A New Proof of the Faithfulness of Brauer's Representation of Temperley-Lieb Algebras

The faithfulness of the orthogonal group case of Brauer's representation of the Brauer centralizer algebras restricted to their Temperley-Lieb subalgebras, which was established by Vaughan Jones, is here proved in a new, elementary and self-contained, manner.Comment: 10 pages, minor correction

Gamma-ray bursts: a Centauro's cry?

A new candidate for the gamma-ray bursts central engine is proposed: if in some energetic cosmic event a macroscopic amount of bubbles of the disoriented chiral condensate can be formed, then their subsequent decays will produce a relativistic fireball without the baryon loading problem. The neutron star to strange star transition is considered as a candidate example of such cosmic event.Comment: 12 pages, LaTeX, somewhat modified, references adde

Thomas rotation and Mocanu paradox -- not at all paradoxical

Non-commutativity of the Einstein velocity addition, in case of non-collinear velocities, seemingly gives rise to a conflict with reciprocity principle. However, Thomas rotation comes at a rescue and the paradox is avoided. It is shown that such a resolution of the so called Mocanu paradox is completely natural from the point of view of basic premises of special relativity.Comment: 6 pages, 3 figures, revtex

Comment on the sums S(n)=∑k=−∞∞1(4k+1)nS(n)=\sum\limits_{k=-\infty}^\infty \frac{1}{(4k+1)^n}

This is a comment on the papers N. D. Elkies, Amer. Math. Monthly 110 (2003), 561-573 and Cvijovic and J. Klinowski, J. Comput. Appl. Math. 142 (2002), 435-439. We provide an explicit expression for the kernel of the integral operator introduced in the first paper. This explicit expression considerably simplifies the calculation of S(n) and enables a simple derivation of Cvijovic and Klinowski's integral representation for $\zeta(2n+1)$.Comment: 11 pages, to be published in Georgian Mathematical Journal. arXiv:1003.3602 is more extended version of this short not

Maxwell's demon through the looking glass

Mechanical Maxwell's demons, such as Smoluchowski's trapdoor and Feynman's ratchet and pawl need external energy source to operate. If you cease to feed a demon the Second Law of thermodynamics will quickly stop its operation. Nevertheless, if the parity is an unbroken symmetry of nature, it may happen that a small modification leads to demons which do not need feeding. Such demons can act like perpetuum mobiles of the second kind: extract heat energy from only one reservoir, use it to do work and be isolated from the rest of ordinary world. Yet the Second Law is not violated because the demons pay their entropy cost in the hidden (mirror) sector of the world by emitting mirror photons.Comment: 28 pages, 3 figures, revtex

TeV scale gravity, mirror universe, and ... dinosaurs

This is somewhat extended version of the talk given at the Gran Sasso Summer Institute: Massive Neutrinos in Physics and Astrophysics. It describes general ideas about mirror world, extra spatial dimensions and dinosaur extinction. Some suggestions are made how these seemingly different things can be related to each other.Comment: 36 pages, 6 figures, presented at the Gran Sasso Summer Institute: Massive Neutrinos in Physics and Astrophysics, 13-24 September, 1999. New references added and some misprints corrected. To be published in Acta Phys. Polonic

Pionium in the elementary particle decays

Some atomic decays of elementary particles with pionium ($\pi^+\pi^-$-dimesoatom) in the final state are considered. Only for K-meson atomic decays are the corresponding branching ratios big enough to make their experimental study realistic. The $O(\alpha)$ order corrections to the lifetime of pionium are also calculated.Comment: 12 pages, to appear in Pis'ma Zh. Eks. Teor. Fiz. 60(1994),67

SO(8) Colour as possible origin of generations

A possible connection between the existence of three quark-lepton generations and the triality property of SO(8) group (the equality between 8-dimensional vectors and spinors) is investigated.Comment: 14 pages, 5 figures is now included in the electronic version (this is the only reason for the replacement), text not changed (except correcting some small typos

SETI and muon collider

Intense neutrino beams that accompany muon colliders can be used for interstellar communications. The presence of multi-TeV extraterrestrial muon collider at several light-years distance can be detected after one year run of IceCube type neutrino telescopes, if the neutrino beam is directed towards the Earth. This opens a new avenue in SETI: search for extraterrestrial muon colliders.Comment: 3 pages, ReVTeX

Citations and the Zipf-Mandelbrot's law

A curious observation was made that the rank statistics of scientific citation numbers follows Zipf-Mandelbrot's law. The same pow-like behavior is exhibited by some simple random citation models. The observed regularity indicates not so much the peculiar character of the underlying (complex) process, but more likely, than it is usually assumed, its more stochastic nature.Comment: 20 pages, 10 figures, important reference and note were adde