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RESEARCH

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results that I'd like to share

The results from my PhD and later work on the coefficients of fractional
parentage (CFPs) have been summarized in a paper published in the International
Journal of Quantum Chemistry, © John Wiley & Sons, Inc., in 1994. I
consider that the ideas by Julius Kaniauskas, when materialized, have appeared
to be quite powerful in revealing the coherent picture of what the CFPs
in the second quantization are. Unfortunately, the paper is not available
on the Web yet (year 1994 isn't accessible from Int.J.Quant.Chem.
), and the published version contains quite many irritating misprints in
the mathematical expressions (partly my fault: I haven't been able to correct
the proofs, but to make matters worse, I haven't ever submitted an errata).
To remedy this situation, I take a freedom as an author of the work to
offer the double-checked version here: CFP_paper.ps
. The second quantization "CFPs", their properties and generalizations,
the "CFPs"-like expansions of the many-fermion wave functions of coupled
momenta in the second quantization representation are all there. Enjoy!
Since 1996 I have been guided by Professor John Hertz of NORDITA in
modeling neural networks. I have collaborated with Thomas Z. Lauritzen,
Andrea Fazzini and Sergio Solinas in Professor's laboratory during my several
stays at NORDITA. The problem that we have investigated is the emergence
of spontaneous asynchronous chaotic activity in neural networks comprising
populations of excitatory and inhibitory neurons. And we have tried to
model this activity via the computer simulations of networks consisting
of "simple neurons" (with the key parameters chosen to be biologically
plausible). Specifically, I have developed an *ifnet* C++ code for
simulating the network of "integrate & fire" leaky neurons. Some of
our results have been presented in the Society for Neuroscience (1999)
meeting poster SN1999.ps.

In 2000, professor Romualdas Karazija sugggested to write a paper on
the application of the particle-hole pair approach to explain some pecularities
of spectra of free atoms and ions (original idea by J.Kaniauskas, again).
The key idea is that the creation or annihilation of the "electric dipole"-coupled
vacancy-electron pairs provide the main contribution to many observed emission,
photoexcitation and Auger spectra. In other words, the eigenfunctions of
the excited atoms are almost the eigenfunctions of the number of such vacancy-electron
pairs, too. We succeeded in relating the experimentally known concentration
of the strongest transitions on the high-energy side of some emission,
photoexcitation and Auger spectra of atoms to the existence of a formal
additional selection rule for the number of these vacancy-electron pairs.
The paper "Additional selection rule for some emission, photoexcitation
and Auger spectra" has appeared in J. Phys. B: At. Mol. Opt. Phys., 2001,
V. 34, No. 23, L741-L747, and is available at http://xxx.lanl.gov/abs/physics/0109006.

Andrius Bernotas
Institute of Theoretical Physics and Astronomy
A. Goštauto 12, 2600 Vilnius, Lithuania