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

indentation of solids with gradients in elastic properties part ii axisymmetric indentors analytical and computational results are presented for the evolution of stresses and deformation fields due to indentation from a rigid axisymmetric indentor on an elastic substrate the theory addresses the variations in young s modulus e of the substrate as a function of depth z beneath the indented surface for two cases 1 a simple power law e e0zk where 0 k 1 is a non dimensional exponent 2 an exponential law e e0e z where e0 is young s modulus at the surface and is a length parameter the indentor geometries for which analytic solutions are derived include flat circular punch sphere and circular cone the analytical results for the punch are compared with finite element simulations the latter validate the theory and offer further insights into the effects of the variation in poisson ratio v with depth

mechanics of non slipping adhesive contact on a power law graded elastic half space abstract in previous work about axisymmetric adhesive contact on power law graded elastic materials the contact interface was often assumed to be frictionless which is however not always the case in practical applications in order to elucidate the effect of friction and the coupling between normal and tangential deformations in the present paper the problem of a rigid punch with a parabolic shape in non slipping adhesive contact with a power law graded half space is studied analytically via singular integral equation method a series of closed form analytical solutions which include the frictionless and homogeneous solutions as special cases are obtained our results show that compared with the frictionless case the interfacial friction tends to reduce the contact area and the indentation depth during adhesion the magnitude of the coupling effect depends on both the poisson ratio and the gradient exponent of the half space this effect vanishes for homogeneous incompressible as well as for linearly graded materials but becomes significant for auxetic materials with negative poisson s ratio furthermore influence of mode mixity on the adhesive behavior of power law graded materials which was seldom touched in literature is discussed in details

bandler kohout subproduct with yager s classes of fuzzy implications the bandler kohout subproduct bks inference mechanism is one of the two established fuzzy relational inference fri mechanisms the other one being zadeh s compositional rule of inference cri both these fris are known to possess many desirable properties it can be seen that many of these desirable properties are due to the rich underlying structure viz the residuated algebra from which the employed operations come in this study we discuss the bks relational inference system with the fuzzy implication interpreted as yager s classes of implications which do not form a residuated structure on 0 1 we show that many of the desirable properties viz interpolativity continuity robustness which are known for the bks with residuated implications are also available under this framework thus expanding the choice of operations available to practitioners note that to the best of the authors knowledge this is the first attempt at studying the suitability of an fri where the operations come from a nonresiduated structure

a receding contact plane problem between a functionally graded layer and a homogeneous substrate abstract in this paper we consider the plane problem of a frictionless receding contact between an elastic functionally graded layer and a homogeneous half space when the two bodies are pressed together the graded layer is modeled as a nonhomogeneous medium with an isotropic stress strain law and over a certain segment of its top surface is subjected to normal tractions while the rest of this surface is free of tractions since the contact between the two bodies is assumed to be frictionless then only compressive normal tractions can be transmitted in the contact area using integral transforms the plane elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact half length the global equilibrium condition of the layer is supplemented to solve the problem the singular integral equation is solved numerically using chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact half length that satisfies the global equilibrium condition the main objective of the paper is to study the effect of the material nonhomogeneity parameter and the thickness of the graded layer on the contact pressure and on the length of the receding contact

on generalized modus ponens with multiple rules and a residuated implication we consider a multiple rule generalized modus ponens inference scheme with an interpretation based on compositional rule of inference cri and a residuated implication we show that such a system is equivalent as far as cri is concerned to a system that satisfies the basic requirement for fuzzy reasoning proposed by turksen and tian fuzzy sets and systems 58 1993 3 40 we establish an analogous conclusion for an alternative interpretation due to magrez and smets of generalized modus ponens which we call consequent dilation rule cdr this method is computationally faster than cri but it produces less specific inference results

equivariant poincare polynomials and counting points over finite fields abstract suppose a finite group acts as a group of automorphisms of a smooth complex algebraic variety which is defined over a number field we show how in certain circumstances an equivariant comparison theorem in l adic cohomology may be used to convert the computation of the graded character of the induced action on cohomology into questions about numbers of rational points of varieties over finite fields this is carried through in three applications first for the symmetric group acting on the moduli space of n points on a genus zero curve second for a unitary reflection group acting on the complement of its reflecting hyperplanes and third for the symmetric group action on the space of configurations of points in any smooth variety which satisfies certain strong purity conditions

bonded dissimilar strips with a crack perpendicular to the functionally graded interface the mode i crack problem for two dissimilar infinite strips bonded through a functionally graded interfacial zone is investigated within the framework of plane elasticity the graded interfacial zone is treated as a nonhomogeneous continuum having the continuously varying elastic modulus between the dissimilar homogeneous strips a crack is assumed to be embedded in one of the strips perpendicular to the nominal interface with the aid of the stiffness matrix approach a set of homogeneous conditions relevant to the proposed crack problem is readily satisfied subsequent application of the mixed conditions on the cracked plane then leads to a singular integral equation of the first kind which is solved numerically in consequence the variations of stress intensity factors are provided as functions of geometric and material parameters of the bonded structure the effect of the material nonhomogeneity in the interfacial zone is further addressed by measuring the degree of correspondence with the results that are obtained based on the use of the homogenized interfacial elastic property

two dimensional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties abstract a multi layered model for frictionless contact analysis of functionally graded materials fgms with arbitrarily varying elastic modulus under plane strain state deformation has been developed based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves the fgm is divided into several sub layers and in each sub layers the shear modulus is assumed to be linear function while the poisson s ratio is assumed to be a constant with the model the frictionless contact problem of a functionally graded coated half space is investigated by using the transfer matrix method and fourier integral transform technique the problem is reduced to a cauchy singular integral equation the contact pressure contact region and indentation are calculated for various indenters by solving the equations numerically

sliding frictional contact between a rigid punch and a laterally graded elastic medium abstract analytical and computational methods are developed for contact mechanics analysis of functionally graded materials fgms that possess elastic gradation in the lateral direction in the analytical formulation the problem of a laterally graded half plane in sliding frictional contact with a rigid punch of an arbitrary profile is considered the governing partial differential equations and the boundary conditions of the problem are satisfied through the use of fourier transformation the problem is then reduced to a singular integral equation of the second kind which is solved numerically by using an expansion collocation technique computational studies of the sliding contact problems of laterally graded materials are conducted by means of the finite element method in the finite element analyses the laterally graded half plane is discretized by quadratic finite elements for which the material parameters are specified at the centroids flat and triangular punch profiles are considered in the parametric analyses the comparisons of the results generated by the analytical technique to those computed by the finite element method demonstrate the high level of accuracy attained by both methods the presented numerical results illustrate the influences of the lateral nonhomogeneity and the coefficient of friction on the contact stresses

checking the coherence and redundancy of fuzzy knowledge bases checking the coherence of a set of rules is an important step in knowledge base validation coherence is also needed in the field of fuzzy systems indeed rules are often used regardless of their semantics and it sometimes leads to sets of rules that make no sense avoiding redundancy is also of interest in real time systems for which the inference engine is time consuming a knowledge base is potentially inconsistent or incoherent if there exists a piece of input data that respects integrity constraints and that leads to logical inconsistency when added to the knowledge base we more particularly consider knowledge bases composed of parallel fuzzy rules then coherence means that the projection on the input variables of the conjunctive combination of the possibility distributions representing the fuzzy rules leaves these variables completely unrestricted i e any value for these variables is possible or at least not more restrictive than integrity constraints fuzzy rule representations can be implication based or conjunction based we show that only implication based models may lead to coherence problems however unlike conjunction based models they allow to design coherence checking processes some conditions that a set of parallel rules has to satisfy in order to avoid inconsistency problems are given for certainty or gradual rules the problem of redundancy which is also of interest for fuzzy knowledge bases validation is addressed for these two kinds of rules

two dimensional thermoelastic contact problem of functionally graded materials involving frictional heating the two dimensional thermoelastic sliding frictional contact of functionally graded material fgm coated half plane under the plane strain deformation is investigated in this paper a rigid punch is sliding over the surface of the fgm coating with a constant velocity frictional heating with its value proportional to contact pressure friction coefficient and sliding velocity is generated at the interface between the punch and the fgm coating the material properties of the coating vary exponentially along the thickness direction in order to solve the heat conduction equation analytically the homogeneous multi layered model is adopted for treating the graded thermal diffusivity coefficient with other thermomechanical properties being kept as the given exponential forms the transfer matrix method and fourier integral transform technique are employed to convert the problem into a cauchy singular integral equation which is then solved numerically to obtain the unknown contact pressure and the in plane component of the surface stresses the effects of the gradient index peclet number and friction coefficient on the thermoelastic contact characteristics are discussed in detail numerical results show that the distribution of the contact stress can be altered and therefore the thermoelastic contact damage can be modified by adjusting the gradient index peclet number and friction coefficient

applications of fuzzy relational equations for methods of reasoning in presence of fuzzy data the paper deals with implementation of a general scheme for fuzzy logic inference with the aid of fuzzy relational equations it is shown that antecedents and consequents are related in terms of a fuzzy relation various implementation methods of generalized modus ponens and modus tollens are put into extensive study it is pointed out that fuzzy relational equations form an effective and plausible tool for implementations of reasoning methods with fuzzy premises two examples of fuzzy controllers being a direct application of schemes of approximate reasoning are also discussed

on the law of importation x wedge y longrightarrow z equiv x longrightarrow y longrightarrow z in fuzzy logic the law of importation given by the equivalence x lambda y rarr z equiv xrarr y rarr z is a tautology in classical logic in a implications defined by turksen et al the above equivalence is taken as an axiom in this paper we investigate the general form of the law of importation j t x y z j x j y z where t is a t norm and j is a fuzzy implication for the three main classes of fuzzy implications i e r s and ql implications and also for the recently proposed yager s classes of fuzzy implications i e f and g implications we give necessary and sufficient conditions under which the law of importation holds for r s f and g implications in the case of ql implications we investigate some specific families of ql implications also we investigate the general form of the law of importation in the more general setting of uninorms and t operators for the above classes of fuzzy implications following this we propose a novel modified scheme of compositional rule of inference cri inferencing called the hierarchical cri which has some advantages over the classical cri following this we give some sufficient conditions on the operators employed under which the inference obtained from the classical cri and the hierarchical cri become identical highlighting the significant role played by the law of importation

solution of the dynamic frictional contact problem between a functionally graded coating and a moving cylindrical punch abstract this paper presents an analytical method developed to investigate the dynamic frictional contact mechanics between a functionally graded coating and a rigid moving cylindrical punch governing partial differential equations of elastodynamics are solved analytically by applying galilean and fourier transformations interface continuity and boundary conditions are written and contact problem is then reduced to a singular integral equation of the second kind the singular integral equation is solved numerically by means of an expansion collocation method developed solution procedures are verified through the comparisons made to the results available in the literature presented parametric analyses illustrate the effects of punch speed coefficient of friction material inhomogeneity and geometric parameters upon the contact stresses it is shown that especially at higher punch speeds the difference between contact stresses obtained through elastodynamic and elastostatic solutions is rather significant a formulation based on the elastodynamic theory as presented in the current study is required to compute more realistic contact stresses

system of fuzzy relation equations with inf composition complete set of solutions the problem of solvability of a system of equations with inf composition is considered on finite universes equations are expressed using operations of a bl algebra we study complete set of solutions of the respective system in the particular case one equation and in the general case in both cases various conditions of solvability are found and proved we characterize all maximal solutions and prove that under certain conditions each solution of the system an equation is less than or equal to a respective maximal one as a result we are able to characterize the complete set of solutions examples of single equations and their systems are considered and complete sets of solutions are found for each

finitary solvability conditions for systems of fuzzy relation equations in this paper we consider the problem of solving systems of fuzzy relation equations two types of these systems with different compositions are considered and processed simultaneously a new sufficient condition and new solvability criteria are proposed for systems of both types all these conditions are finitary and thus can be easily verified the sufficient condition and criteria of solvability characterize a relationship between a skeleton nxn matrix n is a number of equations and a vector of the right hand side

steady and transient green s functions for anisotropic conduction in an exponentially graded solid abstract the problem of the determination of green s function in conduction for a rectilinearly anisotropic solid with an exponential grading along a certain direction is studied domains of an unbounded space and a half space either three dimensional or two dimensional are considered along the boundary of the domain homogeneous boundary conditions of the first and second kinds are imposed we find interestingly that under this specific type of grading the green s functions permit an algebraic decomposition which will in turn greatly simplify the formulation the method of fourier transform is employed for the green s function for a half space or a half plane although the derivation process is quite tedious we show analytically that the inverse transform can be found exactly and their resulting expressions are surprisingly neat and compact in addition both steady state and transient state field solutions are considered by taking laplace transform with respect to the time variable we show that the mathematical frameworks for the steady state and transient state green s functions are entirely analogous thereby the transient state green s function is readily obtained by taking laplace inverse transform back to the time domain these derived fundamental solutions will serve as benchmark results for modeling some inhomogeneous materials in the absence of grading term we have verified analytically that our solutions agree exactly with previously known green s functions for homogeneous media

approximation theory of fuzzy systems based upon genuine many valued implications siso cases it is proved that the single input and single output siso fuzzy systems based upon genuine many valued implications are universal approximators it is shown theoretically that fuzzy control systems based upon genuine many valued implications are equivalent to those based upon t norm implications the general approach to construct fuzzy systems is given it is also shown that defuzzifier based upon center of areas is not appropriate to the fuzzy systems based upon genuine many valued implications

fuzzy inference systems preserving moser navara axioms abstract satisfiability of three naturally proposed axioms which are desirable for fuzzy inference system was discussed by moser and navara in 36 the fuzzy rule base models considered in this study were mainly the mamdani assilian ones and partly also logically motivated implicative fuzzy systems the investigation leads to the fact that often none of these fuzzy systems do satisfy the given axioms simultaneously therefore moser and navara proposed so called conditionally firing rules and proved that the simultaneous satisfaction of the three axioms is feasible under very mild and practically non restrictive conditions note that the inference mechanism tailored to the fuzzy rules in the investigation was the compositional rule of inference abb cri and similarly the concept of conditionally firing rules were stemming from the cri and the mamdani assilian model of a fuzzy rule base for the implicative interpretation of fuzzy rules the original axioms proposed by moser and navara were later on re defined by st pnicka and mandal with the aim to express the meaning of the original axioms initially proposed for the mamdani assilian rules furthermore conditionally firing implicative rules were proposed based on the so called bandler kohout subproduct abb bks inference mechanism and a study similar to the one by moser and navara was undertaken for them the study encompasses the satisfaction of the modified axioms for the use of implicative rules and the bks furthermore some additional results confirming the applicability of the conditionally firing rules satisfying the moser navara axioms are also provided including the universal approximation ability however the solvability criterions for fuzzy relational equations give a strong preference to the usage of the other combinations namely to the combination of cri with the implicative interpretation of fuzzy rules and to the combination of bks with the mamdani assilian interpretation of fuzzy rules therefore also these combinations of fuzzy inference mechanisms and interpretations of fuzzy rules should be investigated with respect to the satisfaction of moser navara axioms the main purpose of this article which extends the short conference contribution 47 by st pnicka is to provide such an investigation jointly with the review on conditionally firing rules and supplementary results

indentation of solids with gradients in elastic properties part i point force abstract analytical and computational results are presented on the evolution of stresses and displacements due to indentation from a normal point force on an elastic substrate whose young s modulus e varies as a function of depth z beneath the indented surface with the exception of variation of properties with depth the material is assumed to be linearly elastic and locally isotropic closed form solutions are derived for several fixed values of the poisson ratio v and variations in e which follow two prescribed functions of z 1 a simple power law e e 0 z k where 0 k e e 0 e z where e 0 is young s modulus at the surface 0 denotes a soft surface e g modulus variations measured as a function of depth beneath the earth s surface for solids and rocks the analytical solutions are checked with detailed finite element simulations it is shown that for the power law case there exists a critical poisson ratio v cr above which drastic changes occur in the stress distribution under the point load finite element results reveal however that the response is relatively less sensitive to the variation of v on either side of v cr than to the variation of e with depth applications of the present results are discussed wherever appropriate to surface treatments of engineering structures thick coatings thin film multilayers for microelectronic devices and settling of foundations in the context of soil mechanics and rock mechanics

correct models of fuzzy if then rules are continuous we show that a system of fuzzy if then rules being modeled correctly works as a partially given fuzzy function its behavior is determined by a chosen structure for if then rules which assigns meaning to fuzzy sets in the if and then parts as well as to basic connectives this partial function can be extended to a whole domain of fuzzy sets with the help of the compositional rule of inference which plays a role of a mechanism for computing the dependent functional values we investigate the question whether this function is continuous two new notions are introduced a correct model of fuzzy if then rules in a structure and a continuous model of fuzzy if then rules with respect to given data we prove that correctness of models of fuzzy if then rules is connected with the problem of solvability of the respective system of fuzzy relation equations in this and only this case a model of fuzzy if then rules is continuous as a side result we have established a new criterion of a solvability of a system of fuzzy relation equations with sup composition

mirror duality and string theoretic hodge numbers we prove in full generality the mirror duality conjecture for string theoretic hodge numbers of calabi yau complete intersections in gorenstein toric fano varieties the proof is based on properties of intersection cohomology

symbolic and numerical solution of the axisymmetric indentation problem for a multilayered elastic coating abstract this paper is concerned with a semi analytical approach to the solution of the axisymmetric indentation problem for a multilayered elastic half space the stress and displacement fields for each layer and the substrate are derived in closed form by using the papkovich neuber potentials and the hankel transform the bonded or sliding interface conditions between the sub layers are handled by the use of the appropriate transfer matrix and then the mixed boundary value problem is reduced to a fredholm integral equation symbolic and numerical computations of the solution are implemented in the symbolic software mathematica in the form of a fast and efficient numerical algorithm allowing rapid determination of the load displacement curves and composite elastic properties for an arbitrary rigid indenter shape a series of results for different indenters flat conical spherical and blunted conical punch shapes and different multilayered composites is presented and discussed the complete set of symbolic and numerical computations are provided as supplementary resources with the paper

representations on the cohomology of hypersurfaces and mirror symmetry abstract we study the representation of a finite group acting on the cohomology of a non degenerate invariant hypersurface of a projective toric variety we deduce an explicit description of the representation when the toric variety has at worst quotient singularities as an application we conjecture a representation theoretic version of batyrev and borisov s mirror symmetry between pairs of calabi yau hypersurfaces and prove it when the hypersurfaces have dimension at most 3 an interesting consequence is the existence of pairs of calabi yau orbifolds whose hodge diamonds are mirror with respect to the usual hodge structure on singular cohomology

cracks problem for non homogeneous composite material subjected to dynamic loading abstract in this paper we present a method to analyse the dynamic and steady response of non homogeneous composite materials differing from the existing works reported in literature the present method can be used for arbitrarily varying material properties through thickness direction and the crack number can be larger than one it is assumed that the composite material is orthotropic and all the material properties depend only on the coordinates y along the thickness direction the material non homogeneity is simulated by dividing the plate into a number of layers each layer is assigned slightly different material properties the method is based upon the fourier and laplace transforms to reduce the boundary value problem to a system of generalized singularity integral equations in the laplace transform domain the singular integral equations for the problem are derived and numerically solved by weighted residual value methods by utilized numerical laplace inversion the time dependent full field solutions are obtained as the numerical illustrates three different cracked specimens a functionally graded material a metal ceramic joint with functionally graded interlayer and a metal substrate functionally graded film structure are presented for various material non homogeneity parameters and or functionally graded layer thickness the results obtained demonstrate that the present model is an efficient tool in the fracture analysis of composite materials with properties varying in the thickness direction

dynamic investigation of a functionally graded layered structure with a crack crossing the interface abstract the dynamic response of a functionally graded layered structure with a crack crossing the interface is analyzed the in plane impact loading condition is considered by using the laplace and fourier integral transforms singular integral equation method and residue theory the present problem is reduced to a singular integral equation in the laplace transform domain the influences of young s modulus ratio thickness ratio and crack length and location on the dynamic stress intensity factors dsifs are investigated particularly the dsifs corresponding to different crack locations are shown in the case when the crack center moves from one layer to another layer through the interface the peak and static values and overshoot characteristics of the dsifs are analyzed it is found that these values typically exhibit kinking behavior when the crack tips arrive at the interface this study is different from previous other investigations in the following respects 1 the dynamic response of a crack crossing the interface of a functionally graded structure is studied analytically which has hardly been done in the past and 2 the present model can be reduced to some important problems such as a functionally graded coating substrate structure with a crack in the graded coating or homogeneous substrate or one intersecting the interface

a short note on fuzzy relational inference systems this paper is a short note contribution to the topic of fuzzy relational inference systems and the preservation of their desirable properties it addresses the two main fuzzy relational inferences compositional rule of inference cri and the bandler kohout subproduct bk subproduct and their combination with two fundamental fuzzy relational models of fuzzy rule bases namely the mamdani assilian and the implicative models the goal of this short note article is twofold firstly we show that the robustness related to the combination of bk subproduct and implicative fuzzy rule base model was not proven correctly in 24 however we will show that the result itself is still valid and a valid proof will be provided secondly we shortly discuss the preservation of desirable properties of fuzzy inference systems and conclude that neither the above mentioned robustness nor any other computational advantages should automatically lead to a preference of the combinations of cri with mamdani assilian models or of the bk subproduct with the implicative models

compactifications of subvarieties of tori we study compactifications of subvarieties of algebraic tori defined by imposing a sufficiently fine polyhedral structure on their non archimedean amoebas these compactifications have many nice properties for example any k boundary divisors intersect in codimension k we consider some examples including m 0 n subset overline m 0 n and more generally log canonical models of complements of hyperplane arrangements and compact quotients of grassmannians by a maximal torus

non slipping adhesive contact of a rigid cylinder on an elastic power law graded half space in this paper adhesive contact of a rigid cylinder on an elastic power law graded half space is studied analytically with the theory of weakly singular integral equation and orthogonal polynomial method emphasis is placed on the coupling effect between tangential and normal directions which was often neglected in previous works our analysis shows that the coupling effect tends to reduce the contact area in the compressive regime the effect of bending moment on the adhesion behavior is also examined like a pull off force there also exists a critical bending moment at which the cylinder can be bended apart from the substrate however unlike pull off force the critical bending moment is insensitive to the gradient exponent of the graded material

a receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate abstract in this paper we consider the axisymmetric problem of a frictionless receding contact between an elastic functionally graded layer and a homogeneous half space when the two bodies are pressed together the graded layer is modeled as a nonhomogeneous medium with an isotropic stress strain law and is subjected over a part of its top surface to normal tractions while the rest of it is free of tractions since the contact between the two bodies is assumed to be frictionless then only compressive normal tractions can be transmitted in the contact area using hankel transform the axisymmetric elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact radius the global equilibrium condition of the layer is supplemented to solve the problem the singular integral equation is solved numerically using orthogonal chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact length that satisfies the global equilibrium condition the main objective of the paper is to study the effect of the material nonhomogeneity parameter and the thickness of the graded layer on the contact pressure and on the length of the receding contact

axisymmetric frictionless contact of a functionally graded piezoelectric layered half space under a conducting punch abstract this paper studies the axisymmetric frictionless contact of a functionally graded piezoelectric layered half space subjected to three typical rigid punches i e flat circular punch spherical punch and conical punch the punch is assumed as a perfect conductor with a constant electric potential the electro mechanical properties of the functionally graded piezoelectric materials fgpms vary exponentially along the thickness direction by employing the hankel integral transform technique the problem is reduced to a set of singular integral equations of the first kind these equations are then discretized and solved numerically to determine the unknown normal contact pressure and electric charge the effects of the gradient index and punch geometry on the surface electro mechanical contact behaviors are discussed in detail

on the suitability of the bandler kohout subproduct as an inference mechanism fuzzy relational inference fri systems form an important part of approximate reasoning schemes using fuzzy sets the compositional rule of inference cri which was introduced by zadeh has attracted the most attention so far in this paper we show that the fri scheme that is based on the bandler kohout bk subproduct along with a suitable realization of the fuzzy rules possesses all the important properties that are cited in favor of using cri viz equivalent and reasonable conditions for their solvability their interpolative properties and the preservation of the indistinguishability that may be inherent in the input fuzzy sets moreover we show that under certain conditions the equivalence of first infer then aggregate fita and first aggregate then infer fati inference strategies can be shown for the bk subproduct much like in the case of cri finally by addressing the computational complexity that may exist in the bk subproduct we suggest a hierarchical inferencing scheme thus this paper shows that the bk subproduct based fri is as effective and efficient as the cri itself

monotonicity of siso fuzzy relational inference with an implicative rule base a fuzzy relational inference fri mechanism is appraised based on the different desirable properties it possesses among these properties monotonicity of an fri has not received much attention in this work we investigate the monotonicity of a single input single output fri with an implicative form of the rule base in all the previous works that deal with monotonicity of an fri with the implicative form of rule base the employed fuzzy implications come from a residuated lattice it can be noticed that this rich underlying structure plays a major role in proving the results further we also modify the given monotone rule base this work differs from the previous works in that 1 the fuzzy implications employed in it do not come from any known residuated structure on text 0 1 and 2 the original rule base is employed without any alteration we determine conditions under which monotonicity of an fri where the rule base is modeled by a strict fuzzy implication can be ensured without transforming the original rule base thus the results in this work further augment the case for considering fuzzy implications other than those from the residuated setting to be used in applications

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

new calabi yau orbifolds with mirror hodge diamonds abstract we prove a representation theoretic version of borisov batyrev mirror symmetry and use it to construct infinitely many new pairs of orbifolds with mirror hodge diamonds with respect to the usual hodge structure on singular complex cohomology we conjecture that the corresponding orbifold hodge diamonds are also mirror when x is the fermat quintic in p 4 and x is a sym 5 equivariant toric resolution of its mirror x we deduce that for any subgroup of the alternating group a 5 the hilbert schemes hilb x and hilb x are smooth calabi yau threefolds with explicitly computed mirror hodge diamonds

reconstruction of inhomogeneous properties of orthotropic viscoelastic layer abstract the consecutive scheme of reconstructing the functions characterizing the instantaneous and long termed modules for inhomogeneous orthotropic viscoelastic layer whose properties continuously vary through a thickness is proposed the identification problem is solved on the basis of the additional information on the integral characteristics of displacement fields measured on top border of a layer iterative process of reconstruction of six unknown functions is formulated to reconstruct the rest six functions systems of fredholm s integral equations of the first kind with smooth kernels are received computational experiment on a reconstruction of various laws of inhomogeneity is conducted a comparative analysis of the results obtained is carried out

dynamic behavior of a cylindrical crack in a functionally graded interlayer under torsional loading in this paper the problem of a cylindrical crack located in a functionally graded material fgm interlayer between two coaxial elastic dissimilar homogeneous cylinders and subjected to a torsional impact loading is considered the shear modulus and the mass density of the fgm interlayer are assumed to vary continuously between those of the two coaxial cylinders this mixed boundary value problem is first reduced to a singular integral equation with a cauchy type kernel in the laplace domain by applying laplace and fourier integral transforms the singular integral equation is then solved numerically and the dynamic stress intensity factor dsif is also obtained by a numerical laplace inversion technique the dsif is found to rise rapidly to a peak and then reduce and tend to the static value almost without oscillation the influences of the crack location the fgm interlayer thickness and the relative magnitudes of the adjoining material properties are examined it is found among others that by increasing the fgm gradient the dsif can be greatly reduced

equivariant ehrhart theory abstract motivated by representation theory and geometry we introduce and develop an equivariant generalization of ehrhart theory the study of lattice points in dilations of lattice polytopes we prove representation theoretic analogues of numerous classical results and give applications to the ehrhart theory of rational polytopes and centrally symmetric polytopes we also recover a character formula of procesi dolgachev lunts and stembridge for the action of a weyl group on the cohomology of a toric variety associated to a root system