On identification in fuzzy systems and its applications in control problems

The problem of identification in fuzzy systems described by the use of fuzzy equation is considered. The identification method and its performance index is also presented. The formal procedure of the identification algorithm is illustrated by means of a numerical example. The possibility of using the proposed algorithm for the solution of a control problem is given as well.     

Sur l’adhérence d’un ensemble partiellement semi-algébrique

Sans résumé dédié à René Thom à l’occasion de son soixante-cinquième anniversaire.     

All possible generators of supersymmetries of the S-matrix

A generator of a symmetry or supersymmetry of the S-matrix has to have three simple properties (see sect. 2). Starting from these properties one can give a complete analysis of the possible structure of the pseudo Lie algebra of these generators. In a theory with non-vanishing masses one finds that the only extension of previously known relations is the possible appearance of “central charges” as anticommutators of Fermi charges. In the massless case (disregarding infrared problems and symmetry breaking) the Fermi charges may generate the conformal group together with a unitary internal symmetry group.     

Central charges and Lorentz and internal symmetries in massive supersymmetric quantum field theory

The properties of central charges in the framework of the massive supersymmetric quantum field theory related to internal symmetries, Lorentz covariance and locality of the fields are investigated. It is shown that in the presence of z central charges the largest semisimple part of the internal symmetry algebra is a direct sum of z compact symplectic group algebras and possibly an additional term representing the unimodular unitary group algebra. Next it is shown that 4j ? N + K, where j is the highest spin value of the underlying fields, N is the number of spinorial charges and K the number of these spinorial charges which are not linked to other spinorial charges by a central charge. It is further demonstrated that, in general, the central charge can not be redefined in such a way that it is at the same time real and preserves the locality principle. The discussion of the obtained results concludes the paper.     

Dispersion of the multiplicity distribution in hadron-nucleus collisions

It is argued that the measurements of the dispersion of the multiplicity distribution in hadron-nucleus collisions favour the processes of particle production in a sequence of collisions of the incident hadron with target nucleons. On the other hand, generation of particles on groups of nucleons treated as single units leads to large discrepancies.     

Symmetries induced by conserved vector currents in the theory of a scalar field

Let us consider a quantum theory of one scalar, real, local, Poincaré covariant fieldA(x) with the restricted spectrum condition (massive one particle states and a unique vacuum). The asymptotic fieldsA _{in out} (x) are assumed to be irreducible. Our conjecture is that under some technical assumptions the charge of every real, hermitean, locally conserved, Poincaré covariant quantum (pseudo) vector fieldj (x) relatively local toA(x), appearing in this theory-vanishes. This means that in a theory of one scalar, real field with a massive particle one can not expect to get symmetry groups induced by conserved (pseudo) vector currents, only by global, selfadjoint, Poincaré invariant generators.Our arguments can be easily extended to a theory of one complex scalar field, in this case the only symmetry transformation induced by a current can be the gauge transformation.We prove also that under very weak assumptions two fields related to each other by a unitary (or similarity) transformation are equal barring some patological cases.     

Local composition in binary mixtures of Lennard-Jones fluids with differing sizes of components

Three Lennard-Jones binary liquid mixture systems obeying Lorentz-Berthelot rules, but having differing component sizes and energy parameters, have been used to calculate the local fractions of the two components around each type of central particle over the entire composition range from molecular-dynamics data. It is found that well-defined local fractions can be determined even in the case where the size difference between the particles is large. The results obtained are compared with values predicted by the Wilson and NRTL equations. It is confirmed that the NRTL equation gives satisfactory agreement only in the case of mixtures of components having the same size parameters. A new correlation is proposed by a modification of the NRTL equation. This correlation can predict reasonably well local-fraction data for all the Lennard-Jones liquid mixtures studied so far.     

Randomly flashing diffusion: Asymptotic properties

The theory of abstract Markov operators and semigroups is applied for studying asymptotics of a randomly flashing diffusion process. The probability distribution of the process is determined by a set of two partial differential equations and sufficient conditions for the existence of a stationary solution of the equations are formulated, and convergence of solutions to the stationary solution is proved.