the μ ordinary hasse invariant of unitary shimura varieties we construct a generalization of the hasse invariant for any shimura variety of pel type a over a prime of good reduction whose vanishing locus is the open and dense mu ordinary locus

fuzzy differential equations and the extension principle we study the cauchy problem for differential equations considering its parameters and or initial conditions given by fuzzy sets these fuzzy differential equations are approached in two different ways a by using a family of differential inclusions and b the zadeh extension principle for the solution of the model we conclude that the solutions of the cauchy problem obtained by both are the same we also provide some illustrative examples

attractors and asymptotic stability for fuzzy dynamical systems abstract in this work we study the asymptotic properties of maps on fuzzy spaces which are extensions of maps on the main results are in section 4 see theorem 21 and we give an illustrative example in the last section

general form of lattice valued fuzzy sets under the cutworthy approach in this note a new solution of problem of synthesis of fuzzy sets is presented in other words necessary and sufficient conditions are formulated under which for a given family of subsets f of a set x and a fixed complete lattice l there is a fuzzy set m x l such that the collection of cuts of m coincides with f moreover it is proved that the general form of lattice valued fuzzy sets considering families of cuts are the type of fuzzy sets having the codomain 0 1 c for a suitable chosen cardinal c

existence theorem to the cauchy problem of fuzzy differential equations under compactness type conditions kaleva fuzzy sets and systems 35 1990 389 396 has concluded that the peano theorem does not hold for fuzzy differential equations on en d this paper deals with the cauchy problem of fuzzy differential equations the existence theorems under compactness type conditions are obtained

vanishing theorems for torsion automorphic sheaves on general pel type shimura varieties abstract we consider the interior cohomology and the hodge graded pieces in the case of the de rham realization of general not necessarily compact pel type shimura varieties with coefficients in the local systems corresponding to sufficiently regular algebraic representations of the associated reductive group for primes p bigger than an effective bound we prove that the f p and z p cohomology groups are concentrated in the middle degree that the z p cohomology groups are free of p torsion and that every f p cohomology class lifts to a z p cohomology class

generalized μ ordinary hasse invariants abstract we give a short proof for the existence of ordinary hasse invariants for the good reduction special fiber of shimura varieties of hodge type using the stack of g zips introduced by moonen wedhorn and pink wedhorn ziegler we give an explicit formula for the power of the hodge bundle that admits a hasse invariant when g is a weil restriction of g 1 we relate the ekedahl oort strata of g and those of g 1

on possibilistic correlation in 2004 fuller and majlender introduced the notion of covariance between fuzzy numbers by their joint possibility distribution to measure the degree to which they interact based on this approach in this paper we will present the concept of possibilistic correlation representing an average degree of interaction between marginal distributions of a joint possibility distribution as compared to their respective dispersions moreover we will formulate the classical cauchy schwarz inequality in this possibilistic environment and show that the measure of possibilistic correlation satisfies the same property as its probabilistic counterpart in particular applying the idea of transforming level sets of possibility distributions into uniform probability distributions we will point out a fundamental relationship between our proposed possibilistic approach and the classical probabilistic approach to measuring correlation

on using a cuts to evaluate fuzzy equations abstract consider an equation y f x1 xn where the extension principle is used to find y f x 1 x n when we subtitute fuzzy numbers x i for the xi 1 i n if x i denotes an cut of x i then we argue that for only certain simple equations will one obtain y equal to f x 1 x n where f is evaluated using interval arithmetic

on generalization on nguyen s theorem abstract the goal of this paper is to generalize certain results of nguyen 1 concerning the cuts of two place functions defined by the zadeh s extension principle to the case of extended two place functions defined via a sup t norm convolution

pattern solutions of the klausmeier model for banded vegetation in semiarid environments iv slowly moving patterns and their stability banded vegetation is a characteristic feature of semiarid environments comprising stripes of vegetation running parallel to the contours on hillsides separated by stripes of bare ground mathematical modelling plays an important role in the study of this phenomenon and the klausmeier model is one of the oldest and most established consisting of coupled reaction diffusion advection equations for plant biomass and water density in this model the dimensionless parameter corresponding to slope gradient is much larger than the other parameters and this paper is part of a series investigating the asymptotic form of pattern solutions for large values of the slope parameter the pattern solutions move uphill with a constant speed c say and the focus of this paper is c o 1 i begin by deriving the leading order form of the patterns and the region of parameter space in which they occur for c o 1 using this i show that all patterns with c o 1 are unstable as model solutions for sufficiently la

simulating continuous fuzzy systems abstract in previous studies we concentrated on utilizing crisp numeric simulation to produce discrete event fuzzy systems simulations then we extended this research to the simulation of continuous fuzzy systems models in this study we continue our study of continuous fuzzy systems using crisp continuous simulation consider a crisp continuous system whose process of evolution depends on differential equations such a system contains a number of parameters that must be estimated usually point estimates are computed and used in the model however these point estimates typically have uncertainty associated with them we propose to incorporate uncertainty by using fuzzy numbers as estimates of these unknown parameters fuzzy parameters convert the crisp system into a fuzzy system trajectories describing the behavior of the system become fuzzy curves we will employ crisp continuous simulation to estimate these fuzzy trajectories three examples are discussed

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

a note on nguyen fuller keresztfalvi theorem and zadeh s extension principle this paper is devoted to the analysis of the generalised form of the nguyen fuller keresztfalvi theorem nfk theorem the classical nfk theorem expresses the zadeh extension principle in terms of a cuts of fuzzy sets but it is subjected to some constraining assumptions these assumptions concern all data in the problem shape of fuzzy sets topology of underlying spaces and regularity of functions and t norms in this paper we analyse consequences of dropping these assumptions in order to prove the generalised version of the nfk theorem we introduce a notion of level sets as a generalisation of the collection of a cuts we discuss properties of the level sets and then we formulate the general nfk theorem which does not require assumptions on the shape of fuzzy sets t norms nor topology of underlying spaces finally we return to the classical formulation of the nfk theorem and we show that it can be extended to the class of fuzzy sets with unbounded supports

a note on zadeh s extensions let f rn rn and f f rn f r n be zadeh s extension of f to the space of fuzzy compact sets f rn the aim of this paper is to show that if f is continuous then f f rn d f rn d is also continuous d being the supremum over hausdorff distances between their corresponding level sets

uniqueness results in the representation of families of sets by fuzzy sets the important concept of identifying a fuzzy subset of a set r with its corresponding chain of level sets is widely used in the literature we investigate in this paper the problem of characterization of all fuzzy subsets of r that can be identified with a given arbitrary family c of subsets of r together with a given arbitrary subset s of 0 1 although our main focus is on the problem of uniqueness we start by giving necessary and sufficient conditions for both existence and uniqueness of such fuzzy subsets we continue by obtaining several algebraic and topological properties under which uniqueness is guaranteed to further support our results we present some examples which we hope will shed more light on the above mentioned problem of identification we finish by raising a few natural questions that are left as open problems for further investigation

a note to the finite t sum of l r fuzzy numbers and further considerations abstract in the first part of this paper we consider the cut of a sum of two fuzzy sets we show that the cut of such a sum can be written as one closed interval determined by the minimum and maximum of some special functions over a set uniquely determined by the considered t norm in the second part of the paper we show that not only cut of a sum of two fuzzy intervals has this property but also cut of a continuous function of two variables strictly increasing in each argument as well two examples of the presented theory are considered

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

the mean values of the weierstrass elliptic function theory and application abstract the weierstrass elliptic functions can be parameterised using either lattice generators or invariants most presentations adopt the former approach in this paper the authors give formulae that enable conversion between the two representations using these they obtain differential equations satisfied by the mean values of over its periods these mean values are considered as functions of the invariants they show how to construct exact solutions for the means in terms of both hypergeometric functions and legendre functions these solutions are valid for both real and complex values of the invariants for the case of real invariants the authors prove various monotonicity results for the means with respect to the invariants they also discuss the numerical computation of the means and show a number of plots of the means against both real and complex valued invariants finally they consider an application of their results to vegetation patterning in semi arid landscapes

embedding of level continuous fuzzy sets on banach spaces abstract in this paper we present an extension of the minkowski embedding theorem showing the existence of an isometric embedding between the class f c x of compact convex and level continuous fuzzy sets on a real separable banach space x and c 0 1 b x the banach space of real continuous functions defined on the cartesian product between 0 1 and the unit ball b x in the dual space x also by using this embedding we give some applications to the characterization of relatively compact subsets of f c x in particular an ascoli arzela type theorem is proved and applied to solving the cauchy problem x t f t x t x t0 x0 on f c x

pattern solutions of the klausmeier model for banded vegetation in semi arid environments iii the transition between homoclinic solutions abstract self organised patterns of vegetation are a characteristic feature of semi deserts on hillsides these typically comprise vegetation bands running parallel to the contours separated by regions of bare ground tiger bush the present study concerns the klausmeier mathematical model for this phenomenon c a klausmeier regular and irregular patterns in semiarid vegetation science 284 1999 1826 1828 which is one of the earliest and most influential of the various theoretical models for banded vegetation the model is a system of reaction diffusion advection equations and after rescaling it contains three dimensionless parameters one of which the slope parameter is much larger than the other two the present study is the third in a series of papers in which the author exploits the large value of the slope parameter to obtain leading order approximations to the parameter regions in which patterns exist and to the form of these patterns the boundary of the parameter region giving patterns consists in part of two loci of homoclinic solutions that are homoclinic to different steady states the present paper concerns behaviour for parameters close to the intersection point of these loci the author shows that this part of parameter space divides naturally into three regions with a different solution structure in each in one region the solution corresponds to a limit cycle of a reduced system of ordinary differential equations the other two regions involve multiple matched layers as part of the analysis the author derives formulae for the homoclinic solution loci and for the location of their intersection all of the results are valid to leading order for large values of the slope parameter the author presents a detailed numerical verification of his analytical results the paper concludes with discussions of the ecological implications of the results and the main outstanding mathematical questions