User talk:LutzL

Welcome!

Hello, LutzL, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers:

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A good mathematical resource is also Wikipedia:WikiProject Mathematics and its talk page. Enjoy! Oleg Alexandrov 17:53, 27 May 2005 (UTC)[reply]

Edit summary

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Oleg Alexandrov 17:00, 30 May 2005 (UTC)[reply]

More welcome

You may also be interested in the discussions at Wikipedia:WikiProject Mathematics -- linas 03:00, 8 December 2005 (UTC)[reply]

Gröbner basis and Hironaka

Hi. Concerning your recent edit of Gröbner basis, I am not sure that Hironaka's theory of "standard bases" is exactly the same. See for example Joachim Apel, Division of entire functions by polynomial ideals, in Proc. AAECC 11, LNCS 948 (1995), pp. 82-95. So if you agree but think the addition is nevertheless important, I propose that you change the text into something like: "In 1964, at almost the same time and independently, Heisuke Hironaka had developed a closely related theory, which he called standard bases." I'm not sure how close this is to your areas of expertise, but I you have interest, time and patience, perhaps you could also add some of this to the Hironaka article, putting it in context, and if possible cite the references as provided by Apel's paper. Cheerio. Lambiam ^Talk 13:46, 3 May 2006 (UTC)[reply]

As I understand it now, the standard bases are defined for ideals in the ring of Puisseux series. Thus they contain Gröbner bases as a special case. The real contribution of Buchberger to the fundamentals is the proof that his algorithm stops in finite time. Perhaps it should be mentioned somewhere that the idea comes from the non-constructive proof by Hilbert of the Basissatz (Kronecker had a constructive proof, but only formulated for bivariate polynomials) -- No, I'm not an expert in the whole of the topic of Gröbner bases. They are interesting to me in the aspect of their inefficiency. I got most of my knowledge from Gethgen/vonzur Gathen: Modern Algebra, where they mention H. Hironaka in the second sentence of the introduction. And from M. Guisty: Bases standard, élimination et complexité, notes of a lecture given at X, where some propositions are attributed to Hironaka.--LutzL 07:29, 5 May 2006 (UTC)[reply]

I'm not an expert either and I don't have access to a library, so I wouldn't be comfortable making any changes of substance. I'll copy this exchange to the talk page of the article in the hope that a next reader can do something with it. --Lambiam ^Talk 14:43, 5 May 2006 (UTC)[reply]

Images of Daubechy spectrum

Would you be so kind to provide me with source code or short description of what you've done used to obtain these:

I need to get fourier transforms of some wavelet functions and I'm kind of stuck with it. I'm totally new to numerical computation of FT and I don't know what I do wrong. I'm not interested in generation of wavelet functions, just the part which does FT.

If I have sampled mother wavelet into vector v of length N, what is right way to compute power spectrum? I'm doing FFT on v and then take positive frequency terms of the resulting vector. Then I i take abs^2 of these positive frequency terms, but the resulting image is quite different:(

I've found that FFT estimates spectrum with errors and the result drastically varies when second FFT parameter (N) changes. I can imagine that this FFT estimation does not converge to spectrum when sampling rate goes to infty.

But your images are just perfect. Have you used some special methods, windows(Hamming e t.c.) ?

Just as you assumed: Compute a sufficiently long vector of values and apply FFT. One should first stabilize the values at integer points via the cascade algorithm (or directly via the pointwise refinement equations) before computing values for smaller step sizes. The values drawn are the absolute values of the complex numbers, so the curves intersect at height 0.71..=sqrt(2). The curves were drawn with gnuplot using thick lines and converted with ImageMagick using antialiasing.--LutzL 09:54, 2 October 2006 (UTC)[reply]

Subsampling

LutzL, long time, no see. At Talk:Sampling (signal_processing)#Sampling_rate_for_bandpass_signals we're talking about changing some math at Sampling (signal_processing)#IF/RF (bandpass) sampling that you worked on back in 2005, originally at Nyquist–Shannon_sampling_theorem#Sampling of non-baseband signals. I'd like to make it simpler, and closer to the sources. You indicated that you thought it was "hopefully simplified" this way, so I'd like to hear why. Comments? Dicklyon (talk) 01:45, 7 January 2008 (UTC)[reply]

Fundamental theorem of algebra

Yesterday, I deleted this sentence from the article about the fundamental theorem of algebra:

But every complex polynomial of degree n is the characteristic polynomial of some complex n × n matrix, for instance, its companion matrix.

You decided to undo my revision, saying “what is wrong about this statement? It is central to this proof.” Concerning this, I have two observations:

I claim that the sentence that I deleted is false. Indeed, I wrote just that when I edited the article (“Elimination of a false sentence”). But if you claim that it is true, then please provide a square matrix whose characteristic polynomial is 2z.
My deletion did not undermine the proof, because it still contained the sentence “So to establish that every complex polynomial of degree n > 0 has a zero, it suffices to show that every complex square matrix of size n > 0 has a (complex) eigenvalue” and the footnote that comes after it, which links to a proof of the fact that, given a field F, if, for every natural number n, every endomorphism of Fⁿ has some eigenvalue, then F is algebraically closed. JCSantos (talk) 09:07, 13 June 2008 (UTC)[reply]

Ok, so it should say "normed polynomial". Since this theorem is concerned with fields, the zeros do not depend if a polynomial or some multiple of it is concerned.--LutzL (talk) 10:31, 13 June 2008 (UTC)[reply]

On the other hand, the introduction to the proof section already restricts the polynomials to have "dominant coefficient 1". Added the division by the leading coefficient.--LutzL (talk) 10:44, 13 June 2008 (UTC)[reply]

The result of all this is that, at present, the text contains a complete proof of the fact that, in order to prove that every monic polynomial has a root it is enough to prove that every endomorphism of Cⁿ has some eigenvalue and a footnote telling the reader where to find such a proof. In my opinion, one of them should be eliminated. The reason why I chose the first one is because (1) the proof exists already on Wikipedia and (2) the proof doesn't seem to me to be important for someone who is trying to learn proofs of the fundamental theorem of algebra. What is your opinion? JCSantos (talk) 22:13, 14 June 2008 (UTC)[reply]

What is so evil about redundancy? In my opinion, neither the short jump from polynomial to matrix nor the referenced section are satisfying. The referenced section is inside the article on algebraically closed fields, whereas the fundamental theorem sets out to show that the complex field is closed. It is not trivial to see that this is not a circle jerk. To come back to the article, the proof is almost too long and has no cited historic foundation unlike many of the other proofs. Shouldn't it go to wikibooks? It is, in some way, just another version of the winding number proof. But do as you want. I just found it curious that the companion matrix was not mentioned and any obvious matrix construction removed, as if this were too technical to be exposed.--LutzL (talk) 14:36, 15 June 2008 (UTC)[reply]

Sorry

... for this button slip. I don't know what is going on since yesterday. I aim to click a linkbutton, and the one immediately above is triggered. That's probably what happened here, although I'm not sure. All I know is that there is something severely wrong with the interface :-( - Cheers - DVdm (talk) 19:55, 17 February 2011 (UTC)[reply]

Wouldn't have noticed, so no damage done. Hope You didn't trigger the 3R-rule with that glitch.--LutzL (talk) 11:03, 18 February 2011 (UTC)[reply]

Big thanks!

Thank you very much for your suggestions/contributions on the talk pages for Ricci calculus and providing a core reference in the first place, then finding an original and historical online source. It really is extremley valuable - all readers can see how it historically began, and from an accessible website also. =) Apologies if I seemed to neglect your comments... F = q(E+v×B) ⇄ ∑_ic_i 19:11, 12 April 2012 (UTC)[reply]

Ricci calculus

Hi, this article is awesome, the first time I have seen such a complete and transparent summary for this concept.

		The Teamwork Barnstar
		This is to be shared between: F=q(E+v^B) - the original author, LutzL - historical content, accuracy and sources, Quondum, JRSpriggs, TimothyRias - corrections and mathematical accuracy, clean up, clarification etc. Maschen (talk) 16:32, 20 May 2012 (UTC)[reply]

Well done and thanks to you all, and sorry this is so late (I would have awarded this earlier but don't get on WP much anymore). Best, Maschen (talk) 16:32, 20 May 2012 (UTC)[reply]

Intolerable behaviour by new user:Hublolly

Hello. This message is being sent to inform you that there is currently a discussion at WP:ANI regarding the intolerable behaviour by new user:Hublolly. The thread is Intolerable behaviour by new user:Hublolly. Thank you.

(I had to include you by WP:ANI guidelines, sorry...)

F = q(E+v×B)⇄ ∑_ic_i 23:04, 9 July 2012 (UTC)[reply]

hi i understand im a bit of a talking like an CIA to you

maybe ill explain those some day.... if really the case ;-) — Preceding unsigned comment added by 93.118.212.93 (talk) 21:15, 7 December 2012 (UTC)[reply]

n... dont forget this one...

considerring reminders 4 common factorization test might help a lot: algo might become polynomial

also , possible dinamic programming n my so called virtual processing, in fact keeping reprezentative info 4 simulating large number of divindings where the dividers r 1...2^m thing that might b able to b considered 4 virtual processing aiding dynamic programming :)

— Preceding unsigned comment added by 93.118.212.31 (talk • contribs) — Preceding unsigned comment added by 93.118.212.93 (talk) 21:43, 7 December 2012 (UTC)[reply]

walking on a region border might help , by keep minx, maxx, miny,maxy of visited border, to plan d&i algo, main routine is seek 4 the border , filling with this occasion the pixels that not produce a (local) regions split, when regions r too little, like O(log(N)) we can fill directly, achieving limits of border is the main programming task betting on O(log(n)) mem, O(n) time :-) 93.118.212.93 (talk) 16:14, 14 February 2013 (UTC)

hi, how old r u? im 39 old...

93.118.212.93 (talk) 17:26, 14 February 2013 (UTC)[reply]

D4 analysis and scaling function

Hi, I think the plot of the D4 wavelet function in the article Daubechies wavelet has the wrong sign, at least if the wavelet coefficients given in the same article {-0.1830127, -0.3169873, 1.1830127, -0.6830127} are used. I plotted the D4 wavelet function in matlab with the code here und got the graphic here here. Conquerist (talk) 19:32, 15 February 2013 (UTC)[reply]

It may be that you are right. I'll have to check the code sometimes to see whether a sign reversal occurs. The images where done with gnuplot from a data series produced with a cascade algorithm that stay stationary on already computed points, so it does not need that many iterations to produce a faithful approximation.--LutzL (talk) 18:33, 18 March 2013 (UTC)[reply]

Telescoping Series Lemma

LutzL,

The elementary lemma on Telescoping series was deleted by you for the following reason:

"It is not wrong, and also not totally out of place (but not in the lede), but the topic is about series where the telescoping form is obvious from the summands. I.e., where your g(k) have an obvious short simple form.)"

The title of the Wiki article is simply "Telescoping series". My brief post gives an elementary relation between telescoping series and general series. The Wiki article seems like a reasonable place to include this simple relation. I have not seen it mentioned elsewhere on the Internet. - gkvp — Preceding unsigned comment added by Gkvp (talk • contribs) 23:35, 15 March 2013 (UTC)[reply]

Well, for starters, your own formulation "I have not seen it mentioned elsewhere on the Internet" should be a red OR flag. I'm not totally against this remark, but please properly formulated, properly formatted, in a notation that is not in clash with the rest of the article. And not in the introduction of the article. Telescoping sums and series are a trick for computing the value of the series in certain circumstances. Of course you have that each addens is the difference of two partial sums

a_{n+1}=S_{n+1}-S_{n}

, giving the appearance of a telescoping series, and one can shift the partial sums by some constant,

a_{n+1}=(S_{n+1}+c)-(S_{n}+c)

. But this is, in general, not a simplification of a computational problem, but its restatement in more complicated terms.--LutzL (talk) 18:28, 18 March 2013 (UTC)[reply]

i m so sorry, i apologise 4 my bad behaviour

it seems to me my hypoglicemia plaied nasty game with me last time we've met. thank u very much 4 the forums sites i already wrote to them. no ofense but here they just look ready to naturalise some more of my ideas, n i dont blame noone, ok. they must know what they r doing: 4 example, when i type on google "partitioning without a pivot" its only one n its mine's n i could go on but i dont wish to. anyway i hope ull forgive me 4 my daring talking style, thank u! Florin — Preceding unsigned comment added by 93.118.212.93 (talk) 06:06, 10 April 2013 (UTC)[reply]

Thanks for the correction

I blame my embarrassing error on acute lack of coffee. Sławomir Biały (talk) 14:26, 17 September 2013 (UTC)[reply]

Reduce transmission errors with science (prelim. results): Walking with coffee: Why does it spill? --LutzL (talk) 17:20, 17 September 2013 (UTC)[reply]

align bug

When will this "fix of the align bug" land? Personally, I feel that some technology that is not working or not available should not be relied upon to encode information in a page, as it stops people from understanding it! If align is not working, it should not be used until it is fixed. ~ Keiji (iNVERTED) (Talk) 12:31, 8 February 2014 (UTC)[reply]

As announced on the math project page, the hotfix for this problem is already worked on. And "not using it" is different from "changing it", please also consider that everything should be changed back since align/aligned is the correct way for multiline equations. -- In total, it is a very sad state of affairs that the developer physikerwelt did not find his way to the math project earlier to discuss his deep changes.--LutzL (talk) 17:38, 8 February 2014 (UTC)[reply]

ArbCom elections are now open!

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ArbCom 2018 election voter message

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