Questions on Thurston's metric on Teichmüller space

Question: I'm reading the famous "Minimal stretch maps between hyperbolic surfaces" by William Thurston and I'm trying to understand the key theorem 8.1. I have many unclear points so I hope someone can help me out.
First let me introduce it: in this (unpublished) article Thurston, between other things, gave two metrics on Teichmüller space of surfaces of genus $g$:
$K(g,h):=\sup_{\alpha\in \mathbb{S}}log(\frac{l_g(\alpha)}{l_h(\alpha)})=\sup_{\alpha\in PML(S)}log(\frac{l_g(\alpha)}{l_h(\alpha)})$ where $\mathbb{S}$ is the set of isotopy classes of simple curves on $S$ which is dense in $PML(S)$, the set of projective classes of measured laminations on $S$.
$L(g,h):=\inf_{Diff_0^+(S)}log(L(\phi))$ where $L(\phi)$ is the Lipschitz constant of $\phi$ with respect to hyperbolic metrics $g$ and $h$.
Thurston proved the equality (theorem 8.5) $K(g,h)=L(g,h)$ for every couple of hyperbolic metrics $g$ and $h$.
Theorem 8.1 is the first step in order to obtain this equality: it states that if $\lambda\in ML(S)$ is such that the ratio $\frac{l_g(\lambda)}{l_h(\lambda)}$ is maximal in a neighborhood of $\lambda$ in $ML(S)$ then there exists a map isotopic to the identity from a neighborhood of the geodesic realization of $\lambda$ in $g$ to the geodesic realization of $\lambda$ in $h$ with Lipschitz constant $\frac{l_g(\lambda)}{l_h(\lambda)}$.
My unclear points regard proof of theorem 8.1:
1) In Proposition 6.4 Thurston computes the tangent space of $ML(S)$ (as a piece-wise linear space, via the structure given by train tracks coordinates) at $\lambda$ : it is the union of the cones $V(\mu)$ where $\mu$ is a chain recurrent lamination containing $\lambda$ and such that $cut(\mu)$ admits a transverse measure of full support.
My question is: are there other references for this construction? Thurston's proofs are not so detailed (expecially about the function $cut$). I've read Harer's book about train tracks but he doesn't mention the tangent space of $ML(S)$. I also know Bonahon studied the tangent space to $ML(S)$ but only in terms of laminations with transverse Holder structure.
2) In theorem 7.1 Thurston computes the first order approximation to the length function $l_g$ on $ML(S)$: for every lamination $\lambda'\in V(\mu)\subset T_\lambda(ML(S))$ the first order approximation to $l_g(\lambda')$ is $i(\lambda',F_g(\mu))$ ($F_g(\mu)$ is the horocyclic foliation of $\mu$ with respect to the metric $g$). I've not followed every detail in the proof, but the result is intuitively clear.
What is not clear to me is how Thurston uses this in the proof of Theorem 8.1: if $\lambda$ is maximal for $\frac{l_g}{l_h}$ then the derivative of $\frac{l_g}{l_h}$ is zero in $\lambda$. But then Thurston says that, "by theorem 7.1, it implies that the measure class of $F_g(\lambda)$ is the multiple $\frac{l_g(\lambda)}{l_h(\lambda)}$ of the measure class of $F_h(\lambda)$" My question is: How does it follow from $d_\lambda(\frac{l_g}{l_h})=0$ that $F_g(\lambda)=\frac{l_g(\lambda)}{l_h(\lambda)}F_h(\lambda)$?
Answer: Here is an answer to question (2). Let $\lambda' \in V(\lambda)$ be a lamination in the near subspace of the tangent cone at $\lambda$. Let $\alpha(t)$ have $\alpha(0) = \lambda$ and $\alpha'(0) =\lambda'$. As $l_h(\lambda)$ is nonzero, the fact that $\frac{d}{dt} l_g(\alpha(t)) / l_h(\alpha(t)) = 0$ implies with the quotient rule and Theorem 7.1 that $$0 = l_h(\lambda) (D l_g)_\lambda(\lambda') - l_g(\lambda)(Dl_h)_\lambda(\lambda') = l_h(\lambda) i(\lambda', F_g(\lambda)) - l_g(\lambda)i(\lambda',F_h(\lambda)).$$ So for all $\lambda'$ in the near subspace of the tangent cone to $ML$ at $\lambda$ we have $i(\lambda', F_g(\lambda)) = \frac{l_g(\lambda)}{l_h(\lambda)} i(\lambda', F_h(\lambda)).$ This determines the measure class of $F_g(\lambda)$ among foliations supported in a neighborhood of stable topological type containing $\lambda$.


How to show Virtuemart Product Type Parameters in a Table Format

Question: Would you please kindly tell me Instead of showing Product Description how to show Virtuemart Product Type Parameters in a Table Format in the fly page, just like in the following image?
Answer: The answer is- You have to go to components/com_virtuemart/themes/default/templates/product_details/  and then open up - flypage.tpl.php. This is the page which basically loads when a user sees a particular product under a category. If you do not want to show the product description then just remove the description area from the fly page and then design the page with CSS just like the way you want. In case you want to show the product type parameters as product specification you may need to change some codes here - administrator/components/com_virtuemart/classes/ps_product_type.php around line 553 to 580.
Thanks :)


Content not refreshing in iOS apps

Question: Everytime I open an iOS, app instead of refreshing to the homepage and showing me new content the app opens to where I was last time I used it. For example, when I open a third party news app, instead of opening to the homepage with new and updated articles, it opens to the article that I was reading when I closed the app. I am experiencing this problem with all my apps and was wondering if it could be related to background app refresh setting which I currently have turned off.
Comment: The way your question is currently worded makes it very difficult to understand the problem you're facing, what apps are being affected, and what you've already done to resolve the problem.  Please see [ask] for tips on asking questions.  Without a substantial revision, your question could be closed as either 'too broad' or 'unclear what you're asking'.
Answer: You are confusing between two different features available in iOS.
What you are observing is the iOS default behaviour and is called state restoration. As long as an iOS device has available memory (main memory or RAM), it preserves the running state of most recently used app(s). The assumption is that the user is likely to re-open the recently used app.
Background app refresh setting is relevant for apps that need to communicate with remote sever over the Internet to fetch data (typical example of such apps is social networking, email client apps etc.). Enabling background app refresh for an app (if enabled), will let iOS fetch data for such app at opportunate moments (such as when iOS device data connection is activated). This enables the apps to instantly present up-to-date data to users when launched, thereby providing a good user experience.
Since invoking device radio costs a relatively higher battery usage penalty, enabling this setting ensures best user experience while optimising resource usage.
Comment: is there any way to adjust this state restoration?
Comment: @Skrrrrrtttt While the default setting works best for most users, you can kill the app by quitting it from the multitasking UI (Double rap on Home Button or swipe up and hold on iPhone X/XS/XS Max/XR). That way when you launch the app again you will start from the Home page.

Content not refreshing in iOS apps


How does Chess.com calculate puzzle rating?

Question: How does chess.com calculate puzzle rating? I am curious because today, I managed to gain rating while incorrectly solving a puzzle. Could someone help me out? (Also on puzzles that are already rated, not just pending)
Answer: According to Chess.com's How do Puzzle ratings work? you can get +1 point for getting pending puzzles incorrect as they have not yet received an established rating.

"About 5% of the puzzles you run into will be new puzzles that have
not yet been rated. You will never lose points for getting one of
these Pending puzzles wrong!"

As for how they calculate the Puzzle ratings, these are similar to the playing ratings with a few key differences:

Correctly solving a puzzle always increases your puzzle rating whereas a win against a much lower rated player may not increase your rating. Solving the lowest rated puzzle will at least give you 1 point.
A new puzzle receives a rating based on the puzzle ratings of those able to solve it. However, after a set amount of time the rating is locked and will not change. Chess.com does have a means to correct the locked rating up or down if needed.

For puzzles with multiple moves, there is a "partial credit" scoring system where you can till receive a net increase in puzzle rating for getting a few moves right even if you missed some at the end of the sequence.
Comment: What if I get 2/3 moves correct? I sometimes gain rating on rated puzzles. (For getting them wrong.)
Comment: @MrChessR Updated answer to include this point.
Comment: @MrChessR did this answer your question?


How to find the memory requirement (RAM) when network load is know on raspberry

Question: I am want to use the Raspberry Pi for my experimental work. My network load will be approximately 2000bits. How I can find the memory (RAM) requirement against the network load? Which formula can be used for finding the memory requirement?
Comment: The network load does not directly correlate to ram usage.  2000bits Total? Per Second?   Is that sending or receiving? Whats the data?  The RAM usage is going to be determined by what processes are running that are sending/receiving this data, and what they have to do with it.  Basically you have not given enough information to actually give you an answer. And really I don't think there is an ANSWER, but more detail might help point you in the right direction.
Comment: I can see no relevance to the Raspberry Pi.
Answer: The underlying driver buffers are static and reused but this message is likely copied several times up and down the IP stack including possibly dynamic buffers with kmalloc .
I would estimate a 2x instantaneous  overhead in raw  memory use for a given Ethernet frame, plus a copy for every thread that is reading the packet.
But it is not clear how you would profile this or how relevant it is to the actual memory commit as this memory is cleared in kernel as soon as it is handed off and kernel memory is seperate. Additionally  Every process is responsible for managing the memory of any packet copies it keeps.
Perhaps you can rephrase the question to address your actual concern or performance issue


Possible to yield a coroutine when it is taking too long to run?

Question: Suppose I have a function that raycasts from (0,0,0) to every object in the scene.  Sometimes the scene contains just a couple objects and sometimes it contains several hundred.  Is it possible to setup the raycasting function in a way that  ensures a good framerate? For example, within the "for" loop that shoots the rays could I somehow evaluate how much time has passed since the loop started and "yield return null" if the time in seconds is greater than the target time of each frame?
Answer: You can use Time.realtimeSinceStartup as reference for the time passed:
IEnumerator Test() {
    float startTime = Time.realtimeSinceStartup;

    foreach( Raycast rc in RaycastArray) {
        if( Time.realtimeSinceStartup - startTime < 0.01f ) { //Process stuff for 10 miliseconds
             //PROCESS A RAYCAST
        }
        else {
            yield return null;
            //Its important that the new time is assigned AFTER the yield
            startTime = Time.realtimeSinceStartup;
        }
    }
}

Comment: Not that I know of. You could probably improve it by dynamically change the time the couroutine spends on each cycle. Like monitor the average deltaTime and never spend enough time to increase the deltaTime above certain threshold. You could even process information every X cycles. I bet there is a lot to it in order to improve performance under several scenarios.
Comment: this is exactly what I needed.  Do you know if this kind of thing is a common/standard practice for optimization?
Comment: I'd say that time slicing tasks like this is pretty common. Not necessarily in this implementation, but in one way or another it is done.
Answer: This is my version of Leo's answer. Pretty handy tool for splitting up the workload of certain loops to help with FPS. Bit hard to predict how long each loop will take though, but probably something I'll work on further.
IEnumerator ForOverTime (int fpsLimit, float timeLimit)
{
    float processStartTime = Time.realtimeSinceStartup;
    float frameStartTime = processStartTime;
    fpsLimit = System.Math.Max(0, fpsLimit);
    fpsLimit = fpsLimit == 0 ? 1 : fpsLimit;
    timeLimit = System.Math.Max(0f, timeLimit);

    for (int i = 0; i < 10000; i++)
    {
        if (Time.realtimeSinceStartup - frameStartTime < 1f / (float)fpsLimit ||  (timeLimit > 0f && Time.realtimeSinceStartup - processStartTime > timeLimit))
        {
            print("Do Something. " + Time.frameCount);
        }
        else
        {
            yield return null;
            frameStartTime = Time.realtimeSinceStartup;
        }
    }
    print("Time taken: " + (Time.realtimeSinceStartup - processStartTime));
}


Can more than one net be used on a creature? If so, how does a creature escape?

Question: If the first party member uses inspiration to land a net, the rest of the party can throw their nets without disadvantage. Would a single strength check remove all nets?
Answer: Depends on the DM
PHB page 148 describes the properties of a Net:

A Large or smaller creature hit by a net is restrained until it is freed. (...) A creature can use its action to make a DC 10 Strength check, freeing itself or another creature within its reach on a success. Dealing 5 slashing damage to the net (AC 10) also frees the creature without harming it, ending the effect and destroying the net. (...)

What happens to a creature when it has multiple nets thrown at it? It is restrained and has multiple nets on itself, and that's about it. The only game effect here is the Restrained condition, applied only once, since conditions do not stack.
How does such a creature free itself? According to the description above, a DC 10 Strength check or dealing 5 slashing damage to the net frees the creature, which could be understood in two ways: "removes the Restrained condition", or "removes the single net the action was taken upon". Those are the same if it's the last net the creature is freed from, but with multiple ones there can be some discussion on which of the two interpretations apply.
My rule would be the first one presented, but I'd probably make it harder to free oneself from multiple nets at once, either by increasing the DC on the Strength check or the AC or hp of the nets, or imposing disadvantage on the check or attack. You could also get closer to the second interpretation and require that every net be dealt with separately, though maybe allow for removing multiple nets at the same time on a really high Strength check or a high-damage attack. My proposition here is +1 net per each 5 points above the DC or each 5 points of damage.


Current carrying wire contradiction

Question: If we have a wire connecting two ends of a battery, a current runs through it. If the movement of electrons is due to an electric field along the wire, then how could the potential difference between two points in the wire be zero? And how could the current be constant, unless the resistance in the wire provides some sort of opposing force to the electric field?
Answer: The potential difference between two points in a real wire is not zero.  The resistance of a real wire is not zero.  I think you are basing your reasoning on an idealized model of a wire, not a realistic one.

Current carrying wire contradiction


I'm in probation period and I cannot fit in with the company culture, how should I answer "why do you want to leave?" to my manager

Question: I'm in my current company, in probation period, for 2 weeks now, and I have the feeling that I just cannot fit in with the culture and environment.
The colleagues here are kinda aggressive (in work-related issues). They are unprofessional compared to my last company (non sense and not on point emails, no sense of responsibility nor reliability...). More importantly, work is poorly organized.
In the interview, my current manager did told me the job here is stressful, but I imagined it was stressful in a different way, not like this.
I kinda like my manager and I think he likes me. I know he had to do a lot during the recruitment process to get me the benefits I currently have. If I leave now, I'll put him in a really tough spot.
With that being said, it's still certain that I'm gonna leave.
Should I tell my manager the reasons, or should I say something comforting?
Comment: People usually advise someone in your situation to not burn any bridges and keep it cordial, but it's better in the long run for yourself to speak your mind.
Answer: If you're leaving don't worry about your manager I doubt very much your 2 weeks has had all that much impact.
Exit interviews are for the benefit of the company, it's best to focus on where your career is heading then waste time griping or otherwise. In fact it can come back to haunt you in future. So my advice would be to use generic terms, .... better opportunities.... career advancement, stuff like that.
Comment: I think this is poor advice from a personal development perspective, but it seems to be the popular choice.
Comment: @mars - "poor advice from a personal development perspective" <- whatever do you mean? The OP is in a chaotic, and unprofessional environment. There's little benefit to sticking around, as identified by the person best suited to do so - the OP. There's nothing to be gained by being truthful about it, because I can assure you that the manager is well aware of the fact that the company is in shambles. Stating that as the reason you're quitting is a surefire way of making enemies, and not much else.
Answer: I recommend to express what you felt in the organisation and never ever attempt to maintain the comfort level of your manager.
What I understood from your statement is that there is no person-organization fit and you took a right call to leave the organisation and find a better one. it is wise decision and the best help what you can offer to the organisation is

tell them the truth and they should not feel that they are doing right. This shall make them change before they hire the next guy
Comment: It may be dangerous to take this approach since he knows his manager for only two weeks. Maybe his manager is really cool and will take the positive criticism well, or he may burn bridges with him/other managers.


Before taking on a project, what to consider?

Question: If someone asks you to work for them, should you ask to see the picture first if it's available?
Answer: I like to get as much information as I can about the project ahead of time:

What's the scope of work
How long is the project
Do I find the project/material interesting
How well have they planned for audio post (or haven't they)? What do they want the audio to do in their project?
Do I have the time to provide what they're looking for?

I've mentioned in another thread on this site that a project can described as "Good," "Fast," or "Cheap." It can be any two of those three ideas, but it will be the direct opposite of the third (i.e. for a project to be "Good" and "Fast," it will NOT be cheap..."Fast" and "Cheap" will not be "Good"). This is one of the biggest factors for me to be involved in a project. Personally, for freelance work, I will not allow myself to work on something that will not be good. [I have less say at my day job. ;)] My work reflects on me and my skills. If the circumstances do not offer me the opportunity to put forth my best effort, I will not take it. Which brings me to the next idea.
Do not oversell yourself...to the client, or yourself. If you have doubts about your ability to handle a particular assignment, make sure you evaluate them carefully. Know what you're getting yourself into. Know what your time is worth, and what the different tasks for a project requires. Completing any project is a system of controlled attrition; you won't be able to do everything perfectly. Make sure priorities are discussed and agreed upon (this goes back to the "scope" bullet-point), before you agree to start on the project.
And don't forget, you don't have to be the only audio person who works on a given project.
Comment: "Do I have the time to provide what they're looking for?"  -- That's probably the most important thing for freelancers.
Answer: Hopefully the picture isn't shot yet and they're taking you on in Pre-Production.
Answer: Ask for information on the project. Is it a paid job? If so, do you have the time to work for free or not? If it is without pay, I would definetely ask to see the film in advance - if available. If it isn't shot yet, I would like to read a synopsis or treatment. If I know the director in advance, either in real life or by reputation, I could also make my decision based on that. If for instance I was asked to work on a film by David Fincher or Lars von Trier, I would probably say yes at once. If my schedule was free and the job is paid I would also say yes.
Comment: With regards to paid/unpaid, I'd like to link to this flowchart here... http://shouldiworkforfree.com/
Comment: glad i found that chart, my life is so much easier now
Comment: @Chris @Daan - i've only got one problem with that chart, it doesn't have a path for "i really like this idea/project." if i'm intrigued enough by something, and i have the availability, i might do it. ;)


Industry Term for "Intentional production halt" department

Question: Is there a name for when production is stopped intentionally in order to allow the factory to perform repairs and maintenance?
Comment: Maintenance window or planned down-time?
Answer: I would use scheduled down-time.
The phrase will leave three impressions:

currently not in operation
not broken or defective
operation will resume at some "scheduled time"
Comment: Sounds good. I had come across "down-time" but it sounded negative.
Answer: In Australian usage the term planned outage is common.
See, for example, this page by Ergon Energy, where they publish a list of upcoming planned outages for the electricity distribution network.

In order to keep the network functioning and carry out necessary maintenance and upgrades, sometimes we need to interrupt the supply of power. However, our aim is to minimise the impact of any outage that may affect you.
Except in emergencies, if an upgrade or maintenance to the network requires us to interrupt supply, we will notify you at least two business days before the planned outage.
The date and the estimated start and finish times of the planned outage will be sent to you by mail, letterbox drop, newspaper or radio advertisement, email, phone, fax, or flyer.

Informally, this is often shortened to the single word outage.

You'll need to arrange an outage before you can repair that machine.
Comment: TIL, but mine was for a friend's resume, she works in the oil industry.


Spark plug and coil only one is bad for 2012 Honda odyssey

Question: I am trying to find out if I have one spark plug (#3 to be exact) as well as the coil can I change just the one or is it bad for the engine to do so?
Comment: They're fairly cheap online, you could just replace them both...or one at a time...
Comment: Has this vehicle had the Honda engine misfire problem repaired in the past?
Answer: If you find the coil is bad, change just the coil. You can do this without issue.
If you find the spark plug is bad, change all of them. When spark plugs start going bad, it is a good bet others will probably follow in short order. It will also ensure all spark plugs are of the same age and useage. This will better help in equalizing power production across the cylinders. If things are tight, you could get away with changing just one, but really, it's not something I'd do.
Answer:
Try swapping the #3 coil with another cylinder and see if the problem follows.
Try swapping the #3 spark plug with another cylinder and see if the problem follows.

That should let you know where the problem lies.


What is the best open source credential manager?

Question: I am looking for an open source / free software password & credentials management tool, capable of isolation for various teams, able to store human passwords but also managing crypto keys for servers, ideally with SCIM provisioning. Any suggestion?
Answer: Did you take a look at Bitwarden? It seems to match all your requirements listed here:

it is open source
it can isolate teams
of course it can store "human passwords", also any sort of keys
it supports SCIM provisioning


How can I submit two papers to the same journal with each paper citing the other?

Question: I have my whole PhD thesis split into two papers to be submitted to the same journal at the same time, and each of them needs to be cited by the other (circular citations). I can publish the first paper to arXiv and get the DOI and cite it in the second paper. But I also want the first paper to cite the second paper. But in order to cite the second paper in the first paper, the second paper needs to be published first, which then becomes the first paper and the same problem arises. I am thinking of this possibility of publishing the first paper in arXiv and get its DOI and then cite it in the second paper and upload the second paper to arXiv and then get its DOI and edit the first paper by adding the DOI of the second paper. But is it fine to do so? I am wondering if the journals would accept each paper citing the other in this way. Also, are there any other better ways having each paper citing the other?
Comment: @BryanKrause: In my world, circular references are perfectly commonplace, since papers discuss related work and researchers discuss their work in progress with each other, frequently leading to situations where two or more papers provide context for each other.  In the most extreme case, two papers report on independent work leading to the same result, so they should of course cite each other.
Comment: What field is this? There are at least some where such circular references are fine, assuming the split into two papers is appropriate.
Comment: It's not normal for papers to cite each other. Citations are for work that a paper builds on. Which of your papers builds on the other?
Comment: In my case both the papers in some sense depend on each other. They apparently can't be published as a single paper because it's a massive work.
Comment: It's in the field of robotics, and I am planning to send it in an Elsevier journal. My supervisor told me that it is possible to make circular citation, but I am wondering if this three-way method (publishing the first in preprint and then citing it in the second and then editing the first to include the citation to the second) is acceptable way of doing it.
Comment: @Sursula-they- Thanks for suggesting the link. I went through it and it seems it is about how to cite an unpublished paper which can be solved by sending it in arXiv but my question is basically about circular citation wherein both the papers are unpublished and each paper needs to cite the other.
Answer: Ask the journal. If the journal has an editor, ask the editor. You are not trying to circumvent the review process. You are not asking about your specific paper at this stage - this is a structural question about submissions.
Remember that the papers you submit will certainly not be published in their present form. There are always edits, refinements and so on. So it should be OK, in the form you are submitting in now, to say "Jacob (2022b) "My second paper", submitted to…".

If your papers are rejected, then you don't need to worry about the format of the references they contain.
If your papers are accepted, the editor will tell you what to do about the references.
If one is accepted and the other is rejected, you and the editor between you can work out what to do about the references from the accepted one to the rejected one. Perhaps they can be omitted altogether.

Read the journal. Has it published interdependent papers before? If so, how did the references work? If not - you need to come up, at submission time, with a good argument as to why they should use this format for the first time.
Comment: Yes, the delay in publication due to review/revision works in your favor here. There will be time to update "temporary" citation statements.
Answer:
"But in order to cite the second paper in the first paper, the second
paper needs to be published first"

In my opinion, that is simply incorrect. To cite a paper it should not be first published or peer reviewed. If you have it on arXiv you can simply cite the arXiv version. But even without it, you can cite it as an "unpublished manuscript".
If you are concerned about reviewers who will doubt the correctness of the results since they have not yet been peer reviewed, then you must first publish the first paper, without basing your results on paper 2 (but only citing it as a related work), and then only publish paper 2.
Comment: Thanks, but your papers are on Arxiv, so I don't see how they're going to be "untraceable".
Comment: Thank you for your answer, and yes unpublished papers can be cited but that makes the citation untraceable. The intention in having circular citations in my papers is to ensure the reviewers of one paper can get to go through the other paper and if published the readers can get to trace the other (companion) paper, and when I said in order to cite the second paper in the first paper the second paper needs to be published, i was saying it in the context of my thesis.
Answer: I agree with Martin Kochanski's answer, but wanted to add some thoughts. Now, I don't know the conventions in robotics, but I've been part of physics papers where we did exactly what you describe, i.e. updated arXiv preprints to have circular references before journal submission.
Our intention was more to benefit preprint readers than the journal(s), however. The journal(s) can and should be notified of the related manuscript at time of submission. Cover letters are very useful for this. Note that this is true whether you include circular references in the submitted files or not, and whether you post preprint versions at all or not. It is also often possible to upload the related manuscript as supplementary information for reviewers, which is especially useful if the publication venue uses double blind referencing, you haven't posted preprints, you submit to different journals, or you have reason to expect the two papers are likely to be reviewed by different people.
Comment: Thank you for your answer. And yes i would be mentioning it in the cover letter. I was thinking of figuring out in advance whether the journal allows it or not, so that I could plan the submission accordingly rather than waiting for the first decision which may take some weeks.


The perfect Number system

Question: I was thinking of the number system presently in use(the decimal system) and its shortcomings. One of them is that all numbers cannot be represented accurately, for example the value of any irrational number. Although I know several attempts have been made for the development of such a system, none of them, as far as I know, have succeeded-none of them can represent all known numbers uniquely and accurately. Is such a number system even possible?
Answer: In any number system that uses a finite (or even countably infinite) set of characters, the set of numbers that are representable in a finite string is at most $\aleph_0$.  Most reals will therefore not be representable by any finite string, so a perfect (as I read your definition) number system is not possible.
Answer: There is a unique continued fraction representation for every real number. In particular, a continued fraction is defined as follows, using the notation $[a_0;a_1,a_2,\ldots]$ for a continued fraction where $a_i$ is a possibly infinite series of positive integers. We say
$$x=[a_0;a_1,a_2,\ldots]$$
exactly when
$$x=a_0+\frac{1}{a_1+\frac{1}{a_2+\frac{1}{a_3+\ddots}}}$$
or, writing this recursively:
$$x=a_0+\frac{1}{[a_1;a_2,a_3,\ldots]}.$$
What this says is, basically, we first approximate any real $x$ by finding the best integer approximation below it - that is $a_0=\lfloor x\rfloor$. Then, there is some remainder $x-a_0$ which is between $0$ and $1$. We take the reciprocal of this, $\frac{1}{x-a_0}$, which is between $1$ and $\infty$ and approximate that, and continue doing so. It is provable that this represents each rational number with a finite continued fraction and each irrational number with an infinite continued fraction and that these representations are unique.
A caveat of this is, although it is possible to do computations on continued fractions, it is not nearly as convenient as positional notations (like decimal). Whereas we can compute a product $ab$ or a sum $a+b$ to some number of decimal places (usually) given a fixed number of digits of $a$ and $b$, there is not a clear correspondence between how many terms of the continued fraction we have and how accurate it is (and how many terms of a sum or product we could find therefrom). Given that computation is often the point of using decimal expansions, where we often don't worry about theoretical issues like non-unique or non-terminating expansions, this makes continued fractions somewhat impractical as an upgrade to decimals (but theoretically, they're quite useful)
Comment: Although this method adheres to the 'unique' requirement very well, it cannot render absolutely accurate values for quantities like 'pi' or any other irrational number.
Comment: There are more real numbers than finite strings (see Ross' answer) - that inevitably means that we *have* to work with infinite sequences to talk about the reals. Every real does have a continued fraction - it's just infinitely long (and in that sense "can't be written down" - but that's not a really rigorous idea). You can't do much better than writing down $\pi$ to express $\pi$ if you want to work exactly.

The perfect Number system


What's the difference between filename and ./filename in Linux

Question: What is the difference between filename and ./filename?  Under what circumstances is one preferred to the other?
Answer: For datafiles, it does not make a difference - both statements will reference the data file in your current directory. (For example, cat filename and cat ./filename are semantically identical.)
It's a different story if the filename in question refers to an executable, i.e. is the first (or even only) thing you type on the command line. ./filename will look for the executable in your current directory, and nowhere else. filename, on the other hand, will evaluate the environment variable PATH, and look for filename in every directory stored therein (which might or might not include your current directory).
./filename (or any other /path/to/filename) is thus preferred when you want to execute a specific executable, not the first one found in your PATH.
Answer: If you're running a program, filename says to run the first one found in your $PATH and the second one says to run the one in the current directory.
If you're using that filename as an argument to a program as in do_something filename or do_something ./filename then they mean the same thing.
Answer: You are referring to command execution, right?
There is an enviroment variable PATH that contains some system directories, delimited by semicolon. When you type command the system looks in these directories in the order they are specified to find an executable file named <command> If it finds it, it tries to execute it. You can see your PATH via echo $PATH in bash. For example:

$ echo $PATH
  /sbin:/bin:/usr/sbin:/usr/bin:/usr/games:/usr/local/sbin:/usr/local/bin:/home/ivanatora/bin:/usr/local/kde4/bin:/usr/local/kde4/bin

When you type ./filename you are specifying exact path: the current directory. You can see that the current directory seldom is in your $PATH (for security reasons). So if you want to execute a file from the current directory, you use ./filename.
To execute a file by its path (especialy if it is not in $PATH) you can also type <path>/file, like:

/sbin/ifconfig
Answer: Executable security is the main reason for this difference.
You do not want . (present working directory or PWD) in your path because someone could trojan
http://en.wikipedia.org/wiki/Trojan_horse_%28computing%29
a crucial executable like ps or ls, in your PWD and fool you by presenting bad data.
Answer: It depends what circumstances you're using it as.
As an argument, eg "program filename", then it's up to the program, but generally they're identical.
As a program name, eg "filename arguments", then "filename arguments" will search PATH to find the binary, while "./filename arguments" will use the program in the current directory. This is obviously useful if . isn't in the PATH, but it's also useful to use this one even if . is in the path, perhaps because it matches an earlier entry.


Derivative of $(y-XB)' h(y-XB)$ with respect to $B$

Question: Let $X$ be a $n\times p$ matrix, $y_{n\times 1}$ a vector and $B_{p\times 1}$ coefficients so that $y=XB$. Then what is the derivative of
$$
(y-XB)' h(y-XB)
$$
with respect to B, where $h(.)$ is an $R^n\rightarrow R^n$ differentiable function e.g. ($h(z)=z$) and $(')$ is the transpose of a matrix?
Comment: Use the Chain Rule and the Product Rule.
Comment: @whuber  I did but the result looks too strange since the dimension is not right for example the first derivative is $p\times 1$ and the second one seems impossible in dimension
Comment: Are you sure the derivative with respect to B is defined? Because as you describe your problem, B is a vector of coefficients and X seems to be a variable of the space. So, as I see it, your question is equivalent to: how do I derive `2 * x` with respect to 2, which does not make sense to me... Or maybe precise what is B.
Comment: @Eskapp  It is a linear function. Assume h(z)=z then the problem reduces to $(y-XB)'(y-xB)$, the familiar form of the multiple regression.
Comment: @whuber please, can you explain to me how to do it? I really need help
Answer: Apply the Chain Rule.  (It's the only rule you need to know.)  To do so, you need to break the overall function into the composition of functions whose derivatives you can find.  This is typically done by inspecting its formula and unwinding it from the outside in.
Let all vectors be column vectors and identify $\mathbb{R}^n\times \mathbb{R}^n$ with $\mathbb{R}^{2n}$ by stacking the two components, $(\mathbf{x}, \mathbf{y}) = \pmatrix{\mathbf{x}\\\mathbf{y}}.$
The last operation is a function
$$u: \mathbb{R}^{2n} \to \mathbb{R};\quad u(\pmatrix{\mathbf{x}\\\mathbf{y}})=\mathbf{x}^\prime \mathbf{y}.$$
The penultimate operation is
$$v:\mathbb{R}^n \to \mathbb{R}^{2n};\quad v(\mathbf{x})=\pmatrix{\mathbf{x}\\ h(\mathbf{x})}.$$
The first, innermost operation is
$$w:\mathbb{R}^p \to \mathbb{R}^n; \quad w(\mathbf{b}) = y - Xb.$$
Their composition is the function
$$u\circ v \circ w: \mathbb{R}^p {\,\xrightarrow{\ w\  }}\,\mathbb{R}^n\,{\xrightarrow{\ v\  }}\,\mathbb{R}^{2n}\,{\xrightarrow{\ u\  }}\,\mathbb{R}; \quad (u\circ v\circ w)(\mathbf{b}) = u(v(w(\mathbf{b})))=h(\mathbf{b}).$$
The Chain Rule asserts that $h$ is differentiable when each of $u,v,w$ are differentiable and its derivative $Dh:\mathbb{R}^p \to \mathbb{R}$ (which will be written as a $1\times p$ matrix) is the composition of the derivatives (each evaluated at the appropriate values),
$$Dh = Du \circ Dv \circ Dw.$$
You need to find those derivatives.  They are
$$(Dw)(\mathbf{b}) = -X,$$
$$(Dv)(\mathbf{x}) = \pmatrix{\mathbb{I}_n \\ (Dh)_\mathbf{x}};\quad \mathbf{x} = w(\mathbf{b});$$
(remember, $Dh$ is an $n\times n$ matrix), and
$$(Du)(\mathbb{x}, \mathbb{y}) = \pmatrix{\mathbf{y},&\mathbf{x}};\quad \mathbf{x}=w(\mathbf{b});\quad \mathbf{y} = h(w(\mathbf{b})).$$
To obtain the answer, do the matrix multiplication and plug in the values $\mathbb{x} = w(\mathbb{b})$ and $\mathbb{y} = h(\mathbb{x}) = h(w(\mathbb{b}))$.

Reference
Michael Spivak, Calculus on Manifolds (1965).
Comment: Your use of the [tag:self-study] tag indicates your intention is to learn *methods and principles* ("explain ... how to do it") rather than to get a one-line answer. Moreover, there is little interest on this site (or anywhere else on Stackexchange) in providing one-liners: we want to help future readers who may have similar problems that can be solved the same way.  Regardless, this answer is detailed and thorough: all the work has been laid out for you and performed, except for the mechanical procedures of multiplying the matrices and making the substitutions described by $u, v,$ and $w$.
Comment: You actually made me more confused, why there are two $h$ in the formula? why Dv comes up with an $I_n$ matrix?
Comment: Rose, the main point is that all these functions are *linear,* which makes finding the derivatives dead simple, because the derivative of a linear function is itself.  In particular, since $\mathbf{x}=\mathbb{I}_n\mathbf{x},$ $(D\mathbf{x})=\mathbb{I}_n.$
Answer: For clarity, I'll use the convention that uppercase letters represent matrices, lowercase vectors, and Greek letters represent scalars.
First, introduce the vector $$z=y-Xb$$ and note that a function like $h(z)$ only makes sense if applied element-wise. Had the function argument been a square matrix, then there is some ambiguity since one could interpret it as a matrix-wise function. But with rectangular matrices (including vectors) there is no ambiguity.
Using a scalar argument, we get the ordinary derivative
$$h=h(\lambda),\,\,\,\,\,g=\frac{dh}{d\lambda},\,\,\,\,\,dh=g\,d\lambda$$
With a vector argument, both $h$ and $g$ must be applied element-wise; we must also use an elementwise/Hadamard product (denoted by $\odot$).
$$h=h(z),\,\,\,\,\,g=g(z),\,\,\,\,\,dh=g\odot dz$$
One final bit of notation is the use of a colon for the trace/Frobenius product.
$$A:B={\rm Tr}(A^TB)=B:A$$
Putting it all together, write the function of interest in terms of these new variables, then find its differential and gradient.
$$\eqalign{
 \phi &= z:h \cr
d\phi
 &= h:dz + z:dh \cr
 &= h:dz + z:(g\odot dz) \cr
 &= (h + g\odot z):dz \cr
 &= (h + g\odot z):(-X\,db) \cr
 &= -X^T(h + g\odot z):db \cr
 &= -X^T\Big(h + g\odot (y-Xb)\Big):db \cr
\frac{\partial\phi}{\partial b}
 &= X^T\Big(g\odot (Xb-y)-h\Big) \cr
}$$
One final trick is to replace the Hadamard product with the matrix product of a diagonal matrix.
$$\eqalign{
G &= {\rm Diag}(g) \cr
\frac{\partial\phi}{\partial b}
 &= X^TG(Xb-y)-X^Th \cr
}$$


Can not see comments via Facebook on fr.sputniknews.com with Tor Browser 7.0.4. Why?

Question: All was fine with Tor Browser 7.0.2, I can see comments via Facebook on https://fr.sputniknews.com under all news. But it seems there's a bug now.  Do you have a solution ? If not, is it risky to still run Tor Browser 7.0.2 ?  Please avoid "Do not read Sputniknews anymore" comment ;-)
Comment: Not sure this is a Tor Browser bug and yes it is risky to run Tor Browser 7.0.2. When I view the facebook comments, I see it's using an `` which is blank. Facebook is returning an empty page?
Comment: On the other hand...it may be relate to [this question](https://tor.stackexchange.com/questions/15450/photos-broken-on-facebook).
Comment: Thank you for your feedback. I have first disabled HTTPS Everywhere with no luck, then I have disabled NoScript and it worked, Facebook comments came back. Read Edit in my first post for more information.
Comment: Hi, could you maybe state your solutions as an answer to your own question instead of an edit to the question? It might help other users more.
Answer: It seems to be a NoScript bug. When I disable 'Sanitize cross-site suspicious requests' in NoScript Options\Advanced\XSS then Facebook comments come back. So, it is the first solution to disable 'Sanitize...', but we are vulnerable to XSS attack if permanently disabled.
Second solution: tweak the NoScript Options|Advanced|XSS|Anti-XSS Protection Exceptions rules but I can not write such rule... not geek enough ;-). And last solution : post a bug report at NoScript forum. What I am going to do.


How to migrate Xbox Minecraft to a tablet?

Question: My son has an Xbox 360 with the game disc for Minecraft separately. He wants to play on his tablet, but I don't know how to retrieve any info regarding Pocket Edition. Can he sign in using the login for Xbox to play on tablet?
Comment: No. The two versions are separate and not compatible. You need to buy the game again on the tablet of choice, and the save files can not be transferred.
Answer: Sadly the two versions are completly parralel and canot be inter-connected so you will have to buy Minecraft again. Sad, I realise, but cross-compatability is not Mojangs strong point.


Is there a build-in function converting a quantity to one with mixed units (such as feet and inches)?

Question: For example, I want to convert 179 centimeters into 5 feet and 10.4724 inches instead of 70.4724 inches (as this website did). Maybe in the future I would need to convert days to {years, months, days} combination, degrees to {degrees, minutes, seconds}, etc. I can indeed write some codes to perform the task, but after all personal codes are full of flaws and lack of exception handling, so I am looking for a built-in function.
Comment: In WolframAlpha (or Mathematica after "==") just type "179 centimeters in English units".  There are built-in functions for time in Mathematica, however, such as FromDate[], all well documented.
Comment: Welcome to Mathematica.SE! I suggest that: 1) You take the introductory [Tour](http://mathematica.stackexchange.com/tour) now! 2) When you see good questions and answers, vote them up by [clicking the gray triangles](http://tinyurl.com/ch98nrh), because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, [by clicking the checkmark sign](http://tinyurl.com/4srwe2t)! 3) As you receive help, try to give it too, by answering questions in your area of expertise.
Comment: @DavidG.Stork Yes, $DateList[{y,m,d,h,m,s}]$ can solve some of the problems concerning time, but it has many restrictions: {y,m,d} cannot be 0; cannot display 3.14 days, but 3 days 3 hours 21 minutes 36 seconds instead.
Comment: Could you please give one very specific example of the kind of problem you want solved?  The conversion of days to {years, months, days} is straightforward.  What else?
Comment: @DavidG.Stork it is interesting that these are called English units. I wondered what W|A would tell me for "32 hogsheads + 9 pints + 17 gills in French units". It replied that this is $2.062\times10^{11}$ cubic Frenches. You learn something new every day. Oh, and it also thinks that this is a measure of engine displacement, although the French gauge system is used to describe the diameter of catheters.
Comment: @Olekasndr -- I confirmed your result, which I don't know whether to take as delightful or terrifying.  Did W|A just make a "funny" or did it just achieve sentience?
Comment: @OleksandrR:  Try "three hectares in metric units" or "two fortnights in weeks" or "seven cubits in meters" or "Mesopatamian vessel in liters" or any other archaic measurement system.
Comment: @DavidG.Stork well, I tried "lakh crore parsecs in Qin dynasty Chinese feet" but regrettably it does not know what number lakh crore is, and it confused Qin with Qing (or maybe it thinks that 1915 is "ancient"). So, it seems that there are limits.
Comment: Indeed, there are limits.  But "lakh crore parsecs" in Google gives the conversion to meters.
Answer: UnitConvert[Quantity[179., "Centimeters"], MixedRadix["Feet", "Inches"]]

returns
Quantity[MixedRadix[5, 10.472440944881885`], MixedRadix["Feet", "Inches"]]

which formats as 5'10.4724"
Comment: @george2079 `UnitConvert[Quantity["Meter"], MixedRadix["Feet", "Inches", "Inches"]]` becomes `3'3"47/127"`.  Not power-of-two fractions though.
Comment: +1 It is a very nice undocumented feature!
Comment: @ybeltukov I actually didn't know this was undocumented; searching in the documentation center gets no results (!!!) but I'm sure I read this in the documentation center somewhere.
Comment: Is there an `undocumented` Tag? This is not the first example. Reasonable to expect WRI at some point may mine this site.
Comment: @alancalvitti `undocumented` tag added.
Comment: +1 for extra credit I want fractional inches :-) ..
Answer: There is no such build-in function. However, one can write it easily
convert[q_Quantity, units_List] := MapAt[{Total@#} &, #, -1][[2 ;;, 1]] &@
  FoldList[Through@{IntegerPart, FractionalPart}[Last@#/#2] #2 &,
   {q, q}, Reverse@Sort[Quantity /@ units]]

convert[Quantity[179., "Centimeters"], {"Feets", "Inches"}]
(* {Quantity[5, "Feet"], Quantity[10.4724, "Inches"]} *)

convert[Quantity[1.2345, "Meter"], {"Millimeters", "Centimeters"}]
(*{Quantity[123, "Centimeters"], Quantity[4.5, "Millimeters"]}*)

convert[Quantity[1.2345, "Degree"], {"Degree", "ArcMinute", "ArcSecond"}]
(*{Quantity[1, "AngularDegrees"], Quantity[14, "ArcMinutes"], Quantity[4.2, "ArcSeconds"]}*)

Answer: 10.4 introduces MixedMagnitude and MixedUnit, eg:
Quantity[MixedMagnitude[{1/2, 2, 3}],
 MixedUnit[{"Hours", "Minutes", "Seconds"}]]

which btw, renders with bogus DisplayForm

0 h 32 min 3 s

And try all 0's.


Can a user benefit from personal powers stored in an empowered object?

Question: I realized while writing this question that I have another issue with empowered objects.  Specifically, it is the object using the stored powers, rather than the wearer/wielder/user.  Can such an object "target" the user with personal or "self-only" powers?  I intend to have a more powerful psionic NPC loan a PC a Psychometabolic item, but most of the powers it'll have access to are self-targeting and I realized I wasn't sure if the PC could even use them.
Answer: There might be outlier cases, but for the most part, the powers used by a vessel should affect the psionicist.
Empowered objects are explained to be intelligent weapons. From the Empower description: "The weapon has its own personality, however, and like all intelligent weapons, it will try to assert its independence at every opportunity."
As such, I would follow the rules for intelligent weapons. From the DMG: "Powers function only when the weapon is drawn and held and the possessor is concentrating on the desired effect. Most powers require that the character stop and concentrate for a full round."
Even though intelligent weapons are their own independent entities, they aren't capable of using their powers on their own. Given the involvement required of the player, I've never seen it ruled other than the wielder is also part of the casting.
2e didn't have a range of self. It just used a range of 0 and from the spell/power description, it was determined who was affected. For example, "Detect Good/Evil" one of the suggested powers for intelligent weapons: That's a spell with a range of 0 that is described as only affecting the caster.
Technically a DM could rule that the weapon is the one that detects who is good/evil and then communicates this to the player, but only 41% of intelligent weapons are even capable of speech. A full 34% are only able to communicate via "tingles and urges," so it seems unlikely to me that the authors intended such a game of telephone.
Comment: I wouldn't call "an urge to Smite Evil this innocent looking old man" a game of telephone. To the contrary, it seems like a perfectly reasonable fiction to go with the game mechanics.
Comment: The idea that the weapon finds out the information through the spell, then communicates this to the player, who presumably communicates this to the party, is what I was referring to as a game of telephone.
Comment: The other 25% of intelligent weapons communicate via Empathy which is described as the ability to "sense the basic needs, drives, and/or emotions generated by any mind. Thirst, hunger, fear, fatigue, pain, rage, hatred, uncertainty, curiosity, hostility, friendliness, love-all these and more can be sensed." The 34% I referenced as "tingles and urges" is the description for Semi-Empathy. Since it has to be less than sensing the weapon's basic emotions, I wouldn't let an urge communicate as much information as your example does.
Comment: Just to update you on this:  the rules I decided to go with are that the object can activate its powers (with its own action), but doing so makes the object the user of the power.  The object and wielder can also cooperatively activate its powers (using both of their actions), allowing the wielder to become the user.  Your answer was helpful in figuring out what I wanted to do.


Refinishing over different polyurethane

Question: I have a lot of door and  window trim that I finished with a satin polyurethane. I recently started a project to finish trim in another location in my house. I somehow managed to use a different satin poly that, about half way through my project, I realized had a different finish. The can said satin as well, but it's clearly glossier than the other trim. So, can I use the old satin over the glossier finish. Should I sand it down, rough it up or something else?
Answer: It's unfortunately a common problem with different finishes that their definition of 'the same' surface finish don't match! Even gloss varnishes aren't all equivalent. This is because there's no standardisation in the finish industry and each company has their own standard for sheen on the ladder from matt to gloss.

So, can I use the old satin over the glossier finish.

I'm assuming here the two polys are the same type, either both oil-based or both waterbased, otherwise you would have noticed.
So should be no problem, different finishes of the same type are all fundamentally similar and this makes them fully compatible, allowing them to be physically mixed1 as well as used one over the other if desired.

Should I sand it down, rough it up or something else?

If the later poly is freshly applied it shouldn't be necessary, any more than it's necessary to sand or scuff between each coat of the same finish.
You should do this if there are any defects in the finish, e.g. dust nibs, but you're sanding just to deal with those and not to ensure adhesion.
Note: multiple layers of a satin finish cause a slight cloudiness or milky effect because the amount of matting agent increases with each coat, not a huge deal but sometimes noticeable. With just one extra coat it may be all right, but it's possible that three coats may not look quite the same as two coats even though the surface gloss level is the same.
It would be advisable to try a coat of the previous finish on a short section to see what it looks like, rather than commit to all the trim around a window or door and then find out it doesn't look as you'd hoped.
Another route
You can matt a finish down by abrading it, and you might be able to mimic the level of gloss of the first poly on the second by scuffing the latter down lightly. A fine grade of steel wool and Scotch-Brite (or similar non-woven nylon abrasive) are both good for this. Steel wool sheds little steel flakes as it wears down so it is messier to use and this could be an issue for work around the house2.
If the poly is still fresh enough it won't be close to fully cured and therefore won't be as hard as it will eventually be. As a result it can be scuffed with things that aren't commonly thought of as being abrasive, including the rough side of brown paper (common grocery bags are an acceptable source for this, thank you Bob Flexner). I've found that even coarse cloth can sometimes be enough. So again you can experiment on a small area and see what result you get.

1 Useful for example if you want to make your own reduced-sheen varnish from a can of matt and a can of gloss. Some waterbased finishes are an exception here as there may be pH differences from one product to another that means they can't be safely intermixed, while still safe to use sequentially.
2 Personally I find it easier to control the sheen using steel wool. But many prefer Scotch-Brite/equivalent and are perfectly happy with how it works for them, and it is most definitely less messy in use and lasts longer.
Comment: Graphus, thanks so much for the thorough reply. That will help a lot. I hadn't though about steel wool, but will give it a try.
Comment: @jdv, rejected edits because matt = British English.

Refinishing over different polyurethane


Show that $e^{\sqrt 2}$ is irrational

Question: I'm trying to prove that $e^{\sqrt 2}$ is irrational. My approach:
$$
e^{\sqrt 2}+e^{-\sqrt 2}=2\sum_{k=0}^{\infty}\frac{2^k}{(2k)!}=:2s
$$
Define $s_n:=\sum_{k=0}^{n}\frac{2^k}{(2k)!}$, then:
$$
s-s_n=\sum_{k=n+1}^{\infty}\frac{2^k}{(2k)!}=\frac{2^{n+1}}{(2n+2)!}\sum_{k=0}^{\infty}\frac{2^k}{\prod_{k=1}^{2k}(2n+2+k)}\\<\frac{2^{n+1}}{(2n+2)!}\sum_{k=0}^{\infty}\frac{2^k}{(2n+3)^{2k}}=\frac{2^{n+1}}{(2n+2)!}\frac{(2n+3)^2}{(2n+3)^2-2}
$$
Now assume $s=\frac{p}{q}$ for $p,q\in\mathbb{N}$. This implies:
$$
0<\frac{p}{q}-s_n<\frac{2^{n+1}}{(2n+2)!}\frac{(2n+3)^2}{(2n+3)^2-2}\iff\\
0<p\frac{(2n)!}{2^n}-qs_n\frac{(2n)!}{2^n}<\frac{2}{(2n+1)(2n+2)}\frac{(2n+3)^2}{(2n+3)^2-2}
$$
But $\left(p\frac{(2n)!}{2^n}-qs_n\frac{(2n)!}{2^n}\right)\in\mathbb{N}$ which is a contradiction for large $n$. Thus $s$ is irrational. Can we somehow use this to prove $e^\sqrt{2}$ is irrational?
Answer: Since the sum of two rational numbers is rational, one or both of $e^{\sqrt{2}}$
and $e^{-\sqrt{2}}$ is irrational. But, $e^{-\sqrt{2}}=1/e^{\sqrt{2}}$,
and hence both are irrational.
Comment: Nice. Here is an easier one :If A,B,C are rational and $Ae^2 +Be+C=0$ then A=B=C=0.
Comment: You did all the hard work :-)
Comment: Uhhh, so close! Thanks for the answer, +1
Comment: Why can't both numbers be rational?
Comment: @DVD: OP proves it in his post
Answer: $e^{\sqrt{2}}$ is transcendental because of Lindemann–Weierstrass theorem:

If $a\neq 0$ is algebraic, then $e^a$ is transcendental.

It is written in the list of transcendental numbers.
Answer: To prove that $e^{\pm\sqrt{n}}\not\in\mathbb{Q}$, it is enough to exploit the Gauss' continued fraction for $\tanh$ and Lagrange's theorem about the periodicity of continued fractions of quadratic irrationals. A detailed explanation of this approach (for $n=2$) is outlined in this answer.
Comment: you might want to look at this method http://math.stackexchange.com/questions/1864678/are-there-any-natural-proofs-of-irrationality-using-the-decimal-characterization/1864796#1864796 here $\sum_{k=0}^\infty \frac{2^k}{(2k)!} = \sum_{n=1}^\infty \frac{1}{b_n}$ where $b_1 = 2,  b_{n+1} = b_n \frac{n (n+1)}{2}$, and the same proof applies. But I'm not sure how to modify it for $e^{\sqrt{n}}$
Comment: @user1952009: to exploit some Taylor expansion is another way for providing tight rational approximations of such numbers (then prove their irrationality) but I somewhat prefer the CF approach since it gives more manageable and more accurate approximations.

Show that $e^{\sqrt 2}$ is irrational


Loading WPF satellite resources dynamically

Question: I've read about satellite-assemblies being used in WPF localizations. However, I would like to ask if there is a way to load the satellite-assemblies without following the pre-defined directory structure that depends on the language (ex. If the system language is English, the WPF application looks for the satellite-assembly inside the "en-US" subfolder).
This is because I would like to simply swap the satellite-assemblies when distributing the software package without having to create a specific folder per language that would hold the assemblies. I would just like to have the satellite-assembly and the main executable in the same directory.
Is this possible and is there even an easy way to do this like simply loading the resource file on application startup once?
Thanks!
Answer: No, you are stuck with using the directories.


dc to ac inverter circuit

Question: I want to design the following inverter circuit, I know the general working of it, but I need some details. in the gates of the FET transistors used in H Bridge there is a design contain 4 diodes 2 resistors and tow capacitors connected to bjt then to the 4013 ic, I want to understand how this component works to determine the floating point in each transistor drain.
Comment: looks like it's already been designed to me! Looks like a 4013 not a 4023 btw. The capacitors are bulk storage capacitors, the diodes are snubbers/clamps?
Comment: Yes 4013 not 4024 thanx I edited it, yes the C19, C20 are bulk storage capacitors, I don't know the diodes types but D14,D15 are 1N4007 and D16,D17 are 1N4148, I want to understand these diode purpose
Answer: You can consider the gate of the IRF740 as being a capacitor. You put charge on it and the mosfets turns on, you discharge it the mosfet turns off.
To turn on the IRF740 you need to apply on the gate pin a voltage 10V-12V bigger than the source pin voltage.
For the low side mosfets (Q7 and Q8) it's easy, the source pin is connected to the earth/return, so you just need to apply a 12V DC on the gate and it turns on. The resistors R52 and R53 slow down the time to turn on the mosfet, limiting the charge current. The diodes D19 and D18 allow the gate to discharge (turn off) without passing to the resistor, making the turn off time faster than the turn on time.
The purpose of this time difference between turn-on and turn-off is the create a dead-time, where both mosfets, low side and high side, are shut down. We do this to minimize the risk of having both turned on at the same time creating a short circuit (called a shoot-through in the H-bridge).
To turn on the high side mosfets (Q5 and Q6) is more difficult, because the source pin voltage varies between 0V and +315V, and we need Vsource+12V to turn it on. So this circuit uses a technique called bootstrap capacitor. The capacitors C19 and C20 are charged do +12V via D14 and D15 and their charge is used to feed the gate and turn on the capacitor. You can have more details if you search for bootstrap capacitor for H-Bridges.
Comment: why do we need the voltage of the gate of ََQ8 equal 12v to turn it on, I know that it's enough to be more than Vt witch is equal about 1V?
Comment: Read the IRF740 datasheet carefully. At Vt the MOSFET turns on enough to conduct a few microamps. To turn it on enough to work well here, you need more voltage - you'll probably find the nice low resistances are specified at Vgs=10V. Dispense with the bootstrap and the FETs won't turn on hard enough. They'll have a high resistance, dissipate a lot of power, and explode.
Comment: @BrianDrummond Mr Brain I analysis the Lm324 circuit and i understand how it work without the C9 and C11 , but I want to know what the function of these tow capacitors
Answer: It may not be obvious, but the charge on capacitors C19 & C20 comes from the combination of the low-side FETs Q7 & Q8 and diodes D14 & D15.
Let's look at what happens when MOSFET Q8 is turned ON.  That pulls the source of Q5 towards ground.  C19 then charges through D15 to almost the full input supply voltage (1 diode drop plus however much voltage is across Q8).
When the flip-flop switches state, Q8 is turned OFF, sometime after that, Q3 turns OFF and allows the charge on C19 to turn Q5 ON.
At the same time, Q7 has turned ON and is charging C20 via D14 for the next half-cycle.
Comment: in the 556 what the benefit of the capacitor C15 on pin 3, I read the datasheet of 555 timer but there is no capacitor in this place.

dc to ac inverter circuit


Experience with submitting HTML/JS apps (e.g., jQuery Mobile & PhoneGap) to Apple AppStore

Question: What's your experience with submitting HTML/JS applications, e.g., jQuery Mobile & PhoneGap to the Apple AppStore?

How to achieve compliance with the Apple UI guidelines?
Performance: PhoneGap seems to aditionally slow down the app?
Answer: We did submit jQuery/Phonegap app to Appstore. Apple block us - we still don't understand why.
We submit same app to Google play (price 5$) - 17 downloads for 12 days WITHOUT any ads or promotion.

We found the user interface of your app is not of sufficient quality to be appropriate for the App Store. Apps that provide a poor user experience are not in compliance with the App Store Review Guidelines.
Specifically, we noticed your app:

has deep and confusing navigation
did not integrate with app content and/or iOS features

We believe it is always best for you to determine what features are best for your users. However, please keep in mind Apple and Apple customers place a high value - and have high standards - for the user interface and the experience an app provides. Apps should be engaging and exciting, enabling users to do something they couldn't do before; or to do something in a way they couldn't do before or better than they could do it before. Focusing on a primary problem to solve or need to fulfill, apps should include a feature set that intuitively and comprehensively addresses those needs and exceeds users' expectations. And apps should be specific to the iOS platform to take the fullest advantage of the iOS in delivering a robust user experience.
Please evaluate whether you can make the necessary revisions to improve the user experience of your app.
If you cannot - or choose not to - revise your app to be in compliance with the App Store Review Guidelines, you may wish to build an HTML5 web app instead. You can distribute web apps directly on your web site; the App Store does not accept or distribute web apps.
HTML5 is the major new version of HTML and enables audio and video to play natively in the browser without requiring proprietary plug-ins. Using HTML5, web apps can look and behave like native iPhone and iPad apps, and using HTML5's Offline Application Cache, a web app can work even when the device is offline. With web apps, you have flexibility to deliver as much or as little functionality as you desire.
To get started with iPhone or iPad web apps, please review Getting Started with iPhone Web Apps.
For a description of the HTML elements and attributes you can use in Safari on iPhone, check out Safari HTML Reference: Introduction.

We dont understand how
-two level deep list can be "has deep and confusing navigation"
-why our app "did not integrate with app content and/or iOS features"
Again before submitting we make beta-testing with users - 12 person from 12 tell us that app navigation and data presentation clean and easy.
But probably not for Apple genius-stuff.
Hope next few years we will forget about Apple.
Answer: Use Phonegap minified in your index.html reference.  The state of jQuery Mobile is Alpha 4 right now; there are some performance issues that are really troubling me, but they look to be going beta soon and I am sure they will address them.  I highly expect Apple to be supportive of an HTML5-produced application and I would expect you are far from the first to do this.  One thing that does concern me is that Apple has yet to find way to distribute HTML5-based apps except through shells such as this.
Answer: I work for AppMobi, which has a competing product...but the end result is very similar.
We've had a bunch of people submit iOS apps (including us) with no issues.  The only time problems arise is due to content or application specific problems, not with how it was built.
As to jquery mobile (along with jqtouch and others), the uiWebView lags behind Safari with updates and performance, so it may run fine with Safari but slower in the container.  That's one problem everyone deals with.  I'd encourage you to look at http://zeptojs instead, since it's smaller and aimed at mobile devices, with an attempt of being jquery compatible.  I'm always testing javascript frameworks and have not found a cross platform UI based one that's performed acceptable.
plug And I'd encourage you to check out http://xdk.appmobi.com if you are just doing html/js/css based apps.
Answer: While I'm working on a PhoneGap-based application myself, I haven't gotten to the point of submitting it to the App Store.
You might consider posting your question over at the PhoneGap Google Group, as several folks there have successfully gone through the submission process.


Word 2013 - captions will not be update

Question: I have copied a section of text, which contains figures and tables, from another Word 2013 document into a new template document from an older version of Word. For some reason the table and figure numbers will not update with F9. When you right click on a caption 'update field' is blocked out. They are still recognised as fields and will update if you right click on them individually, select 'edit field', and then click ok (without making any change to the field code etc.). However, the associated cross-references do not update. This is the case regardless of whether the new document is in compatibility mode or converted to Word 2013. I would really like some advice so that I don't have to manually update all of these numbers and cross references.
Answer: Hi Maybe not a solution but a workaround.
Save the old file into the latest version and copy from that latest version.
It should work.

Word 2013 - captions will not be update


Where to find/ to get Tersoff and Stillinger Weber Potentials for MD simulation using LAMMPS

Question: I'm trying to calculate the thermal properties of Silicene with hydrogen and halogen atoms. My problem is that, there's seems no available potential  for Tersoff and Stillinger Weber Potential. and I'm  looking everywhere to find one. Where I can get one tho? I'm still new to this hope you all understand.
Comment: There is this paper https://www.sciencedirect.com/science/article/pii/S0927025617300782, you can read parameters are given . You can either mail author to get potential or you can fit using python package like https://atsimpotentials.readthedocs.io/en/latest/
Comment: A good place to start would be to contact an author of a published article using the required potentials. If not, I think that the [potentials directory](https://github.com/lammps/lammps/tree/master/potentials) of lammps contained some potential files. However I am not sure about the accuracy of those. If so, it would be best to evaluate some known values (thermal conductivity, youngs modulus etc.) using them as a validation of the data.
Answer: The comments are correct in directing you towards literature and the LAMMPS potential directory. For future reference as well, NIST maintains a page which contains many empirical potentials for most elements: https://www.ctcms.nist.gov/potentials/
Comment: Welcome to the site, and thank you for the constructive answer!


Call overridden method in Dojo

Question: In dojo, one cannot call a overridden superclass method outside of the same method in the derived class (for which there is this.inherited(), other than that one can call using class_name.function_name.apply). This feature is no longer there because of some refactoring and dojo guys are not going to put it back because they are not convinced about a good enough case for this. Please read this mail thread for details. Isn't there a good enough case for this functionality? Why or why not?
Answer: I would think that there is a very valid use case for such behaviour.
Consider implementing a state pattern using javascript objects. You can simply do it by maintaining the member variables in the current object, and all the state specific functions in the prototype. Just keep changing the prototype to move to a different state.
Now, when you want to combine the state pattern with the template method pattern, you can simply call the state functions as super()(like how you can in python). This is important because the state functions may be hooks or abstract functions in the template method class. If they are the former, then you should be able to call the super-class versions of these methods irrespective of which super-class the current super-class is.

Call overridden method in Dojo


Calculate the risk probability with coefficients derived from Cox regression

Question: I am new to survival analysis and I was wondering whether you could, similar to the logistic regression, calculate the intercept and the risk probability with the coefficients you acquire from the cox regression? And how you could do so within R.
Answer: There is no single "intercept" in a Cox regression model. After the model is fit, you can infer a baseline hazard, which can be transformed to a baseline survival curve as a function of time. The covariates then alter that entire baseline hazard or survival function according to their regression coefficients. You can choose whether to display entire survival curves for different covariate values, or estimate median survival (or some other quantile) as a function of covariate values if you want a point estimate of some type.
The predict.coxph function in the R survival package provides basic tools for this. The rms package can be more useful. If you are going to be doing a lot of regression modeling of any type, it's well worth learning how to use that package despite its initially steep learning curve.


What is the difference between "myself vs i myself do."?

Question: Sometimes ago, I was facing with native speakers he used " Myself & I Myself Do." could you help me out about importance of this sentence "I will eat myself." & "I myself will eat."
Comment: Please don't say *"I will eat myself"* - it means you eat your won body parts (i.e., flesh, skin, fingers)
Comment: @AIQ I'm not sure that's the only way to interpret it.
Comment: @userr2684291 Oh yes, you are right. Perhaps one can say that when someone else is trying to feed them. Is that what you mean? Or perhaps they want to eat alone without any company?
Comment: @AIQ I imagined it as a way of saying *I'll eat, too*, with an emphasis on *I*. It's similar to the second example. *Well, I'll be eating myself, so we might as well do it together*.
Comment: @userr2684291 Yes that makes sense. I hadn't thought of putting that part in context. I just assumed (wrongly) that OP's sentence with a period is all that they are trying to say, and for some reason, cannibalism came to mind.
Comment: what is the difference between "Myself & Mine."
Answer: The 'myself' can serve a few purposes here.

As per the other answers, it emphasises the 'I',
As per the other answers, 'I will do it myself' i.e. I don't need your help.
It also serves to contrast that 'I' will be doing something that you/others may or may not be doing. For example

I myself will eat, while you continue to play video games and let your food get cold.
Hope this helps.


Why do some MOOCs close their enrollment?

Question: I have noticed that quite frequently MOOCs close their enrollment, and content is made available only for students who are enrolled. Why?
Example:
Comment: Just in case, many closed courses have another intake of theirs up and running.
Answer: Lacking individual interaction between instructor and student, MOOCs often have a policy that this kind of feedback is replaced by interactions with the "community" of other students on web forums. So my sense is that closing enrollments from time to time recreates traditional semesters, that is, batches up students into similar cohorts in time -- and then hopefully this serves to create a "critical mass" of respondents on the forums, who are all working through like material at about the same time, and more likely to respond to each other's questions and concerns in a coherent fashion.
Answer: And to add to Daniel's answer, the instructors may also want to set a pace, akin to traditional in person lessons. Releasing new material on regular intervals, the are encouraging students to follow it at the set pace.
So, if you sign up, and get a new lecture every week, are more likely to watch them on time, digest the material, and keep on the course, that if you sign up and get a backlog of 30 lessons to watch, and growing.
Answer: From the students' perspective, it doesn't make much sense to close the course. From an institutional perspective, however, it's usually just a budget and reputation concern.
If nobody official is answering questions, the course looks dead, which makes the school look flakey. At the same time, the cost of hiring someone to manage the course all the time is prohibitive. So, courses get closed.


Saving different csv files as different sheets in a single excel workbook

Question: Related to this question, how to save many different csv files into one excel workbook with one sheet per csv ? I would like to know how to do this programmatically in Java.
Answer: You'll need some form of library for accessing Excel from Java. A Google search turned this one up:
http://j-integra.intrinsyc.com/support/com/doc/excel_example.html
An alternative is to use the XML Excel format that came into being with Office 2003. You'll end up with a XML file, but you can open it in Excel and see the different sheets.
http://www.javaworld.com/javaworld/jw-07-2004/jw-0712-officeml.html
Answer: If you want open source, the POI library can be used to generated Excel files.
A nice CSV parser is Open CSV
That should set the stage for what you are trying to do (basically use the CSV parser to get data, then write the data to an XLS file.
Answer: Take a look at the Aspose products, I've used them before when working with Excel and they saved me a huge amount of headache and time.  Excel has several quirks that can make importing and exporting spreadsheets painful.
Aspose.Cells


How to query EFI signature

Question: It appears that Grub-EFI will only boot a "signed" Linux kernel. Is there some command that will allow me to query a given kernel image to find out what signatures (if any) are present on it?
Answer: It depends on what kind of signature you're talking about.  If you have an EFI system, you can have signed EFI executables (*.efi) and force your EFI firmware to only execute those with a known signature.  This is known as Secure Boot.  To check an EFI binary for a signature you can use the tool sbverify:
$ sbverify --no-verify signed-binary.efi
Signature verification OK
$ sbverify --no-verify unsigned-binary.efi
No signature table present
Unable to read signature data from unsigned-binary.efi
Signature verification failed

Unfortunately I didn't see an easy way of extracting and displaying the EFI signature. :(
What's more likely what you are looking for is GRUB's own ability to check its modules and kernels to be booted for valid signatures (Secure Boot just affects the GRUB binary itself, everything GRUB loads does not necessarily need to be EFI-signed).  Those are (as far as I understand) plain old detached GPG signatures (so for example for a kernel called vmlinuz-1.2.3 you'd have a file vmlinuz-1.2.3.sig with the signature).  Those can simply be displayed and verified with
$ gpg --verify vmlinuz-1.2.3.sig vmlinuz-1.2.3
gpg: Signature made Tue Apr  1 12:34:56 2014 CEST using RSA key ID d3adb33f
gpg: Good signature from "John Doe <email@example.com>"

If you don't have a *.sig file to your kernel, it is obviously not signed.
You can disable signature checking in GRUB by entering set check_signature=no at the GRUB command prompt.  You can get more information on that topic here (this functionality is rather new and the official GRUB website only has the manual for version 2.00 online, which lacks this feature).  This also explains how to sign your modules and kernel with your own key and to tell GRUB about it.
Comment: Have a look [here](http://en.opensuse.org/openSUSE:UEFI_Image_File_Sign_Tools).
Comment: Any idea which package contains `sbverify`? (OpenSUSE, in case it matters.)
Comment: The `sbsigntools` package is only available from nonstandard repos, but I was able to install the `pesign` package. It refused to do anything until I created an NSS database (even though I'm not going to use it), but I was then able to verify signatures - which is what the question asked.
Answer: You can use sbverify , for instance:
# sbverify --list /efi/EFI/refind/shimx64.efi.signed
warning: data remaining[1159744 vs 1322936]: gaps between PE/COFF sections?
signature 1
image signature issuers:
 - /C=US/ST=Washington/L=Redmond/O=Microsoft Corporation/CN=Microsoft Corporation UEFI CA 2011
image signature certificates:
 - subject: /C=US/ST=Washington/L=Redmond/O=Microsoft Corporation/CN=Microsoft Windows UEFI Driver Publisher
   issuer:  /C=US/ST=Washington/L=Redmond/O=Microsoft Corporation/CN=Microsoft Corporation UEFI CA 2011
 - subject: /C=US/ST=Washington/L=Redmond/O=Microsoft Corporation/CN=Microsoft Corporation UEFI CA 2011
   issuer:  /C=US/ST=Washington/L=Redmond/O=Microsoft Corporation/CN=Microsoft Corporation Third Party Marketplace Root

or:
# sbverify --list /boot/vmlinuz-5.7.11-amd64
signature 1
image signature issuers:
 - /CN=morfikov's kernel-signing key
image signature certificates:
 - subject: /CN=morfikov's kernel-signing key
   issuer:  /CN=morfikov's kernel-signing key

Answer: Using the information provided by Andreas, I was able to figure out the following:
On the working system, both Grub-EFI itself and the Linux kernel are signed with the same key. On the non-working system, neither Grub nor the Linux kernel are signed. When I try to copy the Linux kernel from one system to the other, Grub complains that the kernel is not signed. There is no detatched GPG signature; it appears Grub is looking for the same thing that Secure Boot is looking for - an internal PE signature.
Now, if I can just figure out how to get OpenSUSE to sign their 32-bit version of the Linux kernel...

How to query EFI signature


Deleted Exchange Password Prohibiting Access to IPad

Question: I had an email account on an Exchange server for a contract I was working on.  The contract ended and my password was deleted from the Exchange server so I could no longer get into the company's email.  Now, when I open my IPad it asks for the Exchange password and when I can't supply it I continue to get the message asking for the password.  I can't cancel out of this error message, it just keeps coming up whether I hit cancel or supply a no longer valid password.  I cannot get into the IPad desktop because I can't get by this message.  I would like to delete the Exchange account from my IPad (I was able to do this on my IPhone) but I can't get to the Settings.  How can I get by this message?  Thanks.
Comment: What happens when you restart, or do a hard reset of the iPad, while out of range of wi-fi?
Answer: Is it a wifi only iPad? If so, you can try to temporarily shutdown your wifi. If the iPad is not connected to Internet, maybe it won't try to fetch mails.
When you are prompted, have you tried to double click the home button and kill the Mail app? Or maybe try to access Settings from there.
You can also try to connect your iPad to your computer, if it's sync to iTunes. From there, in the Info view of the iPad on iTunes, select that you don't want any email account (I believe there is a overwrite current settings checkbox) and erase your accounts from there.
You'll probably have to re-add your others account manually.


Is this a typical growth habit for a cactus?

Question: I was re-potting my 9+ year old cactus to a bigger pot yesterday and noticed a sizable portion of its stem is submerged. Is this a typical growth habit? What are the chances that this stem might rot and cause issues down the line? Also, if anyone knows the species that would be helpful.
Answer: It's an Echinocactus grusonii, that has been standing in the wrong place for maybe two years, thus the elongated growth in the middle. Typically too dark or to warm in winter. Then it has been moved to an apprpriate place where it continous its normal growth, that is, becoming a large sphere eventually. It has than be planted deeper, maybe to make it look better. If the drowned part will eventually rot i can't tell you, this depends heaviky on the environment. Carefull watering, especially in winter will lessen the chance of rotting.
Comment: Ah, so it looks like it should be growing more as a sphere than an elongated shape. By careful watering, do you mean it should be watered much less in winter?
Comment: Exactly. It depends a little on the kind of cactus, e.g. The epiphyte rain forest cacti should be watered normally, whereas the desert cacti should be watered only very occasionally. I water my cacti (residing in central europe) only once or twice from october to april, hibernating them in a lucid, unheated attic.


What swirly bokeh technique is this and how can I achieve it?

Question: What is the technique used to capture this image? How can the result be achieved?  I know that it can be achieved in a digital darkroom but how can I replicate the effect straight out of the camera?
Comment: +1 on editing the title, suggest you use the words ["swirly bokeh"](https://www.google.com/search?q=swirly+bokeh) somewhere in there. :)
Comment: Please use a descriptive title rather than "insane technique".
Comment: possible duplicate of [What is the cause of this non-uniform bokeh effect?](http://photo.stackexchange.com/questions/52126/what-is-the-cause-of-this-non-uniform-bokeh-effect)
Answer: This photo is taken with a petzval lens which corrects all aberrations decently except for, well, petzval aka field curvature.  Because the edges are in focus at a further distance, the blur is smaller there.  Because the lens is fairly highly vignetted, the lens also effectively has a larger f number towards the edges, again reducing the blur.  The result is the swirly bokeh you see in this photo.
Comment: Petzval is not unique to petzval lenses =)  Vignetting is also there in all camera lenses to some degree.  Astigmatism will cause a difference between the tangential and sagittal planes, so you may bokeh with a quasi-[anamorphic](https://s3.amazonaws.com/red_3/uploads/asset_image/image/51bf7a6f17ef0222550009d1/bokeh-anamorphic.jpg) look, but it is not the same.
Comment: Is it just me, or does the photo appear to have been shot centered on the model (at approximately her belly) and then the right side and bottom cropped to make the petzval effect off center?
Comment: @thomasrutter Petzval is a specific optical feature - if a lens has zero astigmatism but uncorrected field curvature, the true image plane is known as the Petzval Surface.  To calculate it, one uses the relationship that T-P = 3(S-P) where T is the tangential focal plane, P is the petzval surface, and S is the sagittal focal plane.
Comment: How does this happen on non-Petzval designs?
Comment: I have seen this effect called everything from "field curvature" to "crazy swirling bokeh" before but have never heard the term petzval before.  Thanks for introducing me to a new term.
Comment: Is it possible to achieve that homemade swirly effect with a 24mm used on a cropped sensor (EOS 50D) ?
Answer: This is a swirl-y bokeh, an often desirable flaw commonly found in some vintage lenses and lenses. There are some lenses known for this this characteristic, most notably the soviet made Zenit Helios 40-2 85mm F1.5 which is still being manufactured. You can find this lens on ebay for ~$600. If you are adventures enough you can convert the Cyclop night vision 85 mm f1.5 device (does not have a diaphragm built in) but it is apparently the same glass for 10% of the price.
There is also another focal length of Helios that can produce this effect, albeit not as well, and is MUCH less expensive (I paid $47 USD for mine ordered from Ukraine but if you look hard you can find it cheaper) version of this lens the Zenit Helios 44-2 58mm (f/2).  HOWEVER, a: you have to work it a bit and get the right kind of busy background/back light b: you probably need to use a full frame camera and c: you have to shoot wide open.
I really like the Helios 44-2 and I also have a chipped adaptor to get a focus confirm which works pretty well. The lens renders really nicely and has many imperfections which lend the images character but I cannot focus to infinity on my Canon full frame body because the rear element protrudes too far back and the mirror will hang on it.  I can only use it up to about 8m from the subject - good enough for portraits.  There are suggestions online to shim the adapter but that creates other issues - the inability to focus at infinity for one... I hear there are no mirror hang issues when used on Nikon bodies??  Also, no issues with my cropped sensor body but the swirly bokeh is much easier to get when the lens is mounted on a full frame body.
EDITED:
I now have a solution on how to fix the mirror catch (only confirmed  for specifically the Helios 44-2 58mm f/2 on Canon full frame bodies):
http://jakubsisak.tumblr.com/post/128680966703/helios-44-2-58-mm-modification-for-canon-full
Comment: I have used the Helios 44-2 58mm and it works very well for that with a lit background. Without it, it will look normalish.
Comment: Good point. The busier the background and the better it is lit the better the result.
Answer: If you have a fast lens, create a circular cover over it, and it should swirl the background. It's best seen with foliage.
Answer: I have never tried the following trick myself, but it seems to be a simple and very cheap alternative to buying yet another lens (yes, it's even cheaper than the Helios 44-2):

Take a piece of light-proof paper, cut a hole in it.
Attach it to the lens hood and put hood on lens.
Swirly bokeh!

See PetaPixel: Homemade Petzval Swirl Bokeh with a 50mm Lens. The effect does not seem to be as strong as in your sample pictures, but it is a very easy and fun way to start experimenting.
Comment: Check out Brandon's comment to an answer on a related question, [here](http://photo.stackexchange.com/questions/52126/what-is-the-cause-of-this-non-uniform-bokeh-effect#comment111850_65192) — the effect is strongest/best when there is both field curvature and vignetting.


How to tell if anything has some technical problem and therefore not working

Question: How to say that something has some technical problem and is therefore not working
"Bus is not working" but that suggests the reason why the bus is not working.
Answer: In your example I'd recommend inoperative [for technical reasons].
In everyday life, depending of the object:

inoperative (a service...),
unusable (a tool...),
defective, faulty (a piece, a device, a component...),
broken (pretty much everything).

More specifically, in IT for software:

buggy (objective),
"rough on the edges" (politically correct),
unstable (optimistic).
patchy (see etymology of the Apache HTTP server).
Answer: Two phrases you may find useful to tell people that a piece of equipment cannot be used at the present time are:

Out of order

or

Not in service

Out of order implies the equipment is not functioning properly. Not in service is a more general phrase, and can be used situations where the equipment is not working, or it may be working but needs inspections of certifications before it can be used, or there are administrative reasons why the equipment cannot be used. For instance, a bus that is returning to the main bus terminal and not on a regular bus route can display "Not in service" as the name of its route.
Comment: "Not in service" is better but it sounds nice if before using anything..What if I have already used and in the middle its not working.
Answer: If don't want to communicate the fact that something is technically wrong (maybe it's your bus line, and a broken bus is admission of failure), you can use one of the following:

Unavailable (very vague)
Disabled (could mean intentionally or unintentionally)
Offline (could apply to buses)

If you do want people to know something is definitely broken, you can use one of these phrases in addition to the ones Jay Elston has provided:

Out of service
Down
Undergoing Maintenance

If your target audience is familiar with the context (buses, computers, tools, whatever it may be), it's often best to just briefly say what the actual problem is. If the target audience is the general public, "Out of Order" is probably the most typical.
Comment: Out of Service is a good phrase as well. The phrases I suggested are common in the southwest United States (where I live). I would not be surprised if England, Australia, New Zealand, and other English speaking nations have common phrases for this situation.


Why couldn't Harry ditch the cup and pour water straight from his wand into Dumbledore's mouth?

Question: In Half Blood Prince, Dumbledore drinks Voldemort's potion; Harry tries to fill up the cup with water, but it keeps emptying. He has to get water from the lake. Why couldn't Harry conjure water to pour straight from his wand into Dumbledore's mouth?
Comment: Related: http://scifi.stackexchange.com/q/8467/3804
Answer: It seemed to be the act of bringing the water (that wasn't from the lake) close to Dumbledore's mouth that caused it disappear.

"But I had some -- wait -- Aguamenti!" said Harry again, pointing
  his wand at the goblet.  Once more, for a second, clear water gleamed
  within it, but as he approached Dumbledore's mouth, the water vanished
  again.
Harry Potter and the Half-Blood Prince - Chapter 26

It is possible that using Aguamenti directly into Dumbledore's mouth would have worked.  However, it is my opinion that Voldemort would have thought of this and it was more an area charm that prevented any water other than the lake's to enter the potion drinker's mouth.  With that said I'm not even positive that the lake water could be drunk without disappearing either since before Harry is able to give the water to Dumbledore the army of Inferi were attacking.
Comment: hmm... was Voldemort aware of infusion? (as in "infusion pump") is it just the area, or is it the water? It would be safer to make the lake's water different, instead of just casting area spells.


Inverter AC details and specifications

Question: How does an "inverter" air conditioner differ from a non-"inverter" air conditioner? What is the advantage of an inverter air conditioner over a standard one?
Answer: An Inverter AC has a compressor that contains a induction motor (commonly, 3 phase) that is driven from a VFD (variable frequency drive) rather than from the mains directly. Due to that an Inverter AC has a compressor that is capable of variable speed operation. Which results it it being able to modulate its cooling capacity. Thus you could have a 2 ton AC that when not so much cooling is needed operates at 1 ton continuously rather than switching on and off. This results in a more even temperature and better dehumidification.
Non-inverter AC have a compressor that operates at constant capacity and as such it must be properly matched with the cooling load. A state that never happens as they are only properly sized for the hottest days and oversized the rest of the year. As they turn on and off, the evaporator coil get too cool when on and too warm when off to dehumidify.
The problem that result from having an oversized AC do not happen with a Inverter AC and its a variable capacity compressor. As it dynamically matches itself to the cooling load of the building. Allowing it to slows down (before turning off) and speed up rather than turning off and on.
Comment: They also save on the power bill, less cycling on and off. Good answer @Dan D

Inverter AC details and specifications


How to Get counts from Cookies that a user Visits to site

Question: I have a website like http://www.mydomain.com/Home.I am accessing many times this website from my system. Now I want to check using cookies that how many times I have Visited this website from my system.
Have I need to create cookies manualy or I have use browser cookies..
Plz let me know that how I can get this done.
Answer: In your server side code, be it PHP or Asp, you can set cookies and send them back to the browser.
If you want to find how many times a website is visited by your browser, you should set and update the cookie in your server side code for every request.


Short distance detecting device

Question: I'm looking for a sensor that would activate at a certain distance from the magnet or whatever would be signaling the location. The distance would range from 2-30cm and there would be obstacles (fabric, human parts,...) in between so that sound and light sensors would probably not work. I would want to be able to change the distance that would activate it. So if I'd set it to 25cm it'd activate when the two parts would get closer than that.
Comment: Magnetic field sensors are called Hall effect sensors.
Comment: sounds like your range requirement is too far for magnetic sensors to work properly - you'd need huge gain/very powerful/sensitive stuff to detect properly, and still have control over detection range as you request
Comment: Do the two parts have any means to communicate?  A sideband electrical communication channel?  Or are they completely independent?
Comment: The two parts could be connected with a wire that would still allow full range of motion if that's what you're asking.
Answer: I'd stick with electromagnets aka inductive loops for doing what you want. Whilst not in the presense of big chunks of metal you can get pretty consistent fields generated inversely proportional to distance cubed. Use an oscilator to excite a central loop and use smaller loops tuned to the resonant frequency for measuring the field strength.
Careful though this only works in the one plane  - if you rotate a loop thru 90 degrees it will likely go thru a position where no field is detected. So then you use diversity if you need 3D distance detection - two transmit loops at right angles operating at different frequencies.
Comment: The movement would be in one plane and it would determine the angle that the arm is suppose to go to, at a certain distance it would stop it. The angle of the arm would range from 20-180 degrees.
Comment: I think you need to show a diagram. Determining angle is more complex than your original question implied. When you say " at a certain distance it would stop" do you mean " at a certain angle it would stop"?
Comment: Yes, I meant at a certain angle, but at the same time it can be at the a certain distance. Let's say you have a triangle ABC. A = joint, B = sensor and C = magnet. The distance between B and C can determine the angle of a joint.
Answer: I just came across a reed sensor. Does anybody know how far I could stretch the distance with a normal AA battery? And if I would be able to manipulate with the distance.

Short distance detecting device