A Quasi-Hopf algebra interpretation of quantum 3-j and 6-j symbols and difference equations

We consider the universal solution of the Gervais-Neveu-Felder equation in the ${\cal U}_q(sl_2)$ case. We show that it has a quasi-Hopf algebra interpretation. We also recall its relation to quantum 3-j and 6-j symbols. Finally, we use this solution to build a q-deformation of the trigonometric Lam\'e equation.Comment: 9 pages, 4 figure

Elliptic Gaudin models and elliptic KZ Equations

The Gaudin models based on the face-type elliptic quantum groups and the $XYZ$ Gaudin models are studied. The Gaudin model Hamiltonians are constructed and are diagonalized by using the algebraic Bethe ansatz method. The corresponding face-type Knizhnik-Zamolodchikov equations and their solutions are given.Comment: LaTex file 18 pages; Errors corrected and references adde

Non-equilibrium Goldstone phenomenon in tachyonic preheating

The dominance of the direct production of elementary Goldstone waves is demonstrated in tachyonic preheating by numerically determining the evolution of the dispersion relation, the equation of state and the kinetic power spectra for the angular degree of freedom of the complex matter field. The importance of the domain structure in the order parameter distribution for the quantitative understanding of the excitation mechanism is emphasized. Evidence is presented for the very early decoupling of the low-momentum Goldstone modes.Comment: 14 LaTeX pages, 5 figures, version published in Phys. Rev.

Considering sensing-intuitive dimension to exposition-exemplification in adaptive sequencing

Proceedings of the Second International Conference, AH 2002 Málaga, SpainThe final publication is available at Springer via http://dx.doi.org/10.1007/3-540-47952-X_83This paper shows a way of using sensing-intuitive dimension of learning styles of students in order to improve the efficiency of adaptive learning systems. Firstly, it introduces the procedure of extracting information about sensing-intuitive students from the Felder-Soloman ILS questionnaire. Then, it presents a mechanism of application of sensing-intuitive dimension to exposition-exemplification sequencing. The example used to explain the adaptation effects is taken from a chess course developed with TANGOW, Task-based Adaptive learNer Guidance On the Web.The Spanish Interdepartmental Commission of Science and Technology (CICYT) has sponsored this paper, project number TEL1999-0181 and project number TIC2001-0685-C02-01

On the Null Vectors in the Spectra of the 2D Integrable Hierarchies

We propose an alternative description of the spectrum of local fields in the classical limit of the integrable quantum field theories. It is close to similar constructions used in the geometrical treatment of W-gravities. Our approach provides a systematic way of deriving the null-vectors that appear in this construction. We present explicit results for the case of the A_1^{1}-(m)KdV and the A_2^{2}-(m)KdV hierarchies, different classical limits of 2D CFT's. In the former case our results coincide with the classical limit of the construction of Babelon, Bernard and Smirnov.Some hints about quantization and off-critical treatment are also given.Comment: 15 pages, LATEX file, to appear in Phys.Lett.