are they both hypotenuses and there is only one (zero-length) cathetus?
Degeneracies allow for many strange results :-)
Answer: There is another way to formally answer this question, namely using the cosine law.
For any triangle, it is true that $a^2+b^2-2ab\cos\gamma = c^2$ where $\gamma$ is the angle between the $a$ and $b$ sides. On the other hand, if $c=a+b$ then $c^2=(a+b)^2=a^2+2ab+b^2$, thus
$$a^2+2ab+b^2 = a^2+b^2-2ab\cos\gamma,$$
which is possible only if $\cos\gamma=-1$ or $\gamma=\pi$, that is, 180 degrees, or if either $a$ or $b$ is zero. Either way, this is a degenerate triangle, as mentioned in Alex M's answer.
Answer: Like Alex M. said, this doesn't have much to do with right triangles, but it's worth knowing the more general fact, and there's an easy visual!
Imagine you have two sides of a triangle, like an adjustable protractor. As you increase the angle between them, the other side is getting longer. But it won't equal their sum until you have your protractor fully opened up to 180°—and then it's not much of a triangle anymore. You also might wonder if there are any triangles where $a-b=c$ If you decrease the angle between your two sides, the other side is getting shorter. But it won't equal their difference until your protractor is totally closed to 0°—and again, then it's not much of a triangle anymore!
So if we have a triangle and know the length of two of the sides, we know that the length of the other side is less than their sum, and greater than their difference.
Comment: Proof: https://proofwiki.org/wiki/Sum_of_Two_Sides_of_Triangle_Greater_than_Third_Side
Answer: One of the principles that this question illustrates is that in Euclidean geometry any path from point A to point B is not shorter than a straight line from A to B, i.e. a straight line segment A->B is the shortest path from A to B. Any deviation made through a point C that is not on the segment A->B makes a path longer and the only way that (A->C)+(C->B) can be equal to (A->B) is that C is on that segment.
Answer: Let $x$ be the angle opposite to altitude.
Now,we want $a+b=c$ or
Dividing both sides by c we get---                   $a/c+b/c=1$
By definition $a/c=sinx$ and $b/c=cosx$
So equation becomes----
$sinx+cosx=1$ or $sinx+(1-(sinx)^2)=1$
By solving we get----
$2(sinx)^2-2sinx=0$
We get 2 solutions that is
$sinx=1$ and $sinx=0$
Or as principle solution we get
angle $x=0$ and $x=π/2$.
Which means $a/c=0$ or $a=0$,$b=c$ and
$a/c=1$ or $a=1$,$b=0$.
We conclude that either base or the altitude should tend to $0$.
Answer: No, it can't. Although in case of simple triangle, make any one angle 180 degree and then the area of triangle will be zero. It will look like straight line.
Answer: It has nothing to do with right triangles. There are two line segments and a third one straddling them. Sometimes it is called a $ diangle,$ a needle like shape enclosing no area between them.
Answer: Maybe, the equations $a^2+b^2=c^2$ and $a+b=c$ can be hold simultaneously in a ring or finite field. Say, over $F_{2^m}$, if we set $c=a+b$, then $c^2=a^2+b^2$ always holds. In fact, we know that $(a+b)^p\equiv a^p+b^p\pmod p$ for any prime $p$.
Comment: If we set c=a+b, wouldn't $c^2=a^2+ab+b^2$?

In a right triangle, can $a+b=c?$


'Failed to fetch updates' shows up when I open AppCenter

Question:
'Failed to fetch updates' shows up when I open AppCenter. Can someone tell me how to stop this?
Answer: The small black window in the center of your screenshot indicates that you must have manually added at least one non-system repository, which doesn't have proper release file, suitable for your current system (apparently, Ubuntu 18.04 if you're on elementary OS 5).
To solve this issue, you should remove that particular PPA from your system:

Right click on Files and select New Window as Administrator.
Go to /etc/apt/sources.list.d folder.
Inside that folder, delete all files that contain sarimkhan in their names.
Then try running an update via AppCenter.

In case of more errors (the messages that begin with E:) post them here.
# Or please execute this command bellow in terminal to remove that repository,
sudo add-apt-repository -r "deb http://download.opensuse.org/repositories/home:/sarimkhan/xUbuntu_14.04/ ./"

Comment: there are no folder named 'etc' there
Comment: @MusabbirKazimNiloy The 'etc' folder is not under your user directory. Please move up to access the directory. Looking at the image attached to your question I can see that the error is due to an outdated repository that does not have a release file for current ubuntu version. Please execute `sudo add-apt-repository -r "deb http://download.opensuse.org/repositories/home:/sarimkhan/xUbuntu_14.04/ ./"` to remove the repository, error will be gone.


When to ask for constructive criticism?

Question: I have 40,000 words of a novel and I am not sure at what point to ask for constructive criticism.
Comment: Welcome to Writing.SE, Mandy. We'd love to offer you help, at any point of your writing, from concept to publishing, but we can only do that if you have a specific question. We cannot offer you criticism of your work. We are not a forum, but a Q&A site: we need a concrete question that we can answer. Take a look at our [tour] and [help] pages to find out more.
Comment: The sooner you get good critiques, the sooner you know if you are going to have to make major revisions, and the easier it will be.  Better to find out at chapter 1 that your main character is boring, or your plot is unbelievable.  Going back and rewriting a single chapter or two is far easier than rewriting an entire book, even if the changes are small.
Comment: @FrancineDeGroodTaylor But you might figure that out for yourself while you're writing it - and I find that giving things to readers at too early a stage has the tendency to kill it for me, particularly if they don't like it. Personally, I don't want other people's ideas about what I should change until I've at least tried having my own ideas about what I should change. But everyone's different :)
Answer: You can ask people for advice/ constructive criticism at any stage of writing, but I would refrain from giving beta readers huge chunks of text at a time (like 40k words) unless they're professionals.
Usually, I divide my work into manageable units that kind of make sense on their own - chapters, short stories, etc, and ask people to give me feedback.
Ash's answer is also good - having people beta-read when you're struggling can give you new directions to take a work.
Answer:
at what point to ask for constructive critisism.

It depends on how you write. Some people plot out their novels in great detail, every foreshadowing, plot turn and twist. They know their characters backward and forward, and everything that will change about them during the story. So when they are done with Chapter One, and have finished X drafts of it, Chapter One is done forever. If that is how you write, then you might as well get feedback on each Chapter as you finish it.
I don't write like that, I am a discovery writer. I typically write at least two openings, in my current story I wrote four. I invent my plot as I go, my additional characters, I may delete them or replace them. I begin with a protagonist I know better than others, but even she may get some personality changes, I'll find out when I put her in new situations.
So I don't seek feedback until I am DONE with the story. Because until then, I might change any part of it! Fortunately, I have friends that think I write well, they know I can finish a novel and it will feel like a novel, and they don't mind reading the whole thing in their spare time.
I will also note that the most important parts you need reviewed are the opening (first 10 pages, first 25 pages) and the climax near the end (the resolution of the protagonist's major problem, which is not necessarily in the last chapter). You don't need detailed critique of the middle, though you might get it. Listen to it.
About asking for constructive criticism: I tell my readers I am looking for negative feedback much more than positive feedback, the whole point is to help me find problems I was too close to see, or too dumb to realize. So no hurt feelings on my part, I want a story that works more than I want any kind of polite praise. I want them to know the next step is sending it to a stranger, likely a brutal agent that rejects 90% of what she reads. So we want to fix any problems before that happens, not learn about them only after I've burned my best prospects.
That is how people that don't want to hurt your feelings actually hurt your chances of success instead.
On answering criticism: I don't reject it, even if they are completely, totally, utterly wrong and don't get it. Either they are right, or I will look at it and see if I can find a solution.
It is hard enough for people to tell me honestly they don't like what I wrote, without getting punished for it by me calling them an ignorant slut reading at the grade level of a Labrador retriever.
Sometimes their own morality or politics conflicts with mine, sometimes their criticism arises from my failure to communicate clearly. Inconsistency is a problem to solve, poor communication is, but a difference in morality or politics or world view is not. Let 'em rant, don't make excuses or try to explain what you meant, don't get in an argument.
Comment: I'm interested in the line, "You don't need detailed critique of the middle" - please could you elaborate? I'm worried that if the readers get bored with the middle they won't make it to the end!
Comment: @DM_with_secrets Not DETAILED critique, but don't prohibit any critique. They are doing you a favor to read it, making it your duty to read and address everything they say, regardless of where it occurs in the story. So if they are bored, and skimmed Chap 11-15, you have a problem. But an agent (or reader for a publisher) will decide within the first 5 pages, often within the FIRST page. The first 1/8 (up to and including inciting incident) are the most important pages to get perfect. The middle should be good, but immersed readers are forgiving. It does not have to be absolutely perfect.
Comment: Ah, I see, thanks! :)
Answer: When you think the work is ready, probably sounds a bit daft but there is no hard and fast rule about when a piece is ready for review; you have to make a judgement call about putting it out to a beta-reader, or readers, to get feedback. It may also be useful to put a draft out to a beta-reader when you don't feel that it's ready but you do feel stuck, fresh feedback can help you move a piece you're struggling with along.
Answer: From the software world we have the phrase "Test early, and test often".

In the writing world this mindset works well with writing-circles and writing focused-social environments where you can begin digging into the good and bad of a piece as soon as possible.
It is not remotely wrong to begin a process of constructive criticism and feedback before you even commit a single word to paper. However it is important to focus on what kind of feedback is actually useful at any given stage of writing.
The earlier on in the process you are, the broader strokes you want to focus on. Catching minor grammar details early on in the process isn't a bad thing, but it also isn't the most useful thing to focus on. Fussing over having 'perfect grammar' on chapters that you might actually need to cut entirely is not a great use of anyone's time. Instead seek to dig into the higher level mechanics of the writing.

Does the overall plot line work?
Does the writing style fit the voice and tone you are aiming for in your piece?
Do the characters act and talk in a way fitting their design and goals?
Do decisions and pacing make sense?
Does anything jump up as a red flag for logic?

Catching that you used "Desert" in place of "Dessert" early on in the process is useful, but hardly critical.
Having someone point out to you that you have a long [and possibly tedious] conversation about the quality and purity of the silverware at a dinner party hosted by a demon who can't touch silver... Well that might be far more useful feedback early on in the writing process, as it is the sort of thing a writer can do real work with:

Do you edit the scenes and conversations to remove the silver, and back away from the problem entirely?
Do you edit things such that the silver clearly remains, but the character carefully avoids directly touching it [Maybe without drawing excessive attention to the fact?]
Does it become a plot point that gets reworked and reused throughout the story? [Seeding hints and references to the character not touching the silver early on in the story, and giving the readers an 'ah-Ha!' moment later in the story when they realize what was going on?]
Answer: Ask the Hungarian
TL;DR

Unsurprisingly, this question has a mathematical solution based on the Hungarian algorithm.
I have not done the calculations, but I imagine that1 the typical answer is:

Always ask for feedback from the very beginning. Start with more feedback from the more willing/less skilled beta-readers early on. Save the feedback of less willing and more professional beta-readers for the later stages, when your product is closer to the final form.

1: this is based on the guess that the time availability of beta-readers does not scale exponentially relative to their feedback quality ranking. See below for details.

A far-from-formal discussion of the problem
The setup
you have an assignment problem, with a series of tasks to be split between agents. The task is to provide feedback on a text whose length increases over time, up to an upper limit of which you have a rough estimate (and the accuracy of the estimate increases over time). The agents are a number of beta readers with varying degrees of professionality (i.e. quality of the feedback), patience (i.e. size of the task that they can digest), and available time (i.e. how many times you can ask them to read your writings).
The goal
distribute the workload between beta readers across time to maximize the benefit of your feedback. In math terms, I see this as the maximization of the impact of the feedback, that is the product between the quality of the feedback and the certainty that the text given to the reader is closer to the final draft. It makes no sense to have high-quality feedback on text which you are going to rewrite anyway.
The assumptions

You cannot discern your beta-readers based on their taste. You can distinguish them based on their reviewing skills, and on their patience and availability, but they will all like (or hate) the same written works.
beta-readers read at the same speed.
beta-readers can read unit chunks of text and do not need to read the entire work at once.

Estimating the total length of the text
This total length is the total number of words that you have written. If you never rewrite your work, then it is exactly the number of workds in your novel. If you rewrite parts of it once, then it is the sum of the words in the initial draft, plus the edited parts.
That being said, imagine that your initial writeup goal is 60k words. If we simplify the problem a lot, we can think that for every word there is a certain chance that you will have to rewrite it. Everytime you rewrite a word, the chance of rewriting that specific word decreases. For simplicity, imagine that when you start writing there is a 50% chance that you will rewrite any word. If you rewrite it, there is still a 50% chance that you will rewrite the new one: how many words would have you been writing? 1 word with 50% chance, plus another word with 25% chance, plus another word with 12.5% chance... if you continue forever, and weight the sum by the probability, you get that a 50% rewriting chance results in writing 2 words for any word in the final manuscript: writing a 40k novel will require writing on average 80k words. Obviously, higher rewriting chance require writing more words.
The beta-readers
The beta readers are characterized by:

the quality of their feedback, which we can treat as a ranking (1: amateurs, 100:professional literary critic)
the patience: the longest chunk of text that they are willing to read in one go.
the available time: i.e. the total amount of text that they are willing to read

We can simplify this enormously by splitting each beta-reader in sub-beta-readers, where each sub-reader is simply a unit of time of work of a beta-reader, for instance, a half-hour beta-reading. From the assumption n.2 this corresponds to a fixed amount of words. Now your most willing beta-readers correspond to an army of tiny half-hour subreaders, while your busy beta-readers may only be represented by one sub-beta-reader. From assumption n.3, for the purpose of determining task assignments, there is no distinction between a single beta-reader and an army of sub-beta readers that read the same amount of text. The only practical distinction is that sub-beta-readers cannot read in parallel as they may correspond to the same person. Considering how long it takes to craft a novel, this is an irrelevant detail.
The tasks
Once you have defined your sub-beta-readers, you also know what is the length of the chunk of text that each sub-beta-reader will read: if you have half-hour sub-beta-readers, then it is the hourly reading speed divided by two. How many tasks do you have? Total text length divided by length of a task.
Each chunk of text has a certainty score, which is the inverse of the chance that you will edit it. For instance, if the initial chance of rewriting a word was 50%, then the chunks from the first pass have a certainty score of 2 (1 divided by 50%), the chunks from the first round of editing have a score of 4 (1 divided by 25%), and so forth. This means that the certainty score is an exponential function, i.e. it grows very rapidly with the number of edits.
The measure to optimize
Each sub-beta-reader reads a chunk of your text. The reader has a quality associated to them, given by their relative ranking, as we said above. The chunk of text assigned to the reader has a certainty score. The product of these two numbers is higher for text of which you are more certain and which were reviewed by the more qualified people.
And now what?
Plug all this in the Hungarian algorithm: the agents are the sub-beta readers, and the chunks of text are the tasks. Map the sub-beta-readers back to your beta-readers and the output of the algorithm should tell you which piece of text to give to which reader.
I hope that helps.
Addenda, Notes and PS

I'm a discovery writer! I don't know how long my novel will be from start!: worry not, you can use the average novel length from your genre as an initial estimate, or you could use a Fermi estimate, or a German tank estimation approach (this may work surprisingly well if you write random scenes to be glued together in the end), or use as upper bound the maximum total length of text that all your beta readers may be willing to read.
I'm bad at estimating chances of rewriting!: Also, not worry. Start with a guess, like 50%. Then you can apply an expectation-maximization algorithm to tune the chance of rewriting as you actually rewrite. In simple terms, at each round of rewriting, you can plug in the number of words you have actually rewritten and come up with a new guess for what your rewriting chance is. Be careful to track how many times you have rewritten each passage, though.
What to do if you write more than the number of available readers?: Add pseudo-readers. The ideal case would be to do a random sampling with replacement from your actual beta-readers. A simple and effective way to do that is just to add a bunch of low-quality beta-readers. This will push reading revisions to later stages. Re-run the algorithm if you get new beta-readers.
What if my readers do not have a similar reading taste?: Group readers in super-readers by taste groups with identical revision quality. Assign chunks of text to each super-reader. Then rerun the algorithm for the group of readers in each super-reader group limiting the text to the collection of chunks assigned to that particular super-reader.
My readers do not read at the same speed: the conversion to sub-beta readers is done in amount of text per unit of available time. You can also convert a reader to sub-beta readers by the number of text chunks of a given length that they can read. In formulas: avilable_time_for_reader * reading_speed / length_of_basic_text_chunk
I have already written 40k words! How do I go from here? subtract these 40k words from the total length of the words that need beta-reading. Distribute the work over the remaining text.
When should I run this algorithm? You can run it even before you start writing. You can re-run it everytime a beta-reader reads a chunk of your text: you remove that amount of text from the total text to be read, remove the corresponding sub-beta-reader, update the estimated total length and the chance of rewriting, and rerun the algorithm. Doing so will allow you to distribute your work more precisely and in a more timely fashion. Once you have it, it is probably a matter of a couple of click.
I want to give my reader single chapters, rather than chunks of text, and they are of different length: as long as the readers will consider all chapters to be equal in terms of workload, replace the text chunks with chapters in the computation above. Each reader is divided in sub-readers corresponding to the total number of chapters that they are willing to read. Your novel length is given in chapters, and the probability of rewriting, refers to a chapter and not to a single word anymore. Leave the rest unchanged. A word of advice, do not disclose whether a chapter is longer or shorter than average to your beta-readers unless you are sure that they are not easily offended by workload inequality.
Is there readily available software to calculate this? yes and no, and sadly the margin is too narrow for me to put it here :)
Comment: Is the downvote due to a mistake in my model, to the length of the answer, to the suggestion, or to the unfathomable?
Comment: (I didn't downvote, but) I would be worried about asking for feedback early on from "more willing/less skilled beta-readers". Personally I'm not a fan of feedback too early anyway - I like to have a chance to fix my own mistakes first - but particularly from people who might be keen to suggest you write the story **they** would have written. I'd rather have their feedback at the end, when the story is more fixed in my mind, and I can decide more easily whether suggestions should be ignored.
Answer: I'd say that you would do well to compile a list for yourself of the type of criticism that you are looking for. Because what you'll get, if you throw your work out to readers without a specific task for the reader, is everything ranging from people deciding not to read it alt all, people saying 'Looks great!' (and you suspect they didn't read it either), people pointing out comma errors and tense mistakes and other minor things that really don't help much in terms of story, people identifying all the technical errors you are blind to or don't know yet, like repeating words / telling instead of showing / viewpoint issues, or people rewriting your work wholesale, or people saying your characters have no goals, your story no arc, your scenes no structure...
In other words, there's a good chance what you'll be given in return is not what you expect if you don't constrain the request up front. (Also, spend time identifying good readers. These are usually writers.)
So. Compile a list of the feedback you want, at any stage of writing that you desire. Compiling the list will also help you find mistakes on your own. Not sure what to put on the list? A good place to get ideas is on writing blogs, and also by spending time critiquing other writers' work.
I recently took a single sheet to a group I'm in, and on this sheet I had story-boarded a trilogy I'd like to write. I wanted constructive feedback on the ideas, and we spent about thirty minutes hashing through the story arcs I had sketched for the trilogy. There was not a single named character yet, no words at all in story, but I wanted feedback on the concepts.
Answer: So, at any stage in the story writing process, you can solicit constructive feedback--but you probably are doing yourself a disservice if you don't know the specific type of feedback you want beforehand. (Most beginning writers say "Is it interesting?" and I'd urge you to look a little deeper than that, because having  been on the receiving end of that a number of times, I've come to realize whether it is interesting or not still boils down to details of crafting a story.)
Answer: There is no set time --this needs to be a personal determination. Getting criticism too early, or in the wrong frame of mind, or from the wrong person can potentially shut down your muse, or shunt your creativity away from the things that resonate the most with you.  But if you never get criticism, you're likely to end up writing only for yourself, and if you get it too late, you'll find yourself doing a lot of rework.
I would advise getting criticism when you need it, meaning (a) when you are stuck, (b) when you are at a stopping place or (c) when you have a need to know how this will appeal to your final audience.  That could be anywhere from the very beginning to the very end.
It can be good to do some preparatory work on shorter, more audience focused projects --for instance, fan fiction or blog posts --where continuous feedback is readily available.  What you learn there can carry over to longer projects that you want to keep private for longer.

When to ask for constructive criticism?


Can an aircraft be stalled at low altitude and safely land on water?

Question: P.S Its just a random question...please consider the fact I have zero knowledge of aerodynamics of a plane.
Comment: Related: https://aviation.stackexchange.com/questions/44740/why-cant-you-ditch-your-aircraft-in-the-sea You can't land an aircraft with zero forward airspeed; so the 'safely' depends on how low the stall speed is.
Answer: That is the normal procedure for water landings with land airplanes. You fly parallel to the water as low as possible until the flight speed is too low to carry the full weight of the airplane. If it can be done safely, however, depends on a lot more than only the landing technique. Some aircraft will not swim and the drag of the landing gear might cause the aircraft to topple over.
Comment: opinions differ but a technically good landing is one that you can feel as both rear wheels toch down firmly and only once. A very soft landing is also not preferably as it can result in more wear on the tires, since they touch the groundly only slightly before the final touchdown. This result in 2 times up spinning the tire.
Comment: @Brilsmurfffje: Do you have any references or more arguments for that idea? It also came up a few weeks ago, and i am not quite convinced. I don't see why there would be more wear if the tires spin up slowly, it wil surely be more even though. I don't think the tires will have much time to slow down again if they spin up in two steps.
Comment: Isn't every landing a stall? Maybe only in the last seconds but it will be a stall. In the end the stick is pulled back such that the nose raises and the wings create an air cushion with the ground on which the aircraft "falls" down on the main landing gear.
For water landings it is essential that drag components, like engines, wheels etc, touch the water symmetrically, so left and right at the same time which will keep the aircraft in a straight line instead of turning and topple it over
Comment: @Brilsmurfffje: No, at some point the wheels carry over without the wing stalling. The best landings are imperceptible except for the wheels spinning up. Details depend on the stall behavior - some aircraft show a clear lift drop in a stall and would produce a bump when the wings refuse to carry all the lift and the aircraft drops on its wheels.
Comment: @rickboender, "slowly" upspinning will smear the rubber over a longer distance on the runway. With crosswinds you also want a firm touchdown as it reduces the skidding over the runway and thus the wear on the tires. If you look up pictures on the internet of runways were mainly 737's land you will see longer and shorter black lines indicating smooth and firm landings respectively.


C++ Overriding logical fail

Question: Hey guys I have a problem with one of my methods (overriding an operator , ~ )
When I try to print my object, something unexpected happens... need some help
this is my whole code
#include"stdafx.h"
#include<iostream>
using namespace std;

class complex
{
private:
    double Re, Im;
public:
    complex(double _Re = 0, double _Im = 0) : Re(_Re), Im(_Im){} //class constructor

    void print() const
    {
        cout << Re << " + " << "i(" << Im << ")" << endl;
    }
    complex operator~() const
    {
        return (Re, -Im);
    }
};

void main()
{
    complex x(2, 3);
    x.print();
    (~x).print();
}

If i compile it, I'll get the correct complex number on the screen, but when I try to execute the ~ overridden operator it displays to me -  -3 + 0 i....
Really need some help.
Thanks
Sorry for posting such brain-dead questions, but I can't figure it out by myself....been looking at the damn code for more than 30 minutes and I can't see where I am wrong.
Comment: return(re , -im) --> return complex (re , -im)....sometimes 20 min and 2 eyes are not enough to notice a missing word!
Comment: Don't use identifiers beginning with underscore then a capital letter, like `_Re` and `_Im`.  These are reserved for the C++ library and other implementation details.
Answer: You are missing a complex(Re, -Im);
in:
complex operator~() const
{
    return (Re, -Im);
}

Hence you return an implicit converted complex(-Im) (comma operator).
You might use explicit constructors to avoid a pitfall like this.
Comment: What this line actually does is use the comma operator.
Answer: The comma in
return (Re, -Im);

does NOT do what you think it does.
Surrounding something in parenthesis does NOT call a constructor.
The parenthesis are discarded and the expression is evaluated as
return Re, -Im;

The comma means rvaluation each term and the result is the rightmost term.
Because the expression Re doesn't do anything the expression is evaluated as
return -Im;

But this calls the constructor which has a default of 0 for the imaginary term.
And so you get -3 for the real part and 0 for the imaginatry part.
Instead that line should read
return complex(Re, -Im);

Which constructs what you thought it should.
Answer:     return (Re, -Im);

This is using the comma operator, where it evaluates Re (numbers do nothing), and then evaluates and "returns" -Im (-3).  Then, the return type is expected to be a complex, so it tries to convert this -3 to a complex.  It finds this constructor: complex(double _Re = 0, double _Im = 0), and uses it: complex(-3, 0);
The immediate solution is to add the word complex to the return
    return complex(Re, -Im);

Or, in C++11, use {} to tell the compiler that you meant to call the constructor:
    return {Re, -Im};

Answer: Since you accept default values for your constructor (0) the compiler takes the expression: return (Re, -Im); evaluates Re (it is 2) throws away and creates a new complex with the -Im by calling the constructor like: complex(-3, 0). So this is how you get the funny value.

C++ Overriding logical fail


How do I fix Flash issues?

Question: I am having problems with Adobe Flash in Ubuntu, what are my options?
Answer: As you have identified - the best solution is usually to follow this Q&A to install flash.  It does work for the vast majority of users.

Flash-Aid was discontinued by it's author and is unknown if it will be back, the following are kept only for historical reasons.

As an alternative, one of the best tools I have found that allows you to configure Flash correctly during installation is the Flash-Aid addon - use the author's site or search on the Firefox addon-manager for Flash-Aid
This will remove any remnants of of Flash installation and install flash directly from the Adobe Website.  During the wizard installation you have a few configuration options that you can try to resolve flash-player issues.

Close & Restart Firefox / reboot for the change to take effect.
See also:

Why are Flash applications so sluggish/crashy?
Answer: There are 2 options.
Enable the HTML5 player
For Youtube this can be done by loggin in, going to http://www.youtube.com/html5 and enabling it there. You can also just add &html5=True behind each video URL.

There is a trick for the cases when there appears to be no HTML5 option available on YouTube: use the "embedded" variant.
For example: https://www.youtube.com/watch?v=3SacL219sic&html5=True appears to be not watchable in HTML5, but https://www.youtube.com/embed/3SacL219sic plays in HTML5!

Whether your browser and the version you are using will support the HTML5 playback of a video on a site that provides such an option (like YouTube or VKontakte) will depend on the codec chosen by the site owners. For example, YouTube and VKontakte (a Facebook clone popuar in Russia) use different codecs for their HTML5 videos, which means that in Ubuntu 12.04 HTML5 video playback at VK.com works in Chromium, but not in Firefox (and in future, these browsers might swap their roles).
Install the Flash Aid Firefox plugin
I don't know for sure if this will work for you as well, but it worked for me.
Install Flash Aid, restart Firefox, and click the Flash button at the upper right corner of Firefox's window. Just follow the instructions in the wizard and you should be fine.
For some more detailed guide on installing Flash using Flash Aid, check out fossfreedom's answer: https://askubuntu.com/a/86260/18953
Comment: This is good advice but note that only videos on Youtube encoded as WEBM are playable in HTML5 currently!
Answer: For Firefox Flash, first try this:
when having issues after an automatic update.
$ sudo apt-get --reinstall install flashplugin-installer

This leaves one with Adobe Flash plugin version 11.2.???.??? in Firefox as Adobe no longer releases any higher flash versions for Linux.
For the moment, the 11.2 series of the Adobe Flash plugin for Linux is still maintained and security updates will trickle in automatically. However, one will miss out on innovations and power efficiency improvements.
For adding the Google Chrome Pepper Flash plugin to Chromium:
$ sudo add-apt-repository --yes ppa:skunk/pepper-flash
$ sudo apt-get update
$ sudo apt-get install pepflashplugin-installer
$ echo '. /usr/lib/pepflashplugin-installer/pepflashplayer.sh' |sudo tee -a /etc/chromium-browser/default

The latest and greatest Adobe Flash version for Chrome (version 12.0 at the time of writing) is installed in Chromium.
This solution can also be scripted for easy installation on multiple machines:
#!/bin/bash
sudo add-apt-repository --yes ppa:skunk/pepper-flash
sudo apt-get update
sudo apt-get install pepflashplugin-installer
STRING='. /usr/lib/pepflashplugin-installer/pepflashplayer.sh'
FILE='/etc/chromium-browser/default'
if ! grep -qe "$STRING" $FILE
  then
    echo "$STRING" |sudo tee -a $FILE
fi

Unlike Firefox Flash, Pepper Flash is not updated automatically by the update manager; it requires a tedious manual process. Forgetting about this leaves one exposed to security threats.
Here is another bash script to render manually updating Pepper Flash just that little bit less cumbersome:
#!/bin/bash
VERSIONS=$(sudo update-pepperflashplugin-nonfree --status)

UPGRADE=$(echo "$VERSIONS" |grep -oE '[^ ]+$' |uniq |wc -l)
UPGRADE=$(($UPGRADE - 1))

if [ $UPGRADE -ne 0 ]
then
    sudo update-pepperflashplugin-nonfree --install
fi

echo "$VERSIONS"

Check your Flash version
In general, this can be done on Adobe's site.
The full story
Here is the full story nicely written up.
Answer: Try installing Flash by entering the following command in the Terminal (make sure to shut down all running Firefox windows first)
sudo apt-get install adobe-flashplugin

Comment: I wouldn't have asked it if it had been as simple as that.
Comment: Well, it might be as easy as `sudo apt-get --reinstall install flashplugin-installer`. This did the trick for me on Xubuntu 12.04 LTS after an automatic update to Firefox 27.
Answer: I am running Ubuntu 12.04 64-bit with an Nvidia GeForce 8400 GS.
I have been having the same issue ever since I corrected another Flash issue on my system related to Nvidia GPUs -- see Flash video appears blue on this forum.  Following the workaround posted at the previous link stopped the unwanted behavior of all Flash video being tinted blue, but ended up causing the Flash plugin to crash nearly every time I attempted to watch a video online.
The solution for me was to look back at /etc/adobe/mms.cfg and remove everything but one line, which should read:
OverrideGPUValidation=true

This idea and others are discussed on ubuntuforums, and many other places.  Please try changing your mms.cfg (or creating it, if it does not already exist) and post back with your results.  Good luck!
Answer: As for the HTML5 video playback option available at some sites:
First, not all sites provide HTML5 videos as an alternative to Flash (hopefully, there will be more).
And second, whether your browser and the version you are using will support the HTML5 playback of a video on a site that provides such an option (like YouTube or VKontakte) will depend on the codec chosen by the site owners. For example, YouTube and VKontakte (a Facebook clone popuar in Russia) use different codecs for their HTML5 videos, which means that in Ubuntu 12.04 HTML5 video playback at VK.com works in Chromium, but not in Firefox (and in future, these browsers might swap their roles).
And third, some videos might appear to not have the HTML5 option on YouTube. (For example: https://www.youtube.com/watch?v=3SacL219sic&html5=True.) But thanks to the answer by Klementine, there is a trick useful for getting at HTML5 playback in these cases -- use the "emdedded" variant. (For my sample video: https://www.youtube.com/embed/3SacL219sic.) And it works!
Answer: First, you need to go to http://get.adobe.com/flashplayer/;
Then, select "APT for Ubuntu 10.04+".
A window should pop up prompting you to select a program to use the apt link: you need to direct it to /usr/share/software-center/software-center.
This file should be a Python script.
When it opens the Software Center, enable the source it tells you to.
Then, once it is done, hit the install button. You may need to restart Firefox for it to work, but that's how I did it, and it worked for me!
Comment: Sorry. I am on 13.04. It shows only tar.gz. and .rpm files.
Comment: if you go to get.adobe.com/flashplayer then there's a selection from the dropdown that says "APT for Ubuntu 10.04+" At least it shows up for me.
Answer: I managed to Enable the Adobe Flash plugin in Opera by following the instructions from this Russian post.
Let us begin installing Flash:

Install PepperFlash via apt: sudo apt-get install pepperflashplugin-nonfree
download & extract the Adobe Flash: https://www.adobe.com/support/flashplayer/debug_downloads.html

get the "Download the Flash Player Plugin content debugger (64-bit) - NPAPI" version (note that if your running on 32-bit architecture, you need to select the 32-bit one)

Extract: tar xvf <archive_name>
Move the file libpepflashplayer.so to /usr/lib/pepperflashplugin-nonfree/
Restart Opera. and you're done.

I can now see them installed:

checked on https://helpx.adobe.com/flash-player.html

and on about://plugins

How do I fix Flash issues?


How do we know how to perform salat?

Question: where does our knowledge of rulings concerning salat comes from.
What are the relevant hadiths and Quran verse that tells us how to perform salat
And How do we know which part of salat is fard and which is sunnah
Answer: These are two questions which need a certain elaboration to be well answered therefore I'll try to give a short answer with some hints.
Basically -you could take it as a rule of thumb- anything which is ordered in the Qur'an is fard (unless we find some exceptions or excuses). And anything which is ordered in the sunnah is at least sunnah and in worst case recommended.
For example if you want to check the ahadith on what is part of the prayer you may open in any hadith compilation the chapter or book of prayer and you will find therein a lot of hadith narrations or narrations that tells us everything about prayer, some of these might not address the HowTo, some would address specific cases etc.. As usually the Qur'an is explained by the doing of the prophet () which is the sunnah we refer to in the Islamic shari'a!
Prayer content of the Qur'an
In the Qur'an the prayer timings are more or less quoted and the Qur'an actually  (Does the idea of praying 5 times a day come from the Qur'an?) the Qur'an also emphasizes on the order of praying at specific timings (4:103). The qur'an covers the prayer of fear in the verses (4:102-103) and the prayer of night in some verses and especially in surat al-Muzzammil (73).And the Qur'an also quotes that we can pray in certain positions often these are quoted in verses that are more or less related to dhikhr Allah, but they are also quoted in the context of prayers as in (4:102):

... And when they have prostrated, let them be [in position] behind you and have the other group come forward which has not [yet] prayed and let them pray with you, taking precaution and carrying their arms.  ...

where sujud or prostration is clearly mentioned and one could easily conclude that other prayer positions must be held.
In the following I'll just quote a few verses of the Qur'an that are related on how to pray:
(4:103) is an example where the positions of prayer also mentioned:

And when you have completed the prayer, remember Allah standing, sitting, or [lying] on your sides.  ...

When Allah mentions worship he often mention both sujud/prostration and ruku'/bowing like in (2:125), (3:43), (22:26) and in (2:43) even in the context of the prayer.
Therefore scholars consider standing, bowing and prostrating (at least one time) as fard in the prayer (for a person who is able to do so).
Prayer content of the Sunnah
I won't quote the details, but I think among the best ahadith that shows how to pray you may find:

I was sitting with some of the companions of Allah's Messenger (ﷺ) and we were discussing about the way of praying of the Prophet. Abu Humaid As-Sa'idi said, "I remember the prayer of Allah's Messenger (ﷺ) better than any one of you. I saw him raising both his hands up to the level of the shoulders on saying the Takbir; and on bowing he placed his hands on both knees and bent his back straight, then he stood up straight from bowing till all the vertebrate took their normal positions. In prostrations, he placed both his hands on the ground with the forearms away from the ground and away from his body, and his toes were facing the Qibla. On sitting In the second rak`a he sat on his left foot and propped up the right one; and in the last rak'a he pushed his left foot forward and kept the other foot propped up and sat over the buttocks." (Sahih al-Bukhari)

or in another version:

Abu Humaid al-Sa'idi once told a company of ten of the companions of the Messenger of Allah (ﷺ) ; Abu Qatadah was one of them:
  I am one among you who is more informed of the way the Messenger of Allah (ﷺ) prayed. They said: Why, By Allah, you did not follow him more than us, nor did you remain in his company longer than us? He said: Yes. They said: Then describe (how the Prophet prayed). He said: When the Messenger of Allah (ﷺ) stood up to pray, he raised his hands so as to bring them opposite his shoulders, and uttered the takbir (Allah is the most great), until every bone rested in its place properly: then re recited (some verses from the Quran); then he uttered the takbir (Allah is most great), raising his hands so as to bring them opposite his shoulders; then he bowed; placing the palms of his hands on his knees and keeping himself straight, neither raising nor lowering his head; then raised his head saying: "Allah listens to him who praise Him"; then raised his hands so as to bring them exactly opposite to his shoulders; then uttered: "Allah is most great"; then lowered himself to the ground (in prostration), keeping his arms away from his sides; then raised his head, bent his left foot and sat on it, and opened the toes when he prostrated: then he uttered: "Allah is most great"; then raised his head, bent his left foot and sat on it so that every bone returned to its place properly; then he did the same in the second (rak'ah). At the end of the two Rak'ahs he stood up and uttered the takbir (Allah is most great), raising his hands so as to bring them opposite to his shoulders; then he bowed, placing the palms of his hands on his knees and keeping himself straight, neither raising or lowering his head: then raised his head saying: "Allah listens to him who praises Him"; then raised his hands so as to bring them exactly opposite his shoulders; then uttered: "Allah is most great"; then lowered himself to the ground (in prostration), keeping his arms away from his sides; then raised his head, bent his left foot and sat on it, and opened the toes when he prostrated himself; then he prostrated; then uttered: "Allah is most great"; then raised his head, bent his left foot and sat on it so that every bone returned to its place properly; then he did the same in the second (rak'ah). At the end of two rak'ahs he stood up and uttered the takbir (Allah is most great), raising his hands so as to bring them opposite to his shoulders in the way he had uttered the Takbir (Allah is most great) at the beginning of the prayer; then he did that in the remainder of his prayer; and after prostration which if followed by the taslim (salutation) he out his left foot and sat on his left hip. They said: You have spoken the truth. This is how he(peace be upon him) used to pray. (Sunan abi Daowd)

The Prophet (ﷺ) said: The key of prayer is purification; takbir (saying "Allah is most great") makes (all acts which break prayer) unlawful and taslim (uttering the salutation) makes (all such acts) lawful.  (Sunan abi Dawod)

Some scholars therefore considered the tasleem and the first takbir fard.
And we are also informed how not to pray in the sunnah for example in:

A man entered the mosque and started praying while Allah's Messenger (ﷺ) was sitting somewhere in the mosque. Then (after finishing the prayer) the man came to the Prophet (ﷺ) and greeted him. The Prophet (ﷺ) said to him, "Go back and pray, for you have not prayed. The man went back, and having prayed, he came and greeted the Prophet. The Prophet (ﷺ) after returning his greetings said, "Go back and pray, for you did not pray." On the third time the man said, "(O Allah's Messenger (ﷺ)!) teach me (how to pray)." The Prophet said, "When you get up for the prayer, perform the ablution properly and then face the Qibla and say Takbir (Allahu Akbar), and then recite of what you know of the Qur'an, and then bow, and remain in this state till you feel at rest in bowing, and then raise your head and stand straight; and then prostrate till you feel at rest in prostration, and then sit up till you feel at rest while sitting; and then prostrate again till you feel at rest in prostration; and then get up and stand straight, and do all this in all your prayers." (Sahih al-Bukhari)

which lead some scholars to consider toma'ninah calmness (الطُّمأْنينة) as essential and therefore fard part of the prayer. As the prophet () said: "Go back and pray as you didn't pray".

Beside this there's a general ruling which is taken as fard by all scholars from:

The reward of deeds depends upon the intentions and every person will get the reward according to what he has intended. So whoever emigrated for worldly benefits or for a woman to marry, his emigration was for what he emigrated for."  (Sahih al-Bukhari)

Finally books of fiqh are also full of the rulings of the prayers and their evidences.
And some scholars even arranged books telling us how the prophet () used to pray based on ahadith.
Also relevant:

What is the proof to pray Dzuhur/Asr silently? ALLAH in Al-Quran says 17/110
How can we offer Fard Namaz with just two people
How does one pray in congregation?
Is there Hadith for the Maliki way of praying?
How does the Maliki school make Tasleem at the end of salat?
What is the Hadith about missing the Takbeer E Oola of salah (takbir at the beginning of the prayer)?
Is there a sect-neutral tashahhud?

How do we know how to perform salat?


Alternator problems: First too much voltage now not enough

Question: I had to put in a new alternator in my 99 Isuzu Amigo. The old one burnt up. Everything seemed fine...output was around 14.4 volts, however, the plug that goes to the "S" & "L" terminals on the alternator had partially melted so I ordered a new one. Well, I put on the new plug by twisting the wires real good and covered them with heat shrink tubing. After doing that my battery light came on, my alarm no longer works and my OBD-II connector no longer works. The output voltage was reading around 15.6 volts. Then I read that the connections had to be soldered (not just twisted). So...I soldered the connections. Now, my battery light is no longer on but I still have no alarm or OBD-II connection and the voltage output is only 10.8 to 11.1 volts. Also, the battery is good and I can't find any blown fuses. HELLLLLLP!!
Comment: No blown fuses, how are the relays... When you put the wires together was the battery disconnected, have you checked all your fuses for an open ground and when you put the new wires onto the old plug, did you color code them or go off a wiring schematic ?
Answer: 15.6 V will probably not do it, but ECUs and parts of them have failed from over voltage.
I believe that on your alternator there is a voltage regulator which can be separately replaced.  Probably $15 to $20.
My suggestions are as follows:

Pull the alternator, and take it to the parts store.  Most of them have a tester to bench test an alternator.
Once you establish that the alternator is OK, reinstall it.
You should not have to run the engine to get the ODB-II port to work.  Simply having the ignition ON should give you access to the ODB-II interface.  If it doesn't work just on battery, you will have to hunt that down.
You say your old alternator burned up.  Do you know why?  Is there some electrical issue in the car which is drawing a high current, so that the alternator ran at full output for an extended period of time?
Are other electronics in the car, such as the radio, still working properly?

It is possible that your ECU has been damaged, but that cannot be determined just by the information you provided.
You will also need to find the root cause of the melting wires, the blown alternator  (if not simply old age), and any other car electrical problems.
If you have access to a DC clamp on ampmeter, it would be nice to know the current coming out of the alternator while the voltage is sitting at 11 v or so.
Comment: Thanks for your reply. The alternator was still under warranty so I just replaced it. The output voltage is ok so far but now the battery light is on> The battery is being charged though. (output is around 14.2 average). My OBD-II is still not working. My alarm appears to be working , however, the horn for the alarm as well as the main horn are not. (It seems I now have a silent alarm). I checked the fuses and they all seem to be ok. I'm really hoping it's not a damaged ECU but at this point I'm starting to wonder.
Comment: . So far, everything else seems to be working ok (all lghts, turn signals, hazard lights etc.) I'll check the current draw with my voltmeter.As to why the alternator burnt up in the first place...I'm really not sure. I do have a small oil leak close to where the alternator is as was wondering if oil getting into the alternator  could cause it to burn up (?). I have to add a quart of oil about every tow to three weeks. As far as testing the current draw, is it correct that I disconnect the main lead to the alternator and put the meter between the post on the alternator and the main lead?
Comment: First, I have not known an alternator to die because of too much engine oil.  I am sure it's possible, but I have seen many very dirty alternators, where engine oil and grime did not overtly cause them to burn up.  Secondly, you might look at a wiring diagram for your car. Is the alarm factory, or aftermarket? What do they, and the horns and the ECU have in common?  Thirdly, the vehicle horn is a fairly simple system electrically...essentially a momentary contact switch, a relay and a device which is a buzzer or vibrator connected to a sort of acoustic horn.  Actually, usually two. Hi/lo.
Comment: Where are you at in diagnosing this?


How many grams of gelatin are in stock/broth?

Question: How many grams of gelatin are in 1 cup of stock made from cartilaginous sources such as pigs or chicken feet?
Answer: You'll need to go by the consistency of the stock. If your cooled stock is just slightly gelatinous, but falls apart easily when handled, it's probably around 1%. If it is as solid as "dessert gelatin" (Jello), it's around 3% or more. (source: "On Food and Cooking")
Answer: This is going to be tough to answer. Too many variables.
I pressure cook all my saved chicken bones until they can be pulverized easily between two fingers (only about 1 hour). Then I reduce the stock from 3 quarts down to about one. When cooled and poured into a can-and-freeze jar it will typically gel at room temperature.
The answer depends highly on the amount of feet used, the amount of water it was cooked in and how much reduction is preformed.
Comment: @free: There are *way* more variables than that. The temperature of the water. The pH. The specific *animal* even makes a difference.  You have no hope of ever controlling all of these variables in a home kitchen.  Industrial processes involve a completely different method of gelatin extraction, and even they don't necessarily have consistent *quantity* at the output (they just guarantee quality).
Comment: I know there are variables but any value for those variables would be fine by me, e.g., 4 chicken feet boiled in 3 quarts water for 24 hours yields X grams.


How are winter tyres different from normal tyres?

Question: Using them all year round, is there a downside to them? Or is it just a matter of costs. I will refrain from further widening the questions scope.
Answer: Driving on winter tires in summer will wear them out MUCH faster. Winter tires are a different rubber compound that shouldn't be used in temps that are consistently above 40°
Answer: Yes, there is a downside.
Some winter tires are studded. They cause terrible air quality and pavement wear issues. They literally kill people, because of the poor air quality caused by them, but at the same time, cause less traffic accidents and save people. Needless to say, there is no reason to use such tires in summer.
It is necessary that a fraction of drivers use studded tires, because they modify the smooth ice on roads to be rough, so that non-studded winter tires can obtain useful grip. So, 100% studded => air quality and pavement wear issues, least amount of accidents, 50% studded / 50% non-studded => half of air quality and pavement wear issues, still acceptably low accident count, 100% non-studded => no air quality and excess pavement wear issues, but a terribly high accident count.
The main question is, should you use non-studded winter tires in the summer then? The answer is no. Due to the different rubber compound, they have poorer than optimal traction and wear extremely fast. Furthermore, the feel to the road is less direct, due to tread squirm.
At least where I live, it is legal to drive on non-studded winter tires in the summer. It is illegal to drive on studded winter tires in the summer. However, for best traction and lowest cost, it makes sense to use summer tires in the summer.
Comment: Sorry, live in a country where winter tires are obligatory in winter, in summer they usually use ordinary tires... However, if the winter tires are nearing the end of their life then people keep them on for the summer as a bit of extra noise does not make much difference and it saves the cost of new summer tires while using up the winter ones. In the area I am, most of the "run about" cars are all on winter tires even though we have just had temperatures of 30 plus degrees C...


What natural phenomena increase stratospheric ozone?

Question: Most of us know that the ozone layer gets depleted due to green house gasses and other factors. Which made me wonder, is there any natural phenomenon that causes an increase in ozone?
Answer: Like BarocliniCplusplus said, ozone is generated when you have a single free oxygen atom. This can come from photolysis of O2 in the upper stratosphere, or photolysis of ozone itself, or photolysis of NO2 in the troposphere. The stratosphere gets its NO2 from the breakdown of N2O by other radical species. But NO and NO2 both react with ozone, typically destroying it.
So if you want a natural process that would enhance ozone, I would look for a process that reduces the amount of N2O (or other ozone-depleting species) reaching the stratosphere. N2O is produced by bacteria in soils, so anything that suppresses that production -- especially in the tropics -- would enhance stratospheric ozone. Carbonyl sulfide (OCS) is another species that only photolyzes in the stratosphere and depletes ozone; its concentrations would similarly decrease if there were a decrease in transfer of it from ocean to atmosphere (it's a product of plankton). You could also have a meteorological effect that suppresses deep convection in the tropics, though I can't offhand think of what this would be.
If you're interested in understanding the specifics a bit more (I'm not great at summarizing all of the cycles involved), I recommend checking out http://acmg.seas.harvard.edu/people/faculty/djj/book/bookchap10.html. Daniel Jacob is a pretty influential atmospheric chemist, and he put his whole book online.
NB: NO2 destroys ozone in the stratosphere, but typically enhances ozone in the troposphere. This is because the troposphere has much, much higher concentrations of organic species and the hydroxyl (OH) radical. Instead of depleting O3, the NO produced when NO2 photolyzes can react with HO2 to re-form NO2 and OH, so the ozone-depleting nature of NO is reduced. Since that process re-forms OH, OH can attack organic species and leave the H radical, which then pulls in O2 to form HO2, which will later end up producing an odd oxygen and thus form ozone. (Sorry if this is a bit rambly. I haven't tried to summarize all of this before, so let me know what things are confusing.)
Answer: Atmospheric ozone is regularly produced by solar radiation energizing O(2) to split it and recombine it into O3.  Similarly, lightning also produces ozone at both low altitudes and higher in the atmosphere to recharge this layer.
Typical human produced ozone is a straight pollutant and does not recharge the "ozone layer".
Answer: Yes, there are ways of regenerating atmospheric ozone. Generally, you need an oxygen atom and an oxygen molecule to react to form ozone (as well as something to take off excess energy). The generation of the oxygen atom has a couple pathways, but near the surface, it is mostly generated from the photolysis of nitrogen dioxide.
Comment: CFCs are greenhouse gases and they do deplete ozone
Comment: CFCs are greenhouse gases that *also* deplete ozone. Not all greenhouse gases deplete ozone.
Comment: You are right, CFC's are one type of greenhouse gases, but so are water vapor, carbon dioxide, and ozone. Had the original question said CFCs or a greenhouse gas, I would definitely be in the wrong. But my answer is at least justifiable by the fact that ozone is a greenhouse gas. I have changed it since the question has been edited.


How do solar eclipse(s) work(s) in a binary stars system?

Question: Say a terrestrial planet is orbiting two stars as if they're a single gravitational well.(I haven't worked out the distance yet as I still on the phone...) I don't need the planet to be habitable but it does come in full packages; moons and lots of it. So how would the spectacular event differs between ours and this? While you're at it could you do lunar eclipse too? The terrestrial planet is as five times as big as Earth and as for the pair of identical Sun-like stars I think they are cute!
Comment: Keep in mind that the spectacular solar eclipses we get on Earth are the result of an exceptionally unlikely set of circumstances, resulting in the Earth's Moon subtending almost exactly the same angle as seen in the sky from Earth as does Earth's Sun. That's a consequence of the relative sizes of the Moon and the Sun, and the relative distances from the Earth to the Moon and the Sun respectively. Insofar as I know, at least in our solar system, even with the abundance of moons around other planets, Earth is unique in this regard.
Comment: I started to answer this, and realized there are two many possibilities. We need the mass and luminosity of the two stars (so we can calculate the barycenter around which the planet orbits), orbital characteristics of the planet (inclined orbit? eccentricity? distance from the barycenter?), and characteristics of the moons (orbital inclination, size, distance, eccentricity). Needs specifics or it is too broad.
Answer: There are numerous possible scenarios.

An annular eclipse of one star if its angular diameter is larger than that of the moon, or total eclipse if it isn't, with the other star providing daylight. Partial eclipse is possible whether the angular diameter of the moon is larger or smaller.
An annular, total or partial eclipse of both stars while one is hidden behind the other, looking similar to when there is only one star.
A partial eclipse of both stars while they are close together in the sky (i.e. the moon covers a part of each).
Or one star can be partly hidden behind the other, so that there is a total or annular eclipse of one of them while the other is only partly eclipsed.
An annular, total or partial eclipse of one star shortly after the first dawn or before the last sunset, so that the other star is still hidden, also looking similar to when there is only one star.

Expect to see less of the corona than on Earth. The stars are close together so it will be outshone by the other star when only one is eclipsed. When there is a total eclipse of both stars it should be visible, though the angular size of the moon probably isn't so neatly matched (as on Earth) so the inner part (or more) of the corona may be also hidden.
Lunar eclipse is more similar to those on Earth. An eclipse will happen when the moon is in the umbra of the planet's shadow as seen in the light from either star.

This shadow will no longer be circular, depending on how the stars are arranged. In other words, if one star isn't behind the other, the shadow will look like the overlapping part of two mostly overlapping (since the stars are close together in the sky) circles. It may be possible to see this dark shape on the moon, with illuminated parts on either side.
If the angular size of the moon is small enough, there can be a total lunar eclipse. Unlike on Earth, if the orbit of the moon is highly inclined this may start and end as a dark wedge moving onto the moon, due to the previous point.
Eclipses with one star behind the other are similar to those on Earth, except that whether total eclipse or annular eclipse of the moon is possible depends on angular sizes.

There will still be some darkening in the penumbra illuminated at least partly by at least one of the stars, as in the Earth's shadow on the moon.
Answer: Your moon would be there for the effects only for a while.
The stars orbit around each other, so the gravitational force on the planet and moon would change. That means that the planet's orbit isn't a ellipse; the planet will "wobble". The moon, in the planet's gravitational field, will "wobble" too - but because the planet wobbles around it.
Soon (a few years to millions of years, but most likely years), our moon would get wobbled too far off it's orbit; One of the following scenarios would happen:

Our moon gets way too far towards our planet; It crashes at a very small angle and part of it gets into space

It gets so close to our planet, it "uses" it as a gravitational slingshot and gets propelled into the stars or to open space

It starts to orbit closer and closer to the planet until it gets torn to parts due to the Roche Limit (the minimum distance to which a satelite can approach its primary body without being torn apart by tidal forces). It will maybe steal some of the water in the oceans, if any.

It starts to orbit farther... and farther... until it loses Planet's gravity and gets disintegrated by one of the stars, or slingshoted into space

It gets too far from out Planet; it will orbit as a planet around the binary star system

According to this planet simulator and many, many tries, scenario #5 is the most probable (67/80).
But until that happens...
Assuming each sun and the moon covers the same angle distance as here on Earth:
You'll have eclipses a bit (almost 2x) more often; The main change is that partial eclipses, eg. when at least a part of one sun is visible almost 10x more often against full (both suns covered) eclipses; Eclipses covering one sun only would be 2x more often in this binary system then in a "normal" one.
If the moon gets torn apart by the gravity of the planet, a spectacular view would occur: The planet would have it's own rings! Imagine half the derbis blocking the sun... and a few years later, crashing into your spaceship! Astonishing!
Helpful links, some used to calculate values:

Object orbit simulator

Is there a simple formula to calculate solar eclipse timings from any position on Earth?

Eclipses and Transits, nasa.gov

nasa.gov data about eclipses

Eclipse finder (Earth only)

How many solar eclipses per one year?

Prediction and calculation of solar eclipses

Wikipedia: Roche Limit


Difference between j, q, x sounds and z, c, s sounds?

Question: I'm struggling with some sounds in Chinese. I can't distinguish J, Q, X initials and Z, C, S initials. I feel that they are pronounced similarly.
Am I right? Can you tell me how to pronounce these initials correctly?
Comment: Try these English spelling for J, Q, X: gee, chi, shi(but with smiling face). And for Z and C, try to pronounce from your teeth.
Comment: Updated, gee, chee, shee, with smiling face.
Answer: most of the time you don't need to distinguish them. JQX are always followed by i or ü, which never happens with ZCS. In fact, in many dialects, JQX are pronounced as ZCS. People will understand you with 0 confusion or information loss.
On the other hand, if you do wish to improve your pronunciation, try this:

ZCS are articulated between your teeth and gum. English J and Sh are pronounced more back. JQX are even more back, but before palatal consonants like y in "yes" or German ch in "China", which is why they're called alveolo-palatal.
Just try to feel the continuous spectrum, it'll be hard to step on the exact point where JQX are pronounced, but it's definitely reachable. With sufficient training you'll surely remember that location.
Answer: The way I think of it is that they are pronounced similarly, except they are used with different vowels, as you can see in a Pinyin table. Vowels starting with an "i" or "ü" sound are only used with J, Q, and X (except that "ü" is written as "u" since there is no need to disambiguate), whereas vowels starting with an "a", "e", "o", or "u" sound, or the special "i" sound like in "si", are only used with Z, C, and S.
Answer: Q = Ch (as an "chocolate")
X = Sh (as in "shower")
J = J (as in "Jennifer")
Z = Ds (as in "beds", plural of "bed")
C = Ts (as in "cats", plural of "cat")
S = S (as in "sand")


How can I view BASIC code hidden by SYS?

Question: I ran a validation of an old disk, and it turns out this ruined a game (won't load) and deleted my old high score list on David's Midnight Magic. I would like to edit the code to get the high score list back, but when I load the program and type list, it displays 711 SYS(2069) DMM. What does this mean? I notice a similar message from Jumpman Jr. (which incidentally allows me to run the game by typing the sys command). Further, as per above, how can I move past this and actually view the code? The high score list must be there somewhere.
Comment: The *Validate* DOS command rearranges the free blocks on the disk. If the highscore list was hidden somewhere in the free blocks (not unlikely), it's gone now.
Comment: It's possible that the "validation" destroyed the high score list entirely. Which tool did you use to validate it? (This is tangential to the actual question.)
Comment: I typed first `OPEN 15,8,15` then `PRINT#15,"V"`. Before doing anything else, I allowed the drive to finish, even though the screen displayed READY. I am using an original CBM64 with a 1541-II floppy drive, so no emulator. In other words: No tools in particular, but the commands supported natively by the floppy drive.
Comment: Make sure everything you want to keep comes off that floppy; I think it is dying.
Answer: SYS is the BASIC instruction to execute a routine written in machine code.  There is no more BASIC code to view, the entire game is implemented as a machine code program, and the BASIC only exists as a stub to make it easier to load and run.
The best approach to viewing what the code actually does and potentially being able to restore your table (if it is still there at all) is to load the program into an emulator that has an integrated machine-level monitor/debugger.  The most popular C64 emulator is VICE and although I've never used it so can't comment on how good it is, it definitely includes a monitor with the ability to disassemble code.
Comment: How would you go about doing that when it is saved on LD floppies? Is there any way to connect a 1541-II to a modern PC? I know it runs on a serial connection. Might there be ways to connect it to an IBM serial connection?
Comment: I'm afraid I've never worked with C64 disks at all, so have no idea about that.  If there isn't a question here on the subject already, it would be a very good topic for a new one...
Comment: Have a look at the ZoomFloppy: http://www.go4retro.com/products/zoomfloppy/
Answer: A lot of Commodore 8-bit computer games used a disk that had random-access files on them.  This means they were written directly to disk blocks, not via a program, sequential or relative file, which are the three ways Commodore DOS officially supports files.
Random files are protected by having the programmer manually mark the blocks as being used.  This works perfectly well... unless you validate the disk like you did.  When this happens, Commodore DOS scans the disk and sees if any blocks (sectors) aren't tied to a file in the disk directory.  This means all PRG, SEQ and REL files will continue to be protected (or re-protected, if some of the blocks were accidentally de-allocated).  However, it means if there are any random file blocks, they will be marked as being available.
Even now, you still don't have a problem, but if you write a file to the disk, there is a chance DOS will use a block that had a random file on it, and this data will then be overwritten.
I suspect this is what happened to you, in which case you'll need a backup to restore your high score list (now you've learned the importance of backups :) ).
Answer: As Jules said, SYS is the BASIC instruction to execute a routine in machine code.  Very much like GOSUB.  USR is the equivalent of DEF FN.
There are 2 ways in which machine code is loaded

It is saved with the code.  This is great against piracy but it is a pain to modify.  Also any minor mod you make might wipe out the assembler.
There is a bunch of data statements with a whole bunch of numbers and somewhere in the code, there is a loop which reads the data and pokes it to consecutive locations.

If the second method is used, you're in luck.  Somewhere in the code, it will overwrite one of the data statements and resave the file.  All you have to do is convert the bunch of numbers to assembler to work out what it is doing.
If you haven't used 6502 assembler before be aware of the switch statement trick in 6502 assembler which jumps to the middle of the BIT instruction.
Also noticed that the instruction said
711  SYS(2069) DMM

DMM probably means David's Midnight Magic.  There may be others using the same routine which pass different parameters across.


Does a marriage last beyond death?

Question: Looking for some sources as to the connection (if any) between husband and wife in the afterlife, at least in the simple case where neither remarried.
Comment: Can you be a little more specific please ? Do you mean a Halachic connection ? Techiat HaMaytim ?
Comment: any kind of connection in the afterlife or perhaps they part ways after death and that's all folks
Comment: Today is your lucky day. Seems like the question is well addresssed here: http://judaism.stackexchange.com/questions/26901/if-a-woman-had-more-than-one-husband-to-which-would-she-be-united-at-the-resurr
Comment: [אמרה ליה ניחא לך דמיכל אכלי כולי עלמא אפתורא דמשלם ואנן אפתורא דמחסר](http://en.wikipedia.org/wiki/Hanina_ben_Dosa#The_Miracle_of_the_Golden_Table-Leg) ([*Ta'anis* 25a](http://hebrewbooks.org/shas.aspx?mesechta=10&daf=25&format=pdf)).
Answer: Although I can not preclude any other opinions on the topic Rav Saadai Gaon writes:

Likewise, apropos
   of the subject of marriage, I will say that our minds are capable only of grasping  present state. As for what is forbidden or permitted in a situation that has no parallel at all in our earthly existence, such as whether or not marriage bonds will be abrogated for those who are resurrected, we need not concern ourselves therewith, since there will be available in the beyond prophets and prophetic inspiration and divine guidance. (Emunos v'Deos 7:7, translation Friedlander, The book of Beliefs and Opinions, Yale)
Answer: In the Cave of Machpelah, Abraham lies in Sarah's arms while she gazes at his head, (B. Bath 58a).
The Mhrs"a in his aggadic explanations writes that righteous' deaths are likened to sleep, so Sarah was looking at his head while he slept, (perhaps inspecting it?), as is Derekh Eretz for a one to do for a sleeping person. He cites the wife of Rabbi Elazar Brebi Shimon's wife, B. Metz 84b, who inspected her dead husband's hair regularly. Obviously both Abraham and Sarah are dead during this story. It would seem that There is some sort of interaction or connection between a couple after death.
The Ben Jehoaida, writes that the whole experience was a dream to be interpreted allegorically, and that it refers to how Abram's name was changed to Abraham by way of a heh that was taken from the yud at the end of Sarah's name, and how that heh interacts with the aleph of Abraham's name. According to this interpretation, a transcending connection between the two names is suggested.
Man comes into the world with his portion, but woman comes into this world clean, her fortune being dependent upon the man's. Man pursues woman, like a person who lost something, in this case his rib/side while he slept. Woman looks up at man, from whom she was created, during intimacy. (Kiddushin 2b, Niddah 31b, see Rashi, Mhrs"a in both places. Probable context).
These sayings imply that the woman was taken from the man at some point. That she comes from him implies that they were connected at some point, and clearly not in this world.
Comment: thanks. but could be the tzadikim are in a different category as the masses.
Comment: @ray added in more generally applied sources.
Answer: Rav Elchonon Wasserman in Kovetz Shiurim chelek beis os 28 says that the wife of Eliyahu Hanavi was not allowed to marry because he did not go through "death" even though he was no longer alive in the normal sense.  So at least according to Rav Elchonon there is some kind of marital connection that transcends this world.
To clarify: R' Elchonon proves from the fact that the gemara asks "misas haba'al minayin" (From where do we know that the death of the husband permits a woman to remarry?) that his not being alive would not automatically end the marriage.  Rather, it is the "act of death" that ends the connection.  Therefore, Eliyahu who did not have an "act of death" is still connected to his wife.
Comment: maybe it is because he was halachically still alive regarding the kidushin of his wife.
Comment: She could be an eshet ish even if there is no ish.
Comment: @ray R' Elchonon's starting assumption is that even though she is no longer אשת רעהו there was no "act of death" to end the marriage - see it yourself, but it is pretty clear he accepts that Eliyahu is not alive as far as marriage is concerned - his whole point is to prove that not being alive is not enough to end a marriage.
Comment: @DoubleAA - That is kind of my point - even though he is no longer alive, there is still a connection created by the marriage.  I acknowledged in my answer that this is not a direct correlation to "the afterlife" but at least that marriage can exist after one party is not alive.
Comment: @YEZ My point is there doesn't need to be a marriage (at least not from the husband's perspective) for the issur eshet ish to remain.
Comment: I think the issur is indicative of the marriage although I can't prove it.

Does a marriage last beyond death?


Support Vector Machines

Question: What is it the relationship between the number of support vectors in an SVM and its generalization ability?  When lots of support vectors are used to classify, is the error rate minimized, but only to certain threashold?
Comment: Some more detail would be helpful, and would prevent your question from being closed as not a real question.
Comment: 1. for this audience define (or point to definitions of) support vectors and generalization. 2. Define the "error rate" (since there are different kinds of error)
Comment: Should I take a crack at restating the question to what I think it's asking?
Answer: The answer to your question is a bit tricky and here are good lecture notes to read to understand the various generalization error bounds. Let me try to summarize what's happening with SVMs and their generalization.  These PAC bounds are also found in "An Introduction to Support Vector Machines: And Other Kernel-Based Learning Methods" by
Cristianini and John Shawe-Taylor.
Assuming a linear classifier correctly classifies all training examples (separable case), one bound (Vapnik '95 (I think)) on the generalization error of a linear classifier is (ignoring log factors):
$$
\epsilon = \tilde{O}\left(\frac{1}{n}\left( \frac{R^2}{\gamma^2} \right)\right),
$$
where $R$ is a bound on the size of the vectors, $n$ is the number of samples, and $\gamma$ is the margin, which is the distance to the support.  This bound says that the margin (the only quantity the learner has control over if the number of training examples are fixed), is an important quantity to maximize in SVM.
However, there is an intuition the margin is maximized in sparse solutions, and the sparseness of a solution is measured by the number of support vectors, so there is a relationship between the generalization bound and the quantity you're interested in.
Another relevant bound for any classifier (not just the linear case) is the following "compression bound" (Littlestone and Warmuth '86), which basically says that if a classifier gets $n$ examples right but can be obtained by training it on just $m$ examples then you can bound its generalization error by
$$
\epsilon \approx \frac{m \log n}{n-m}.
$$
Here, you can think of $m$ as the number of support vectors.  This directly relates the number of support vectors to the generalization error.
These two bounds help explain the interplay between the margins, the number of support vectors, and the generalization ability of an SVM (in the separable case).  In the non-separable case where you do not classify all training examples correctly, you get slack variables, slightly messier bounds, etc.
Comment: I do not really understand all these bounds. How do we know $R$ and $\gamma$ a-priori?! Seems to me that all these bounds are a-posteriori bounds, therefore one still cannot know how to choose $N$ to achieve a desired $\epsilon$ in the generalization error. Am I wrong?!
Comment: Unless you know something about the target distribution, you are right -- these are generally problem-dependent parameters that are not known in advance.  This is still a valid bound.  In practice, though, you have as much data as you have, and you use as much as you can.
Comment: I see your point and I understand that in practice it works. However, in theory, using more samples does not guarantee that the expected generalization error decreases. I mean that only upper bounds on the generalization error are known.
Answer: See Theorem 6.27 in "Structural risk minimization over data-dependent hierarchies" (Shawe-Taylor et al., http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=705570&tag=1) attributed to Littlestone and Warmuth, "Relating Data Compression and Learnability".

Support Vector Machines


Define "difficultyHardforkTransition" parameter?

Question: I have looked through all of the glossaries I know of for genesis/chain spec files but I don't see this one.  Can anyone tell me what "difficultyHardforkTransition" means?
Answer: Looks like this has been defined for a while - it's not new code. It also seems like the value is set to 0x59d9 (= 23001) in the Parity spec, which doesn't equate to any of the public hard forks. This isn't defined in the Geth code. Someone from the Parity team may have a clearer explanation.

Looking in the Parity Master branch, in ethash.rs:
/// Transition block for a change of difficulty params (currently just bound_divisor).
    pub difficulty_hardfork_transition: u64,

Used in the following way in the calculate_difficulty() function (also in ethash.rs):
    let difficulty_hardfork = header.number() >= self.ethash_params.difficulty_hardfork_transition;
    let difficulty_bound_divisor = if difficulty_hardfork {
        self.ethash_params.difficulty_hardfork_bound_divisor
    } else {
        self.ethash_params.difficulty_bound_divisor
    };

So we check the current block number against the value in difficulty_hardfork_transition, and then use a different bound divisor for the calculation of the current block difficulty if we're past the block where the fork was defined.
You can check in that function how the bound divisor is normally used in the difficulty calculation. Looking at couple of example spec files, it looks like the bound divisor is set to a lower value when a fork occurs.
Comment: Thank you for this but I've been reading and re-reading this for about 30 minutes and I don't know what it says.  For example: what is a "bound divisor"?  What is a "bound" for that matter?  And "hardfork"? I'm not dumb I just don't know this very specific terminology.  I think this code shows "difficulty_hardfork" is being evaluated as if it is greater-than-or-equal-to "difficulty_hardfork_transition" but that doesn't tell me what "difficulty_hardfork_transition" is.
Comment: PS I know what a hard fork is in general obviously.  But how does it apply here.  Which fork is being referenced?  Etc.