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

first order linear fuzzy differential equations under generalized differentiability first order linear fuzzy differential equations are investigated we interpret a fuzzy differential equation by using the strongly generalized differentiability concept because under this interpretation we may obtain solutions which have a decreasing length of their support which means a decreasing uncertainty in several applications the behaviour of these solutions better reflects the behaviour of some real world systems derivatives of the h difference and the product of two functions are obtained and we provide solutions of first order linear fuzzy differential equations using different versions of the variation of constants formula some examples show the rich behaviour of the solutions obtained

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

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

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

tight closure and projective bundles abstract we formulate problems of tight closure theory in terms of projective bundles and subbundles this provides a geometric interpretation of such problems and allows us to apply intersection theory to them this yields new results concerning the tight closure of a primary ideal in a two dimensional graded domain

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

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

canonical elements in local cohomology modules and the direct summand conjecture one of the objectives of this paper is to show that the usual homological consequences of the existence of big cohen macaulay henceforth c m modules e g the new intersection conjecture of peskine szpiro and roberts and the evans griffith syzygy conjecture follow from the direct summand conjecture when the residual characteristic of the local ring is positive this gives a new and substantially more elementary proof of the standard homological conjectures in case the characteristic of the ring itself is positive and reduces the general case of all these conjectures to one rather down to earth conjecture of course this places the direct summand conjecture in a position of central importance so that it now merits an allout attack some partial results on this problem are given in section 6 the conjecture asserts that a regular noetherian ring r is a direct summand as an r module of every module finite extension ring s 3 r the other main objective of this paper is to formulate and develop a theory of certain canonical elements in the local cohomology of special modules of syzygies neither the modules of syzygies nor the induced maps between them are canonical but the identification between the canonical elements is independent of the choices in particular a canonical element qr e hz syz k is associated see section 3 for details with each ndimensional local ring r m k rings are commutative associative with identity local ring means noetherian ring with a unique maximal ideal the conjecture that qr is nonzero for all local rings r turns out to be equivalent to the direct summand conjecture for a given r an infinite family of cases of the latter implies the former

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

the hyers ulam stability constants of first order linear differential operators let x be a complex banach space h a complex valued continuous function on the real line r and th c1 r x c r x the linear differential operator defined by thu u hu we completely determine the hyers ulam stability constant of th

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

a characterization of hyers ulam stability of first order linear differential operators abstract let x be a complex banach space and h r c a continuous function let t h c 1 r x c r x be the linear differential operator defined by thu u hu we give a necessary and sufficient condition in order that the operator th has the hyers ulam stability

open sets with stein hypersurface sections in stein spaces let d c cn n 3 be an open set such that for any linear hyperplane h c cn the intersection h n d is stein according to a theorem of lelong 13 it then follows that d is itself stein using the solution of the levi problem by docquier grauert 7 this result can easily be generalized to open subsets in stein manifolds therefore it is natural to raise the following question see also 4

on superheight conditions for the affineness of open subsets in this paper we consider the open complement u of a hypersurface y v a in an affine scheme x we study the relations between the affineness of u the intersection of y with closed subschemes the property that every closed surface in u is affine the property that every analytic closed surface is stein and the superheight of a defining ideal a

on the hyers ulam stability of the linear differential equation abstract we obtain some results on generalized hyers ulam stability of the linear differential equation in a banach space as a consequence we improve some known estimates of the difference between the perturbed and the exact solutions

on the convexity of a solution of liouville s equation the main purpose of the present note is to give a simple complex variable proof of the fact 3 10 11 that h z is convex whenever is convex the major step in our proof can be formulated as a coefficient inequality for convex univalent functions

the structure stability of periodic solutions for first order uncertain dynamical systems abstract this paper studies the structural stability of periodic solutions for first order fuzzy differential equations fdes understood as differential inclusions i e first order uncertain dynamical systems the existence and uniqueness of periodic solutions for this first order fuzzy problems have been obtained on general fuzzy number space when the forcing function has specific perturbations the structural stability of the periodic solutions are discussed by using the support function the dini theorem and the convergence theorem in the differential inclusion theory

first order linear fuzzy differential equations on the space of linearly correlated fuzzy numbers abstract the present paper is concerned with the solutions of first order linear fuzzy differential equations where differentiability of fuzzy functions is defined under an assumption of linear correlation between fuzzy numbers motivated by the fact that the structure of the space of linearly correlated fuzzy numbers strongly depends on the symmetry of the basic fuzzy number here we address first order linear fuzzy differential equations by distinguishing whether the basic fuzzy number is symmetric or not in the non symmetric case a first order linear fuzzy differential equation may be transformed into an equivalent system of ordinary differential equations related to the representation functions of the linearly correlated fuzzy number valued function in the symmetric case according to the monotonicity of the diameter of the fuzzy solution a first order linear fuzzy differential equation may be transformed into a system of ordinary differential equations associated with the representation functions of the canonical form of the linearly correlated fuzzy number valued function in addition using our extension method one may obtain solutions with either increasing or decreasing diameters several examples are provided in order to illustrate the proposed method

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

generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equations the usual concept of differentiability of fuzzy number valued functions has the following shortcoming if c is a fuzzy number and g a b r is an usual real valued function differentiable on x 0 a b with g x 0 0 then f x c g x is not differentiable on x 0 in this paper we introduce and study generalized concepts of differentiability of any order n n which solves this shortcoming newton leibnitz type formula is obtained and existence of the solutions of fuzzy differential equations involving generalized differentiability is studied also some concrete applications to partial and ordinary fuzzy differential equations with fuzzy input data of the form c g x are given

a note on fuzzy differential equations and the extension principle in this note we show by an example that the main result in a paper by bassanezi et al m t mizukoshi l c barros y chalco cano h roman flores r c bassanezi fuzzy differential equations and the extension principle information sciences 177 2007 3627 3635 is incorrect

on the restudy of fuzzy complex analysis part 1 the sequence and series of fuzzy complex numbers and their convergences this paper studies the convergence of the sequence and series of fuzzy complex numbers we define the metric convergence and levelwise convergence of sequences on the metric space of fuzzy complex numbers and discuss the relationship between two convergences all this may be a foundation for researching fuzzy complex analysis

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

purity of branch and critical locus abstract to a dominant morphism x s y s of n therian integral s schemes one has the inclusion c x y b x y of the critical locus in the branch locus of x y starting from the notion of locally complete intersection morphisms we give conditions on the modules of relative differentials x y x s and y s that imply bounds on the codimensions of c x y and b x y these bounds generalise to a wider class of morphisms the classical purity results for finite morphisms by zariski nagata auslander and faltings and grothendieck and van der waerden s purity for birational morphisms

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

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

on the ulam stability of first order linear fuzzy differential equations under generalized differentiability in this paper we investigate under some suitable conditions and generalized differentiability the ulam stability problems of three variants of first order linear fuzzy differential equations respectively

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

fuzzy versions of hyers ulam rassias theorem we introduce three reasonable versions of fuzzy approximately additive functions in fuzzy normed spaces more precisely we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in a fuzzy sense

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

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

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

hyers ulam stability of linear differential equations of first order iii abstract let x be a complex banach space and let i a b be an open interval in this paper we will prove the generalized hyers ulam stability of the differential equation t y t y t t r x 0 0 for the class of continuously differentiable functions f i x where and r are complex constants and x 0 is an element of x by applying this result we also prove the hyers ulam stability of the euler differential equation of second order

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

convexity of solutions of semilinear elliptic equations on considere le probleme elliptique suivant u f u dans u m sur ou est un domaine convexe de r 2 et m est soit une constante reelle soit on etablit que pour une bonne fonction monotone g t pout toute solution u on a g u est strictement convexe dans

hyers ulam stability of fuzzy fractional volterra integral equations with the kernel ψ function via successive approximation method abstract in this paper we investigative the hyers ulam stability and the hyers ulam rassias stability of fuzzy fractional volterra integral equations ffvies involving the kernel function we propose conditions for the existence uniqueness and stability of ffvie by employing the method of successive approximation to visualize the theoretical results some examples and numerical simulations are given

variation of constant formula for first order fuzzy differential equations in this paper we study first order linear fuzzy differential equations by using the generalized differentiability concept and we present the general form of their solutions we also correct and complete some previous results finally some examples are given to illustrate our results

fuzzy approximation by fuzzy convolution type operators here we introduce and study four sequences of naturally arising fuzzy integral operatorsof convolution type that are integral analogs of known fuzzy wavelet type operators defined via a scaling function their fuzzy convergence with rates to the fuzzy unit operator is established through fuzzy inequalities involving the fuzzy modulus of continuity also their high order fuzzy approximation is given similarly by involving the fuzzy modulus of continuity of the n t h order n 1 h fuzzy derivative of the engaged fuzzy number valued function the fuzzy global smoothness preservation property of these operators is demonstrated also

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

fuzzy stability of the jensen functional equation we establish a generalized hyers ulam rassias stability theorem in the fuzzy sense in particular we introduce the notion of fuzzy approximate jensen mapping and prove that if a fuzzy approximate jensen mapping is continuous at a point then we can approximate it by an everywhere continuous jensen mapping as a fuzzy version of a theorem of schwaiger we also show that if every fuzzy approximate jensen type mapping from the natural numbers into a fuzzy normed space can be approximated by an additive mapping then the fuzzy norm is complete

grobner deformations connectedness and cohomological dimension abstract in this paper we will compare the connectivity dimension c p i of an ideal i in a polynomial ring p with that of any initial ideal of i generalizing a theorem of kalkbrener and sturmfels m kalkbrener b sturmfels initial complex of prime ideals adv math 116 1995 365 376 we prove that c p lt i min c p i dim p i 1 for each monomial order as a corollary we have that every initial complex of a cohen macaulay ideal is strongly connected our approach is based on the study of the cohomological dimension of an ideal a in a noetherian ring r and its relation with the connectivity dimension of r a in particular we prove a generalized version of a theorem of grothendieck a grothendieck cohomologie locale des faisceaux coherents et theoremes de lefschetz locaux et globaux sga 2 in seminaire de geometrie algebrique du bois marie 1962 as consequence of these results we obtain some necessary conditions for an open subscheme of a projective scheme to be affine

generalized hukuhara differentiability of interval valued functions and interval differential equations abstract in the present paper we use a recently proposed generalization of the hukuhara difference for compact convex sets to introduce and study a generalization of the hukuhara differentiability to the case of interval valued functions we also consider several possible definitions for the derivative of an interval valued function recently proposed in the literature and we study connections between them and their properties using these concepts we study interval differential equations local existence and uniqueness of two solutions is obtained together with characterizations of the solutions of an interval differential equation by ode systems several examples are also shown

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 some existence and uniqueness results in contact problems with nonlocal friction the workwe present is a mathematical study of signorini s problem with friction i e the problem of equilibrium of a linearly elastic body in contact with a rigid foundation until recently the questions of existence and uniqueness of solutions to such problems were open recently two ideas have appeared which have led to some positive results the first presented by netas jarusek haslinger 11 involves a concept of small friction and provides for the development of an existence result for a very special case of a uniformly loaded infinite strip the second established by duvaut 5 is based on the idea of a nonlocal friction law which enables one to establish an existence result for any friction and also to establish uniqueness for small friction in this paper we present some new results in this direction and a new proof of a non local existence theory our approach differs considerably from the proof outlined in 5 instead of using fixed point arguments we develop a theory of perturbed variational inequalities the origin of which can be found in 9 and establish a generalization for the class of nonlinear variational inequalities characterizing the non local signorini problem this approach should prove to be very useful in studies of approximations of friction prohlems

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

a variational inequality approach to hele shaw flow with a moving boundary this paper is concerned with the study of a mathematical model of the injection of fluid into a finite hele shaw cell the mathematical problem is one of solving laplace s equation in an unknown region whose boundary changes with time by a transformation of the dependent variable an elliptic variational inequality formulation of the moving boundary problem is obtained the variational inequality is shown to have a unique solution up to the time at which the cell is filled regularity results for the solution of the inequality are obtained by studying a penalty approximation of the inequality

on the stability of the linear differential equation of higher order with constant coefficients abstract we obtain a result on stability of the linear differential equation of higher order with constant coefficients in aoki rassias sense as a consequence we obtain the hyers ulam stability of the above mentioned equation a connection with dynamical sytems perturbation is established

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

set valued and fuzzy stochastic differential equations driven by semimartingales abstract in the paper we present set valued and fuzzy stochastic integrals with respect to semimartingale integrators as well as their main properties then we study the existence of solutions to set valued and fuzzy set valued stochastic differential equations driven by semimartingales the stability of solutions is also established

ulam type stability of first order linear impulsive fuzzy differential equations abstract in this paper we consider ulam stability concepts for first order linear impulsive fuzzy differential equations which generalize standard definitions for impulsive differential equations sufficient conditions are established to guarantee that our equations are ulam stable numerically examples are also provided to illustrate our results

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

almost periodic fuzzy number valued functions in this paper we develop a theory of almost periodic fuzzy functions i e of the almost periodic functions of real variable and with values fuzzy real numbers although the class of fuzzy real numbers does not form a linear normed space the majority of main properties of almost periodic functions with values in banach spaces are extended to this case applications to fuzzy differential equations and to fuzzy dynamical systems are given

existence and interrelation between set and fuzzy differential equations abstract an existence result is proved for set differential equation when the function involved is upper semicontinuous and the result is very general then the connection between the solutions of fuzzy differential equation and the set differential equation that is generated from it is studied

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