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Collector
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Re: Stupid question of the day

October 24th, 2020, 9:59 am

Is there a good list of all standard well known operators ? I found a list on wiki, but even many well known operators where not in the list, and I am wondering about operator symbols for some operators that I not are aware of is standardized or not

We have the well known d'Alembert operator. \(\Box=\frac{\partial^2}{\partial t^2}-\nabla^2\), is there also a standardized operator symbol for

\(\frac{\partial}{\partial t}-\nabla\)

? if not I could call it the heart operator for example \(\heartsuit=\frac{\partial}{\partial t}-\nabla\). An alternative would be \(\sqrt{\Box}\), but that I think would be very confusing and possibly misleading.

Second is there any standardized operator symbols for when time is three dimensional, have direction in space, I need something for 

\(\nabla_t-\nabla=\frac{\partial}{\partial t_x}+\frac{\partial}{\partial t_y}+\frac{\partial}{\partial t_z}-\frac{\partial}{\partial x}-\frac{\partial}{\partial y}-\frac{\partial}{\partial z}\)

I could naturally just use \(\nabla_t-\nabla\), but if pages up and down then why not a more compact form. If not a standardized operator symbol for it already, then I was thinking of diamond symbol (is it used for something else in math?)

\(\Diamond=\nabla_t-\nabla=\frac{\partial}{\partial t_x}+\frac{\partial}{\partial t_y}+\frac{\partial}{\partial t_z}-\frac{\partial}{\partial x}-\frac{\partial}{\partial y}-\frac{\partial}{\partial z}\)
and "naturally"

\(\Diamond^2=\nabla_t^2-\nabla^2=\nabla_t\cdot\nabla_t-\nabla\cdot\nabla=\frac{\partial^2}{\partial t_x^2}+\frac{\partial^2}{\partial t_y^2}+\frac{\partial^2}{\partial t_z^2}-\frac{\partial^2}{\partial x^2}-\frac{\partial^2}{\partial y^2}-\frac{\partial^2}{\partial z^2}\)
 
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Cuchulainn
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Re: Stupid question of the day

October 24th, 2020, 10:15 am

Mathemticians use [$]\Delta[$] instead of [$]\nabla^2[$]. Is [$]\Box[$] not a bit silly?

Unless these operators have universal appeal I would not try to define fancy names, Why not names like [$]L\psi[$] where [$]L[$] is an operator. Or maybe Greeks [$]\Lambda[$].

The question: how did these come into existence?
Last edited by Cuchulainn on October 24th, 2020, 10:33 am, edited 1 time in total.
My C++ Boost code gives
262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

http://www.datasimfinancial.com
http://www.datasim.nl
 
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Collector
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Joined: August 21st, 2001, 12:37 pm

Re: Stupid question of the day

October 24th, 2020, 10:30 am

I thought heart operator is a name "students" would actually remember ;-) (one student so far = me), not fancy but practical!  It is an operation, on the very heart of physics, space and time.

"Mathemticians use \(\Delta\) instead of [$]\nabla^2[$]".  good they like to be compact! so do I, so heart and diamond operator going forward!
Last edited by Collector on October 24th, 2020, 10:40 am, edited 1 time in total.
 
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Cuchulainn
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Re: Stupid question of the day

October 24th, 2020, 10:39 am

BUT, mathematicians are parsimonious and only Laplace is allowed to concoct new names.

https://en.wikipedia.org/wiki/Lagrangia ... flow_field
My C++ Boost code gives
262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

http://www.datasimfinancial.com
http://www.datasim.nl
 
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Collector
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Joined: August 21st, 2001, 12:37 pm

Re: Stupid question of the day

October 24th, 2020, 10:52 am

"Is [$]\Box[$] not a bit silly?"

at least it makes it harder for fresh young students (like me) to understand connections between different papers. One read one paper with  \(\frac{\partial^2 }{\partial t^2}-\frac{\partial^2}{\partial x^2}-\frac{\partial^2}{\partial y^2}-\frac{\partial^2}{\partial z^2}\)  then another one with  \(\frac{\partial^2 }{\partial t^2}-\nabla^2\), then another paper with \(\frac{\partial^2 }{\partial t^2}-\Delta\), then a third paper with \(\Box\). After three years one suddenly understand the papers where about the same equation, and was mathematically little more than high school partial derivatives, yes I am very very slow.  Well it make sure math professor and physics professors keep their jobs and looks smarter than they are. But every field has their language too keep outsiders out, medicine likely even worse.... When I worked with plants, it was norwegian plant names for retail customers and all latin names for the professional customers, there it made sense as many small varieties of same plant (genetic difference and visual etc.) have the same norwegian name, but all different latin names. But math has 4 different "words" for the same thing, confusing, in plants we only have 2 (mother language and latin).

\(\heartsuit^{TM}\) first order space-time operator!
Last edited by Collector on October 24th, 2020, 11:56 am, edited 2 times in total.
 
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Cuchulainn
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Re: Stupid question of the day

October 24th, 2020, 11:32 am

Professors get sloppy as they grow older. Too long in ivory tower.
It's the physicists who don't know maths formuiae.

Image
My C++ Boost code gives
262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

http://www.datasimfinancial.com
http://www.datasim.nl
 
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Cuchulainn
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Re: Stupid question of the day

October 24th, 2020, 11:37 am

My C++ Boost code gives
262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

http://www.datasimfinancial.com
http://www.datasim.nl
 
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Cuchulainn
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Re: Stupid question of the day

October 24th, 2020, 11:39 am

We had the same discussions a while back and I recommended 
My C++ Boost code gives
262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

http://www.datasimfinancial.com
http://www.datasim.nl
 
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Alan
Posts: 10497
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Location: California
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Re: Stupid question of the day

October 24th, 2020, 7:34 pm

Is there a good list of all standard well known operators ? I found a list on wiki, but even many well known operators where not in the list, and I am wondering about operator symbols for some operators that I not are aware of is standardized or not

We have the well known d'Alembert operator. \(\Box=\frac{\partial^2}{\partial t^2}-\nabla^2\), is there also a standardized operator symbol for

\(\frac{\partial}{\partial t}-\nabla\)

? if not I could call it the heart operator for example \(\heartsuit=\frac{\partial}{\partial t}-\nabla\). An alternative would be \(\sqrt{\Box}\), but that I think would be very confusing and possibly misleading.

You could call it a (type of) Dirac operator: see Example 4 
Also, somewhat related is a (type of) pseudodifferential operator
As for compact notations, Feynman had the abbreviation Dirac slash for the standard Dirac operator. You don't need gamma matrices, and there are other issues, but still maybe some variation on that would work for you. More
 
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Collector
Posts: 4838
Joined: August 21st, 2001, 12:37 pm

Re: Stupid question of the day

October 24th, 2020, 11:09 pm

Is there a good list of all standard well known operators ? I found a list on wiki, but even many well known operators where not in the list, and I am wondering about operator symbols for some operators that I not are aware of is standardized or not

We have the well known d'Alembert operator. \(\Box=\frac{\partial^2}{\partial t^2}-\nabla^2\), is there also a standardized operator symbol for

\(\frac{\partial}{\partial t}-\nabla\)

? if not I could call it the heart operator for example \(\heartsuit=\frac{\partial}{\partial t}-\nabla\). An alternative would be \(\sqrt{\Box}\), but that I think would be very confusing and possibly misleading.

You could call it a (type of) Dirac operator: see Example 4 
Also, somewhat related is a (type of) pseudodifferential operator
As for compact notations, Feynman had the abbreviation Dirac slash for the standard Dirac operator. You don't need gamma matrices, and there are other issues, but still maybe some variation on that would work for you. More
thank u, I have much to learn, but good to see that when the student finally is ready the two masters appear! 

but it is late here, and I need a break with Operator, operator ..
 
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Cuchulainn
Posts: 63816
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Re: Stupid question of the day

October 25th, 2020, 12:15 am

+ a pinch of Faith, bro

www.youtube.com/watch?v=66i8VQrYPNw

For  [$]C^\infty[$] smoothy manifolds see this

www.youtube.com/watch?v=4TYv2PhG89A
My C++ Boost code gives
262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

http://www.datasimfinancial.com
http://www.datasim.nl
 
User avatar
Paul
Posts: 11057
Joined: July 20th, 2001, 3:28 pm

Re: Stupid question of the day

October 25th, 2020, 1:20 am

Mathemticians use [$]\Delta[$] instead of [$]\nabla^2[$]. Is [$]\Box[$] not a bit silly?

Unless these operators have universal appeal I would not try to define fancy names, Why not names like [$]L\psi[$] where [$]L[$] is an operator. Or maybe Greeks [$]\Lambda[$].

The question: how did these come into existence?
They are like shoes. They all perform (on) the same function but they tell you a lot about a chap’s personality. Such as which club they belong to and thus whether you should hire them.
 
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Cuchulainn
Posts: 63816
Joined: July 16th, 2004, 7:38 am
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Re: Stupid question of the day

October 25th, 2020, 12:58 pm

We had a lecturer who called [$]\nabla[$] "nabla".
Sapir-Whorf.

Not to mention (re)defining one's own notation willy-nilly, with abandon. There are at least 5 names for learning rate.
Last edited by Cuchulainn on October 25th, 2020, 1:50 pm, edited 3 times in total.
My C++ Boost code gives
262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

http://www.datasimfinancial.com
http://www.datasim.nl
 
User avatar
Cuchulainn
Posts: 63816
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

Re: Stupid question of the day

October 25th, 2020, 1:06 pm

More operator overloading

City canal/docklands (why live so close to water??)  folk probably don't know who Garth Brooks is but he has something to say.

www.youtube.com/watch?v=aDnJcvM6wrU
My C++ Boost code gives
262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

http://www.datasimfinancial.com
http://www.datasim.nl
 
User avatar
Cuchulainn
Posts: 63816
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
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Re: Stupid question of the day

October 25th, 2020, 7:55 pm

BTW if you thinks maths is full of symbols..

Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire

https://maartenfokkinga.github.io/utwente/mmf91m.pdf
My C++ Boost code gives
262537412640768743.999999999999250072597198185688879353856337336990862707537410378210647910118607313

http://www.datasimfinancial.com
http://www.datasim.nl

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