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I seem to not to become familiar with the concept of Superfunctions. But I understand now at least one reason. If we say "S(z) = f(f(f(...f(t))), where f is evaluated z times" then we obscure, that we evaluate f initially *at the point t*. That means, for each *t* we have another superfunction! So a) we should notice that in the article and b) should change the notation, to something like "S_t(z) = f(f(f(...f(t))), where f is evaluated z times beginning at t".
We'll see then, that the range of the "superfunction at some t" is limited to intervals around t between fixpoints and that "S_t(z)" cannot exceed that intervals by change of the parameter z (as long as z is real, there is one option for complex z to step to a neighboured interval). An example is "f(t)=2^t-1 ", whose superfunction -if evaluated beginning at any value "0<t<1" - cannot exceed this range.
--Gotti 07:00, 24 November 2011 (UTC)
Cuzkatzimhut ( talk) 22:38, 25 November 2011 (UTC)
That is the question that led me to this discussion page.
I say, Yes indeed, they should be merged. But only after the enormous number of errors, incongruities, and infelicitous attempts at exposition be fixed in both articles.
For one thing, Superfunctions refers many times to the [function with some property], in many cases where there is no uniqueness, although the author seems unaware of or unconcerned with this issue.
For another, Flows discusses one-parameter semigroups of operators on Hilbert space, which is sufficiently unrelated to the ordinary definition of flow (a group action of the real numbers on a manifold) that it absolutely does not belong in the same article.
Finally, all of these articles have many statements where the domain and/or codomain of some function remain unmentioned and hence a total mystery to anyone who comprehends mathematical notation but who is trying to learn the subject of the article. This happens time and again, and I seriously wish that people would learn how to write expository essays before tampering with a Wikipedia article.
And post-finally, the "celebrated Bernoulli flow" is by no means the first flow that comes to mind among most people who are familiar with flows. It does not deserve mention in the Flows article, since it requires a lot more explanation than an example should require. Daqu ( talk) 20:26, 19 April 2013 (UTC)
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File:Sqrt(exp)(z).jpg, has been nominated for speedy deletion at
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commons:COM:SPEEDY has further information). Otherwise consider finding a replacement image before deletion occurs.
A further notification will be placed when/if the image is deleted. This notification is provided by a Bot, currently under trial -- CommonsNotificationBot ( talk) 21:44, 23 May 2011 (UTC) |
I seem to not to become familiar with the concept of Superfunctions. But I understand now at least one reason. If we say "S(z) = f(f(f(...f(t))), where f is evaluated z times" then we obscure, that we evaluate f initially *at the point t*. That means, for each *t* we have another superfunction! So a) we should notice that in the article and b) should change the notation, to something like "S_t(z) = f(f(f(...f(t))), where f is evaluated z times beginning at t".
We'll see then, that the range of the "superfunction at some t" is limited to intervals around t between fixpoints and that "S_t(z)" cannot exceed that intervals by change of the parameter z (as long as z is real, there is one option for complex z to step to a neighboured interval). An example is "f(t)=2^t-1 ", whose superfunction -if evaluated beginning at any value "0<t<1" - cannot exceed this range.
--Gotti 07:00, 24 November 2011 (UTC)
Cuzkatzimhut ( talk) 22:38, 25 November 2011 (UTC)
That is the question that led me to this discussion page.
I say, Yes indeed, they should be merged. But only after the enormous number of errors, incongruities, and infelicitous attempts at exposition be fixed in both articles.
For one thing, Superfunctions refers many times to the [function with some property], in many cases where there is no uniqueness, although the author seems unaware of or unconcerned with this issue.
For another, Flows discusses one-parameter semigroups of operators on Hilbert space, which is sufficiently unrelated to the ordinary definition of flow (a group action of the real numbers on a manifold) that it absolutely does not belong in the same article.
Finally, all of these articles have many statements where the domain and/or codomain of some function remain unmentioned and hence a total mystery to anyone who comprehends mathematical notation but who is trying to learn the subject of the article. This happens time and again, and I seriously wish that people would learn how to write expository essays before tampering with a Wikipedia article.
And post-finally, the "celebrated Bernoulli flow" is by no means the first flow that comes to mind among most people who are familiar with flows. It does not deserve mention in the Flows article, since it requires a lot more explanation than an example should require. Daqu ( talk) 20:26, 19 April 2013 (UTC)