green s functions for transversely isotropic piezoelectric functionally graded multilayered half spaces by virtue of two systems of vector functions and the propagator matrix method greens functions for transversely isotropic piezoelectric functionally graded exponentially graded in the vertical direction and multilayered half spaces are derived it is observed that the homogeneous solution and propagator matrices for each functionally graded layer in the transformed domain are independent of the choice of the two systems of vector functions for a point force and point charge density applied at any location of the functionally graded half space greens functions are expressed in terms of one dimensional infinite integrals to carry out the numerical integral involving bessel functions an adaptive gauss quadrature approach is introduced and modified the piezoelectric functionally graded greens functions include those in the corresponding elastic functionally graded media as special results with the latter being also unavailable in the literature two piezoelectric functionally graded half space models are analyzed numerically one is a functionally graded pzt 4 half space and the other a coated functionally graded pzt 4 layer over a homogeneous batio3 half space the effects of different exponential factors on greens function components are clearly demonstrated which could be useful in the design and manufacturing of piezoelectric functionally graded structures 2004 elsevier ltd all rights reserved

implementing dempster s rule for hierarchial evidence this article gives an algorithm for the exact implementation of dempster s rule in the case of hierarchical evidence this algorithm is computationally efficient and it makes the approximation suggested by gordon and shortliffe unnecessary the algorithm itself is simple but its derivation depends on a detailed understanding of the interaction of hierarchical evidence

perfect powers expressible as sums of two cubes abstract let n 3 this paper is concerned with the equation a 3 b 3 c n which we attack using a combination of the modular approach via frey curves and galois representations with obstructions to the solutions that are of brauer manin type we shall show that there are no solutions in coprime non zero integers a b c for a set of prime exponents n having dirichlet density 28 219 44 928 0 628 and for a set of exponents n having natural density 1

on probability possibility transformations abstract a probability possibility transformation is a purely mechanical transformation of probabilistic support to possibilistic support and vice versa that is a conversion of the measure of support of one theory into that of the other that is independent of the problem domain in this paper it is shown that any bijective mapping between probability distributions and normalized possibility distributions that is symmetric and expansible cannot preserve the properties of projection noninteraction or conditionalization

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

a modified fuzzy c means algorithm for bias field estimation and segmentation of mri data we present a novel algorithm for fuzzy segmentation of magnetic resonance imaging mri data and estimation of intensity inhomogeneities using fuzzy logic mri intensity inhomogeneities can be attributed to imperfections in the radio frequency coils or to problems associated with the acquisition sequences the result is a slowly varying shading artifact over the image that can produce errors with conventional intensity based classification our algorithm is formulated by modifying the objective function of the standard fuzzy c means fcm algorithm to compensate for such inhomogeneities and to allow the labeling of a pixel voxel to be influenced by the labels in its immediate neighborhood the neighborhood effect acts as a regularizer and biases the solution toward piecewise homogeneous labelings such a regularization is useful in segmenting scans corrupted by salt and pepper noise experimental results on both synthetic images and mr data are given to demonstrate the effectiveness and efficiency of the proposed algorithm

green s function evaluation for three dimensional exponentially graded elasticity the numerical implementation of the green s function for an isotropic exponentially graded three dimensional elastic solid is reported the formulas for the nonsingular lq grading term rq in this green s function originally deduced by martin et al emph proc r soc lond a 458 1931 1947 2000 are quite complicated and a small error in one of the formulas is corrected the evaluation of the fundamental solution is tested by employing indirect boundary integral formulation using a galerkin approximation to solve several problems having analytic solutions the numerical results indicate that the green s function formulas and their evaluation are correct

boundary elements and the analog equation method for the solution of elastic problems in 3 d non homogeneous bodies abstract the application of the boundary element method bem to elastostatic problems involving 3d non homogeneous materials like functionally graded materials fgms is presented in this paper the analog equation method aem is used to transform the original problem into a new problem with unknown fictitious source but known fundamental solution by means of this transformation a system of uncoupled domain boundary integral equations d bies is first obtained combining standard boundary element discretization and radial basis functions rbfs approximation for the fictitious source the application of the original differential operator to the displacement bie provides the extra equations to compute the unknown fictitious source the boundary character of the method is maintained since the integrals involved in the equations are limited only to the boundary since the rbfs are selected in such a way that the corresponding analog equation could be solved analytically numerical examples for three dimensional problems in continuously non homogeneous isotropic and linear elastic fgms are presented and discussed

a weighted fuzzy classifier and its application to image processing tasks many image processing applications involve a pattern classification stage in this paper we propose a classifier based on fuzzy if then rules that allows the incorporation of weighted training patterns which can be used to adjust the sensitivity of the classification with respect to certain classes the antecedent part of fuzzy if then rules are specified by partitioning each attributes into fuzzy sets while the consequent class and the degree of certainty are determined from the compatibility and weights of training patterns we also introduce a learning method which adjusts the degree of certainty in order to provide improved classification performance and reduced costs experimental results on several image processing tasks demonstrate the efficacy of the proposed method

direct evaluation of hypersingular galerkin surface integrals a direct algorithm for evaluating hypersingular integrals arising in a three dimensional galerkin boundary integral analysis is presented the singular integrals are defined as limits to the boundary and by integrating two of the four dimensions analytically the coincident integral is shown to be divergent however the divergent terms can be explicitly calculated and shown to cancel with corresponding singularities in the adjacent edge integrals a single analytic integration is employed for the edge and vertex singular integrals this is sufficient to display the divergent term in the edge adjacent integral and to show that the vertex integral is finite by explicitly identifying the divergent quantities we can compute the hypersingular integral without recourse to stokes s theorem or the hadamard finite part the algorithms are developed in the context of a linear element approximation for the laplace equation but are expected to be generally applicable as an example the algorithms are applied to solve a thermal problem in an exponentially graded material

semi supervised classification method for dynamic applications the behaviour of a dynamic system can assume different operating states in the course of time in pattern recognition methods each state is represented by a set of similar patterns forming restricted regions in the feature space called classes recognising the state class of a new incoming pattern can be performed using a membership function the membership function accuracy depends on the prior knowledge about the system functioning for dynamic systems this knowledge often suffers from two drawbacks firstly there is no prior information about some states thus the occurrence of new states must be detected and integrated online in the data set secondly the prior information about some states especially the faulty ones is not sufficient to properly estimate their membership functions the missing information can be obtained from the new classified patterns thus these membership functions must be adapted online with the classification of new incoming patterns in this paper we propose a semi supervised classification method based on fuzzy pattern matching fpm the goal is to learn membership functions with a limited initial data set the class membership function according to each feature is sequentially learned with the occurrence of patterns and then it is updated online using an incremental or recursive approach this learning method does not require any prior information about the nature of classes or their number

evaluation of green s function derivatives for exponentially graded elasticity effective formulas for computing green s function of an exponentially graded three dimensional material have been derived in previous work the expansion approach for evaluating green s function has been extended to develop corresponding algorithms for its first and second order derivatives the resulting formulas are again obtained as a relatively simple analytic term plus a single double integral the integrand involving only elementary functions a primary benefit of the expansion procedure is the ability to compute the second order derivatives needed for fracture analysis moreover as all singular terms in this hypersingular kernel are contained in the analytic expression these expressions are readily implemented in a boundary integral equation calculation the computational formulas for the first derivative are tested by comparing with results of finite difference approximations involving green s function in turn the second derivatives are then validated by comparing with finite difference quotients using the first derivatives published in 2010 by john wiley sons ltd

semi analytical elasticity solutions for bi directional functionally graded beams abstract elasticity solutions are presented for bending and thermal deformations of functionally graded beams with various end conditions using the state space based differential quadrature method the beams are assumed to be macroscopically isotropic with young s modulus varying exponentially along the thickness and longitudinal directions while poisson s ratio remaining constant the state space method is adopted to obtain analytically the thickness variation of the elastic field and when coupled with differential quadrature the longitudinal discretization can be analyzed in an approximate manner this approach is then validated by comparing the numerical results with the exact solutions for a special functionally graded beam and with finite element solutions the influences of material gradient indices on the response of bi directional functionally graded beams are finally investigated

automatically determine the membership function based on the maximum entropy principle abstract fuzzy set theory has been successfully applied to many image processing and pattern recognition tasks in order to use the fuzzy logic approach membership functions for fuzzy sets must be determined first because many properties of images such as brightness of graylevels are strongly context dependent it is not easy to determine the membership function correctly in this paper the fuzzy set brightness of graylevels of an image is used as an example to illustrate how the membership function can be determined automatically we start with the concept of fuzzy event and use the maximum entropy principle as the criterion to find a membership function which will best represent the membership of brightness for each graylevel in an image that is the membership function is determined by finding a membership function such that the corresponding fuzzy event has maximum entropy the membership of brightness can be represented by an s function whose shape can be determined by the parameters a b and c the problem becomes to find a best parameter combination aopt bopt copt which is a combinatorial optimization problem the simulated annealing algorithm is used to solve this problem in this paper we have done the experiments on several images the results have shown that the proposed method can automatically and effectively find the brightness membership function for images the robustness of the proposed algorithm is also proved by the experiments though we used image processing as the application domain of the proposed approach the basic idea can be extended to other applications easily

green s function for a two dimensional exponentially graded elastic medium the freespace green function for a twodimensional exponentially graded elastic medium is derived the shear modulus is assumed to be an exponential function of the cartesian coordinates x y i e

on serre s uniformity conjecture for semistable elliptic curves over totally real fields let k be a totally real field and let s be a finite set of non archimedean places of k it follows from the work of merel momose and david that there is a constant b k s so that if e is an elliptic curve defined over k semistable outside s then for all p b k s the representation overline rho e p is irreducible we combine this with modularity and level lowering to show the existence of an effectively computable constant c k s and an effectively computable set of elliptic curves over k with cm e 1 cdots e n such that the following holds if e is an elliptic curve over k semistable outside s and p c k s is prime then either overline rho e p is surjective or overline rho e p sim overline rho e i p for some i 1 dots n

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

on hypersingular surface integrals in the symmetric galerkin boundary element method application to heat conduction in exponentially graded materials a symmetric galerkin formulation and implementation for heat conduction in a three dimensional functionally graded material is presented the green s function of the graded problem in which the thermal conductivity varies exponentially in one co ordinate is used to develop a boundary only formulation without any domain discretization the main task is the evaluation of hypersingular and singular integrals which is carried out using a direct limit to the boundary approach however due to complexity of the green s function for graded materials the usual direct limit procedures have to be modified incorporating taylor expansions to obtain expressions that can be integrated analytically several test examples are provided to verify the numerical implementation the results of test calculations are in good agreement with exact solutions and corresponding finite element method simulations copyright 2004 john wiley sons ltd

measurement of membership functions and their acquisition abstract three basic views of the representation of membership functions are reviewed together with fundamental measurement of linguistic terms of linguistic variables the conclusion is that such measurements are either on an ordinal or an interval scale based on whether the appropriate axioms are validated by the empirical data with an allowance for stochastic variation the conjoint measurement is introduced for the case of multi dimensional linguistic variables whose linguistic terms are compositions of two or finitely many more component linguistic terms of distinct independent linguistic variables it is shown that any composition of distinct independent component linguistic terms of component linguistic variables by any t norm or s norm or any finite convext linear combination preserves the monotonic weak order property of the components in the composite once the scale properties of the measurement values of particular terms are validated composition procedures may be applied to the experimental data to obtain compound membership functions of fuzzy sets induced by meaningful representations of compositions of linguistic terms of linguistic variables finally four methods of membership acquisition and construction are reviewed from the perspective of fundamental measurement

iterative refinement of possibility distributions by learning for pixel based classification this paper proposes an approach referred as iterative refinement of possibility distributions by learning irpdl for pixel based image classification the irpdl approach is based on the use of possibilistic reasoning concepts exploiting expert knowledge sources as well as ground possibilistic seeds learning the set of seeds is constructed by incrementally updating and refining the possibility distributions synthetic images as well as real images from the rider breast mri database are being used to evaluate the irpdl performance its performance is compared with three relevant reference methods region growing semi supervised fuzzy pattern matching and markov random fields the irdpl performance in terms of recognition rate 87 3 is close to the markovian method 88 8 that is considered to be the reference in pixel based image classification irpdl outperforms the other two methods respectively at the recognition rates of 83 9 and 84 7 in addition the proposed irpdl requires fewer parameters for the mathematical representation and presents a reduced computational complexity

automorphic lifts of prescribed types we prove a variety of results on the existence of automorphic galois representations lifting a residual automorphic galois representation we prove a result on the structure of deformation rings of local galois representations and deduce from this and the method of khare and wintenberger a result on the existence of modular lifts of specified type for galois representations corresponding to hilbert modular forms of parallel weight 2 we discuss some conjectures on the weights of n dimensional mod p galois representations finally we use recent work of taylor to prove level raising and lowering results for n dimensional automorphic galois representations

semi analytical analysis for multi directional functionally graded plates 3 d elasticity solutions semi analytical 3 d elasticity solutions are presented for orthotropic multi directional functionally graded plates using the differential quadrature method dqm based on the state space formalism material properties are assumed to vary not only through the thickness but also in the in plane directions following an exponential law the graded in plane domain is solved numerically via the dqm while exact solutions are sought for the thickness domain using the state space method convergence studies are performed and the present hybrid semi analytical method is validated by comparing numerical results with the exact solutions for a conventional unidirectional functionally graded plate finally effects of material gradient indices on the displacement and stress fields of the plates are investigated and discussed copyright 2009 john wiley sons ltd

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

unfair coins and necessity measures towards a possibilistic interpretation of histograms this short note defines a bijective mapping which turns a probability measure into a possibility measure this transformation has intuitive grounds especially the converse mapping corresponds to the usual assignment of identical probability values to elementary events of a given set when no information is available

semi analytical response of acoustic logging measurements in frequency domain this work proposes a semi analytical method for simulation of the acoustic response of multipole eccentered sources in a fluid filled borehole assuming a geometry that is invariant with respect to the azimuthal and vertical directions the solution in frequency domain is expressed in terms of a fourier series and a fourier integral the proposed semi analytical method builds upon the idea of separating singularities from the smooth part of the integrand when performing the inverse fourier transform the singular part is treated analytically using existing inversion formulae while the regular part is treated with a fft technique as a result a simple and effective method that can be used for simulating and understanding the main physical principles occurring in borehole eccentered sonic measurements is obtained numerical results verify the proposed method and illustrate its advantages

a spectral multipole method for efficient solution of large scale boundary element models in elastostatics in this paper we introduce a method to reduce the solution cost for boundary element be models from o n3 operations to o n2logn operations where n is the number of elements in the model previous attempts to achieve such an improvement in efficiency have been restricted in their applicability to problems with regular geometries defined on a uniform mesh we have developed the spectral multipole method smm which can be used not only for problems with arbitrary geometries but also with a variety of element types the memory necessary to store the required influence coefficients for the spectral multipole method is o n whereas the memory required for the traditional boundary element method is o n2 we demonstrate the savings in computational speed and fast memory requirements in some numerical examples we have established that the break even point for the method can be as low as 500 elements which implies that the method is not only suitable for extremely large scale problems but that it also provides a useful bridge between the small scale and large scale problems we also demonstrate the performance of the multipole algorithm on the solution of large scale granular assembly models the large scale be capacity provided by this algorithm will not only prove to be useful in large macroscopic models but it will also make it possible to model microscopic damage processes that form the fundamental mechanisms in plastic flow and brittle fracture

green s functions of an exponentially graded transversely isotropic half space abstract by virtue of a complete set of displacement potential functions and hankel transform the analytical expressions of green s function of an exponentially graded elastic transversely isotropic half space is presented the given solution is analytically in exact agreement with the existing solution for a homogeneous transversely isotropic half space employing a robust asymptotic decomposition technique the green s function is decomposed to the closed form green s function corresponding to the homogeneous transversely isotropic half space and grading term with strong decaying integrands this representation is very useful for numerical methods which are based on boundary integral formulations such as boundary element method since the numerically evaluated part is not responsible for the singularity the high accuracy of the proposed numerical scheme is confirmed by some numerical examples

a galerkin symmetric boundary element method in elasticity formulation and implementation a symmetric boundary element method based on a weighted residual galerkin approach for elastoplastic analysis is revisited and its computer implementation for two dimensional homogeneous problems is described

a boundary element formulation for the heterogeneous functionally graded viscoelastic structures structural analysis of the heterogeneous viscoelastic materials is among the most important subjects in the engineering design stages several attempts have been performed so far for employing the integral equation approach to heterogeneous viscoelastic structures in the present research employing two viscoelastic constitutive equations and a weighted residual technique a simple but effective boundary element formulation is implemented for heterogeneous kelvin voigt and boltzmann viscoelastic solid models the boltzmann model provides proper behavior predictions for realistic structures manifest viscoelastic natures present formulation needs only fundamental solution of the heterogeneous elastostatic problem with materials whose properties are prescribed as explicit functions of time heterogeneous exponentially graded materials and quasistatic time variations are considered in the present formulation present approach does not require using the relaxation functions and mathematical transformations and is capable of solving quasistatic viscoelastic problems with arbitrary load time dependencies and boundary conditions some numerical examples are provided to verify the proposed boundary element approach

fermat type equations of signature 13 13 p via hilbert cuspforms in this paper we prove that for p 13649 equations of the form x 13 y 13 cz p have no non trivial primitive solutions a b c such that 13 not mid c for an infinite family of values for c our method consists on relating a solution a b c to the previous equation to a solution a b c 1 of another diophantine equation with coefficients in mathbb q sqrt 13 then we attach to a b c 1 a frey curve e a b defined over mathbb q sqrt 13 that is not a mathbb q curve we prove a modularity result of independent interest for certain elliptic curves over totally real abelian number fields satisfying some local conditions at 3 this theorem in particular implies modularity of e a b this enables us to use level lowering results and apply the modular approach via hilbert cuspforms over mathbb q sqrt 13 to prove the non existence of a b c 1 and consequently of a b c

fuzzy logic based generalized decision theory with imperfect information the existing decision models have been successfully applied to solving many decision problems in management business economics and other fields but nowadays arises a need to develop more realistic decision models the main drawback of the existing utility theories starting from von neumann moregnstern expected utility to the advanced non expected models is that they are designed for laboratory examples with simple well defined gambles which do not adequately enough reflect real decision situations in real life decision making problems preferences are vague and decision relevant information is imperfect as described in natural language nl vagueness of preferences and imperfect decision relevant information require using suitable utility model which would be fundamentally different to the existing precise utility models precise utility models cannot reflect vagueness of preferences vagueness of objective conditions and outcomes imprecise beliefs etc the time has come for a new generation of decision theories in this study we propose a decision theory which is capable to deal with vague preferences and imperfect information the theory discussed here is based on a fuzzy valued non expected utility model representing linguistic preference relations and imprecise beliefs

on green s function for a three dimensional exponentially graded elastic solid the problem of a point force acting in an unbounded three dimensional isotropic elastic solid is considered kelvin solved this problem for homogeneous materials here the material is inhomogeneous it is functionally graded specifically the solid is exponentially graded which means that the lame moduli vary exponentially in a given fixed direction the solution for the green9s function is obtained by fourier transforms and consists of a singular part given by the kelvin solution plus a non singular remainder this grading term is not obtained in simple closed form but as the sum of single integrals over finite intervals of modified bessel functions and double integrals over finite regions of elementary functions knowledge of this new fundamental solution for graded materials permits the development of boundary integral methods for these technologically important inhomogeneous solids

study and solution of bem singular integral equation method in the case of concentrated loads abstract the boundary element method has been widely used in order to obtain numerical solutions in many problems in science and engineering on the other hand the singular integral equation method can treat successfully the singular fields appearing in engineering problems when the right hand side of it is a regular function in this paper we consider the case where the right hand side of a boundary integral equation singular integral equation is a distribution this problem arises in the case of concentrated forces and or moments our main scope is to propose appropriate methods for the numerical solution of singular integral equations when the loading is a concentrated force or a moment before that we are obliged to analyze the solvability of such equations the main key for the proof of the solvability is the proof of existence of cauchy integrals of distributions as a by product we find a very interesting result that the solution behaves as 1 r or 1 r2 at the point where the concentrated force or moment respectively is applied obviously the existence of essential singularities in the solution creates difficulties in the numerical treatment of integral equations thus two appropriate numerical methods and an interpolatory quadrature method are proposed for the numerical solution of bie sie numerical examples illustrate the importance of the proposed methods

green s function expansion for exponentially graded elasticity new computational forms are derived for the green s function of an exponentially graded elastic material in three dimensions by suitably expanding a term in the defining inverse fourier integral the displacement tensor can be written as a relatively simple analytic term plus a single double integral that must be evaluated numerically the integration is over a fixed finite domain the integrand involves only elementary functions and only low order gauss quadrature is required for an accurate answer moreover it is expected that this approach will allow a far simpler procedure for obtaining the first and second order derivatives needed in a boundary integral analysis the new green s function expressions have been tested by comparing with results from an earlier algorithm

moduli of finite flat group schemes and modularity we prove that under some mild conditions a two dimensional p adic galois representation which is residually modular and potentially barsotti tate at p is modular this provides a more conceptual way of establishing the shimura taniyama weil conjecture especially for elliptic curves which acquire good reduction over a wildly ramified extension of 3 the main ingredient is a new technique for analyzing flat deformation rings it involves resolving them by spaces which parametrize finite flat group scheme models of galois representations introduction