Portal talk:Mathematics/Archive2012

number 7

lots of people say 7 is a lucky number

70.187.228.11 (talk) 20:36, 16 April 2011 (UTC)

Not done: please be more specific about what needs to be changed. — Bility (talk) 21:42, 16 April 2011 (UTC)

This seems to be more simple opinion rather than a specification of anything needing to be changed, I would suggest that this be removed. 82.33.215.26 (talk) 09:53, 27 September 2012 (UTC)

Handling of intentionally incorrectly written equations

Please advise to me about how to handle intentionally incorrectly written equations.

On the article Additive synthesis#Theory, some IP user posted intentionally incorrect equations in 2007. On his post in 2007, he introduced at least two wrong substitutions,

1. On simple substitution                 k f₀           →       f_k[n],
   he really substitute term     (2 π k f₀ / Fs)   →   (2 π / Fs)∑ ⁿ_i=1 f_k[i]

   Note: On the discussion in the article, the context requires substitution of constant   k f₀   with inharmonic version (on here, "inharmonic" means "arbitrary")   f_k .

   However, he declared substitution of constant   k f₀   with time-varying inharmonic version   f_k[i] .

   And his real substitution   ∑ ⁿ_i=1 f_k[i] / n   imply time-average of time-varying inharmonic version. (if he intent to extend equations towards "time-varying inharmonic" version, this average operation spoil the time-varying nature)

   His word and real substitution are contradicted, and also contracted with context.

2. On the case required multiple substitutions (by his definition), he irrationally erased several terms without showing details of each substitutions

   Note: it seems originally derived from 1.

As a result, equations he posted are totally incorrect. The mistake is too much bold and understandable at a glance (too complicated), probably nobody reads the equations, and problem seems to be neglected on last five years.

I want to correct it if possible. However, IP user (probably same person) is repeatedly reverting the corrections, and also posted delusions written in almost unreadable English, on article's talk page. (inability of conversation is a very sad thing) What is the best way to solve the problem ? I expect your kindly advices. sincerely, --Clusternote (talk) 05:32, 8 January 2012 (UTC)

P.S. Last my corrections seem not reverted yet : ) --Clusternote (talk) 05:39, 8 January 2012 (UTC)

I think you want Wikipedia talk:WikiProject Mathematics rather than the talk page of the portal which is just for improving the portal. The people there will helpyou with this and to cope with the other editor. Dmcq (talk) 23:22, 8 January 2012 (UTC)

Thanks for your kindly advice, I'll follow it. Sorry for my inappropriate post. ... --Clusternote (talk) 04:40, 9 January 2012 (UTC)

Helmholtz decomposition is wrong

Dear members of world mathematical community!

The Fundamental theorem of vector calculus, (Helmholtz decomposition) states that any sufficiently smooth, rapidly decaying vector field in three dimensions ${\mathbf {F} }$ can be constructed with the sum of an irrotational (curl-free) vector field and a solenoidal (divergence-free) vector field (scalar potential $\varphi$ and a vector potential ${\mathbf {A} }$)

${\mathbf {F} }=-\operatorname {grad} \psi +\operatorname {rot} {\mathbf {A} }\Rightarrow {\mathbf {F} }=\operatorname {grad} \varphi +\operatorname {rot} {\mathbf {A} }$ (1)

However, the gradient of scalar function does not form the vector field. As well known from textbook [1, p. 15] « … under co-ordinate change the gradient of function transforms differently from a vector »: hence the theory requiring (1) must be false. The next unpleasant things we can see for such well-known classical rules. In mathematics and physics the rot (or curl) is an operation which takes the vector field ${\mathbf {A} }$ and produces another vector field $\operatorname {rot} {\mathbf {A} }$ . However it is well-known that $\operatorname {rot} {\mathbf {A} }$ is an Antisymmetric Tensor . Therefore under co-ordinate change the tensor $\operatorname {rot} {\mathbf {A} }$ transforms differently from a true vector. For elimination of these contradictions the Fundamental theorem of vector calculus can be written as follows:

${\vec {F}}=\operatorname {grad} \varphi +\operatorname {rot} \operatorname {rot} {\vec {A}}$. (2)

This formula completely corresponds to transformed Navier–Stokes equations(NSE) for incompressible fluids ( $\operatorname {div} {\dot {\vec {u}}}=0$)

$\rho {\vec {F}}-\operatorname {grad} p+\mu \nabla ^{2}{\dot {\vec {u}}}=\rho {\ddot {\vec {u}}}\Rightarrow \rho ({\vec {F}}-{\ddot {\vec {u}}})=\operatorname {grad} p+\operatorname {rotrot} \mu {\dot {\vec {u}}}$ . (3)

Here, ${\vec {F}}={\vec {F}}_{1}+{\vec {F}}_{2}+...$ -¬¬ vectors sum of a given, externally applied forces (e.g. gravity ${\vec {F}}_{1}$ , magnetic ${\vec {F}}_{2}$ and other), $p$- pressure (scalar function), ${\dot {\vec {u}}}$- velocity vector, ${\ddot {\vec {u}}}=d{\dot {\vec {u}}}/dt$ - acceleration vector, $\rho$ - density (const), $\mu$ - viscosity (const), $\nabla ^{2}$ - Laplace operator.

Equations (3) and (2) are consistent. Hence there is no reason to say that the theory requiring (2) must be false. As we can see from NSE the sum - $\operatorname {grad} p+\mu \nabla ^{2}{\dot {\vec {u}}}=-(\operatorname {grad} p+\operatorname {rotrot} \mu {\dot {\vec {u}}})$ forms the vector field.

Note that we will receive the formula (2) also after similar transformation of the Navier–Stokes for a compressible fluid and after transformation of the Lame equations for an elastic media.

From this brief note follows that Helmholtz decomposition is wrong and demands major revision. This follows from comparison of two articles in Wikipedia (http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations and http://en.wikipedia.org/wiki/Helmholtz_decomposition ).

Therefore let's try to formulate the text for editing of this article.

1.B. A.; Fomenko, A. T.; Novikov, Sergeĭ Petrovich (1992). Modern Geometry--methods and Applications: The geometry of surfaces, transformation groups, and fields] (2nd ed.) . Springer. (p. 15).ISBN 0387976639.

--Alexandr 17:58, 4 February 2012 (UTC) — Preceding unsigned comment added by Continuum-paradoxes (talk • contribs)

I see you have already started a discussion about this at Talk:Helmholtz_decomposition, that's good. If you don't get a response there then Wikipedia talk:WikiProject Mathematics would be where to ask. This is the talk page for improving the portal, not the talk page for the project. It is better to ask people at the project to go to Talk:Helmholtz_decomposition for the discussion rather than repeating yourself at the project. Dmcq (talk) 21:38, 4 February 2012 (UTC)

Thanks for your help!--Alexandr (talk) 18:17, 7 February 2012 (UTC)

Vedic Mathematics

Need a section on Vedic Mathematics 20.143.240.21 (talk) 11:36, 13 February 2012 (UTC)

Did you try typing in Vedic mathematics? Dmcq (talk) 13:43, 13 February 2012 (UTC)

Error in an image of the complex graph of the sine function

Not sure if this is the right place to mention it, but I thought I'd bring attention to the mistakes I just noted on File talk:Sine.png. The image is hosted on commons but I'm more familiar with how wikipedia works so I've brought attention to it here. Hopefully I've pointed this out in a useful place. 78.105.8.153 (talk) 23:15, 17 February 2012 (UTC)

Portal:Mathematics/Featured article template at MfD

Portal:Mathematics/Featured article template has been nominated for deletion. The nomination page is Wikipedia:Miscellany for deletion/Portal:Mathematics/Featured article template. Chris Cunningham (user:thumperward) (talk) 16:59, 23 February 2012 (UTC)