Abstract. Fluid (or Hybrid) Petri Nets are Petri net based models with two classes of places: discrete places that carry a natural number of distinct objects (tokens), and fluid places that hold a positive amount of fluid, represented by a real number. With respect to previous formulations, the FSPN model presented in this paper, is augmented with a new primitive, called flush-out arc. A flush-out arc connects a fluid place to a timed transition, and has the effect of instantaneously emptying the fluid place when the transition fires. The paper discusses the modeling power of the augmented formalism, and shows how the dynamics of the underlying stochastic process can be analytically described by a set of integro-differential equations. A procedure is presented to automatically derive the solution equations from the model specifications. The whole methodology is illustrated by means of various examples.

We examine the electrostatic properties of exceptional and regular zeros of X m -Laguerre and X m -Jacobi polynomials. Since there is a close connection between the electrostatic properties of the zeros and the stability of interpolation on the system of zeros, we can deduce an Egerváry-Turán type result as well. The limit of the energy on the regular zeros is also investigated.

Computing asymptotics of the recurrence coefficients of X1-Jacobi polynomials we investigate the limit of Christoffel function. We also study the relation between the normalized counting measure based on the zeros of the modified average characteristic polynomial and the Christoffel function in limit. The proofs of corresponding theorems with respect to ordinary orthogonal polynomials are based on the three-term recurrence relation. The main point is that exceptional orthogonal polynomials possess at least five-term formulae and so the Christoffel-Darboux formula also fails. It seems that these difficulties can be handled in combinatorial way.2010 Mathematics Subject Classification. 33C47,33C45.

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We give the connections among the Fekete sets, the zeros of orthogonal polynomials, 1(w)-normal point systems, and the nodes of a stable and most economical interpolatory process via the Fejér contants. Finally the convergence of a weighted Grünwald interpolation is proved.