Wikipedia:Reference desk/Archives/Mathematics/2011 April 8

= April 8 =

Hysterisis
I am looking for simple analytic examples of;

$$f(x,y)=0 \ $$

where the time derivatives of the variables x ' and y ' are related in a hysterisis curve relationship.  Sp in ni ng  Spark  16:36, 8 April 2011 (UTC)


 * Okay, so what would you like to discuss? Fly by Night on Tour (talk) 23:16, 8 April 2011 (UTC)
 * I was hoping that some examples would be forthcoming. I am not good enough at mathematics to find them for myself (assuming that such functions even exist).  Sp in ni  ng  Spark  01:06, 9 April 2011 (UTC)
 * I don't know why you would expect them exist, the whole point of hysteresis is that it requires a system with memory. Hence the name. —Preceding unsigned comment added by 92.20.218.201 (talk) 01:50, 9 April 2011 (UTC)
 * I don't follow why memory causes the function not to exist. Is there a proof? If so, that answers my question.  Sp in ni  ng  Spark  02:06, 9 April 2011 (UTC)


 * Could you try reformulating your question? It's not clear what it is that you're asking for. Do you have a particular f in mind, or are you asking for an example of an f that fits some conditions? Which conditions? The hysteresis article does not seem to present any canonical "hysteresis equation" that you could be thinking of. –Henning Makholm (talk) 14:33, 9 April 2011 (UTC)
 * I need examples of f which force the time derivatives of x and y to be related in a hysterisis-like curve, an example of which is shown in the graphic. That is, $$\scriptstyle \dot {y} $$ depends on the previous values of $$\scriptstyle \dot {x} $$.  Curves crossing through the origin are acceptable, even desirable for this.  Sp in ni  ng  Spark  19:57, 9 April 2011 (UTC)
 * But what is f, and what does it have to do with x and y? Apparently x and y are inputs to it, but what comes out of it, and what will you use that output for? What do you mean by f "forcing" x and y to do something? –Henning Makholm (talk) 21:34, 9 April 2011 (UTC)
 * @Henning. I don't understand why you don't understand.  If $$\scriptstyle f = x + y = 0 $$ for instance, that forces a definite relationship between $$x \ $$ and $$ y \ $$ (a straight line function) which in turn determines a definite relationship between $$ \dot x $$ and $$ \dot y $$.  Sp in ni  ng  Spark  22:11, 9 April 2011 (UTC)
 * But how do you think a relation between x and y (which does not have any history information avaialble to it) can possibly force a hysteresis relation? Can you give an example of how a function of only x and y can do that? –Henning Makholm (talk) 14:46, 10 April 2011 (UTC)
 * Umm...no, I can't. That was my question to this board I think.  Sp in ni  ng  Spark  20:49, 10 April 2011 (UTC)

You can get a Hysterisis effect from a Cusp catastrophe.--Salix (talk): 20:38, 9 April 2011 (UTC)



A good introduction to a mathematical formulation can be found at Systems with Hysteresis. The simplest example there is a "Nonideal relay" which has two output values 0 and 1, this has two critical points a and b with a<b. At point a a falling input will give a change from 1 to 0, at b a rising input will give a change from 0 to 1. An operator to describe this behaviour requires an internal state, $$\nu_0$$ set to the previous value of y. A simplified formulation for the operator can be written as
 * $$y=

\begin{cases} 0, & x \le a \\ \nu_0, & a < x < b \\ 1 & x \ge b \end{cases}$$ More complicated forms of hysteresis build upon this example but the all require some internal state.--Salix (talk): 07:04, 11 April 2011 (UTC)


 * Thanks, but it was not a formulation of hysterisis per se that I was looking for. Or are you implying that the requirement for an internal variable prevents a hysterisis relationship existing in the derivatives?
 * Your question is problematic as there are many different places where hysteresis occur which have different response curves. Indeed it is possible to start with two monotonically increasing curves and construct a device exhibiting hysteresis with those as the increasing and decreasing curve. So this kind of makes your problem under-derermined. Another problem is wanting time derivatives the modern formulations are "invariant with respect to time scaling", so the response does not depend on how fast the input is changing. So you can talk about dy/dx but not dy/dy or dx/dt.
 * For the Nonideal relay you could say that dy/dx=0 apart from the at two transitional points where its infinite. But thats now a particularly useful answer.
 * The closest tractable example I've found to the picture you gave is the Preisach model of hysteresis see . Here the output is the area of a polygon where the position of one vertex controlled by the input.   If you study the figure you'll find the response curves are all quadratics - roughly corresponding to the area of a triangle with base x and height x plus some constant which depends on the current state of the system. The gradient of these curves can be readily calculated.--Salix (talk): 23:03, 11 April 2011 (UTC)

Prime number
I discover a prime number form.i live in a smoll village in India.I publis my new invention but i dnt know what to do?plz slove my probler — Preceding unsigned comment added by Prime007 (talk • contribs) 17:33, 8 April 2011 (UTC)
 * How do you know it is really new? Robinh (talk) 20:24, 8 April 2011 (UTC)


 * I know quite a bit about prime number forms. If you post it here then I may be able to say whether it is already known or seems mathematically interesting. Thousands of more or less interesting prime number forms have been listed and often named. Your user name made me think of James Bond primes (less interesting). PrimeHunter (talk) 20:59, 8 April 2011 (UTC)


 * It's a tricky one. If he does list it here then how does he know that some dirty, low-down, good-for-nothing pirate like me might not steal it? I wouldn't trust him me if I were me him. Fly by Night on Tour (talk) 23:19, 8 April 2011 (UTC)


 * I doubt Prime007 has something a peer-reviewed journal will publish, or something others will consider "stealing". When amateur mathematicians say they "discover" a prime form it usually just means they pick some subset of the primes and maybe invent a name for it, as shown with the "James Bond primes". They may then compute some examples and guess or try to prove how many there are. Selfpublishing on the Internet is the way to go for most people dabbling with primes. It might as well start here. It will give a public diff with date and time to show first publication. If you are worried about "stealing" then post a real name with the publication or make sure not to forget the password if you want to stake a claim to the prime form later. PrimeHunter (talk) 23:38, 8 April 2011 (UTC)
 * I know&hellip; I was just trying to be funny. Sorry :-( At least I know that I can safely divulge my comedic material without fear of plagiarism. Fly by Night on Tour (talk) 00:20, 9 April 2011 (UTC)
 * OK, but fear of having their work stolen is a frequently expressed concern for amateur mathematicians who seek advice on the Internet. It gives 10 points at . PrimeHunter (talk) 02:07, 9 April 2011 (UTC)


 * I assume that this would be your first article. If you have a new idea then you might like to subject it to the peer review process. This process is very difficult, and work needs to meet the highest standards. Why not read our article on the Journal of number theory? It is a nice journal that focuses on the area that you seemed to be interested in. Please be aware that it is very difficult for a piece of work to be accepted by such a journal. Even professional mathematicians, with numerous publication, will have work reject over their career. Please make sure that any work that you submit is of a sufficiently high standard. Rejection can be very upsetting. Fly by Night on Tour (talk) 00:44, 9 April 2011 (UTC)
 * It would be better to find a professional number theorist at a nearby university and get them to review it (or post it here and we can review it). Submitting something to a journal without having had someone else take a look at it first is probably a waste of time. --Tango (talk) 15:53, 9 April 2011 (UTC)
 * If it is rejected from a peer reviewed journal, he can submit it here. Count Iblis (talk) 17:44, 9 April 2011 (UTC)
 * If it is rejected then send it to another journal. I had a paper rejected that was snapped up by another journal. The refereeing process is quite subjective. Especially if, like me, you're working in a cross-over field, say applying A to B. If the referee is only an A-theorist or a B-theorist then the chances are they'll miss 50% of the meaning. Of course, Tango does that the best solution in the meantime. Fly by Night on Tour (talk) 19:03, 9 April 2011 (UTC)


 * Okay, let's stop dancing around the issue: With the grasp of written English that the OP demonstrates in his question, there is no chance at all that he'll be able to write something by himself that any English-language journal will accept, ever. I don't know whether he's a child, illiterate, dyslexic, not a native speaker, just stupid, a troll, or any combination of the above, but whatever the cause, the result is what we can see. To suggest that he submit to a journal himself, is at best meaningless, at worst a callous prank.
 * Assuming that he really has discovered something new, the only way he will get it out is to team up with someone else to write it up. Wikipedia may not be a good place to recruit such a partner, because it's a written medium and he will at least have to explain his idea to the volunteer. He should find some way to discuss his idea with a collaborator either in his native language or orally (depending on what it is his underlying problem is). –Henning Makholm (talk) 21:48, 9 April 2011 (UTC)
 * There are still non-english journals out there. Taemyr (talk) 21:52, 9 April 2011 (UTC)
 * Sure, which is why I explicitly qualified with "English-language". –Henning Makholm (talk) 22:00, 9 April 2011 (UTC)
 * What's happened to you recently Henning? You used to be a superstar. Now you're suggesting that someone's mathematics might not be worth publication because they are "a child, illiterate, [or] dyslexic&hellip;". It's not compulsory for you to write something. In this case you should not have written anything. And not just that it was rude, but that it was plain silly. History has many brilliant youthful mathematician, blind mathematicians (and hence illiterate), and dyslexic mathematicians. As for your pathetic claim that my journal comments were a prank, well: I gave someone the information that they asked for, while at the same time telling them how damn hard it was going to be. A generally polite and accurate answer I would think. What would you rather me do, be an intellectual snob, tell him he's not worthy? Fly by Night on Tour (talk) 00:53, 10 April 2011 (UTC)


 * No, it is not compulsory for me to write something; we are all volunteers. I chose to call you out on your mocking of the OP. Sure, his question was not eloquent, but he does not deserve how you're treating him here. –Henning Makholm (talk) 01:20, 10 April 2011 (UTC)
 * I'm mocking the OP?! I'm the one assuming good faith and answering his question. You're the one saying he's a child, illiterate, or dyslexic. Hmmm&hellip; Fly by Night on Tour (talk) 13:25, 10 April 2011 (UTC)
 * Yes, you're mocking him. The only thing we know about him is that he is apparently unable to produce English prose. As I've stated, we don't know which of the many different possible causes of that is the real one, but the fact that he cannot write readable English is not in doubt. When you pretend it is a realistic possibility for him to write an article by himself and send it to a journal, you're implicitly mocking his lack of written skills and setting him up to be the laughingstock of some journal editor somewhere. That is not helpful; it is just cruel. –Henning Makholm (talk) 14:43, 10 April 2011 (UTC)
 * I can assure you that I was not mocking him. I'm sorry that you have misinterpreted my intentions. The very fact that we don't know anything about the OP means that we cannot judge if the OP is or is not capable of writing a publishable article. The only thing to do in such cases it to assume good faith and to answer by providing a truthful response, i.e. it's damn hard but if you want to then you should do this&hellip;. Fly by Night on Tour (talk) 17:08, 10 April 2011 (UTC)
 * Can we continue this on a talk page rather than the referenece desk.--Salix (talk): 20:41, 10 April 2011 (UTC)
 * Salix, you may continue wherever you choose; I'd finished. Fly by Night on Tour (talk) 21:23, 10 April 2011 (UTC)

For what it's worth, Prime007 has now attempted to post his invention, but was immediately reverted. He speaks of primes of the form (p-2)n+2 where p is prime and n even. He then claims that 2 and 3 are the only such primes. (But I may be misunderstanding him, because if n is even, then (p-2)n+2 is even too, so the only prime of that form is 2). –Henning Makholm (talk) 00:38, 12 April 2011 (UTC)


 * He wrote: "Of the Form (P-2)n +2 ,P = Prime Number, n=0,1,2,4,6,8,10,12,....................(Even Number)".
 * He apparently means n is either 1 or an even number. As Henning says, if n is even, then (p-2)n+2 is even too. I'm not sure Prime007 understands why or the implication of this: Any product with an even factor is even, so (p-2)n is even. Any sum of two even numbers is even, so (p-2)n+2 is even. All even numbers are divisible by 2, so the only even prime is 2 itself.
 * If n is 1 then (p-2)n+2 = p. Prime007 apparently allows this for p=3 but not for larger primes. The definition is a little unclear but whatever he means exactly, it is definitely not something a journal would publish and it is not mathematically interesting. Also note that it is considered inappropriate to name something after yourself. PrimeHunter (talk) 13:43, 12 April 2011 (UTC)
 * I assume you mean a mathematical concept, and not a baby. There would be a lot of inappropriate Juniors ;-) It's a pity that the OP's ideas are flawed. But at least we tried our best to make him feel welcome, and at least he's taking an interest in mathematics. Fly by Night on Tour (talk) 23:39, 12 April 2011 (UTC)
 * I suppose if Stephen Hawking showed up and asked for directions to the physics colloquium, you would "try to make him feel welcome" by pointing him towards the right staircase? Perhaps even warn him that the steps are a bit slippery because they've just been washed? –Henning Makholm (talk) 01:45, 13 April 2011 (UTC)
 * LOL&hellip; you're losing the plot. — Fly by Night  ( talk )  19:49, 13 April 2011 (UTC)
 * P.S. The link to Prime007's post needs to be removed because it may give his name and email which goes against Wikipedia guidelines. In fact, that post by Prime007 may be a candidate for WP:REVDEL, per criterion 4 as it is maybe oversightable information. Maybe one of our admins could take a look. Fly by Night on Tour (talk) 23:50, 12 April 2011 (UTC)

Here is what Prime007 wrote latest truncated and slightly tidied by me for reasons mentioned above. Could I please ask Prime007 not to delete other peoples contributions Dmcq (talk) 13:12, 13 April 2011 (UTC)

Of the Form (P-2)n +2 ,P = Prime Number ,n=0,1,2,4,6,8,10,12,....................

(next allays Even Number) When n=0 and n=1 the calculation of (P-2)n +2 is 2 and 3 those are prime number and when n=2,n=4,n=6.n=8.........

all ar even number


 * (2-2 )X0 +2 =2
 * (3-2)X1 +2 =3
 * (5-2)X2 +2=8
 * (7-2)X4 +2=22
 * (11-2)X8 +2 =56 ………………………………………….

No gaps between two prime

The only TWO Ghosh prime is 2,3

As of 11 April 2011 these are the only