Entropy arising in quantum mechanics? Friday, Jan 14 2011

Recently I published a preprint on the possible information-theoretic foundation of relational quantum mechanics. In this paper I evaluate an entropy associated with a quantum mechanical system:

Is this entropy perhaps related to holographic theories of gravitation? I previously made a speculative attempt on that, but the interpretation of the entropy is still open.

 

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Is there an attractor in the fractional logistic equation? Saturday, Nov 13 2010

I recently published a paper entitiled “Numerical Chaos in a Fractional Order Logistic Map” in which I numerically hint that a fractional generalization of the famous logistic map exhibits chaos. The challenge is now to algebraically prove that there is a chaotic attractor for certain parameter values. This challenge I leave to you.

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How to create a Déjà vu? Wednesday, Mar 17 2010

The challenge put forth today is not really tangled with mathematics, rather a general scientifically interesting issue. Nevertheless the challange is:

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How to create a Déjà vu? Is there an “algorithm” or series of actions to produce this?

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A Déjà vu is the sensation of familiarity with something new, but without recollection of when or where this familiarity comes from, see wiki. Any proposal is welcome!

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A possible solution might be on the form:

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Think of something in the past, think of something possible in the future, think of you favourite color, and then viola! A Déjà vu appears.

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But as we, all matrix fans, know Déjà vu is not something created by the human herself, but rather an effect of that something has been changed in the code of the matrix .

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Is there a chaotic Zombie attractor? Wednesday, Feb 24 2010

In a recent paper researchers from Ottawa University created a model on the outbreak of Zombies. They considered three classes:

- Susceptible (S)

- Zombie (Z)

- Removed (R)

from which they created a three dimensional dynamical system for (S,Z,R) with a number of constants. Now here comes the challenge: Is there a chaotic attractor in the parameter space of these equations? A numerical verification will do fine as proof here (unless you want to prove it for real).

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The clock with infinite speed Thursday, Jan 21 2010

Imagine a regular clock with discrete time steps (eg seconds, minutes, hours). If this clock is broken, and thus stand still, then it is correct twice a day (due only twelve hours on it). If it happens to go forward with double the speed of a regular clock it will be correct four times a day. Now ponder, what happens if its rotational speed reaches infinity? How often is it correct then?

(A frence decimal clock dating back to the french revolution)

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What makes a dust attractor? Tuesday, Jan 5 2010

When cleaning the house one often detects that certain places attract more dust than others, for example under the bed, sofa etc. What is the primary mechanism for these “dust attractors”?

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Does the bystander always attract the smoke? Friday, Aug 14 2009

Conjecture. Is it true that the smoke from a charcoal grill or a person smoking tobacco

always attracts its bystander? Here we propose a conjecture for proving this using

gas/fluid dynamics. I would like to thank Johan Nilsson for suggesting this topic.

Conjecture. Is it true that a bystander to a charcoal grill always attracts the smoke? Here we propose a conjecture for proving this using gas/fluid dynamics. I would like to thank Johan Nilsson for suggesting this topic. Challenge number CH0908141

A generic example of turbulent fluid flows.

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An alternate version of Fermat’s Last Theorem Wednesday, Jun 24 2009

Conjecture. There exists no three integers a,b and c such that:

holds. Challenge number:

Conjecture. There exists no three integers a,b and c such that:

holds. Challenge number: CH0906231

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