gradient estimates in orlicz space for nonlinear elliptic equations abstract in this paper we generalize gradient estimates in l p space to orlicz space for weak solutions of elliptic equations of p laplacian type with small bmo coefficients in reifenberg flat domains our results improve the known results for such equations using a harmonic analysis free technique

a fuzzy syllogistic reasoning schema for generalized quantifiers in this paper a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways i a number of different types of quantifiers logical absolute proportional comparative and exception taken from theory of generalized quantifiers and similarity quantifiers taken from statistics are considered and ii any number of premises can be taken into account within the reasoning process furthermore a systematic reasoning procedure to solve the syllogism is also proposed interpreting it as an equivalent mathematical optimization problem where the premises constitute the constraints of the searching space for the quantifier in the conclusion

sobolev embeddings in metric measure spaces with variable dimension in this article we study metric measure spaces with variable dimension we consider lebesgue spaces on these sets and embeddings of the riesz potential in these spaces we also investigate hajlasz type sobolev spaces and prove sobolev and trudinger inequalities with optimal exponents all of these questions lead naturally to function spaces with variable exponents

linguistic quantifiers modeled by sugeno integrals since quantifiers have the ability of summarizing the properties of a class of objects without enumerating them linguistic quantification is a very important topic in the field of high level knowledge representation and reasoning this paper introduces a new framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures and the truth value of a quantified proposition is evaluated by using sugeno s integral this framework allows us to have some elegant logical properties of linguistic quantifiers we compare carefully our new model of quantification and other approaches to linguistic quantifiers a set of criteria for linguistic quantification was proposed in the previous literature the relationship between these criteria and the results obtained in the present paper is clarified some simple applications of the sugeno s integral semantics of quantifiers are presented

global weighted lorentz estimates to nonlinear parabolic equations over nonsmooth domains abstract an elaborate method is developed to establish a global calderon zygmund type theory in weighted lorentz spaces l q t for zero cauchy dirichlet problem of nonlinear parabolic equations of p laplacian type with p 2 d d 2 here we assume that the nonlinearity a a t x is merely measurable in the time variable t and has a mall bmo semi norm in the spatial variables x uniformly in variables while the boundary of bounded domain is flat in the sense of reifenberg our result not only develops nonlinear calderon zygmund theory under weak regularity assumptions on the datum but also extends the related framework from lebesgue spaces to refined weighted lorentz spaces

error estimation of perturbations under cri the analysis of stability and robustness of fuzzy reasoning is an important issue in areas like intelligent systems and fuzzy control an interesting aspect is to what extent the perturbation of input in a fuzzy reasoning scheme causes the oscillation of the output in particular when the error limits restrictions of the input values are given what the error limits of the output values are in this correspondence we estimate the upper and lower bounds of the output error affected by the perturbation parameters of the input and obtain the limits of the output values when the input values range over some interval in many fuzzy reasoning schemes under compositional rule of fuzzy inference cri

on the operator l f f log f abstract the present note deals with the operator l h 1 r n d r n which takes a given element f of the hardy space to the function f log f in general this function need not be locally integrable nevertheless due to peculiar cancellations of large positive and negative terms in the integral f log f with c 0 r n we are able to give meaning to f log f as a schwartz distribution we find several alternatives for this interpretation of f log f

regularity results for a class of functionals with non standard growth we consider the integral functional under non standard growth assumptions that we call p x type namely we assume that a relevant model case being the functional under sharp assumptions on the continuous function p x 1 we prove regularity of minimizers energies exhibiting this growth appear in several models from mathematical physics

besov spaces with variable smoothness and integrability abstract in this article we introduce besov spaces with variable smoothness and integrability indices we prove independence of the choice of basis functions as well as several other basic properties we also give sobolev type embeddings and show that our scale contains variable order holder zygmund spaces as special cases we provide an alternative characterization of the besov space using approximations by analytic functions

existence and multiplicity results for a new p x kirchhoff problem abstract in this work we study the existence and multiplicity results for the following nonlocal p x kirchhoff problem 0 1 a b 1 p x u p x d x d i v u p x 2 u u p x 2 u g x u in u 0 on where a b 0 are constants r n is a bounded smooth domain p c with n p x 1 is a real parameter and g is a continuous function the analysis developed in this paper proposes an approach based on the idea of considering a new nonlocal term which presents interesting difficulties

weighted orlicz estimates for general nonlinear parabolic equations over nonsmooth domains we introduce a parabolic analogue of muckenhoupt weights to study optimal weighted regularity in orlicz spaces for a general nonlinear parabolic problem of p laplacian type in divergence form over a nonsmooth domain assuming that the nonlinearity is measurable with respect to the time variable and has a small bounded mean oscillation bmo with respect to the spatial variables that the lateral boundary of the parabolic cylinder is reifenberg flat and that the associated weight belongs to a suitable parabolic muckenhoupt class we obtain a global gradient estimate for such a nonlinear parabolic problem by essentially proving that the gradient of the weak solution is as globally integrable as the nonhomogeneous term in the weighted orlicz space our results extend the existing regularity estimates in lebesgue spaces to weighted orlicz spaces

parabolic equations in time dependent reifenberg domains in this paper we define time dependent parabolic reifenberg domains and study lp estimates for weak solutions of uniformly parabolic equations in divergence form on these domains the basic assumption is that the principal coefficients are of parabolic bmo space with small parabolic bmo seminorms it is shown that lp estimates hold for time dependent parabolic d reifenberg domains

regularity results for stationary electro rheological fluids we prove regularity results for weak solutions to systems modelling electro rheological fluids in the stationary case as proposed in 27 31 a particular case of the system we consider is

l fuzzy quantifiers of type determined by fuzzy measures the aim of this paper is first to introduce two new types of fuzzy integrals namely fuzzy integral and fuzzy integral the first integral is based on a fuzzy measure of l fuzzy sets and the second one on a complementary fuzzy measure of l fuzzy sets where l is a complete residuated lattice some of their properties and a relation to the fuzzy sugeno integral are investigated second using these integrals two classes of monadic l fuzzy quantifiers of type are defined these l fuzzy quantifiers can be used for modeling the semantics of natural language quantifiers like all some many none at most half etc several semantic properties of these l fuzzy quantifiers are studied

eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent in this paper we are concerned with a new class of anisotropic quasilinear elliptic equations with a power like variable reaction term one of the main features of our work is that the differential operator involves partial derivatives with different variable exponents so that the functional analytic framework relies upon anisotropic sobolev and lebesgue spaces existence and nonexistence results are deeply influenced by the competition between the growth rates of the anisotropic coefficients our main results point out some striking phenomena related to the existence of a continuous spectrum in several distinct situations

metric regularity tangential distances and generalized differentiation in banach spaces abstract in this paper we establish new generalized differentiation rules in general banach spaces regarding normal cones to set images under functions coderivatives of compositions of set valued mappings as well as calculus results for normal compactness of sets and their images in addition to the metric regularity of mappings our results involve tangential distances of sets for which we also provide a fairly complete study by exploring its variations basic properties as well as relations to similar notions some related results are also established

an optimal interpolation theorem of marcinkiewicz type in orlicz spaces abstract an extension of the marcinkiewicz interpolation theorem is proved yielding a necessary and sufficient condition for every quasilinear operator satisfying given endpoint estimates of weak type to be bounded from an orlicz space into another

harmonic type approximation lemmas we give a survey of known and not known harmonic type approximation lemmas which are descendants of the classical de giorgi s one and we outline some of their recent or possible applications

regularity of solutions to a class of variable exponent fully nonlinear elliptic equations abstract in the present paper we propose the investigation of variable exponent degenerate singular elliptic equations in non divergence form this current endeavor parallels the by now well established theory of functionals satisfying nonstandard growth condition which in particular encompasses problems ruled by the p x laplacian operator under rather general conditions we prove viscosity solutions to variable exponent fully nonlinear elliptic equations are locally of class c 1 for a universal constant 0 1 a key feature of our estimates is that they do not depend on the modulus of continuity of exponent coefficients and thus may be employed to investigate a variety of problems whose ellipticity degenerates and or blows up in a discontinuous fashion

higher integrability for minimizers of integral functionals with p q growth abstract we prove higher integrability for minimizers u r n of integral functionals f du a x u dx where f satisfies a non standard growth condition of p q type z p f z l 1 z q p

integral operators on the halfspace in generalized lebesgue spaces lp part ii in this paper we generalize a version of the classical calderon zygmund theorem on principle value integrals in generalized lebesgue spaces lp proved in j reine angew math 563 2003 197 220 to kernels which do not satisfy standard estimates on rd 1 this result will be used in part ii of this paper to prove the classical theorem on halfspace estimates of agmon douglis and nirenberg comm pure appl math 12 1959 623 727 for generalized lebesgue spaces lp

lp λ regularity for fully nonlinear elliptic equations abstract we establish the variable exponent morrey spaces l p estimate to the dirichlet problem for fully nonlinear elliptic equations on a c 1 1 bounded domain for variable exponents p and

epi lipschitz like sets in banach space theorems and examples on considere un espace de banach x et on etudie quelles proprietes un ensemble c dans x doit avoir pour que le cone tangent de clarke t c x et le cone normal n c x mesurent adequatement le comportement a la frontiere de x dans c

fuzzy quantifiers defined over fuzzy domains abstract in this paper we introduce a generalization of the concept of fuzzy quantifier called fuzzy quantifiers over fuzzy domains the development of this generalization is motivated by the impossibility to satisfactorily define the important operation of relativization for standard fuzzy quantifiers we provide basic examples of these quantifiers and define and investigate also several semantic properties of them finally we prove a theorem saying among other things that all these two argument fuzzy quantifiers that possess properties of extension and conservativity are relativizations of one argument fuzzy quantifiers of this kind

gradient estimates for a class of parabolic systems we establish local calderon zygmund type estimates for a class of parabolic problems whose model is the nonhomogeneous degenerate singular parabolic p laplacian system ut div du p 2du div f p 2f proving that f lqloc du lqloc q p we also treat systems with discontinuous coefficients of vanishing mean oscillation vmo type

l q estimates of gradients for evolutional p laplacian systems abstract we study l q estimates of gradients for evolutional p laplacian systems with discontinuous coefficients and external force given by the divergence of bmo functions the result obtained here may be regarded as a partial generalization of the calderon zygmund theory in l q estimate for the parabolic operator of second order to the evolutional p laplace operator

optimal regularity estimates for parabolic p harmonic equations in this paper optimal regularity estimates for weak solutions of quasilinear parabolic equations of p laplacian type with small bmo coefficients are investigated our results improve the known results for such equations using a harmonic analysis free technique

developments and perspectives in nonlinear potential theory abstract nonlinear potential theory aims at replicating the classical linear potential theory when nonlinear equations are considered in recent years there has been a substantial development of this subject mostly linked to the possibility of proving pointwise estimates for solutions to nonlinear equations via linear and nonlinear potentials here we give a brief account of such developments and outline the connections with different fields

abstract hardy spaces with variable exponents abstract in this paper we introduce the definition of abstract hardy spaces with variable exponents via the atomic decomposition and molecular decomposition we prove the continuity from our variable hardy space h a t o p into l p where p r n 0 1 0 p p 1 moreover we investigate the bilinear theory finally we give an application of the abstract hardy spaces with variable exponents

variational analysis in nonsmooth optimization and discrete optimal control this paper is devoted to applications of modern methods of variational analysis to constrained optimization and control problems generally formulated in infinite dimensional spaces the main focus is on the study of problems with nonsmooth structures which require the usage of advanced tools of generalized differentiation in this way we derive new necessary optimality conditions in optimization problems with functional and operator constraints and then apply them to optimal control problems governed by discrete time inclusions in infinite dimensions the principal difference between finite dimensional and infinite dimensional frameworks of optimization and control consists of the lack of compactness in infinite dimensions which leads to imposing certain normal compactness properties and developing their comprehensive calculus together with appropriate calculus rules of generalized differentiation on the other hand one of the most important achievements of the paper consists of relaxing the latter assumptions for certain classes of optimization and control problems in particular we fully avoid the requirements of this type imposed on target endpoint sets in infinite dimensional optimal control for discrete time inclusions

relaxing constraints in enhanced entity relationship models using fuzzy quantifiers while various articles about fuzzy entity relationship er and enhanced entity relationship eer models have recently been published not all examine how the constraints expressed in the model may be relaxed in this paper our aim is to relax the constraints which can be expressed in a conceptual model using the modeling tool so that these constraints can be made more flexible we will also study new constraints that are not considered in classic eer models we use the fuzzy quantifiers which have been widely studied in the context of fuzzy sets and fuzzy query systems for databases in addition we shall examine the representation of these constraints in an eer model and their practical repercussions the following constraints are studied the fuzzy participation constraint the fuzzy cardinality constraint the fuzzy completeness constraint to represent classes and subclasses the fuzzy cardinality constraint on overlapping specializations fuzzy disjoint and fuzzy overlapping constraints on specializations fuzzy attribute defined specializations fuzzy constraints in union types or categories and fuzzy constraints in shared subclasses we shall also demonstrate how fuzzy min max notation can substitute the fuzzy cardinality constraint but not the fuzzy participation constraint all these fuzzy constraints have a new meaning they offer greater expressiveness in conceptual design and are included in the so called fuzzy eer model

global gradient estimates for the parabolic p x t laplacian equation abstract in this paper we consider the global gradient estimates for weak solutions of the parabolic p x t laplacian type equation in a reifenberg flat domain

the singular set of minima of integral functionals in this paper we provide upper bounds for the hausdorff dimension of the singular set of minima of general variational integrals open image in new window where f is suitably convex with respect to dv and holder continuous with respect to x v in particular we prove that the hausdorff dimension of the singular set is always strictly less than n where open image in new window

regularity and existence of solutions of elliptic equations with p q growth conditions for some positive constants m a4 and for exponents q 2 p 2 2 under 1 2 1 3 and some other assumptions by assuming also that the quotient q p is sufficiently close to one in dependence on n precisely if q p c n n 2 then we prove that every weak solution to 1 1 of class 4 4 0 is locally lipschitz continuous in q moreover there are positive constants 8 c and 0 2 1 such that

global regularity for higher order divergence elliptic and parabolic equations abstract in this paper we obtain the global regularity estimates of the weak solutions in sobolev spaces and orlicz spaces for higher order elliptic and parabolic equations of divergence form with small bmo coefficients in the whole space we only focus on the parabolic case while the corresponding result in the elliptic case can be obtained as a corollary

on w1 p estimates for elliptic equations in divergence form first we will apply the method to study w 1 p regularity for a nonlinear elliptic operator in divergence form we would like to point out that in the particular case of a linear elliptic equation this method gives an alternative proof to the classical one which uses the general theory of singular integrals the utility of the method that we describe below is that hypotheses a and b are obtained directly by studying the deviation of the coefficients of a from the coefficients of a0 and this is usually not a difficult task a more interesting application of this kind of approximation method is to elliptic homogenization problems for which we obtain results that give w 1 p estimates with a weak hypothesis of regularity in the coefficients for instance we are able to study the following cases

calderon zygmund estimates for a class of quasilinear parabolic equations abstract in this paper we obtain the following local calderon zygmundestimates g f l l o c q t g u l l o c q t for any q 1 of weak solutions for a class of quasilinear parabolic equations u t div a u u div a f f in t where g t 0 t a d for t 0 we remark that g t t p log 1 t for p 2 satisfies the given conditions in this work moreover we would like to point out that our results improve the known results for such equations

lipschitz type smoothness of the fractional integral on variable exponent spaces fil ramseyer mauricio javier consejo nacional de investigaciones cientificas y tecnicas centro cientifico tecnologico conicet santa fe instituto de matematica aplicada del litoral universidad nacional del litoral instituto de matematica aplicada del litoral argentina

l p estimates for parabolic equations in reifenberg domains abstract the inhomogeneous neumann problem for parabolic equations in divergence form is studied an optimal regularity requirement on the domain for the l p theory is investigated assuming that the principal coefficients are supposed to be in the john nirenberg space with small bmo semi norms and that the domain is a reifenberg flat domain

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

on the continuity of weakly monotone functions abstract a criterion for the continuity of weakly monotone functions is proposed in terms of the decreasing rearrangement of their gradient its use in the proof of the continuity of weakly monotone functions with gradient in rearrangement invariant spaces is also demonstrated in particular weakly monotone functions whose gradient belongs to an orlicz space or to a lorentz space are discussed and results available in the literature in this regard are extended and refined

an eigenvalue problem with variable exponents abstract a highly nonlinear eigenvalue problem is studied in a sobolev space with variable exponent the euler lagrange equation for the minimization of a rayleigh quotient of two luxemburg norms is derived the asymptotic case with a variable infinity is treated local uniqueness is proved for the viscosity solutions

a generalization of discounted multistage decision making andcontrol through fuzzy linguistic quantifiers an attempt to introduce commonsense knowledge abstract this paper is an extension of work published by kacprzyk in 1983 in which by using a fuzzy logic based calculus of linguistically quantified propositions some generalizations of multistage decision making and control have been proposed namely a new class of models has been developed that make it possible roughly speaking to find an optimal sequence of controls best satisfying fuzzy constraints and goals at say most or any other suitable linguistic quantifier for example almost all at least a few of the control stages in this paper we further extend the above mentioned approach by introducing discounting a variable importance of particular control stages in principle the earlier the more important we propose a new model that can find an optimal sequence of controls best satisfying the fuzzy constraints and goals at say most of the earlier control stages we employ a fuzzy logic based calculus of linguistically quantified propositions and develop a branch and bound algo

maximum principles for anisotropic elliptic inequalities we establish some maximum and comparison principles for weak distributional solutions of anisotropic elliptic inequalities in divergence form both in the homogeneous and non homogeneous case the main prototypes we have in mind are inequalities involving the p laplace operator and the generalized mean curvature operator

stability and instability of stationary solutions for sublinear parabolic equations abstract in the present paper we study the initial boundary value problem of the sublinear parabolic equation we prove the existence of solutions and investigate the stability and instability of stationary solutions we show that a unique positive and a unique negative stationary solutions are exponentially stable and give the exact exponent we prove that small stationary solutions are unstable for one space dimensional autonomous equations we elucidate the structure of stationary solutions and study the stability of all stationary solutions

higher integrability for nonlinear elliptic equations with variable growth abstract in this paper based on the theory of variable exponent spaces we study the regularity for a class of nonlinear elliptic equation with p x laplacian under suitable assumptions we obtain a local gradient estimate in the orlicz space for weak solution

linear second order divergence equations in lipschitz domains abstract in this paper we generalize gradient estimates in l p spaces to orlicz spaces for weak solutions of second order divergence elliptic equations with small bmo coefficients in lipschitz domains our results improve the known results for such equations using the harmonic analysis method

higher integrability for a quasilinear parabolic equation of p laplacian type abstract in this paper we generalize classical l q q p estimates of the gradient to the orlicz space for weak solutions of a quasilinear parabolic equation of p laplacian type

sequential normal compactness versus topological normal compactness in variational analysis abstract we study relationships between two normal compactness properties of sets in banach spaces that play an essential role in many aspects of variational analysis and its applications particularly in calculus rules for generalized differentiation necessary optimality and suboptimality conditions for optimization problems etc both properties automatically hold in finite dimensional spaces and reveal principal features of the infinite dimensional variational theory similar formulations of these properties involve the weak convergence of sequences and nets respectively containing generalized normal cones in duals to banach spaces we prove that these properties agree for a large class of banach spaces that include weakly compactly generated spaces we also show that they are always different in banach spaces whose unit dual ball is not weak sequentially compact moreover the sequential and topological normal compactness properties may not coincide even in non separable asplund spaces that admit an equivalent c smooth norm

mappings of bmo bounded distortion this paper can be viewed as a sequel to the work 9 where the theory of mappings of bmo bounded distortion is developed largely in even dimensions using singular integral operators and recent developments in the theory of higher integrability of jacobians in hardy orlicz spaces in this paper we continue this theme refining and extending some of our earlier work as well as obtaining results in new directions the planar case was studied earlier by g david 4 in particular he obtained existence theorems modulus of continuity estimates and bounds on area distortion for mappings of bmo distortion in fact in slightly more generality we obtain similar results in all even dimensions one of our main new results here is the extension of the classical theorem of painleve concerning removable singularties for bounded analytic functions to the class of mappings of bmo bounded distortion the setting of the plane is of particular interest and somewhat more can be said here because of the existence theorem or the measurable riemann mapping theorem which is not available in higher dimensions we give a construction to show our results are qualitatively optimal another surprising fact is that there are domains which support no bounded quasiregular mappings but admit

hardy inequalities in orlicz spaces we establish a sharp extension in the framework of orlicz spaces of the n dimensional hardy inequality involving functions defined on a domain g their gradients and the distance function from the boundary of g

variational analysis of extended generalized equations via coderivative calculus in asplund spaces abstract this paper is devoted to the development of variational analysis and generalized differentiation in the framework of asplund spaces we mainly concern the study of a special class of set valued mapping given in the form s x y y 0 f x y q x y x x where both f and q are set valued mappings between asplund spaces models of this type are associated with solutions maps to the so called extended generalized equations and play a significant role in many aspects of variational analysis and its applications to optimization stability control theory etc in this paper we conduct a local variational analysis of such extended solution maps s and their remarkable specifications based on dual space generalized differential constructions of the coderivative type the major part of our analysis revolves around coderivative calculus largely developed and implemented in this paper and then applied to establishing verifiable conditions for robust lipschitzian stability of extended generalized equations and related objects

on usual values in commonsense reasoning abstract in many cases commonsense knowledge consists of knowledge of what is usual in this paper we develop a system for reasoning with usual information this system is based upon the fact that these pieces of commonsense information involve both a probabilistic aspect and a granular aspect we implement this system with the aid of probabilistic possibilistic granules

interior a priori estimates for solutions of fully non linear equations on etend une theorie de perturbations aux solutions d equations uniformement elliptiques d ordre 2 totalement non lineaires

upward slopes and inf convolutions nonsmooth analysis and exact penalty methods give much prominence to functions that exit from certain lower level sets with positive upward slope a novel weak version of such slopes is formalized here and studied in terms of differential properties applied to inf convolutions those properties help to recover and extend recent results on nonconvex separation cooperative production or market games and welfare economics

local calderon zygmund estimates for parabolic minimizers abstract we establish local calderon zygmund estimates for parabolic minimizers u to certain variational inequalities the formal corresponding parabolic partial differential equation would be t u div f z u d u u f z u d u div f p 2 f h with p 2 n n 2 however since we do not impose any condition on the existence of the derivative u f the pde above may not have any meaning at all for proving the calderon zygmund estimates we thus remain solely on the level of parabolic minimizers precisely for q p we prove that d u l loc q if u is locally holder continuous and f l loc q and h l loc q for a q depending on q

robustness of fuzzy reasoning and spl delta equalities of fuzzy sets fuzzy reasoning methods or approximate reasoning methods are extensively used in intelligent systems and fuzzy control in this paper the author discusses how errors in premises affect conclusions in fuzzy reasoning that is he discusses the robustness of fuzzy reasoning after reviewing his previous work 1996 he presents robustness results for various implication operators and inference rules all the robustness results are formulated in terms of spl delta equalities of fuzzy sets two fuzzy sets are said to be spl delta equal if they are equal to an extent of spl delta

an overview of fuzzy quantifiers ii reasoning and applications abstract in the second part of the overview reasoning with fuzzily defined quantifiers and applications are presented possibility based reasoning is summarized in detail the widely used quantifier extension principle and various reasoning schemas derived from it are discussed some disadvantages of the quantifier extension principle are pointed out although intervalvalued quantifiers are only a special case of general quantifiers some specific properties and results arise from them furthermore they suggest another approach to interence with fuzzy quantifiers reasoning with quantification and several kinds of qualification is introduced this kind of reasoning requires a seamless synthesis of probability theory possibility theory fuzzy logic and belief theory at last the applications of fuzzily defined quantifiers in decision making and fuzzy database systems are introduced

riesz potential estimates for a class of double phase problems abstract a double phase problem with a bounded borel measure on the right hand side is studied we prove an optimal pointwise gradient estimate for such a measure data problem via riesz potentials of the measure under log dini continuity assumption on the modulating coefficients as a consequence we find an optimized c 1 regularity criterion

on the analysis of set based fuzzy quantified reasoning using classical syllogistics syllogism is a type of deductive reasoning involving quantified statements the syllogistic reasoning scheme in the classical aristotelian framework involves three crisp term sets and four linguistic quantifiers for which the main support is the linguistic properties of the quantifiers a number of fuzzy approaches for defining an approximate syllogism have been proposed for which the main support is cardinality calculus in this paper we analyze fuzzy syllogistic models previously described by zadeh and dubois et al and compare their behavior with that of the classical aristotelian framework to check which of the 24 classical valid syllogistic reasoning patterns or moods are particular crisp cases of these fuzzy approaches this allows us to assess to what extent these approaches can be considered as either plausible extensions of the classical crisp syllogism or a basis for a general approach to the problem of approximate syllogism

non monotonic logic i abstract non monotonic logical systems are logics in which the introduction of new axioms can invalidate old theorems such logics are very important in modeling the beliefs of active processes which acting in the presence of incomplete information must make and subsequently revise assumptions in light of new observations we present the motivation and history of such logics we develop model and proof theories a proof procedure and applications for one non monotonic logic in particular we prove the completeness of the non monotonic predicate calculus and the decidability of the non monotonic sentential calculus we also discuss characteristic properties of this logic and its relationship to stronger logics logics of incomplete information and truth maintenance systems

type fuzzy quantifiers determined by fuzzy measures on residuated lattices part i basic definitions and examples abstract we study fuzzy quantifiers of type 1 1 defined using fuzzy measures and integrals residuated lattices are considered as structures of truth values we present basic notions on fuzzy measures over algebras of fuzzy subsets of a given fuzzy set and the definition and necessary properties of so called fuzzy integrals residuated lattice operations are established to derive operations between fuzzy sets describing degrees in which formulas expressing relations between fuzzy sets are true finally a general definition of type 1 1 fuzzy quantifiers determined by fuzzy measures and integrals is introduced and several examples of important natural language quantifiers are modeled using this approach

gradient estimates for the p x laplacean system we prove calderon and zygmund type estimates for a class of elliptic problems whose model is the non homogeneous p x laplacean system div jduj p x 2 du div jf j p x 2 f

an extended extremal principle with applications to multiobjective optimization we develop an extended version of the extremal principle in variational analysis that can be treated as a variational counterpart to the classical separation results in the case of nonconvex sets and which plays an important role in the generalized differentiation theory and its applications to optimization related problems the main difference between the conventional extremal principle and the extended version developed below is that instead of the translation of sets involved in the extremal systems we allow deformations the new version seems to be more flexible in various applications and covers in particular multiobjective optimization problems with general preference relations in this way we obtain new necessary optimality conditions for constrained problems of multiobjective optimization with nonsmooth data and also for multiplayer multiobjective games