Fast transform decoding of nonsystematic Reed-Solomon codes

A Reed-Solomon (RS) code is considered to be a special case of a redundant residue polynomial (RRP) code, and a fast transform decoding algorithm to correct both errors and erasures is presented. This decoding scheme is an improvement of the decoding algorithm for the RRP code suggested by Shiozaki and Nishida, and can be realized readily on very large scale integration chips

Development and application of computer software techniques to human factors task data handling problems Final report, 21 Jun. 1965 - 21 Jun. 1966

Computer software techniques applied to human factors task data handling problem

Representations for Three-Body T-Matrix on Unphysical Sheets: Proofs

A proof is given for the explicit representations which have been formulated in the author's previous work (nucl-th/9505028) for the Faddeev components of three-body T-matrix continued analytically on unphysical sheets of the energy Riemann surface. Also, the analogous representations for analytical continuation of the three-body scattering matrices and resolvent are proved. An algorithm to search for the three-body resonances on the base of the Faddeev differential equations is discussed.Comment: 98 Kb; LaTeX; Journal-ref was added (the title changed in the journal

Representations for Three-Body T-Matrix on Unphysical Sheets

Explicit representations are formulated for the Faddeev components of three-body T-matrix continued analytically on unphysical sheets of the energy Riemann surface. According to the representations, the T-matrix on unphysical sheets is obviously expressed in terms of its components taken on the physical sheet only. The representations for T-matrix are used then to construct similar representations for analytical continuation of three-body scattering matrices and resolvent. Domains on unphysical sheets are described where the representations obtained can be applied.Comment: 123 Kb; LaTeX; Journal-ref was added (the title changed in the journal

Bose Einstein condensation on inhomogeneous amenable graphs

We investigate the Bose-Einstein Condensation on nonhomogeneous amenable networks for the model describing arrays of Josephson junctions. The resulting topological model, whose Hamiltonian is the pure hopping one given by the opposite of the adjacency operator, has also a mathematical interest in itself. We show that for the nonhomogeneous networks like the comb graphs, particles condensate in momentum and configuration space as well. In this case different properties of the network, of geometric and probabilistic nature, such as the volume growth, the shape of the ground state, and the transience, all play a role in the condensation phenomena. The situation is quite different for homogeneous networks where just one of these parameters, e.g. the volume growth, is enough to determine the appearance of the condensation.Comment: 43 pages, 12 figures, final versio

Is Weak Pseudo-Hermiticity Weaker than Pseudo-Hermiticity?

For a weakly pseudo-Hermitian linear operator, we give a spectral condition that ensures its pseudo-Hermiticity. This condition is always satisfied whenever the operator acts in a finite-dimensional Hilbert space. Hence weak pseudo-Hermiticity and pseudo-Hermiticity are equivalent in finite-dimensions. This equivalence extends to a much larger class of operators. Quantum systems whose Hamiltonian is selected from among these operators correspond to pseudo-Hermitian quantum systems possessing certain symmetries.Comment: published version, 10 page

An empirical study on the preferred size of the participant information sheet in research

Background: Informed consent is a requirement for all research. It is not, however, clear how much information is sufficient to make an informed decision about participation in research. Information on an online questionnaire about childhood development was provided through an unfolding electronic participant sheet in three levels of information. \ud Methods: 552 participants, who completed the web-based survey, accessed and spent time reading the participant information sheet (PIS) between July 2008 and November 2009. The information behaviour of the participants was investigated. The first level contained less information than might be found on a standard PIS, the second level corresponded to a standard PIS, and the third contained more information than on a standard PIS. The actual time spent on reading the information provided in three incremental levels and the participants' evaluation of the information were calculated. \ud Results: 77% of the participants chose to access the first level of information, whereas 12% accessed the first two levels, 6% accessed all three levels of information and 23% participated without accessing information. The most accessed levels of information were those that corresponded to the average reading times. \ud Conclusion: The brief information provided in the first level was sufficient for participants to make informed decisions, while a sizeable minority of the participants chose not to access any information at all. This study adds to the debate about how much information is required to make a decision about participation in research and the results may help inform the future development of information sheets by providing data on participants' actual needs when deciding about questionnaire surveys.\u

Weak commutation relations of unbounded operators and applications

Four possible definitions of the commutation relation [S,T]=\Id of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space \H where the operators act. Some consequences on the existence of eigenvectors of two number-like operators are derived and the partial O*-algebra generated by $S,T$ is studied. Some applications are also considered.Comment: In press in Journal of Mathematical Physic