The Abdus Salam International Centre for Theoretical Physics Yang-baxter Equation on Two-dimensional Lattice and Some Infinite Dimensional Algebras

THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS A q-DEFORMATION OF VIRASORO AND U(1) KAC-MOODY ALGEBRAS WITH HOPF STRUCTURE

Using a general formalism of a q-deformation of an arbitrary Lie algebra, new kinds of qdeformed centerless Virasoro and U(1) Kac-Moody algebras are found. This q-deformation is associated to an R-matrix of unit square satisfying the quantum Yang-Baxter equation and allows a nontrivial Hopf structure. The central extension is also incorporated in this formalism. MIRAMARE { TRIESTE August 1998 J...

United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS A CLASSIFICATION OF TWO-DIMENSIONAL HYPOREDUCTIVE TRIPLE ALGEBRAS

Two-dimensional hyporeductive triple algebras (h.t.a) are investigated. Using the K. Yamaguti's approach for the classification of two-dimensional Lie triple systems (L.t.s), a classification of two-dimensional h.t.a is suggested. MIRAMARE TRIESTE May 1998 Regular Associate of the ICTP. Fax: (229)212525

The Abdus Salam International Centre for Theoretical Physics Higher Dimensional Complex Kleinian Groups

New Integrable Lattice Models From Fuss-Catalan Algebras

We construct new hyperbolic solutions of the Yang-Baxter equation, using the Fuss-Catalan algebras, a set of multi-colored versions of the Temperley-Lieb algebra, recently introduced by Bisch and Jones. These lead to new two-dimensional integrable lattice models, describing dense gases of colored loops.

Dosimetric Evaluation of Dose calculation algorithms of Monaco Treatment Planning System in the heterogeneities area

Introduction: In radiation therapy, the accuracy of dose calculations by a treatment planning system (TPS) is important to achieve tumor control and to spare normal tissue. Treatment planning system calculations in the heterogeneous situation may present significant inaccuracies. In this study, three different dose calculation algorithms, pencil beam (PB), collapsed cone (CC), ...