If I write my thoughtd in Polymath style (with all negative results, ideas, etc.) it could help me to organize my own thoughts (even if nobody other helps me). Could it really help me to organize my thoughts?

]]>However I am not sure if this makes much sense, because only people who have already read my book can reasonably participate in my research. So I don’t expect that many people will come in nearby time.

I ask your advice whether it is worth my time to attempt to set several Polymath-like projects there.

]]>By “all” I mean all math what could be possibly collaborated.

One way to do this is to use PlanetMath.org. Or maybe we should use Polymath wiki?

I ask for this because I would like to receive help from the community for some my conjectures and other my research projects. My projects do NOT suit for polymath project because they require reading my book (freely available) first (most of them require the book to understand the terms and maybe some don’t require it but would be probably really easier for a person who have read my book).

We just need a venue where we would collect links to all math research projects in the middle which somebody bothers to post online.

Please discuss. What we need: a full collaboration wiki site where all such collaborations would be discussed or just a list of links?

]]>I realize that this would have to involve new mathematics formula conventions since it has been proven that conventional formulation can’t avoid this? ]]>

https://bitbucket.org/portonv/algebraic-general-topology

http://www.mathematics21.org/algebraic-general-topology.html

I’ve recently uploaded my book LaTeX source to a Git hosting, so it is easy to edit it collaboratively.

One example problem is whether my categories Fcd and Rld (extensions of the well known category Top) are cartesian closed. ]]>

The problem is as follows:

$\displaystyle\min_{V}$ trace(**$V^TH^T\Phi HV$**)$\\$ s.t. $V^TV=I_d$ when $H$ is some arbitrary matrix of size $N \times M$, full column rank matrix, $V$ is a $M \times d$ matrix and $\Phi$ is $N \times N $ symmetric and positive semidefinite matrix.

When $H$ is known, the solution is given by the eigenvectors corresponding to $d$ minimum eigenvalues of $ H^T\Phi H$.

Are there any ways or techniques or ideas already solved on this in the absence of $H$? The problem may sound simple to some of you but I am sorry about that.

Thank you for your suggestions and information about the existing techniques.

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