an optimal control problem for a two prey and one predator model with diffusion abstract an optimal control problem is studied for a reaction diffusion system that models an ecosystem composed by one predator and two prey populations one proposed to maximize the total density of the three populations to do this one proves the existence of an optimal solution and one establishes first and second order optimality conditions several numerical simulations performed in both one dimensional and two dimensional isolated environments and using different holling type functional responses support the theoretical results

optimal control problem for an ecosystem with two competing preys and one predator abstract this work is devoted to the optimal control problem for an ecosystem composed of one predator and two competing preys and our goal is to maximize the total density of the three populations we first investigate the existence and uniqueness of the positive strong solution for the controlled system and find an optimal solution under given initial conditions then we establish the first order necessary optimality condition and point out that the optimal control has a bang bang form moreover the second order necessary and sufficient optimality conditions are established

remarks on chirka s proof of slodkowski s theorem by applying schauder s fixed point theorem to an integral operator chirka de veloped a remarkably simple proof for slodkowski s theorem on extending holomorphic motions in this paper we first present our understanding of a motive for designing the integral opera tor from which we also recapitulate the main work in chirka s proof when applying chirka s operator in different ways to obtain the extensions of holomorphic motions a question on the uniqueness of extensions arises after a brief summary on some known sufficient conditions for the uniqueness of extensions we raise two questions concerning the necessary conditions for the uniqueness of the extensions of the holomorphic motions of four points at the end we present an application when the extension is unique that is we show that there is a holomorphic map from the unit open disk d to the teichmuller space of symmetric circle homeomorphisms such that it can not be lifted to a holomorphic map from d to the complex banach space of vanishing beltrami coefficients

lyapunov functionals for delay differential equations model of viral infections we study global properties of a class of delay differential equations model for virus infections with nonlinear transmissions compared with the typical virus infection dynamical model this model has two important and novel features to give a more complex and general infection process a general nonlinear contact rate between target cells and viruses and the removal rate of infected cells are considered and two constant delays are incorporated into the model which describe i the time needed for a newly infected cell to start producing viruses and ii the time needed for a newly produced virus to become infectious mature respectively by the lyapunov direct method and using the technology of constructing lyapunov functionals we establish global asymptotic stability of the infection free equilibrium and the infected equilibrium we also discuss the effects of two delays on global dynamical properties by comparing the results with the stability conditions for the model without delays further we

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

holomorphic motions and teichmuller spaces we prove an equivariant form of slodkowski s theorem that every holomorphic motion of a subset of the extended complex plane c extends to a holomorphic motion of c as a consequence we prove that every holomorphic map of the unit disc into teichmuller space lifts to a holomorphic map into the space of beltrami forms we use this lifting theorem to study the teichmuller metric

mathematical insights and integrated strategies for the control of aedes aegypti mosquito we consider a delayed model for the control of a mosquito population which is subject to an integrated strategy that includes pesticide release the use of mechanical controls and the use of the sterile insect technique sit the existence of positive equilibria is characterized in terms of two biologically relevant threshold quantities a nonstandard finite difference nsfd scheme is used to approximate the continuous model it is observed that a combination of all three controls has the highest impact upon the size of the aquatic population at higher environmental temperatures the oviposition rate is seen to possess the most prominent influence upon the outcome of the control measures this paper proposes and investigates a delayed model for the dynamics and control of a mosquito population which is subject to an integrated strategy that includes pesticide release the use of mechanical controls and the use of the sterile insect technique sit the existence of positive equilibria is characterized in terms of two threshold quantities being observed that the richer equilibrium with more mosquitoes in the aquatic phase has better chances to be stable while a longer duration of the aquatic phase has the potential to destabilize both equilibria it is also found that the stability of the trivial equilibrium appears to be mostly determined by the value of the maturation rate from the aquatic phase to the adult phase a nonstandard finite difference nsfd scheme is devised to preserve the positivity of the approximating solutions and to keep consistency with the continuous model the resulting discrete model is transformed into a delay free model by using the method of augmented states a necessary condition for the existence of optimal controls then determined the particularities of different control regimes under varying environmental temperature are investigated by means of numerical simulations it is observed that a combination of all three controls has the highest impact upon the size of the aquatic population at higher environmental temperatures the oviposition rate is seen to possess the most prominent influence upon the outcome of the control measures

modeling the dynamics of stage structure predator prey system with monod haldane type response function a stage structure predator prey model is proposed and analyzed in this paper in which predators are divided into juvenile and mature predators using monod haldane type response function the dynamical behavior of this system both analytically and numerically is investigated from the view point of stability and bifurcation we investigate global stability around the interior equilibrium point e by constructing suitable lyapunov function our model simulation indicates that the conversion of prey population to juvenile predators can destabilize the model system which lead to limit cycle oscillations we also investigate that the rate of juvenile predators becoming mature predators play an important role to destabilize the model system for the stable coexistence of both the populations we carried out extensive numerical simulations of the model to confirm the analytical findings

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

regular or stochastic dynamics in real analytic families of unimodal maps in this paper we prove that in any non trivial real analytic family of quasiquadratic maps almost any map is either regular i e it has an attracting cycle or stochastic i e it has an absolutely continuous invariant measure to this end we show that the space of analytic maps is foliated by codimension one analytic submanifolds hybrid classes this allows us to transfer the regular or stochastic property of the quadratic family to any non trivial real analytic family

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

global stability for a virus dynamics model with nonlinear incidence of infection and removal global dynamics of a compartmental model which describes virus propagation in vivo is studied using the direct lyapunov method where the incidence rate of the infection and the removal rate of the virus are assumed to be nonlinear in the case where the functional quotient between the force of infection and the removal rate of the virus is a nonincreasing function of the virus concentration the existence of a threshold parameter i e the basic reproduction number or basic reproductive ratio is established and the global stability of the equilibria is discussed moreover in the absence of the above mentioned monotonicity property estimations for the sizes of the domains of attraction are given biological significance of the results and possible extensions of the model are also discussed

families of rational maps and iterative root finding algorithms in this paper we develop a rigidity theorem for algebraic families of rational maps and apply it to the study of iterative root finding algorithms we answer a question of smale s by showing there is no generally convergent algorithm for finding the roots of a polynomial of degree 4 or more we settle the case of degree 3 by exhibiting a generally convergent algorithm for cubics and we give a classification of all such algorithms in the context of conformal dynamics our main result is the following a stable algebraic family of rational maps is either trivial all its members are conjugate by mobius transformations or affine its members are obtained as quotients of iterated addition on a family of complex tori our classification of generally convergent algorithms follows easily from this result as another consequence of rigidity we observe that the eigenvalues of a nonaffine rational map at its periodic points determine the map up to finitely many choices this implies that bounded analytic functions nearly separate points on the moduli space of a rational map

permanence and stability of a stage structured predator prey model abstract a predator prey model with a stage structure for the predator which improves the assumption that each individual predator has the same ability to capture prey is proposed it is assumed that immature individuals and mature individuals of the predator are divided by a fixed age and that immature predators do not have the ability to attack prey we obtain conditions that determine the permanence of the populations and the extinction of the populations furthermore we establish necessary and sufficient conditions for the local stability of the positive equilibrium of the model by exploiting the monotonicity of one equation of the model we obtain conditions for the global attractivity of the positive equilibrium which allow for long delay as long as the predator birth rate is large or the death rate of immature predators is small by constructing liapunov functionals we also obtain conditions under which the positive equilibrium is globally stable when the delay is small

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

global existence and uniqueness of positive solutions and optimal control for a novel model of pest control abstractin the present paper a novel model of pest control governed by coupled sets of partial and ordinary differential equations is investigated in detail global existence and uniqueness of positive solutions to the above model are obtained also the existence of optimal control is proved and the first order and second order optimality conditions satisfied by optimal control are verified in particular the optimal control is demonstrated to be of bang bang form

grafting pruning and the antipodal map on measured laminations grafting a measured lamination on a hyperbolic surface de nes a self map of teichmuller space which is a homeomorphism by a result of scannell and wolf in this paper we study the large scale behavior of pruning which is the inverse of grafting speci cally for each conformal structure x t s pruning x gives a map ml s t s we show that this map extends to the thurston compacti cation of t s and that its boundary values are the natural antipodal involution relative to x on the space of projective measured laminations we use this result to study thurston s grafting coordinates on the space of cp structures on s for each x t s we show that the boundary of the space p x of cp structures on x in the compactication of the grafting coordinates is the graph ix of the antipodal involution ix pml s pml s

canonical models for a class of polynomially convex hulls we use holomorphic motions and beltrami equation to study a class of polynomially convex hulls in 2 with jordan fibers over the disc d it is shown that every such hull is biholomorphically equivalent to a unique up to suitable normalisation canonical model these models are the hulls whose complements in d macr are biholomorphic to a bidisc and are further characterized in terms of capacity of the fibers green s function pseudoconcavity and approximability by very special analytic polyhedra

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

quasiconformal and bi lipschitz homeomorphisms uniform domains and the quasihyperbolic metric let d be a proper subdomain of r and kd the quasihyperbolic metric defined by the conformal metric tensor ds2 dist x dd 2ds2 the geodesies for this and related metrics are shown by purely geometric methods to exist and have lipschitz continuous first derivatives this is sharp for kd we also obtain sharp estimates for the euclidean curvature of such geodesies we then use these results to prove a general decomposition theorem for uniform domains in r in terms of embeddings of bi lipschitz balls we also construct a counterexample to the higher dimensional analogue of the decomposition theorem of gehring and osgood the defining density dist x 3d 1 need not be differentiable we primarily are interested in studying the geometry of the quasihyperbolic meric and its geodesies we show that the geodesies of this metric are c11 i e the arclength parametrisation has lipschitz continuous derivatives we show that this is best possible and obtain a sharp result on the euclidean curvature of such geodesies these results are proved for a more general class of metrics in particular metrics defined by locally lipschitz densities we then use these results to prove a gener alisation of the decomposition theorem of gehring and osgood for uniform domains in ri space i wish to express my sincere thanks to f w gehring for suggesting many of these problems for many helpful ideas and simplifications throughout and for allowing me to present his proof of theorem 3 7 i also wish to thank him and d herron for carefully reading the manuscript

the grafting map of teichmuller space one of the underlying principles in the study of kleinian groups is that aspects of the complex projective geometry of quotients of by these groups reflect properties of the three dimensional hyperbolic geometry of the quotients ofh by these groups yet even though it has been over thirty five years since lipman bers exhibited a holomorphic embedding of the teichmuller space of riemann surfaces in terms of the projective geometry of a teichmuller space of quasi fuchsian manifolds no corresponding embedding in terms of the three dimensional hyperbolic geometry has been presented one of the goals of this paper is to give such an embedding this embedding is straightforward and has been expected for some time ta97 mc98 to each member of a bers slice of the space qf of quasi fuchsian 3manifolds we associate the bending measured lamination of the convex hull facing the fixed conformal end the geometric relationship between a boundary component of a convex hull and the projective surface at infinity for its end is given by a process known as grafting an operation on projective structures on surfaces that traces its roots back at least to klein kl33 p 230 50 with a modern history developed by many authors ma69 he75 fa83 st83 go87 gkm00 ta97 mc98 the main technical tool in our proof that bending measures give coordinates for bers slices and the second major goal of this paper is the completion of the proof of the grafting conjecture this conjecture states that for a fixed measured lamination the self map of teichmuller space induced by grafting a surface along is a homeomorphism of teichmuller space our contribution to this argument is a proof of the injectivity of the grafting map while the principal application of this result that we give is to geometric coordinates on the bers slice of qf one expects that the grafting homeomorphism might lead to other systems of geometric coordinates for other families of kleinian groups see 5 2 thus we feel that this result is of interest in its own right we now state our results and methods more precisely throughout s will denote a fixed differentiable surface which is closed orientable and of genus g 2 let tg be the corresponding teichmuller space of marked conformal structures on s and let pg denote the deformation space of complex projective structures on s see 2 for definitions

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

strongly hyperbolic metrics on ptolemy spaces abstract recently strongly hyperbolic space as certain analytic enhancements of gromov hyperbolic space was introduced by b nica and j spakula in this paper we prove that the log metric log 1 d on the ptolemy space x d is a strongly hyperbolic metric using our result we construct two metrics on the ptolemy space and prove they are strongly hyperbolic

dynamics of a general prey predator model with prey stage structure and diffusive effects in this paper we propose and study the dynamics of a diffusive prey predator model with general functional response and stage structure for the prey firstly we consider the asymptotical stability of equilibrium points and hopf bifurcation for the reduced ode system secondly the existence and uniform boundedness of global solutions and stability of equilibrium points for the corresponding reaction diffusion system are discussed finally we establish the existence and the nonexistence of nonconstant positive steady states of this reaction diffusion system which indicates the effect of large diffusivity our results shows the importance of the diffusion rate of the predator species i e d 3 the large diffusion rate of the predator alone will help the generation of patterns however a large diffusion rate of the immature prey species or a large diffusion rate of the mature prey species can lead to the nonexistence of spatial patterns

the hausdorff dimension of the boundary of the mandelbrot set and julia sets it is shown that the boundary of the mandelbrot set m has hausdorff dimension two and that for a generic c e am the julia set of z i z2 c also has hausdorff dimension two the proof is based on the study of the bifurcation of parabolic periodic points

dynamic behavior of a beddington deangelis type stage structured predator prey model abstract this paper deals with a robust stage structured predator prey model with beddington deangelis type functional response the proposed mathematical model consists of a system of three nonlinear ordinary differential equations to stimulate the interactions between prey population juvenile predators and adult predator population the positivity boundedness and the conditions for uniform persistence have been derived the dynamical behavior of the system both analytically and numerically investigated from the point of view of local stability persistence and global stability the global stability of the system has been derived by using the theory of competitive systems stability of periodic orbits and compound matrices for the interior equilibrium point depending on the conversion rate of the prey population to juvenile predator the model exhibits hopf bifurcation the model admit periodic solutions which is produced from the stage structure of the predator populations numerical simulations have been accomplished to validate our analytical findings

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

the distribution of free path lengths in the periodic lorentz gas and related lattice point problems the periodic lorentz gas describes the dynamics of a point particle in a periodic array of spherical scatterers and is one of the fundamental models for chaotic diffusion in the present paper we investigate the boltzmann grad limit where the radius of each scatterer tends to zero and prove the existence of a limiting distribution for the free path length we also discuss related problems such as the statistical distribution of directions of lattice points that are visible from a fixed position

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

braiding of the attractor and the failure of iterative algorithms le mouvement de l attracteur dans une famille stable d applications rationnelles determine un groupe de tresses sur la sphere de riemann on montre que le groupe correspondant des classes d application est soit reductible soit fini soit fixe l un des attracteurs ceci conduit a un critere topologique d existence des bifurcations dans les algorithmes iteratifs de recherche de racines bases sur des applications rationnels

extending isotopies of planar continua in this paper we solve the following problem in the affirmative let z be a continuum in the plane c and suppose that h z x 0 1 c is an isotopy starting at the identity can h be extended to an isotopy of the plane we will provide a new characterization of an accessible point in a planar continuum z and use it to show that accessibility of a point is preserved during the isotopy we show next that the isotopy can be extended over small hyperbolic crosscuts which are shown to remain small under the isotopy the proof makes use of the notion of a metric external ray which mimics the notion of a conformal external ray but is easier to control during an isotopy it also relies on the existence of a partition of a hyperbolic simply connected domain u in the sphere into hyperbolically convex subsets which have limited distortion under conformal maps to the unit disk

frontiers in complex dynamics rational maps on the riemann sphere occupy a distinguished niche in the general theory of smooth dynamical systems first rational maps are complexanalytic so a broad spectrum of techniques can contribute to their study quasiconformal mappings potential theory algebraic geometry etc the rational maps of a given degree form a finite dimensional manifold so exploration of this parameter space is especially tractable finally some of the conjectures once proposed for smooth dynamical systems and now known to be false seem to have a definite chance of holding in the arena of rational maps in this article we survey a small constellation of such conjectures centering around the density of hyperbolic rational maps those which are dynamically the best behaved we discuss some of the evidence and logic underlying these conjectures and sketch recent progress towards their resolution

an extended fatou shishikura inequality and wandering branch continua for polynomials abstract let p be a polynomial of degree d with julia set j p let n be the number of non repelling cycles of p by the famous fatou shishikura inequality n d 1 the goal of the paper is to improve this bound the new count includes wandering collections of non pre critical branch continua i e collections of continua or points q i j p all of whose images are pairwise disjoint contain no critical points and contain the limit sets of eval q i 3 external rays also we relate individual cycles which are either non repelling or repelling with no periodic rays landing to individual critical points that are recurrent in a weak sense a weak version of the inequality reads n n irr i eval q i 2 d 1 where n irr counts repelling cycles with no periodic rays landing at points in the cycle q i form a wandering collection b c of non pre critical branch continua 1 if b c is non empty and 0 otherwise

stable periodic orbits for a class of three dimensional competitive systems abstract it is shown that for a dissipative three dimensional competitive and irreducible system of ordinary differential equations having a unique equilibrium point at which point the jacobian matrix has negative determinant either the equilibrium point is stable or there exists an orbitally stable periodic orbit if in addition the system is analytic then there exists an orbitally asymptotically stable periodic orbit when the equilibrium is unstable the additional assumption of analyticity can be replaced by the assumption that the equilibrium point and every periodic orbit are hyperbolic in this case the morse smale conditions hold and the flow is structurally stable

on connectivity of julia sets of yang lee zeros we prove that the julia sets of the yang lee zeros of the potts model on the diamond hierarchical lattice are connected sets on the complex plane

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

a predator prey system with stage structure for predator abstract this paper studies the asymptotoc behavior of a predator prey model with stage structure it is found that an orbitally asymptotically stable periodic orbit exists in that model when time delay due to gestation of predator and time delay from crowding effect of prey are incorporated we establish the condition for the permanence of populations and sufficient conditions under which positive equilibrium of the model is globally stable

comparing poincare densities however there is no formula for the poincare density pn of a general plane domain q and so one must resort to estimates many research articles have been devoted to finding and working with such estimates see for example 4 5 15 19 24 and 25 the first tool to establish such estimates is schwarz s lemma which says that every holomorphic map is a contraction with respect to the poincare metric that is ps f ldf i pd z idzl for any holomorphic map f from a riemann surface d to another riemann surface q applying this lemma

global dynamics of a predator prey model with stage structure for the predator the global properties of a predator prey model with nonlinear functional response and stage structure for the predator are studied using lyapunov functions and lasalle s invariance principle it is found that under hypotheses which ensure the uniform persistence of the system and the existence of a unique positive steady state a feasible a priori lower bound condition on the abundance of the prey population ensures the global asymptotic stability of the positive steady state a condition which leads to the extinction of the predators is indicated we also obtain results on the existence and stability of periodic solutions in particular when 4 2 fails to hold and the unique positive steady state e becomes unstable the coexistence of prey and predator populations is ensured for initial populations not on the one dimensional stable manifold of e albeit with fluctuating population sizes

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

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

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

the schwarzian derivative and measured laminations on riemann surfaces a holomorphic quadratic differential on a hyperbolic rie mann surface has an associated measured foliation which can be straight ened to yield a measured geodesic lamination on the other hand a quadratic differential can be considered as the schwarzian derivative of a 1 structure to which one can naturally associate another measured geodesic lamination using grafting we compare these two relationships between quadratic differentials and measured geodesic laminations each of which yields a homeomor phism ml s q x for each conformal structure x on a compact surface s we show that these maps are nearly the same differing by a multiplicative factor of 2 and an error term of lower order than the maps themselves which we bound explicitly as an application we show that the schwarzian derivative of a 1 structure with fuchsian holonomy is close to a 2 integral jenkins strebel differential we also study compactifications of the space of 1 structures using the schwarzian derivative and grafting coordinates we show that the natural map between these extends to the boundary of each fiber over teichmuller space and we describe this extension

boundary behavior and the martin boundary problem for p harmonic functions in lipschitz domains boundary behavior and the martin boundary problem for p harmonic functions in lipschitz domains

continuity of capacity of a holomorphic motion abstract we study the behavior of various set functions under holomorphic motions we show that under such deformations logarithmic capacity varies continuously while analytic capacity may not