a general theory of canonical induction formulae abstract so far there exist three independent constructions of two different canonical versions of brauer s induction theorem for complex characters due to v snaith p symonds and the author canonical in this context means functorial with respect to restrictions along group homomorphisms in this article we axiomatize the situation in which the above canonical induction formulae are constructed mackey functors and related structures arise in this way naturally as a convenient language this approach allows us to construct canonical induction formulae for arbitrary mackey functors in particular we obtain canonical induction formulae for the brauer character ring the group of projective characters the ring of trivial source modules and the ring of linear source modules in most cases it is not difficult to construct such formulae over the rational numbers a much more subtle question is whether the constructed formula comes from a canonical induction formula defined over the integers we give a sufficient condition in the general framework of mackey functors for a canonical induction formula to be integral as an application we show how canonical induction formulae allow the construction of functorial maps on representation rings in terms of functorial maps on subrings as for example the span of linear characters in the case of the canonical brauer induction formula this will be used in a subsequent article in the case of adams operations and chern classes

numerical solution of volterra integral and integro differential equations of convolution type by using operational matrices of piecewise constant orthogonal functions in this paper we use operational matrices of piecewise constant orthogonal functions on the interval 0 1 to solve volterra integral and integro differential equations of convolution type without solving any system we first obtain laplace transform of the problem and then we find numerical inversion of laplace transform by operational matrices numerical examples show that the approximate solutions have a good degree of accuracy

brief note on the variation of constants formula for fuzzy differential equations this note gives a theory of state transition matrices for linear systems of fuzzy differential equations this is used to give a fuzzy version of the classical variation of constants formula a simple example of a time independent control system is used to illustrate the methods while similar problems to the crisp case arise for time dependent systems in time independent cases the calculations are elementary solutions of eigenvalue eigenvector problems in particular for nonnegative or nonpositive matrices the problems at each level set can easily be solved in matlab to give the level sets of the fuzzy solution

representation of uncertain multichannel digital signal spaces and study of pattern recognition based on metrics and difference values on fuzzy n cell number spaces in this paper we discuss the problem of characterization for uncertain multichannel digital signal spaces propose using fuzzy n cell number space to represent uncertain n channel digital signal space and put forward a method of constructing such fuzzy n cell numbers we introduce two new metrics and concepts of certain types of difference values on fuzzy n cell number space and study their properties further based on the metrics or difference values appropriately defined we put forward an algorithmic version of pattern recognition in an imprecise or uncertain environment and we also give practical examples to show the application and rationality of the proposed techniques

a note on the embedding problem for multidimensional fuzzy number spaces this paper generalize the results in wu and zhang fuzzy sets and systems in press the embedding is extended from one dimensional to n dimensional case

open fuzzy cubature rule with application to nonlinear fuzzy volterra integral equations in two dimensions abstract in this paper we propose an open fuzzy cubature formula and as application we construct an iterative numerical method for solving nonlinear fuzzy volterra integral equations in two dimensions the convergence of the method is proved by providing the error estimate and it is tested on two numerical experiments

the s differentiability of a fuzzy valued mapping several approaches to define the differential of fuzzy valued mappings can be found in the literature in this paper we introduce a new concept of differential of a fuzzy valued mapping which is based on the notion of differential of the support function associated with such a mapping properties of the new concept as well as the relation between it and previous approaches are also analyzed in detail

fibred permutation sets and the idempotents and units of monomial burnside rings we study the units of monomial burnside rings and the idempotents of monomial burnside algebras introducing a tenduction map we realise the unit group and the torsion unit group as a mackey functor

embedding problem of fuzzy number space part ii abstract using a concrete structure into which we embed the fuzzy number space e1 several necessary and sufficient conditions of fuzzy set valued functions are given by means of abstract function theory

the periodic nature of the positive solutions of a nonlinear fuzzy max difference equation we investigate the periodic nature of the positive solutions of the fuzzy difference equation x n maxa 0x n k a 1x n m where k m are positive integers a 0 a 1 are positive fuzzy numbers and the initial values x i i d d 1 1 d max k m are positive fuzzy numbers in addition we give conditions so that the solutions of this equation are unbounded

embedding problem of noncompact fuzzy number space e abstract in this paper we use the embedding j wu and zhang from noncompact fuzzy number space e into the concrete frechet space c 0 1 c 0 1 to discuss some properties of the e valued functions such as measurability integrability etc

on the fuzzy difference equation x n 1 a x n x n m in this paper we study the existence the boundedness and the asymptotic behavior of the positive solutions of the fuzzy equation xn 1 a xn xn m n 0 1 where xn is a sequence of fuzzy numbers a is a fuzzy number and m 1 2

solution of a system of volterra integral equations of the first kind by adomian method in this article we consider linear and non linear systems of integral equations of the first kind the problem of existence and uniqueness are considered the adomian decomposition method is being used to solve these linear and non linear systems of volterra integral equations of the first kind some examples are prepared to show the efficiency and simplicity of the method

on differential equations with interactive fuzzy parameter via t norms abstract in this paper we study fuzzy differential equations with uncertain parameters modeled by interactive fuzzy numbers the interactivity is formalized with the help of upper semicontinuous t norms to obtain solutions to fuzzy differential equations we use two different approaches the first uses a family of differential inclusions while the second is the fuzzification of the deterministic problem using the zadeh extension principle we show that the solutions obtained by the two methods are equal interactivity among the parameters and variable of the problem are studies with respect two methods we show that a hierarchy in uncertainties of the solutions arises when we chose one of the basic t norm the minimum the t norm of the product the t norm of lukasiewicz and t norm of the drastic product to model the interaction between parameters finally to illustrate the concepts introduced in the paper we study the malthusian model with interactive parameters

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

simple modules over green biset functors we present three examples of green biset functors for which their simple modules can be parametrized these are particular cases of a conjecture by serge bouc classifying the simple modules over a green biset functor a that generalizes the classification of simple biset functors we also prove this conjecture under certain hypothesis for a

boundedness and asymptotic behavior of the solutions of a fuzzy difference equation in this paper we study the existence the uniqueness the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation xn 1 i 0kai xn ipi where k 1 2 ai i 0 1 k are positive fuzzy numbers pi i 0 1 k are positive constants and xi i k k 1 0 are positive fuzzy numbers

generalized differentiability of fuzzy valued functions in the present paper using novel generalizations of the hukuhara difference for fuzzy sets we introduce and study new generalized differentiability concepts for fuzzy valued functions several properties of the new concepts are investigated and they are compared to similar fuzzy differentiabilities finding connections between them characterization and relatively simple expressions are provided for the new derivatives

a continuous time dynamic fuzzy system ii fuzzy potentials abstract this paper is a sequel of yoshida 9 fuzzy potentials are introduced in a continuous time dynamic fuzzy system and a fuzzy relational differential equation is given to characterize the fuzzy potentials

existence and uniqueness for solutions to fuzzy stochastic differential equations driven by local martingales under the non lipschitzian condition abstract this paper makes a research into a class of fuzzy stochastic differential equations fsdes driven by a continuous local martingale under the non lipschitzian condition such equations can be useful in modelling of hybrid systems where the phenomena are subjected to two kinds of uncertainties randomness and fuzziness simultaneously the solutions of fsdes are the fuzzy stochastic processes and their uniqueness is considered to be in a strong sense thus the existence and uniqueness of solutions to fsdes under the non lipschitzian condition is first proven and the continuity of solutions to fsdes with respect to the initial data or the coefficients of the equations is investigated

initial and boundary value problems for fuzzy differential equations we prove a wintner type result for fuzzy ivps and a superlinear type result for fuzzy bvps both results rely on a generalized schauder theorem in metric spaces

the functor of complex characters of finite groups abstract we determine the structure of the fibered biset functor sending a finite group g to the complex vector space of complex valued class functions of g previously it is studied as a biset functor by bouc and as a c fibered biset functor by boltje and the second author in this paper we complete the study by considering proper non trivial subgroups of c as the fiber group as a corollary we obtain a previously known set of composition factors of the biset functor of p permutation modules

foncteurs d ensembles munis d une double action resume sommaire 1 introduction 2 notations generalites 3 ensembles munis d une double action 3 1 notations 3 2 formule de mackey 3 3 decomposition d un morphisme 3 4 sous categories 3 4 1 ensembles p q libres 3 4 2 groupes reductifs 4 foncteurs simples 5 une theorie de vortex et de source 6 une seconde theorie de vortex et source 7 le foncteur de burnside 7 1 un homomorphisme deb g dans end g 7 2 les sous foncteurs du foncteur de burnside en caracteristique 0 7 2 1 premier exemple 7 2 2 les constantesmg n 7 2 3 lesb groupes 7 2 4 les sous foncteurs deb 7 2 5 exemples deb groupes 8 exemples de foncteurs simples 8 1 le cas des foncteurs de mackey globaux 8 2 les foncteurssh k 8 3 certains foncteurs simples en caracteristique 0 9 l algebreegg end g egg 9 1 une base naturelle 9 2 multiplication 9 3 semi simplicite 10 le foncteur des representations complexes 10 1 caracteres 10 2 sous foncteurs et decomposition 10 3 semi simplicite

almost periodic solutions of fuzzy systems we prove the existence of almost periodic solutions and asymptotically almost periodic solutions for the fuzzy functional differential equations moreover we consider uniform stable and uniformly asymptotically stable of almost periodic solutions for the fuzzy system

towards fuzzy differential calculus part 1 integration of fuzzy mappings abstract this paper deals with fuzzy set valued mappings of the real line and more particularly focuses on mappings from the real line to the set of convex normal fuzzy sets of the real line these mappings can also be viewed as fuzzy relations using zadeh s extension principle the integral of such fuzzy mappings over a crisp interval is defined provided a special analytical representation of the fuzzy mapping the practical computation of such an integral is shown to be easy practically speaking it yields the fuzzy surface of a fuzzily bounded area

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

on the fuzzy difference equation xn f xn 1 xn k abstract in this paper we study the global asymptotic behavior of the positive solutions of the following fuzzy difference equation x n f x n 1 x n k n 0 1 under appropriate assumptions where k 1 2 and the initial values x k x k 1 x 1 are positive fuzzy numbers we give sufficient conditions under which every positive solution of the above equation converges to a positive equilibrium

a new bernoulli wavelet method for accurate solutions of nonlinear fuzzy hammerstein volterra delay integral equations in this article bernoulli wavelet method has been developed to solve nonlinear fuzzy hammerstein volterra integral equations with constant delay this type of integral equation has a particular case the fuzzy variant of a mathematical model from epidemiology bernoulli wavelets have been generated by dilation and translation of bernoulli polynomials the properties of bernoulli wavelets and bernoulli polynomials are first presented the present wavelet method reduces these integral equations to a system of nonlinear algebraic equations and again these algebraic systems have been solved numerically by newton s method convergence analysis of the present method has been discussed in this article also the results obtained by present wavelet method have been compared with that of by b spline wavelet method some illustrative examples have been demonstrated to show the applicability and accuracy of the present method

stability in possibilistic linear programming with continuous fuzzy number parameters abstract we prove that possibilistic linear programming problems introduced by buckley in 2 with continuous fuzzy number parameters are well posed i e small changes of the membership function of the parameters may cause only a small deviation in the possibilistic distribution of the objective function

haar wavelet collocation method for lane emden equations with dirichlet neumann and neumann robin boundary conditions abstract in this paper we present a numerically stable algorithm based on the haar wavelet collocation method hwcm for numerical solution of a class of lane emden equation with dirichlet neumann and neumann robin type boundary conditions arising in various physical models the haar wavelet collocation method uses simple box functions and hence the formulation of the numerical algorithm is straightforward unlike other methods the hwcm can be applied easily and accurately to the neumann type boundary conditions the advantage of the haar wavelet method is its efficiency and simple applicability for a variety of boundary conditions the haar wavelet collocation method is utilized to reduce the lane emden equation with boundary conditions to a system of algebraic equations then the newton s method is employed for numerical solutions nine examples of the lane emden equation with various types of boundary conditions are provided to demonstrate the accuracy and efficiency of the hwcm the numerical results are compared with the results obtained by other techniques and the exact solution

the and constructions for biset functors abstract in this article we define the construction and the construction that was crucial in the theory of canonical induction formulas see 3 in the setting of biset functors thus providing the necessary framework to define and construct canonical induction formulas for representation rings that are most naturally viewed as biset functors additionally this provides a unified approach to the study of a class of functors including the burnside ring the monomial burnside ring and global representation ring

on first order fuzzy ricatti difference equation this paper deals with the existence the boundedness and the asymptotic behavior of the positive solutions to a first order fuzzy ricatti difference equation xn 1 a xnb xn n 0 1 where xn is a sequence of positive fuzzy numbers a b and the initial value x0 are positive fuzzy numbers moreover an example is given to demonstrate the effectiveness of the results obtained

on the convergence of fuzzy sets three kind of convergences are defined on a space of fuzzy sets relationships between these convergences are studied some comments on the fixed point property are represented

stability and periodicity in fuzzy differential equations formulations of fuzzy differential equations des in terms of the hukuhara derivative do not reproduce the rich and varied behavior of crisp des another interpretation in terms of differential inclusions expressed level setwise overcomes much of this deficiency and opens up for profitable investigation such properties as stability attraction periodicity and the like this is especially important for investigating continuous systems which are uncertain or incompletely specified this paper studies studies lyapunov stability of fuzzy des and the periodicity of the fuzzy solution set for both the time dependent and autonomous cases

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

periodic boundary value problems for impulsive fuzzy differential equations the peculiarity of the hukuhara derivative makes it impossible to find periodic solutions for fuzzy differential equations with the exception of very restrictive situations in this work we consider a boundary value problem associated with an impulsive fuzzy differential equation and approximate the extremal solutions in a fuzzy functional interval using the monotone method fuzzy comparison results are useful in our procedure and the expression of the solution for some impulsive periodic linear differential problems is also provided

membership induced on manifolds by vector fields and flows abstract in many engineering and scientific applications the need arises to perform differential calculations on manifolds if such calculations involve imprecise data methods for computing with such data must be determined definitions and results are given for memberships on manifolds induced by differentiation along vector fields and by flows of vector fields with uncertain parameters examples are presented which illustrate the concepts

existence uniqueness and asymptotic behavior of the solutions of a fuzzy differential equation with piecewise constant argument in this paper we study the existence the uniqueness and the asymptotic behavior of the solutions of the fuzzy differential equation of the form x t px t qx t email protected 0 where p q are constant real numbers and the initial value x 0 is a fuzzy number

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

non asymptotic fuzzy estimators based on confidence intervals abstract in this paper we study and generalize the method of fuzzy estimation which is based on confidence intervals we provide definitions and the corresponding formulas the method we propose allows new additional ways in constructing fuzzy estimators in particular instead of constructing fuzzy estimators as the exact set of confidence intervals of the parameters to be estimated we generalize them in such a way that we eliminate discontinuities and ensure compact support preserving the statistically derived triangular shape of the estimators our approach is particularly useful in critical situations where subtle fuzzy comparisons between almost equal statistical quantities have to be made an example of this application is provided

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

haar wavelet method for some nonlinear volterra integral equations of the first kind we present here a simple efficient haar wavelet method for numerical solution of a class of nonlinear volterra integral equations of the first kind the present method is based on converting nonlinear volterra integral equations of the first kind into linear volterra integral equations of the second kind numerical examples are given to illustrate efficiency and accuracy of the present method comparison with numerical methods in the past has also been done solving some nonlinear first kind volterra integral equations using haar wavelet haar wavelet method is simple and fast solved examples demonstrate the accuracy and efficiency of the present method present method gives better results than the numerical methods described in past necessary accuracy may be obtained by increasing the number of calculation points

a note on numerical solutions of fuzzy differential equations by extended runge kutta like formulae of order 4 in this note we show that the example presented in a recent paper by ghazanfari et al is incorrect namely the exact solution suggested by the authors is not solution of the given fuzzy differential equation fde indeed the authors have proposed an exact solution which is independent from the initial condition so we obtain the correct exact solution using the characterization theorem proposed by bede et al under seikkala differentiability also some details are given for the mentioned example

on fibred biset functors with fibres of order prime and four abstract this note has two purposes first to present a counterexample to a conjecture parametrizing the simple modules over green biset functors appearing in an author s previous article this parametrization fails for the monomial burnside ring over a cyclic group of order four second to classify the simple modules for the monomial burnside ring over a group of prime order for which the above mentioned parametrization holds

fibered biset functors abstract the theory of biset functors introduced by serge bouc gives a unified treatment of operations in representation theory that are induced by permutation bimodules in this paper by considering fibered bisets we introduce and describe the basic theory of fibered biset functors which is a natural framework for operations induced by monomial bimodules the main result of this paper is the classification of simple fibered biset functors

towards fuzzy differential calculus part 2 integration on fuzzy intervals abstract the problem of integrating mappings over fuzzy domains has already received some attention in the literature however there is not a unique approach but several definitions have been proposed each carrying its own meaning this paper tries to emphasize the relationships and the differences between the various points of view

towards fuzzy differential calculus part 3 differentiation this paper deals successively with differentiation of ordinary functions at a fuzzy point and with differentiation of fuzzy valued functions at a nonfuzzy point in both cases the concept of differentiation is extended and the problem of the linearity is addressed in the second case practical methods of computation are presented in practical situations the available knowledge about mappings may be fuzzy it is the motivation of this work

numerical solutions of fuzzy differential and integral equations using the embedding method numerical procedures for solving fuzzy differential equations fdes and fuzzy integral equations fies with arbitrary kernels have been investigated sufficient conditions for convergence of the proposed algorithms are given and their applicability is illustrated with examples this work and its conclusions may narrow the gap between the theoretical research on fdes and fies and the practical applications already existing in the design of various fuzzy dynamical systems

a possibilistic argument for irreversibility abstract our aim is to explicate the idea of irreversibility by a mathematical representation of irreversible processes occurring in possibilistic dynamical systems with this in mind solutions of the cauchy problem in the space of fuzzy points are examined to meet the correspondence argument solutions of the cauchy problem in the space of concentrated points are examined too

the group of endo permutation modules the group d p of all endo permutation modules for a finite p group p is a finitely generated abelian group we prove that its torsion free rank is equal to the number of conjugacy classes of non cyclic subgroups of p we also obtain partial results on its torsion subgroup we determine next the structure of q otimes d viewed as a functor which turns out to be a simple functor s e q indexed by the elementary group e of order p 2 and the trivial out e module q finally we describe a rather strange exact sequence relating q otimes d p q otimes b p and q otimes r p where b p is the burnside ring and r p is the grothendieck ring of qp modules

direct method to solve volterra integral equation of the first kind using operational matrix with block pulse functions this article proposes a simple efficient direct method for solving volterra integral equation of the first kind by using block pulse functions and their operational matrix of integration first kind integral equation can be reduced to a linear lower triangular system which can be directly solved by forward substitution some examples are presented to illustrate efficiency and accuracy of the proposed method

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

hukuhara derivative of the fuzzy expected value in this paper we establish sufficient conditions to guarantee the exchange of the fuzzy expected value for a fuzzy random variable depending on certain parameter and its hukuhara derivative with respect to the parameter main results are obtained for two different sets of general conditions one of them requiring measurability conditions with respect to the product space the fuzzy random variable is defined from and the second one just requiring conditions over the projections of the fuzzy random variables