circle action on sphere

Question: surely $S^1$ can act on $S^n$ as a rotation.I want to know if there is some other way that a circle can act on sphere.
Comment: It is not hard to list a few other actions... While we are at this: are such actions classified up to isotopy?
Answer: Classification of circle actions on (standard and on exotic) spheres is a classical activity in transformation groups, see e.g. the article of Schultz in the collection "Group actions on manifolds", proceedings from 1983 conference, or earlier account in Bredon's book "Introduction to compact transformation groups".
One standard example is this. Take a smooth compact contractible $(n+1)$-manifold $C$ and consider $C\times D^k$ where circle acts trivially on $C$ and linearly
on the $k$-disk $D^k$, $k>0$. Now if $n+k>4$, the boundary of $C\times D^k$ is diffeomorphic to the standard sphere (after the corners of $C\times D^k$ are rounded). But the fixed point set of the action is the original homology sphere that bounds $C$. I think it is clear that the fixed point sets of linear actions are standard spheres.
Incidentally, in dimensions $k>4$ any homology $k$ sphere bounds a contractible manifold after possibly changing its smooth structure; also any homology $4$-sphere bounds a smooth contractible manifold, while any homology $3$-sphere bounds a topological contractible manifold, but not necessarily smooth ones. References to the above results can by found e.g. in my paper pp.8-9.
Answer: One example: The sphere $S^{n+m+1}$ is the join $S^n*S^m$of $S^n$ and $S^m$, so having $S^1$ act on each of the factors you get an action on $S^{n+m+1}$.
Comment: No. Think of a double rotation (where the action on the two factors rotate by different speeds) on S^3. A standard rotation (on R^4) fixes a two-plane. A double rotation fixes only the center.
Comment: Is that not a standard rotation action around a diagonal axis?
Answer: A nice example is the Hopf fibration: $S^1 \subset C$ acts on $S^3\subset \mathbb C^2$ by scalar multiplication. The quotient is $\mathbb CP^1.$ Of course there are various generalizations.
Comment: Incidentally, higher (odd) dimensional spheres admit lots of non-linear free circle actions. They correspond to fake homotopy projective spaces.
Comment: This action is linear.
Answer: I do not know, in which category your actions live. In the following answer I want to consider isometric actions.
Another classification problem might be:
Classify all periodic one parameter subgroups of $SO(n)$ up to conjugacy, which is the same problem as the classification of all such actions up to isometry.
There is a normal form for orthogonal matrices over the reals, which says, that every such matrix is conjugated to a block matrix consisting of $(2,2)$ rotation matrices and $(1,1)$ diagonal entries, which are $\pm 1$.
My claim would be that every isometric action decomposes (after congugation) uniquely as a induced action on each of the components of the decomposition
$S^n = S^1 * S^1 * \ldots * S^1 * S^0 * \ldots * S^0$
($*$ should denote the join here). The isometric actions of $S^1$ on $S^1$ can be classified by the integers. The only possibilities are $(t,x)\mapsto mt+x$ for $m\in\mathbb{Z}$.
I think the upper normal forms for matrices should imply this. But I am not sure.

circle action on sphere


How accurate is the ultrasound sensor when moving?

Question: Can I use an ultrasound sensor while the Robot is moving, or will it give bad data?
Answer: Short answer: The ultrasonic sensor is perfectly accurate while moving!
A regular NXT robot will move at a maximum speed of several meters per second (usually about 1 or 2 m/s max.). Ultrasound, on the other hand, travels with about 330 meters per second through air. So during the "snapshot" the ultrasound sensor does (basically it sends a ping, listens for the pong-echo, and takes the time difference), your robot appears to be frozen for this brief moment.
So this is why, whenever your ultrasonic sensor makes a measurement, you get a freze-frame snapshot of the current distance to the nearest object it detects. In reality, the sensor sends out pings all the time during default operation, and you just get the very latest measurment -- but essntially, this feels the same.
Since the ultrasonic sensor is digital and offers its data via the I²C protocol, this is where the main latency comes from. On the other hand, you shouldn't poll (i.e. read out) your sensor too frequently, if that is what you're worried about. In several tests we've concluded with hundred NXT kits, that a polling rate of 50 Hz (50 times per second, delay of 20ms between each poll) does work perfectly with no problems at all. When you're using NXT-G, you shouldn't worry at all: You won't get values faster anyway. When you're working with other languages, and you feel your ultrasonic sensor doesn't work so well in a tight loop with constant polling, try to insert this little 20ms break!
Far more important are the objects you try to detect. This is due to the wavelength of ultrasound. You can't detect objects with dimensions of just a couple of centimeters.

The US works best when facing walls, perpendicular to the sensor
It has big problems detecting furr, carpet- or cloth-like surfaces (the ultrasound doesn't get reflected)
It has big problems detecting smooth surfaces, facing the sensor at skew angles (not 90°) -- the ultrasound gets reflected away
It has problems detecting round objects (e.g. a water bottle or a football) accurately. The ultrasound gets reflected too widely, so you'll see the bottle or ball "bigger and wider" than it is in reality.
It will miss tiny objects

The first rule is, as always: Experiment on your own! For more resources, try the LEGO NXT Hardware SDK or at least the pictures in this german paper, pages 24, 27ff.
Answer: The ultrasound sensor will only be affected by the rate in which it captures and processes data, which could be a matter of milliseconds.
Supposing the ultrasound sensor captured data at one second intervals whilst moving towards an object at a rate of ten inches a second. If the rate at which it was moving was consistent the sensor would report measurements of say 60, 50, 40, 30 inches. This is not 'bad data', it can be considered insufficient depending on objective.
LEGO haven't specified the rate at which the ultrasound sensor processes data, if it hasn't been documented, you might want to try a couple of controlled experiments to see how it is affected by motion.
Answer: The shooterbot, one of the robots that can be built from the instructions in the nxt 2.0 set, uses this sensor while rotating in place, which proves this works pretty well.
please note that your results might be different, depending on the angle, speed of movement and distance of the objects you're measuring. Basically, there's no problem - but the best way to find out is to start building ;)


Backup Google Drive to Dropbox

Question: I want to...

automatically perform a one way sync from Google Drive to Dropbox
convert the files to a format supported by LibreOffice or HTML during the synchronization. But any non proprietary and easily editable format will do!

The solution is better if...

I can pick the destionation folder freely
the destination format is supported by LibreOffice, as it's my preferred office suite.
the destination format is ODF/OpenDocument, as it's my preferred free and open office suite format
it detects which files are new, deleted and updated so it doesn't have to synchronize everything each time
the same solution can handle other similar use cases, such as doing the same thing for Evernote instead of Google Drive

It doesn't matter if...

the solution is free of charge or has a reasonable price
Comment: See my answer to your other question.
Answer: Brive does this. Will backup all your documents in a variety of formats.

Backup Google Drive to Dropbox


How to lay one video over another

Question: I have two video clips. What I need is for the first video clip to play behind the second. I need to be able to choose the offset since the two videos are not exactly in sync.I need to adjust the position of the second clip on the first. (It should be at different places at different times).What would be the right software to do this. Also are there any blog posts about this?
Answer: It is not clear to me what you mean by laying "one video over another." This could mean you want to show both simultaneously in the same frame. One way to do this is using a split screen. Another is to superimpose each over the other then reduce the opacity so you see both images. Yet another is to superimpose each over the other but use a mask on the top layer so only portions of the bottom layer are exposed.
Summary of possible overlays with links to examples.
1) Split Screen
https://vimeo.com/22564317
2) Double Exposure
https://vimeo.com/42863351
3) Compositing
https://vimeo.com/44747735
You will need an NLE that is capable of rendering multiple video tracks at once. Sony Vegas Movie Studio would allow up to 4 video simultaneously, while Vegas Pro will allow as many as your computer can handle (on my 3 year old quad core this can be up to 9 SD tracks or 5 HD tracks). Other NLE video editors to check out would be Avid, Adobe Premiere, and FCP.
Once you know which one of the effects I listed above fits your situation, you will be able to find tutorials on YouTube specific to the NLE you are using. For instance, here is a tutorial I found on YouTube by searching for "how to use split screen on vegas movie studio".
https://www.youtube.com/watch?v=HnsWKDXIxJA

How to lay one video over another


I am 24 years old. I found marijuana and ecstasy my 17 year old sister's room. What should I do?

Question: I went to borrow bus fair from my sister this morning and found a small clear bottle with a small amount of marijuana and four mysteriously labeled, handmade pills in her change box. I don't know what to do: turn her in to my parents, or talk to her myself. I never saw her getting into this stuff, although this does explain how she's been acting (and her mood) around the house lately. I'm worried and scared and I do not have the slightest clue what to do. PS. I took the bottle and hid it.
Comment: "You know, when I got the bus fair from your room the other day, I couldn't help but notice...." & "Can we talk about it?"
Comment: Comments removed. Please do not use comments to answer questions, thanks.
Answer: This is an iffy situation, especially if you have a good relationship with your sister. On one hand, you don't want her to be mad at you and on the other, you want her to be safe and you want to protect her.
First of all, not doing anything is wrong. It would be turning a blind eye to a potentially dangerous situation. If something did happen to her in the future and you hadn't done anything, you'd regret it for the rest of your life.
Secondly, you cannot defeat this by yourself and you can't approach this with a mind for her rehabilitation. You coming to this site and asking for help in and of itself proves that you are incapable. You are not a trained professional and all the worry, doubt, conviction, love, caring you could put into her mind that would convince a normal person won't do a thing over the power of addiction. Trust me, I tried to handle it myself with a friend who was a cocaine addict. It didn't turn out well.
Third, tell someone. Approach her first, but don't let her convince you to not tell someone else.
If this was just pot, then whatever. That's less harmful than some legal drugs. Ecstasy however is a different subject. A 15 year old girl at my high school actually died because of combining a drug with ecstasy and alcohol. The school was devastated.

Do not do this on your own.
Get help.
Do not let her convince you that "It will be ok". It's never ok.
I reiterate, get help!

If you have the fear that she will hate you, she probably will...temporarily. But which sister would you have 5 years from now. The drug user who hates you and everyone else because internally she hates herself or the one who is healthy and loves you that much more for being by her side?
Tread carefully and good luck.
Answer: One thing nobody else has picked up on: If you ignore the drug thing for a moment, you were going through her stuff, when she clearly wasn't expecting you to. The best way to open the conversation might be to apologise for that.
Otherwise, in effect what you'll be saying is "I was going through your stuff and found this, now I've confiscated it, and need to tell you why you're wrong to have it", which is very different from "Sorry, I needed change desperately and panicked when I found this. Here, take it back, but if you're okay with it, I would like to talk about this, because I'm worried about you".
It moves the conversation from "What the Hell is this, you criminal?" to "I don't know what to do about this and I want to talk", which is where you really are.
She may have a healthy attitude towards drugs, and be aware of the risks. She may be acting out and just have them to be rebellious. She may be seriously struggling and be using them to cope.
Note that I am not saying that having illegal drugs in the house is a good idea, nor is taking them. But I agree with some of the commenters on ChristoperW's answer that "It is Never Okay", is not a healthy way to approach the conversation, if nothing else because it makes you look naive (the two drugs in question have a very low "active to lethal" ratio, especially compared to alcohol or nicotine). "This is why it is Not Okay in this case" - The possibility of arrest, the possibility of lethal cocktailing, the fact she's only 17 and living at home.
There are National Helplines in most Western Nations you can call.

US: http://psychcentral.com/lib/common-hotline-phone-numbers/0001302
UK: http://www.talktofrank.com/worried-about-a-friend
Answer: I'm seeing a lot of hysterical overreaction here.  Ecstasy, used occasionally and in small quantities, is not a high-risk drug: something goes wrong about 1 out of 10,000 times, compared with 1 in 350 for horse riding.  The UK's Academy of Medical Sciences ranks it at 18 out of 20 in dangerousness, way below alcohol (5) and tobacco (9).  In short, the short-term risk of your sister physically harming herself through casual Esctasy use is very low.
That said, there are two things she needs to be aware of, and you as her brother should make sure she understands:

Ecstasy doesn't kill, but dehydration can.  She should drink water regularly and avoid alcohol and caffeinated energy drinks, both of which are dehydrating.
Tolerance to Ecstasy builds up fast.  When one pill doesn't do what it did last time, some people ramp up to two, and then four, and then eight... and then when that stops working, they switch to a genuinely dangerous drug like meth or cocaine (#8 and #2 on the previous list) and end up addicted or dead.  The solution is simple: don't increase the dose, stop.  A month later, if she's still keen, the single pill will work again.

The other big concern is the legal side of things: depending on where you live, the penalties for getting busted by police or school authorities with even a pill or two can be life-ruiningly harsh, and since the stuff is illegal in the first place, you can never really be sure what's in those pills.  Unfortunately there's no easy solution to either, all she can do is be very, very careful about her stash (never take it to school!) and who she gets it from.
I see no possible benefit in getting the parents involved: they aren't going to understand, they are almost certainly going to freak out in counterproductive ways, and you'll burn your bridges with her by snitching.  Far better to be on her side as someone she can trust and turn to (and, yes, apologize about going through her stuff in the first place!).
Final anecdote: I've seen a lot of drug use in my early years in the rave scene, but I know of precisely one person who died as a result.  He was arrested by the police for possession, convicted of a felony and and sentenced to a few months in jail.  As a result, his girlfriend left him, his parents disowned him, and his flourishing car business went down the tubes -- so he became severely depressed and eventually hung himself.  Was it the drugs that killed him?
Comment: +1, especially for hard data and for highlighting that the legal issues are more critical than the medical ones. I would say, that *depending on the parents*, telling them could be a good idea, as much to support the original questioner as to do anything about the real problem.
Comment: @kleineg ecstasy is not addictive. MDMA, the active ingredient, is actually quite neurotoxic and you do develop a tolerance, but that does not imply addiction.
Comment: @kleineg absolutely. There is, however, a huge difference between physical and non-physical addiction and the two should not be lumped together. Also, ecstasy that does not contain MDMA is simply not ecstasy. What is known as ecstasy is, by definition, MDMA and often mixed with other amphetamines. I never said it was safe, it is actually one of the more (if not the most) neurotoxic of all recreational drugs.
Comment: A few people die of over hydration while on ecstasy.  In the UK more people die from over hydration the under hydration.
Comment: I have a hard time putting my thumb on why I dislike this answer. I like the use of statistics, I like the added bit that legal ramifications are possibly more dangerous than the drug itself. I think you may be a little flippant, and are ignoring the fact that if you hide the information from your parents you are involved in your sister's current and future behavior. And you only touch on addiction by mentioning tolerance buildup of Ecstasy. It is a tricky situation, you need to be aware that if you make a bad call (either way) you may end up blaming yourself if something goes wrong.
Comment: @terdon There is a difference between physical addiction (stopping would cause withdrawal symptoms) and psychological addiction. MDMA does not cause physical addiction but scores quite high in causing psychological dependency. Also, Ecstasy which has not been tested for the presence of MDMA (and to not include other stimulants commonly passed off as MDMA) is quite simply not safe.
Comment: -1 "I see no possible benefit in getting the parents involved..."
Answer: It's a complicated issue that doesn't have an easy answer. Arguments for involving parents include protecting her from becoming an addict; substance abuse could ruin her life. Arguments against involving parents include the consequences (particularly legal, if your parents would involve law enforcement). Despite the stigma, there are worse things she could be doing than  (casually?) using drugs; both that you mentioned are comparable to alcohol, which everyone seems to mistakenly regard as safe.
I'd start by talking to her with love to find out why she's taking them and if she's using responsibly or abusing. Depending on what's going on, you'll have to decide what to do by weighing the risks and benefits of your choice.
Just don't listen to cookie-cutter advice that claims there's only one right answer. The illicit drug stigma often causes people to overstate risks of substance use while ignoring the risks of involving the justice system. Don't pretend drugs are harmless though; tobacco, alcohol, pot, MDMA, etc. are all risky to abuse, but the legal/illegal distinction isn't that important.
Edit: You should at least make sure she understands the drugs and their possible interactions with other substances. Consider the fatal alcohol and MDMA interaction described in the answer by @ChristopherW; it would certainly be tragic if she died from ignorance.
Comment: I am sorry but what parents would ever involve law enforcement against their own child at that point? They are very dangerous substances, and a child in my house would be in a world of trouble... but locking your own child up in prison? Not for my life.
Comment: @kleineg I've known of it happening though.
Answer: Be honest - you're concerned & have a reason to be.
If we ignore it and act like everything is ok, how are teens going to get the message of where to draw the line?
She may be mad, but you obviously just happened to have seen the stuff by accident and are honestly worried about her.   Let her know why you are worried and how much she means to you.
Does she know how decisions she makes now can limit her choices in the future?
You care and don't want to see her get hurt.
She needs to know that good people sometimes make bad choices or choices that will harm them eventually - we're human - we all make bad decision at some time - but it is important to know someone loves her and only wants what's best for her and is there through the tough times too.  She may be angry for a while.
I'm not sure that you "hiding" the drugs is a very good idea.  There are legal ramifications for drugs being in your home or on your person and it is not fair to risk your parents' home or your future as well.
Comment: There some good advice in the other answers, but this is by far the one I like the best. Being honest (your own rifling) & showing genuine concern for her will likely be the best way to get her to open up. Once you know her real needs you can share what you know & enable her to make her own best choices. If this turns out to be way beyond recreational seek outside help.
Comment: +1, this situation creates just plain legal risk for you, her, your parents, your parent's house - besides her getting sick or worse, she could get busted, and is at the age where maybe it's juvie and maybe it's real jail. Tell your parents, get things on the right track.
Answer: I would talk to a professional first. I was friends with a drug addict for a while, and in my experience they can be masters at deflection. For example, if you confront your sister, my guess is that she'd say she's keeping the pills for someone else. A professional could tell you what to expect from the confrontation, and give you some pointers on what to do and what to avoid doing.
As for whether you should tell the parents, it really depends on the parents. In most cases I would say that the parents should be told, but it's your call. From what I've seen, the emotional damage of nobody reacting can be worse than the physical damage that drugs like these can do.
If you're a student, I'd go to a college counsellor and tell about your situation. If not, to some other consellor if you have the chance, maybe someone who deals with troubled youths. There might also be some helplines in the phone book, which you could call to describe the situation. If your sister really has a drug problem, the whole family might need some form of help. If she doesn't, someone who is more into the subject matter could help you see that the situation is more benign than you initially thought.
Answer: I'm coming late to this discussion.  I won't tell you what to do, but I'll tell you what not to do.
Don't call the police or involve the law in any way.  The law will likely do far more damage than marijuana or ecstasy are likely to do.  Even if you think that a stint in jail will "scare her straight", she will have a permanent stigma for life that will result in lost opportunities.
I would only even consider involving the law if she is doing something that is likely to seriously harm someone who doesn't want to be involved; such as if she were doing hard drugs while 30 weeks pregnant, for example.
Answer: You are the only one who can make the decision on what to do based off information you get from others and your personal values and beliefs.
The question that I recommend you ask yourself is whether you're willing to risk your relationship with your sister (and possibly have her hate you) in order to potentially save her life. There is no guarantee that the drugs will kill her or that your efforts will save her life; however, if she died of something related to the drugs (overdose, association with the wrong crowd, etc), would you blame yourself?
The "textbook" answers of telling someone, telling parents, confronting her are easier said than done.  The personal relationship you have with someone makes it much more difficult to address such a situation.
Answer: You should take it to your parents and explain the situation to them immediately. The only exception is if your parents are particularly unhinged and are going to beat her or throw her out on the street or something for the offense; in that case talk to someone else responsible and trustworthy who can intervene.
She is a minor, living in your parents' house, and engaging in illegal and possibly dangerous activity (blah blah blah about the merits/risks of any specific drug notwithstanding). It is a risk to her, to your parents, your parents' property, and you. (And possibly others, if she's driving, babysitting, etc. under the influence.) It's not your place to decide what to do, it's your parent's place, as it's their house and they're her guardian. She could get busted, you could get busted, your parents could get busted and/or in CPS trouble. You don't have the right to let that happen by collusion/negligence because she might get mad.
For what it's worth, this is my eleven year old's answer too.  "Take away the drugs and tell your parents. Duh, everyone knows that." Oddly no one's actually given this simple answer to this question yet, so I'm adding it.
Answer: "this does explain how she's been acting (and her mood) around the house lately"
Or, perhaps, her mood around the house lately explains why she's looking to drugs for happiness. Perhaps she's depressed and needs drugs for legitimate reasons? Without talking to her about what's going on in life and what/where the issues are, taking away the thing in life that gives her pleasure will not solve the problem. She needs to find a way to be involved in life again.
OR, she's just experimenting with safe recreational drugs, and you're freaking out over nothing. Hard to tell without knowing the family, but the tone of the question implies that legitimate use of such drugs, for dissolving ego barriers and assisting with social anxiety issues and forming a social bond, etc., is not an attitude that is likely to be displayed toward her. Maybe she needs the freedom to experiment and show that she's trusted to handle serious situations in an appropriate manner?
Comment: Is ecstasy a _safe_ recreational drug?
Comment: I think you're saying, She's self-medicating; find out why." In that case, I agree with you. But I'm not sure the other answer is to trust her and do nothing.
Answer: You should instantly tell everyone everything.  Tell her friends, your parents, other siblings, tell distant relatives - tell them all straight away as soon as you read this.
(If you're concerned your sister will "be mad" because you "tattled" or something .. well, that's how literally 4 or 5 year olds think.  If you actually think that - which is hard to believe - set that aside and tell everyone everything straight away. if she's mad at you that will last a couple hours.  Just walk straight up to the parents and say "Shit, what's this about XYZ with ecstasy in her room?"  Just forget the issue that "you're telling about it" and just immediately, instantly, get everyone talking about it. Especially call her friends, all of them, and talk to them about it.)
Regarding "are drugs dangerous" it's totally irrelevant. If I'm not mistaken pot is legal in most US states now right?  So forget that question.
The problem is not that she's suddenly going to die of a pot overdose, the problem is that (almost always) casual drug users at that age become "losers" - i.e., people with low income, bad education, rubbish or no jobs.
(Sure there are a handful of exceptions - billionaire pop stars etc.  Fantastic.)
Regarding heavier drug use, I recommend the book Million Little Pieces by James Frey. Have her read it and see what she thinks.
So again (if you're asking about) the issue "Should I Tell!?" - that's just puerile, absurd.  Of course just immediately talk to EVERYONE about it. Get EVERYONE talking about it.
Regarding the issue "will she become a slacker / loser" the answer is "almost certainly yes."  If you want to, just do everything you can to see that that doesn't happen.
(Inevitably, there will be a chorus of "I know A Person who took Recreational Drugs heavily and she went on to be a Brain Surgeon."  That's fantastic.  In the vast majority of cases they become beavis and butthead.  Your sister is en route to being beavis and butthead.  it's just that simple.  If there's something you can do to stop that path ()and you want to), go for it.)
And again, regarding the slim chance she becomes a crackhead or alcoholic, just read Million Little Pieces which will fix that up. (If that doesn't nothing will.)
Comment: This is probably the worst answer in the history of Parenting.SE.  Telling "everyone everything" will result in the sister being branded a druggie, probably expelled from school, and quite possibly arrested: it's *this* that would turn her into "Beavis & Butthead", not the drugs themselves.
Comment: Bad answer. Why tell everyone everything? This will only ruin.the situation more.


How are Catholic priests chosen and assigned to specific parishes?

Question: I know that a certain amount of education is necessary before men can be ordained as a Catholic priest. But are all men that received the necessary education ordained as priests? If not, what is the selection process? And how are they assigned to a specific parish?
Comment: While assigning priests, bishop's sense of humor might play a significant role. Once a man named Mrtvý (it means "Dead" in Czech) was ordained for a priest and assigned to a town called Hrob (it means "Grave"). Recently in the same diocese, Kamil Škoda was ordained and he was assigned to Mladá Boleslav, where is a Škoda car factory.
Answer: Many vocational offices explain this process in detail (the Diocese of Fall River has a good explanation, for example), but I'll try to explain it as best I know.
Before that, there are a few things to keep in mind:

There are two different "tracks": the diocesan track, where you are ordained as part of a diocese, and the religious track, where you are ordained as part of a religious order. You seem to be interested in the former, so this answer mostly answers to that. The processes are similar, it's just a question of where you end up.
Priests are, to put it somewhat bluntly, proxies for the bishop. A bishop cannot perform all the duties required of him for everyone, so the priests act as surrogates, performing many of the functions that are needed to successfully tend to the flock. In many ways, the process is about finding suitable matches for the bishops who need more priests: this is sort of the short answer to your question (the bishop decides).
One way to understand the full Ordination process and how the bishop makes his selection is to think of it like a very long, very structured introspection. Accepting the Sacrament of Holy Orders is a huge deal, one that will shape the rest of a person's life. The time in Seminary Formation and up to the Rite of Ordination into the Priesthood is basically the trial run period to see whether a person really, truly wants to commit to the life of a priest: committing one's life to the Church, taking a vow of celibacy, etc.

Process
The process starts off something like a Ph.D. track education in academia: when you go towards getting your Ph.D., you usually find out that you're interested in it during undergraduate school, then you go through an application process, then a core education (Master's) process, then you move into the meat of actually getting a Ph.D. (doctoral thesis).
Similarly, the path to ordination starts off with talking to a priest or other members of one's parish about being interested Holy Orders. The person will then apply to the diocese office of vocations, usually answering some basic questions about why they want to begin the process (example from the Archdiocese of Portland, PDF).
The vocation director will then make contact to begin the application process. This usually consists of a series of interviews, getting letters of recommendation, background checks, and other vetting processes to make sure the person has a high likelihood of succeeding.
Once accepted, the Bishop assigns the person to a seminary (with the recommendation of the vocations director) where they begin the process of Seminary Formation: they'll learn everything they need to know to begin the transition into the clergy. Simultaneously (if they don't already have it), they'll be receive the education to get a Master's Degree in Divinity (generally a requirement to receive Holy Orders).
They'll also begin the process of introspection and guidance to determine whether or not this is something really want to do and whether or not God is calling them to Holy Orders. This is done under the guidance of the vocation director who recruited them.1
Towards the end of Seminary Formation, men are ordained to the diaconate2 as a transitional deacon: similar to a permanent deacon, but with the understanding that they will soon be ordained a priest (usually in about 6 months).
It's at this point the bishop assigns them to a parish. This is sort of a "last chance" period to change one's mind and to start helping with the Liturgy in a real-world setting. The person is still in Seminary, but it's something like a "work-study" or "student teacher" program: he'll split his time between completing Seminary and doing the duties of a deacon.
At the end of Seminary, successful candidates undergo the Rite of Ordination into the Priesthood. Amongst other activities, the bishop will ask them a series of questions to make certain they'll ready to undergo the call of Holy Orders, but this is largely a formality: the Seminary Formation process was intended to weed out the candidates who would not make a good fit long before this moment. Think of it like a "swearing in" ceremony: candidates are going to know beforehand the answer is "yes", "I do", or "I will" to every question asked.
After which, the bishop will consecrate the candidates via the Laying on of Hands and ordain them into the Priesthood.
Once Ordained, priests serve under the bishop. The bishop can work with other bishops to transfer priests between dioceses depending on the needs of the Church.
Notes
1 It's important to note here that not everyone who goes through this process becomes a priest: many are never called by the Holy Spirit to receive Holy Orders and withdraw from the process within the first couple of years of Seminary.
2 If you're not familiar with the term, a Deacon is someone who is able to perform many sacraments one usually associates with a Priest: conduct sermons, baptize, and oversee marriages. But they can't do things like confer Holy Orders themselves or consecrate the bread and the wine used in the Eucharist (but they can help administer it).
Comment: @JustinY It's also done during Confirmation; I didn't think there was any other usage, but the [Catholic Encyclopedia mentions](http://www.newadvent.org/cathen/07698a.htm) a form of its use during baptism. On the non sacrament side, it's also used during exorcisms.
Comment: Thank you for this very thorough and informative answer. It is fascinating for me to see the practical similarities with [ministerial training in the Church of Scotland](http://www.churchofscotland.org.uk/serve/ministries_in_the_church/training_for_ministries), despite the differences in philosophy.
Comment: I had no idea that the Roman Catholic Church performed any sacraments with the laying on of hands. Is ordination the only time it is used? That's what the wiki article seems to imply, but doesn't specifically state.
Comment: Nice Answer. I think it applies for US. I know differences in Germany, so if someone is interested in other countries, please ask a new question.
Answer: Mark's answer was exceptional an complete so I'll just add an anecdote I heard a few weeks ago relating to the way priests are formed and trained.
While they're going through schooling (seminary) they're consistently being tested in ways they're not used to being tested. For instance, man who doesn't do well with death is put in a hospital and a man who doesn't do well with kids is put in a school. So the positions they have later in their priesthood are probably informed by their performance in priestly formation.
Also, when a priest (diocesan priest) is starting out he's usually not the one left in charge all by himself, so more than likely he's going to go to a place where there both is a need for another priest and that need doesn't need to be filled by an experienced priest. So new priests don't usually get sent out to Podunk Ohio until they're a few years into it.
Beyond that, it's a crapshoot and only the Bishop (who is the head of quite a number of parishes generally covering a geographic area) gets to decide based on his preferences. Often times stellar priests are given the more challenging assignments (and bigger parishes) but you can't really judge a priest by the size of his congregation. If a Bishop really likes a priest he'll make him a Monsignor (which has a slightly ironic meaning). From what I can tell, and this is speculation because it can't really be documented anywhere, Bishops favor obedience, prayer and managerial skills. So, in general those factors will determine the direction and duration of a given priest's stay.


Merge Replication SQL

Question: I am currently having a problem with the following
Creating a merge replication is simple if the servers are on the same network, i would like to know how can i do a merge replication if the servers are on seperate networks
I am using SQL 2008 R2
Answer: There's some very good tutorials on the web about this that go in depth and have lots of screenshots.
I'm assuming you also have to cross untrusted domains, correct?  Usually if the domains are trusted it means some sort of network link with AD/LDAP has been established.  If that's the case, you're looking at:
Merge replication across untrusted domains using web synch
Pull Merge Replication Security with Sql Server 2005 with no Domain Set Up (Largely applies to 2008)
http://www.jstawski.com/archive/2007/03/06/pull-merge-replication-security-with-sql-server-2005.aspx
How to: Configure a Subscription to Use Web Synchronization (SQL Server Management Studio)
http://msdn.microsoft.com/en-us/library/ms345214.aspx
You will also run into questions such as 'do I use a sql user, do I use security certs?  SSL or SQL certs, etc.?'  There's going to be a lot of decisions you'll have to make so be prepared to re-do it several times.

Merge Replication SQL


What to check for when purchasing a used and/or imported motor

Question: I'm planning to perform a motor swap on a Z32 chassis (1990-1996) 300zx twin turbo.  Low mileage japanese motors are plentiful and cost a bit less than motors sourced from US cars.  The specs and engine codes appear identical, and I've verified that they bolt right in and work with existing US wiring.  Are there any other precautions or caveats that I should consider before buying one of these?
Answer: If you are able to get your hands on it be sure to do a compression test on it.  If the compression is bad you will need to basically do a rebuild which will cost quite a bit more than what I am guessing you want to spend.  Check the condition of the timing belt, good way to see if the engine was taken care of.  That's all I can think of right now but of course there is more.
Comment: Adding to this, buying from a trusted source is huge. Some of the more well known, well verified stores put guarantees on their motors, and are better know to provide good motors.
Answer: Make sure you doublecheck on the laws in your state before you buy any imported engines.  I know in California you have basically zero chance of getting a Japanese engine smogged, even if the specs look the same as the US version.
Answer: I have only done this once, but I had incredibly good luck with it.  In my case, it was a '86 Subaru GL-10, also turbo.  I'm sure some will apply and some won't...
Check the sources warranties, some will say they're compression tested and what the different readings were, some will offer warranties, etc...  The engine I got was in extremely good shape, and I had absolutely no problems with it for several years until I sold the car later.  The story, as I was told it, is that emissions in Japan are extremely strict, and basically require a new engine to pass emissions after, say, 40K miles.  I don't know that that's true, but that's the story I've heard as to why you can get good, low-mileage engines from Japan.
Know your responsibilities when receiving the engine.  If they are shipping it, are they going to show up at your house with an engine in a crate and require you to unload it?  Can you pick it up at the shipping company's freight yard where they have a forklift?  What vehicle are you going to put it in?  How are you going to get it out when you get it home?
My engine came with hoses cut and then taped off.  It looked like a really fast job of removal.  It had all the sensors, full induction system, turbo, and headers on it, even the belts, oil pan, etc...  Mine did not come with the transmission.
I removed all the included sensors and induction/exhaust, and used what was originally on my engine.  This way I knew they were 100% compatible with my computer.
At the same time, I replaced all the seals related to the parts I was replacing, and put new hoses on.  I also replaced the clutch.
I was extremely happy with the engine.
In comparison, around a decade later I did a replacement engine for my VW Vanagon, and there weren't really engines from Japan available for it...  I instead found a guy who was well respected in the VW community and bought a rebuilt engine from him, and shipped him my old engine after the swap (to rebuild for someone else).  This guy knew the engine really well, and the cost was around the same as the used engine from Japan.  The engine was basically brand new at that point, but on the other hand it didn't come with a spare turbo and all sorts of sensors, so...  :-)
If I were in your situation, I'd probably be looking at having someone rebuild the engine, because then it has the opportunity to do some tweaks to bring the power further up.  The VG30DETT is generally considered to be good for around 400HP before you need to start modifying the engine itself, so this is probably a good excuse to get some of those beefed up parts put in.  But, that's going to push the price up (pretty much, the sky is the limit)...
Answer: I agree with ursa, if you can get hands on the motor before purchase then I'd pull the plugs and see how they look. Dip the oil in the dip stick and see how the oil looks, whether there is a lot of sludge or shavings or anything. Overall condition of the motor will tell you a lot about how it has been maintained. But the compression test is the best thing to do if you can, that will tell you a lot.


a little question about Heegaard splitting

Question: for any compact orientable hyperbolic 3-manifold with totally geodesic boundary, is there a strongly irreducible heegaard splitting?
Answer: I believe this is true for a small 3-manifold, one which contains no closed incompressible surfaces which are not boundary parallel. I think the argument of Casson and Gordon carries over to this case (if there is a weakly reducible yet irreducible splitting, then this should give a closed incompressible surface). Many simple examples of manifolds with totally geodesic boundary are small, and therefore should have a strongly irreducible splitting.
There are many Haken 3-manifolds which contain strongly irreducible surfaces. There are pretzel knot examples due to Casson-Gordon. I expect one may be able to construct analogous
examples of manifolds with totally geodesic boundary which have this property too, e.g. by
taking careful branched covers, and which are not small.
Comment: still, we don't get  an example of not small 3-manifold. is that right?
Answer: Casson and Gordon's argument goes through for minimal genus splittings of manifolds with boundary.  See Moriah's paper "On boundary primitive manifolds and a theorem of Casson–Gordon".  Now we follow Agol's idea:  A small manifold is an (irreducible, connected, compact, orientable) three-manifold where all incompressible surfaces are boundary parallel.  By Moriah's version of Casson-Gordon, any minimal genus splitting of a small manifold must be strongly irreducible.
Now, a manifold (irreducible, connected, compact, orientable) that is not small is called large.  So your question reduces to asking "does every large hyperbolic manifold with totally geodesic boundary admit a strongly irreducible splitting?"
I would conjecture that the answer is "No".  I guess this is suggested by the following construction: take two small manifolds $X$ and $Y$ with a homeomorphic incompressible boundary components $F_X$ and $F_Y$.  Glue $F_X$ to $F_Y$ by a sufficiently complicated map $f$.  Then (hopefully) all splittings of $X \cup_f Y$ should be amalgamations and thus none are strongly irreducible.  This is just conjecture, as nobody knows how to rule out the possibility of very high genus strongly irreducible splittings.  (If that has changed recently I'd be really interested to hear about it!)
I would next conjecture that a careful modification of the above discussion can give $Y$ an extra boundary component which is totally geodesic.
There are many papers in this general area.  See "The Heegaard genus of amalgamated 3-manifolds" by Lackenby and "On the Heegaard splittings of amalgamated 3-manifolds" by Tao Li, for example.
Comment: yeah,i hope  somebody can give an answer.
Comment: @yanqing - What I am saying is "your question reduces to a known open problem".  So you are unlikely to get a more complete answer than what Ian and I have written.
Comment: T.kobayashi has constructed an interesting example. http://arxiv.org/PS_cache/arxiv/pdf/0812/0812.4476v1.pdf


Security of PPTP vs IPSec

Question: Is PPTP or IPSEC VPN more secure than the other for 'dial in' VPN, if so, why?
Answer: PPTP is a tunneling protocol just like L2TP is - it does not provide security.
PPTP uses MPPE for encryption which may have some disadvantages compared to IPSEC (which is commonly used with L2TP). IPSEC can also be used on its own as a tunneling protocol and this is pretty common.
An advantage with IPSEC in general would be if it's used with certificates to authenticate on the machine-level in addition to the user-level. L2TP enforces this but IPSEC alone could be used with just a pre-shared key just as the encryption in PPTP can - lowering the level of security to similar levels in my opinion.
Most old vulnerabilities in PPTP are fixed these days and you can combine it with EAP to enhance it to require certificates as well. I'd say there's no clear winner, but PPTP is older, more light-weight, works in most cases and clients are readily pre-installed, giving it an advantage in normally being very easy to deploy and configure without EAP.
However, getting something more secure by machine-level authentication might give IPSEC an advantage in being designed for this to begin with (L2TP in particular) - and hence possibly be easier to deploy with that requirement than getting PPTP to work with EAP.
If we compare PPTP with L2TP straight off - L2TP wins by a fair amount due to the requirements for decent authentication on several levels, preventing several scenarios PPTP won't prevent (in theory).
Answer: The current wisdom is that IPSec is better, but no (known) full exploits exist for PPTP, so it's still commonly used. IPSec is certainly newer, and has more optional extras, and (IMHO) broader support.
Lot of people criticize that PPTP sends some unencrypted control packets, but, again, this hasn't resulted in a big exploit, it just makes people think that there MUST be one in there somewhere. I think a lot of it is just residual sour grapes because PPTP was a Microsoft initiative, and patent encumbered (they recently allowed open implementations, so this isn't as much of a concern.)
Answer: It should be noted that a new attack on MS-CHAPv2 by Moxie Marlinspike and David Hulton makes PPTP tunnels less desirable.  Based on this I would go with an IPSEC or SSL VPN based tunnel for remote access.
More info:

Infosecurity Article Covering Attack
IT Security Article Covering Attack
Answer: Good answers, but somewhat inaccurate. They can give wrong ideas about the role of L2TP.
L2TP does not use IPsec. It is not built on IPSec. L2TP is "Level 2 Tunneling Protocol", which performs one and only one function - tunneling other protocols. It does not provide any kind of security whatsoever, just because it is not meant to. And that is exactly why it is usually used together with IPSec. The two protocols being used together does not mean that they are dependent in any way. L2TP can be used without IPSec, just like IPSec can be used without L2TP. It does not make any sense to talk about security of L2TP - there is none. When one is talking about security of IPSec/L2TP VPN then he is talking about security of IPSec.
Answer: If you are considering microsoft PPTP you may find this useful: PPTP FAQ
Also, PPTP vs. IPSec is a bit Fish vs. Bicycles - you might want to look at L2TP rather than straight IPSec (L2TP is built on IPSec, and is supported in Windows same as PPTP, and has decent open source implementations).

Security of PPTP vs IPSec


Good source for a dark/weird dryad concept?

Question: I'm working on an adventure that involves obtaining the wood from a dryad's tree, and would like to present the dryad as something other than the typical depiction.  I have some ideas, but am curious as to whether anyone remembers seeing a dryad that stuck out to them from any system, setting, adventure, or piece of fiction.  Bonus points if it comes from appendix N, as the adventure is for DCC RPG.
Comment: Thanks all, that's some good stuff.  I also read Algernon Blackwood's short story "The Willows" yesterday and although it doesn't deal with dryads per se, it has some great concepts.  I'll probably steal the setting of that story and drop in a dryad based on some of the concepts below.
Answer: I find the best source for finding dark/weird versions of nature spirits is to look to the wiccan community. They often find old stories that date back to the origins of these creatures, where they were often created to scare people into good behavior.
I found a few links you might find helpful:
http://www.witchvox.com/va/dt_va.html?a=uspa&c=words&id=13299
A Visual: http://www.coolminiornot.com/191571
And here is a thread all about the new dryad in DnD 4e and different speculations on it's nature.
http://www.enworld.org/forum/4e-discussion/212064-dragon-360-art-gallery-dryad.html
The new 4e version of the dryad to me, is not of the "typical depiction" so perhaps that might be good enough.
Wikipedia might also be a good spring board to give you various incarnations of the Dryad so you can pick non-oak tree based drayds and even give it one of the different names from Greek Mythology.  http://en.wikipedia.org/wiki/Hamadryad
Answer: Earthdawn had a unique take on dryad but really I thought it was more taking a name and putting it on something different.
Warhammer (Fantasy RolePlay) has a cool dark version as well.
I seem to recall that RA Salvatore's Demon Wars saga had some interesting creatures, but I can not find any reference to the dryads, though I thought they were in there.  I am not aware of any sourcebooks around this world.
Answer: Another option is to use another forest spirit, like http://en.wikipedia.org/wiki/Leshy


Very simple example of the way the Fourier transform is used in quantum mechanics?

Question: According to a book I'm reading, the Fourier transform is widely used in quantum mechanics (QM). That came as a huge surprise to me. (Unfortunately, the book doesn't go on to give any simple examples of how it's used!) So can someone provide one please?
Answer: Given that leftaroundabout and vonjd have addressed the fundamental place of the Fourier transform in the formalism, let me talk a little about an experimental application.
What is the shape and size of a atomic nucleus?
From Rutherford we learned that the nucleus is rather a lot smaller than the atom as a whole. Now, electron microscopy can just about provide vague picture of a medium or large atom as a out-of-focus ball, but there is no hope of employing that technique to something orders of magnitude smaller.
What we do is scatter things off of the component parts of the nucleus. A nice reaction here is
$$ e + A \to e + p + B $$
where $A$ represents that target nucleus and $B$ the remnant after we bounce a proton out. (This is what nuclear physicists call "quasi-elastic scattering".) Now, if (1) we are shooting a beam of electrons at a stationary target, (2) we have a precision measurement of the momenta of the incident and scattered electrons and the ejected proton, (3) we are willing to neglect excitation energy of the remnant nucleus, and (4) we assume that $p$ mostly did not interact with the remnant after being scattered, we know the momentum of the proton inside the nucleus at the time it was struck.
Collect enough statistics on this and we have sampled the proton momentum distribution of the nucleus.
Now, here's the fun part: you can show that the spacial distribution of protons in the nucleus is the Fourier transform of the momentum distribution.
And bingo, a measurement of the size of the nucleus.
Do it with a polarized target and you can get info on the shape as well.
Answer: In quantum mechanics, the momentum and position wave functions are Fourier transform pairs, to within a factor of Planck's constant. With this constant properly taken into account, the inequality above becomes the statement of the Heisenberg uncertainty principle.
You can find more here:
http://en.wikipedia.org/wiki/Fourier_uncertainty_principle#Uncertainty_principle
Answer: Apart from its physical meaning (canonically conjugated observables (energy and time, position and momentum...) are fourier transforms of one another), the fourier transform is an important tool in any field that deals with linear differential equations. In quantum mechanics, everything is linear, so it is quite often useful to perform a fourier transform to make solving the equations easier.


Most suitable metric for the Solar system?

Question:
If I wanted to solve the Einstein equations for the solar system, which choice of $g_{\mu\nu}$  and $T_{\mu\nu}$ is more suitable?
I thought about using a Schwarzschild metric near each planet, but how to connect them?
Answer: Solving the Einstein equation for a system as complex as the Solar System could only be done numerically, and in any case it's not terribly useful. Nothing in the Solar System, is relativistic enough to need more than a linearised treatment (this is how Einstein calculated the precession of Mercury).
Actually even solving Newton's equation for a system as complex as the Solar System can only be done numerically. The way you actually do things like detecting the presence of Neptune is done using perturbation theory. If you were interested in relativistic effects you start with a symmetric solution, apply classical perturbations using Newton's law then finally apply corrections using linearised GR.
To take the example of Mercury that I mentioned above: if the Solar System consisted only of the Sun and Mercury (and both were perfect spheres) the orbit of Mercury wouldn't precess. However it's observed to precess by 574 arc-seconds per century. 531 arc-seconds of this are down to classical perturbations by other planets, and this was known before GR was formulated. Only 43 arc-seconds was left for Einstein to explain, which he did using a linearised approximation.
Comment: Ok, I didn't read this carefully enough, you mention linearized approximation, but it's still wrong--- the question asks how to superpose Schwarzschild metrics, you do it by adding up the metric perturbations (for stationary objects) and using boosts (for moving objects).
Answer: You just add the metric in isotropic form. You need the isotropic Schwartschild solution, which is found by transforming the r coordinate so that the metric looks like:
$$ - g_{00}(u) dt^2 + g_{uu}(u) (du^2 + u^2 d\Omega^2)$$
This requires choosing $u(r)$ appropriately. Then you note that the result can be transformed again:
$$ - g_{00}(u) dt^2 + g_{uu} (dx^2 + dy^2 + dz^2) $$
Where $u = \sqrt{x^2 + y^2 + z^2}$. Then you write the linearized approximation, which turns out to be:
$$ - dt^2 + dx^2 + dy^2 + dz^2 - h(u) dt^2 - g(u)( dx^2 + dy^2 + dz^2) $$
And then you superpose the solution for the invidual masses, since the linearized small perturbation metric is additive among separate sources (like any other linear field theory). The result can be simply expressed in terms of the Newtonian potential:
$$ h_{tt} = 2 \phi(x,y,z)$$
$$ h_{ii} = 2 \phi(x,y,z) $$
Where $\phi(u)$ is the ordinary Newtonian potential. The superposition is valid in the weak field limit, which for the Solar system is essentially exact. The result can also be derived without going through isotropic coordinates, because the difference in r and u is higher order in the gravitational field, but I prefer to do it this way.
For moving objects, you have to tensorially boost the Schwarzschild metric to a moving frame. This introduces the Gravitomagnetic forces, and it is important in the solar system. The boosting is by the tensor law using the Lorentz boost. This gives the off diagonal h's for a moving source, and it is fine as long as the retardation effects are negligible, which is true throughout the solar system.
This approximation is introduced by Einstein in 1916 in the original papers on GR, and he uses it to calculate the effects of GR in the solar system, a few months before the exact Schwarzschild solution appears. Einstein thought the field equations were too complicated for an exact solution until Schwarzschild proved him wrong.


Will Ubuntu 12.10 run on intel core 2 duo 2.00GHz?

Question: I have a laptop with an Intel core 2 duo and i do believe it supports 64-bit OS. Will Ubuntu 12.10 64bit run on it without any trouble? Thanks!
Comment: Why would you expect it not to run?
Answer: You can take a look at this site:
https://help.ubuntu.com/community/Installation/SystemRequirements
There you find the minimum Requirements for Ubuntu.
I think it should run, it also runs on my Intel Core2Duo (2x 3.0GHz) machine ;-)
Answer: It should run.
The best thing to do is to make an Live USB /DVD of Ubuntu. The instructions are on the ubuntu.com website.
Boot your laptop from the USB or DVD and select the option "Try Ubuntu". This will allow you to test Ubuntu without installing it on your hard drive. You may want to check Ubuntu runs with your graphics card, sound card, wifi chip, web cam (if the laptop has it) etc. rather than just the CPU. Even though driver issues are less common than they used to be they crop up from time to time.
If something does not work out of the Live USB, it does not mean it won't work at all. It means you have to ask some questions and do some extra downloads and configurations yourself.
See Installing 64bit ubuntu on Intel(R) Core(TM)2 Duo CPU T5870 , possible? for some more information.
Best of luck.
Answer: I installed Ubuntu 12.10 on my notebook with an Intel Core Duo P8600 processor, that is just a little faster than yours. I think that there should be no problem installing on yours, according to the Ubuntu 12.10 system requirements.
However, the best way to know if it runs fast on your PC or notebook is using the Ubuntu Live DVD or USB (for 12.10, all you need is one DVD or a capable USB pen drive).
Answer: The laptop upon which I am writing this has an Intel® Core™2 Duo CPU 2.00GHz × 2 processor, same as yours, and Ubuntu runs great on it.  I have 4GB of RAM, and don't know how much you have, but since your processor appears to be the same as mine, I'd say that it won't limit your Ubuntu experience at all.


is $\pi_k(X_1,A_1)$ a direct summand of $\pi_{k}(X_1\vee X_2,A_1\vee A_2)$

Question: For space pairs $(X_1,A_1)$ and $(X_2,A_2)$ ,is there a groups M,such that  $\pi_{k}(X_1\vee X_2,A_1\vee A_2)\cong \pi_k(X_1,A_1)\oplus M$?
Comment:  $\pi_3(S_2 \vee S_2) = \mathbb Z^3\neq  \mathbb Z^2 = \pi_3(S_2) \oplus \pi_2(S_2)$. I can't imagine that the relative homotopy groups would make it more well-behaved.
Answer: The pair $(X_1,A_1)$ is a retract of the pair $(X_1\vee X_2,A_1\vee A_2)$, so the map $\pi_k(X_1,A_1)\to \pi_k(X_1\vee X_2,A_1\vee A_2)$ is a split injection for all $k$. If $k\ge 3$ then the groups are abelian, and your result follows with $M$ the cokernel.
Answer: There are some cases when one can give complete information.   We know that the relative  homotopy group
$\pi_k(X_i,A_i)$ is a $\pi_1(A_i)$-module for $k >2$, crossed  $\pi_1(A_i)$-module if $k=2$.
Suppose that  the spaces are connected, well  pointed, and the pairs
$(X_1,A_1), (X_2,A_2)$ are $(k-1)$-connected.  This result is a special case of the Higher Homotopy Seifert-van Kampen Theorem (HHSvKT) stated and proved in the book ``Nonabelian Algebraic Topology", that we have a pushout diagram
$$\matrix{(1,1)&\to&(\pi_1(A_1),\pi_k(X_1,A_1)) \cr \downarrow & & \downarrow \cr (\pi_1(A_2),\pi_k(X_2,A_2)) &\to & (\pi_1(A_1 \vee A_2),\pi_k(X_1 \vee X_2,A_1 \vee A_2))}$$
which is of modules if $k >2$, crossed modules if $k=2$. Here we write a $G$-module $M$ as a pair $(G,M)$, and we also use that notation in the crossed case though that involves also a morphism $\mu: M \to G$. Thus the result of the pushout is a kind of free product.
This pushout diagram, or  ``free product'', yields an explicit description of the resulting relative group.  For convenience let us write the pushout as
$$\matrix{(1,1)& \to & (G_1,M_1) \cr \downarrow & & \downarrow \cr
(G_2,M_2) & \to &(G_1*G_2, M_1 \vee M_2)} $$
Let $i; G_1 \to G_1 * G_2, i_2; G_2 \to G_1 * G_2$ be the canonical morphisms. We can form the induced $G_1 * G_2$-modules  $i_*(M_1), j_*(M_2)$. Then for $k>2$, $M_1 \vee M_2 \cong i_*(M_1) \oplus j_*(M_2)$.  For $k=2$ we have to use induced crossed modules and the coproduct of crossed $G_1 * G_2$-modules, but the relevant constructions are of course more complicated.
For the case $k>2$ there is presumably  a proof using covering spaces and homology, but the case $k=2$, being nonabelian, looks inaccessible to those methods, and being a part of  low dimensional topology, might also be relevant to geometric group theory.  (The main theorem referred to dates from 1981, in a paper entitled ``Colimit theorems for relative homotopy
groups'', JPAA. )


Getting upload file size before upload

Question: When the user selects a file to be uploaded, is there a way I can get the exact size of this file before the upload even begins? I'm guessing this needs to be done on the client side with jQuery or JavaScript. Any ideas how?
Answer: This cannot be done in pure Javascript in current browsers.
Instead, you can use Uploadify, which uses Flash.
In non-IE browsers, you can also use HTML5 to read files on the client.
Comment: re: http://www.caniuse.com/.  Informative but depressing link.  I wonder if IE will forever be in the red.
Answer: <code>$("#file_input_selector").bind('change', function(){
 alert(this.files[0].size);
});
</code>
Not sure of all the compatibility issues, but this seems to be working just fine for me.
Answer: Take a look at this post:

http://forums.digitalpoint.com/showthread.php?t=6704
Answer: Javascript doesn't have the ability to check file sizes (or access the file system for that matter). You'll need to upload the file to get the size
Answer: I suggest you look at the HTML5 File API. This, combined with some JS might be able to help you. I only say might because I have not yet had a chance to browse at this part of the HTML5 standard.
http://www.w3.org/TR/FileAPI/#dfn-filereader
The way PHP file uploads work, it is very hard to check file details before, or during a file upload (since the file is uploaded before your code even gets loaded).
I know it is possible to do some fancy things in some other languages (possibly Perl or Python) that handle the file uploading directly with the script (where the script opens the socket and handles the whole transfer itself), however PHP does this for you and accepts any file on your script's behalf. The file gets discarded if it is not within PHP's acceptable limits, but only after the file is completely uploaded.
There have also been several file upload implementations made using Flash, but not being an ActionScript coder, I can't really help too much there either.

Getting upload file size before upload


Physical Meaning of Constant Velocity Gradient

Question: I'm interested in representing homogeneous elastic deformations using Lie groups/algebras. Homogeneous deformations are those with a deformation gradient F which depends only on time (not position). If the velocity gradient L = (df/dt)F^-1 also is constant (independent of time or position), F = e^(Lt) where F is Lie (sub)group of GL(3,R) & L is Lie (sub)algebra of gl(3,R). This obviously is what I want but I'm unsure what a constant L means physically in terms of the deformation. Thanks, John.
Comment: I don't quite understand what the formulas mean, but I think you want $L$ to be a function from (time,position) configuration space to the Lie algebra, rather than having $L$ be an actual Lie algebra.  In your special case, I think it should a constant function.
Answer: I'm not sure this is what you're after, but are you familiar with pseudo-rigid bodies?  These are elastic media where the deformation tensor $F$ is constant in time and hence is an element of $GL(3)$.  I'm a little vague on the details, but different continuum models are specified in terms of different subgroups of $GL(3)$.  For instance, rigid bodies are obviously described in terms of $SO(3)$ while homogeneous fluids can be described in terms of $SL(3)$.
I have never checked the literature, but apparently Chandrasekhar used these descriptions for the study of relative equilibria of rotating, self-gravitating blobs of gas.  Casey has a number of introductory papers on the continuum aspects, and this seems to be a good survey.  I found this paper, Pseudo-rigid bodies: a geometric lagrangian approach,  a good introduction to the geometric aspects, which IMHO are more interesting anyway.
Comment: Thanks for your answer. I read the Casey papers on pseudo-rigid bodies which were quite useful. My interest is inhomogeneous deformation but in the finite element context (so finite number of nodes &, hence, dofs). Thanks again, John
Comment: Hi John, this sounds like an interesting problem.  I'm sure there would be a lot of nice geometry involved if you modelled a continuum as something which is locally a pseudo-rigid body.  Moreover, this could lead to some novel ways of doing FEM.
Answer: I have received two answers from chatting with colleagues:
1) Constant L assumes constant strain throughout the body. For example, a 3-noded triangle in finite element analysis (fea).
2) Constant L assumes constant acceleration which is a common fea assumption & reasonable with small time steps.
I'm comfortable with these explanations so wanted to share.
Thanks, John.
PS: Re Scott's comment:
Scott
Thanks for your thoughts. Sorry that my thoughts often are a bit vague. But, I'm using the def'n of a matrix Lie algebra: "Lie algebra g of a matrix Lie group G is the set of all matrices X such that e^(Xt) is in G for all real numbers t". That's why I'm calling matrices L a Lie algebra.
L has to be constant for df/dt = LF = Le^(Lt) (above equ'n rearranged) to be true. But, I'm still puzzled as to what a constant L means physically in terms of deformation. It certainly means that velocity varies linearly with position but unsure beyond that. The assumption of L being constant is made very often in the literature as a simplifying assumption but never explained beyond that.
Thanks, John


2 accounts under same email preventing me from loging in

Question: A year ago I set up a WP account with email account A. I was unable to work with WP effectively.
I came back a year later with more knowledge & brought WP into a domain (abc) I already owned. I linked this second account to email A as well. I have made a website with abc using WP. After making the website, I decided to switch hosting providers from Go Daddy to Fat Cow. Somewhere in the process of switching the website from one provider to the next, my word press account got lost in cyberspace. I have attempted calling Go Daddy & Fat cow for support help, however they say I have to get ahold of WP support. Not only is my word press account gone, but also I somehow have to get my "SQL dump file" to Fat Cow. It may be obvious b/c of the language I'm using, but I am fairly new to this whole website design thing.
The second part to my problem, is that everytime I try to log into my new WP account that is linked to abc, it sayis I am using the incorrect password. I know i am using the correct password as I wrote down what it was. I got to the password reset link, & it has me enter my email so that it can send me an email with another password reset link. However, when I go to my email to find the password reset email from WP, I go to reset my password & it is directed to my first WP account that I built over a year ago. It's as though WP has deleted my abc account & is telliung me I ccan only access my account from a year ago. Please help me.
Answer: I'm not sure what the hosting provider Fat Cow gives you but if you have cPanel and phpMyAdmin, you can log into phpMyAdmin, find the database for your WordPress installation, and then find the wp_users table. Find one of the duplicates (2 entries with the same name) and delete one of them. Reset your password again and it should work.


Are residual starches bad for the beer?

Question: I was reading another question here and it appears that the consensus is that the iodine test isn't all that useful if your recipe is good. But, while reading through everything, I had a thought: if you're hitting your OG, is there anything bad that might be caused by starch remaining in the beer (e.g. extra haziness, early spoilage, possible food for infections)? Or will it just settle out/remain harmlessly in solution?
Comment: Good question. This will obviously have ramifications for my "dry-malting" idea.
Comment: Just to be clear, residual starch is a function more of process errors not so much a function of a good (or bad) recipe.
Answer: Yeast cannot metabolize starches, so any starch left provides a food source for infections. You can also get starch haze from too much unconverted starch. In general starches are bad things and should be avoided as much as possible.
Answer: I have yet to have an infected batch so I cannot really comment too much on the problems of unconverted starch in your beer. However, this page is quite interesting. There are two tables provided giving data on the use of adjuncts/unmalted grains and malted grains.
The author has a little rant about the evils of starch and that
"With the exception of Roasted Barley these grains must absolutely be mashed with enzymatic grains in order to convert their starches to sugars. Do not under any circumstances use these without doing so."
"Starch bad. Sugar good."
Scary stuff, but I do get the point.

Are residual starches bad for the beer?


How long do sanitized bottles keep?

Question: If you sanitize a bunch of bottles and store them upside down on a tree or in a box (still upside down); how long can you store them like that before you feel the need to resanitize them?
Is there a better way to store them to keep them sanitary?
Answer: In my opinion, then answers here are overly cautious. Not to say that they are "wrong" but beer is very forgiving.
I've personally sanitized a batch of bottles, left them to dry on the bottling tree, then returned to do the actual bottling the next day without any problems whatsoever. Here's why i belive this approach works:
(1) The plastic arms of the bottling tree are fairly unfriendly to bacteria due to their non-porous nature. Especially because they get hit with a small dose of sanitizer as the bottles drain out onto them. Just make sure they are cleaned of any gunk before bottling.
(2) The beer bottles are very inhospitable to bacteria after you've sanitized them. Bacteria cannot really live on glass without something else to cling to, so as long as your bottles were cleaned, then sanitized (not just one or the other), then the bacteria will find it very, very hard to live inside that bottle.
(3) So long as the bottles are upside down, no wild bacteria riding in on dust can get into them. The bacteria cannot really "climb" up the bottling tree, assuming its been cleaned of any organic material in between uses.
(4) Whatever random spec of bacteria that just happens to survive this inhospitable environment gets immediately dosed in a weak acid solution that has preservative herbs (hops) and a fair abount of alcohol. I'm talking about your beer of course! Remember, beer is not an easy environment for most bacteria to live in, this is why mankind kept on making beer to begin with.
So to summarize, make sure your bottling tree and your bottles are cleaned & sanitized, and make sure the bottles are stored upside down, which is their normal position on a bottling tree. If you do that, then you certainly have several hours, if not several days, to get around to bottling. Sounds like it could be a cool experiment too!
Answer: The general rule of thumb is that you want to use anything you sanitize within 30 minutes of sanitizing it. That is, sanitize and use, don't sanitize and then store.
Answer: I wouldn't trust bottles stored for more than a few hours. While bottles are being kept in the box, air can circulate inside them, bringing any sort of unwanted predators. What I always do is sanitise the bottles and, as soon as they are dry, bottle the beer. I may be over-cautious but I can't see any that you can keep germs out of the bottles for longer times.
Answer: If you sanitized them and then covered the tops with foil/plastic wrap, I would feel pretty safe using them again. However, I always sanitize everything right before use - always! I use StarSan, and it takes literally seconds to spray or dunk my gear and have it sanitized and ready to go.
Answer: I realize the question wasn't "how do you do it" and more "what is the rule", but, not being a microbiologist, I'll stick with how I do it.
I use sani in a bucket with a spigot. I fill about 6 bottles to the brim, and by the time the 6th is full, the first has had its 30 seconds of contact time. I dump it out, dip the neck in the sani, and set it next to the bottling bucket. After all 6 are there, I fill them all. If any of them look dry, I'll dip them again just to be safe.
Don't fear the foam!
So, I guess in answer to your question, less than 5 minutes in my setup.
Answer: In "How to Brew", John Palmer claims that if you wrap a bottle top with aluminum foil and then sanitize it in the oven, the bottle will remain sanitized indefinitely (as long as the top stays wrapped in foil).
Comment: I believe that will sterilize it, similar to an autoclave.

How long do sanitized bottles keep?


How to clean my unanodized aluminium pot?

Question: I got some acidic food in the pot and its starting to look ugly.
Can this pot be saved, or do I need to throw it out?
Comment: Define "look ugly"?
Answer: If it's a small spot you can rub half a lemon on it till it's gone. If the entire inside has darkened you can fill it with water, add several tablespoons of cream of tartar (2 per quart) and boil it for 10 minutes.
You can also buy aluminum cleaner, but the do it yourself is typically cheaper.
In case you're wondering why I'm suggesting an acid for cleaning. It's actually alkali foods that stained your pot, not acidic. e.g. boiling potatoes. Acid actually cleans the spots put there by alkali foods.
The common warning against cooking acidic foods in an aluminum pot is to prevent excessive amounts of aluminum being leeched into your food.
Answer: If it's just a matter of darkening and isn't significantly affecting your cooking (i.e. burnt on areas that will cook more quickly) there's no need to worry about it.
I like nice looking pans too but performance is more important than appearance.
As for maintaining a nice clean surface in aluminum and stainless pans, particularly when things have burned or oil and fat have splattered and are creating that "sticky" feel on the edges of cookware, spray it with degreaser or oven spray and let sit for 5-10 minutes before scrubbing with a steel scouring pad.  The degreaser works on non-stick pans too but just use a soft nylon pad, not steel for scrubbing it.
Comment: Using degreaser and steel wool to clean pots?  You must be industry, because that's what I was about to suggest.
Answer: When camping with the Boy Scouts our aluminum pots and pans would frequently get burned and stained (cooking on a wood fire, lack of expertise...), but steel wool and detergent would always bring them back to their pristine state. In a pinch, a handful of sand or even plain dirt, as long as it contains enough finely subdivided hard materials, will also work.
When you don't have a delicate/shiny surface to worry about, life is so much simpler.
Answer: On cheap steel pots I use a very fine emery cloth that is usable in water. (Sand paper would disintegrate.) I use an old one left on the side for this particular purpose so it is not too rough. You can get very fine grades. My pots are really very clean and I even at times clean the base. Although some pans you shouldn't  do this as they have special copper impregnated patterns engraved. Obviously not to be used on non-stick or special surfaces.


Is there a way to link the animation of two layers?

Question: I am building a kinetic type-style video and am struggling to get some of the animations to sync correctly.
In this particular example I am trying to have a text box (imported .ai file) rotate with the text inside (made with an AE animation preset) but at the moment they fall out of alignment part way through the animation.
Is there a simple means of link their animations so they stay in the same position (relative to each other) or do I have to fiddle with the registration point to make sure their animations sync together?
Answer: What you want is layer parenting.
Answer: You are looking for Anchor Point.
Position on composition is the sum of Position+Anchor Point. Play a little with it to understand how it works. Simple press "A" on keyboard to show this propertie on timeline.
If you need to link values (position to anchor points or whatever) of each layer use the @ operator (on timeline too). This will give u an moving "arrow" to link both values. The icon of this tool really looks like a "@". After linked, propertie 'childed' will follow propertie "father" . Parenting is the name of this tool in AE.