on integration of fuzzy mappings abstract in this paper we introduce the concept of an integral of a fuzzy mapping this generalises the integral introduced by matloka 10 and also extends riemann stieltjes integral over a closed interval to fuzzy mappings

approximating the solution of nonlinear hammerstein fuzzy integral equations abstract in this paper we prove the convergence of the method of successive approximations used to approximate the solution of nonlinear hammerstein fuzzy integral equations and define the notion of numerical stability of the algorithm with respect to the choice of the first iteration this numerical stability is proved and finally some numerical experiments confirm the theoretical results and illustrate the accuracy of the method

reinjection probability density in type iii intermittency a method to obtain the reinjection probability density rpd for systems showing type iii intermittency phenomenon is presented the method emerges as a natural extension of a recent procedure we established to derive the rpd for type ii intermittency a new two parameter class of reinjection probability densities is presented to describe a broad class of type iii intermittency maps our rpd expression also provides information about the lower bound of the reinjection lbr the new characteristic relation e depends on the lbr and it has a critical exponent such that 1 0 5 the corresponding analytical duration probability densities are also derived in agreement with the numerical computation the main classical results can be extracted from our rpd as particular cases

error estimation in the approximation of the solution of nonlinear fuzzy fredholm integral equations using a fixed point technique the sequence of successive approximations and a recent quadrature formula for fuzzy number valued functions it is constructed a numerical method for the solution of nonlinear fuzzy fredholm integral equations moreover the error estimate of the method and a criterion to stop the corresponding algorithm are given

routes to complete synchronization via phase synchronization in coupled nonidentical chaotic oscillators we study the transition route to complete synchronization through phase synchonization in generic coupled nonidentical chaotic oscillators through numerical studies two routes are found i e one via lag synchronization the other via the intermittent chaotic burst state without lag synchronization we claim that these two routes are universal as evidence we analyze several examples on the basis of the conventional theory of intermittency in the presence of noise

generalized phase synchronization in unidirectionally coupled chaotic oscillators we investigate phase synchronization between two identical or detuned response oscillators coupled to a slightly different drive oscillator our result is that phase synchronization can occur between response oscillators when they are driven by correlated but not identical inputs from the drive oscillator we call this phenomenon generalized phase synchronization and clarify its characteristics using lyapunov exponents and phase difference plots

numerical solution of nonlinear fuzzy fredholm integral equations using iterative method in this paper we propose an iterative procedure based on quadrature formula to solve nonlinear fuzzy fredholm integral equations of the second kind moreover the error estimation of the proposed method in terms of uniform and partial modulus of continuity is given finally illustrative examples are included in order to demonstrate the accuracy and the convergence of the proposed method

obstructions and hypersurface sections minimally elliptic singularities we study the obstruction space t 2 for minimally elliptic surface singularities we apply the main lemma of our previous paper 3 which relates t 2 to deformations of hypersurface sections to use this we classify general hypersurface sections of minimally elliptic singularities as in the rational singularity case there is a simple formula for the minimal number of generators for t 2 as a module over the local ring this number is in many cases e g for cusps of hilbert modular surfaces equal to the vector space dimension of t 2

a calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves any graph manifold can be obtained by plumbing according to some plumbing graph i a calculus for plumbing which includes normal forms for such graphs is developed this is applied to answer several questions about the topology of normal complex surface singularities and analytic families of complex curves for instance it is shown that the topology of the minimal resolution of a normal complex surface singularity is determined by the link of the singularity and even by its fundamental group if the singularity is not a cyclic quotient singularity or a cusp singularity in this paper we describe a calculus for plumbed manifolds which lets one algorithmically determine when the oriented 3 manifolds m tx and a ftj ob tained by plumbing according to two graphs tx and t2 are homeomorphic 3 mani folds are oriented 3 manifolds throughout this paper and homeomorphisms of 3 manifolds are orientation preserving we then apply the calculus to answer several questions about the topology of isolated singularities of complex surfaces and one parameter families of complex curves these results are described below since the class of 3 manifolds obtainable by plumbing is precisely the class of graph manifolds which were classified with minor exceptions by waldhausen 24 a calculus for plumbing is in some sense implicit in waldhausen s work moreover it has been known for some time that the calculus can be put in a form like the one given here but the details have never appeared in the literature a related calculus for plumbing trees has been worked by bonahon and siebenmann 1 in order to classify their algebraic knots we describe the calculus in greater generality than is needed for the present applications since this involves minimal extra work and the calculus is needed elsewhere 4 14 and 15 in particular in an appendix we describe two generalizations of it the calculus consists of a collection of moves one can do to a plumbing graph t without altering the plumbed manifold m t to see these moves are sufficient we describe how they can be used to reduce any graph to a normal form which is

elementary fuzzy calculus abstract in 2 dubois and prade introduced the notion of fuzzy numbers and defined the basic operations of addition subtraction multiplication and division a slightly modified definition of fuzzy numbers was presented in 4 and in that paper a metric was defined for this family of fuzzy sets another less restrictive definition of fuzzy numbers can be found in 1 in the present paper we consider fuzzy numbers from a somewhat different perspective basically we shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in 4 we will define differentiation and integration of fuzzy valued functions in ways that parallel closely the corresponding definitions for real differentiation and integration

length distribution of laminar phases for type i intermittency in the presence of noise we consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type i intermittency and random dynamics we analytically deduce the laws for the distribution of the laminar phases with the law for the mean length of the laminar phases versus the critical parameter deduced earlier w h kye and c m kim phys rev e 62 6304 2000 being the corollary fact of the developed theory we find a very good agreement between the theoretical predictions and the data obtained by means of both the experimental study and numerical calculations we discuss also how this mechanism is expected to take place in other relevant physical circumstances

characteristic relations of type i intermittency in the presence of noise near the point of tangent bifurcation the scaling properties of the laminar length of type i intermittency are investigated in the presence of noise based on analytic and numerical studies we show that the scaling relation of the laminar length is dramatically deformed from 1 sqrt ensuremath epsilon for ensuremath epsilon g0 to mathrm exp 1 d ensuremath epsilon 3 2 for ensuremath epsilon l0 as ensuremath epsilon passes the bifurcation point ensuremath epsilon 0 the results explain why two coupled r ossler oscillators exhibit deformation of the scaling relation of the synchronous length in the nearly synchronous regime

intermittent phase synchronization of coupled spatiotemporal chaotic systems phase synchronization is studied with a discrete system formed by two coupled map lattices in which phases are measured in two dimensional vectors simulation results show that by imposing external coupling between the two lattices phase synchronization can be found in all two dimensional phase planes between them when the system is approaching the phase synchronizing state unstable phase synchronization is observed this is referred to as intermittent phase synchronization that appears when the trajectories on two interacting phase planes have opposite directions of rotation but with only a small phase difference the intermittent phase synchronization could also be observed in coupled autonomous systems with diffusive attractors although their phase concepts are inconsistent our results show that the intermittent phase synchronization of both discrete and autonomous systems relates to the diffusion or the complexity of the attractors

numerical solutions of the nonlinear fuzzy hammerstein volterra delay integral equations in this paper an iterative numerical method that solves nonlinear fuzzy hammerstein volterra integral equations with constant delay is developed by using the error estimates a practical stopping criterion of the algorithm is obtained the convergence and the numerical stability of the method is proved and its accuracy is illustrated on three numerical examples the study of this integral equation is important because it has as a particular case the fuzzy variant of a mathematical model from epidemiology

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

two computational methods for solving linear fredholm fuzzy integral equation of the second kind in this paper we present two methods which will exploit hybrid legendre and block pulse functions and legendre wavelets as bases for l 2 0 1 x 0 1 to find an approximate solution for a system of linear fredholm integral equation of the second kind with two variables we will apply our methods for an applied example linear fredholm fuzzy integral equation of the second kind m friedman ma ming a kandel numerical solutions of fuzzy differential and integral equations fuzzy sets and systems 106 1999 35 48

numerical solution of linear fredholm fuzzy integral equations of the second kind by adomian method using parametric form of fuzzy numbers we convert a linear fuzzy fredholm integral equation of the second kind to a linear system of integral equations of the second kind in crisp case we use adomian method and find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the linear fuzzy fredholm integral equation of the second kind we apply the method to some examples

zero lyapunov exponent in the vicinity of the saddle node bifurcation point in the presence of noise we consider a behavior of the zero lyapunov exponent in the vicinity of the bifurcation point that occurs as the result of the interplay between dynamical mechanisms and random dynamics we analytically deduce the laws for the dependence of this lyapunov exponent on the control parameter both above and below the bifurcation point the developed theory is applicable both to the systems with the random force and to the deterministic chaotic oscillators we find an excellent agreement between the theoretical predictions and the data obtained by means of numerical calculations we also discuss how the revealed regularities are expected to take place in other relevant physical circumstances

a note on fuzzy integral equations in this paper existence theorems for certain volterra integral equations and fredholm integral equation for the fuzzy set valued mappings are obtained

on the existence and uniqueness of solutions of fuzzy volterra fredholm integral equations abstract in this paper we study the problem of existence and uniqueness of solutions of volterra fredholm integral equation for the fuzzy set valued mappings