User talk:Julius

Welcome to ProofWiki! Since you're new, you may want to check out the general help page. It's the best first stop to see how things are done (next to reading proofs, of course!). Please feel free to contribute to whichever area of mathematics interests you, either by adding new proofs, or fixing up existing ones. If you have any questions please feel free to contact one of the administrators, or post your question on the questions page.

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• Community Portal - To see what needs to be done, and keep up to date with the community.
• Recent Changes - To keep up with what's new, and what's being added.
• Check out our house style if you are keen on contributing.
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Cheers! prime mover (talk) 15:47, 3 January 2017 (EST)

House style

While your contributions are useful, you are encouraged to make an attempt to pick up on house style.

While I appreciate that you are already familiar with $\LaTeX$ and MediaWiki, and have developed your own coding style, it is different from the house style of presentation that we strongly adhere to on $\mathsf{Pr} \infty \mathsf{fWiki}$.

You may be able to perceive stylistic differences between the pages you are generating and those which already exist on the website.

It is also expected that every concept is linked internally to a definition page. The reason for this becomes obvious as you become familiar with our ultimate philosophy.

Please feel free to take advantage of this advice.

Many thanks in advance. --prime mover (talk) 09:01, 29 January 2017 (EST)

Thank you for the notification. Indeed I am aware of the differences. They arise partially from focusing on the volume of presented material regarding the target branch of mathematics first, to fulfil encyclopaedical aspect of this website. Coding differences come mostly from my own habits, and that will take some time to adjust. The presentation of material could be improved, and I am planning that as soon as the material by Gelfand has been covered. Most of divergence from the house rules come from the fact that I am trying to limit my time spent here (it's almost too easy too lose track of time while surfing and improving this website) while maximizing the volume of contribution. Another culprit are the proofs themselves. Due to brevity they are lacking some nonobvious steps, which still explanation, and the lack of these slightly demotivates proper phrasing as it is not clear how much adjustment a reasonable chunk of material will require. As for linking every concept I believe I am linking everything on the given page at least once, but I will check upon that. I will attempt to staying closer to the house rules, at least when it comes to coding. As for style of presentation, that probably will get improved by iterative reexamination. Julius (talk) 12:53, 29 January 2017 (EST)

What to do with Sturm-Liouville Problem?

Hey, I see you blanked the page Sturm-Liouville Problem. Was this as a reaction to someone's tyranny, or has the content been moved elsewhere?

If it has simply been removed, I propose to restore it and mark it with something like {{serious issues}} or {{rewrite}}. --barto (talk) (contribs) 15:56, 11 November 2017 (EST)

Currently, Definition:Sturm-Liouville Theory, which is not my page, contains the majority of results, which have to be formalised and presented within the House Rules. The contents of my page have been moved to Sturm-Liouville Problem/Unit Weight Function, since it is a special case of Sturm-Liouville Problem. The empty page was initially created to house the proof I had, but after noticing a more general description which was unfamiliar to me, I decided to give it a proper name. There was also a disagreement about the presentation (I am for making an unfinished article public vs the other party's presentation of appropriately formatted article), but that only shifted the time of actions. Fell free to fill or delete the empty page. --Julius (talk) 14:30, 18 November 2017 (EST)

More on house style

A quick request ... can you--prime mover (talk) 10:25, 13 January 2019 (EST) cut down on the number spaces that you put between every symbol? We aim for a happy medium between no spaces at all and everything separated by spaces. If you are using an automatic tool that generates the $\LaTeX$ for you, consider modifying its parameters. Inspect the source code of other pages for an example of how we like it here. It is tedious and wasteful of time changing all your pages into house style, and we would really not have to do it. Your cooperation is requested. --prime mover (talk) 17:15, 4 October 2018 (EDT)

No problem. I noticed an increased implementation of various shortcuts like "paren", "sqbrk", etc. which partially solves the problem. Could they be added to the list of "Common LaTeX Commands" below the editor? --Julius (talk) 04:17, 5 October 2018 (EDT)

That section is already big enough that it takes up a fair amount of real estate. Besides, the allowed formats for inserted code is limited in that it does not allow spaces to be included, which limits its usefulness: any code generated using more complex constructs than simple inclusion of $\LaTeX$ tags would need manual reformatting to start with. I'll experiment with different formats. --prime mover (talk) 05:01, 5 October 2018 (EDT)

Call for Deletion

Hi,

When you completely blank a page and move all its content into a new one, and then replace the original content with a Delete, please can you make sure that you first find all the pages that link to the new page and change everything that links to it? Otherwise we end up with loads of redlinks.

It is a better strategy to use the "Move" option to move pages around rather than create a new page and copy everything over, but I appreciate that you may not have the privileges to do that. In that case, rather than doing what you just did, can you instead invoke the {{rename}} template at the top of the page with an indication of what you think it ought to be renamed to?

Many thanks. --prime mover (talk) 10:24, 13 January 2019 (EST)

P.S. Can I rely on you to go ahead and change the links to the pages in question? Again, many thanks. --prime mover (talk) 10:24, 13 January 2019 (EST)

P.P.S. Right okay, I see you are already doing this. Cheers.

Sorry about that. There was some glitch in my thinking process. Actually I remember once having "Move" option, but that was over a year ago. Either way, I promise to use template you mentioned. --Julius (talk) 10:31, 13 January 2019 (EST)

I see you still prefer to use the write-new-page-and-delete option rather than the {{rename}} template technique on pages whose names you want to amend.

While it's okay and it works (as long as linked pages get renamed) it's suboptimal as you don't get any indication of the history.

Again, as I say, it would be better if you would use the {{rename}} template instead of deleting pages and recreating them as new pages, if that could be achieved.

thx --prime mover (talk) 07:07, 24 December 2020 (UTC)

No problem. Probably my exposure to outstanding to-be-renamed articles skewed my impression of how efficient this approach was. I wanted to make sure that I don't leave any bugs before I move to the next chapter, and, as the volume of material grows, I tend to forget what I did or planned to do. Anyway, I will adjust according to your advice. --Julius (talk) 20:30, 24 December 2020 (UTC)

Does not really matter how long it takes for a page to be renamed. We get round to them sooner or later. Problem is I don't get paid a salary for this. --prime mover (talk) 00:38, 25 December 2020 (UTC)

Source works

While the work you're doing on documenting every single source work on functional analysis ever written is applauded, we might want to step back a bit.

In particular, the instance of Book:Kösaku Yosida/Functional Analysis/Reprint of Sixth Edition.

IMO it's going a bit far to specify exact reprints of editions. The reason we started separating out editions into separate pages is because very frequently the works change significantly between editions. Different contributors may have access to different editions, and may be working a different citation thread. So to make sure that a citation is exact and accurate, we specify the edition so as to make sure it stays accurate.

However, as a reprint usually has exactly the same material as a new edition (although the pagination may change), it seems of little worth making a distinction between them. If contributor A has one printing and contributor B has a different printing (of the same edition) they will feel the need both to add their own copy, leading to two wiki pages exactly alike except for the printing.

So recommend we have just Book:Kösaku Yosida/Functional Analysis/Sixth Edition and date it to when it was actually first printed. --prime mover (talk) 18:12, 19 November 2019 (EST)

This was my attempt to test the ground on reprints, i.e. how to formulate the title and make links work and not deform their appearance. I am yet to attempt something similar with Shilov's case, where the reprint is partial, and is of the book with a different title. --17:57, 20 November 2019 (EST)

Enhanced editing rights

You will notice that you now have an enhanced set of rights. For some reason you had not been added to the "Trusted" group. That oversight has now been redressed.

This means that you should now have the ability to move and delete pages, along with other sundry powers.

Sorry this took so long to achieve, it is only just now that this had not been done. --prime mover (talk) 22:43, 10 January 2021 (UTC)

Thank you for trusting me. Probably this was due to certain disagreements we had some time ago. Anyway, being able to contribute is sufficient enough, and I don't think I will use new options that much, maybe with exception of "move". Thanks again. --Julius (talk) 04:47, 11 January 2021 (UTC)

We had a MediaWiki upgrade a while back where another level of user was added which by default did not have a whole bunch of more-or-less basic authorizations. Hence and so. --prime mover (talk) 06:20, 11 January 2021 (UTC)

Permanent links / redirects

A quick heads-up (something which I thought you'd pick up on at some stage):

When you are linking to a page with a forward slash in it, e.g. Definition:Derivative/Real Function, please always check to see if there is a non-slashed redirect, as in this case Definition:Derivative of Real Function.

We do it like this so as to make any subsequent refactoring easier. If we want to change the structure of the underlying pages (as we often seem to do) then all we need to do is change the target of the redirect within Definition:Derivative of Real Function, rather than have to go through every single page that link directly to Definition:Derivative/Real Function, which is tedious.

Thanks --prime mover (talk) 07:12, 9 March 2021 (UTC)

Incidentally, the link in question actually needed to be Definition:Derivative of Vector-Valued Function, or so I believe. --prime mover (talk) 07:15, 9 March 2021 (UTC)

No problem. Looking at functions as basis vectors is foreign to me, so some polishing may be needed.--Julius (talk) 07:50, 9 March 2021 (UTC)

Distributions

Good job, this is starting to take shape nicely. --prime mover (talk) 15:20, 2 April 2021 (UTC)

Conceptionally, not much more is left. Mostly trivial extensions of differential calculus and a few distributional ode's. But eventually, we'll have to tackle those definitions of Dirac function. This is not addressed in Sasane, but should be doable in principle.--Julius (talk) 15:57, 2 April 2021 (UTC)

$L^p$ spaces

It's my understanding that we haven't really done anything with $L^p$ spaces beyond defining $L^p := \LL^p/\sim$ (no basic arithmetic or integration) and wanted to pick your brains on future plans. Of course usually a function is not distinguished from the equivalence class it's contained in under $\sim$ but I think such abuses of notation are against the spirit of ProofWiki, (I feel like annoyances with such abuses are a large part of the reason why this project exists) so I was wondering whether we should go for a very dry uncompromising approach with equivalence classes, (at the risk of putting off more casual readers) or use notation more in line with the "meta" as is already here on a few pages. I've started a few pages on showing that A.E. equality works in basically the same way as everywhere equality, (for use with Radon-Nikodym derivatives, I couldn't bring myself to "only define an object almost everywhere", whatever that's supposed to mean) and the machinery showing that integration works fine is also there, there's just nothing to put it all together yet. Might even lead on to some actual coverage of PDEs here. Interested to hear what you think, don't think we've spoken before despite us both seemingly working on adjacent areas. Caliburn (talk) 23:02, 16 December 2021 (UTC)

Excuse me joining ... in fact notation abuse is not against the spirit of $\mathsf{Pr} \infty \mathsf{fWiki}$ as such -- but when basic theorems about the basic behaviour of all the objects in question it is essential to be as clear as can possibly be. In Group Theory for example, in those early stages we have made a point of insisting that the full group spec is used, and same with linear algebra and so on -- because then it is absolutely explicit exactly which elements of an aggregated structure are being directly considered at a particular point in spacetime. Good luck. --prime mover (talk) 23:18, 16 December 2021 (UTC)

At the moment I am interested in $L^p$ spaces only marginally. In Sasane they mostly pop up in simple exercises where the abuse of notation does not confuse. I am almost done with the topic of distributions, and I was thinking to move to an appendix in Sasane where he develops $L^p$ spaces in more detail. I don't mind abusing the notation if the situation at hand considers sufficiently standard functions. We just have to write a few articles showing that in certain cases certain types of functions and their equivalence classes behave in the same way. On the other hand, a lot of results in the theory of distributions reduce the notational load by stating "in the sense of distributions". For a newcomer it can be confusing when the same symbol is used as a function and a functional because there is a difference. This is why my presentation is more explicit and often restates the theorem twice - with and without the abuse of notation. I think that for now we should more or less stick to the standard presentation while clearly explaining in which sense the expressions are to be understood. I could imagine that in the future we could provide two proofs for a selection of examples with first being the textbook presentation and the second being the exact explicit approach, so that students could compare both ways. Recall that we have an option of posting several proofs.--Julius (talk) 20:45, 19 December 2021 (UTC)

Note of thanks

Just a quick note of appreciation of all the work you have been doing on $\mathsf{Pr} \infty \mathsf{fWiki}$ over the last few years.

I am unable (through lack of application) to follow everything you have been doing -- I'm more focused on abstract algebra and foundations -- but the results are glorious. --prime mover (talk) 19:57, 30 March 2022 (UTC)

NP. I am almost done with the intro to the theory of distributions including all this delta sequence stuff. Once I am done with images for delta sequences and my last review of the material here I will write down a short report on the main talk page.--Julius (talk) 20:02, 30 March 2022 (UTC)

Spelling of nul(l-)homotopic

By User:Prime.mover's edit of Definition:Loop (Topology)/Null-Homotopic Loop, we have been ordered to standardize the spelling. I have used nulhomotopic because Munkres uses it, but I am indifferent to the spelling. Should we keep Definition:Nulhomotopic, or change it to null-homotopic? --Anghel (talk) 16:25, 3 January 2023 (UTC)

Heh. "Ordered". Yes. Sorry. But you agree it's a thing worth doing?

My personal view is that whichever is the most prevalent in the contemporary usage should be used, but I am not close enough to the coal face to know what that is. --prime mover (talk) 16:30, 3 January 2023 (UTC)

What will of course happen is that you can decide which is to be used, and I can go through and standardise, embedding redirects as necessary for mutual interlinking as need be. Catch the inconsistency now and it's so much easier to fix when there's only a handful of pages using it. --prime mover (talk) 16:33, 3 January 2023 (UTC)

I don't really care, feel free to change it. Just leave something in "Also known as". If it stays as it is, I will get back to this once I am done with homotopy. The chapter is not that long.--Julius (talk) 22:56, 3 January 2023 (UTC)

Both Wikipedia and MathWorld use null-homotopic, so that seems to be the popular choice. I'll make the necessary changes in the near future. --Anghel (talk) 16:12, 4 January 2023 (UTC)

Yes, Null-Homotopic works for me too. --prime mover (talk) 17:38, 4 January 2023 (UTC)

Differential Operator: Help Needed

Hi

I see you have set up a merge request for Definition:Differential Operator and Definition:Partial Differential Operator. There are a lot of references in the Sasane treatment of the subject which link to Definition:Differential Operator, despite it not having been "formally" set up as a definition page, merely copied in place from Wikipedia (yes I know, that was me, I was trying to reduce some of the redlinks from the Sturm Liouville material in Dan Nessett's sandbox). This perfectly illustrates why it is a mistake to "just" drop definitions into place without them being properly sourced and without dependencies having been properly thought through.

That was a while ago. I wonder why I did not refer to the page I created. Probably I wanted to avoid derailing my work on distributions by sticking to what I had in my book. I will have a look when I am back from work.

My problem is that I find in my beloved 1990: I.S. Grant and W.R. Phillips: Electromagnetism (2nd ed.), which I am currently sourcing with a view to building up the coverage on electromagnetism (in parallel I intend to do QM at some stage too), they define "differential operator" to mean the Definition:Gradient Operator, Definition:Divergence Operator and Definition:Curl Operator which undergraduate physicists know and love, while knowing and caring little about the more highly abstract concepts in this area.

Are you able to help rationalise this awkward nomenclature issue? --prime mover (talk) 06:53, 24 March 2023 (UTC)

I see that we are again getting sandwiched between engineers and mathematicians, both claiming the notion of "differential operators". I am familiar with operators such as $\dfrac d {dx}$, $\dfrac \partial {\partial x}$, $\dfrac {d} {d x} + \map f x$, $a(x,y) \dfrac \partial {\partial x} + b(x,y) \dfrac \partial {\partial y}$, $\tuple{\partial_x, \partial_y, \partial_z}$, Laplacian and the Schwarzian derivative (and I am avoiding pseudo-differentials and distributional derivatives). So it seems, that everything that involves a good old ordinary or partial derivative can be called the differential operator. Now, we can try to distinguish them by purity, i.e. raw differential operators vs those with all these multiplicative and additive functions, but strict boundaries sometimes can cause confusion. For example, Laplacian in flat space in cartesian coordinates would appear quite pure when compared to its expression in some fringe coordinates. So we have the dilemma whether we talk about the differential operator as something more than its representation. But at least it's linear. In comparison, Schwarzian is not. I believe that we should rename the differential operator into the linear differential operator (and then get rid of my own partial differential operator, with a small note left on the main page).

I don't really have a problem with having the very general definitions we have for the linear differential operator, but the multi index notation is not something engineers or physicists use. What I would really welcome is a couple of explicit forms of these operators which would illustrate the entire counting procedure. And I believe we need to generalize our definitions to handle curl and gradient. Then most of well known differential operators could be shown to fit the linear differential operator definition (lots of trivial theorems here).

If you are afraid of hiding well known differential operators as lemmas, maybe it's worth creating a separate category or a summary page to highlight them.

But please, tell me more. I am not sure I got your question right.--Julius (talk) 18:04, 24 March 2023 (UTC)

I'm challenged here, because I don't know what the right question actually is.

We need a solidly sourced definition for a "differential operator" from a source which provides explanations, examples and exposition. I may have some in the colossal quantity of books on my shelves, but I can penetrate such works only with an effort.

For the moment I will leave the definition page as it is, with the undergraduate-physics understanding of div, grad and curl, because they are useful for getting results and it's convenient to bracket them together like that. Generalisation will need to wait until we have a source which provides this. --prime mover (talk) 19:22, 24 March 2023 (UTC)