Inertia on relativistic mass when particle is near speed of light

Question: Inertia is directly proportional to mass but what happens when something travel to speed near to light. Its relativistic mass tends to infinity but that is false mass so I want to know if inertia is applied to relativistic mass. Because if we infinite the mass then the inertia would also be infinite then it will never reach speed of light.
Answer: By inertia I assume you mean momentum. The momentum is related to the energy of the object by:
$$ E^2 = p^2c^2 + m^2c^4 $$
and to the velocity by:
$$ p = \frac{mv}{\sqrt{1 - \frac{v^2}{c^2}}} $$
The momentum does indeed tend to infinity as $v \rightarrow c$, but note that it will never reach an infinite value because no massive object can travel at the speed of light so $v$ never reaches $c$.
Comment: @Danu: *inertia* is one of those common terms that has no precise meaning (and isn't used by physicists!). But I'd guess it's generally used to mean that proprty of a body that makes it require a force to stop it. Force is of course the rate of change of ...
Comment: *"By inertia I assume you mean momentum."* Eh.. what? :P As far as I know, inertia of a body is (vaguely!) defined as "the (inherent) quantity that causes a body to resist acceleration". My guess is that it's ill-defined in relativity (speeding up by a certain amount may cost more than stopping altogether, so it should become dependent on $F\cdot v$, and lose its inherent status).
Comment: Even if lacking a precise definition, I still think we can be certain it is *not* momentum (my "definition" above makes this clear, but it appears that you may simply disagree on this definition). It is not important in any case, so let's just leave it at this :)
Comment: The books I use define inertia in a qualitative way "the property of resisting acceleration" and momentum and a quantification of a body's inertia between two different states of motion. That said, I believe that you find considerable variation in the precise meaning of "inertia" assigned by different texts.
Answer: Particles that have no mass, as photons, have momentum based on their energy, more especificaly on the relation
$$p=\frac{E}{c}$$
Where $p$ is the momentum, $E$ is the energy and $c$ is the speed of light.
You can think of it intuitively by noticing Einstein's famous equation, $E=mc^2$, and substituting it on the classical momentum formula $p=mv$, using $c$ in $v$'s place.
Answer: A Non-Relativistic Interpretation of Relativistic Results
Million years ago, when self-studying special relativity, an exercise was created in order to understand non-relativistically the relativistic result that a force could not accelerate a particle to speed greater than $\:c\:$. The exercise, the Figure and the solution are already in LaTeX and are copy-paste here. May be is useful.
The solution to the following exercise yields a non-relativistic interpretation of the relativistic result that energy $\:E\:$ has inertia, that is resistance to be accelerated, as material objects. The inertia of material objects is expressed by their inertial mass $\:m\:$ while the inertia of energy $\:E\:$ is expressed by its mass equivalent$\: m_{E}=E/c^{2}\:$. Also, based on this interpretation, an explanation of the impossibility of a force to accelerate an object to velocity greater than that of light ($c$) is given.

A body of mass $\:m_{o}\:$ initially at rest is moving on a surface without friction under the influence of a constant force $\:\mathbf{f}\:$, as in Figure above.  As it is moving, it is carrying away material from a straight line above it. The straight line has a constant linear mass density $\:\rho_{\ell}=f/c^{2}\:$, where $\:\rm{f}\:$ the magnitude of the constant force $\:\mathbf{f}\:$ and $\:c\:$ a quantity with dimensions of speed.
The exercise concerns the determination of the following :
(a) the position $\:x(t)\:$, the velocity $\:\upsilon(t)\:$ and the mass $\:m(t)\:$ as functions of time.
(b) any explicit relation, if there exists, between above quantities.
Solution :
For the mass we have
\begin{equation}
dm=\rho_{\ell} dx=\dfrac{f}{c^{2}}dx \Longrightarrow
\nonumber
\end{equation}
\begin{equation}
m\left(x\right)=m_{o}+\dfrac{f}{c^{2}}x
\tag{01}
\end{equation}
Now,
\begin{equation}
f=\dfrac{dp}{dt}=\dfrac{d\left(m\upsilon\right)}{dt}=m\dfrac{d\upsilon}{dt}+\upsilon\dfrac{dm}{dt}
\tag{02}
\end{equation}
that is
\begin{align*}
fdx & =\left( m\dfrac{d\upsilon}{dt}+\upsilon\dfrac{dm}{dt}\right)\upsilon dt=m\upsilon d\upsilon +\upsilon^{2}dm =\dfrac{1}{2}md\upsilon^{2}+\upsilon^{2}\dfrac{f}{c^{2}}dx\\
& =\dfrac{1}{2}\left(m_{o}+\dfrac{f}{c^{2}}x\right) d\upsilon^{2}+\upsilon^{2}\dfrac{f}{c^{2}}dx
\end{align*}
so
\begin{equation*}
\left(1-\dfrac{\upsilon^{2}}{c^{2}}\right)fdx = \dfrac{1}{2}\left(m_{o}+\dfrac{f}{c^{2}}x\right)d\upsilon^{2}
\end{equation*}
Separating the variables $\:x\:$ and $\:\upsilon \:$
\begin{equation*}
\dfrac{fdx}{\left(m_{o}+\dfrac{f}{c^{2}}x\right)} = \dfrac{1}{2}\dfrac{d\upsilon^{2}}{\left(1-\dfrac{\upsilon^{2}}{c^{2}}\right)}\:\Longrightarrow \: \dfrac{fdx}{\left(m_{o}+\dfrac{f}{c^{2}}x\right)} = \dfrac{1}{2}\dfrac{d\upsilon^{2}}{\left(1-\dfrac{\upsilon^{2}}{c^{2}}\right)}
\end{equation*}
or
\begin{equation}
\dfrac{d\left(m_{o}+\dfrac{f}{c^{2}}x\right)}{\left(m_{o}+\dfrac{f}{c^{2}}x\right)} =\;-\; \dfrac{1}{2}\dfrac{d\left(1-\dfrac{\upsilon^{2}}{c^{2}}\right)}{\left(1-\dfrac{\upsilon^{2}}{c^{2}}\right)}
\tag{03}
\end{equation}

Note: We don't know a priori that the expression $\:\left(1-\dfrac{\upsilon^{2}}{c^{2}}\right)\:$  will not take negative values as the body moves in time. Since at $\:t=0\:$ the body is at rest ($\:\upsilon = 0 \:$), the value of this expression is positive ($\:=1\:$) at the beginning . Our analysis will prove then that this expression remains always positive. Anyway, to overcome this difficulty we could do something like this :
Since
\begin{equation}
\dfrac{dx}{x}=\dfrac{1}{2}\dfrac{dx^{2}}{x^{2}}
\nonumber
\end{equation}
equation (03) can be written as
\begin{equation}
\dfrac{d\left(m_{o}+\dfrac{f}{c^{2}}x\right)}{\left(m_{o}+\dfrac{f}{c^{2}}x\right)} =\;-\; \dfrac{1}{4}\dfrac{d\left(1-\dfrac{\upsilon^{2}}{c^{2}}\right)^{2}}{\left(1-\dfrac{\upsilon^{2}}{c^{2}}\right)^{2}}
\nonumber
\end{equation}
so that in the equations that follow to replace the expression  $\:\sqrt{1-\dfrac{\upsilon^{2}}{c^{2}}}\:$ by
$\:\sqrt{\left\vert 1-\dfrac{\upsilon^{2}}{c^{2}}\right\vert}\:$.

Integration yields
\begin{equation}
\ln\left(m_{o}+\dfrac{f}{c^{2}}x\right) =\;-\; \dfrac{1}{2}\ln\left(1-\dfrac{\upsilon^{2}}{c^{2}}\right)+C\:\Longrightarrow \: \left(m_{o}+\dfrac{f}{c^{2}}x\right)=C\cdot\left(1-\dfrac{\upsilon^{2}}{c^{2}}\right)^{-\frac{1}{2}}
\nonumber
\end{equation}
At $\:x=0\:$ we have $\:\upsilon=0\:$, so $\:C=m_{o}\:$ and above equation yields
\begin{equation}
x\left(\upsilon\right)=\dfrac{m_{o}c^{2}}{f}\left(  \dfrac{1}{\sqrt{1-\dfrac{\upsilon^{2}}{c^{2}}}}-1\right)
\tag{04}
\end{equation}
Replacing $\:x\:$ by this expression in equation (01) yields
\begin{equation}
\bbox[#FFFF88,5px,border:1px solid black]{
m\left(\upsilon\right)=\dfrac{m_{o}}{\sqrt{1-\dfrac{\upsilon^{2}}{c^{2}}}}}
\tag{05}
\end{equation}
Solving (04) with respect to $\:\upsilon\:$ we have
\begin{equation}
\left(\dfrac{\upsilon}{c}\right)^{2} = 1-\dfrac{1}{\left(1+\dfrac{f}{m_{o}c^{2}}x\right)^{2}}
\tag{06}
\end{equation}
that is
\begin{equation}
\upsilon\left(x\right) = c \sqrt{1-\dfrac{1}{\left(1+\dfrac{f}{m_{o}c^{2}}x\right)^{2}}}
\tag{07}
\end{equation}
From this last equation we'll find the function $\:x\left(t\right)\:$ :
\begin{equation}
\dfrac{dx}{dt} = \upsilon = c \sqrt{1-\dfrac{1}{\left(1+\dfrac{f}{m_{o}c^{2}}x\right)^{2}}}
\tag{08}
\end{equation}
Changing the variable $\:x\:$ to $\:y\:$ where
\begin{equation}
   y=1+\dfrac{f}{m_{o}c^{2}}x
\tag{09}
\end{equation}
and since from this
\begin{equation*}
dx =\dfrac{m_{o}c^{2}}{f}dy  \quad  \text{and} \quad y>1
\end{equation*}
equation (08) yields
\begin{equation*}
\dfrac{y}{\sqrt{y^2-1}}dy =\dfrac{f}{m_{o}c}dt
\end{equation*}
or
\begin{equation}
d\left(\sqrt{y^2-1}\right) =\dfrac{f}{m_{o}c}dt \:\Longrightarrow \:  y^2 =\left[ \left(\dfrac{f}{m_{o}c}\right)t + \text{constant}\right]^{2} +1
\tag{10}
\end{equation}
Since $\: t=o \Rightarrow x=0  \Rightarrow y=1 \Rightarrow \text{constant}=0 \:$, returning to variable $\:x\:$
\begin{equation}
x\left(t\right)=c \left[\sqrt{t^2+\left(\dfrac{m_{o}c}{f}\right)^{2}}-\left(\dfrac{m_{o}c}{f}\right)\right]
\tag{11}
\end{equation}
Inserting this expression of $\:x\:$ on one hand in (07) yields
\begin{equation}
\upsilon\left(t\right)=c \sqrt{1-\dfrac{1}{\left(\dfrac{f}{m_{o}c}t\right)^2+1}}
\tag{12}
\end{equation}
and on the other hand in (01) gives
\begin{equation}
m\left(t\right)=\sqrt{m_{o}^{2}+\left(\dfrac{f t}{c}\right)^{2}}
\tag{13}
\end{equation}
From above equations we have :
\begin{equation}
\lim_{t\rightarrow +\infty}x\left(t\right) = +\infty
\tag{14}
\end{equation}
\begin{equation}
\bbox[#FFFF88,5px,border:1px solid black]{
\lim_{t\rightarrow +\infty}\upsilon\left(t\right) = c \;,\quad \upsilon\left(t\right) < c}
\tag{15}
\end{equation}
\begin{equation}
\lim_{t\rightarrow +\infty}m\left(t\right) =  +\infty
\tag{16}
\end{equation}
The force could not accelerate the particle to speed greater than $\:c\:$ because its work is feeding continuously back as mass (inertia) to this particle.
Comment: The problem with taking $\gamma m v$ as "inertia" in relativity is that it is not correct for forces applies transverse to the current direction of motion. See for instance http://www.mathpages.com/home/kmath674/kmath674.htm . To go this route you end up with two different relativistic inertias for the same particle (one in the direction of boost and one perpendicular to boost). People have gone that road in the past, and some defined it as clear and useful, but I never mastered it to my own satisfaction.
Answer: Thanks.  Looks good.  I trust there are no errors.  Saved me a bunch or work.  Let me share the reasons for the request.
Say you have an interstellar craft which, though having only a modest thrust, can just keeps the foot on the gas without stop, if so desired.  So, given that one will want to stop, eventually, when is it good to turn off the thrust?  The advantage to keeping the gas on is that hibernating passengers will age less, and that, if you are looking for an exoplanet, how much ground can you cover?  (If that sounds like a book, well ...)  And yes, if you are only turning the craft about and using the same thrust to stop, it will take the same time to stop as you spent accelerating.


Unable to get members of Universal Distribution List using Powershell

Question: I am trying to write a script to list out all members of a "Universal Distribution List" using Powershell.  However I keep getting an empty result set back.
When I run the following command against a "Global Distribution List" it works fine and I can see who belongs to it.
<code>dsquery group -name "SomeGroup" | dsget group -members -expand
</code>
However as I mentioned when I run this against a "Universal Distribution List" I get no results.  Can anyone help?
Answer: take a look at the quest AD cmdlets.


What is this symbol, showing a wavy line crossed by an arrow?

Question: What is the following electrical symbol, used in the EU?

From here:
Answer: I don't know whether the EU assigns a special meaning to that symbol but the wavy line means "AC power" and the diagonal arrow means "adjustable" or "variable". So, given this is a wireless switch, that output is the switched hot line. The outer "N" and "L" terminals are the neutral and hot supply connections, respectively, and the inner "N" is the neutral output connection.
Comment: @Sabuncu: OK well in this case it probably means "switched". As in, that is the controlled AC output of the device. The "N" ones are neutral and the "L" one is the constant input AC voltage (line).
Comment: I would like to believe you, but I saw this in the installation documentation for a wireless wall switch where it says nothing about the switch being intended for use with a dimmer.  I have updated the question with the picture of the documentation. Thanks.
Comment: I should have supplied the additional information up front, my fault.  If you could replace your answer with your comment above, I will accept it. Thanks again.


AWS Cognito Pre authentication/Define Auth Challenge lambda hooks are not invoked if user doesn't exist

Question:

I'm essentially trying to create a middleware that will do some work before logging a user in. However, none of the lambda hooks run when I try to log in with a user that doesn't exist in aws cognito.
Answer: This is expected. Before calling the pre-authentication trigger, Cognito checks to see if the user exists. This is so that it can pass required information like 'sub', 'email', 'phone' etc. to the triggers. Now, when you put the wrong user in the UI, the Cognito check results in a 'User does not exist' error.


Gears of War 4 Split Screen Hordes?

Question: I want to know if you can use a guest account on Xbox Live to add a second person to play horde with or do you need a second Xbox Live account to do this?
Answer: Splitscreen is supported in all the coop modes for Gears of War 4 and even online.
You should not need a second Xbox Live account.  I've never seen a game do that for splitscreen.  Usually, the second player assumes the first players name with a number in parentheses next to it indicating which player they are.
Answer: yes you can play split screen horde online with a guest account the guest player will show in game as your gamertag with a (1) after just like it was on gears 3

Gears of War 4 Split Screen Hordes?


How was this repeating and blurring created?

Question: How do I achieve the effect below where the repeating subject getting blurry each time it repeats with every reflection, and the subject repeating at a slant in the picture?
Answer: Recursively including an image within itself is known as mise en abyme or the Droste effect.

Mise en abyme refers to coat of arms within a coat of arms.  It was later applied to recursive art.

Droste effect is named for a Dutch brand of cocao in which a woman is holding a tin of cocao containing an image of herself holding a tin of cocao containing an image ...

The image in question was created using a video feedback loop.  A video camera was pointed at a projection of its own output.  The blurry, fading appearance is produced by defocusing the lens and extraneous light.

YouTube: Video Feedback Loop using a camera and a projector

Another way to create the effect is with mirrors facing each other.  Frosting one mirror would create the blurred fade, but that is not how this particular image was created because the object on the right is not reflected in the wall.
Yet another way to create this effect is using a photo editor to repeatedly paste a resized copy into the image.  Use standard editing tools to blur and fade each copy after pasting.  A similar method can be used to create a variation in which a photo spirals into itself.

Discover Digital Photography: How to create a Droste Effect recursive photo
Flickr: New Droste Effect Tutorial
Comment: Thank you so much!


ASP.Net MVC - Webform View Engine Performance

Question: I heard viewengines like Razor or NHaml is giving much performance than WebForm View engine. Can someone advice me if this is true and which will be the best view engine
Comment: In a recent (December) web conference, Scott Hanselman stated that Razor is faster than the WebForms view engine. Although any performance benefits are relatively minor.
Answer: If changing the view engine significantly impacts performance, there is something wrong with your design. Views are for simple display of properties in the model - nothing in there would be taking nearly as long as things like database access which happen in the controller. An order of magnitude improvement in the view rendering probably wouldn't be a noticeable difference in the time for the whole request.
MVC 3 may perform better than MVC 2, but that's just a matter of using the latest version which has improvements in all parts of the system. View engine choice is about your preferred syntax, not performance.
Answer: MVC 3.0 still in development, so in final release performance will be even much better i guess.
Here is some Razor tests ASP.NET MVC 3 Razor performance and asp.net mvc3 razor documentation? and of cause http://haacked.com/
Answer: I would expect that the WebForms view engine and Razor view engine to yield similar performance as they are built on similar principles.  Both work by parsing a file (ASPX vs CSHTML) to generate a codedom which itself is used to generate a compiled class. The big difference comes in the optimisations built into the parsers/code generators used by each.
Answer: Don't know about the exact performance between Webforms and MVC. Been working with webforms for a while and i'm currently working with MVC2 and experimenting with MVC3's Razor View Engine.
Though MVC3 is still in the RC2 state the performance is pretty good but i guess it still have to be tweaked before the final release .Rumours are that the performance should be equal to MVC2.
If you ask me i think that MVC2 and the new Razor Engine aren't any slower than Webforms applications. But personally i find the code easier maintainable with MVC, that's for me the biggest reason i switched from Webforms to MVC. Don't know anything about NHaml, but would personally choose Razor, works great! It's easy to use, understandable and gives good and clean code.
EDIT:
Read Scott Guthries blogs about the MVC3 RC2 candidate. He talks about performance. See this link.
Another topic on SO already exists about performance. Read it here
It always interessting to follow the blog pages of Scott Guthrie and Phil Haacked. Both work at Microsoft and regular post about MVC3.


Contracting Unity EditorWindow UI

Question: How can I make scalable(contracting) EditorWindow UI(not in-game UI) like in inspector example?
Comment: Can you clarify for us where your new UI lives? Is it also in the inspector, or in a standalone editor window, or in-game? Showing us a target visual or what you have now could help too.
Comment: Could you provide some more details on what you've tried? My experience with custom editor window isn't that great, but last time I tried it I believe all fields scale automatically.
Answer: When speaking about the UI, all objects have a RectTransform instead of a Transform. One of it's values is the Anchors one. An anchor basically defines where the child is "attached" in relation to it's parent. Each object has 2 anchors, Min (for bottom-left corner) and Max (for top-right). Their values go from 0 to 1, which signifies the percentage of the screen width/height.
If for example you've set both anchors like this:
anchorMin.x = 0.1;
anchorMax.x = 0.9;

anchorMin.y = 0.1;
anchorMax.y = 0.9;

And the RectTransform's positions are all 0, then all edges of that object will be 10% away from the edge of the screen, regardless of screen size (The object basically stretches from 10% to 90% of screen size).
Keep in mind that if both x or y of both anchors are the same value, the Inspector changes, and gives you a new "width" or "height" field, which you can use to give a specific size to your element. So with this example:
anchorMin.x = 0.1;
anchorMax.x = 0.9;

anchorMin.y = 0.5;
anchorMax.y = 0.5;

This object is now stretching only horizontally from 10% to 90% of screen space, and it's also anchored vertically in the middle of the screen, but on a single point. This means you can give it your own height (for example 100px) and the object will now stretch to fit the screen horizontally, while keeping itself at 100px height.
See also, Unity: Basic Layout and Unity: Designing UI for Multiple Resolutions
Comment: I am developing Unity EditorWindow(https://docs.unity3d.com/ScriptReference/EditorWindow.html), so my tag is right.
Comment: Thank you for a great answer, but I was talking about EditorWindow UI.
Comment: @GuardFromUA Sorry but you tagged your post with `unity` and this being a game development community, I assumed it's a video game made using `unity`. If that's not the case could you provide some more details about what platform/tools you use? In general you'd use the same technique, but with some tools you may have to do it manually.

Contracting Unity EditorWindow UI


Are there any protections or policies people do differently in case of a large scale police walkout?

Question: Recently Atlanta has begun a police walkout, in which the police in certain zones are no longer able to respond to the majority of calls. In case something like this happens where I live, are there policies in place that a business or home owner needs to know in case of a break in? In particular if I stop someone at gunpoint, am I allowed to now hold or transport a person I find breaking and entering if the police cannot come to take them? Do I just let them go?
Answer: Georgia law statutorily recognizes the common law right of citizen's arrest in OCGA 17-4. 17-4-61 requires you to take the arrestee before a judicial officer, or to deliver him to the police.

A private person who makes an arrest pursuant to Code Section 17-4-60
shall, without any unnecessary delay, take the person arrested before
a judicial officer, as provided in Code Section 17-4-62, or deliver
the person and all effects removed from him to a peace officer of this
state.

You must do so immediately, and the person must be released if they are not brought before a judicial officer within 48 hours.


Does unitarity apply in between measurements?

Question: Sorry if this is a silly question (engineer here), but I was wondering if the math in particle physics assumes that unitarity applies even between measurements.  In other words, I take it that the evolution of quantum states is governed by an operator that ensures the probability of all possible events adds up to 1 at all times.  What I'm wondering -- is there an operator for which this does not apply at all times but still gives measurement results with probability between 0 and 1?
Comment: You are asking if you can violate unitarity in intermediate steps? THe answer is yes, using ghosts.
Answer: Yes, you can make a unitary asymptotic S-matrix (so asymptotic measurements) when the intermediate states do not evolve in a unitary way. This is what ghost fields do--- the intermediate states in ghost-descriptions include negative probability objects, but when you make asymptotic measurements you don't see the ghosts, you only see the positive probability objects.
In cases where you have a ghost description, there are often no-ghost formulations, like light-cone or axial gauges. In these formulations, the Hamiltonian is well defined, so that you can ask about measurements on the intermediate states and get well defined answers. These formulations have a reduced symmetry compared to the ghost formulation, but they are manifestly unitary.
In ghost formulations, you assume that every measurement is made on asymptotic states which have no ghosts. Even if it is not true that every measurement is of an S-matrix quantity, the existence of the unitary formulation guarantees that anything you build out of asymptotic states will only end up measuring a quantity which has a reasonable positive probability interpretation.
Comment: But these intermediates involving ghosts are only virtual, without an associated state vector. Any state vector must always evolve unitarily, as this is dictated by Schroedinger's equation, which remains valid in QFT.
Comment: The physical wave functions are functionals of all fields, annihilating the BRST operator $Q$. These evolve unitarily according to Schroedingers equation. The Hamiltonian is the generator of the time translations of the corresponding unitary representation of the Poincare group defined on $Ker~Q$. There is no room for a separate non-unitary dynamics of some states - unless they are unphysical states without any relevance.
Comment: yes, but the full state space is physically irrelevant, as only states annihilated by $Q$ can be prepared or observed. Therefore they are also the only states that exist at finite time, i.e., between measurements. - The others are just mathematical constructs. They may appear in perturbative calculations, but not in the dynamics.
Comment: @ArnoldNeumaier: The ghosts are "virtual" for S-matrix calculations, the fields themselves have wavefunctions, and the ghost fields intermediate states evolve nonunitarily.
Comment: @ArnoldNeumaier: You can consider the full state space to include unphysical states which are not annihilated by the BRST operator, and consider the BRST condition as an asymptotic condition on incoming states. The nonunitary dynamics is on states which are not physical, I agree, but they are fine intermediate states. The question was about theories where intermediate states are not unitary, but asymptotic states are.


Quotient of principal congruence subgroups

Question: This is a direct follow-up to this question. What is the quotient $\Gamma(2)/\Gamma(2^n)?$ (the principal congruence subgroups are in $SL(2, \mathbb{Z}).$ It is a 2-group, but what else?
Comment: If you have a finite 2-group $G$, then the set of automorphisms acting as the identity on $G/G^2$ is a normal 2-subgroup, and the quotient is a subgroup of automorphisms of $G/G^2$ which should be computable with not too much effort in your case.
Comment: The derived length and nilpotence class aren't difficult to calculate. What sort of things are you looking for?
Comment: @GeoffRobinson Well, for the source question, it would be good to get enough information to find the automorphism group...
Answer: This is far from a full answer, but here a few things I've figured out, hope it helps.
First of all, $\Gamma(2)$ is the direct product of $\{\pm 1\}$ and the subgroup $\Gamma(2)'$ consisting of all matrices in $\Gamma(2)$ whose diagonal elements are $1$ modulo $4$.  So it suffices to determine each $\Gamma(2)' / \Gamma(2^{n})$.  Clearly $\Gamma(2)' / \Gamma(4) \cong (\mathbb{Z} / 2\mathbb{Z})^{2}$.  Also,
$$\Gamma(2)' / \Gamma(8) \cong \langle \sigma, \tau \ | \ \sigma^{4} = \tau^{4} = [\sigma, \tau]^{2} = [\sigma^{2}, \tau] = [\sigma, \tau^{2}] = [[\sigma, \tau], \sigma] = [[\sigma, \tau], \tau] = 1 \rangle.$$
More generally, each $\Gamma(2)' / \Gamma(2^{n})$ is generated by two elements $\sigma$ and $\tau$ each of order $2^{n - 1}$, whose commutator $[\sigma, \tau]$ has order $2^{n - 2}$ and generates the whole commutator subgroup.  I think one should be able to derive a full set of relations in the form of embedded commutators as above, and there should be some recursive pattern to this set of relations as $n$ increases, but I haven't figured it out.


Citroen C3 2006

Question: I have a Citroen C3 2006 petrol engine that for some reason it never been used from new. It only have 33 km, it was stood all this time, obviously without battery.
Now we are trying to start it but it is only turning but not starting.
so we already changed inlet, injectors, all spark plugs, fuel pump.
spark is coming well fuel is coming as well and we made a compression test and is making around 9 and 10 psi
Now we noticed that when opening and locking the car from the door lock it is locking and opening only the drivers door
Answer: Ok, 9-10 psi, are you SURE about that?  If so, this engine has a major problem.  Generally the compression should be 90-100 psi or more depending on the engine.  But you're nowhere close to that.  Are you sure you're using the compression gauge properly?
For an engine to run you need air, fuel, compression, and spark.  You've addressed fuel and spark, and I'm assuming you have air.  But without compression it will not run at all.
Just guessing here but I'm thinking you have stuck valves and/or rust in the cylinder bores which have ruined the rings.
Comment: that what i was thinking at the beginning but than i noticed that it is not locking and unlocking, so it mixed me up because i am not an expert on electric
Comment: and about the compression i tested it again with a new compression gauge and it is marking +-7 bar on all 4 pistons
Comment: 7 bar (I'm not sure about +-7 though) is just over 100 psi.  Perhaps low but I'm not sure what's normal for that model.  I think it's high enough to support combustion though.
Comment: Are you sure fuel is getting into the engine?

Citroen C3 2006


Saving and Editing JSON on iPhone/iPod

Question: What's the best method for editing and saving a JSON file on the iPhone/iPod? I know there are libraries that allow you to easily read JSON data, but are there any that allow you to generate it?
Answer: TouchJSON reads and generates JSON, is quite fast, and uses very little memory.
JSON Framework is supposedly faster, but uses much more memory.
The iPhone also includes a built-in JSON parser/generator, but it's only available through private APIs. You probably shouldn't use this one.
Answer: TouchJSON allows conversion both to and from JSON with a single call like:
<code>[[CJSONSerializer serializer] serializeObject:someDictionaryofYours];</code>

Saving and Editing JSON on iPhone/iPod


Why is this redemptionPeriod so long?

Question: There is a domain i want, using who.is i see "Expiration Date: 2010-11-28" status is redemptionPeriod. Why hasnt it become available yet? I did notice a "Last Update Date:  2011-01-09". Does this mean? The other domain does not have a last update date.
Answer: Domain Name registrars often tend to hold domains for a period after they expire in order to give the previous owner a second chance at renewing them.  Note, this isn't something they do out of the goodness of their heart.  The domain registrars add a pretty hefty surcharge (sometimes upwards of $100us or more) for this service offering.
More money for them if they get the previous owner to renew the domain and pay their surcharge, than letting it expire and get registered by someone else.

Why is this redemptionPeriod so long?


Disadvantage of decision tree

Question: I read in a blog that the decision tree has this disadvantage:

Not fit for continuous variables

If this is true, then why?
Answer: Continuos Variable in training data (X)
If you look at decision trees they try to split data based on categories in case of categorical data and based on threholds in case of continuous data. Now to split on continuous data it randomly tries to create BINs and calculate the entropy/ Gain etc whatever you have chosen. This implies that Decision Trees is able to use contnuous variable for training and their is no disadvanatge except it can take a little bit more time to train due to preocess of Bin creation and finding best split on the Bin.
Continuos Variable in target (X)
Decision trees works well for regression problem but now objective is not to find splits which give maximum information gain but which reduces variance amongs onservation withing the same leaf nodes.
Based on my understanding, In general Decison Trees has been modified to work well with both continuous and categorical data
Answer: Decision trees work well with categorical variables because of the node structure of a tree. A categorical variable can be easily split at a node. For example, yes or no or 0 or 1. A continuous variable is just that, continuous along a range which cannot be easily split at a node. For example, a floating point number between 0 and 100.
Comment: Also the ordering of the categorical variables value matters to some extent also
Answer: It can't be used for micro trend detection as each node looks for values greater than or smaller than the threshold value.
Answer: Decision trees can handle continuous variables, so this shouldn't be a disadvantage. They just make it categorical by defining thresholds to separate continuous variables into classes.
However, if you have a model with continuous variables only, neural networks will probably be the better solution for such an use-case.

Disadvantage of decision tree


prevent wordpress from rendering line breaks as br tags

Question: I am tired of WordPress's horrible HTML editor and have decided to write all my html in Notepad++ and then just copy it over. However, simple line breaks "\n" that would be normally ignored in html are converted to
 tags. I have disabled the visual editor, so everything I save should be the exact html that is presented. But it's not. how do I stop wordpress from converting my html?
Comment: Well, the `` tag is exactly a line break in HTML. If you use line breaks in Notepad++ to create new paragraph just make two line breaks, WordPress will end the previous and begin a new paragraph. If you don't want line breaks in your post then why did you make them when writing the post in Notepad++?
Answer: That's handled by a filter called wpautop (declared in wp-includes/formatting.php, line 189).
You can remove it with this:
remove_filter('the_content', 'wpautop');

Comment: Great solution! And it still works on Wordpress: 4.7.5 I added **remove_filter('the_content', 'wpautop');** to "/wp-content/themes/my_theme/functions.php" to keep everything in the same place.
Comment: You can also do this using plugin wpautop control and set site-wise default as well as per post setting. More info at http://blog.bigsmoke.us/2010/12/09/wpautop.
Comment: Above solution from @jlenstorf does not appear to apply to my most-recent WordPress 4.x installs. This mature plugin seems popular. http://wordpress.stackexchange.com/a/227428/93125
Comment: @JohnnyUtahh I'm not sure if there's something else going on in your 4.x installs, but I just checked on a site running 4.5.2 and disabling the filter still works. If you look at [the source](https://plugins.svn.wordpress.org/toggle-wpautop/trunk/toggle-wpautop.php) of the plugin you linked, it's essentially doing exactly the same thing, but with a bunch of overhead on the admin side.
Answer: Toggle wpautop plugin.
It's the most-popular solution I found, and works well for me. Above plugin page shows 10,000+ installs and 100% 5-star ratings (23 of them) as of 2016-05-21.
The description of the above plugin page:
Before WordPress displays a post's content, the content gets passed
through multiple filters to ensure that it safely appears how you
enter it within the editor.

One of these filters is wpautop, which replaces double line breaks
with
 tags, and single line breaks with
 tags. However, this
filter sometimes causes issues when you are inputting a lot of HTML
markup in the post editor.

This plugin displays a checkbox in the publish meta box of the post
edit screen that disables the wpautop filter for that post.

Also adds a 'wpautop', or 'no-wpautop' class to the post_class filter
to help with CSS styling.

jlengstorf's answer does not appear to apply to my WordPress 4.x installs.
Comment: While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference.  Link-only answers can become invalid if the linked page changes. - [From Review](/review/low-quality-posts/104477)
Comment: Got it, thanks. Does my recent update to the answer solve this?


new at electric guitar need help

Question: Which pedal should I put first, overdrive pedal or chorus pedal? Can they be on at same time ? I don't want to burn them out. I was wondering if an overdrive pedal would make a chorus pedal function better.
Comment: @NeilMeyer Questions about pedal order are very common among electric guitarists and are not related to what specific pedals are being used or what brand or model pedal to buy. This is in no way a gear recommendation question. This is more like a "how do I use a trumpet mute?" and it's not "which trumpet mute should I buy?"
Comment: this seems like a recommendation for gear question.
Comment: Check out the playing of Zack Wylde. He is the one that comes to mind when I think of overdriven tones with a chorus.
Comment: OK then you have convinced me.
Answer: Pedal order is 100% personal preference, and there will be a difference with different placements. I would say it's more common to put overdrive before chorus but I've built pedalboards that have chorus in between two overdrives before. If they are both guitar pedals then you won't burn them out no matter how you place them in the signal chain. The main way you could damage a pedal electrically is by using the wrong power supply or battery.
As to whether one might make the other sound better, not exactly, but they can definitely sound awesome together.
Answer: There are no hard and fast rules with regards to the order of pedals in the signal chain, however, there are some general guidelines that may be of help.
Usually, a multi-fx signal chain will go something like this:
Wah -> OD/distortion -> EQ -> modulation FX (chorus/flanger/phasing etc.) -> delay -> reverb
So, if you were to subscribe to the "standard" set-up, you would put your chorus after your overdrive pedal.
Why this particular order? The general reasoning is to establish your general tone first and then successively colour it. Thus: the wah pedal acts almost like an additional, foot-controlled tone knob, following which overdrive determines the amount of distortion in your sound and the EQ shapes the overall tone. After you've established this base, you can further embelish it with modulation FX and if you wish to apply spatial effects - such as reverb or delay - these generally give the best results when they affect the entire sound.
In your particular case, a chorus effect will apply some measure of detuning to your sound by introducing an additional, slightly delayed signal. If you apply distortion (especially heavy distortion) to that, you might find that it becomes too noisy and dissonant. Conversely, if you apply the distortion beforehand, the two distorted signals will be separated and mixed within the chorus processor and offer a more "civilized" end effect.
Do bear in mind, that the above guidelines are just that: if you find the sound from a different order of effects more to your liking - go for it.
There should be no danger to the circuitry of the effects units from placing them in any particular order, but bear in mind that effects that boost the signal level (most notably OD/distortion, but compressors and EQ may also fall in this category) may overdrive the circutry in further effects down the signal chain, making the overall signal more distorted than planned. Every effect will also introduce some noise into the signal, which will be amplified by any signal-boosting effects further down the line, possibly becoming quite prominent. This is another reason to put such effects early in the signal chain and possibly put a noise gate between them and the rest of your effects.
Comment: Guilty! I also forgot the guitar... :)

As to breaking the "rules": yeah, I've seen and heard all sorts of crazy combinations. I thought that the above would be a good starting point, especially since there are simple to understand reasons behind it.
Comment: You forgot the amp in the signal chain. :-) Also I have to say the best sound I got on the last album my old band recorded was chorus into some heavy distortion. It sounded awesome. Chorus, phaser, and flanger before an overdriven amp is actually very popular. See also Eddie Van Halen.
Comment: @Todd I just gotta say that chorus into a distorted amp is very different than chorus into a distortion pedal. Seems to be most common practice is chorus pedal after distortion pedal, or chorus pedal before amp input (not in fx loop). Sure there are people who deviate, but this seems standard.
Comment: Depends on the distortion pedal. Many are very amp like. On the one hand I'm hesitant about calling anything "standard" when it comes to rock guitar. On the other hand, it's nice to have a label on what you should try the opposite of when you want to craft a unique sound.

new at electric guitar need help


gwt panel flow panel

Question: i like to design entire html with GWT.
but when i press ctrl and +  then entire html must be zoomed from center not from upper left
corner.
then what type of panel should i use?
flow panel , stack panel i dont know.
Answer: Any, but your root panel should have a fixed (or minimum) width and be centered.
Flowpanels are based on divs, so that's what you probably want.

gwt panel flow panel


Pre-Defined Numbers to be used in Sizing Mechanical Parts

Question: I recall there was a set of "engineering numbers" that were to be used when deciding how big to make something. So that if, for example, you wanted your screw to be 1.36mm you'd instead round up or down to the nearest of these prescribed numbers, perhaps to 1.2 or 1.5. This way everyone's things were more likely to be the same size because instead of randomly selecting sizes that were particular to a specific situation, we'd all be using the same set of pre-selected numbers instead. Does anybody know what this concept was called? Thanks!
Comment: "Making use of economies of scale"?
Comment: Find a relevant international standard, and follow it - unless you are in the USA, in which case find some standard that nobody else in the world follows, and use that instead.
Answer: You probably mean preferred numbers or any of the other names they go under. There are actually many such series defined in the standards.
It looks like you are talking of the 1-2-5  series in your example.
Comment: Thank you so much, that's exactly what I was looking for!
Answer: It is also worth adding that preferred numbers are highly contextual as what numbers are actually sensible will depend a lot on manufacturing processes and existing standards.
For example many standard steel sections, even when nominally metric are actually based on inch sizes so you often see fairly odd mm dimensions on rolled steel sections, simply because it is too much trouble to convert to round metric numbers for no real benefit. Especially for things like structural sections and pipe where new stock needs to be compatible with legacy installations. Similarly BSP is still the norm for gas and hydraulic fittings.
Equally with the rise of international trade most things that need to be standardised are so this is much less of an issue that it once was.
This probably should be a comment really but is a bit too long.


Emacs 24.5.1 search and replace

Question: I can find the string I'm looking for by using Ctrl+s, but then I cannot figure out how to replace it at all. Even though there is something in the status bar that kind of seems like it's telling me how to replace, it's not clear enough for me and I cannot do it.
Comment: M-x `replace-string`?
Comment: I don't know how to use that. Where do I put the words that are supposed to be replaced? It keeps giving me a word that it wants to replace, but I didn't tell it to replace that word, and in fact, the word doesn't exist in the file. Please explain further how I'm supposed to use that.
Comment: Alt+s, type the word you want to replace, enter, type the word you want to replace it with, enter, then y for each instance. There might be more elegant ways, but that is what worked for me.
Answer: 1) Find and replace can be done by the shortcut Alt + %,
(in most of the keyboard layouts you will have to do Alt + Shift + 5)
2) Enter your search string and then [ret]followed by the  string you want to replace your search string with and again [ret].
3) You can press y to replace a given instance of the search string or press n to keep it as it is, you can also press ! to replace all the occurrences of the search string (Shift + 1).
There are various other options available after step 2 which can be viewd by pressing the ? key (Shift + /).

Emacs 24.5.1 search and replace


Select only one table row on high parallel connections

Question: I'm looking for a way to select one table row explicitly for one thread. I've written a crawler, that works with about 50 parallel processes. Every process has to take one row out of a table and process it.
CREATE TABLE `crawler_queue` (
 `id` int(10) unsigned NOT NULL AUTO_INCREMENT,
 `url` text NOT NULL,
 `class_id` tinyint(3) unsigned NOT NULL,
 `server_id` tinyint(3) unsigned NOT NULL,
 `proc_id` mediumint(8) unsigned NOT NULL,
 `prio` tinyint(3) unsigned NOT NULL,
 `inserted` int(10) unsigned NOT NULL,
 PRIMARY KEY (`id`),
 KEY `proc_id` (`proc_id`),
 KEY `app_id` (`app_id`),
 KEY `crawler` (`class_id`,`prio`,`proc_id`)
) ENGINE=InnoDB AUTO_INCREMENT=1 DEFAULT CHARSET=utf8

Now my processes do the following:

start DB transaction
do a select like SELECT * FROM crawler_queue WHERE class_id=2 AND prio=20 AND proc_id=0 ORDER BY id LIMIT 1 FOR UPDATE
then update this row with UPDATE crawler_queue SET server_id=1,proc_id=1376 WHERE id=23892
commit transaction

This should help that no other process can grab a row that is processed yet. Doing an EXPLAIN on the select shows
id  select_type  table          type  possible_keys    key      key_len  ref    rows    Extra
1   SIMPLE       crawler_queue  ref   proc_id,crawler  proc_id  3        const  617609  Using where

But the processes seem to cause too high parallelism, because sometimes I can see two types of errors/warnings in my log (every 5 minutes or so):
mysqli::query(): (HY000/1205): Lock wait timeout exceeded; try restarting transaction (in /var/www/db.php l
ine 81)

mysqli::query(): (40001/1213): Deadlock found when trying to get lock; try restarting transaction (in /var/www/db.php line 81)

My question is: can anybody point me in the right direction to minimize these locking problems? (in production state, the parallelism would be 3-4 times higher than now, so I assume, that there would be much more locking problems)
I modified SELECT to use index crawler by hint USE INDEX(crawler). My problem now are lockwait timeouts anymore (deadlocks disappeared).
EXPLAIN with USE INDEX() shows now (no. of rows is higher, because table contains more data now):
id  select_type  table          type  possible_keys    key      key_len  ref                rows     Extra
1   SIMPLE       crawler_queue  ref   proc_id,crawler  crawler  5        const,const,const  5472426  Using where

Answer: Your EXPLAIN report shows that you're using only the single-column index proc_id, and the query has to examine over 600K rows.  It would probably be better if the optimizer chose the crawler index.
InnoDB may be locking all 600K rows, not just the rows that match the full condition in your WHERE clause.  InnoDB locks all the examined rows to make sure concurrent changes don't get written to the binlog in the wrong order.
The solution is to use an index to narrow the range of examined rows.  This will probably help you not only to find the rows more quickly, but also to avoid locking large ranges of rows.  The crawler index should help here, but it's not immediately clear why it's not using that index.
You might have to ANALYZE TABLE to make sure to update InnoDB's table statistics to know about the crawler index before it uses that index in the optimization plan.  ANALYZE TABLE is an inexpensive operation.
The other option is to use an index hint:
SELECT * FROM crawler_queue USE INDEX(crawler) ...

This tells the optimizer to use that index, and do not consider other indexes for this query.  I prefer to avoid index hints, because the optimizer is usually able to make good decisions on its own, and using the hint in code means I may be forcing the optimizer not to consider an index I create in the future, which it would otherwise choose.

With more explanation, it's now clear you're using your RDBMS as a FIFO.  This is not an efficient use of an RDBMS.  There are message queue technologies for this purpose.
See also:

https://stackoverflow.com/a/13851231/20860
The Database as Queue Anti-Pattern.
Comment: Hey Bill, that's what I've done yet (sorry for not updating my question, will give +1 though). But what's strange is, that explain has shown sometimes the usage of `crawler` instead of `proc_id`. But for now I force usage of index `crawler`. I'll give the analyze table command a try, also. Thanks
Comment: Check the `rows` field in the EXPLAIN output.  With the compound index, the number of rows examined should be lower, I hope.
Comment: No, it doesn't (see above)
Comment: What about forcing usage of primary key? This table works like a FIFO, so the process looks for the first free row. In most cases the first 400-500 rows are already processed by other threads, so a `USE INDEX(PRIMARY)` should request only some hundred rows, doesn't it?
Answer: From what I can tell the problem that you're facing is that two threads are vyying for the same row in the table and they both can't have it.  But there isn't any elegant way for the database to say "no you can't have that one, find another row" and thus you get errors.  This is called resource contention.
When you're doing highly parallel work like this one of the easiest ways to reduce contention-based problems is to completely eliminate the contention by inventing a way for all the threads to know which rows they're supposed to work on ahead of time.  Then they can lock without having to contend for the resources and your database doesn't have to resolve the contention.
How best to do this?  Usually people pick some kind of thread-id scheme and use modulo arithmetic to determine which threads get which rows.  If you 10 threads then thread 0 gets row 0, 10, 20, 30, etc.  Thread 1 gets 1, 11, 21, 31, etc.
In general if you have NUM_THREADS then each of your threads would pick the ids which are THREAD_ID + i*NUM_THREADS from the database and work on those.
We have introduced a problem in that threads may stall or die, and you could end up with rows in the database which never get touched.  There are several solutions to that problem, one of which is to run a "cleanup" once most/all of your threads have finished where all the threads grab piecemeal whatever rows they can and crawl them until there are no un-crawled URLs left.  You could get more sophisticated and have a few cleanup threads constantly running, or have each thread occasionally perform cleanup duties, etc.
Answer: A better solution would be to do the update and skipping the select entirely. Then you can use last_insert_id() to pick up the updated item. This should allow you to skip locking completely, while performing the update at the same time. Once the record is updated, you can start processing it, since it will never be selected again by the exact same query, considering not all the initial conditions are matching anymore.
I think this should help you aleviate all the problems related to locking and should allow you to run as many processes as you want in parallel.
PS: Just to clarify, i am talking about update ... limit 1 to make sure you only update one row.
EDIT:
Solution
is the correct one as pointed below.
Comment: Nice idea, but `LAST_INSERT_ID()` will return a value only if you `INSERT` data or an `UPDATE` increments the autoincrement column: **EDIT** I'll give http://stackoverflow.com/questions/1388025/how-to-get-id-of-the-last-updated-row-in-mysql a try
Comment: For some reason i got a last_insert_id value when i tested, but it tricked me (it looked like the correct one, but it was not). I believe the solution described in that SO question is the way to go. I will update my answer as well.


Where can I travel from London and return to London with single entry UK visa?

Question: Where can I travel with single entry UK visa? I have a Schengen visa as well. If I possess a single entry UK visa, can I travel to Schengen zone from London and return to London?
I am an Indian passport holder.
Comment: You could go to Scotland and Wales which we often call separate countries.
Comment: Is this 'single-entry visa' something you actually have? Or a conjecture?
Comment: No you can't do that.
Comment: You can travel freely within the UK.  I am not certain whether you can travel to other jurisdictions in the common travel area, such as Ireland, and then return to the UK.  You certainly cannot Leanne the common travel area and then return to the UK, so no, you cannot go to Schengen and return to the UK.
Comment: Oops! *Leave,* not Leanne.  Have to remember to proofread!
Answer: If you go to the Schengen zone and then try to go back to the UK it will be another entry, and as your visa is single entry, you're not allowed. And there is border control at the UK border for passengers arriving from the Schengen zone.
Answer: Once you cross the UK borders, your visa is considered "used".
Since yours is only for a single entry, it is no longer valid for entry. You can stay in the UK as long as the provisions of your visa permit, once you exit the UK - you will need a new visa.
As the UK is not party to Schengen, your Schengen visa is not valid for entry into the UK.


Why is it a lot faster to call rm on a directory than deleting a folder from the GUI (Linux) over SSH

Question: Out of curiosity, why is it a lot faster to delete a folder / folders in Linux (I'm using Ubuntu) over SSH by calling rm -rf somefolder than deleting the folder from the GUI (right-click then "Move to Trash)? The folders I'm deleting contain about 100 image files each, and it probably takes a couple minutes to delete the folders in the GUI whereas rm -rf runs instantaneously. Do the two actions actually achieve the same effect, or does rm -rf only remove the link to the files?
Comment: Note: when someone on a Stack Exchange site suggests asking on a different one, they usually also flag it for migration, without your having to do anything. It's therefore best to wait for it to be migrated to the other site, rather than ask a new question.
Comment: You're being taken in by the pretty colours, that's all. rm isn't faster necessarily, but the file enumerator is. In the GUI, it has to show the user what files it's deleting, whereas rm doesn't show anything and does enumeration behind the scenes. The actual deleting, sans UI, is the same speed.
Comment: Randolph: But everything behind the scenes remains the same?
Comment: Mechanical snail: Gotcha, didn't know that before :P
Answer: You didn't specify this in your question, but I suspect that your GUI is based on some kind of filesystem-over-ssh feature. That might be slowing things down as every low-level operation (open directory, read directory, unlink file1, unlink file2, ... close directory) is passed over the ssh channel as a separate command.
When you run rm -rf x from the shell prompt on the remote machine, the only thing being passed over the network are the keystrokes you used to enter rm -rf x and Enter. (Those do get bloated up somewhat by the network protocol headers, but they're still reasonably small.) The low-level operations are conducted by the rm program on the remote end, talking directly to the kernel on the remote end, so naturally it's faster.
ssh was designed to provide a shell interface (the name should be a clue). The other stuff that's been bolted onto it is less efficient.
It would be possible for a filemanager-over-ssh implementation to optimize the recursive removal case and simply ask the server to run a rm -rf. I don't know if any of them have done this.
Comment: I should add: even in the worst implementation I can imagine, with a round trip to the server for every file, 100 files per 2 minutes implies you have a 1.2sec ping time to the server, which is ridiculously slow. There may be more to your problem that we haven't uncovered yet.
Comment: Thanks for the detailed explanation! The GUI is accessing the remote server's contents over SSH with Ubuntu's "Connect to Server" option. I can remove the files both ways, but I noticed the drastic difference in speed and wanted to find out why for curiosity's sake. I would upvote your answer but I don't have enough reputation... :P
Comment: That makes sense; the remote server I am working with is located in Korea with a public IP address, yet the network I am on is being routed to Taiwan from Korea and back (yay for large company networks... -_-) to the desktop in Korea, so there is noticeable lag even when using SSH through the Terminal.
Answer: You are connecting to a remote system with the "nautilus" file manager or similar, using an ssh:// URL, with the sftp protocol.
My version of nautilus refuses to move such a remote directory to local trash.  Moving a remote directory tree to local trash would be slow, it would have to download all the files before deleting them.
My nautilus is just deleting the files. The sftp protocol did not have any 'recursive delete' function until earlier this year (2012 R1). You're not using this newer sftp system, and nautilus probably doesn't know about it yet. So the file manager must list all the files, and delete them one at a time. It receives a confirmation message for each file that the deletion has been done, before going on to the next file. So the minimum time to delete a file is like your normal ping time to the server (or worse).
This one-at-a-time remote delete is much slower than running rm -rf /whatever or even rm -vrf /whatever over a normal ssh connection.  I'm deleting gcc source code as a test case, and it estimates 40 minutes to go for these 28300 files.  nautilus is using only 2% CPU so it's clearly not CPU bound drawing the GUI.
The problem has nothing to do with the GUI, it's due to a weakness in the (old) sftp protocol: there is no recursive delete function.  But, this is why I use the command-line!  No self-respecting hacker would wait 40 minutes for this!!
A file manager could delete files reasonably quickly while showing what files are being deleted, if it was using something like rm -vrf /whatever.  Some servers provide sftp access but not full ssh access.  Nautilus seems to be assuming the worst, and using only sftp.
Comment: +1 for the sftp info. I didn't mention it in my answer only because I forgot it existed. Now I'm off to try to forget again.


Confusing mealtimes

Question: In "Great Expectations" by Charles Dickens, when Pip returns after his meeting with the escaped convict, how come it says that he had dinner right afterwards? Did he skip lunch? Or did his meeting take all day? Can someone explain this for me?
Comment: Would you be able to provide a quote to clarify the question for people who have not read the book? It could be difficult to determine what you're asking without explanation of what occurs in the book. Including the time at which the meeting with the escaped convict occurs would be a good start.
Answer: The original meaning of dinner was a noon meal (the most significant meal of the day).
In most dialects it now means the evening meal, but some folks still refer to the noon meal as dinner and the evening meal as supper.
Comment: I remember reading (but don't have a reference) that it became fashionable among the upper crust to have dinner later and later in the day, eventually necessitating a light luncheon to stave off hunger pangs during the wait. The middle and lower crusts later followed suit.

Confusing mealtimes


Algebraic inequalities on different means

Question: If $a^2+b^2+c^2+d^2=1$ in which $a,b,c,d>0$, prove or disprove
\begin{equation*}
\begin{aligned}
(a+b+c+d)^8&\geq 2^{12}abcd;\\
a+b+c+d+\frac{1}{2(abcd)^{1/4}}&\geq 3.
\end{aligned}
\end{equation*}
Can you tell any general algorithm for this type of problems? Thanks.
Answer: Put
\begin{align*}
 f(a,b,c,d) &= \frac{(a+b+c+d)^8}{2^{12}abcd} \\
 g(a,b,c,d) &= \frac{a+b+c+d}{3} + \frac{1}{6(abcd^{1/4})}
\end{align*}
so the conjecture is that $f,g\geq 1$.  I used Maple to search randomly for places where $f$ is as small as possible, then used Maple's fsolve() to find a local minimimum of $f$ numerically, then used Maple's identify() function to see whether there was any simple closed expression for the local minimum.  I found that
$$ f\left(\frac{1}{2\sqrt{3}},\frac{1}{2\sqrt{3}},\frac{1}{2\sqrt{3}},\frac{3}{2\sqrt{3}}\right) = \frac{3^5}{2^8} = \frac{243}{256} < 1;
$$
this is a local minimum and probably a global minimum.
Numerical methods also indicate that $g$ has a local minimum at a point of the form $(a,a,a,d)$.  This must have $3a^2+d^2=1$, so for some $t\in(0,1)$ we have
\begin{align*}
 a &= \frac{1}{\sqrt{3}} \frac{1-t^2}{1+t^2} \\
 d &= \frac{2t}{1+t^2}.
\end{align*}
Define $G(t)=g(a,a,a,d)$, with $a$ and $d$ as above.  We find that for $t_0=2-\sqrt{3}$ we have $G(t_0)=1$ and $G'(t_0)=G''(t_0)=0$, so this is not a local minimum.  Instead, there is a local minimum at a point $t_1\simeq 0.3868865016$ which is algebraic of degree 21 over $\mathbb{Q}(\sqrt{3})$, with $G(t_1)\simeq 0.99970268716$.
Comment: Thanks. From Lagrange Multiplier method, one can see that $a,b,c,d$ can take at most two values. Then one can try setups as you display here. But is there any elementary way to tackle this type of problems?
Comment: What do you mean by "elementary"? The first step in my process was to try some randomly generated cases; I'd say that's pretty elementary (and certainly much faster than theoretical analysis as in Iosif Pinelis's answer).  When the function is not too complicated, and the number of variables is not too large, random search is quite reliable for suggesting the right answer, which you can then try to prove rigorously.
Comment: I agree on your process and I tried variational method which gives the maximum at $(a,a,a,d)$ or something like that. I was thinking any method without using calculus.
Answer: These are problems of real algebraic geometry (I have added the corresponding tag) and as such can, at least in principle, be solved completely algorithmically. In Mathematica, such algorithms are implemented via Reduce[], FindInstance[], Maximize[], and other similar commands. However, solving such problems on a computer may take too much time and/or memory.
In this case, it took several hours (I forgot to measure the execution time) to get the following results:

and

Thus, for each of the two conjectured inequalities FindInstance[] found an instance when the inequality fails to hold.
Relevant literature on real algebraic geometry includes the following items, among many other ones: Computer Algebra, Computational real algebraic geometry, Real algebraic and semi-algebraic sets, and Fewnomials. Much of this goes back to Tarski, A Decision Method for Elementary Algebra and Geometry.
Comment: Can you give me an elementary book or any resources that tells the connection between inequalities and algebraic geometry, thanks!
Comment: @HaoranChen : I have now provided references to a few relevant sources on real algebraic geometry.
Answer: There is a general algorithm for this type of problems.
We can use the Vasc's EV Method: https://www.emis.de/journals/JIPAM/images/059_06_JIPAM/059_06.pdf
For example, your second inequality is wrong, but the following is true.

Let $a$, $b$, $c$ and $d$ be positive numbers such that $a^2+b^2+c^2+d^2=1$. Prove that:
  $$a+b+c+d+\frac{2}{3\sqrt[4]{abcd}}\geq\frac{10}{3}.$$

Indeed, let $a+b+c+d=constant.$
Thus, it's enough to prove our inequality for a maximal value of $abcd$, which  by Corollary 1.8(b)
happens for equality case of three variables.
After homogenization we need to prove that
$$a+b+c+d+\frac{2(a^2+b^2+c^2+d^2)}{3\sqrt[4]{abcd}}\geq\frac{10}{3}\sqrt{a^2+b^2+c^2+d^2}.$$
Now, let $a=x^4$, where $x>0$ and $b=c=d=1$.
Thus, we need to prove that
$$x^4+3+\frac{2(x^8+3)}{3x}\geq\frac{10}{3}\sqrt{x^8+3}$$ or after squaring of the both sides
$$(x-1)^2(4x^{14}+8x^{13}+12x^{12}+28x^{11}+44x^{10}+60x^9-15x^8-54x^7-69x^6-84x^5-45x^4+30x^3+105x^2+180x+36)\geq0,$$ which is obvious by AM-GM.
By this method you can create infinitely many inequalities.
Comment: Thanks I will read it when I have time!
Answer: Too long for a comment, but in fact, there is an algorithm to decide whether an arbitrary (finite) collection of inequalities has a real solution. This is called the Tarski-Seidenberg theorem. For a textbook proof of that theorem one can refer to Chapter 1 (especially Section 1.4) of the book Real Algebraic Geometry by Jacek Bochnak, Michel Coste and Marie-Françoise Roy.


Ceiling Fan Lights not burning brightly

Question: My Hampton Bay ceiling fan with light is about 8 years old.  The light recently burned out, so replaced with with a 100 E11 halogen 100 watt bulb, resulting in very little light - about 50 watts.  I have since tried 150 haologen watt bulb, same results - about 50 watts shinning.  I replaced the E11 socket, no change.  The three-speed fan works okay.  I have replaced the Hampton Bay remote control - no difference, so not the problem. What is the problem?  Can the problem be in the the remote modual.
Comment: Are the lights dimmable? On my remotes, pressing and holding the light toggle will dim or brighten the lights. Check to see that the lights aren't dimmed
Comment: What happens with a "150 watt" (more like 20) LED?  GE sells an excellent one made to replace a 50/100/150 incandescent.  One trick: if  you power *only* the tip (as would happen in a non-3way socket), you get the 150 not the 100. Slick design trick, that's why GE is the best.  Color temp is 2700k and CRI is very good, so hard to tell from a trad. incandescent.
Comment: Harper, you are a hero.  I had always just pressed the on/off switch, never holding it down.  Tried it just now and WOW, it moves to the bright position.  Thanks
Answer: The limiting circuit isn't just government nonsense.  The bigger problem is the fan's mechanism is not made for that much heat.  If you put a bulb whose watts-actual are larger than rating, you will slowly cook internal parts of the fan such as the wiring to the socket.  We've seen overheated scorched light fixtures, it's not pretty.
A high-wattage lamp also defeats the purpose of a fan by adding heat to the room.  Even if you want heat, it's the most expensive kind - electric.
I have been steadily increasing the light in my house by going LED.  I know there,s some resistance to "gub'mint" bulbs, but LEDs actually won on the merits despite the government's best efforts to promote the dreadful CFLs.  They have solved early color temperature and CRI problems, and now  cannot be distinguished from incandescent.  My favorite is a non-subsidized GE bulb that is 50/150/100W equivalent, and if used in a non-3way base, gives 150W (not 100W as a normal 3way bulb will). That is a wonderful bunch of light at around 20W actual, with no chance of scorching a fixture rated for 40-60W.
Sometimes, if the power limiting circuit is cheap (because the fan is cheap), it must be bypassed to play well with LEDs.
Comment: I had to bypass my wattage limiter because the dumb thing broke.  I'm not so much interested in overloading my lights as I am in having a working light.
Answer: Blame the government, these dumb things have wattage limiters, so you don't use too much electricity.  It's an environmental thing, not a safety concern.  They're pretty easy to remove if you're handy.
One of the many videos on Youtube on removal
Comment: I guess I have not messed with any newer fans that had lamps, good to know (although the video was not so great) it was enough. +
Comment: Surely you meant "thank the government". Almost no one would be using LEDs right now if the Edison 60w hadn't been banned. Our planet would still be getting crapped up at four times the current tragic rate.
Comment: The government did *not* ban them.  You can buy them at the Target store in Berkeley, California.  When they say the challenge  "Welcome to Target" say the password "what aisle are the lightbulbs in?"  Make sure you're not followed!

Ceiling Fan Lights not burning brightly


What are single particle quantum states?

Question: Can someone explain what is the meaning of single particle states? I found this on Huang's book on statistical mechanics while writing distribution functions (e.g, Bose-Einstein or Fermi-Dirac). We were dealing with states of the full system in the partition function and suddenly why did we need single particle states? I cannot understand. Please help.
Answer: A single-particle state is the eigenstate of a single-particle hamiltonian, i.e., a hamiltonian describing a single particle, usually without interactions with other particles.
Comment: If you talk about distribution functions, like the Fermi-Dirac distribution, or the Bose-Einstein distribution function, the reason is that they describe non-interacting systems, where the total system energy is simply the sum of single-particle energies of occupied states.
Comment: Why do single-particle states appear in distribution functions? The partition function contains energy levels of the full system.
Comment: @ flaudemus, "describe non-interacting systems..."  System or subsystems? Maybe more clear be:   Describe systems that can be represented as a set of non-interacting subsystems, and then the partition function of a system is the product of the partition functions of subsystems?
Comment: @AlekseyDruggist: to be more precise: systems of non-interacting fermions or bosons.
Answer: A single particle state is defined as that which belongs to a vector space associated with an irreducible representation of the Poincare algebra and other internal symmetries. Please refer to The Quantum Theory of Fields, Volume 1, Chapter 2 by Steven Weinberg.
Comment: Maybe you can clarify how and why the QFT definition applies in this case.
Comment: The question doesn't give enough information on what is the calculation being referred to. Weinberg's definition gives a good notion of how to interpret bound states as single particle states which seemed relevant to me here. I don't think this definition is restricted to QFT or should be termed "QFT definition". It is the clearest definition I know of single particle states. The other upvoted answer here is in fact circular.


GLM Dependent Variable Incorporating Independent Variables?

Question: A bit of a newbie statistics question. In a GLM, would it be sound to use a dependent variable that incorporates one (or more) independent variables? For example, if my dependent variable is number-of-occurences-per-sq-km of a site ("density"), could I use site area (measured in sq km) as one of my independent variables? My intuition says that's a bad idea, but I'm not sure if that's the case.
Answer: I do not know the exact problem you are looking to solve. But If I was to extrapolate from what you are suggesting, we can look at something like number of fire stations in a city.
It would absolutely matter how big the city is area wise to look at the trends, and once again its a subjective call based on the problem you are solving and the other variables involved, in my case it could the number of chemical industries around, fuel depots and so on.
So contrary to your intuition might not be a bad idea after all.
Hope my perspective helps!
Comment: You've got the exactly the right idea. Let's say I have data for a number of cities, and my dependent variable is firestations-per-unit-area. I was wary of using the area of a city in my independent variables, as it's obviously part of the calculations for my dependent variable values. But you're right, cities of different areas could easily have different firestation densities. So I guess using the city area as a predictior in my GLM is OK?
Comment: Yes! I think it should be okay. Check the accuracy metrics of your model on your test data with and without. I am guessing with Area will be more accurate. (Working with limited information here, so just an intuition!)


Intersection of two open sets in the projective plane

Question: I want to compute the cohomology groups of the real projective plane, $P^2$, using Mayer Vietoris exact sequence. Now $H^0(P^2)=\mathbb{R}$, $H^2(P^2)=0$ being $P$ not orientable, so my problem really is compute $H^1(P^2)$. In order to do that, I choose $U_i=\{(x_1:x_2:x_3)\in P^2|x_i \neq 0\}\quad i=1,2,3$, then I set $U=U_1=\mathbb{R^2}$ and $V=U_2\cup U_3=P^2-\{(1:0:0)\}=P^1$. And that's ok. But who is $U\cap V$?
Answer: $U \cap V$ consists of all triples whose first coordinate is nonzero, but whose second and third coordinate are not both zero.
A point $(x_1 : x_2 : x_3)$ corresponds to the points $\pm s(x_1, x_2, x_3)$ in $S^2$, where $s = 1/\sqrt{x_1^2 + x_2^2 + x_3^2}$.
Now look at the portion $V_1 = \{(a, b, c) \in S^2 : a > 0 \}$. This is in bijective correspondence with $U_1$ by the map $(a, b, c) \to {(a:b:c)}$, so I'm going to look at $V_1$ instead of $U_1$. I'm going  to also place my coordinates so that $(1,0,0)$ is the north pole, and hence $V_1$ is the northern hemisphere.
All points of $V_1$ correspond to points of $U^2 \cup U^3$ (i.e.,  either 2nd coord or 3rd coord is nonzero) except the point $(1, 0, 0)$. So as seen in $V_1$, the set $U \cap V$ is the  (open) northern hemisphere minus the north pole.
This admits an obvious deformation retraction onto any northern line of latitude,
such as the circle defined by $a = 1/2$.
So it's got the homology/cohomology groups of a circle.
Comment: There's a typo in the expression for $s$


Run script simulatneously with loading desktop

Question: I am running Kali 2, and have a script that I want to run on startup. Right now, I have the script in my profile.d directory, but it takes too long to execute. The effect is that after I login, the desktop loading stalls until the script execution is complete. Instead, I would like to be able to use my desktop while the script is executing, also I tried implementing a delay in the script (sleep 20s), but this just locks the desktop out for 20s longer.
Answer: Hey what you need to do is add an '&' to the end of the command. This will make the command be forked to the background and your startup will continue.
eg.
<code># echo 'This will make it run in the background' &
</code>


Why is creating a bitcoin fork very difficult and a Ethereum fork easy?

Question: There are a dozen of projects based on Ethereum but very few based on the Bitcoin network. Why is this?
Comment: I'd like to point out that, technically, a fork is as difficult as it is modifying the source code of the project involved. Anyway, what makes a fork successful is the amount of adoption it manages to reach. So, if you want to measure the "difficulty" of a fork in terms of adoption, then we can say bitcoin forks struggle because they're overshadowed by the enormous popularity of bitcoin itself.
Answer: Forks of both are equally hard. What you're describing as "Ethereum forks" are actually tokens/smart-contracts that run on the Ethereum network, which isn't very common on Bitcoin (but there's Omni)
EDIT: Remved Rootstock as per darosior's clarification. Its only to relation to Bitcoin is that it uses merged mining, just like Namecoin.
Comment: I think it's also useful to mention that the reason why they are some many Ethereum-based tokens is that Ethereum was designed specifically for that purpose.
Comment: Rootstock is not on the Bitcoin network.
Comment: @darosior Right, thanks.


What should be the right width of an image for each document-classes?

Question: I would like to print good images in A4 document (300 or 600 dpi). Using an external software,I have to merge differents big images to create a bigger one so I have to resize it with the same software (e.g. Gimp). I would like to know the best width (for example, for use them in a A4 report or a book class) so I can directly resize this big image to the proper size with the external software.
Comment: Welcome to TeX.SX! You can have a look at [our starter guide](http://meta.tex.stackexchange.com/q/1436) to familiarize yourself further with our format.  Do you have a printing company for your book? Ask them what they need ...
Answer: I wanted to post this as a comment, but I ran out of space.
There is always some confusion on the resolution of graphics. Usually the smaller the print gets the higher resolution is required. The dpi actually stands for dots per inch an is a printer specific detail. Graphic programs usually use ppi pixels per inch. It is often referred to as the same, but it is not.
Resizing in the source document is only a good option if you are using vector graphics, which will be directly rendered by the printer.
In all bitmap graphics you schould try to resize it with an actual graphic programm. Usually there is a connection between dots and pixels. Many common printers use 1dot(per colour) = 1 pixel, some can do more.
For an optimal result you just need to know how large your picture shall be in the document. I it is 15 inches width and your printer can do 300 dpi, and you say 1 dot = 1 px, then 4500 pixels is the desired width.
You can then include your graphic without resizing it. However, if you are not printing on a high quality printer, this is fairly unnecessary.
Answer: There's an interplay between graphics format and original graphic size and desired print size here which makes answering this question pretty much impossible.
As an initial starting point, my suggestion would be to always scale the graphics to \textwidth when placing them --- then, if need be you can re-work the graphics (say it's vector and the line widths have become too anemic, so one should then increase the stroke weight, or it's a pixelmap and is grainy 'cause of the re-sizing, so one should source higher-resolution original, &c.)
\resizebox{\textwidth}{!}{\includegraphics[]{/Users/williamadams/Desktop/post-34-1161137990.png}}

It is left as an exercise for the reader to create a more generalized version which will handle portrait images and scale them to \textheight.
Comment: I tried to clarify the meaning of my question. This could be a pratical example:in A4,book class,I've an image 10'000 pixel to insert into. How much I have to rescale it to make a GOOD 300 dpi image in my LaTeX document?
Comment: Then you'd want to resample it to `\textwidth in inches * 300 pixels wide` (or 400 --- 600 would only be needed for text and other things probably better represented as vector graphics) --- in addition to resampling it, you'd want to apply an unsharp mask or other filters to make it look nice and be ready to print.
Answer: Printing is not a very simple challenge.  You have to look for several things, for example all your images should use the same color scheme, for example cymk.  You should prepare all images to be included without resizing, because resizing usually results in a smaller image quality.
All of this depends on the printing system that is used to print your document.  So the best way is to ask your printing company what you have to do.  You can show them a current pdf version of your document and they can tell you what you should change.  If you have Adobe Acrobat pro you can use the build-in tool preflight to check your pdf file.  Otherwise the printing company will do it for you.


How to move part of torrent in rtorrent?

Question: Searching for "move" and "rtorrent" only leads to questions about completed torrents. I'm interested in moving a single file that is part of a larger torrent to a different directory.
Comment: Can you explain what you are trying to accomplish?
Comment: You can make a hardlink to it if the directory is on the same filesystem (`ln your/file other/dir`). But the file will be garbage before it is fully downloaded (torrent segments are not downloaded sequentially, and even a file that's 99% may be completely unusable, but you probably already know that)
Comment: I want to clear up the directory that file is staying in. Since it is less important I want to move it off into a subdirectory. I asked the question about one file, since I assume the method would be similar if it was a thousand files instead. I'm migrating from azureus 4.X where it was a simple act of right clicking a file and then selecting what I wanted to do. Like renaming or moving.
Answer: You cannot move part of a torrent to a different directory without breaking the Download/Seeding process, but you can copy an individual file of an existing torrent to a different directory while the torrent is continuing to Download/Seed.
Having said that, you could try:

stopping the torrent
move the file to another directory
creating a symlink in the torrent's file directory to the new location
resume the torrent

Note: Try as it should theoretically work, but I'm not currently torrenting anything right now so cannot test...
Comment: It's not about space, I want that file to disappear from the directory it's in. After your method I'd still be left with a symlink.
Comment: I could do it without problems in azureus/vuze 4.X, so it's definitely possible. Worst case I can't migrate over, since this is one of those basic features I'm heavily reliant on.
Comment: It's not missing. It's just moved to a different directory and seeded from there. As long as my client knows where the file is everything works fine. I move files I seed to different directories for most of my torrents and have trouble understanding why rtorrent shouldn't be able to accomplish that just fine. Can you at least rename files with rtorrent?
Comment: Well, then we've come full circle: use the symlink option: that uses just a few bytes of storage. (all other comments deleted)
Comment: The point isn't to save storage, the point is to reduce clutter by moving unneeded files. Imagine a directory with 2000 files. I want to move 1950 files away, so it's easier to see the relevant 50 files. In vuze I would have selected the 1950 files, right clicked and then clicked on move from the menu. After that the files were moved to a different directory while still being downloaded/seeded.


Estoppel from international phase amendments

Question: In a PCT filing, is there any estoppel effect of arguments presented during the international phase (under art 19 or art 34) on national phase filings?
Comment: What country are you interested in? Since this is a matter of national law and practice, the answer will differ by country.
Comment: @Maca if you find a single example where the answer is yes, the answer to the whole question is yes.
Comment: @Maca - For example, United States and in say two scenarios a) US patent is already issued and b) US patent is still under examination
Answer: Under Art 19 and 34 of WIPO, for an amendment, a statement for basis of amendment is required.
I feel, if amendment is made to specification and/or drawing than the section of specification and the drawing prior to amendment and statements thereto may cause estoppel action because the later version is chosen as the best mode of practice and applicant is supposed to frame claims for protection of best mode of practice.
For claims it's a bit different. USPTO allows reinstatement of withdrawn claims and canceled claims (with new serial number). So, prima facie, amendment of claims and arguments thereto need not have estoppel effect. But, if your claim includes limitations as to what your invention can not do, then it surely will have estoppel effect. Because, if it is explicitly claimed that a certain invention can not do a function A and afterwards an amendment is done to claim list to include that the invention can perform the function A, that will face estoppel.
Comment: From WIPO web site - "1.05.   What is a statement accompanying an amendment?  Any amendment MAY BE accompanied by a brief statement by the applicant explaining the amendment and indicating any impact it might have on the description and the drawings." I capitalized the MAY BE.  The statement is not required.
Comment: Claims that are withdrawn can be brought back - that is why they were withdrawn instead of cancelled.  A new claim can be added that has the identical text of a canceled claim.  It may be objected to as being outside the scope of an election made in response to a restriction requirement.
Answer: Yes. Japan (at least). see: https://aippi.org/download/commitees/175/GR175japan.pdf
In particular where it says:  For example, the following may be taken into account for the purpose of claim interpretation
and may be subject to estoppel: the description of the prior art cited in the application
of the disputed patent (Tokyo District Court decision, December 22, 1986); an
allegation made during the prosecution of the original application in the case of a divisional
application; statements made in a corresponding foreign patent application; statements
made during negotiations for licensing; and statements made during actions for an
injunction or actions for a declaratory judgement for no right to demand compensation for
damages.
As a general rule, however, no Examiner appreciates being told the opposite of what was told to another Examiner.


Export VM from Proxmox

Question: I want to export the vm from proxmox to virtualbox or vmware.
Is it possible? and how?
Answer: You may not be able to export an entire VM to another hypervisor, but you can at least export the disk(s):
With VirtualBox:
First, if the disk is not a "raw" type, then run the following on the KVM hypervisor/server:
qemu-img convert -f qcow2 kvm_source.img -O raw kvm_destination.img

Then, from VirtualBox:
VBoxManage convertfromraw   <filename> <outputfile>
                            [--format VDI|VMDK|VHD]
                            [--variant Standard,Fixed,Split2G,Stream,ESX]
                            [--uuid <uuid>

With KVM:
qemu-img convert -O vdi kvm_source.img vbox_destination.vdi

No promises because I've never had to do this myself, but they should work.  Also, I would put my money on the KVM solution, personally...
http://www.krisbuytaert.be/blog/converting-kvm-virtualbox
Answer: Proxmox supports two kinds of virtualization technologies, namely full virtualization and container. There are several well known full virtualization productions such as KVM, Xen, and Vmware while container prodcutions includes lxc and OpenVZ. Proxmox only supports KVM and OpenVZ at the moment. So I think your problem is the same as "how to convert a KVM VM to virtualbox or vmware VM". As far as I know, there is not a easy way to convert a KVM vm to a vmware VM. Just Google it by yourself.
Answer: This answer is incomplete, but it should help get you started.

I want to export the vm from proxmox to virtualbox or vmware. Is it possible ?

Yes

How ?

The exact method really depends on how your VM is stored.
Assuming you have a simple setup with 1 computer acting as both the hypervisor and the storage.

ssh to the hypervisor (or otherwise get a shell). You will probably need to be root for commands later
Determine how your VM is stored

File on disk, eg qcow, vmdk etc will typically be in /var/lib/vz/images
On a logical volume use lvs to list the logical volumes

You can now copy the files somewhere else and convert them using qemu-img convert per Soviero's response.
If you're behind a firewall you might need to pipe data in reverse via ssh
As an example I needed to move some VM's from one hypervisor to another. Both were using logical volumes to store the raw images so I did the following
source# lvs --units b  2>/dev/null | grep vm-111
  vm-111-disk-1 vglocal01  -wi-ao---  17179869184B

destination# lvcreate -L 17179869184b -n vm-111-disk-1 vg_vms

source# dd if=/dev/vglocal01/vm-111-disk-1 | ssh destination dd of=/dev/vg_vms/vm-111-disk-1

Export VM from Proxmox


Will entropy continue to increase even if the universe begins to contract?

Question: If the universe is heading for a big crunch, when the universe starts to collapse will entropy decrease and the arrow of time consequently reverse or not? I'm interested in the explanations, not just the answer.
Answer: The expansion of the universe have no influence at all on smaller scales (small in this case means the size of galaxies). The universe expands but galaxies are held together by their gravity.
If the universe would stop expanding and start to collapse the galaxies would keep on rotating, the stars would keep on turning nice, well ordered, nuclear enery into plain old heat, your metabolism would still turn the well ordered chemical energy in your food into heat and poop... Simply put, entropy will keep on increasing.
The only scenario where the arrow of time disappears is when all energy is converted to heat, uniformly spread throughout the universe. Then the entropy is maxed out and the arrow of time ceases to exist. Since nothing can happen in this universe the need to sort events chronologically also disappears so no one will miss the arrow.
Comment: Roberth, what if the universe only begins to contract after the heat death.  Can you explain why a collapse after a heat death would not lead to a decrease in entropy.
Answer: Total entropy of the universe is equal to the total area of the space boundary, according to holographic principle.
Our universe is expanding, asymptotically approaching de Sitter space. In de Sutter space the radius of the cosmic horizon is constant and equal to the Hubble radius - the distance at which cosmological red shift becomes infinite.
For expanding universe to start contracting, it should first stop expansing. Not expanding and not contracting universe is flat. This means it does not have the horizon, and its entropy is infinite.
In other words, before the universe to start to contract, its entropy should reach infinity.
Comment: That people believe a good theory of quantum gravity should obey it does not mean you should present it as a fact. The currently accepted theories of nature (quantum field theory and classical general relativity) do *not* obey it.
Comment: You should mention that the status of the holographic principle is, in general, that of a conjecture, and not a feature of e.g. classical general relativity.
Comment: @ACuriousMind all new theories are usually tested against holographic principle and if they contradict it, the theories are usually discarded.


How to force HTTP and stop SSL completey on Wordpress website

Question: We have a Wordpress website wich uses Video files from a local sever without SSL. If we use SSL on the main website url, it can't play Videos because of CORS policies so we need to completely disable the SSL and run the website on http not on https.
We have already disabled the SSL from hosting cpanel and replaced all urls from https to http in Wordpress, also the Site Url and Wordpress URL in setting page is all in http but when we open the url, it force to https even if we put the http:// directly.
In permalinks page all links start with https instead of http. We already deleted the .htacess file and replaced it with a fresh one but no effect on the result.
What should we do to completey run the website without ssl and only http?
Answer: You can force it in the .httaccess file
<code># Force HTTP
RewriteEngine On
RewriteCond %{HTTPS} on
RewriteRule ^(.*)$ http://%{HTTP_HOST}%{REQUEST_URI} [L,R=301]
</code>
Comment: But it causes `ERR_TOO_MANY_REDIRECTS` Error.
Comment: Try In the "WordPress Address (URL)" and "Site Address (URL)" fields, replace "https://" with "http://".

In Settings General
Comment: Already did all this staf but didn't work!


How do out of phase tell us the amplitude of gravitational wave?

Question: When gravitational waves hit the 2 mirrors in LIGO and causes the signals to switch between in-phase and out-of-phase, it should only show the changes in frequency. What about the amplitude of the wave?
Answer: Changes in the interference pattern are due to changes in the distances between the mirrors, shifting by a fraction of a wavelength. The oscillating fractional change in this distance tells you the amplitude of the metric perturbation.
Answer: They are not looking at amplitude. They are looking into time-frequency domain, where they have density of energy per 1 s and per 1 Hz. Technically they have J/s/Hz (Joule per s per Hz).
They see both changes in frequency and in time. But it does not make a task easier because majority of singals is just noise and they filter it all by very complex constructions and computer pattern recognition.


How to make lines visible on rendering

Question: So I want to make a wall similar to this one.I want to have squares on the walls with small lines between them that have a bit of depth(hence why I am not using UV-Mapping) and that actually show up in the render.How can I make these lines?
Comment: Could you please explain this in a way a starter could understand this?
Answer: You could use 3 ways:

model this geometry as contents of one mesh (i.e. subdividing or inset and bevel etc);
create it as it's created in real world - tiles as one object, cement as another.
or just find image of tiles somewhere and apply it as a texture (while it would mean completely another way of adding details, you'll still be able to bake a normal map from that image in order to create a vision of details).

First way is faster, while the second one is better, more flexible and correct.
Since first way was already described, I add details only about second. This technique is described in tutorial Creating a Grungy Brick Wall in Blender.

Model tiles as separate objects (so Array modifier fits perfectly). Leave gaps between them which will be closed afterwards.

Add another object, make it very thin, a bit thiner than tiles and a bit shorter than they are. Add some geometry only to avoid Multiresolution modifier turning object into a ball.
Subdivide added mesh enough to sculpt in the gaps between tiles. Sculpt with both objects visible in order to see how much of effect should be added (i.e. in the beginning of the sculpting you won't really see the object you sculpt on except for the gaps. Keep in mind that cement shouldn't be visible very much and it shouldn't cover tiles with itself).

You could create one more mesh (e.g by duplicating the mesh which represents the cement and deleting Multires from it), bake these 2 meshes into the third one in order to get normal map which you can apply to the third object. See How do I bake a texture using Cycles bake about baking in Cycles. See Baking Normal maps in Cycles for more info about baking normal maps.
This is not needed in order to render scene. This will be needed to lower amount of time to render result and computer resources involved for it to work.
Setup lighting which is desired. Create adjacent materials for objects which represent cement and tiles and render.

Possible result of tiles:

Advantages of this way:

You can model tiles in any way you'd like to; it's lot simpler to bevel cubes when they are separate objects and you don't need to track topology of the whole model, at the same time modeling it to get mesh looking as desired. After modeling you're left only to spread it over the scene with Array modifier.
It's a lot easier to setup materials (no vertex colors, at least for this task; this doesn't mean you won't need to fake dirt).
It's easier to fake inaccuracies of cement surface (which isn't flat).
Answer: This is a relatively simple problem if you're willing to add geometry. For a game model where low vert count is critical, this would be a poor solution...
Select your wall plane. Subdivide it to taste, depending on how big you want the tiles to be.

Add an edge loop to the inside and outside of each subdivision (easiest way is to use Ctrl+R).

Select the tile faces and move them out a little bit, depending on how deep you want the crack to be.

And voila.
Comment: This could also relatively easily be done *with* UV mapping, by adding a bump map to _simulate_ depth or a displacement map to physically create depth.
Answer: You can do this in Cycles without mesh manipulation.
I will circle back and do a formal writeup, but everything is here (just do a UV unwrap first):

How to make lines visible on rendering


Converting from 7-speed to 10-speed rear wheel

Question: My Bridgestone MB-5 currently has a 7-speed rear wheel. I'd like to convert it to a 10-speed. Is this possible? Is it practical?
Comment: What is 7 x 1.5? What is wheel casket? 2 x 10 sounds like a drivetrain.
Comment: Yes, you need to clarify.  Are you talking about changing the sprocket cluster ("cassette") on the wheel?  If so, what change precisely are you proposing?
Comment: right now i'm running a 2x8 set up my cassette is 7. my sifters are a shimano sora 8x3 . May be all I need to to find some older road bike derailluer sp that are 3x8 ?
Answer: You may be interested in this .. The 1992 Bridgestone catalogue (8meg PDF)
The bike is the lower end of the range (MB-6 being lowest), meaning its not worth that much and never started out as a great bike. As its steel (one redeeming feature), its possible to cold form the frame to widen the rear drop outs to take a 10speed, so technically its possible......
Practically its not worth it. The bike is old and low end. To upgrade to 10Speed you would need

Complete Wheel (at least a new Hub and cassette)
Dérailleur
Shifters
Chain rings

Probably

Shifter Cables
Chain


Is Robocop immortal?

Question: He's half man and half machine so he's gotta have a living flesh still in him. But considering he didn't age as time goes by later on in the series. Is he technically immortal then?
Comment: Are you assuming that machines are immortal? Can you name three complex machines that have continued to function longer than a human life span?
Comment: @Lexible I don't think your comment addresses the question.  Machine parts can be changed, upgraded, and fixed.  If they are all that is necessary to keep Robocop alive and well, then he could very well survive indefinitely by replacing or repairing them.
Comment: That's fair-ish, @MishaR ... still, I think that the "immortality" of machines is still worth questioning.
Answer: Of course he is not immortal.  Robocop's body did indeed contain a significant amount of organic material—such as his brain (although not his arm, even though they could have kept it).  The unusual environment could certainly change how his organic flesh appeared to age, but the neurons making up his brain simply would not last forever.  Eventually, they would succumb (perhaps to Alzheimer's Disease, if nothing else), and he would die.
Comment: Given how they can interface with his brain for accessing of memories, maybe in-universe they could eventually download his "soul" into a computer

Is Robocop immortal?