fourier integral operators on lie groupoids abstract as announced in 36 we develop a calculus of fourier integral g operators on any lie groupoid g for that purpose we study lagrangian conic submanifolds of the symplectic groupoid t g this includes their product transposition and inversion we also study the relationship between these lagrangian submanifolds and the equivariant families of lagrangian submanifolds of t g x t g x parametrized by the units x g 0 of g this allows us to select a subclass of lagrangian distributions on any lie groupoid g that deserve the name of fourier integral g operators g fios by construction the class of g fios contains the class of equivariant families of ordinary fourier integral operators on the manifolds g x x g 0 we then develop for g fios the first stages of the calculus in the spirit of hormander s work finally we illustrate this calculus in the case of manifolds with boundary

noncommutative residues and manifolds with conical singularities abstract for every singular point on a manifold with conical singularities a trace can be constructed on the cone algebra with asymptotics introduced by b w schulze each of them vanishes on operators supported in the interior and is therefore different from the noncommutative residue established by wodzicki on the ideal of operators with zero conormal symbol however we find another trace which coincides with the noncommutative residue in the interior all these traces are shown to be essentially unique on a slightly extended version of the cone algebra

applications of a generalized complementary energy principle for the equilibrium analysis of softening structures an interpretation for computational solution is given for a new global extremum principle that models a generalized form of elastic softening structural behavior the principle and its interpretation are expressed in a form that accommodates arbitrary heterogeneity and anisotropy in the structural material also the stress strain properties that reflect evolution of local softening are represented in the model by a set of parameters defined over the field of the structure thus the model may be used to predict the general behavior of solid structures having non uniform stress strain fields that evolve with change in external load a discretized version of the principle used for computation is based on a consistent mixed form finite element interpretation of the principle as stated for the general softening continuum example computational solutions are provided covering the evolution of softening for a uniformly loaded homogeneous sheet with a hole and simulations of a sheet with various configurations of softer or stiffer inclusions in an otherwise uniform structure the purpose of this paper is to demonstrate the application of a recently developed extremum principle covering equilibrium problems for structures made of softening materials as described for a one dimensional stress state a material for which change in stress per unit change in strain diminishes as the magnitude of the load increases is referred to here as a softening material 11 the formulation makes use of a superposition of an arbitrary number of fields here termed constituent fields to represent total stress and this feature provides for a constructive approach to the simulation of stress strain properties associated with any softening material this representation of the total stress tensor is in contrast to a number of other approaches to the analysis of non linear material response e g 2 41 with this construction the non linear problem is established in a form that in effect affords all of the advantages for analysis generally associated with having the continuum problem interpreted in terms of potentials for convenience we first present a brief description of the principle stated for the non linear continuum an interpretation of the continuum model into discretized form is presented next the discrete form expression for the extremum problem statement is obtained using a self consistent mixed form finite element construction this leads to a convex constrained nonlinear programming problem computational solutions are obtained conveniently using standard software written for such problems numerical results are presented showing for several example problems involving twodimensional softening continua the evolution of softening and the corresponding stress and or deformation fields under increasing load these results are demonstrated for a rectangular sheet of bilinear softening material that has variously located sets of stiffer or less stiff inclusions and also for a rectangular sheet with a central hole solved for each of two choices of softening materials

possibilistic linear systems and their application to the linear regression model abstract it is the purpose of this paper to illustrate possibilistic linear systems based on possibility measure and to formulate a linear regression analysis by possibilistic linear models linear regression by a possibilistic model is called possibilistic linear regression this is a new interpretation of fuzzy linear regression and also includes a new method by which interval analysis can be done in fuzzy numbers

quantum ergodicity of c dynamical systems we define a notion of quantum or non commutative ergodicity for a class ofc dynamical systems a g which we callquantized gns systems such a system possesses a natural classical limit state which induces a classical limit system by the gns construction the criterion for quantum ergodicity is that the time average a of an observable a a equals the space average a i plus an errork which is negligible in the classical limit we prove that ergodicity of is a sufficient condition for quantum ergodicity of a g if the classical limit system is abelian give a conditional converse and discuss a number of applications

on the handling of fuzziness for continuous valued attributes in decision tree generation abstract in this paper fuzziness existing in the process of generating decision trees by discretizing continuous valued attributes is considered in a sense a better way to express this fuzziness via fuzzy numbers is presented using possibility theory the fact that selection of membership functions in a class of symmetric distributions does not influence the decision tree generation is proved the validity of using the tree to classify future examples is explained on the basis of likelihood possibility maximization the existing algorithm is revised the revised algorithm leads to more reasonable and more natural decision trees

variational principles and convergence of finite element approximations of a holonomic elastic plastic problem it is shown that a boundary value problem based on a holonomic elastic plastic constitutive law may be formulated equivalently as a variational inequality of the second kind a regularised form of the problem is analysed and finite element approximations are considered it is shown that solutions based on finite element approximation of the regularised problem converge

fuzzy linear regression analysis abstract in this paper a generalized fuzzy linear regression model y 1x1 2x2 mxm where all j and xj j 1 m are fuzzy is considered a new principle of estimating parameters which is called minmax principle is introduced via the possibility distribution the minmax estimation of the regression model parameters and the ls estimation of the approximation model parameters are discussed procedures of estimating these parameters are given

trace expansions and the noncommutative residue for manifolds with boundary for a pseudodifferential boundary operator a of order 2 z and class 0 in the boutet de monvel calculus on a compact n dimensional manifold with boundary we consider the function tr ab s where b is an auxiliary system formed of the dirichlet realization of a second order strongly elliptic differential operator and an elliptic operator on the boundary we prove that tr ab s has a meromorphic extension to c with poles at the half integers s n j 2 j 2 n possibly double for s 0 and we prove that its residue at 0 equals the noncommutative residue of a as defined by fedosov golse leichtnam and schrohe by a different method to achieve this we establish a full asymptotic expansion of tr a b k in powersl 2 and log powersl 2 log where the noncommutative residue equals the coefficient of the highest order log power there is a related expansion of tr ae tb the paper will appear in journal reine angew math crelle s journal then is a holomorphic function of s for large re s we show that it extends to a mero morphic function on the whole complex plane with at most double poles moreover we prove that the noncommutative residue res a of a can be recovered as a residue in this

designing fuzzy sets with the use of the parametric principle of justifiable granularity this study is concerned with a design of membership functions of fuzzy sets the membership functions are formed in such a way that they are experimentally justifiable and exhibit a sound semantics these two requirements are articulated through the principle of justifiable granularity the parametric version of the principle is discussed in detail we show linkages with type 2 fuzzy sets which are constructed on a basis of type 1 fuzzy sets several experimental studies are reported which illustrate a behavior of the introduced method

spectral asymptotics of toeplitz operators on zoll manifolds we prove a generalization of the strong szego limit theorem for zoll type operators on smooth compact closed manifolds more precisely letxbe a compact manifold and letq c x c x be a self adjoint first order elliptic dowhose spectrum is 1 2 3 letabe a zeroth order do onxwhose spectrum does not contain zero in its closed convex hull writepnfor the projector onto the span of the eigenfunctions ofqwith eigenvalues in 1 n our main result is a second order asymptotic formula for log detpnapn asn

parameter estimations of normal fuzzy variables abstract although fairly much attention has been paid to theoretical applications of nahmias fuzzy variables little effort has been focused on the related parameter estimation issues this keeps down the practical use of fuzzy variables in this note we make a preliminary discussion on parameter estimation of normal fuzzy variables with parameters a b and distinguish three situations estimation of a with b known estimation of b with a known and estimation of unknown a and b formulae for calculating parameter estimates by use of practical collected data are presented

non smooth multisurface plasticity and viscoplasticity loading unloading conditions and numerical algorithms rate independent plasticity and viscoplasticity in which the boundary of the elastic domain is defined by an arbitrary number of yield surfaces intersecting in a non smooth fashion are considered in detail it is shown that the standard kuhn tucker optimality conditions lead to the only computationally useful characterization of plastic loading on the computational side an unconditionally convergent return mapping algorithm is developed which places no restrictions aside from convexity on the functional forms of the yield condition flow rule and hardening law the proposed general purpose procedure is amenable to exact linearization leading to a closed form expression of the so called consistent algorithmic tangent moduli for viscoplasticity a closed form algorithm is developed based on the rate independent solution the methodology is applied to structural elements in which the elastic domain possesses a non smooth boundary numerical simulations are presented that illustrate the excellent performance of the algorithm

extremum properties of finite step solutions in elastoplasticity with nonlinear mixed hardening abstract the class of elastic plastic constitutive laws assumed herein can be described as follows we envisage y 1 yield criteria or modes which define the current yield surface each yield function consists of two addends an effective stress and a yield limit y 1 y the former is an order one positively homogeneous function of the difference between the stresses ii and reference stresses ii which are generally nonlinear functional of the plastic strain history so that kinematic hardening is accounted for the yield limit y is generally a nonlinear function of y nondecreasing internal variables so that another hardening mechanism which may reduce to isotropic hardening is accommodated in the model the rates of these variables play the role of plastic multipliers in the flow rule a finite step in the geometrically linear evolutive analysis of such solids is defined according to the backward difference or stepwise holonomic strategy for approximate time integration for the finite step boundary value problem thus arising various extremum characterizations of solutions are established and the underlying constitutive restrictions are pointed out and discussed

the three dimensional fuzzy sets and their cut sets in this paper a new kind of l fuzzy set is introduced which is called the three dimensional fuzzy set we first put forward four kinds of cut sets on the three dimensional fuzzy sets which are defined by the 4 valued fuzzy sets then the definitions of 4 valued order nested sets and 4 valued inverse order nested sets are given based on them the decomposition theorems and representation theorems are obtained furthermore the left interval valued intuitionistic fuzzy sets and the right interval valued intuitionistic fuzzy sets are introduced we show that the lattices constructed by these two special l fuzzy sets are not equivalent to sublattices of lattice constructed by the interval valued intuitionistic fuzzy sets finally we show that the three dimensional fuzzy set is equivalent to the left interval valued intuitionistic fuzzy set or the right interval valued intuitionistic fuzzy set

the canonical trace and the noncommutative residue on the noncommutative torus using a global symbol calculus for pseudodifferential operators on tori we build a canonical trace on classical pseudodifferential operators on noncommutative tori in terms of a canonical discrete sum on the underlying toroidal symbols we characterise the canonical trace on operators on the noncommutative torus as well as its underlying canonical discrete sum on symbols of fixed resp any non integer order on the grounds of this uniqueness result we prove that in the commutative setup this canonical trace on the noncommutative torus reduces to kontsevich and vishik s canonical trace which is thereby identified with a discrete sum a similar characterisation for the noncommutative residue on noncommutative tori as the unique trace which vanishes on trace class operators generalises fathizadeh and wong s characterisation in so far as it includes the case of operators of fixed integer order by means of the canonical trace we derive defect formulae for regularized traces the conformal invariance of the function at zero of the laplacian on the noncommutative torus is then a straightforward consequence

about membership functions estimation abstract a logical approach to fuzzy sets method originated by giles is developed the infinitely many valued logic t is taken as basic we accept it is correct to use the strong conjunction by the logical analysis of the summation of fuzzy items under some broad conditions it is proved that the sum of many fuzzy variables is a variable whose membership function is approximately equal to x max 1 1 2 c x 2 0 where a and c are some constant parameters a method of estimation of the unknown parameters is developed in a general case the proposed fuzzy method coincides with the method of maximum likelihood if used in problems of classical mathematical statistics

variational inequality formulation in strain space and finite element solution of an elasto plastic problem with hardening abstract a variational inequality formulation in strain space is derived for certain problems of flow theory elasto plastic deformation with hardening an algorithm is given for implementing a finite element approximation to the variational inequality formulation

deformations of momentum maps and g systems in this note we give an explicit formula for a family of deformation quantizations for the momentum map associated with the cotangent lift of a lie group action on rd this family of deformations is parametrized by the formal g systems introduced in b dherin and i mencattini g systems and deformations of g actions on rd j math phys 55 011702 2014 see also b dherin and i mencattini quantization of volume preserving actions on rd e print arxiv 1202 0886 and allows us to obtain classical invariant hamiltonians that quantize without anomalies with respect to the quantizations of the action prescribed by the formal g systems

a force method for elastic plastic analysis of frames by quadratic optimization abstract a numerical method for the analysis of elastoplastic planar frames is developed on the basis of a minimum principle in finite increments of stresses and plastic factors local elastic unloading and plastic admissibility of final stresses are considered in this theoretical formulation avoiding additional iterative procedures since all possible stress distributions can be represented exactly only an interpolation of plastic multiplier fields is required to transform the formulation in the functional space into a problem with a finite number of variables plastic admissibility for any section along a beam element is substituted by a finite number of contraints the interpretation of this approximation is used to choose appropriate interpolation bases the resulting discrete version of the principle is a quadratic optimization problem solved in this work by dualization condensation to a problem in plastic factors only and application of lemke s algorithm the advantages of the force method when compared with kinematical approaches for planar frames are discussed and demonstrated by examples

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

development of a cost function for wastewater treatment systems with fuzzy regression abstract a fuzzy linear regression analysis is performed to study the cost function of wastewater that is developed by using a pool of data from 26 municipal wastewater treatment systems in taiwan the choice of a primary or more higher wastewater treatment process is intimately related to financial land availability effluent standards and managerial factors especially financial consideration plays an important role in the planning stage in addition cost estimation is difficult to precisely evaluate in an uncertain environment in the conventional regression model deviations between the observed values and the estimated values are supposed to be due to measurement errors here taking a different perspective these deviations are regarded as the fuzziness of the system s parameters thus these deviations are reflected in a linear function with fuzzy parameters using linear programming algorithm this fuzzy linear regression model might be very convenient and useful for finding a fuzzy structure in an evaluation system in this paper the details of the fuzzy linear regression concept and its applications to the cost function in an uncertain environment are shown and discussed

a displacement like finite element model for j2 elastoplasticity variational formulation and finite step solution abstract the displacement like finite element formulation for finite step j2 elastoplasticity is revisited in this paper the classical computational strategy according to which plastic loading is tested at the gauss points of each element and an independent return mapping algorithm is performed for given incremental displacements is consistently derived from a suitably discretized version of a min max variational principle the sequence of solution phases to be performed within each load step adopting a full newton s method is illustrated in detail and the importance of a correct update of the plastic strains is emphasized it is further shown that in order to increase the rate of convergence and the stability properties of the newton s method the consistent elastoplastic tangent operator must be exploited even at the first iteration of each load step subsequent to the first yielding of the structural model this is in contrast with the traditional implementation according to which the elastic operator is used at the first iteration of each load step the effectiveness of the present approach is shown by a set of numerical examples referred to plane strain problems

noncommutative residue for heisenberg manifolds applications in cr and contact geometry abstract this paper has four main parts in the first part we construct a noncommutative residue for the hypoelliptic calculus on heisenberg manifolds that is for the class of h do operators introduced by beals greiner and taylor this noncommutative residue appears as the residual trace on integer order h dos induced by the analytic extension of the usual trace to non integer order h dos moreover it agrees with the integral of the density defined by the logarithmic singularity of the schwartz kernel of the corresponding h do in addition we show that this noncommutative residue provides us with the unique trace up to constant multiple on the algebra of integer order h dos in the second part we give some analytic applications of this construction concerning zeta functions of hypoelliptic operators logarithmic metric estimates for green kernels of hypoelliptic operators and the extension of the dixmier trace to the whole algebra of integer order h dos in the third part we present examples of computations of noncommutative residues of some powers of the horizontal sublaplacian and the contact laplacian on contact manifolds in the fourth part we present two applications in cr geometry first we give some examples of geometric computations of noncommutative residues of some powers of the horizontal sublaplacian and of the kohn laplacian second we make use of the framework of noncommutative geometry and of our noncommutative residue to define lower dimensional volumes in pseudohermitian geometry e g we can give sense to the area of any 3 dimensional cr manifold endowed with a pseudohermitian structure on the way we obtain a spectral interpretation of the einstein hilbert action in pseudohermitian geometry

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

shuffle relations for regularised integrals of symbols we prove shuffle relations which relate a product of regularised integrals of classical symbols int reg sigma i d xi i i 1 ldots k to regularised nested iterated integrals prod i 1 k int reg sigma i d xi i sum tau in sigma k int reg d xi 1 int vert xi 2 vert leq vert xi 1 vert d xi 2 cdots int vert xi l vert leq vert xi k 1 vert d xi k otimes i 1 k sigma tau i where k is the group of permutations over k elements we show that these shuffle relations hold if all the symbols i have vanishing residue this is true of non integer order symbols on which the regularised integrals have all the expected properties such as stokes property mmp in general the shuffle relations hold up to finite parts of corrective terms arising from a renormalisation on tensor products of classical symbols a procedure adapted from renormalisation methods to compute feynman diagrams familiar to physicists we relate the shuffle relations for regularised integrals of symbols with shuffle relations for multiple zeta functions adapting the above constructions to the case of a symbol on the unit circle

a global extremum principle for the analysis of solids composed of softening material an extremum principle is presented covering problems in solid mechanics equilibrium analysis for piecewise linear softening materials problems formulated according to this principle are expressed in a mixed stress and deformation form the mechanics interpretation is limited according to linear deformation kinematics more specialized models such as an exfremumprinciple in mixed form for linearly elastic materials an equivalent to the minimum complementary energy principie and a statement of a bound theorem of limit analysis are identified as special cases within the general formation numerical results are presented for two examples of one dimensional structures made of inhomogeneous softening material the evolution of material degradation is demonstrated via a set of solutions obtained for increasing load each solution of the set is produced from a single application of a general purpose computer program for constrained nonlinear programming problems operating on a finite element interpretation of the nonlinear continuum i introduction the purpose of this paper is to present a global formulation of equilibrium problems in solid mechanics for systems made of softening material the formulation is expressed in a way to accommodate arbitrarily inhomogeneous anisotropic materials local state is represented in terms of a mixed stress and defo ation measure also material properties enter the formulation partly in implicit form through a combination of local and global constraints by virtue of these several features a substantial flexibility in the representation of constitutive properties is available in the model how this is accomplished explicitly becomes clear with the presentation of the problem statement given below the formulation itself comprises an extremum principle where a load factor is to be maximized w r t the set of stress and deformation fields as a result the sometimes most challenging issues related to existence and uniqueness are in the present circumstances moot i e established results from nonlinear optimization analysis of convex problems fully support a math ematical inte retation of the fo ulation also making the association in the usual way between convexity of the global problem statement and mechanical stability a category of problems can be identified for which independent of the specific form of material softening or degradation the extremum character and thus the stability is preserved indefinitely with increasing load the model presented here provides a convenience for the treatment of mechanics problems that require for their interpretation the representation of a set of separate fields where each field is associated with a separate interval of the region of the solid of course problems in the analysis of composites where the separate fields are identified nominally with the physical structure of constituent materials belong to this category problems involving material degradation for example where an o ginally homogeneous medium is rendered through the evolution of structural response into a set of regions each with distinctive constitutive character e g elasto plasticity have this property as well also availability of the extremum problem formulation described below is advantageous with respect to the treatment of many of the issues arising routinely in analysis and in the construction of models for computational purposes considerations in the treatment of convergence and error analysis the construction of algorithms modelling of mechanisms of material degradation and so on identify examples of the cited routinely arising issues in addition the present formulation makes it possible to obtain computational solutions

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

fuzzy linear regression analysis of fuzzy valued variables abstract our work includes the following three aspects 1 the concepts of possibility variable and its distribution are introduced and the independence among possibility variables is discussed on the basis of the theory of possibility presented by zadeh 4 2 maximin e estimation for the parameters of the distribution of the possibility variable is studied 3 two different fuzzy linear regression models of fuzzy valued variables are presented

optimization of structure and material properties for solids composed of softening material an existing formulation for the prediction of the optimal material properties tensor for systems made of linear material is extended here to encompass design with nonlinear softening material the original model for the linear case was stated as a convex constrained nonlinear programming problem and this property is preserved in the extension the development is exemplified for the case of design for minimum global compliance an extremum problem formulation for elastostatics is incorporated into the design problem as a convenient way to model the structural analysis of general softening systems unlike the case for design with linear material in the nonlinear problem the form of the solution for optimal material properties and the associated stress fields as well evolve with increasing load computational results are presented for a two dimensional example problem in which a system is designed for different loads while parameters in the material model are held fixed

note on maxmin m e estimation we present a solution to the maxmin e estimation problem of the family of fuzzy numbers with two parameters location and scale and show certain important properties of the maxmin e estimator

regularizing feynman path integrals using the generalized kontsevich vishik trace a fully regulated definition of feynman s path integral is presented here the proposed re formulation of the path integral coincides with the familiar formulation whenever the path integral is well defined in particular it is consistent with respect to lattice formulations and wick rotations i e it can be used in euclidean and minkowski space time the path integral regularization is introduced through the generalized kontsevich vishik trace that is the extension of the classical trace to fourier integral operators physically we are replacing the time evolution semi group by a holomorphic family of operators such that the corresponding path integrals are well defined in some half space of c the regularized path integral is thus defined through analytic continuation this regularization can be performed by means of stationary phase approximation or computed analytically depending only on the hamiltonian and the observable i e known a priori in either case the computational effort to eval

fuzzy nonlinear regression analysis using a random weight network modeling a fuzzy in fuzzy out system where both inputs and outputs are uncertain is of practical and theoretical importance fuzzy nonlinear regression fnr is one of the approaches used most widely to model such systems in this study we propose the use of a random weight network rwn to develop a fnr model called fnrrwn where both the inputs and outputs are triangular fuzzy numbers unlike existing fnr models based on back propagation bp and radial basis function rbf networks fnrrwn does not require iterative adjustment of the network weights and biases instead the input layer weights and hidden layer biases of fnrrwn are selected randomly the output layer weights for fnrrwn are calculated analytically based on a derived updating rule which aims to minimize the integrated squared error between cut sets that correspond to the predicted fuzzy outputs and target fuzzy outputs respectively in fnrrwn the integrated squared error is solved approximately by riemann integral theory the experimental results show that the proposed fnrrwn method can effectively approximate a fuzzy in fuzzy out system fnrrwn obtains better prediction accuracy in a lower computational time compared with existing fnr models based on bp and rbf networks

geometry of pseudodifferential algebra bundles and fourier integral operators we study the geometry and topology of filtered algebra bundles z over a smooth manifold x with typical fiber z z v the algebra of classical pseudodifferential operators acting on smooth sections of a vector bundle v over the compact manifold z and of integral order first a theorem of duistermaat and singer is generalized to the assertion that the group of projective invertible fourier integral operators pg fc z v is precisely the automorphism group of the filtered algebra of pseudodifferential operators we replace some of the arguments in their work by microlocal ones thereby removing the topological assumption we define a natural class of connections and b fields on the principal bundle to which z is associated and obtain a de rham representative of the dixmier douady class in terms of the outer derivation on the lie algebra and the residue trace of guillemin and wodzicki the resulting formula only depends on the formal symbol algebra z examples of pseudodifferential algebra bundles are given that are not associated to a finite dimensional fiber bundle over x

generalized midpoint finite element dynamic analysis of elastoplastic systems the application of a four parameter generalized midpoint integration method to small displacement elastoplastic dynamic problems is considered the integration of the governing relations over a time step is formulated as a non linear algebraic problem finite step problem by making use of generalized variables finite element modelling uniqueness and an extremum characterization of the solution of the finite step problem are discussed sufficient conditions for convergence of various iterative algorithms including newton raphson are given the b stability of the proposed procedure is assessed

on possibilistic inference abstract the estimation problem for an unknown parameter of a given possibility distribution function is used to throw some light onto zadeh s assertion that possibilistic inference is non statistical in nature

some comments on fuzzy variables abstract nahmias introduced the concept of a fuzzy variable as a possible axiomatic framework from which a rigorous theory of fuzziness may be constructed in this paper we attempt to shed more light on fuzzy variables in analogy with random variables in particular we study the problem if x1 x2 xn are mutually unrelated fuzzy variables with common membership function and 1 2 n are real numbers satisfying i o for every i and i 1n i 1 when does does z i 1n ixi have the same membership function

variational principles for a class of finite step elastoplastic problems with non linear mixed hardening a class of elastoplastic relations with non linear mixed hardening is addressed in the framework of an internal variable theory the relevant finite step structural problem resulting from the time integration of the constitutive laws according to a backward difference scheme is then formulated in a geometrically linear range convex analysis and potential theory for monotone multi valued operators are shown to provide the rationale for the development of a consistent variational theory as a special result a convex minimum principle in the final values of displacements plastic strains and plastic parameters is formulated and a critical comparison with an analogous result proposed in the literature is presented

possibilistic and probabilistic likelihood functions and their extensions common features and specific characteristics we deal with conditional probability in the sense of de finetti and with t conditional possibility with t a triangular norm we prove that dubois and prade conditional possibility is a particular min conditional possibility and then we compare the two notions of conditioning by an inferential point of view moreover we study t conditional possibilities as functions of the conditioning event putting in evidence analogies and differences with conditional probabilities this allows to characterize likelihood functions and their aggregations consistent either with a t conditional possibility or a conditional probability this analysis highlights many syntactical coincidences nevertheless the main difference is a weak form of monotonicity which arises only in the possibilistic case

a new approach to fuzzy rule generation fuzzy extension matrix this paper proposes a new approach to fuzzy rule generation from a set of examples with fuzzy representation the new approach called fuzzy extension matrix incorporates the fuzzy entropy to search for paths and generalizes the concept of crisp extension matrix by discussing paths of the fuzzy extension matrix a new heuristic algorithm for generating fuzzy rules is introduced compared with the crisp extension matrix the proposed method has the capability of handling fuzzy representation and tolerating noisy data or missing data a case study shows that the proposed heuristic algorithm partially inherits the advantages from the crisp case such as simplicity of rules and high learning accuracy the proposed approach offers a new practical way to automatically acquire imprecise knowledge

parameter estimations of mutually t related fuzzy variables abstract cai fuzzy sets and systems 55 1993 179 185 discussed parameter estimation methods for normal fuzzy variables in nahmias sense in this paper we investigate more the parameter estimations of general t related not necessarily normal fuzzy variables

the local and global parts of the basic zeta coefficient for operators on manifolds with boundary for operators on a compact manifold x with boundary x the basic zeta coefficient c0 b p1 t is the regular value at s 0 of the zeta function tr b p 1 t s where b p g is a pseudodifferential boundary operator in the boutet de monvel calculus for example the solution operator of a classical elliptic problem and p1 t is a realization of an elliptic differential operator p1 having a ray free of eigenvalues relative formulas e g for the difference between the constants with two different choices of p1 t have been known for some time and are local we here determine c0 b p1 t itself with even order p1 showing how it is put together of local residue type integrals generalizing the noncommutative residues of wodzicki guillemin fedosov golse leichtnam schrohe and global canonical trace type integrals generalizing the canonical trace of kontsevich and vishik formed of hadamard finite parts our formula generalizes a formula shown recently by paycha and scott for manifolds without boundary it leads in particular to new definitions of noncommutative residues of expressions involving log p1 t since the complex powers of p1 t lie far outside the boutet de monvel calculus the standard consideration of holomorphic families is not really useful here instead we have developed a resolvent parametric method where results from our calculus of parameter dependent boundary operators can be used

the formal path integral and quantum mechanics given an arbitrary lagrangian function on rd and a choice of classical path one can try to define feynman s path integral supported near the classical path as a formal power series parameterized by feynman diagrams although these diagrams may diverge we compute this expansion and show that it is formally if there are ultraviolet divergences invariant under volume preserving changes of coordinates we prove that if the ultraviolet divergences cancel at each order then our formal path integral satisfies a fubini theorem expressing the standard composition law for the time evolution operator in quantum mechanics moreover we show that when the lagrangian is inhomogeneous quadratic in velocity such that its homogeneous quadratic part is given by a matrix with constant determinant then the divergences cancel at each order thus by cutting and pasting and choosing volume compatible local coordinates our construction defines a feynman diagrammatic formal path integral for the nonrelativistic q

non commutative residues for anisotropic pseudo differential operators in rn abstract in this paper we define a non commutative residue for the algebra of classical anisotropic pseudo differential operators on r n modulo regularizing operators furthermore by means of the weyl formula we show that this trace coincides with the dixmier trace on operators of order m

residue traces for certain algebras of fourier integral operators abstract in this paper a trace functional is defined for certain algebras of fourier integral operators including for instance the algebra of toeplitz operators on the boundary of a strictly pseudoconvex domain and it is shown that vanishing of this trace characterizes commutators in each of these algebras