User talk:Sławomir Biały

SEMI-RETIRED

This user is no longer very active on Wikipedia.

I laughed out loud reading your post about reverting the code inserted into the prime numbers article.... I fell out of my chair when I actually saw the code.... The fact that the guy wanted to solve the Goldbach conjecture with that... RockvilleRideOn (talk) 03:48, 4 February 2013 (UTC)

I saw your talk on 'Fourier transform'. If you have time, could you just explain a little more on normalization problem? Or state in the page so reader could be aware of this. Thanks. Allenleeshining (talk) 17:34, 4 January 2013 (UTC) http://en.wikipedia.org/wiki/Talk:Fourier_transform#Suspect_wrong_equations_in_section_.27Square-integrable_functions.27

Talkback

Hello, Sławomir Biały. You have new messages at 2001:db8's talk page.
Message added 23:27, 11 February 2013 (UTC). You can remove this notice at any time by removing the {{Talkback}} or {{Tb}} template.

– 2001:db8:: (rfc | diff) 23:27, 11 February 2013 (UTC)

Talkback

I responded to your question at the Math reference desk at Wikipedia:Reference desk/Mathematics#Penrose tiles puzzle pieces. Best. -- Toshio Yamaguchi 13:00, 7 March 2013 (UTC)

Examples of convolution

I saw the wiki page, but I couldn't find any examples using actual numbers evaluating the formula. Could you give some examples of convolution, please? Mathijs Krijzer (talk) 22:14, 9 March 2013 (UTC)

Definition

The convolution of f and g is written f∗g, using an asterisk or star. It is defined as the integral of the product of the two functions after one is reversed and shifted. As such, it is a particular kind of integral transform:

$(f * g )(t)\ \ \,$	$\stackrel{\mathrm{def}}{=}\ \int_{-\infty}^\infty f(\tau)\, g(t - \tau)\, d\tau$
	$= \int_{-\infty}^\infty f(t-\tau)\, g(\tau)\, d\tau.$       (commutativity)

Domain of definition

The convolution of two complex-valued functions on R^d

$(f*g)(x) = \int_{\mathbf{R}^d}f(y)g(x-y)\,dy$

is well-defined only if f and g decay sufficiently rapidly at infinity in order for the integral to exist. Conditions for the existence of the convolution may be tricky, since a blow-up in g at infinity can be easily offset by sufficiently rapid decay in f. The question of existence thus may involve different conditions on f and g.

Circular discrete convolution

When a function g_N is periodic, with period N, then for functions, f, such that f∗g_N exists, the convolution is also periodic and identical to:

$(f * g_N)[n] \equiv \sum_{m=0}^{N-1} \left(\sum_{k=-\infty}^\infty {f}[m+kN] \right) g_N[n-m].\,$

Circular convolution

Main article: Circular convolution

When a function g_T is periodic, with period T, then for functions, f, such that f∗g_T exists, the convolution is also periodic and identical to:

$(f * g_T)(t) \equiv \int_{t_0}^{t_0+T} \left[\sum_{k=-\infty}^\infty f(\tau + kT)\right] g_T(t - \tau)\, d\tau,$

where t_o is an arbitrary choice. The summation is called a periodic summation of the function f.

Discrete convolution

For complex-valued functions f, g defined on the set Z of integers, the discrete convolution of f and g is given by:

$(f * g)[n]\ \stackrel{\mathrm{def}}{=}\ \sum_{m=-\infty}^\infty f[m]\, g[n - m]$

$= \sum_{m=-\infty}^\infty f[n-m]\, g[m].$       (commutativity)

When multiplying two polynomials, the coefficients of the product are given by the convolution of the original coefficient sequences, extended with zeros where necessary to avoid undefined terms; this is known as the Cauchy product of the coefficients of the two polynomials.

How to request IP block exemption

I saw your post at WP:VPT. It appears that WP:UTRS is currently down due to toolserver problems. Your best bet is to try Wikipedia:Sockpuppet investigations#Quick CheckUser requests. Thanks, EdJohnston (talk) 04:13, 13 April 2013 (UTC)

Thanks. I didn't know about this. Wikipedia has obviously become too large and complex for me to handle :-) Sławomir Biały (talk) 19:58, 13 April 2013 (UTC)

About axiom of global choice

Hello, Sławomir, I replied to you last comment here: http://en.wikipedia.org/wiki/Wikipedia_talk:Articles_for_deletion/Axiom_of_global_choice Eozhik (talk) 06:07, 22 April 2013 (UTC)

Talk: Manifold

[1] No. You apparently do not understand the difference between the ring Z of integer numbers, which is a specific ring, and the ring of integers O_K of a number field K, not a specific ring but a functor from fields(?) to commutative rings. Of course, the ring of integers of p-adic numbers contains some extra elements which Z does not have. Incnis Mrsi (talk) 06:18, 22 April 2013 (UTC)

Oh, indeed! You presume quite a lot about what others do not understand, while in the same breath betraying your own ignorance of the very subject that you would presume to "correct" me on. Thanks, but I'll pass. Sławomir Biały (talk) 13:49, 22 April 2013 (UTC)

Another wiki

Being "semi-retired" here, you could be welcome there. Boris Tsirelson (talk) 07:23, 22 April 2013 (UTC)

Transpose: best abstract definition?

If you feel that way inclined, I'd appreciate a quick "yes" or "no" at Talk:Transpose#Transpose_of_linear_maps: why defined in terms of a bilinear form?. — Quondum 14:17, 1 June 2013 (UTC)

about angle

Thank you very much for your answers to my question. I've learned many from you. Could you please make some comments on my newly posted words about the angle in Wikipedia:Reference desk/Mathematics? Thanks. Armeria wiki (talk) 03:38, 13 June 2013 (UTC)

Banach space article

Dear Sławomir, Thanks for your comments and your interest for the Banach space article. I certainly agree with your comments, and I reply here because what I want to say is a bit personal. Actually, I would like some help of yours on the following points:

I don't feel like rewriting a lead in English. I can manage talking to mathematicians, but not to "a general audience".

I started writing a primitive sketch for an Introduction, but was blocked by the same language barrier. It was something like:

Introduction

Functional analysis aims to find functions that are solutions of various equations, several arising from physics. Abstract solutions, namely, functions that cannot be expressed by an explicit formula, are often obtained as limits in a well chosen vector space of functions X of a sequence of approximate solutions. Completeness of X is needed in order to make sure that the limit exists in X. Many examples of such spaces X, but not all, are Banach spaces.

Various type of compact sets in function spaces (norm compact, weak compact) are also used to prove the existence of abstract solutions, for example to optimization problems. In this respect, it is important to characterize compact subsets of function spaces.

I would like to have a section on differential equations in "Banach space", but I am not expert about this.

With best wishes, Bdmy (talk) 12:59, 17 June 2013 (UTC)

Hi Bdmy, I didn't mean to lay the task of improving the article entirely at your feet, just to suggest directions in which I think the article needs to be expanded. These are tasks that I wish I myself had time to undertake. Your mathematical edits to that article are most appreciated. There is now a solid foundation on which to build. Best, Sławomir Biały (talk) 17:45, 17 June 2013 (UTC)