Structure Constants of the Fractional Supersymmetry Chiral Algebras

The fractional supersymmetry chiral algebras in two-dimensional conformal field theory are extended Virasoro algebras with fractional spin currents. We show that associativity and closure of these algebras determines their structure constants in the case that the Virasoro algebra is extended by precisely one current. We compute the structure constants of these algebras explicitly and we show that correlators of the currents satisfy non-Abelian braiding relations.Comment: 44 page

Quantum Dynamical Rˇ\check{R}- Matrix with Spectral Parameter from Fusion

A quantum dynamical $\check{R}$-matrix with spectral parameter is constructed by fusion procedure. This spin-1 $\check{R}$-matrix is connected with Lie algebra $so(3)$ and does not satisfy the condition of translation invariance.Comment: 6 pages, LaTeX, no figure

Unusual magnetic properties of the low-dimensional quantum magnet Na2V3O7

We report the results of low-temperature measurements of the specific heat Cp(T), ac susceptibility chi(T) and 23Na nuclear magnetic resonance NMR of Na2V3O7. At liquid He temperatures Cp(T)/T exhibits broad field-dependent maxima, which shift to higher temperatures upon increasing the applied magnetic field H. Below 1.5 K the ac magnetic susceptibility chi(T) follows a Curie-Weiss law and exhibits a cusp at 0.086 mK which indicates a phase transition at very low temperatures. These results support the previous conjecture that Na2V3O7 is close to a quantum critical point (QCP) at mu_{0}H = 0 T. The entire data set, including results of measurements of the NMR spin-lattice relaxation 1/T1(T), reveals a complex magnetic behavior at low temperatures. We argue that it is due to a distribution of singlet-triplet energy gaps of dimerized V moments. The dimerization process evolves over a rather broad temperature range around and below 100 K. At the lowest temperatures the magnetic properties are dominated by the response of only a minor fraction of the V moments.Comment: 10.5 pages, 15 figures. Submitted to Phys. Rev.

Preheating in Supersymmetric Theories

We examine the particle production via preheating at the end of inflation in supersymmetric theories. The inflaton and matter scalars are now necessarily complex fields, and their relevant interactions are restricted by holomorphy. In general this leads to major changes both in the inflaton dynamics and in the efficiency of the preheating process. In addition, supersymmetric models generically contain multiple isolated vacua, raising the possibility of non-thermal production of dangerous topological defects. Because of these effects, the success of leptogenesis or WIMPZILLA production via preheating depends much more sensitively on the detailed parameters in the inflaton sector than previously thought.Comment: 24 pages, 3 figures; references adde

Fock space resolutions of the Virasoro highest weight modules with c<=1

We extend Felder's construction of Fock space resolutions for the Virasoro minimal models to all irreducible modules with $c\leq 1$. In particular, we provide resolutions for the representations corresponding to the boundary and exterior of the Kac table.Comment: 14 pages, revised versio

Knizhnik-Zamolodchikov equations and the Calogero-Sutherland-Moser integrable models with exchange terms

It is shown that from some solutions of generalized Knizhnik-Zamolodchikov equations one can construct eigenfunctions of the Calogero-Sutherland-Moser Hamiltonians with exchange terms, which are characterized by any given permutational symmetry under particle exchange. This generalizes some results previously derived by Matsuo and Cherednik for the ordinary Calogero-Sutherland-Moser Hamiltonians.Comment: 13 pages, LaTeX, no figures, to be published in J. Phys.

Strong Electron-Phonon Coupling in Superconducting MgB2_2: A Specific Heat Study

We report on measurements of the specific heat of the recently discovered superconductor MgB$_2$ in the temperature range between 3 and 220 K. Based on a modified Debye-Einstein model, we have achieved a rather accurate account of the lattice contribution to the specific heat, which allows us to separate the electronic contribution from the total measured specific heat. From our result for the electronic specific heat, we estimate the electron-phonon coupling constant $\lambda$ to be of the order of 2, significantly enhanced compared to common weak-coupling values $\leq 0.4$. Our data also indicate that the electronic specific heat in the superconducting state of MgB$_2$ can be accounted for by a conventional, s-wave type BCS-model.Comment: 4 pages, 4 figure

A novel algorithm for dynamic student profile adaptation based on learning styles

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.E-learning recommendation systems are used to enhance student performance and knowledge by providing tailor- made services based on the students’ preferences and learning styles, which are typically stored in student profiles. For such systems to remain effective, the profiles need to be able to adapt and reflect the students’ changing behaviour. In this paper, we introduce new algorithms that are designed to track student learning behaviour patterns, capture their learning styles, and maintain dynamic student profiles within a recommendation system (RS). This paper also proposes a new method to extract features that characterise student behaviour to identify students’ learning styles with respect to the Felder-Silverman learning style model (FSLSM). In order to test the efficiency of the proposed algorithm, we present a series of experiments that use a dataset of real students to demonstrate how our proposed algorithm can effectively model a dynamic student profile and adapt to different student learning behaviour. The results revealed that the students could effectively increase their learning efficiency and quality for the courses when the learning styles are identified, and proper recommendations are made by using our method