generalization of the stolarsky type inequality for pseudo integrals in this paper we prove a stolarsky type inequality for two classes of pseudo integrals one of them deals with pseudo integrals where pseudo operations are defined via a monotone and continuous generator function the other one concerns the pseudo integrals based on a semiring with an idempotent addition and a generated pseudo multiplication

on some advanced type inequalities for sugeno integral and t s evaluators in this paper strengthened versions of the minkowski chebyshev jensen and holder inequalities for sugeno integral and t s evaluators are given as an application some equivalent forms and some particular results have been established

a liapunov type inequality for sugeno integrals abstract the classical liapunov inequality shows an interesting upper bound for the lebesgue integral of the product of two functions this paper proposes a liapunov type inequality for sugeno integrals that is we show that h s t r s 0 1 f x s d r t s 0 1 f x t d r s s 0 1 f x r d s t holds for some constant h s t r where 0 t s r f 0 1 0 is a non increasing concave function and is the lebesgue measure on r we also present two interesting classes of functions for which the classical liapunov type inequality for sugeno integrals with h s t r 1 holds some examples are provided to illustrate the validity of the proposed inequality

sandor s inequality for sugeno integrals abstract in this paper we prove a fuzzy integral inequality for convex functions our results improve recent results that appear in literature some examples are given to illustrate our theorems

general related inequalities to carlson type inequality for the sugeno integral in this paper the carlson type inequality for the sugeno integral is generalized on an abstract fuzzy measure space x moreover several examples are given to illustrate the validity of main results

steffensen type inequalities for fuzzy integrals we provide several steffensen type inequalities for the sugeno integral the inequalities are of the form a b f g d a a a f d b or a b f g d a b b f d b where a b are constants is a fuzzy measure on r g a b 0 1 f a b r is nonincreasing or nondecreasing and b a a b g d we show that some of our sufficient conditions are also necessary

on the stability of the reduced basis method for stokes equations in parametrized domains we present an application of reduced basis method for stokes equations in domains with affine parametric dependence the essential components of the method are i the rapid convergence of global reduced basis approximations galerkin projection onto a space wn spanned by solutions of the governing partial differential equation at n selected points in parameter space ii the off line on line computational procedures decoupling the generation and projection stages of the approximation process the operation count for the on line stage in which given a new parameter value we calculate an output of interest depends only on n typically very small and the parametric complexity of the problem the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation design optimization and real time control particular attention is given i to the pressure treatment of incompressible stokes problem ii to find an equivalent inf sup condition that guarantees stability of reduced basis solutions by enriching the reduced basis velocity approximation space with the solutions of a supremizer problem iii to provide algebraic stability of the problem by reducing the condition number of reduced basis matrices using an orthonormalization procedure applied to basis functions iv to reduce computational costs in order to allow real time solution of parametrized problem

reversed version of a generalized sharp holder s inequality and its applications in this paper we give a reversed version of a generalized sharp holder s inequality which is due to wu the results are then used to improve beckenbach s inequality and minkowski s inequality moreover as an application in information theory we present a refinement of singh s inequality which is one generalized shannon s inequality

general barnes godunova levin type inequalities for sugeno integral integral inequalities play important roles in classical probability and measure theory non additive measure is a generalization of additive probability measure sugeno s integral is a useful tool in several theoretical and applied statistics which has been built on non additive measure for instance in decision theory the sugeno integral is a median which is indeed a qualitative counterpart to the averaging operation underlying expected utility in this paper barnes godunova levin type inequalities for the sugeno integral on abstract spaces are studied in a rather general form and for this we introduce some new technics for the treatment of concave functions in the sugeno integration context also several examples are given to illustrate the validity of this inequality moreover a strengthened version of barnes godunova levin type inequality for sugeno integrals on a real interval based on a binary operation is presented

on the computation of multi dimensional solution manifolds of parametrized equations a new algorithm is presented for computing vertices of a simplicial triangulation of thep dimensional solution manifold of a parametrized equationf x 0 wheref is a nonlinear mapping fromr n tor m p n m 1 an essential part of the method is a constructive algorithm for computing moving frames on the manifold that is of orthonormal bases of the tangent spaces that vary smoothly with their points of contact the triangulation algorithm uses these bases together with a chord form of the gauss newton process as corrector to compute the desired vertices the jacobian matrix of the mapping is not required at all the vertices but only at the centers of certain local triangulation patches several numerical examples show that the method is very efficient in computing triangulations even around singularities such as limit points and bifurcation points this opens up new possibilities for determining the form and special features of such solution manifolds

the sugeno integral with respect to α preinvex functions abstract in this paper we establish the left hand side of the hermite hadamard inequality for preinvex functions and illustrate that the hermite hadamard inequality for preinvex functions is not valid for the sugeno integral moreover we give several upper bounds for the sugeno integral related to preinvex functions some examples are also provided to show the validity of our results

sugeno integral of monotone functions based on lebesgue measure roman flores et al h roman flores a flores franulic y chalco cano the fuzzy integral for monotone functions applied mathematics and computation 185 2007 492 498 gave some optimal upper bounds for the sugeno integral of continuous and strictly monotone functions and provided yong type inequalities for the sugeno integral these results are generalized to monotone functions in this paper two algorithms are given for calculating the sugeno integral of monotone functions based on lebesgue measure several illustrative examples are presented

a convolution type inequality for fuzzy integrals in this paper we show a bushell okrasinski type inequality for fuzzy integrals more precisely we show that s 01 1 t s 1g t sdt 01g t dts where g 0 1 0 is a continuous and strictly decreasing function and s 2

streamflow simulation a nonparametric approach in this paper kernel estimates of the joint and conditional probability density functions are used to generate synthetic streamflow sequences streamflow is assumed to be a markov process with time dependence characterized by a multivariate probability density function kernel methods are used to estimate this multivariate density function simulation proceeds by sequentially resampling from the conditional density function derived from the kernel estimate of the underlying multivariate probability density function this is a nonparametric method for the synthesis of streamflow that is data driven and avoids prior assumptions as to the form of dependence e g linear or nonlinear and the form of the probability density functions e g gaussian we show using synthetic examples with known underlying models that the nonparametric method presented is more flexible than the conventional models used in stochastic hydrology and is capable of reproducing both linear and nonlinear dependence the effectiveness of this model is illustrated through its application to simulation of monthly streamflow from the beaver river in utah

on a computational method for the second fundamental tensor and its application to bifurcation problems an algorithm is presented for the computation of the second fundamental tensorv of a riemannian submanifoldm ofr n fromv the riemann curvature tensor ofm is easily obtained moreover v has a close relation to the second derivative of certain functionals onm which in turn provides a powerful new tool for the computational determination of multiple bifurcation directions frequently in applications thed dimensional manifoldm is defined implicitly as the zero set of a submersionf onr n in this case the principal cost of the algorithm for computingv p at a given pointp m involves only the decomposition of the jacobiandf p off atp and the projection ofd d 1 neighboring points ontom by means of a local iterative process usingdf p several numerical examples are given which show the efficiency and dependability of the method

solving large nonlinear systems of equations by an adaptive condensation process we present an algorithm which efficiently solves large nonlinear systems of the form au f u u in mathbb r n whenever an iterative solver a 1 for the symmetric positive definite matrixa is available andf u is symmetric such problems arise from the discretization of nonlinear elliptic partial differential equations by means of an adaptive decomposition process we split the original system into a low dimensional system to be treated by any sophisticated solver and a remaining high dimensional system which can easily be solved by fixed point iteration specifically we choose a newton type trust region algorithm for the treatment of the small system we show global convergence under natural assumptions on the nonlinearity the convergence results typical for trust region algorithms carry over to the full iteration process the only large systems to be solved are linear ones with the fixed matrixa thus existing software for positive definite sparse linear systems can be used

on the equivalence of convergences of fuzzy sets abstract the aim of this paper is to compare d h and l convergences with the variational covergence our analysis which is carried out in is made through the introduction of the space c of compact fuzzy sets u on for which the level function 0 1 l k is continuous we prove that in this space all the above notions of convergence are equivalent

an inequality related to minkowski type for sugeno integrals an inequality related to minkowski type for the sugeno integral on abstract spaces is studied in a rather general form some previous results on chebyshev type inequality obtained by the authors are generalized several examples are given to illustrate the validity of this inequality the conditions such that this inequality becomes an equality are also discussed finally conclusions and some problems for further investigations are included

multiple parameter reduced basis technique for bifurcation and post buckling analyses of composite plates a multiple parameter reduced basis technique and a problem adaptive computational algorithm are presented for the bifurcation and post buckling analyses of composite plates subjected to combined loadings the computational algorithm can be conveniently divided into three distinct stages the first stage is that of determining the stability boundary the plate is discretized by using displacement finite element models and the analysis region is reduced by exploiting the special symmetries exhibited by the response of the plate the vector of unknown nodal displacements is expressed as a linear combination of a small number of path derivatives derivatives of the nodal displacements with respect to path parameters and a rayleigh ritz technique is used to approximate the finite element equations by a small system of algebraic equations the reduced equations are used to determine the stability boundary of the plate in the second stage a nonllnear solution in the vicinity of the stability boundary is obtained by using a bifurcation buckling mode as a predictor and a set of reduced equations is generated in the third stage the reduced equations are used to trace post buckling paths corresponding to various combinations of the load parameters the potential of the proposed approach is discussed and its effectiveness is demonstrated by means of a numerical example of laminated composite plate subjected to combined compressive and shear loadings

estimation of the error in the reduced basis method solution of nonlinear equations the reduced basis method is a projection technique for approximating the solution curve of a finite system of nonlinear algebraic equations by the solution curve of a related system that is typically of much lower dimension in this paper the reduced basis error is shown to be dominated by an approximation error this in turn leads to error estimates for projection onto specific subspaces for example subspaces related to taylor lagrange and discrete least squares approximation

the reduced basis method for initial value problems this paper deals with the application of the reduced basis method to the initial value problem of ordinary differential equations a global approximation of the true solution curve is defined in terms of a sequence of reduced basis curves error bounds are established and these lead to order estimates for specific choices of reduced basis subspaces the effects of numerical integration are then incorporated into the estimates a numerical study is included

the autocontinuity of set function and the fuzzy integral abstract the autocontinuity and some other concepts of a set function are introduced and sugeno s fuzzy measure with some annexed conditions is studied on a fuzzy measure space egoroffs theorem is proved it is also proved that f mean convergence is equivalent to convergence in measure for a sequence of measurable functions finally some convergence theorems of sequence of fuzzy integrals are proved especially using the concept of autocontinuity a necessary and sufficient condition for the convergence in measure theorem is given

on the continuity of fuzzy integrals abstract we establish minimal conditions on a fuzzy measure to make the measure convergence a sufficient condition for continuity of the fuzzy integral in particular we give conditions such that measure convergence of fuzzy sets with respect to a fuzzy measure implies the convergence of the fuzzy integral with respect to another fuzzy measure

on stolarsky inequality for sugeno and choquet integrals recently flores franulic roman flores and chalco cano proved the stolarsky type inequality for sugeno integral with respect to the lebesgue measure l the present paper is devoted to generalize this result by relaxing some of its requirements moreover stolarsky inequality for choquet integral is added too

hermite hadamard inequality for fuzzy integrals in this paper we prove a hermite hadamard type inequality for fuzzy integrals some examples are given to illustrate the results

certified reduced basis methods and output bounds for the harmonic maxwell s equations we propose certified reduced basis methods for the efficient and reliable evaluation of a general output that is implicitly connected to a given parameterized input through the harmonic maxwell s equations the truth approximation and the development of the reduced basis through a greedy approach is based on a discontinuous galerkin approximation of the linear partial differential equation the formulation allows the use of different approximation spaces for solving the primal and the dual truth approximation problems to respect the characteristics of both problem types leading to an overall reduction in the off line computational effort the main features of the method are the following i rapid convergence on the entire representative set of parameters ii rigorous a posteriori error estimators for the output and iii a parameter independent off line phase and a computationally very efficient on line phase to enable the rapid solution of many query problems arising in control optimization and design the versatility and performance of this approach is shown through a numerical experiment illustrating the modeling of material variations and problems with resonant behavior

reduction methods for nonlinear steady state thermal analysis hybrid analysis techniques based on the combined use of finite elements and the classical bubnov galerkin approximation are presented for predicting nonlinear steady state temperature distributions in structures and solids in these hybrid techniques the modelling versatility of the finite element method is preserved and a substantial reduction in the number of degrees of freedom is achieved by expressing the vector of nodal temperatures as a linear combination of a small number of global temperature modes or basis vectors the bubnov galerkin technique is then used to compute the coefficients of the linear combination i e the amplitudes of the global temperature modes the basis vectors chosen are the path derivatives commonly used in perturbation techniques namely the derivatives of the nodal temperature vector with respect to a preselected control or path parameter s the vectors are generated by using the finite element model of the initial discretization also the performance of alternate sets of basis vectors is investigated in the alternate sets only a few path derivatives are generated and they are augmented by a constant vector representing a uniform temperature rise or drop and by reciprocal vectors with nonzero components equal to the reciprocals of the nonzero components of the path derivatives a problem adaptive computational algorithm is presented for efficient evaluation of global approximation vectors and generation of the reduced system of equations and for monitoring the accuracy of the reduced system of equations the potential of the proposed reduction methods for the solution of large scale nonlinear steady state thermal problems is also discussed the effectiveness of these methods is demonstrated by means of four numerical examples including conduction convection and radiation modes of heat transfer this study shows that the use of the uniform temperature mode and the path derivatives as global approximation vectors significantly increases the accuracy of the solutions obtained by reduction methods thereby enhancing the effectiveness of these methods for the solution of large scale nonlinear thermal problems

jensen type inequalities for sugeno integral in this paper the classical jensen inequalities for concave function i e f x d f d and i 1 n i x i i 1 n i x i are adapted for the sugeno integral using the notion of the supergradient moreover we give some modifications of previous results of roman flores et al concerning jensen type inequalities for sugeno integral some examples in the framework of the lebesgue measure and counting measure to illustrate the results are presented

a hardy type inequality for fuzzy integrals abstract in this paper we prove a hardy type inequality for fuzzy integrals more precisely we show that 0 1 f p x d x 1 p 1 0 1 f x p d x where p 1 f 0 1 0 is an integrable function and f x 0 x f t d t an analogous inequality is also obtained on the interval 0

estimation of the error in the reduced basis method solution of differential algebraic equation systems in this paper the reduced basis method is described as it applies to the solution of the differential equations with algebraic constraints the approximate solution is defined in terms of a sequence of reduced basis curves and error bounds are derived these are used to produce order estimates for direct sum taylor lagrange and hermite subspaces

on chebyshev type inequalities for generalized sugeno integrals abstract we give the necessary and sufficient conditions guaranteeing the validity of chebyshev type inequalities for generalized sugeno integrals in the case of functions belonging to a much wider class than the comonotone functions for several choices of operators we characterize the classes of functions for which the chebyshev type inequality for the classical sugeno integral is satisfied

holder type inequality for sugeno integral two inequalities for the sugeno integral on abstract spaces are studied in rather general forms which generalize most of the results on the same topic obtained by other authors thus closing the series of papers on this topic as an application a holder type inequality is obtained finally some conclusions are drawn and some problems for further investigation are suggested

on a version of fuzzy jensen inequality based on the measure of level set abstract in this paper we present a sufficient condition for the continuity of distribution function f based on a condition of the measure of level sets from this result an estimate of jensen type inequality for sugeno integral is stated finally it is applied to establish jensen type estimates for several kinds of fuzzy numbers

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

finite dimensional approximation of nonlinear problems part ii limit points note univ paris 6 f 75230 paris 05 france ecole polytech ctr math appl cnrs equipe rech 747 f 91128 palaiseau france univ pavia cnr ist anal numer i 27100 pavia italy brezzi f univ pavia cnr ist math appl i 27100 pavia italy isi document delivery no lr761times cited 54cited reference count 13 reference asn article 1981 002doi 10 1007 bf01396184 record created on 2006 08 24 modified on 2017 05 12

on the level continuity of fuzzy integrals in this paper we define the level convergence of measurable functions on a fuzzy measure space by using the closure operator in the moore sense we study some of the properties of this convergence and give conditions for the continuity of the fuzzy integral in relation to the level convergence

estimation and validation of contemporaneous parma models for streamflow simulation seasonal streamflow series generally exhibit periodicity in the autocovariance structure such periodicity can be represented by parma models i e autoregressive moving average arma models with parameters that vary with the seasons statistical properties of low order models such as the parma 2 2 model are examined the periodic moment equations are derived they can be used to compute the periodic covariance structure of a given model simulation of streamflow at several sites can be done using the contemporaneous parma model the main problem in using such models is to determine the covariance matrices of innovations traditionally this has been done by the method of maximum likelihood however this method generally leads to significant underestimation of the cross correlation of flows a moment estimator is developed herein for the contemporaneous parma 2 2 model along with three approximate moment based estimators for those cases where a feasible moment solution cannot be obtained the applicability of the proposed methods is illustrated by fitting parma models to weekly flow data for two catchments in the ottawa river basin

general chebyshev type inequalities for sugeno integrals chebyshev type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the real line and product operation

convolution of fuzzy sets and applications the purpose of this work is studying the approximation in d metric of upper semi continuous and normal fuzzy sets with compact support on rn by using the convolution f g x sup f x y g y y x between two fuzzy sets where the distance d f g is the supremum of the hausdorff distances of their corresponding level sets in particular by using convolution a density result is proved and some applications in choquet integration of fuzzy numbers are presented

a note on fuzzy integral inequality of stolarsky type abstract in this paper we prove a stolarsky type inequality for fuzzy integrals more precisely we show that 0 1 f x 1 a b d 0 1 f x 1 a d 0 1 f x 1 b d where a b 0 f 0 1 0 1 is a continuous and strictly monotone function and is the lebesgue measure on r

a jensen type inequality for fuzzy integrals in this paper we show a jensen type inequality for the sugeno integral we also discuss some conditions assuring the satisfaction of opposite inequality reverse jensen inequality

averaging procedures in defuzzification processes defuzzification is the ultimate step in approximate reasoning consisting in the replacement of a fuzzy set with a suitable crisp value this process is decomposed in two steps first replacing a fuzzy set by a crisp set then replacing the obtained crisp set by a single value we investigate the natural conditions the first replacement called averaging procedure should satisfy some interesting examples are given the compatibility of averaging procedures with algebraic and order structures is studied the algebraic structure of the set of averaging procedures is investigated

finite dimensional approximation of nonlinear problems in the first two papers of this series 4 5 we have studied a general method of approximation of nonsingular solutions and simple limit points of nonlinear equations in a banach space we derive here general approximation results of the branches of solutions in the neighborhood of a simple bifurcation point the abstract theory is applied to the galerkin approximation of nonlinear variational problems and to a mixed finite element approximation of the von karman equations

on making large nonlinear problems small abstract a number of aspects of reduction methods for solution of large scale nonlinear problems are discussed including a selection of basis vectors for steady state problems b identification and determination of bifurcation and limit points and tracing post limit point and post bifurcation point paths using reduction methods c application of reduction methods to nonlinear problems with prescribed nonzero values of the field variable and d use of reduction methods in conjunction with multifield mixed finite element models four numerical examples are presented to demonstrate the effectiveness of using reduction methods for the solution of nonlinear thermal and structural problems also a number of research areas which have high potential for application of reduction methods are identified

on the jensen type inequality for generalized sugeno integral we prove necessary and sufficient conditions for the validity of jensen type inequalities for generalized sugeno integral our proofs make no appeal to the continuity of neither the fuzzy measure nor the operators for several choices of operators we characterize the classes of functions for which the corresponding inequalities are satisfied

disaggregation procedures for generating serially correlated flow vectors the structure of disaggregation models places severe constraints on the feasible values of the lagged covariance of generated flow vectors a new and simple class of disaggregation models is presented which employ the valencia schaake disaggregation model structure but allow the models innovations to be serially correlated these models can reproduce 1 the covariance matrix of the disaggregated flows 2 their covariance with the upper level flows and 3 reasonable approximations to the lag one covariance of the disaggregated flow vectors given the constraints imposed by a disaggregation approach the mejia rousselle disaggregation model is shown in general to fail to reproduce the anticipated variances and covariances of the disaggregated flows because the model and its parameter estimators are not self consistent the paper closes with a discussion of practical modeling considerations and of staged disaggregation procedures which reduce the size of multisite multiseason models

on the theory and error estimation of the reduced basis method for multi parameter problems abstract in an earlier paper zamm 63 1983 21 j p fink and w c rheinboldt developed a priori local error estimates for the scalar parameter case of the reduced basis method by considering the method in a differential geometric setting here it is shown that an analogous setting can be used for the analysis of the method applied to problems with a multidimensional parameter vector and that this leads to a corresponding local error theory also in this general case

h continuity of fuzzy measures and set defuzzification the purpose of this work is to analyze the continuity of fuzzy measures with respect to the hausdorff metric on k r n the class of all nonempty compact subsets of r n as an application we study the continuity of set defuzzification processes on r n which are defined by aumann integral methods

berwald type inequality for sugeno integral abstract nonadditive measure is a generalization of additive probability measure sugeno integral is a useful tool in several theoretical and applied statistics which has been built on non additive measure integral inequalities play important roles in classical probability and measure theory the classical berwald integral inequality is one of the famous inequalities this inequality turns out to have interesting applications in information theory in this paper berwald type inequality for the sugeno integral based on a concave function is studied several examples are given to illustrate the validity of this inequality finally a conclusion is drawn and a problem for further investigations is given

a chebyshev type inequality for fuzzy integrals abstract in this paper we prove a chebyshev type inequality for fuzzy integrals more precisely we show that 0 1 fg d 0 1 f d 0 1 g d where is the lebesgue measure on r and f g 0 1 0 are two continuous and strictly monotone functions both increasing or both decreasing also some examples and applications are presented

mixed models and reduction techniques for large rotation nonlinear problems abstract mixed models and reduction techniques are presented for the large rotation nonlinear analysis of curved beams a total lagrangian description of the beam deformation is used and the analytical formulation is based on a form of reissner s large deformation theory with the effects of transverse shear deformation and extensibility of the centerline included only planar deformations are considered and the fundamental unknowns consist of the three internal forces and the three generalized displacements of the beam the element characteristic arrays are obtained by using the hellinger reissner mixed variational principle the polynomial interpolation or shape functions used in approximating the internal forces are in general of different degree than those used for approximating the generalized displacements and the forces are discontinuous at interelement boundaries the use of reduction methods in conjunction with the mixed models is outlined and the advantages of mixed models over displacement models are delineated numerical results are presented to demonstrate the high accuracy and effectiveness of both the mixed models and the reduction techniques

fatou s lemma for sugeno integral abstract fatou s lemma plays an important role in classical probability and measure theory non additive measure is a generalization of additive probability measure sugeno s integral is a useful tool in several theoretical and applied statistics which have been built on non additive measure in this paper a fatou type lemma for sugeno integral is shown the studied inequality is based on the classical fatou lemma for lebesgue integral to illustrate the proposed inequalities some examples are given

probabilistic envelope curves for design flood estimation at ungauged sites 1 castellarin et al 2005 introduced the probabilistic regional envelope curves precs of flood flows and formulated an empirical estimator of the recurrence interval t associated with the prec for m synthetic cross correlated and concurrent sequences of annual maxima with length n in principle a prec can be used to estimate the t year flood design flood for any basin in a given region as a function of the catchment area alone a number of fundamental issues hamper the construction of precs and the estimation of their t for historical regional samples of flood flows some of these issues are addressed by this study which presents an algorithm for the application of the empirical estimator of t to historical annual maximum series of unequal length and assesses how the selection of a particular cross correlation formula and plotting position affects the accuracy of design flood estimates retrieved from precs prec flood quantiles the reliability of the proposed algorithm and the accuracy of the flood quantiles are discussed through a comprehensive cross validation the results show that the reliability of prec flood quantiles for ungauged sites is comparable with the reliability of regional estimates produced by the application of the index flood approach the results of the cross validation also show that the selection of a particular correlation formula or plotting position may produce biased prec flood quantiles and suggest that the accuracy of the approach could be significantly enhanced by relaxing the assumption that the design flood scales with catchment area alone

the brunn minkowski inequality in 1978 osserman 124 wrote an extensive survey on the isoperimetric inequality the brunn minkowski inequality can be proved in a page yet quickly yields the classical isoperimetric inequality for important classes of subsets of rn and deserves to be better known this guide explains the relationship between the brunn minkowski inequality and other inequalities in geometry and analysis and some applications

local error estimates for parametrized nonlinear equations this paper is concerned with the development of error estimates for parametrized nonlinear equations f z lambda 0 and their discretizations f h z lambda 0 the estimates obtained are local error estimates in the sense of the local error in the numerical solution of ordinary differential equations they represent a different approach to the general problem of error estimation an approach which involves only a single discretized equation instead of a converging family of such equations

the equivalence of convergences of sequences of fuzzy numbers and its applications to the characterization of compact sets in this paper with the help of the convergence of sequences of fuzzy numbers with respect to the lebesgue measure we study the relationship between convergences of sequences of fuzzy numbers with respect to the endograph metric the sendograph metric and the l p metric we prove that these convergences are equivalent under proper conditions in addition by applying our result we give a new characterization of compact sets in fuzzy number space with the sendograph metric

chebyshev inequality for sugeno integrals in this paper we study chebyshev inequality for sugeno integrals on an arbitrary fuzzy measure space particularly we obtain other chebyshev type inequalities which relate the measure of a level set of the maximum and the sum of two non negative integrable functions and their integrals finally we apply our results to the case of comonotone functions

the fuzzy integral for monotone functions abstract in this paper we give some optimal upper bounds for the sugeno s integral of monotone functions more precisely we show that if g 0 0 is a continuous and strictly monotone function then the fuzzy integral value p 0 a g d with respect to the lebesgue measure verifies the following sharp inequalities a g a p p for the increasing case and b g p p for the decreasing case moreover we show that under adequate conditions these optimal inequalities provides a powerful tool for solving fuzzy integrals also some examples and application are presented

generalization of the lyapunov type inequality for pseudo integrals we prove two kinds of lyapunov type inequalities for pseudo integrals one discusses pseudo integrals where pseudo operations are given by a monotone and continuous function g the other one focuses on the pseudo integrals based on a semiring 0 1 sup where the pseudo multiplication is generated some examples are given to illustrate the validity of these inequalities

markov type inequalities for fuzzy integrals in this paper we study some fuzzy markov type inequalities and its connections with some fundamental properties of the sugeno integral

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

periodic gamma autoregressive processes for operational hydrology a number of models have been suggested for hydrologic time series in general and streamflow series in particular most of them are normal autoregressive ar of order 1 with either constant or periodic parameters since generally hydrologic time series are nonnormal skewed transformations have been suggested to make the series approximately normal a new class of univariate models is proposed herein which incorporates skewed and correlation properties within the model structure without the necessity of transformations such models assume a gamma marginal distribution and a constant or periodic autoregressive structure the models may be additive gamma multiplicative gamma or a mixed model which incorporates properties of both additive and multiplicative models the gamma models were tested and compared in relation to transformed normal ar models by computer simulation studies based on five weekly streamflow series with samples varying from 35 to 40 years of record the results show that the new class of gamma models compares favorably with respect to the normal models in reproducing the basic statistics usually analyzed for streamflow simulation it is expected that the proposed gamma models will be of interest to other researchers for further developments and applications to hydrologic and geophysical time series

estimating correlations in multivariate streamflow models multivariate log normal distributions are often used to model and generate multisite and multiseason streamflow sequences a monte carlo study evaluated alternative estimators of the cross correlation between autocorrelated streamflow series and the lag 1 autocorrelation of a single series when some or all of the flows have a log normal distribution generally smaller mean square error estimates of the correlations of flows are obtained by using the variances and covariances of the flow s logarithms to estimate a streamflow model s parameters sometimes it is advantageous to prewhiten two series before calculating their cross correlation and to unbias the estimated autocorrelation of the streamflow s logarithms

reduced basis approximation and a posteriori error estimation for a boltzmann model abstract we present a reduced basis approximation and associated rigorous a posteriori output flow rate error bound for a simple linearized bgk boltzmann model for flow in a channel we consider two parameters the knudsen number and the accommodation coefficient the reduced basis approximation is built upon and the reduced basis error is measured relative to a truth mapped weighted spectral discretization of a stabilized petrov galerkin weak formulation we exploit the affine nature of the parametric dependence to provide an offline online computational procedure that decouples the spectral and reduced basis quantities the computational complexity of the online stage in which given a new parameter value we evaluate the reduced basis flow rate prediction and associated error bound depends only on the typically very small dimension of the reduced basis space n and not on the typically very large dimension of the truth spectral approximation n we demonstrate that the reduced basis approximation converges very rapidly with n and that the error estimator effectivities remain bounded albeit somewhat large in the online stage the reduced basis approximation achieves a certifiable relative accuracy of 10 2 with respect to the truth spectral result at only 1 100th the computational effort the method is appropriate in the many query and real time e g parameter estimation contexts in which there is a premium on reduced marginal cost and a tolerance for significant offline pre processing effort

a note on defuzzification of type 2 fuzzy intervals abstract in this paper we introduce a new form of defuzzification for a type 2 fuzzy interval over a referential interval a b this new procedure is performed in two steps first calculating the crisp set level average of the type 2 fuzzy interval via aumann integration with respect to 0 1 over the class of all level sets of the corresponding type 1 fuzzy membership grades with x a b and then taking the mid point of the resultant interval for obtaining the defuzzification value furthermore we prove the continuity of this defuzzification method with respect to a suitable metrics over the class of type 2 fuzzy intervals

minimum variance streamflow record augmentation procedures traditional approaches for augmentation of short streamflow records have exploited the cross correlation among flows at two or more gages to obtain maximum likelihood estimates of the mean and variance of the flows at the short record gage while such estimators asymptotically have minimum variance among all asymptotically unbiased estimators they are not necessarily optimal for the small samples of interest in hydrology improved estimators of the mean and variance of the flows at the short record gage are developed the gains in information transfer associated with the use of both the traditional and improved estimators of the mean and variance are documented monte carlo results illustrate the performa1 ce of these estimators when the true cross correlation of the flows must be estimated the information transfer gains when the true cross correlation must be estimated are com parable to the gains achieved when the cross correlation is known the potential advantages and limi tations of these new estimators are discussed within the framework of augmentation and or extension of both peak annual floods and also monthly streamflow records

general minkowski type inequalities for sugeno integrals minkowski type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the pseudo additive operation

a sugeno integral inequality of carleman knopp type and some refinements abstract in this paper a carleman knopp type inequality for sugeno integrals is studied in a similar form than classical one considering all involved integrals in the sugeno sense with respect to the lebesgue measure also some refinements and examples are presented