Where do "new" humans come from?

Question: If all of us are re-incarnations of prior human beings, how do we account for the growing population? Where do "new" humans come from?
Comment: Comments are not for extended discussion; this conversation has been [moved to chat](http://chat.stackexchange.com/rooms/42658/discussion-on-question-by-ransara009-where-do-new-humans-come-from).
Answer: We are not necessarily re-incarnations of prior human beings. There are 31 planes of existence in Buddhism. So the  present human beings could result from any of the 26 planes out of 31 planes of existence(except 5 non-returner Bhrama realms) which consist of unaccountably large number of beings. For example, imagine the number of beings living in  Animals realm (tiracchana yoni).
Comment: This did not cross my mind. Thanks for the insight!
Answer: There is no evidence all of us are re-incarnations of prior human beings. If we were, the Buddha would have explicitly explained this.
MN 38 explains how a new child comes to be:

Bhikkhus, the conception of an embryo in a womb takes place through the union of three things. Here, there is the union of the
mother and father...it is the mother's season and the
gandhabba is present....

SN 31.1 gives the impression 'gandhabba' is similar to sperm, i.e., sexual seeds that create life:

Bhikkhus, I will teach you about the devas (gods) of the gandhabba order. Listen to that....
And what, bhikkhus, are the
devas of the gandhabba order? There are, bhikkhus, devas dwelling in
the fragrant roots, devas dwelling in the fragrant heartwood, devas
dwelling in the fragrant softwood, devas dwelling in fragrant leaves,
devas dwelling in fragrant flowers, devas dwelling in fragrant fruits,
devas dwelling in fragrant sap and devas dwelling in fragrant scents.
These bhikkhus are called the devas of the gandhabba order.

Commentary by Bhikkhu Bodhi:

The gandhabbas are associated with fragrant substances, no doubt because the word is based on the stem gandha, meaning scent.

In the Pali language, the word for 'human' is 'manussa', which means 'high minded' or 'noble/good heart'. The word 'manussa' is not the same as 'puggala' ('people').
SN 56.102-131 explain 'animals', 'ghosts' & 'hell' beings are reborn 'human' & 'godly' by seeing the Four Noble Truths and also explain gods & humans pass away into hell, the animal realm & the animal kingdom by not seeing (adiṭṭhā) the Four Noble Truths.
Comment: There is zero connotation in the verses cited or anything else that would equate gandhabba with sperm. The gandhabba are spirits. Not sperm.
Comment: gandhabba thoughout the vedic & even pali literature appears equated with or related to sexual or reproductive potency
Answer: This question is born out of the misconception that Buddhism teaches reincarnation as in after death you can only become a human (I've seen this same question and criticism of reincarnation on many websites before), this portrayal in the media is completely wrong and inaccurate.
The Buddha says:

"Sariputta, there are these five destinations. What are the five? Hell, the animal realm, the realm of ghosts, human beings and devas" (Maha-sihanada Sutta, MN 12)

Those are the five possibilities for anyone's prior existence.
Modern day humans were not necessarily humans on Earth in their previous existence (actually quite unlikely), they could've been in a hellish world, an animal, a spirit, or in a heavenly world in their very last previous existence.
This means a growing human population does not contradict rebirth or re-existence (the world population was 3 billion in 1960, now it's more than 7 billion).
The Buddha for instance was not thought to have been a human on Earth in his last existence, but existing in the Tusita heaven before taking birth on Earth. He had a great childhood, good-natured parents, and lots of luxuries which few humans even in modern times have.
In short all "new" humans in their prior existence before taking birth as a human existed in a hellish world, as an animal, a ghost, a human, or in a heavenly world (and very unlikely to have been a human right before this existence).
It is just a popular misconception that Buddhism teaches that after death one is only born as a human on Earth again and again.
UPDATE: The Buddha seems to explain that the majority of humans and devas (heavenly beings) do not take birth as humans after passing away:

Then the Blessed One, picking up a little bit of dust with the tip of his fingernail, said to the monks, "What do you think, monks? Which is greater: the little bit of dust I have picked up with the tip of my fingernail, or the great earth?"
"The great earth is far greater, lord. The little bit of dust the Blessed One has picked up with the tip of his fingernail is next to nothing. It doesn't even count. It's no comparison. It's not even a fraction, this little bit of dust the Blessed One has picked up with the tip of his fingernail, when compared with the great earth.
"In the same way, monks, few are the beings who, on passing away from
the human realm, are reborn among human beings. Far more are the
beings who, on passing away from the human realm, are reborn in
hell... in the animal womb... in the domain of the hungry ghosts."
"In the same way, monks, few are the beings who, on passing away from
the deva realm, are reborn among human beings. Far more are the beings
who, on passing away from the deva realm, are reborn in hell... in the
animal womb... in the domain of the hungry ghosts." (Pansu Suttas, SN
56.102-113)

The stereotype portrayed in the media of Buddhist reincarnation (after death one is born as a human again) is here stated as extraordinarily rare by The Buddha himself.
The majority of humans and devas after death go to hell, the animal womb, or the realm of ghosts instead of being reborn as a human or a deva in a heavenly world.
So based on what The Buddha says I would expect that the majority of "new" humans came from hellish worlds, the animal realm, or the realm of ghosts since The Buddha explains how extremely unlikely birth as a human is after death as a human or deva.
But the number of existences is countless so everyone existed in one the five realms many times before which may cause confusion.
The Buddha also explains in the Cula-kammavibhanga Sutta (MN 135) how one can exhaust their good and bad kamma in a human state instead of in a heavenly or hellish world.
The Buddha also explains in the Maha Kammavibhanga Sutta (MN 136) how it's not true that all good people go to heaven or that all evil people go to hell and that some evil people go to heaven and some good people go to hell by explaining the different variables involved (one's past kamma, later kamma, views at the time of death).
I still don't know where the popular media portrayal view of rebirth only as a human comes from debunked by The Buddha himself.
Birth as human is really rare, usually more pleasant than many other destinations, and gives one many opportunities.
Comment: A down vote is supposed to mean that the answer isn't useful (not that you personally disagree)...why is this not considered useful? It answers the question and explains more.
Comment: People might downvote if they [think an answer is incorrect](http://buddhism.stackexchange.com/help/privileges/vote-down). I didn't downvote this answer, it looks mostly orthodox to me (I thought the questionable paragraphs are those which correlate developed countries with a previous heavenly existence, and "bad areas" with a previous hellish world). My guess is that someone might have downvoted it because they think it's incorrect, because they take the view that doctrines about heaven, hell and birth should be interpreted as states of existence and/or becoming in this life.
Comment: Oh I see the reason for the down vote now but The Buddha seems to confirm what I said in suttas like Cula-kammavibhanga Sutta (MN 135). Of course conditions in countries change from time to time and a variation of good and bad beings would take birth in every country. There are only five possibilities if The Buddha is right, all humans in their previous existence right before this one were either in a hellish world, an animal, a spirit, human, or in a heavenly world. Of course everyone in one lifetime existed as one of these possibilities since there are a countless number of past existences.
Comment: +1 This answer is more correct than the chosen answer. If anyone truly wanted to learn correct Buddha's teachings by following the promoted ideologies of medias such as Bu SE is going to the pitchfall. Increased population for more beings from the lower realms get reborn as humans, so + because the quality of humans are declining (technological-wise termed "advancement"). Buddha described those characters of humans from lower realms; also said these beings would incline to be reborn back to the lower realms after finishing human lives for their residue Karmas of greed hatred etc. were strong.
Answer: As per My knowledge of Buddhism Lord Buddha said this is a Question That Time Wast's. Buddha said you cannot ever find end for where new Humans come from.. its like you cannot find End of the Universe..
Answer: Overpopulation is sure to become a dilemma of human existence in another couple of centuries. Even in the present day it is a major concern to us all. We would all love to escape this forever becoming samsara. But how? Only way out is through the practice and realization of Dhamma. Now, with more population, more desirous things out there, more things to rouse your desire, promote your greed, selfishness, worry, fear, etc. it is actually more difficult to practice the true dhamma. But your question is "where do new humans come from' according to the scriptures.
When studying the discourses of the Supreme Buddha, there is one thing that is clear to us: it tells us that the beings in the Samsāra have the tendency to 'reincarnate' in the four low-level worlds. They tend to get a birth in great hell (Niraya), Animal, Preta (ghost), and Asura worlds. Only rarely would a few go to the higher planes of existence.
If one is to take Buddha's word on this, only very rarely will a person will get to be born in the human world again. In the Chiggala Sutta: The Hole (SN 56.48) Buddha says:

Monks, suppose that this great earth were totally covered with water, and a man were to toss a yoke with a single hole there. A wind from the east would push it west, a wind from the west would push it east. A wind from the north would push it south, a wind from the south would push it north. And suppose a blind sea-turtle were there. It would come to the surface once every one hundred years. Now what do you think: would that blind sea-turtle, coming to the surface once every one hundred years, stick his neck into the yoke with a single hole?"
"It would be a sheer coincidence, lord, that the blind sea-turtle, coming to the surface once every one hundred years, would stick his neck into the yoke with a single hole."
"It's likewise a sheer coincidence that one obtains the human state.
It's likewise a sheer coincidence that a Tathagata, worthy &
rightly self-awakened, arises in the world.
It's likewise a sheer coincidence that a doctrine & discipline
expounded by a Tathagata appears in the world."

http://www.accesstoinsight.org/tipitaka/sn/sn56/sn56.048.than.html
Comment: There seems to be a contradiction in this post, which seems to claim that 'overpopulation is a major concern' yet physical human birth is a good thing. Why would the Buddha praise reincarnation into a physical world of population pressures, wars, starvation, murders for food, etc? There are 7 billion people on the planet therefore a physical human birth is certainly not something "rare". As physical human birth is not rare, the Supreme Buddha must have been supremely illogical for using the blind sea-turtle metaphor. Or is it our interpretation that  makes the Supreme Buddha look illogical?
Comment: The insect population in my backyard alone outnumber the 7 billion people on this planet.  It is estimated that there are double the number of unidentified insect species in the world than which are identified. Do you know that dust mites cannot be seen with the naked eye? So there is no contradiction in this post, and more importantly in the scriptures. But in it there's this quality of 'you get what you ask for'. If you go looking for contradictions, that is exactly what you will find.
Answer: I'm not an expert on this subject by any means, but based off of what buddhist texts/commentary I have read, I'll try to answer the question.
When you ask the question, you assume that whatever the "quantity" for human life is, that it is finite (e.g. 1 "unit-of-life per person) ( I know that's kind of a reduculous comparison, but I couldn't think of anything better).  However, life isn't finite and so, theoretically, so long as there are enough physical recourses, there never would come a time when life simply can't occur due to too much already existing life.
My next point is that there are two "entities" of our lives. The first is the one that we know, have experienced, and remember. It is our life according to out memories and basically what it is that makes us different on the surface from someone else. On the other hand, every living thing also posseses its "life force". It is from that that we derive karmic chains, karma from "past lives" and really just karma in general, as well as the ten worlds. This too is from where we derive, "the nature of our lives".
What is important to know is that our, "life force" is existant as a single entity in everything. Not only that, but, its existance is constant. Our life force is eternal in that it has existed since the infinite past and will forever exist into the future. (Sorry if right here I'm getting a bit confusing. I'm having a hard time explaining this, so please feel free to ask clarifying questions) What I'm trying to say is that, were the life force a concious being just as we are, it wouldn't precieve time nor space. The past is occuring right now, in its present, just as the future is. All of time and space exists within the "life force" that I'm trying to explain. Just as a photon, since it is going at the speed of light, "precieves" no time, the same is true of the "life force". To it, something that happened a countless number of years ago is, and forever will be, happening at the same time as you are reading this.
It is for this reason that in one of the first paragraphs I put "past lives" in quotations. We don't really have past lives in terms of past recolections. We do though in terms of our life force which has existed since the infinite past. This is what is meant by the fifth supernatural power that the Buddha has which is, "the ability to see past lives". Basically, what the Buddha really was able to do is precieve the nature of his life, and therefore "see" past lives (this is where the karmic chain stuff I said earlier becomes relevant). So we are, as living beings, more physical manifestations of our life force than we are our own singular entity, which would mean that there is no physical limitation of our life. And that therefore, the population could reach quadrillions and we still will have been "reincarnated".

Where do “new” humans come from?


What are the benefits of publishing papers in mathematical finance/trading?

Question: What are the benefits of publishing papers in mathematical finance and trading. Let us assume that the primary goal of a person/entity is to make money and reduce losses. Wouldn't publishing techniques/results give away secrets to competition?
Answer: There is an interesting article "How Derivatives and Risk Models Really Work: Sociological Pricing and the Role of Co-Ordination" by R. Rebonato answering your question.
In section "3.8 Conferences and Journals" the author formulate his version of the question as follows:

It is worth mentioning one last aspect ... of the 'institutional
  ecology' in which derivatives models are produced and used: the large international conferences devoted to discussing the latest innovation in option pricing.
  The speakers at these conferences are typically established quants, and the
  delegates junior quants, or quants from bank that want to become involved in
  complex derivatives pricing, risk managers and controllers.
The advantage for the quants in doing so is easy to understand: they can
  showcase their skills and prowess, and can become recognized and marketable
  in a relatively small industry. But why would a bank allow, let alone encourage,
  these quants and traders to speak about their 'trading secrets' (and, by doing
  so, to become 'poachable' by competing firms)? And why would a bank allow
  exotic quants and traders to publish the in-house-developed research in refereed
  academic journals, where, to be publishable, every model variant and improvement must be documented with precise and reproducible formulae?

And then the author answers:

The answer, again, lies in how money is made in derivatives trading (ie,
  by adding new trades, by taking no directional positions, by using sparingly
  the hedgeable-risk limits). Given this modus operandi, making money becomes
  much easier when model uniformity is enforced across the industry.
Comment: @oronimbus you are welcome
Answer: For the house, there are reputational advantages of publishing (" we have smart quants").  This may not outweigh the loss of competitive information, depending on the material published.  As you imply, the main benefit seems to accrue to the quants themselves, in terms of enhancing their own brand.
Perhaps this paradox arises from the question of what is the objective ?  Do we have a communal objective of advancing the overall knowledge level of mathematical finance (as is the case for scientific endeavor)?  Or are we trying to advance the knowledge only within our own organizations ?  In the case of banks, presumably the latter.
Comment: Hi: There's not that much to be gained by a non-academic publishing aside from reputation, marketing etc. This is why, if you read non-academic material regarding strategies, how to make profit, etc,  be very wary. Derivatives could be somewhat different because the profit angle is more indirect.
Answer: There are different types of publication by banks

paid publication: this is what is called "research" where bank analysts or quants offer the bank client various sorts of market insights or reviews. This is paid research and usually under condition that client does not broacast it to others. Of course some very famous ones get so popular that they effectively end up in the public domain.
academic publications: those can be themselves of various sorts. There can be review papers where some quant will effectively publicly present methodologies which have been more or less used by every desk in the street for some time (in this case there is no competitive reason not to publish), there can be publications that aim to create consensus from the street on how to best price a new sort of risk (think of counterparty risk/CVA which became essential after the crisis of 2008 and Basel III), there can be other publications which are more speculative/unimplemented in practice (like supersymmetric methods in finance maybe ? :) ) .

In addition there is a number of desks which maintain active relationship with people in academia which can be as formal as say the financing of a research chair at some public institution. In those circumstances a researcher will offer support/insight say developping a model and the bank quants will offer the academic the benefit of knowing some practical aspects that make the new model more relevant to industry inn addition to market data etc.... It's usually win/win situation and the counterpart for the academic is usually to be allowed to make a publication on some simplified form of the model in order to illustrate the main ideas behind. For example I can think of some publications on optimal execution that fall into this category.
Comment: Good answer, if you can it would be nice if you could give examples of the papers you mention.
Answer: If a company has actually built a superior model, they may publish it in order to benefit from the remaining market participants adopting it.
Say you have built a model showing that asset X is overpriced. Hence, prior to publishing, you simply short asset X and wait for the correction when market participants begin pricing according to your model.


What calendar or time cycle would an underground civilization use?

Question: The majority of the calendars on earth have used either lunar or solar cycles to keep track of time, ie days, months, years.
What would a civilization cut off from the sun or moon use to keep track of time? Are there any geothermal or geomagnetic cycles that are regular enough for time keeping?
Comment: See also [this question](https://worldbuilding.stackexchange.com/questions/71953/a-world-without-natural-time-measures) and [this one](https://worldbuilding.stackexchange.com/questions/53090/how-would-my-dwarves-tell-time-underground).  Oh, [and this one](https://worldbuilding.stackexchange.com/questions/32657/how-would-people-tell-time-if-it-was-always-day).  **Let's not duplicate answers, folks!**  Link to the content and then go over the differences, rather than saying the same thing again.
Comment: Humanoid?  If so, it couldn't have developed underground.  (Look how not-big and not-seeing underground creatures are.)   Thus, they could maintain the surface calendar from the time when they moved under.
Comment: I assume you're talking about a civilization that has always been underground, not one that had to move underground at some point in its past?  Is that correct?
Comment: I think you should specify what you mean by 'cut off'. Have they evolved in sunlight, and went into caves at some point, or have they evolved underground? Do they go to the surface regularly, or do they spend their entire lives in their caves and tunnels? Do they live on a planet orbiting a star at all?
Comment: First question to ask is why would they want time keeping in the first place?  Reliably, whatever causes them to want timekeeping is also cyclical enough to serve as a benchmark to start the process of finding good cyclical time sources. (also, not all time systems are cyclical)
Comment: Sorry for being sort of a duplicate, my cursory search hadn't found those questions. As for the creatures, they never evolved in sunlight, being geothermally supported. My world involves a shadow biosphere completely cut off from out world type deal.
Comment: How is this a duplicate? While those other answers are definitely applicable for considering, they really don't answer the same question. The top answer here is what I was looking for, I would never have found it at those other ones.
Answer: It would be good to note here that the way we currently keep track of time is completely arbitrary in the first place. We define seconds, minutes, hours, years and so on, but the truth is that any definition would make just as much sense as long as it was consistently applied throughout your underground society.
For the sake of convenience, let's assume that they use the same units with the same hierarchy as we do. Assuming also that these creatures have 10 digits, and thus use a decimal numbering system, it would seem to make sense that their units of time follow a decimal system too - i.e. 100 seconds = 1 minute, 100 minutes = 1 hour, and so on.
In that case, the main question here would be: what consistent, reliable natural pattern would they use as the basis for their second? Since most geological phenomena happen pretty slowly, these would not be great for timekeeping. Instead, consider that your society, at some point, developed The Pendulum. Perhaps some great thinker saw a large block of stone tangled up in an underground creeper, swinging all by its lonesome, and he had an " eureka"  moment.
I imagine a small group of Watchers (pun intented), people whose job is to monitor The Pendulum and to reset it to some initial state at regular intervals (for instance, every 10,000 periods) so that the rest of the society may continue ticking along.
Answer: Biological clocks for cave dwellers are driven by hunger
In experiments on Somali Cavefish, which have been isolated from sunlight for million of years, the fish were found to be unresponsive to artificially imposed dark light cycles, but that their circadian rhythm could be modified by feeding them at certain time intervals during the day.
Other variables that can control circadian rhythms include temperature changes and social interaction. Most fish species in rest-activity cycle studies maintain a near-24 hour circadian rhythm; this is probably due to having been derived from a surface-dwelling fish and having no reason to change the activity cycle. However, one species in the last linked study changed their rhythm to 38 hours. The authors do not propose any specific reason for the change to a 38-hour schedule, but it is possible that it was driven by the food availability or social interaction mentioned in the previous studies.
Lastly, in the last linked study, the cave dwelling species that maintained a 24 hours cycle usually slept much less than their surface dwelling counterparts. Surface fish slept in 2-3 hour bouts for a total of 12+ hours. The cave fish slept for many 15 min or less segments for a total of only 2-3 hours.
A cave dwelling civilization organizes around communal feasts
For a species of cave dwellers with absolutely no contact with the surface and the sun, a likely result would be organize a time schedule around communal meals, ticking off both the hunger and social activity blocks for maintaining schedules. These schedules could be 24 hours, or any other time unit, apparently.
These creatures would probably not sleep continuously through a 'night' but would catnap throughout the day. Every 4 to 6 hours, perhaps, there would be a community meal, where everyone gets together and eats. For a stone-age level people, this meal would be regulated by the genetic circadian rhythm of each individual; the social interaction provide a means for calibrating the internal clock with the other members of the tribe. As technology advances, water-clocks or hour-glasses would begin to be used to help time the meals more precisely, until eventually mechanical clocks are invented.
Answer: Sleep cycles / Days.
Humans isolated from outer time signals slightly shift their routines to a 25/26-hour day. So it will be days for them.
Years
Years and seasons have still discernible effects. Water supply will be low in summer and high in winter.
[continued]
Comment: You need to explain how underground dwellers know when it's " day" or " night". Humans lose track of time when they can't see the sun rising and falling. See  http://www.alaskasleep.com/blog/alaska-summer-sleep-tips-how-to-sleep-under-the-midnight-sun and http://nypost.com/2017/01/22/this-explorer-discovered-human-time-warp-by-living-in-a-cave/
Comment: i feel like I'm presently misadjusted to a 25/26 hour day
Answer: The earths rotation would still work. Pendulum deviation could be measured. once they built long pendulums for any reason they will notice it.
Foucault pendulums in particular are particularly noticeable.
Timekeeping is even easier. Simple sand glasses, water clocks, and other escapement based measurements still work fine as well. The first of these did not match known cycles they just made them tailor made for particular purposes.
Edit: dumped the tidal force idea, possible but too unlikely to be noticed in the first place.
Comment: Your answer is currently in the low-quality review queue. You might want to elaborate your point in greater detail.
Comment: One thing you would definitely want to discuss is the technology level at which a civilization might be able to measure them accurately enough for them to be useful for timekeeping purposes.
Answer: The concept of days and years was forced onto humans due to the existence of natural cycles we have no control over. Things like the sleep cycle and impact of the seasons. Our existing calendar is a mess mathematically, we have to somehow reconcile the length of a day with the length of a year which don't factor nicely, hence hacks like leap years.
Underground though with no seasons there is no such problem. The need to organise activity around the sleep cycle would probably require some kind of "day" unit being created to synchronise society. After-all you can't organise a meeting by saying "lets meet at sunrise or noon" in that case. The need for some kind of clock system to organise future events would probably be a lot more pressing. I can imagine people scurrying around the caverns whose sole purpose is to synchronise sand timers.
Once they have a day unit they don't need anything more. They can measure time just in number of days. Any official calendar created with longer periods would probably be far more logical, say base 10. Or they might use the age of their current king in days to denote historical events.
Any faint geological cycle, or even some sort of impression from the surface - perhaps some kind of bat species migrates down in accordance to season at the surface the humans cannot see - I doubt it would affect their calendar, such things would just be of some academic interest to a few mathematicians who are the equivalent of astronomers (or astrologers), who would look at the cycles to try and find meaning and generally be frustrated at how they aren't predictable and don't align properly with their measure of a day.
Comment: Months are natural, too.
Comment: I'm pretty sure things like bat migrations would be considered important to the lay cave-dweller, as a seasonal food source.


Is it possible to get a cut from being elbowed in the head?

Question: So I was at a basketball game, and sometime mid-way through it, I got elbowed in the head. At the end of the game, I found that I got a small cut that was slightly bleeding and, at that point, the blood had sorta dried. So how is it that I got a cut (it resembles a cut from a knife; straight and no width) on my head from being elbowed? I felt a little bit of pain that felt like it was coming from the bone, as I've felt that pain before and could recognize it, right after being elbowed. After the game, I didn't feel any pain until I took a shower. Then there was a really sharp pain. So, yeah, how did I get a cut from being elbowed in the head?
Comment: Welcome to heath SE :-) and sorry about your head. Which part of the head was it?
Answer: There are a few different types of injury to the skin. You can have a contusion (Bruise), abrasion (scrape), puncture, laceration or incision. The injury that you suffered is a laceration, as opposed to an incision. The main difference between the two is the cleanliness of the edges, lacerations are more jagged, incisions are clean slices.
There's a few different reasons that this could occur, but basically it's because the skin was suddenly stretched or compressed beyond it's ability to hold shape, and a tear results. You can see a few different laceration causes at this page. This can be fairly common in the head, as the skin is very close to the bone in most areas of the face and head.
Depending on the depth, location and severity, it can be taken care of from anything starting with a bandaid, up to wound glue or sutures.
Comment: I wasn't sure if I should just edit this, but I think your first sentence, especially with the link provided, could use a little tweaking.  I would think replacing injury with wound, (maybe also with a link to the Wiki article on wound), would be better.  Things like burn injuries confound the way it is written now.
Comment: How do I know if it requires sutures?
Comment: A laceration is a laceration, regardless of the cause. It's erroneous to say that a laceration can't result from a bite, from broken glass or a blade. [E.g. "*Facial lacerations from dog bites or cat bites are almost always closed*.... - **NEJM**.] You're right, though, in saying that blunt trauma causes lacerations by compression (a type of stretching.) That site is not in keeping with the actual medical literature. (I did do a quick search of the medical literature to verify.)


WordPress Plugin Development In MVC Architecture, How?

Question: I think, the wordpress plug-in architecture is not MVC. So I want to use/do the MVC architecture in WordPress plug-in development (like cakephp, codeIgniter ). How can I use them in plguin development. Does WordPress support CakePHP, or other frameworks?
Answer: You could definitely use an MVC philosophy in the development of a plugin, but you would be really silly to try to incorporate CI or Cake in addition to WP.
For instance, you could build out a plugin using the following pseudo structure (FYI, there are a ton of ways to build this, depending on your interpretation of MVC. This is just the quick example that pops into mind):
class Plugin(){
    function __construct(){ // controller?
        run conditionals/determine query
        process model
        process view
    }
    function model(){
        get query from database
        return variables
    }
    function view(){
        echo html
    }
}

This might be a horrible example of a plugin structure, or even of MVC, but it is simply to illustrate that MVC architecture !== MVC frameworks and that MVC can be used in plugin design. Widget classes and other functionality throughout WP are similar, although without any explicit separation of concerns.
Comment: I agree see my ref to lesdorf article MVC without framework
Answer: You asked multiple questions at once:
Q: I think, the wordpress plug-in architecture is not MVC.
A: Yes, that's true. It's not MVC in the Design Pattern Sense. It's MVC in a more general view: Model: Mysql, View: HTML/CSS, Controller: PHP. Main Frontend Controller is index.php, Commands are HTTP requests. The router is .htaccess (if you use pretty permalinks), the 404 controller (if you use that one) or index.php if you use the standard setup.
Q: So I want to use/do the MVC architecture in WordPress plug-in development (like cakephp, codeIgniter ). How can I use them in plguin development. Does WordPress support CakePHP, or other frameworks?
A: No, Wordpress does not support CakePHP or CodeIgniter out of the box. You can write an adapter for codeIgniter or Cake so that you can re-use an existing MVC (e.g. by encapsulating the HTTP Request and removing the slashes from request variables / the superglobals). But you can overrider Wordpress as well to just run any other PHP Framework Application as well, e.g. by adding rewriterules to the .htaccess and adding php files. It just depends on what you want to do.
Answer: The plugin architecture of wordpress by itself has nothing to do with MVC. But if you wanna do MVC WITHIN your own plugin why not. You're not obliged to use a framework, MVC is a concept which could be implemented without hevay framework see
http://toys.lerdorf.com/archives/38-The-no-framework-PHP-MVC-framework.html
Answer: I had this same question a while back, and at the moment, unfortunately, the only way to do MVC in a WordPress theme or plugin was to role your own.
So that's what I did, and I've been using it in my plugins and themes for a few months now. You can view the source on github here: https://github.com/philipwalton/PW_Framework
It's called PW_Framework, and it's loosely based on the Yii Framework, a very good MVC framework for PHP.
At it's core, PW_Framework is a quick and easy way to create options pages complete with client and server side validation. It handles the ajax validation as well as all the WordPress security issues (like nonce), so you can focus your development efforts on what your plugin actually does.
All you have to do is define your model with the attributes, attribute labels, descriptions, and options:
public function data()
{
  return array(
    'name' => array(
      'label' => 'Name',
      'default' => '',
    ),
    'email' => array(
      'label' => 'E-mail',
      'default' => '',
    ),
    'sex' => array(
      'label' => 'Sex',
      'default' => 'male',
      'options' => array( 'm' => 'Male', 'f' => 'Female'),
    ),

  );
}

Then you define the validation rules:
protected function rules() {
  return array(
    array(
      'properties' => 'name, email, sex',
      'validator'=> array('PW_Validator', 'required'),
    ),
    array(
      'properties' => 'email',
      'validator'=> array('PW_Validator', 'email')
    ),
    array(
      'properties' => 'sex',
      'validator'=> array('PW_Validator', 'match'),
      'pattern' => '/^m|f$/'
    ),
  );
}

And the view would look something like this:
<?php $form = new PW_Form( $model ); ?>
<?php $form->begin_form(); ?>
  <?php $form->begin_section('Year Options'); ?>

<?php $form->textfield( 'name' ); ?>

<?php $form->textfield( 'email' ); ?>

<?php $form->radio_button_list( 'sex' ); ?>

  <?php $form->end_section(); ?>
<?php $form->end_form(); ?>

Then in the controller, you simply write all of your code functionality.
Here's a working example of it in live use: http://wordpress.org/extend/plugins/pw-archives
Answer: WordPress is pretty much framework for itself, it takes care of stuff that is usually covered by framework with own (or bundled) code. Well, technically parts of it is BackPress framework but it's really very internal and not too relevant.
WordPress extensions (plugins or themes either) use provided WP APIs to retrieve and modify data. It doesn't matter for WP what your extensions uses, as long as it uses proper API to interact with WP itself.
So basically you can include and use any framework, library or whatever in your plugin. As long as you use WP API properly and it makes sense for performance and licensing constraints.
Comment: You're not answering the question(s) asked.
Answer: WP MVC (an MVC framework for WordPress) is the best plugin. We are using it now,  maybe it will suit your needs.
Answer: I assume you mean using MVC as cakePHP and codeigniter do, not 'use an MVC framework' to create a plugin or theme.  The second option would require users to download the framework you used as well as the extension files.
Answer: I think I am late to the party but if anyone is still looking for an answer, I have been working on MVC boilerplate for WordPress plugin development for some time. This boilerplate aims to separate concerns between Model, View & Controller.
With this boilerplate, developer gets a chance to write individual Model, View & Controller classes. Also, the concern of whether to load a controller/model or not is delegated to Router, so that your controller & model can focus only on what they are supposed to do. I believe this would help in keeping the footprint small.
This is not a full fledge MVC Framework, it is just a boilerplate allowing developer to write code in MVC style. Because of this, it has only those features which are required to build plugin in MVC way - No ORM - No Extra Goodies - No Huge Learning Curve.
Here is the link to a project: https://github.com/sumitpore/mvc-plugin-boilerplate-for-wordpress


Avoid subquery in this mysql statement

Question: I have a query as mentioned below:
select a_value as itemname, (
    select a_value from attributes where a_name = 'EAN'
) AS EAN
from attributes
where a_name = 'NAME';

Here I want 2 values from same table using different where clauses and I am displaying them in same front end table also. Can I avoid subquery here?
Comment: i can't get what you mean by here. can you give sample records? if this subquery `select a_value from attributes where a_name = 'EAN'` returns more than one value, it simply generates an error.
Answer: Try this:
SELECT a1.a_value AS itemname, a2.a_value AS EAN
FROM attributes a1
LEFT JOIN attributes a2 ON s2.a_name = 'EAN'
WHERE a_name = 'NAME';

OR
SELECT a_value
FROM attributes
WHERE a_name IN ('NAME', 'EAN');

OR
SELECT MAX(IF(a_name = 'NAME', a_value, NULL)) AS itemname,
       MAX(IF(a_name = 'EAN', a_value, NULL)) AS EAN
FROM attributes
WHERE a_name IN ('NAME', 'EAN');

Answer: this would return the two values as separate rows :

select a_value as itemname from attributes where a_name in ('EAN', 'NAME')

do you need to have all the results returned as a single row?
and do you need completely independent where clauses (rather than just different values)?
Answer: SELECT a_name, a_value
FROM attributes
WHERE a_name IN ('EAN', 'NAME');

In your app, fetch two rows, and then pivot it into a single array:
$item = array();
while ($row = fetch()) { -- pseudocode
  $item[ $row["a_name"] ] = $row["a_value"];
}
print_r($item);

You might want to do the operation in SQL, but it looks like this:
SELECT aname.a_value AS itemname, aean.a_value AS EAN
FROM attributes AS aname
JOIN attributes AS aean ON aname.entity = aean.entity
WHERE aname.a_name = 'NAME' AND aean.a_name = 'EAN';

And it gets more complex in the future when you need three attributes.  Basically one more self-join for each additional attribute you want.  There's a practical limit to how many joins you can do in a single query, so this solution doesn't scale up.
There's also a solution with GROUP BY but it's also hard to write and performs badly.

Avoid subquery in this mysql statement


Mavic wheels out of true after 200km, is normal?

Question: I bought set of Mavic wheels, and today I noticed that the front and rear wheel is around 1,5mm out true after 200km of ride. Im curious whether it is normal.
I have pair of those
Comment: The wording of the question could be changed to apply to all new wheels. As there is nothing Mavic specific in the answer.
Comment: A lot has to do with whether the wheel builder pre-stresses (and then retrues) the wheels as the last step in manufacturing.  Premium wheel builders will do this, but most "factory" wheels are not pre-stressed, and hence they need a break-in.
Answer: It is normal for a new rim to be out of true after first rides. Once the first service for the rim is done, it should remain true for thousands of kilometers.
It is recommended to check a new rim after 200-1000 km of riding.
I recommend using a professional mechanic to true the wheel. It is easy to overtighten some of the spokes, if you don't know exactly what you are doing.
Answer: Yes, this is expected. The wheel needs to set. The interfaces to the spokes in the rim and the hub flanges are slightly deformed during the first rides. You may also find the spoke tension much too low now.
The spokes need to be properly tensioned now and the wheels centred again. They should hold well afterwards.
Comment: This is not expected at all for a decent quality wheelset. We don't know which wheels the OP has and whether they should be expected to be decently built.
Comment: The OP posted a link to Mavic Cosmic Carbon.


Would the Inuzuka or Nara technique count as a kekkei genkai?

Question: Kekkei genkai are considered abilities passed on through bloodlines, from this question: How is a technique characterized as a kekkei genkai? When discussing kekkei genkai, however, people never seem to include clan abilities such as the Nara shadow possession or the Inuzuka collaborative jutsu with their dog partners. Would these (or similar) abilities count as kekkei genkai, and if not, why not?
Answer: Nope, they are not. The abilities that you mentioned are just hiden (秘伝, not to be confused with "hidden") techniques, exclusive to a specific clan. There is a difference between them and kekkei genkai abilities.
Kekkei Genkai is passed down genetically, so every member of a clan has an aptitude for it.
The hiden techniques, on the contrary, are not passed down genetically, but rather "taught", so in fact anyone could learn them if they were not kept in secret.
For example, take Parasitic Destruction Insect Technique, which is exclusive to Aburame clan. However, it's not a genetically-passed ability, it's rather that only Aburame clan knows what needs to be done in order to place the insects into one's body and to learn how to live in symbiosis with them.
You can read more on the subject here.
Answer: Also the ability to use a Kekkei genkai is affected by the chakra type you are born with, normally a shinobi is born with a single chakra type hiwever in the case of a Kekkei genkai user, the shinobi is born with two nature types


How to play songs that contain one guitar when we have two or more guitarists?

Question: I am playing drums in an alternative punk band we just started. I am wondering how to play songs that basically are from bands that contain one guitarist, as we have two guitarists. What can be the best approach? Both playing the same, or at some moments playing the same and some moments one of them will do like bass?
Comment: Just send one out crowdsurfing during that song :)
Comment: Have a listen to how Bloc Party use two guitars in the beginning of the song Banquet: https://www.youtube.com/watch?v=vdkmhquF60o
Comment: Iron Maiden frequently send their spare guitarist off to fight a monster. https://www.youtube.com/watch?v=y-LRSlc0NaA
Answer: Some alternatives from the top of my head

Double the guitar part on both guitars
Double the bass part on one guitar
Split the roles inside the chord: guitar 1 plays power chords (root and fifth only), and guitar 2 plays the third and the fifth or seventh, without root note.
Split the parts rhythmically: guitar 1 playing kick/snare and guitar 2 playing "hi-hat". (Coordinate with the drummer - you want the whole band to play tightly together, not just the two guitarists.)
Split between rhythm and "harmony only": Guitar 1 plays normal rhythm chords, guitar 2 plays long pad-like chords from a high position up the neck. (or harmonics but it's difficult)
Split between rhythmic chords and "almost only rhythm" with a single note: guitar 1 plays full chords lower and guitar 2 plays single-note lines higher.
Split between rhythmic chords and unpitched sounds. Guitar 1 plays chords, guitar 2 plays unpitched muted noises only.
Just play different voicings: guitar 1 plays open string chords or low position barre chords, and guitar 2 plays barre chords higher on the neck.
Another way to split voicings: guitar 1 plays chords where the root note is on the E string, guitar 2 plays chords where the root note is on the A string or the D string.
Split roles to harmony and melody: guitar 1 plays chords, guitar 2 doubles the lead vocal melody
Make guitar 2 play like vocal harmonies that background singers would do, doubling the rhythm of the vocals, but with different pitches. There are basically two strategies for vocal harmonies. For a single-voice vocal harmony, either (1) track the lead melody a third or sixth above or below (and if you want more than one voice, add fifth or seventh etc) within the scale, or (2) do chord tones on either side of the melody, but without keeping a constant third or sixth distance. Strategy 2 is a bit easier to do, because you don't have to keep track of what the scale is, only what the chords are, which is what guitarists do anyway. And it's perhaps more rock-n-roll oriented than the more jazzish strategy 1.
Play "horn riffs", additional lines that a brass section would do, usually filling any empty holes left by the lead melody, or accenting big rhythmic hits in the drum beat or in the melody.
Split between picking patterns. Guitar 1 plays full strummed chords, guitar 2 plays arpeggiated chords.

There's a lot of fun to be had, and better music to be made, when band members coordinate their playing and singing like this, trying to make the whole group work as one "engine". Quite often, drummers and bass players are used to coordinating their playing, usually so that the bass and kick drum play the same pattern together, which sounds really nice and feels rewarding and motivating. But I'd say, not only the bassist and the drummer, but everybody should think about the whole, listen to other players and try to coordinate their playing. What's the guitar's rhythm - does it double one or more of the drum parts? What's the relationship between vocals and guitars? Is everybody playing and singing notes in the same register - does it work as one single big voice, or is it just big a mess? How about giving everybody their own space in the pitch spectrum? Is there a single common idea of the song's rhythm to begin with - does everybody agree if it's a 1/16th or 1/8th beat song? Etc. The more players you have, the more coordination is needed. :)
Comment: @elliotsvensson Yes I think so, although a keyboard and a guitar cannot create the kind of chorusing-doubling that two very tightly played guitars can, sort of like if it was a single 12-string. But the general principle is the same: you divide the musical roles and elements between instruments. For most of the things I listed, you could image it being a guitar+keyboard situation just as well.
Comment: what I like mostly from this answer is that you're telling OP that a band doesn't always have to play a textbook song, it's about playing it your own way, and my favorite advice in this answer is the third one from the bottom
Comment: Would this advice be just as applicable (when practical) for a keyboardist added to the group?
Comment: Also, "guitar 1" and "guitar 2" aren't fixed roles; the two guitarists can trade off during a set or during a song, according to their talents, their egos, or good showmanship.
Comment: Is "give one of the guitarists a break for that track" not an option?
Comment: Why not just have one guitarist sit back and do nothing, or play another instrument?
Answer: Generally I would have only one guitar play during the quieter parts and both guitars play the same thing during the loud parts. Often this means both guitars play during the chorus and only one during the verses.
For instance, in "Smells Like Teen Spirit", one guitar would play the intro, both the opening chorus riff, then one guitar plays the verse and pre-chorus, both guitars play the chorus, etc.
For "Basket Case", I would have one guitar play up until the drums come in, and then basically have both guitars play the same thing for the rest of the song. This matches with what it sounds like they did on the recording, where the double-tracked the guitar starting when the drums enter.
For "What's My Age Again", it also sounds like they double tracked it starting with the first chorus, and then the double track stops for the bridge, and then comes back in for the last chorus and ending.
The secret is that even for bands with only one guitarist, a lot of times on the recording they record multiple guitar tracks in layers. So by listening carefully for those layers, you can figure out where the best places are to have two guitarists playing.
If one guitarist is getting bored, you could switch off who is playing each quiet section. So one guitarist plays alone for the first verse, both together for the first chorus, then the second guitarist plays alone for the second verse.
Having one guitarist quietly double the bass an octave higher can bring out the bass part, which could be good or bad depending on the song.
Overall, you want to take it on a song-by-song basis. Use your artistic sense and tastes to figure out what sounds best.

One more note: Kurt Cobain said that punk music is about freedom. To me, that means freedom to do whatever you want, and especially to express yourself. Think about that and keep that in mind when you are playing punk. You can always add a guitar part to a song that was recorded with only one guitar part. But more than that, I think if you really want to get punk, you have to write your own stuff. Playing covers is a great way to learn and to connect with an audience, but writing your own songs is really what making music is about. You're free to play anything you want, however you want. Don't hesitate and don't be afraid. The world needs everyone to speak in their own voice. Punk means you've decided not to keep quiet about it.
Answer: Something to try:
I saw an (oldskool) R&B band play once. They weren't bad musically, but not great.
The setup: Drums in the middle, 2 x Les-Paul-&-Marshall amp guitars, bass and a singer in the middle.
The guitars were setup up one on each side of the (small) stage.
A lot of the songs they played would have had one gutar orignally, so both guitarists played the same thing. It sounded GREAT! But the trick they had learnt was both guitarists played exactly the same thing, especially the timing. The effect was like listening to a huge stereo, with a lovely wide guitar sound. It probably also helped that they had the same gear.
And that's the trick:  Notes-wise, 2 x guitarists would have to play un unison or same chord or some relationship to each other, of course.
But timing-wise: If you have two guitarists playing almost the same thing timing-wise, you just get a mush. If they're syncapated or exactly in unison, it suddenly sounds sharp, but huge.
Comment: I wonder how it would work if the guitarists swapped places but keeping the amps in place ... player 1 would stand in front of player 2's amp and vice versa. ;) Gotta play very tight together to get the illusion that it's your sound you're hearing. Probably a bad idea.
Comment: @piiperi I've had some experience of that at a jam night when people kept moving about and me and the other guitarist ended up in each other's 'spot'. Surprisingly, it's not bad, although it depends on the amp setup a bit (how they're aimed): The worst place to stand if you want to hear an amp is right in front of it. Assuming the amp's op the floor, you don't have ears in your knees, so you probably aren't hearing it wholly. Standing aside a bit  (and in front) possibly means you hear more of it! The problem would be that to adjust a setting, you'd need to ask your colleague to adjust the amp
Comment: However I get what you're suggesting: If you were playing in unison, it'd sound/feel probably a bit weird. If you made a mistake you could look at the other guitarist as if it was their fault hahaa
Answer: I personally think the best three ideas to try are:

Double up the guitars to give a louder impact on the guitar parts. It creates a bigger sound, possibly a good idea for a punk band.
Improv lead. This can be more challenging without much theory to back you up, but if you know the key, one guitarist can just improv some basic riffs (much like The Clash)
Two different rhythms. Try two different rhythms that compliment each other. I find the Libertines do this pretty well, and I for one tend to use off-beat chunks whilst my friend plays a more consistent rhythm part.
Answer: I was about to say use stacked triads, but then I realized it is punk rock, so very likely this won't work. This is also the reason why the first bit of the top-rated answer is not really senseful to me.
Punk is mostly distorted power chords, so there is little room to play the fancy harmony card. Therefore, you probably have to rely on playing the same thing which isn't that great in the first place, and it's more error-prone as we can hear the slight inaccuracies very easy when two things play the exact same thing.
The good thing is that you can play solos, licks and other melodic elements without stopping the main riff.
This is last bit is probably somewhat off-topic, but I personally would try to convince one of them, to play bass instead, in case you don't have one, which you don't specified so far. I only can guess from your statement that one of them "could do like bass".
Comment: not true at all. Listen to The Clash.
Comment: Clash is an exception, I said mostly, not never. Majority of punk bands play 3 chords and those really sloppy. And distortion is also extremely common.


Hard drive device name on Solaris

Question: I need to figure out the hard drive name for a solaris box and it is not clear to me what the device name is.  On linux, it would be something like /dev/hda or /dev/sda, but on solaris I am getting a bit lost in the partitions and what the device is called.  I think that entries like /dev/rdsk/c0t0d0s0 are the partitions, how is the whole hard drive referenced?
Answer: /dev/rdsk/c0t0d0s0 means Controller 0, SCSI target (ID) 0, and s means Slice (partition) 0.
Typically, by convention, s2 is the entire disk. This partition overlaps with the other partitions.
prtvtoc /dev/rdsk/c0t0d0s0 will show you the partition table for the disk, to make sure.
Comment: thanks.  I found this also.

http://initialprogramload.blogspot.com/2008/07/how-solaris-disk-device-names-work.html
Comment: Indeed! The real fun is when you start trying to translate the REAL device names. Do an 'ls -l /dev/dsk/c0t0d0s0' and look at the hideous path through the "real" device tree. Once upon a time I could translate that for specific CPU/IO boards in larger servers. Uuuuugly!
Answer: If you run Solaris on non SPARC hardware and don't use EFI, the whole hard drive is not c0t0d0s2 but c0t0d0p0, s2 is in that case just the Solaris primary partition.
Answer: What do you want to do to the whole disk? Look at the EXAMPLES section of the man page for the command in question to see how much of a disk name the command requires.
zpool doesn't require a partition, as in: c0t0d0
newfs does: c0t0d0s0
dd would use the whole disk partition: c0t0d0s2
Note: s2 as the entire disk is just a convention. A root user can use the Solaris format command and change the extent of any of the partitions.
Answer: The comments about slice 2 are only correct for drives with an SMI label.
If the drive is greater than 1TB, or if the drive has been used for ZFS, the drive will have an EFI label and slice 2 will NOT be the entire disk. With an EFI label, slice 2 is "just another slice". You would then refer to the whole disk by using the device name without a slice, e.g. c0t0d0.
Answer: There are two types for disk label, one is SMI(vtoc), the other is GPT(EFI).
On X86 platform and the disk is SMI labeled(default behavior):
cXtXdXp0 is the whole physical disk
cXtXdXp1-cXtXdXp4 are primary partitions, included the solaris partitions.
cXtXdXs0-cXtXdXs8 are the partitions(slices) of the activate Solaris partitions.
cXtXdXs2 is the whole activate Solaris partition, maybe not the whole disk.
Hope I am clear.
/Meng
Answer: C0 - Controller
T0 - Target
D0 - Disk
S- - Slice
Answer: c0t0d0s0 is the entire drive. The breakdown is:
/dev/[r]dsk/c C t A d0s S
...where C is the controller number, A is the SCSI address, and S is the "slice". Slice 0 is the whole disk; the other slices are the partition numbers.
See this for more info.
Answer: cXtYdZs2 is the whole drive. period.

Hard drive device name on Solaris


What is a D-brane?

Question: I know that in string theory, D-branes are objects on which open strings are attached with Dirichlet boundary conditions. But what exactly is a brane? Are they equally fundamental objects like string? If so then do they also vibrate? If the visible universe itself is not a brane then what is the dynamics of these branes within the universe? Do individual D-Branes interact, collide? Can an open string tear itself off from the D-brane? If so what are the results?
Answer: Branes are (usually) extended objects; $p$-branes are objects with $p$ spatial dimensions.
D-branes are a special and important subset of branes defined by the condition that fundamental strings can end on the D-branes. This is literally the technical definition of D-branes and it turns out that this simple fact determines all of the properties of D-branes.
Perturbatively, fundamental strings are more fundamental than branes or any other objects. In that old-fashioned description, D-branes are "solitons" - configurations of classical fields that arise from the closed strings. They are analogous to magnetic monopoles - which may also be written as classical configurations of the "more fundamental fields" in field theory. In a similar way, D-branes' masses diverge for $g\to 0$.
Non-perturbatively, D-branes and other branes are equally fundamental as strings. In fact, when $g$ is sent to infinity, some D-branes may become the lightest objects - usually strings of a dual (S-dual) theory. When we include very strongly coupled regimes (high values of the string coupling constant $g$), there is a brane democracy.
Back to the perturbative realm. The condition that open strings can end on D-branes - and nowhere else - means that there exists a particular spectrum of open strings stretched between such D-branes. By quantizing these open strings, we obtain all the fields that propagate along (and in between) such D-branes. The usual methods (world sheets of all topologies, now allowing boundaries) allow us to calculate all the interactions of these modes, too.
So yes, D-branes also vibrate. But because their tension goes to infinity for $g\to 0$, you need even more energy to excite these vibrations than for strings. The quanta of these vibrations are particles identified with open strings - that move along these D-branes but are stuck on them. The insight that the D-branes are dynamical and may vibrate, and the insight that they carry Ramond-Ramond charges (generalizations of the electromagnetic field one obtains from superstrings whose all RNS fermionic fields are periodic on the world sheet) were the main insights of Joe Polchinski in 1995 that made D-branes essential players and helped to drive the second superstring revolution.
Other branes typically have qualitatively similar properties as D-branes but one must use different methods to determine these properties.
When we quantize a D-brane, we find open string states which are scalars corresponding to the transverse positions. It follows that D-branes may be embedded into the spacetime - in any way. The shape oscillates according to a generalized wave equation again. Also, all D-branes carry electromagnetic fields $F_{\mu\nu}$ in them. These fields are excited by the endpoints of the open strings that behave as quarks (or antiquarks). For a stack of $N$ coincident branes, the gauge group gets promoted to $U(N)$. The electric flux inside the D-branes may be viewed as a "fuzzy" continuation of the open strings that completes them to "de facto closed strings".
Those fields have superpartners in the case of the supersymmetric D-branes which are stable and the most important ones, of course. D-branes may collide and interact much like all other objects.
The most appropriate interaction that allows the open strings to "disconnect" from D-branes is the event in which two end points (of the opposite type, if the open strings are oriented) collide. Much like a quark and antiquark, these two endpoints may annihilate. In this process, an open string may become a closed string - which may escape away from the D-brane. The same local process of "annihilation of the endpoints" may also merge two open strings into one. Such interactions are the elementary explanations of all the interactions between the fields produced by the open strings - for example between the transverse scalars and the electromagnetic fields within the D-brane.
Aside from that, some branes may also be open branes, and end on another kind of branes. The latter brane always includes some generalized electromagnetic fields that are sourced by the endpoints or end curves or whatever is the $(p-1)$-dimensional geometry of the boundary of the former brane.
Comment: Thanks for the answer. Two more questions :) what is the typical size of a D-brane? If they vibrate then are they also attached to any other similar object with specific boundary conditions?
Comment: Hi @sb1! D-branes may have any size. Because they're so heavy at weak coupling, one usually wants them to be in a stable configuration - e.g. stretched across the whole spacetime or wrapped on some non-contractible cycles of the compact dimensions. But their shape and size are dynamical just like for strings, so they can be of any size - and they can also be contractible (then they contract and disappear)!
Comment: The vibrations of D-branes are completely analogously described by open string modes just like the vibrations of the spacetime - gravitational waves - are described by closed string modes. A single (closed or open) string is a quantum of the vibration, with $E=hf$ of energy, and a "coherent state" of many such strings (particles) describes a classical gravitational wave in spacetime, or a classical wave propagating on a D-brane.
Comment: I miss some extra discussion on Dirichlet vs Neumann conditions. Perhaps the opportunity is when it is said "move along these D-branes but are stuck on them"

What is a D-brane?


Compiling code via terminal

Question: How can I compile my code via terminal? I am working on a Chrome app that allows you to write, compile, and upload code to an Arduino, and I need to know this so I can use the command line compiler on my Linux server. Mac or Linux terminal, it doesn't matter.
Comment: I'm not really sure what exactly you need but to compile in the command line you need something like `avr-gcc`.
Answer: Check out platformio.org it's the best solution out there for command line compiling.
Comment: See [my answer to a related question](https://arduino.stackexchange.com/a/88216/13174) for an example PlatformIO CLI session.
Answer: Assuming an AVR-based Arduino, you would need the avr-gcc compiler, the
avr-libc and the Arduino libraries. Also avrdude if you want to upload.
The only issue is that the commands used for the build process are quite
long (lots of options). You can see them by enabling verbose compilation
in the IDE. Thus you will probably want some way to automate the whole
thing.
There are several options for this. The most straightforward seems to be
the arduino-builder command-line tool. This is part of the Arduino
project and should ensure maximum compatibility. Otherwise you could use
a plain old Makefile. I personally use Sudar Muthu' Makefile. It can
be installed on a Debian-based Linux distribution by:
sudo apt install arduino-mk

It is not fully compatible with the classic Arduino build process
though: it does automatically include <Arduino.h> into your sketch,
but it does not add forward declarations. Some prefer it this way, as
the automatic inclusion of forward declarations is somewhat buggy and
does not play well with some C++ features.
Answer: There is an Arduino CLI (command line interface):
https://github.com/arduino/arduino-cli
You use commands such as to access Arduino IDE functions:
arduino-cli compile --fqbn arduino:avr:leonardo sketch
and
arduino-cli upload -pCOM14 --fqbn arduino:avr:leonardo sketch
(obviously port will be different under Linux)

Compiling code via terminal


My Avocado's leaf are turning brown

Question:
I have planted my avocados in soil a month ago and since then they started getting brown edges on the leaf. What should I do?
Comment: What sort of soil did you use - new potting soil or something else? Is there a drainage hole in its pot?
Comment: Possible duplicate: https://gardening.stackexchange.com/questions/31481/young-avocado-plant-has-brown-spots-spreading-on-leaves?rq=1
Comment: Welcome Sue! My name is Sue too! Would you mind taking a look at the other question I just linked to? It seems very similar to me. Does it help you with this question, in addition to the answers you have here?
Answer: It could be the water, is it tap water that you use? It could be that there are too many minerals in it, or chlorine. A solution would be to use demineralized water for a while.
It can also be caused by too much fertilizer, but not enough info in your question to point out the real reason.
Comment: _Demineralized water_ is also called _distilled water,_ most supermarkets and grocery stores will carry.  Use distilled water until the plant is well established.  Plus, after that only use water that has sat out overnight, so it has time to off-gas any chloride and fluorides it might contain it.  Also, many potting soils already contain 3 to 6 months worth of fertilizer for moderate feeders plants.  Also, Avocados are light nitrogen feeders so you probably won't need to add anything for a year or so.
Answer: I agree, high salts most likely.  You've not had enough time to build up the salts from tap water to include the worst; fluoride.  Hydrofluorosalicic acid.  Heavy metals.  Chlorine actually dissipates.  So the culprit seems to be whatever was added to your soil such as compost, fertilizer, sand/rocks/gravel at the bottom of the soil which would cause the soil to stay too wet too long.
Your leaves look thin as if they've not been in much light for a good month or something is wrong with the chemistry (fertilizer) or the roots are rotting from too much water not enough air and drainage.  Planting avocado seeds with water roots into soil is a huge shock to a plant.  Water roots are not meant for soil. But seems to work more often than not...did you start your avocado in water and then recently plant in soil?
I am worried that you've got too much fertilizer in your soil.  What have you used for soil, amendments, fertilizer and when do you know to water your plant?  Is there gravel or rocks at the bottom of the soil in the bottom of the pot?  Is there a drain hole?  Check out the bag of soil you used to see if fertilizer was added to the soil.
Please get back to us with even more details...and soon, okay?

My Avocado’s leaf are turning brown


Shaking hands with the opposite gender?

Question: What's the story: Can a man shake hands with a woman (or vice versa) in a business setting?
Comment: @chaney, welcome to Judaism.SE! Please consider [posting](http://judaism.stackexchange.com/questions/ask) a follow-up question as an actual question, if the link in the above comment doesn't already address your issue. Keep in mind, though, that this site [offers](http://meta.judaism.stackexchange.com/questions/312/perhaps-the-community-moderators-should-enact-a-more-strict-policy-regarding-hal/314#314) generally-applicable information rather than personal guidance; for the latter, I recommend that you consult your Rabbi.
Comment: Related non-duplicate: http://judaism.stackexchange.com/questions/7531
Comment: Can I ask? I am an unmarried frum Jewish women who would LIKE to be SHOMER NEGIAH, but working among goyim I cannot get them to keep from always touching me. Or it is some disparaging comment to their friends as I leave that infringes on my Tznalus.
Also, if a certain Jewish man keeps touching my hand, the back of my hand; is this interest? But he talks to others people in front of me about getting fixed up with other girls. He wouldn't do that if he was interested? Or is he trying to see if I am immodest or is this meaning he thinks I am not up to his standards? Maybe he thinks I don't merit
Answer: There's a prohibition against touching any member of the opposite gender other than your spouse or close relatives.  Many opinions say that's only "affectionate" touching, "such as hugging and kissing."  Others say no, it includes all touching.  (Rabbi Yehuda Herzl Henkin, in Hakira Journal, discusses these opinions and their sources; he strongly believes that the former is the majority opinion.)  So we have three questions:
A.) Is the prohibition all touching, or only "affectionate" touching?
B.) What is the Halachic definition of "affectionate"?  (See above article for more on this)
C.) How to interpret a business handshake?
Depending on how you answer A, B, and C, the modern-day opinions will literally range from "it's absolutely fine, even in a social setting" (as had been the practice among Orthodox Jews of German ancestry not that long ago) to "not even if your life is at stake!" (R' Chaim Kanievsky).  There's also the distinction between you offering your hand first, and responding to someone else's outstretched hand.  (If the other person isn't looking for a handshake, do you need to go there?)  R' Moshe Feinstein noted that many people do it, though he wasn't crazy about the idea.*  It's said that the Bostoner Rebbe would shake a woman's hand if she offered it; Rabbi Dovid Cohen of Brooklyn quotes his mentor, Rabbi Yitzchak Hutner, that a handshake isn't about affection, it's about basic human respect ("derech eretz, not derech chiba").  On the other hand (pun intended), many Orthodox Jews have long worked with the assumption that it's prohibited (which also avoids slippery-slope problems), so be prepared to meet people with that practice.

Note: Rabbi Hershel Schachter (in his Issues in Nursing mp3) cites several students of Rabbi Feinstein who said he was more lenient on the subject when asked in person.

For those who don't shake hands, it often helps to explain that the practice is 100% gender-symmetric and is not about Judaism disparaging women.   Another way to say it is "I'm sorry but as a religious policy, I don't touch any woman/man other than my spouse."  (This may get the response "gee I wish my spouse had the same policy ...")
Comment: `It's said that the Bostoner Rebbe would shake a woman's hand if she offered it` could you please provide a source for this? Having been very close to to HaRav Levi Yitchok ZTKL"V, I know it to be untrue. Or where you referring to another Bostoner Rebbe?
Comment: IMHO affectionate is highly misleading,  and IIRC against the point that R. Henkin makes. חיבת ביאה would more appropriately be translated as "sexual" rather than affectionate; more akin to דרך חיבה, a term arising, at least according to his presentation, from misunderstanding.
Comment: @MordZuber it is debated, unsurprisingly. http://tzvee.blogspot.com/2009/12/david-e-y-sarna-guest-blog-bostoner.html
Answer: The main Charedi Rabbis forbade it, though others more MO Rabbis permitted it where necessary.
From http://doseofhalacha.blogspot.co.uk/search/label/Shomer%20Negiah

The question of whether it is okay for a non related man and woman to shake hands largely depends on whether this contact is classified as a דרך תאוה וחיבה, a 'way that is based on attraction'.
Lenient authorities have quoted the Shach (R' Shabbatai HaKohen 1621-1662, YD 195:20), who, quoting the Rambam, writes that it is (only) forbidden for a man and woman to touch in any manner that causes attraction (chibah). Where touching yields no pleasure, it would be permissible (YD 157:10). Thus, R' Moshe Feinstein paskens (EH 2:14) that one can sit on a tram next to a woman even if they are accidentally touching. R' Chaim Berlin (Netziv's son, 1832-1912, Nishmas Chaim, EH) writes that today, shaking hands is a regular way of greeting people. One has to bear in mind what reputation such a refusal will leave Religious Jews with. Rather shake hands than give others the impression that we're crazy and are lacking Derech Eretz. R' Chaim Pinchos Scheinberg also allowed it in extenuating circumstances. (Halichos Yisroel, p282)
R' Moshe Feinstein maintains, however (EH 1:56), that it is difficult to claim that shaking hands is not considered an expression of affection. In another responsum (OC 1:113) he wrote that doing so is forbidden. Likewise, the Steipler (R' Yaakov Yisroel Kanievski 1899–1985, Kreina Deigresa 162) defines hand shaking as touching with chibah, and therefore a most severe prohibition.
Even the lenient authorities only allow shaking hands in extenuating circumstances. As leading Poskim have forbidden it, one must try their utmost to avoid it.
Comment: I've never heard Rabbi _Chayim_ Berlin called "MO" before that I recall.
Comment: I don't have sources for the more MO Rabbis, though posted the link that most Charedi Rabbis forbade it..
Comment: fair enough! I stand corrected..
Comment: ... I mentioned that only because he's the only rabbi you mention as permitting it in other than extenuating circumstances.
Answer: I've been turned away from an interview for not shaking hands. Subsequent to that incident, I called a posek who permitted it, but only for the interview. If I were to be subsequently hired, I need to explain that I don't shake hands with members of the opposite sex for religious reasons.
My personal experience may be due to inadequate communication. If you're good with words and your hand-withholding comes across as easy-going and friendly (as opposed to holier-than-thou or zealotry) you may never have an issue.
Comment: I have had a similar issue with not wearing a Kippah to an interview and then showing up on my first day on the job wearing one. I owners though I was being untruthful from the start.
Comment: Observing different standards during an interview and subsequently with the same people could look bad. Regarding communication skills, I wrote some advice once here: http://www.cross-currents.com/archives/2010/01/03/advice-for-the-job-forlorn/comment-page-2/#comment-381906
Comment: Most jobs I have had have started around summer. Come a certain time of year I inform them I'm going to be leaving early every Friday.
Answer: Saifer chasidim 1090
A Jewish man can not slap hands with a non Jewish woman
And a Jewish woman can not slap hands with a non Jewish man
Even when the hand is coverd with clothing
(The commentaries explain that if they are both Jewish it is OK when the hand is covered with clothing (but only if it is not done for the man to be able to see the woman for a longer time))

The commentary on bottom brings more sources on the subject
Comment: I believe the translation is simply "shake hands", not "slap." (The root appears as in "to pitch a tent." We talk about *kinyan T'kiat kaf*, a deal executed by handshake.) Sefer Hassidim reflects the viewpoint of what is pious, not necessarily what is required by the letter of the law. (And let's not get started on whether a cross-gender handshake had the exact same context in Germany a thousand years ago as it does in today's corporate America.)
Comment: @Shalom it seems to be an Halacha here. Seyag is a loshon of Halacha
Comment: Chafetz Chaim notes that he has to be careful quoting Sefer Hassidim because some of what's in it -- even if described as -- "you must do this!" -- is intended for those who are hassidim, i.e. extra-pious.

Shaking hands with the opposite gender?


Multithreading vs creating a child process

Question: How does a browser handle creation of new tabs. Does it fork or create a new thread? Can you point me how I choose between creating a new thread and a child process.
Answer: Some modern browser these days create separate processes for new tabs. The reason is that if some site (tab) contains malicious code and is for example frozen the rest of the browsed sites can be still seen.
If you used for example Chrome and you would be on Windows, you could try to kill some chrome.exe processes and you will see only one tab will die. However, in case of chrome it is not completely 1 to 1 (tabs to processes). Some processes are vital for running the browser as is (if you kill them the whole browser will die), so be aware of that if you are gonna to try. :)
Note that almost all browser now have separate processes for plugins (3rd party plugins written e.g. using Netscape API). The reason is the same as with tabs (and is even more understandable).
To find answer for your second question, look for example here:
http://jayant7k.blogspot.com/2010/01/for.html


SharePoint 2010 Trigger JavaScript when going to Edit Mode

Question: So I'm looking for some JavaScript code that will trigger once a user goes into Edit mode on a page. I basically want to have two layouts in a content editor. One for display and one for edit. I have found plenty of examples of detecting if a page is in Edit mode, the problem is I can't find an event to listen to, to see if the user has gone into Edit mode. Only thing I can think of is a While loop but that seems messy. Also I want this script to be a attach and forget so I would like to avoid having to edit the page itself in designer.
Comment: You can have a custom button in content editor webpart and trigger edit mode from there, I've implemented something like this in 2013 not sure if this works in 2010. https://sharepoint.stackexchange.com/questions/151425/how-to-set-up-on-default-view-quick-edit/151523#151523
Comment: I believe you can define a function on page load, something like a function on document.ready which can help you with what needs to be shown and what needs to be hidden.
Comment: Tried to do a windows.onload but it breaks my page. I can't click on the 'page' tab and when I try to edit through site actions, it says, "Unable to get property 'PageState' of undefined or null reference". Then when I remove the code it works fine. My code below...
Comment: and a jQuery document.ready doesn't recognize a load when switching to edit mode
Comment: Also attempted to use

 _spBodyOnLoadFunctionNames.push("testing");

and while it fires my function, it doesn't fire on switching to edit mode
Answer: I can think of two ways.
First:
$("#EditButtonID").click(function() {
    if(SP.Ribbon.PageState.Handlers.isInEditMode()) FunctionToTrigger();
});

Second:
$("#EditButtonID").click(function() {
    if($(this).text() == "Stop") FunctionToTrigger();
});

If it doesn't work, you can add a setTimeOut() to wait 1 second or less just before ifs
Comment: Yeah I thought of this too but the issue with that is that there is a few different edit button ids on a site. You can go through the ribbon or you can edit through site actions. Also I think the id changes based on if its a wiki page or not. In the end I decided to look for a PageState after a refresh. The page doesn't refresh after entering edit mode but it does when you edit the the content editor and really I just need the script to apply to the content editor.


Is incestuous marriage a Valyrian practice, or unique to the Targaryens?

Question: In A Song of Ice and Fire, the Targaryens continued to practice incest even after they adopted the Westerosi Seven Gods. Is this custom unique to the family, or was it widely practiced by the Valyrians before the Doom? A Wiki of Ice and Fire states that this was a "[continuation of] the Valyrian practice", but I can't find any statement in the actual text that bears this out.
Comment: Based on how Martin makes his fiction similar to history, I'd speculate that this was something only royalty did... as was the case among the Egyptians (pharaohs often married their siblings).
Comment: @Skooba No, it was the Andals who bought it with them, and the Targaryens then nominally adopted it as a strategic decision to make themselves more acceptable to the people they now ruled
Comment: @JohnO I agree that it would have been confined to the Valyrian nobility / royalty, but the Targaryens were not the only noble family of the Valyrian Freehold
Comment: Didn't the Targaryens bring The Faith of the Seven to Westeros, not the other way around? Or was that the Andals?
Answer: Here's a relevant passage:

"The dragon kings had wed brother to sister, but they were the blood
  of old Valyria where such practices had been common, and like their
  dragons the Targaryens answered to neither gods nor men."
A Clash of Kings, Chapter 33 (Catelyn)

So is this a distinctly Targaryen custom, or was it a Valyrian custom?
We know from Martin himself that Valyria was not a kingdom or an empire, but a freehold somewhat similar to the old Roman Republic where several noble houses ruled together.

The Freehold of Valyria is correct. Valyria at the zenith of its power was neither a kingdom nor an empire... or at least it had neither a king nor an emperor. It was more akin to the old Roman Republic, I suppose. In theory, the franchise included all "free holders," that is freeborn landowners. Of course in practice wealthy, highborn, and sorcerously powerful families came to dominate.

The Targaryens were only one of many houses. A Wiki of Ice and Fire claims that it was one of forty houses and was not the most powerful one, though this claim is unsourced.
Regardless, since we know the Targaryens were not the only noble family in Valyria I think it's safe to interpolate that the custom of incestuous marriage was not unique to them.
Comment: Good find. I think the line "where such practices had been common" pretty well confirms that this wasn't unique to the Targaryen family.
Answer: In the appendix to A Game of Thrones, under the heading "The Old Dynasty / HOUSE TARGARYEN", is this line:

To preserve the blood royal and keep it pure, House Targaryen has often followed the Valyrian custom of wedding brother to sister.

So yes, it is explicitly called out as a Valyrian custom. Not in the narrative portion of the text, but I believe that the appendices are canon as well.
Comment: Great find! We probably all skip over the appendix normally.
Answer: If you look at this rather comprehensive tree (Credit: Reddit):

you can see that even before Aegon's conquest, the Targs were still practicing incest, so it does seem to be a Valyrian practice.
Interestingly though we don't know who Aenys' wife was. If she was not a Targaryen that would mean all Targ Kings (except for Aegon I and Aenys) had only at most half Targ blood.
Comment: All that shows is that the Targaryens were doing it before the went to Westeros, not whether it was a Valyrian practice or not.
Comment: Very cool family tree.
Comment: Nice. For anyone who might be interested, we now know which unknown Baratheon did Princess Rhaelle marry. He was [Ormund Baratheon](http://awoiaf.westeros.org/index.php/Ormund_Baratheon), son of Lord Lyonel Baratheon. And Aegon V's unnamed son is Prince Daeron who died in youth.


At what temperature does DNA re-anneal?

Question: If primers weren't present in PCR at what temperature would DNA re-anneal? I am wondering how primers manage to bind on DNA strands before DNA manages to anneal back together.
Answer: To answer your second question, one of the main reasons primers anneal before your target re-anneals to itself is not because it binds stronger, but because you add primers in large molar excess to their targets.  The primers will find your template faster than your template will find another matching template, and once the primer is annealed the template cant bind onto another template even if that reaction is more energetically favorable.  This molar excess is a requirement for the exponential amplification in PCR, and when you start to lose the excess primer concentration you lose exponential increase due to your targets re-annealing (and you get the production of unwanted PCR artifacts like chimeras).  As for the temperature, it depends on your template, but I guess it has to be somewhere between the primer annealing temp and the temp of your melting step.

At what temperature does DNA re-anneal?


Can $\delta(t+\infty)$ be a legitimate signal?

Question: Mathematically speaking, when I try to use some signal to disprove a system is invertible, can I use the signal like $\delta(t+\infty)$ ($\delta$ representing the Dirac distribution)? For example, the two inputs $0$ and $\delta(t+\infty)$ are distinct, but their outputs from the system $\int_{-\infty}^{t}e^{\tau}x(\tau)d\tau$ will then both be $0$. In this way, can I say the system is invertible?
Comment: Personally, I'd say that you can't do that. In any case, it wouldn't be useful, since the system _might_ be invertible for all signals that one actually cares about.
Answer: It's possible, in mathematics, to complete real numbers with "infinite" values, with sound topological properties; for instance non-standard analysis or the Extended real number line (discussion at Math StackExchange).
However, in this context, for any standard real number $t$, the rule is to set $t\pm \infty = \pm \infty$ (see Arithmetic operations). So, using your notations, for every $t$, you would have [CAUTION ADVISED] $\delta(t+\infty)=\delta(\infty)$, to which I am not able to give a meaning, else than something being a constant evererywhere equal to $\delta(\infty)$. Of course, $\delta$ is a distribution, and should not be treated as a function, but defined as a functional operator, or via limits of functions.
However, so far, I have never seen

a (serious and useful) use of the extended real system in signal processing,
a reference trying to define such a Dirac at infinity.

For the latter, I fear (just intuition) that constructing this with test functions can be troublesome, since two different limits are required (location and amplitude). This is just an analogy, but $\delta(0)\times \delta(0)$ is, as far as I know, not defined.
Comment: The only sensible use I could see of this would be to use it as a test function, e.g. to have something to convolve a system with to get the value it converges to at $\infty$; but that would essentially require us to define that the convolution with $\delta(t+\infty)$ does that; it would feel consistent, but exactly as you state, there's nothing inherently meaningful about $\delta(\infty)$
Comment: Yes, I feel that one would need a double limit, one classical on the amplitude, and one on the ordinal variable, which could lead to ambiguities
Comment: As far as I can remember when I used then, that mostly simplifies proofs and notationt
Answer: The Dirac delta generalized function is only defined under an integral
$$
Dirac(t-a) = \int_{-\infty}^\infty f(t)\delta(t-a)dt = f(a)\,
$$
Typically there's also a function under the integral.
Hence
$$
Dirac(t-\infty) = f(-\infty)\,
$$
if one considers $-\infty$ to be a point - not to mention problems evaluating the $Dirac$ at -$\infty$.


Notation for the set of all $x_i$

Question: Maybe a silly question, but what is the most compact way of clearly expressing the set of all $x_i$ if it is obvious that $i$ runs from 1 to $n$?  $\{x_i\}$?  $\{x_i\}_i$?  $\{x_i\}_{i=1}^n$?  $\{x_1, x_2, \dotsc, x_n\}$?
Answer: The third: $\{x_i\}_{i = 1}^n\;$ would be the most compact, but could open the door for ambiguity.
For example, $\{a_n\}$ and/or $\{a_n\}_{i = 1}^n$ is sometimes used (unfortunately, for the same reason: ambiguity) to denote a sequence.
So I'd prefer $$\{x_i\mid i\in \mathbb N,\;1 \leq i \leq n\},$$ as this more clearly denotes the set as defined in your last alternative: $$\{x_1, x_2, x_3, \cdots, x_n\}$$
and doesn't rely on "it being clear that $i$ runs from $1$ to $n$." (Assuming also $n \in \mathbb N$ ...)
Comment: Hi Amy. :-+)...
Comment: Thanks, Babak! How are you this evening?
Comment: Great! Thanks. Greeting you always makes me this feelings. ;-)
Answer: It depends on what you mean by "the most compact" as there is a trade-off between notation with a short number of strokes to write on a chalkboard and expressive power to avoid confusion. For what I have seen in papers, if the index is the same throughout a proof then it is customary to call $I$ the index and write $$\{x_{i}\}_{i \in I}$$
when there is not a constant index and the index is finite with upper bound $n$ we would write $$\{x_{i}\}_{i=1}^{n}$$
and if there is not a constant index and the index is infinite we write
$$\{x_{i}\}_{i=1}^{\infty}$$

Notation for the set of all $x_i$


Solve $\frac{4}{x+1}+\frac{2}{x-2} \leq 3$

Question: Solve
$$\frac{4}{x+1}+\frac{2}{x-2} \leq 3$$
I must be making a very stupid mistake somewhere ... been stuck on this for 1hr+ or even more ...
Answer: You made no mistake. Note however that you need to exclude the cases $x=-1, x=2$ by hand because your initial inequality is not defined for such $x$.
Then you have to see that
$$x^4 - 4 x^3 + x^2 + 6=(x-3) (x-2) x (x+1)$$
Now look at the plot and you should know what to do:
Answer: $$
\begin{eqnarray}
\frac{2(x-1)}{(x+1)(x-2)}             &\leq& 1 \implies \\
\frac{2(x-1)}{(x+1)(x-2)} - 1         &\leq& 0 \\
\frac{(2x-2)-(x+1)(x-2)}{(x+1)(x-2)}  &\leq& 0 \\
\frac{(2x-2)-(x^2-x-2)}{(x+1)(x-2)}   &\leq& 0 \\
\frac{(2x-2)-(x^2-x-2)}{(x+1)(x-2)}   &\leq& 0 \\
\frac{-(x^2-3x)}{(x+1)(x-2)}          &\leq& 0 \\
\frac{-(x^2-3x)}{(x+1)(x-2)}          &\leq& 0 \implies \\
\frac{x(x-3)}{(x+1)(x-2)}             &\geq& 0 \\
\end{eqnarray}
$$
If we look at this on a number line,
first note that for $x$ large enough, the LHS is positive.
Next, note that the LHS changes sign each time $x$ crosses
a root of one of the terms in the top or bottom, i.e. when
$x \in \{-1,0,2,3\}$. Thus the LHS is nonnegative for
$x \in (-\infty,-1) \cup [0,2) \cup [3,\infty)$.
Answer: @jiewmeng: As Listing pointed the graph tells you what you want, however, the below image would assist you. I made it as you posted your question:
Comment: Nice table! What did you use to make it?
Comment: @amWhy: Office word.
Comment: Did you save as an image and import? Or did you scan, and import the scanned image?
Comment: @amWhy: Image and then import. I convert it to pdf and then import.
Answer: One solution is given below. Another one, very close in spirit to your attempt, is given in a comment at the end.
It turns out that the numbers fit together perfectly!  Rewrite our inequality as
$$\frac{4}{x+1}-4 +\frac{2}{x-2}-1 \le 0.$$
This simplifies to
$$-\frac{4x}{x+1}+\frac{x}{x-2} \le 0.$$
The problem now breaks up into two natural cases.
Case (i): $x\ge 0$.  Here our inequality is equivalent to
$$\frac{1}{x-2}\le \frac{4}{x+1}.$$
For $x >2$ this can be rewritten as $4(x-2)\ge x+1$, giving $x\ge 3$.  For $0\le x<2$, we get in a similar way $x \le 3$, which holds automatically. We have obtained the intervals $[3,\infty)$ and $[0,2)$.
Case (ii): $x<0$.  Here our inequality is equivalent to
$$\frac{1}{x-2}\ge  \frac{4}{x+1}.$$
This is automatically false if $-1<x<0$, since the left side is negative and the right side is not. When $x<-1$, the inequality is equivalent to $x+1 \ge 4(x-2)$, which holds. This gives us the additional interval $(-\infty, -1)$.
Comment: In order to solve the inequality, you used the nice strategy of multiplying by $(x+1)^2(x-2)^2$. When we do that, we have to note that $x\ne -1, 2$.  Minor point.  The major point is that you should "multiply out" only when you have to.  Multiplying out tends to create a mess. If you keep the common factors of the two sides separated out, your calculation pushes through smoothly.  Starting from your
$$2(x-1)(x+1)(x-2)\le (x+1)^2(x-2)^2,$$
we obtain
$$(x+1)(x-2)\left[(x+1)(x-2)-2(x-1)\right]\ge 0,$$
which simplifies to
$$(x+1)(x-2)(x^2-3x) \ge 0.$$
Since $x^2-3x=x(x-3)$, the analysis becomes routine.


Merge Illustrator objects into one object not group?

Question: How do I merge several objects into a single object? I have many sloppy looking objects that when combined they create the one final object that looks great. If I could print out the vector but then keep it vectored that is what I'm looking for.
Answer: You might try selecting everything, then clicking the Unite button on the Pathfinder Panel.
More info on the Pathfinder commands ----- > HERE