extension of noncommutative soliton hierarchies a linear system which generates a moyal deformed two dimensional soliton equation as an integrability condition can be extended to a three dimensional linear system treating the deformation parameter as an additional coordinate the supplementary integrability conditions result in a first order differential equation with respect to the deformation parameter the flow of which commutes with the flow of the deformed soliton equation in this way a deformed soliton hierarchy can be extended to a bigger hierarchy by including the corresponding deformation equations we prove the extended hierarchy properties for the deformed akns hierarchy and specialize to the cases of deformed nls kdv and mkdv hierarchies corresponding results are also obtained for the deformed kp hierarchy a deformation equation determines a kind of seiberg witten map from classical solutions to solutions of the respective noncommutative deformed equation

convergence of an iterative method for total variation denoising in total variation denoising one attempts to remove noise from a signal or image by solving a nonlinear minimization problem involving a total variation criterion several approaches based on this idea have recently been shown to be very effective particularly for denoising functions with discontinuities this paper analyzes the convergence of an iterative method for solving such problems the iterative method involves a lagged diffusivity approach in which a sequence of linear diffusion problems are solved global convergence in a finite dimensional setting is established and local convergence properties including rates and their dependence on various parameters are examined

weighted minimum and maximun operations in fuzzy sets theory abstract this short note comments on the interpretation of weighted minimum and maximum operations introduced in a previous paper as medians and corrects a misleading statement about it

interpolation of fuzzy data analytical approach and overview we propose a general framework for the interpolation problem our framework stems from the classical elaboration of the problem we introduce the notion of an interpolating fuzzy function and show how this function can be characterized we examine and analyze previously published fuzzy interpolation algorithms to choose those algorithms that can be represented analytically we also propose an analytic solution of the interpolation problem that unifies various algorithmic approaches

possibilistic instance based learning a method of instance based learning is introduced which makes use of possibility theory and fuzzy sets particularly a possibilistic version of the similarity guided extrapolation principle underlying the instance based learning paradigm is proposed this version is compared to the commonly used probabilistic approach from a methodological point of view moreover aspects of knowledge representation such as the modeling of uncertainty are discussed taking the possibilistic extrapolation principle as a point of departure an instance based learning procedure is outlined which includes the handling of incomplete information methods for reducing storage requirements and the adaptation of the influence of stored cases according to their typicality first theoretical and experimental results showing the efficiency of possibilistic instance based learning are presented as well

diagnosability of fuzzy discrete event systems in this paper discrete event systems dess are reformulated as fuzzy discrete event systems fdess and fuzzy discrete event dynamical systems fdedss these frameworks include fuzzy states events and if then rules in these frameworks all events occur at the same time with different membership degrees fuzzy states and events have been introduced to describe uncertainties that occur often in practical problems such as fault diagnosis applications to measure a diagnoser s fault discrimination ability a fuzzy diagnosability degree is proposed if the diagnosability of the degree of the system yields one a diagnoser can be implemented to identify all possible fault types related to a system for any degree less than one researchers should not devote their time to distinguish all possible fault types correctly thus two different diagnosability definitions fdeds and fdes are introduced due to the specialized fuzzy rule base embedded in the fdeds it is capable of representing a class of non linear dynamic system computationally speaking the framework of diagnosability of the fdeds is structurally similar to the framework of diagnosability of a non linear system the crisp des diagnosability has been turned into the term fuzzy diagnosability for the fdes the newly proposed diagnosability definition allows us to define a degree of diagnosability in a class of non linear systems in addition a simple fuzzy diagnosability checking method is introduced and some numerical examples are provided to illustrate this theoretical development finally the potential applications of the proposed method are discussed

dromions in 2 1 dimensional ferromagnetic spin chain with bilinear and biquadratic interactions we study the dynamics of 2 1 dimensional ferromagnetic spin chain with bilinear and biquadratic interactions by using holstein primakoff hp representation and the coherent state ansatz the dynamical equations of motion are obtained by using long wavelength approximation the sine cosine function method is used to study the complete nonlinear excitation and the effect of the different types of interactions is investigated graphically

some qualitative properties for the total variation flow we prove the existence of a finite extinction time for the solutions of the dirichlet problem for the total variation flow for the neumann problem we prove that the solutions reach the average of its initial datum in finite time the asymptotic profile of the solutions of the dirichlet problem is also studied it is shown that the profiles are nonzero solutions of an eigenvalue type problem that seems to be unexplored in the previous literature the propagation of the support is analyzed in the radial case showing a behaviour entirely different to the case of the problem associated with the p laplacian operator finally the study of the radially symmetric case allows us to point out other qualitative properties that are peculiar of this special class of quasilinear equations

the gauge equivalence of the davey stewartson equation and 2 1 dimensional continuous heisenberg ferromagnetic model the gauge equivalence between the davey stewartson ds equation and the 2 1 dimensional continuous heisenberg ferromagnetic model is shown explicitly through the gauge transformation solutions of the dsii are obtained from the vortex type solutions of the former equation

the total variation flow in rn the purpose of this chapter is to prove existence and uniqueness of the minimizing total variation flow in n frac partial u partial t div left frac du left du right right in left 0 infty right times mathbb r n 3 1 coupled with the initial condition u 0 x u 0 x text x in mathbb r n 3 2 when u0 l loc 1 l n

the gauge equivalence of the nls and the schrodinger flow of maps in 2 1 dimensions the gauge equivalence of the analogues of the nonlinear schrodinger equation nls and those of the schrodinger flow of maps into h2 the minkowski hf model in 2 1 dimensions are proved respectively combining these with the already known results we obtain a complete understanding of the gauge equivalence of the analogous models of the nonlinear schrodinger equation for 1 or 1 and those of the heisenberg ferromagnet model for euclidean or minkowski in 2 1 dimensions

bi differential calculi and bi hamiltonian systems we discuss the relationship between the analysis of completely integrable systems using bi differential calculi which was introduced by dimakis and muller hoissen 2000 bi differential calculi and integrable models j phys a math gen 33 957 74 and the bi hamiltonian formalism in the finite dimensional case

some integrable hierarchies in 2 1 dimensions and their twistor description the twistor space construction due to mason and sparling for solutions of the nonlinear schrodinger and korteweg devries hierarchies is generalized resulting in families of integrable models in 2 1 dimensions soliton solutions to one such hierarchy associated with the gauge group su 2 are constructed by adapting the methods used to construct instanton and monopole solutions these integrable models have the feature that their solutions depend on a number of arbitrary functions as well as arbitrary constants in contrast to the closely related davey stewartson hierachy

bi differential calculi bi hamiltonian systems and conformal killing tensors the theory of dimakis and m ller hoissen dimakis a and m ller hoissen f 2000 j phys a math gen 33 957 74 concerning bi differential calculi and completely integrable systems is related to bi hamiltonian systems of the poisson nijenhuis type in the special case where the ambient manifold is a cotangent bundle one is able to recover and elucidate the theory of ibort et al ibort a magri f and marmo g 2000 j geom phys 33 210 23 which is in turn a reworking in the bi hamitonian context of benenti s theory of hamilton jacobi separable systems in particular it is shown that benenti s conformal killing tensor which is central to his theory has an even more special form than has hitherto been realized and that when it is converted into a field of endomorphisms by raising an index with the ambient metric it necessarily has vanishing nijenhuis torsion

linearized fe approximations to a nonlinear gradient flow we study fully discrete linearized galerkin finite element approximations to a nonlinear gradient flow applications of which can be found in many areas due to the strong nonlinearity of the equation existing analyses for implicit schemes require certain restrictions on the time step and no analysis has been explored for linearized schemes this paper focuses on the unconditionally optimal l 2 error estimate of a linearized scheme the key to our analysis is an iterated sequence of time discrete elliptic equations and a rigorous analysis of its solution we prove the w 1 infty boundedness of the solution of the time discrete system and the corresponding finite element solution based on a more precise estimate of elliptic pdes in w 2 2 epsilon 1 and h 2 epsilon 2 and a physical feature of the gradient dependent diffusion coefficient numerical examples are provided to support our theoretical analysis

integrable equations in 2 1 dimensions associated with symmetric and homogeneous spaces generalizations of the n wave davey stewartson and kadomtsev petviashvili equations associated with homogeneous and symmetric spaces are presented these equations are 2 1 dimensional generalizations of those presented by fordy and kulish commun math phys 89 427 1983 and athorne and fordy j phys a 20 1377 1987 examples are explicitly presented that are associated with the simplest spaces in particular a new single component 2 1 dimensional generalization of the kdv equation is presented

some reductions of the self dual yang mills equations to integrable systems in 2 1 dimensions a reduction of the self dual yang mills sdym equations is studied by imposing two space time symmetries and by requiring that the connection one form belongs to a lie algebra of formal matrix valued differential operators in an auxiliary variable in this article the scalar case and the canonical cases for 2 2 matrices are examined in the scalar case it is shown that the field equations can be reduced to the forced burgers equation in the matrix case several well known 2 1 integrable equations are obtained also examined are certain transformation properties between the solutions of some of these 2 1 equations

noncommutative burgers equation we present a noncommutative version of the burgers equation which possesses the lax representation and discuss the integrability in detail we find a noncommutative version of the cole hopf transformation and succeed in the linearization of it the linearized equation is the noncommutative diffusion equation and exactly solved we also discuss the properties of some exact solutions the result shows that the noncommutative burgers equation is completely integrable even though it contains infinite number of time derivatives furthermore we derive the noncommutative burgers equation from the noncommutative anti self dual yang mills equation by reduction which is an evidence for the noncommutative ward conjecture finally we present a noncommutative version of the burgers hierarchy by both the lax pair generating technique and sato s approach

reduction techniques for infinite dimensional hamiltonian systems some ideas and applications in the language of tensor analysis on differentiable manifolds we present a reduction method of integrability structures and apply it to recover some well known hierarchies of integrable nonlinear evolution equations

dispersionless limit of the noncommutative potential kp hierarchy and solutions of the pseudodual chiral model in 2 1 dimensions the usual dispersionless limit of the kp hierarchy does not work in the case where the dependent variable has values in a noncommutative e g matrix algebra passing over to the potential kp hierarchy there is a corresponding scaling limit in the noncommutative case which turns out to be the hierarchy of a pseudodual chiral model in 2 1 dimensions pseudodual to a hierarchy extending ward s modified integrable chiral model applying the scaling procedure to a method generating exact solutions of a matrix potential kp hierarchy from solutions of a matrix linear heat hierarchy leads to a corresponding method that generates exact solutions of the matrix dispersionless potential kp hierarchy i e the pseudodual chiral model hierarchy we use this result to construct classes of exact solutions of the su m pseudodual chiral model in 2 1 dimensions including various multiple lump configurations

the dirichlet problem for the total variation flow suppose that is an open bounded domain with a lipschitz boundary the purpose of this chapter is to study the dirichlet problem left begin gathered frac partial u partial t div left frac du left du right right in q left 0 infty right times omega hfill u left t x right phi left x right on s left 0 infty right times partial omega hfill u left 0 x right u 0 left x right in x in omega hfill end gathered right 5 1 where u0 l1 and l1 this evolution equation is related to the gradient descent method used to solve the problem begin gathered minimize int omega left du right int omega f udx int partial omega left u phi right d mathcal h n 1 hfill u in bv left omega right hfill end gathered 2 where f l1 l existence for this variational problem was proved in 118 theorem 1 4

hierarchies of cofactor systems we assign to any cofactor system a whole hierarchy of such systems a sufficient condition for their complete integrability is given the hierarchies admit construction of non trivial integrable systems from trivial ones

error analysis of finite element approximations of the inverse mean curvature flow arising from the general relativity this paper proposes and analyzes a finite element method for a nonlinear singular elliptic equation arising from the black hole theory in the general relativity the nonlinear equation which was derived and analyzed by huisken and ilmanen in j diff geom 59 353 437 represents a level set formulation for the inverse mean curvature flow describing the evolution of a hypersurface whose normal velocity equals the reciprocal of its mean curvature we first propose a finite element method for a regularized flow which involves a small parameter a rigorous analysis is presented to study well posedness and convergence of the scheme under certain mesh constraints and optimal rates of convergence are verified we then prove uniform convergence of the finite element solution to the unique weak solution of the nonlinear singular elliptic equation as the mesh size h and the regularization parameter both tend to zero computational results are provided to show the efficiency of the proposed finite element method and to numerically validate the jumping out phenomenon of the weak solution of the inverse mean curvature flow numerical studies are presented to evidence the existence of a polynomial scaling law between the mesh size h and the regularization parameter for optimal convergence of the proposed scheme finally a numerical convergence study for another approach recently proposed by r moser the inverse mean curvature flow and p harmonic functions preprint u bath 2005 for approximating the inverse mean curvature flow via p harmonic functions is also included

gauge equivalence between dimensional continuous heisenberg ferromagnetic models and nonlinear schrodinger type equations the gauge equivalence between the 2c 1 dimensional zakharov equation and the 2c 1 dimensional integrable continuous heisenberg ferromagnetic model is established their integrable reductions are also shown explicitly

analogical proportion based methods for recommendation first investigations analogy making is widely recognized as a powerful kind of common sense reasoning this paper primarily addresses the relevance of analogical reasoning for recommender systems which aim at providing suggestions of interest for end users a well known form of analogy is that of analogical proportions which are statements of the form a is to b as c is to d encouraged by good results obtained in classification by analogical proportion based techniques we study the potential use of analogy as the main underlying principle for implementing rating prediction algorithms we investigate two ways of using analogical proportions for that purpose first we exploit proportions between four users each described by their respective ratings on items that they have commonly rated the second prediction method only relies on pairs of users and pairs of items and leads to better performances finally in order to know to what extent it may be meaningful to apply analogical methods in data analysis we address the problem of mining analogical proportions between users or items in ratings datasets altogether this paper initiates a general investigation of the potential use of analogical proportions for recommendation purposes

constraint preserving implicit finite element discretization of harmonic map flow into spheres discretization of the harmonic map flow into spheres often uses a penalization or projection strategy where the first suffers from the proper choice of an additional parameter and the latter from the lack of a discrete energy law and restrictive mesh constraints we propose an implicit scheme that preserves the sphere constraint at every node enjoys a discrete energy law and unconditionally converges to weak solutions of the harmonic map heat flow

a convergent and constraint preserving finite element method for the p harmonic flow into spheres an explicit fully discrete finite element method which satisfies the nonconvex side constraint at every node is developed for approximating the p harmonic flow for p in 1 infty convergence of the method is established under certain conditions on the domain and mesh computational examples are presented to demonstrate finite time blow ups and qualitative geometric changes of weak solutions of the p harmonic flow

intrinsic characterization of the variable separation in the hamilton jacobi equation the nonorthogonal separation of variables in the hamilton jacobi equation corresponding to a natural hamiltonian h 12gijpipj v with a metric tensor of any signature is intrinsically characterized by geometrical objects on the riemannian configuration manifold killing vectors killing tensors and killing webs comparisons with previous characterizations and some illustrative examples are given

quasi hamiltonian structure and hojman construction abstract given a smooth vector field and assuming the knowledge of an infinitesimal symmetry x hojman s hojman the construction of a poisson structure out of a symmetry and a conservation law of a dynamical system j phys a math gen 29 1996 667 674 proposed a method for finding both a poisson tensor and a function h such that is the corresponding hamiltonian system in this paper we approach the problem from geometrical point of view the geometrization leads to the clarification of several concepts and methods used in hojman s paper in particular the relationship between the nonstandard hamiltonian structure proposed by hojman and the degenerate quasi hamiltonian structures introduced by crampin and sarlet m crampin w sarlet bi quasi hamiltonian systems j math phys 43 2002 2505 2517 is unveiled in this paper we also provide some applications of our construction

riemann equations in bidifferential calculus we consider equations that formally resemble a matrix riemann or hopf equation in the framework of bidifferential calculus with different choices of a first order bidifferential calculus we obtain a variety of equations including a semi discrete and a fully discrete version of the matrix riemann equation a corresponding universal solution generating method then either yields a continuous or discrete cole hopf transformation or leaves us with the problem of solving riemann equations hence an application of the hodograph method if the bidifferential calculus extends to second order solutions of a system of riemann equations are also solutions of an equation that arises on the universal level of bidifferential calculus as an integrability condition depending on the choice of bidifferential calculus the latter can represent a number of prominent integrable equations like self dual yang mills as well as matrix versions of the two dimensional toda lattice hirota s bilinear difference equation 2 1 dimensional nonlinear schrodinger nls kadomtsev petviashvili kp equation and davey stewartson equations for all of them a recent non isospectral binary darboux transformation result in bidifferential calculus applies which can be specialized to generate solutions of the associated riemann equations for the latter we clarify the relation between these specialized binary darboux transformations and the aforementioned solution generating method from arbitrary size matrix versions of the riemann equations associated with an integrable equation possessing a bidifferential calculus formulation multi soliton type solutions of the latter can be generated this includes breaking multi soliton type solutions of the self dual yang mills and the 2 1 dimensional nls equation which are parametrized by solutions of riemann equations

a class of poisson nijenhuis structures on a tangent bundle equipping the tangent bundle tq of a manifold with a symplectic form coming from a regular lagrangian l we explore how to obtain a poisson nijenhuis structure from a given type 1 1 tensor field j on q it is argued that the complete lift jc of j is not the natural candidate for a nijenhuis tensor on tq but plays a crucial role in the construction of a different tensor r which appears to be the pullback under the legendre transform of the lift of j to t q we show how this tangent bundle view brings new insights and is capable also of producing all important results which are known from previous studies on the cotangent bundle in the case when q is equipped with a riemannian metric the present approach further paves the way for future generalizations

bicomplexes and conservation laws in non abelian toda models a bicomplex structure is associated with the leznov saveliev equation of integrable models the linear problem associated with the zero curvature condition is derived in terms of the bicomplex linear equation the explicit example of a non abelian conformal affine toda model is discussed in detail and its conservation laws are derived from the zero curvature representation of its equation of motion

error analysis for implicit approximations to solutions to cauchy problems exact error analyses for two implicit approximation schemes to the cauchy problem du t dt mathcal a u t mathrel backepsilon 0 u 0 u 0 in d mathcal a are presented the operator mathcal a is required to be maximal monotone on a hilbert space mathcal h the approximations considered are u h kh i h mathcal a k u 0 and solutions u lambda to the approximating problems du lambda t dt mathcal a lambda u lambda 0 u lambda 0 u 0 where a lambda is the yosida approximation of mathcal a the special case of a being a subgradient is considered and tight estimates of the convergence of both u h and mathcal a h u h or u h and a h u h are given the new results in this case are the linear rates of convergence of u h in l infty 0 infty mathcal h and in the energy norm and the sublinear rate of convergence of a h u h in l 2 0 infty mathcal h applications to both linear and

derivative nonlinear schrodinger equations and hermitian symmetric spaces it is shown that to each hermitian symmetric space there corresponds an integrable system of generalised derivative nonlinear schrodinger equations nls the nonlinear terms are related to the curvature tensor of the associated symmetric space the hamiltonian form of the equations is presented the results are an extension of those presented in an earlier paper 1983 on generalised nls equations associated with symmetric and reductive homogeneous spaces

multiple valued extensions of analogical proportions this paper provides a discussion of different multiple valued extensions of logical expressions of analogical proportions that are equivalent in the boolean case it is advocated that these extensions may serve different goals or at least reflect different views boolean expressions of analogical proportions modeling statements of the form a is to b as c is to d are first restated and commented an approach to handling the case of binary attributes that may not apply in the boolean setting is also outlined via a proper encoding

on the simplest 2 1 dimensional integrable spin systems and their equivalent nonlinear schrodinger equations using a moving space curve formalism geometrical as well as gauge equivalence between a 2 1 dimensional spin equation m i equation and the 2 1 dimensional nonlinear schrodinger equation nlse originally discovered by calogero discussed then by zakharov and recently rederived by strachan have been estabilished a compatible set of three linear equations are obtained and integrals of motion are discussed through stereographic projection the m i equation has been bilinearized and different types of solutions such as line and curved solitons breaking solitons induced dromions and domain wall type solutions are presented breaking soliton solutions of 2 1 dimensional nlse have also been reported generalizations of the above spin equation are discussed

darboux transformation and soliton solutions for the 2 1 dimensional nonlinear schrodinger hierarchy with symbolic computation abstract in this paper the n fold darboux transformation is applied to the lax pair associated with the 2 1 dimensional nonlinear schrodinger hierarchy the general explicit formula for n soliton solution is derived in terms of vandermonde like determinant expression on the zero background two different families of soliton solutions multi line soliton and multi parabola soliton solutions are constructed by applying the darboux transformation successively based on the figures for several sample solutions the soliton interactions are discussed by virtue of the physical parameters amplitude velocity and direction of the interacting solitons

geometric characterization of driven cofactor systems we discuss the geometry of partially decoupling submersive second order equations in general and illustrate the theory with an application to the case of lagrangian systems of mechanical type it is shown that submersiveness implies decoupling into separate subsystems in that case unless non conservative forces are added to the system the main purpose of the paper is to explain the geometric structures underlying so called driven cofactor systems which constitute a special class of non conservative lagrangian systems in doing so we generalize the original set up of driven cofactor systems lundmark and rauch wojciechowski 2002 j math phys 43 6166 from a euclidean space to an arbitrary riemannian one

what are fuzzy rules and how to use them abstract fuzzy rules have been advocated as a key tool for expressing pieces of knowledge in fuzzy logic however there does not exist a unique kind of fuzzy rules nor is there only one type of fuzzy logic this diversity has caused many a misunderstanding in the literature of fuzzy control the paper is a survey of different possible semantics for a fuzzy rule and shows how they can be captured in the framework of fuzzy set and possibility theory it is pointed out that the interpretation of fuzzy rules dictates the way the fuzzy rules should be combined the various kinds of fuzzy rules considered in the paper gradual rules certainty rules possibility rules and others have different inference behaviors and correspond to various intended uses and applications the representation of fuzzy unless rules is briefly investigated on the basis of their intended meaning the problem of defining and checking the coherence of a block of parallel fuzzy rules is also briefly addressed this issue has been neglected in the fuzzy control literature although it looks important for validation purposes

darboux s problem of quadratic integrals the problem of determining all standard classical hamiltonians in two dimensions with euclidean metric which admit constants of motion quadratic in the momenta is resolved several general results are given which make it obvious that the systems found do possess such integrals

bi hamiltonian partially integrable systems given a first order dynamical system possessing a commutative algebra of dynamical symmetries we show that under certain conditions there exists a poisson structure on an open neighborhood of its regular not necessarily compact invariant manifold which makes this dynamical system into a partially integrable hamiltonian system this poisson structure is by no means unique bi hamiltonian partially integrable systems are described in some detail as an outcome we state the conditions of quasiperiodic stability the kam theorem for partially integrable hamiltonian systems

completely integrable nonlinear schrodinger type equations on moving space curves using the lamb formalism we show that some completely integrable homogeneous and inhomogeneous nonlinear schr odinger nls type equations such as derivative nls extended nls higher order nls inhomogeneous nls circularly and radially symmetric nls and generalized inhomogeneous radially symmetric nls equations can be related to certain types of moving helical space curves

bi differential calculi and integrable models the existence of an infinite set of conserved currents in completely integrable classical models including chiral and toda models as well as the kp and self dual yang mills equations is traced back to a simple construction of an infinite chain of closed respectively covariantly constant 1 forms in a gauged bi differential calculus the latter consists of a differential algebra on which two differential maps act in a gauged bi differential calculus these maps are extended to flat covariant derivatives

a discretization of the matrix nonlinear schrodinger equation in this paper we shall show that a class of solutions to the discrete coupled matrix nonlinear schrodinger equation dcmnlse is gauge equivalent to the discrete equation of the schrodinger flow of maps into the grassmannian and the realizing gauge transformation is only the discretization of a classical gauge transformation between the matrix nonlinear schrodinger equation mnlse and the schrodinger flow of maps into the grassmannian in other words from the viewpoint of gauge equivalence a class of solutions of the dcmnlse is a correct discretization of the mnlse

deformation of surfaces integrable systems and chern simons theory a few years ago some of us devised a method to obtain integrable systems in 2 1 dimensions from the classical non abelian pure chern simons action via the reduction of the gauge connection in hermitian symmetric spaces in this article we show that the methods developed in studying classical non abelian pure chern simons actions can be naturally implemented by means of a geometrical interpretation of such systems the chern simons equation of motion turns out to be related to time evolving two dimensional surfaces in such a way that these deformations are both locally compatible with the gauss mainardi codazzi equations and completely integrable the properties of these relationships are investigated together with the most relevant consequences explicit examples of integrable surface deformations are displayed and discussed

fuzzy set based methods in instance based reasoning a formal framework of instance based prediction is presented in which the generalization beyond experience is founded on the concepts of similarity and possibility the underlying extrapolation principle is formalized within the framework of fuzzy rules thus instance based reasoning can be realized as fuzzy set based approximate reasoning more precisely our model makes use of so called possibility rules these rules establish a relation between the concepts of similarity and possibility which takes the uncertain character of similarity based inference into account inductive inference is possibilistic in the sense that predictions take the form of possibility distributions on the set of outcomes rather than precise deterministic estimations the basic model is extended by means of fuzzy set based modeling techniques this extension provides the basis for incorporating domain specific expert knowledge thus our approach favors a view of instance based reasoning according to which the user interacts closely with the system

commuting flows and conservation laws for noncommutative lax hierarchies we discuss commuting flows and conservation laws for lax hierarchies on noncommutative spaces in the framework of the sato theory on commutative spaces the sato theory has revealed essential aspects of the integrability for wide class of soliton equations which are derived from the lax hierarchies in terms of pseudodifferential operators noncommutative extension of the sato theory has been already studied by the author and toda and the existence of various noncommutative lax hierarchies are guaranteed in this paper we present conservation laws for the noncommutative lax hierarchies with both space space and space time noncommutativities and prove the existence of infinite number of conserved densities we also give the explicit representations of them in terms of lax operators our results include noncommutative versions of kp kdv boussinesq coupled kdv sawada kotera modified kdv equation and so on

model adaptation in possibilistic instance based reasoning this paper extends the possibilistic approach to instance based reasoning that has recently been developed in a companion paper within the framework of this approach the similarity guided extrapolation principle underlying instance based learning is formalized by means of so called possibility rules a special type of fuzzy rules proceeding from this idea a methodology has been outlined which allows a human expert to specify a model of the inference mechanism in a linguistic way in this paper a method for adapting a linguistic model automatically to observed data is proposed this extension frees the expert from specifying mathematical concepts such as similarity measures and membership functions of fuzzy sets precisely rather the expert determines only the qualitative structure of the model which is then calibrated bit using the cases stored in memory

bicomplexes and backlund transformations a bicomplex is a simple mathematical structure in particular associated with completely integrable models the conditions defining a bicomplex are a special form of a parameter dependent zero curvature condition we generalize the concept of a darboux matrix to bicomplexes and use it to derive backlund transformations for several models the method also works for moyal deformed equations with a corresponding deformed bicomplex

bi quasi hamiltonian systems a general notion of bi quasi hamiltonian systems is introduced and is related to previous work on various special cases of such systems

reduced systems of 2 2 pseudo euclidean noncommutative self dual yang mills theories self dual yang mills equations on noncommutative spaces associated with pseudo euclidean space of signature 2 2 are shown to be related via dimensional reductions to noncommutative formulations of toda equations of generalized nonlinear schrodinger ns equations of the super korteweg de vries super kdv as well as of the matrix kdv equations the noncommutative extensions of their linear systems and bicomplexes associated with conserved quantities are discussed as well a q plane version of the kdv equation with linear system is also shown

similarity rules and gradual rules for analogical and interpolative reasoning with imprecise data similarity rules and gradual rules in the form of functional mappings of imprecise data are proposed to implement analogical and interpolative reasoning the rules are deduced from the property of the horizontal graduality of fuzzy sets and the horizontal graduality is represented by introducing a horizontal difference function as an alternative to the proposed extensions of distance between fuzzy concepts a thorough discussion of the main characteristics of fuzzy sets and horizontal difference function is given an analogical reasoning algorithm based on these characteristics and a set of intuitively sound axioms are proposed the algorithm is consistent with the intuitive concepts of analogical reasoning expressed by the axioms it guarantees a convex and normal output regardless of the shape of the precondition and action patterns and input data when some axiomatic conditions are not satisfied the algorithm relaxes the less important ones and produces an approximate solution the fuzziness cardinality and shape of an output fuzzy set are easily controlled some steps of the algorithm can be carried out in parallel numerical examples confirm the theoretical analysis of the properties of the algorithm some extensions for interpolative reasoning are discussed the proposed rules are particularly well suited for systems which support qualitative reasoning and qualitative modelling

bicomplex formulation and moyal deformation of 2 1 dimensional fordy kulish systems using bicomplex formalism we construct generalizations of fordy kulish systems of matrix nonlinear schrodinger equations on two dimensional space time in two respects firstly we obtain corresponding equations in three space time dimensions secondly a moyal deformation is applied to the space time coordinates and the ordinary product of functions replaced by the moyal product in a suitable way both generalizations preserve the existence of an infinite set of conservation laws

error bounds for finite difference methods for rudin osher fatemi image smoothing we bound the difference between the solution to the continuous rudin osher fatemi rof image smoothing model and the solutions to various finite difference approximations to this model these bounds apply to typical images i e images with edges or with fractal structure these are the first bounds on the error in numerical methods for rof smoothing

unified forms of triple i method first the present paper provides unified forms of triple i method for fuzzy modus ponens and fuzzy modus tollens of which diverse implication operators can be employed second it is clarified that in a sense zadeh s cri method for fuzzy modus ponens can be brought into line with the unified form of the triple i method lastly a unified form of a triple i method is established as well and a duality result concerning a triple i solutions of fuzzy modus ponens and fuzzy modus tollens is obtained

the three semantics of fuzzy sets abstract three main semantics for membership functions seem to exist in the literature similarity preference and uncertainty each semantics underlies a particular class of applications similarity notions are exploited in clustering analysis and fuzzy controllers uncertainty is captured by fuzzy sets in the framework of possibility theory the membership function of a fuzzy set is also sometimes a kind of utility function that represents flexible constraints in decision problems this paper advocates the claim that progress in operational semantics of membership functions presupposes that these distinct semantics be acknowledged and related to more basic measurement issues in terms of distance cost and frequency on which scientific traditions exist

a new class of induced localized coherent structures in the 2 1 dimensional nonlinear schrodinger equation in this paper we report a novel way of constructing a new class of localized coherent structures for the 2 1 dimensional nonlinear schrodinger nls equation proposed by zakharov by utilizing the freedom arbitrary function in the linearized version of the bilinear equation the localized solutions for the potential are realized mainly by the interaction of the line soliton with a curved soliton we call such solutions induced localized structures induced dromions as the line soliton is induced by the arbitrary function present in the system

numerical analysis of a steepest descent pde model for surface relaxation below the roughening temperature we study the numerical solution of a pde describing the relaxation of a crystal surface to a flat facet the pde is a singular nonlinear fourth order evolution equation which can be viewed as the gradient flow of a convex but nonsmooth energy with respect to the h per 1 inner product our numerical scheme uses implicit discretization in time and a mixed finite element approximation in space the singular character of the energy is handled using regularization combined with a primal dual method we study the convergence of this scheme both theoretically and numerically

the motion of surfaces in geodesic coordinates and 2 1 dimensional breaking soliton equation the system of evolution equations for general motion of surfaces in geodesic coordinates is analyzed to reduce the number of variables as well as equations a special choice for some variants deduces that the surface and the motion of surface correspond to a nonlinear schrodinger equation and a 2 1 dimensional breaking soliton equation respectively we also study some geometric properties corresponding to the integrals of the motion of surface and the motion of the curve on the surface the spectral parameter is introduced

a class of recursion operators on a tangent bundle we generalize the construction of a class of type 1 1 tensor fields r on a tangent bundle which was introduced in a preceding paper the generalization comes from the fact that apart from a given lagrangian the further data consist of a type 1 1 tensor j along the tangent bundle projection tq q rather than a tensor on q the main features under investigation are two kinds of recursion properties of r namely its potential invariance under the flow of the given dynamics and the property of having vanishing nijenhuis torsion the theory is applied in particular to the case of second order dynamics coming from a finsler metric

nonlinear schrodinger equations and simple lie algebras we associate a system of integrable generalised nonlinear schrodinger nls equations with each hermitian symmetric space these nls equations are considered as reductions of more general systems this time associated with a reductive homogeneous space the nonlinear terms are related to the curvature and torsion tensors of the appropriate geometrical space the hamiltonian structure is investigated using r matrix techniques and shown to be canonical for all these equations throughout the reduction procedure this hamiltonian structure does not degenerate each of the above systems of equations is gauge equivalent to a generalised ferromagnet reductions of the latter are discussed in terms of the corresponding nls type equations

a class of nonconservative lagrangian systems on riemannian manifolds we generalize results of rauch wojciechowski marciniak and lundmark concerning a class of nonconservative lagrangian systems from the euclidean to the riemannian case

rate of convergence of regularization procedures and finite element approximations for the total variation flow we derive rates of convergence for regularization procedures characterized by a parameter and finite element approximations of the total variation flow which arises from image processing geometric analysis and materials sciences practically useful error estimates which depend on open image in new window only in low polynomial orders are established for the proposed fully discrete finite element approximations as a result scaling laws which relate mesh parameters to the regularization parameter are also obtained numerical experiments are provided to validate the theoretical results and show efficiency of the proposed numerical methods