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#1 2013-04-26 01:49:24

pellerinb
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Anyone know of a function like this?

Hi all,

I have this function's shape in mind...

plot y = |(x-5)|^[1-|(x-5)|]  from x=0 to 5

Anyone seen this kind of curve before in a similar (i.e. simpler) function? I really had to "mess around" to make it lol!

math is fun!  :-D


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.
 

#2 2013-04-26 03:04:14

bobbym
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Re: Anyone know of a function like this?

Hi;

This is what I got:


Uploaded Images
View Image: 2013-04-25_100424.gif      


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#3 2013-04-26 19:57:03

pellerinb
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Re: Anyone know of a function like this?

Yes... so... I'm just wondering if you have seen this shape elsewhere in a simpler function (I'm not considering the rest, just this part of the plot as you got).


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.
 

#4 2013-04-26 20:13:23

bobbym
Administrator

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Re: Anyone know of a function like this?

The general shape looks like a skewed Standard Normal Curve. Sort of like the ones that are produced for Chi Square.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#5 2013-04-26 21:03:09

pellerinb
Member

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Re: Anyone know of a function like this?

That's true... do you have an equation in mind?


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.
 

#6 2013-04-26 21:25:51

bobbym
Administrator

Online

Re: Anyone know of a function like this?

Hi;

I might be able to fit one of those forms to that curve but why would that equation be better than the one we used to generate the curve?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#7 2013-04-26 21:59:58

pellerinb
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Re: Anyone know of a function like this?

Very true. I guess if I represent it as

y = |x|^[1-|x|]  from x=-5 to 0

It looks more simple and orderly


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.
 

#8 2013-04-26 22:43:00

bobbym
Administrator

Online

Re: Anyone know of a function like this?

Hi;

You could simplify that a bit to


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#9 2013-04-26 22:49:40

pellerinb
Member

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Re: Anyone know of a function like this?

Whoa! That is good, bobbym. Thank you!


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.
 

#10 2013-04-26 22:50:55

bobbym
Administrator

Online

Re: Anyone know of a function like this?

I only tested it from -5 to 0, so use with caution.

Mathematica believes that is true for x≤0. I would try to prove that first.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#11 2013-04-30 05:02:44

pellerinb
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Re: Anyone know of a function like this?

What type(s) of function(s) would it be? I assume it is a power function and an exponential function.


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.
 

#12 2013-04-30 05:10:29

bobbym
Administrator

Online

Re: Anyone know of a function like this?

Hi pellerinb;

I am not following you.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#13 2013-04-30 05:21:05

pellerinb
Member

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Re: Anyone know of a function like this?

Would it be a power function because it is y = | x ^...|

...likewise, would it be an exponential function because it has a variable in the exponent? Just curious.


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.
 

#14 2013-04-30 05:23:02

bobbym
Administrator

Online

Re: Anyone know of a function like this?

Hi;

You mean this expression?




You mean is it a function? Or would you like to approximate that with a something else?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#15 2013-04-30 06:07:29

anonimnystefy
Real Member

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Re: Anyone know of a function like this?

bobbym wrote:

Hi;

You could simplify that a bit to

That does not look correct.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#16 2013-04-30 06:12:37

bobbym
Administrator

Online

Re: Anyone know of a function like this?

It is a simplification of his answer in post #7. They are algebraically the same but not numerically!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#17 2013-04-30 06:35:04

anonimnystefy
Real Member

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Re: Anyone know of a function like this?

They are not algebraically the same either!


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#18 2013-04-30 06:39:01

bobbym
Administrator

Online

Re: Anyone know of a function like this?

Have you plotted both?

Also

Code:

FullSimplify[Abs[x]^(1 - Abs[x]) == Abs[x^(1 + x)], {x <= 0}]

True

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#19 2013-04-30 22:12:12

pellerinb
Member

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Re: Anyone know of a function like this?

bobbym wrote:

Hi;

You mean this expression?




You mean is it a function? Or would you like to approximate that with a something else?

Yup, I mean, is it a function or what kind of function is it?


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.
 

#20 2013-04-30 22:50:34

anonimnystefy
Real Member

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Re: Anyone know of a function like this?

Yes, it is a function, but it does not have any particular name.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#21 2013-04-30 22:57:50

pellerinb
Member

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Re: Anyone know of a function like this?

Thanks!


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.
 

#22 2013-04-30 23:02:43

anonimnystefy
Real Member

Offline

Re: Anyone know of a function like this?

You are welcome.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#23 2013-05-01 04:16:09

bobbym
Administrator

Online

Re: Anyone know of a function like this?

It does now have a name.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#24 2013-05-02 03:07:28

pellerinb
Member

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Re: Anyone know of a function like this?

It appreciates being addressed by unsaid name.


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.
 

#25 2013-05-02 04:28:24

bobbym
Administrator

Online

Re: Anyone know of a function like this?

The unsaid function is what it shall be called henceforth.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

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