Drinfeld twists and symmetric Bethe vectors of supersymmetric fermion models

We construct the Drinfeld twists ( factorizing F-matrices) of the gl(m-n)-invariant fermion model. Completely symmetric representation of the pseudo-particle creation operators of the model are obtained in the basis provided by the F-matrix ( the F-basis). We resolve the hierarchy of the nested Bethe vectors in the F-basis for the gl(m-n) supersymmetric model.

Higher order Painleve equations and their symmetries via reductions of a class of integrable models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Gravitational interactions of integrable models

We couple non-linear sigma-models to Liouville gravity, showing that integrability properties of symmetric space models still hold for the matter sector. Using similar arguments for the fermionic counterpart, namely Gross-Neveu-type models, we verify that such conclusions must also hold for them, as recently suggested.

Soliton spectrum of integrable models with local symmetries

The soliton spectrum (massive and massless) of a family of integrable models with local U(1) and U(1) ⊗U(1) symmetries is studied. These models represent relevant integrable deformations of SL(2,ℝ) ⊗U(1) n-1-WZW and SL(2,ℝ) ⊗ SL(2,ℝ) ⊗U(1) n-2-WZW models. Their massless solitons appear as specific topological solutions of the U(1)(or U(1) ⊗ U(1)-) CFTs. The nonconformal analog of the GKO-coset formula is derived and used in the construction of the composite massive solitons of the ungauged integrable models. © SISSA/ISAS 2002.

Monoidal categories for the physics of integrable models

Scopo di questa tesi é di evidenziare le connessioni tra le categorie monoidali, l'equazione di Yang-Baxter e l’integrabilità di alcuni modelli. Oggetto prinacipale del nostro lavoro é stato il monoide di Frobenius e come sia connesso alle C∗-algebre. In questo contesto la totalità delle dimostrazioni sfruttano la strumentazione dell'algebra diagrammatica. Nel corso del lavoro di tesi sono state riprodotte tali dimostrazioni tramite il più familiare linguaggio dell’algebra multilineare allo scopo di rendere più fruibili questi risultati ad un raggio più ampio di potenziali lettori.

Density profiles in the raise and peel model with and without a wall; physics and combinatorics

We consider the raise and peel model of a one-dimensional fluctuating interface in the presence of an attractive wall. The model can also describe a pair annihilation process in disordered unquenched media with a source at one end of the system. For the stationary states, several density profiles are studied using Monte Carlo simulations. We point out a deep connection between some profiles seen in the presence of the wall and in its absence. Our results are discussed in the context of conformal invariance ( c = 0 theory). We discover some unexpected values for the critical exponents, which are obtained using combinatorial methods. We have solved known ( Pascal`s hexagon) and new (split-hexagon) bilinear recurrence relations. The solutions of these equations are interesting in their own right since they give information on certain classes of alternating sign matrices.

Stability of Growth Models with Generalised Lag Structures

This paper considers the lag structures of dynamic models in economics, arguing that the standard approach is too simple to capture the complexity of actual lag structures arising, for example, from production and investment decisions. It is argued that recent (1990s) developments in the the theory of functional differential equations provide a means to analyse models with generalised lag structures. The stability and asymptotic stability of two growth models with generalised lag structures are analysed. The paper concludes with some speculative discussion of time-varying parameters.

Integrable Models: from Dynamical Solutions to String Theory

We review the status of integrable models from the point of view of their dynamics and integrability conditions. A few integrable models are discussed in detail. We comment on the use it is made of them in string theory. We also discuss the SO(6) symmetric Hamiltonian with SO(6) boundary. This work is especially prepared for the 70th anniversaries of Andr, Swieca (in memoriam) and Roland Koberle.

Solvable models of Bose-Einstein condensates: A new algebraic Bethe ansatz scheme

A new algebraic Bethe ansatz scheme is proposed to diagonalize classes of integrable models relevant to the description of Bose-Einstein condensation in dilute alkali gases. This is achieved by introducing the notion of Z-graded representations of the Yang-Baxter algebra. (C) 2003 American Institute of Physics.

T-duality of axial and vector dyonic integrable models

A general construction of affine nonabelian (NA)-Toda models in terms of the axial and vector gauged two loop WZNW model is discussed. They represent integrable perturbations of the conformal sigma -models (with tachyons included) describing (charged) black hole type string backgrounds. We study the off-critical T-duality between certain families of axial and vector type integrable models for the case of affine NA-Toda theories with one global U(1) symmetry. In particular we find the Lie algebraic condition defining a subclass of T-selfdual torsionless NA-Toda models and their zero curvature representation. (C) 2001 Academic Press.

A class of mixed integrable models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Periodic orbits of integrable birational maps on the plane: blending dynamics and algebraic geometry, the Lyness' case

Contingut del Pòster presentat al congrés New Trends in Dynamical Systems

Automated formulation of optimisation models for steel beam structures

Over 70% of the total costs of an end product are consequences of decisions that are made during the design process. A search for optimal cross-sections will often have only a marginal effect on the amount of material used if the geometry of a structure is fixed and if the cross-sectional characteristics of its elements are property designed by conventional methods. In recent years, optimalgeometry has become a central area of research in the automated design of structures. It is generally accepted that no single optimisation algorithm is suitable for all engineering design problems. An appropriate algorithm, therefore, mustbe selected individually for each optimisation situation. Modelling is the mosttime consuming phase in the optimisation of steel and metal structures. In thisresearch, the goal was to develop a method and computer program, which reduces the modelling and optimisation time for structural design. The program needed anoptimisation algorithm that is suitable for various engineering design problems. Because Finite Element modelling is commonly used in the design of steel and metal structures, the interaction between a finite element tool and optimisation tool needed a practical solution. The developed method and computer programs were tested with standard optimisation tests and practical design optimisation cases. Three generations of computer programs are developed. The programs combine anoptimisation problem modelling tool and FE-modelling program using three alternate methdos. The modelling and optimisation was demonstrated in the design of a new boom construction and steel structures of flat and ridge roofs. This thesis demonstrates that the most time consuming modelling time is significantly reduced. Modelling errors are reduced and the results are more reliable. A new selection rule for the evolution algorithm, which eliminates the need for constraint weight factors is tested with optimisation cases of the steel structures that include hundreds of constraints. It is seen that the tested algorithm can be used nearly as a black box without parameter settings and penalty factors of the constraints.

Many valued algebraic structures as measures of comparison

This thesis studies the properties and usability of operators called t-norms, t-conorms, uninorms, as well as many valued implications and equivalences. Into these operators, weights and a generalized mean are embedded for aggregation, and they are used for comparison tasks and for this reason they are referred to as comparison measures. The thesis illustrates how these operators can be weighted with a differential evolution and aggregated with a generalized mean, and the kinds of measures of comparison that can be achieved from this procedure. New operators suitable for comparison measures are suggested. These operators are combination measures based on the use of t-norms and t-conorms, the generalized 3_-uninorm and pseudo equivalence measures based on S-type implications. The empirical part of this thesis demonstrates how these new comparison measures work in the field of classification, for example, in the classification of medical data. The second application area is from the field of sports medicine and it represents an expert system for defining an athlete's aerobic and anaerobic thresholds. The core of this thesis offers definitions for comparison measures and illustrates that there is no actual difference in the results achieved in comparison tasks, by the use of comparison measures based on distance, versus comparison measures based on many valued logical structures. The approach has been highly practical in this thesis and all usage of the measures has been validated mainly by practical testing. In general, many different types of operators suitable for comparison tasks have been presented in fuzzy logic literature and there has been little or no experimental work with these operators.