calculation of cfie impedance matrix elements with rwg and n spl times rwg functions the method of moments mom solution of combined field integral equation cfie for electromagnetic scattering problems requires calculation of singular double surface integrals when galerkin s method with triangular vector basis functions rao wilton glisson functions and the cfie are applied to solve electromagnetic scattering by a dielectric object both rwg and n spl times rwg functions n is normal unit vector should be considered as testing functions robust and accurate methods based on the singularity extraction technique are presented to evaluate the impedance matrix elements of the cfie with these basis and test functions in computing the impedance matrix elements including the gradient of the green s function we can avoid the logarithmic singularity on the outer testing integral by modifying the integrand in the developed method all singularities are extracted and calculated in closed form and numerical integration is applied only for regular functions in addition we present compact iterative formulas for computing the extracted terms in closed form by these formulas we can extract any number of terms from the singular kernels of cfie formulations with rwg and n spl times rwg functions

necessary and sufficient consensus conditions for the eventwise aggregation of lower probabilities the paper gives sufficient and necessary conditions of consensus requirement for eventwise aggregation of various families of lower probabilities in particular of coherent lower probabilities and properties of the corresponding aggregation functions

boundedness and symmetry of comonotonically additive functionals the relations between a comonotonically additive and monotone functional i and the induced fuzzy measures i and i are discussed we present a necessary and sufficient condition of the functional i for i x i x and i x i x

a progressive simultaneous iteration solution for dynamic element vibration analysis development and employment of dynamic elements can result in substantial gain in solution convergence for vibration analysis when compared with the usual finite element discretization efficient solution of the associated quadratic matrix eigenproblem is crucial in achieving a superior and relatively economical solution this paper first describes a novel eigensolution of the quadratic matrix equation by a progressive simultaneous iteration method free vibration analysis results of a rectangular prestressed membrane are next presented in detail that provides an assessment of relative solution convergence and computing expenses of the two idealization procedures

on fuzzy measure and fuzzy integral on fuzzy set abstract on a fuzzy algebra of fuzzy sets we discuss some structural characteristics of a fuzzy measure the pseudo autocontinuity and some other concepts for a fuzzy measure are introduced and the relations between these cre discussed for the case of fuzzy sets riesz s theorems and lebesgue s theorems for a sequence of measurable functions are proved the concept of the fuzzy integral on a fuzzy set is given and some properties of fuzzy integrals on fuzzy sets are studied finally we prove some convergence theorems of a sequence of fuzzy integrals on fuzzy sets

least squares element method for boundary eigenvalue problems linear and non linear boundary eigenvalue problems are discretized by a new finite element like method the reason for the new construction principle is the non linear dependence of the dynamic stiffness element matrix on an eigenparameter the dynamic stiffness element matrix is evaluated for a fixed number of parameters and is then elementwise replaced by a polynomial in the eigenparameter by solving least squares problems a fast solver is introduced for the resulting non linear matrix eigenvalue problem it consists of a combination of bisection method and inverse iteration the superiority of the newconstructionprinciple in comparison with the finite or dynamic element method is demonstrated finally for some numerical examples

highly convergent dynamic models obtained by modal synthesis with application to short wave pulse propagation a general approach for obtaining the matrices of a substructure ensuring minimum modal frequency errors of the whole structure is presented the mass and stiffness matrices of a small component domain of selected dimension are obtained by applying the modal synthesis of a limited number of close to exact modes such that after assembling a larger joined domain model the modal convergence rate of the latter should be as high as possible the goal is achieved by formulating the minimization problem for the penalty type target function representing the cumulative relative modal frequency error of the joined sample domain and by applying the gradient descent minimization method after the optimum matrices of a component domain are obtained they can be used in any structure as higher order elements or super elements the well known generalized mass matrices obtained as a weighted sum of lumped and consistent components can be treated as a special case of the presented approach the obtained dynamic models are used for modelling short transient waves and wave pulses propagating in elastic or acoustic environments by using a only a few nodal points per pulse length copyright 2004 john wiley sons ltd

stable discretization of combined source integral equation for scattering by dielectric objects a stable discretization scheme is presented for the combined source integral equation csie of electromagnetic scattering from three dimensional arbitrarily shaped homogeneous dielectric objects the discretization scheme uses both the primary rao wilton glisson rwg and the dual buffa christiansen bc functions and avoids numerical problems that would appear if the equations were discretized with the rwg functions only

on the choice of expansion and weighting functions in the numerical solution of operator equations one of the objectives of this paper is to discuss the mathematical requirements that the expansion functions must satisfy in the method of moments mm solution of an operator equation a simple differential equation is solved to demonstrate these requirements the second objective is to study the numerical stability of point matching method galerkin s method and the method of least squares pocklington s integral equation is considered and numerical results are presented to illustrate the effect of various choices of weighting functions on the rate of convergence finally it is shown that certain choices of expansion and weighting functions yield numerically acceptable results even though they are not admissible from a strictly mathematical point of view the reason for this paradox is outlined

on non monotonic fuzzy measures of p bounded variation abstract this paper discuss some properties of non monotonic fuzzy measures of bounded variation we show that there is an example of such that b v x f is a proper subspace of b v x f and also we prove that b v x f is a real banach space furthermore we investigated some properties of non monotonic fuzzy measures

extension and representation of comonotonically additive functionals the domain of comonotonically additive and monotone functionals on the class of continuous functions with compact support is extended in a natural way a necessary and sufficient condition for which the extended functional is comonotonically additive and monotone is presented it is shown that the extended functional can be represented by a choquet integral when the extended functional is comonotonically additive and monotone

on the determination of resonant modes of dielectric objects using surface integral equations although surface integral equations have been extensively used for solving the scattering problem of arbitrarily shaped dielectric objects when applied to the resonance problem there are still some issues not fully addressed by the literature in this paper the method of moments with rao wilton glisson basis functions is applied to the electric field integral equation efie for solving the resonance problem of dielectric objects the resonant frequency is obtained by searching for the minimum of the reciprocal of the condition number of the impedance matrix in the complex frequency plane and the modal field distribution is obtained through singular value decomposition svd the determinant of the impedance matrix is not used since it is difficult to find its roots for the exterior efie the original basis functions are used as testing functions for the interior efie the basis functions rotated by 90 spl deg are used as testing functions to obtain an accurate modal field solution the impedance matrix needs to be reduced by half before svd is applied to it numerical results are given and compared with those obtained by using the volume integral equation

the autocontinuity of set function and the fuzzy integral abstract the autocontinuity and some other concepts of a set function are introduced and sugeno s fuzzy measure with some annexed conditions is studied on a fuzzy measure space egoroffs theorem is proved it is also proved that f mean convergence is equivalent to convergence in measure for a sequence of measurable functions finally some convergence theorems of sequence of fuzzy integrals are proved especially using the concept of autocontinuity a necessary and sufficient condition for the convergence in measure theorem is given

a note on the choice weighting functions in the method of moments the objective is to show from a mathematical standpoint that there are certain rules that must be followed in the choice of weighting functions used in the method of moments mm it is shown that for a particular problem it is the operator that dictates the method galerkin s method or another method such as the method of least squares to be applied and it is not computational considerations only for example it is shown that in solving hallen s and pocklington s equation by the method of moments it is unnatural to choose the weighting functions which are zero at the ends of the domain of the solution the deficiency of certain weighting functions is presented based on mathematical reasoning and a numerical example is given to illustrate the effect of the choice of the weighting functions on the rate of the convergence of the solution

regular fuzzy measure and representation of comonotonically additive functional this paper discusses the functional i defined on the class of continuous functions which is comonotonically additive and monotone the notion of regular fuzzy measure is proposed and the uniqueness theorem of regular fuzzy measure is shown it is also shown that i can be represented by the difference of two choquet integrals with respect to regular fuzzy measures when the universal set x is a locally compact hausdorff space and that i can be represented by one choquet integral with respect to a regular fuzzy measure when x is a compact hausdorff space

set valued choquet integrals revisited this paper performs a further investigation on the set valued choquet integral given by jang and kwon fuzzy sets and systems 112 2000 233 some incorrect properties are revised it is pointed out that the definition for convergence of sequence of sets or set valued functions is unreasonable by using the usual kuratowski s convergence some new convergence theorems for the set valued choquet integral are shown meanwhile some other properties are obtained

fuzzy measures and integrals defined on algebras of fuzzy subsets over complete residuated lattices this paper presents basic notions about fuzzy measures over algebras of fuzzy subsets of a fuzzy set it also presents basic ideas on fuzzy integrals defined using these fuzzy measures definitions of new types of fuzzy measures and integrals are motivated by our research on generalized quantifiers several useful properties of fuzzy measures and fuzzy integrals are stated and proved definitions presented in this paper and its results will be employed in subsequent papers on generalized quantifiers defined using this type of fuzzy integral

a subspace forward iteration method for solving the quadratic eigenproblem associated with the fde formulation this paper presents the development of an efficient and numerically stable algorithm for accurately computing the eigensolutions of the quadratic real symmetric eigenproblem arising in the finite dynamic element fde formulation closely related to the subspace forward iteration method the proposed scheme is well suited to extracting the lowest natural frequencies and associated mode shapes of large practical eigenproblems takes full advantage of the banded configuration of the stiffness inertia and dynamic correction matrices involved in the eigenproblem and ensures a monotonic convergence from above to the required eigenpairs a shifting technique for convergence acceleration and an eigenpair verification scheme are also presented numerical examples are shown demonstrating the excellent performance of the solution procedure

improving condensation methods for eigenvalue problems via rayleigh functionals abstract the dynamic analysis of structures using the finite element method leads to very large eigenvalue problems condensation is often required to reduce the number of degrees of freedom of these problems to manageable size the statically or dynamically condensed problem can be considered as linearization of a matrix eigenvalue problem which is nonlinear with respect to the eigenparameter as a consequence only a few natural frequencies can be obtained with sufficient accuracy we use the rayleigh functional of the nonlinear problem to improve the eigenvalue approximations considerably two examples are presented to demonstrate the efficiency of the method

mass matrices by minimization of modal errors a new approach to constructing mass matrices is presented based on expressing it through use of a variable parameter this allows the mass matrix to be adjusted in such a way that a simple eigenvalue problem get the best solution possible in terms of some error measure this procedure is used to create both diagonal mass matrices and mixed mass matrices 1997 john wiley sons ltd

an extension of sugeno integral abstract in this paper we extend the concept of sugeno fuzzy integral from nonnegative fuzzy measurable functions to extended real valued fuzzy measurable functions and discuss the lost genuine properties for this extension several necessary and sufficient conditions of absolute s integrability for extended real valued fuzzy measurable functions are given moreover the space s of all fuzzy measurable functions will be proved to be a pseudo metric space under a necessary and sufficient condition finally as an application of this extension the pettis integral will be established for this kind of fuzzy integral

transformation theorems for fuzzy integrals on fuzzy sets abstract in this paper sugeno s fuzzy integrals studied in 5 8 9 are generalized some equivalent definitions of fuzzy integrals on fuzzy sets are given and several transformation theorems of such type of fuzzy integrals are proved these results reveal the relations between the fuzzy integrals on fuzzy sets and on classical sets

fuzzy random reliability of structures based on fuzzy random variables abstract using fuzzy random variables as basic variables the relationship between fuzzy random variables and fuzzy random events is established in this paper formulas of measures of a fuzzy random event and its cut set are presented the fuzzy random reliability of structures is defined on the basis of fuzzy measure and fuzzy integral further by using fuzzy random variables the fuzzy random failure function of structures is defined and the fuzziness between structural reliable state and failure state is also analyzed moreover the fuzzy random limit state equation of structures is built the probability calculation method of structural reliability under the reliable level is given finally the calculation procedures of structural fuzzy random reliability is proposed

fuzzy number fuzzy measures and fuzzy integrals i fuzzy integrals of functions with respect to fuzzy number fuzzy measures this paper based on the fuzzy measures and fuzzy integrals given by sugeno first defines interval number fuzzy measures inf measures and fuzzy number fuzzy measures fnf measures and the fuzzy integral of function with respect to inf measures are given then it defines the fuzzy integral of functions with respect to fnf measures and the properties and convergence theorems are obtained all these are generalizations of sugeno s works

choquet integral and fuzzy measures on locally compact space the concept of outer regular fuzzy measures is proposed and it is shown that a functional of certain type on the cone of positive continuous functions with compact supports is represented as a choquet integral with respect to a outer regular fuzzy measure it is also shown that the choquet integral of positive continuous functions with compact supports is represented as a lebesgue integral with the same integrands this representation is a generalization of certain previous results of others which are useful for computation of the upper and lower expected value

on the null additivity and the autocontinuity of a fuzzy measure abstract in this paper further research on the null additivity and autocontinuity of fuzzy measures is made we prove that autocontinuity from below and autocontinuity from above of a fuzzy measure are equivalent when this fuzzy measure is finite furthermore if the space x is countable then the null additivity is equivalent to the autocontinuity

the general pettis sugeno integral of vector multifunctions relative to a vector fuzzy multimeasure abstract in this paper we define and study the general pettis sugeno integral of a vector multifunction relative to a vector fuzzy multimeasure both taking values in a locally convex space x ordered by a closed convex pointed cone x with nonempty interior several classic properties of this integral and some estimation and comparative results with the pettis lebesgue integral are established

quadrature over a pyramid or cube of integrands with a singularity at a vertex a simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex

numerical formulation for a higher order plane finite dynamic element the paper describes the development of an eight node plane rectangular finite dynamic element and presents detailed descriptions of the associated numerical formulation involving the higher order dynamic correction terms pertaining to the related stiffness and inertia matrices numerical test results of free vibration analyses are presented in detail for the newly developed eight node element and also the corresponding four node element in order to make a clear comparison of the relative efficiencies of the corresponding finite element and dynamic element procedures such results indicate a superior pattern of solution convergence of the presently developed dynamic element

the bounded convergence in measure theorem for nonlinear integral functionals in this paper we introduce a new notion of the perturbation of nonlinear functionals to formulate a functional form of the convergence theorems for nonlinear integrals in nonadditive measure theory as its direct consequences we obtain the bounded convergence in measure theorems for typical nonlinear integrals which show that the autocontinuity of a nonadditive measure is equivalent to the validity of the bounded convergence in measure theorems for the choquet the sugeno and the shilkret integrals as well as their symmetric and asymmetric extensions

new concepts for finite element mass matrix formulations improved finite element formulations are presented for dynamic analysis the improvements are based on modifications of the finite element mass matrix and are of high importance since no additional computational effort is required compared with the necessary effort for the standard consistent mass matrix formulation formulations are presented for the one dimensional bar two dimensional membrane and the pure bending beam element free vibration analysis and forced vibration results are presented employing new mass matrices in general the frequency errors and stress errors are at least three times smaller than the corresponding consistent or lumped mass formulation errors accurate model data can be achieved for all the modes of relatively coarse meshes

chebyshev filtering lanczos process in the subspace iteration method bathe s basic algorithm of subspace iteration for the solution of the symmetric eigenvalue problem is improved by including a chebyshev filtering mechanism to obtain satisfactory convergence for the largest eigenvalues a shifting strategy is adopted the shift factor is approximately computed by the lanczos process

on development of a finite dynamic element and solution of associated eigenproblem by a block lanczos procedure the paper first presents the details of the development of a new six noded plane triangular finite dynamic element a block lanczos algorithm is developed next for the accurate and efficient solution of the quadratic matrix eigenvalue problem associated with the finite dynamic element formulation the resulting computer program fully exploits matrix sparsity inherent in such a discretization and proves to be most efficient for the extraction of the usually required first few roots and vectors including repeated ones most importantly the present eigenproblem solution effort is shown to be comparable to that of the corresponding finite element analysis thereby rendering the associated dynamic element method rather attractive owing to superior convergence characteristics of such elements presented herein

on the construction of fuzzy measures a relation defined on a s algebra called relative likelihood is introduced it is shown how to construct fuzzy measures which are compatible with a relative likelihood

asymptotic structural characteristics of fuzzy measure and their applications abstract in fuzzy measure theory as sugeno s fuzzy measures lose additivity in general the concept almost which is well known in classical measure theory splits into two different concepts almost and pseudo almost in order to replace the additivity it is quite necessary to investigate some asymptotic behaviors of a fuzzy measure at sequences of sets which are called waxing and waning and to introduce some new concepts such as autocontinuity converse autocontinuity and pseudo autocontinuity these concepts describe some asymptotic structural characteristics of a fuzzy measure in this paper by means of the asymptotic structural characteristics of fuzzy measure we also give four forms of generalization for both egoroff s theorem riesz s theorem and lebesgue s theorem respectively and prove the almost everywhere pseudo almost everywhere convergence theorem the convergence in measure pseudo in measure theorem of the sequence of fuzzy integrals in the last two theorems the employed conditions are not only sufficient but also necessary

lattice valued fuzzy measure and lattice valued fuzzy integral abstract in this paper 1 the concepts of lattice valued fuzzy measure with no valuation property and lower resp upper lattice valued fuzzy integral are proposed which give the unified discription to the fuzzy measures and fuzzy integrals studied by delgado and moral qiao ralescu adams sugeno wang and zhang 2 some asymptotic structural characteristics of lattice valued fuzzy measures are introduced and some relations between them are given 3 some concepts of convergences for lattice valued functions are defined and riesz theorem egoroff s theorems and lebesgue s theorem for lattice valued measurable function are proved 4 the monotone increasing resp decreasing convergence theorem and almost resp pseudo almost everywhere convergence theorrem for lower resp upper lattice valued fuzzy integral are shown under some weak conditions

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

development of a solid hexahedron finite dynamic element this paper presents the pertinent details of a newly developed solid rectangular hexahedron finite dynamic element involving the derivation of the higher order stiffness and inertia dynamic correction matrices numerical results of a test case are also presented which indicate that adoption of the dynamic elements significantly improves the solution convergence when compared with the related performance of the corresponding finite elements

singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedra a numerical solution of integral equations typically requires calculation of integrals with singular kernels the integration of singular terms can be considered either by purely numerical techniques e g duffy s method polar co ordinate transformation or by singularity extraction in the latter method the extracted singular integral is calculated in closed form and the remaining integral is calculated numerically this method has been well established for linear and constant shape functions in this paper we extend the method for polynomial shape functions of arbitrary order we present recursive formulas by which we can extract any number of terms from the singular kernel defined by the fundamental solution of the helmholtz equation or its gradient and integrate the extracted terms times a polynomial shape function in closed form over plane triangles or tetrahedra the presented formulas generalize the singularity extraction technique for surface and volume integral equation methods with high order basis functions numerical experiments show that the developed method leads to a more accurate and robust integration scheme and in many cases also a faster method than for example duffy s transformation copyright 2003 john wiley sons ltd

a method for solving high order real symmetric eigenvalue problems a new method for solving structural dynamics problems has been proposed by the author in a separate paper 1 this method of solution produces a high order real symmetric eigenvalue problem of the form a b 2c 3d u 0 an algorithm for solving such an eigenvalue problem using simultaneous iteration is presented in this paper methods of accelerating the convergence and reducing the amount of computation are also described a numerical example is given in which the algorithm is used to calculate the eigenvalues and eigenvectors of a framed structure

some properties of fuzzy integrable function space l 1 μ abstract we introduce definitions of fuzzy orlicz class l and fuzzy mean convergence we show that fuzzy mean convergence is equivalent to convergence in fuzzy measure and l l1 for any orlicz function this conclusion refines a result of d ralescu toward a general theory of fuzzy variable j math anal appl 86 1982 176 193 moreover a necessary and sufficient condition for l1 s is given it also improves a result of d ralescu and g adams the fuzzy integral j math anal appl 75 1980 562 570

detecting hyperbolic and definite matrix polynomials hyperbolic or more generally definite matrix polynomials are important classes of hermitian matrix polynomials they allow for a definite linearization and can therefore be solved by a standard algorithm for hermitian matrices they have only real eigenvalues which can be characterized as minmax and maxmin values of rayleigh functionals but there is no easy way to test if a given polynomial is hyperbolic or definite or not taking advantage of the safeguarded iteration which converges globally and monotonically to extreme eigenvalues we obtain an efficient algorithm that identifies hyperbolic or definite polynomials and enables the transformation to an equivalent definite linear pencil numerical examples demonstrate the efficiency of the approach

convergence of sequences of fuzzy random variables and its application abstract this paper defines two types of generalized metrics in the set of all fuzzy random variables on a probability space several different kinds of convergence for sequences of fuzzy random variables with respect to the generalized metrics are introduced e g everywhere convergence almost everywhere convergence almost uniform convergence convergence in probability measure etc the relations of these kinds of convergence are also investigated moreover this paper proves some convergence theorems for sequences of integrals of fuzzy random variables e g monotone convergence theorems lebesgue dominated convergence theorems etc under different convergence senses

q scale measures of fuzzy sets abstract in an attempt to generalize nahmias scale measure to apply to fuzzy sets in this paper we introduce the notion of q scale measure a q scale measure is slightly different from a crisp valued possibility measure in several ways we use a number of examples to demonstrate the validity of the notion of q scale measure in various circumstances and give preliminary discussions on basic properties of q scale measure induced q scale measure semigroup of q scale measures q scale measure of probabilistic sets and q scale measure of l fuzzy sets

on the extension of possibility measures abstract in this paper the theory of extension of possibility measures is discussed first we introduce two classes b and b of sets called the ecp system and the cp system respectively and prove that the class a d of all atoms of a class d introduced in 3 4 must be an ecp system and a cp system furthermore the extension theorem from b resp b to u b resp the generalized field or the topology generated by b of the possibility measures is proved

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 the dual basis for solving electromagnetic surface integral equations a powerful technique for solving electromagnetic em surface integral equations sies for inhomogenous objects by the method of moments mom involves the well known rao wilton glisson rwg basis function to represent the electric current and for field orthogonality and numerical stability reasons a variation of the rwg basis known as the ntilde x rwg basis where ntilde is a unit normal vector at the object surface to represent the magnetic current though this combination provides a numerically efficient and effective solution that has been demonstrated on a variety of structures one cannot feel entirely comfortable because of the presence of fictitious magnetic current associated with the modified basis chen and wilton proposed a different smoother basis in 1990 that avoids the fictitious line charges but because of computational cost issues it has not been used beyond chen s dissertation recently this basis was rediscovered and has received considerable attention our work reexamines the dual basis exploring issues not addressed by chen and wilton and showing accurate solutions for a variety of em scattering structures

inner and outer representation by choquet integral the representations of comonotonically additive and monotone functionals are investigated an i regular non additive measure is defined as a non additive measure whose values can be calculated from its values on the inner compact sets and the values on compact sets can be calculated from its values on the outer open sets the basic properties of an i regular non additive measure are shown the inner representation of the functional is proposed and is compared with the outer representation

solving ibc cfie with dual basis functions the surface integral equation method is applied to solve electromagnetic scattering by arbitrarily shaped three dimensional imperfectly conducting objects modeled with the leontovitch impedance boundary condition ibc dual basis functions are used to remove previously reported difficulties associated with the solution of the combined field integral equation for objects with the ibc by expanding the magnetic current with quasi curl conforming dual functions and the electric current with divergence conforming primary rwg functions leads to a stable discretization procedure for the rotation n operator required by the ibc

the emergence of fifty fifty probability judgments through bayesian updating under ambiguity this paper explains the empirical phenomenon of persistent fifty fifty probability judgments through a model of bayesian updating under ambiguity to this purpose i characterize an announced probability judgment as a bayesian estimate given as the solution to a choquet expected utility maximization problem with respect to a neo additive capacity that has been updated in accordance with the generalized bayesian update rule only for the non generic case in which this capacity degenerates to an additive probability measure the agent will learn the event s true probability if the number of i i d data observations gets large in contrast for the generic case in which the capacity is not additive the agent s announced probability judgment becomes a persistent fifty fifty probability judgment after finitely many observations

acceleration of subspace iteration an algorithm is presented and discussed which gives 40 per cent reduction in the cost of the basic subspace iteration for eigenvalues

fuzzy integrals on l fuzzy sets abstract the fuzzy measures and fuzzy integrals for zadeh s fuzzy sets were studied by qiao and wang 5 6 7 12 in this paper we consider the real valued fuzzy measures and fuzzy integrals for l fuzzy sets where l is a pseudocomplemented infinitely distributive complete lattice on a fuzzy algebra of l fuzzy sets the concepts of fuzzy measure and fuzzy integral are introduced some equivalent forms of fuzzy integrals on l fuzzy sets are given moreover we discuss several properties of fuzzy integrals on l fuzzy sets and prove some convergence theorems for a sequence of fuzzy integrals on l fuzzy sets

a new approach to the dynamic analysis of structures using fixed frequency dynamic stiffness matrices the dynamic analysis of structures by the standard finite element method introduces additional inaccuracies into the solution which are not present when the method is used for static analyses these inaccuracies can arise from two sources i the element formulation and ii the reduction of the size of the matrices by a static condensation i e using the guyan method1 2 the errors in both cases are caused by neglecting frequency dependent terms in the functions relating the displacements at any point in the structure to the displacements at certain fixed points i e nodes in the element formulation and masters in the condensation a new method of solution is proposed in this paper in which the frequency dependent terms are retained implicitly by using dynamic stiffness matrices defined at a number of fixed frequencies the dynamic stiffness matrices may be condensed efficiently to a relatively small number of master degrees of freedom using a front solution algorithm the final stage in the solution uses these matrices to synthesize a high order eigenvalue problem a method of solving such an eigenvalue problem of arbitrary order is described in a separate paper 3 numerical examples are given to show the accuracy and efficiency of the proposed method compared with conventional methods of solution

on the closure of families of fuzzy measures under eventwise aggregations the paper contains some results on eventwise aggregation of fuzzy measures from the various families of lower probabilities this investigation includes coherent lower probabilities k monotone measures belief measures etc we study sufficient and necessary conditions on aggregation operators satisfying the closure property it is necessary to guarantee that the aggregation belongs to the same family as generating measures we also propose an efficient way for constructing aggregation operators using the found unique properties of multilinear extension this representation method for fuzzy measures generalizes to the n dimensional case the well known one giving distorted probabilities

on the numerical integration of the linear shape functions times the 3 d green s function or its gradient on a plane triangle formulas for the static and dynamic potentials due to linearly varying source distributions defined on a planar triangle are presented the general linear variation of the source is represented in terms of three linear basis functions each one associated with a different vertex of the triangular domain the singular kernels considered are given by the 3 d green s function and its gradient both for the static and dynamic case in the static case the evaluation of potentials is performed analytically and compact form results are given in the dynamic case the results are given in a form suited for numerical integration

fast convergence of fast multipole acceleration using dual basis function in the method of moments for composite structures the dual basis function proposed by chen and wilton in 1990 is used to represent the magnetic current for solving electromagnetic em surface integral equations sies with penetrable materials and the solution process is accelerated with multilevel fast multipole algorithm mlfma for large problems the mlfma is a robust accelerator for matrix equation solvers by iterative method but its convergence rate strongly relies on the conditioning of system matrix if the mlfma is based on the method of moments mom matrix in which the electric current is represented with the rao wilton glisson rwg basis function then how one represents the magnetic current in electric field integral equation efie and magnetic field integral equation mfie really matters for the conditioning of system matrix though complicated in implementation the dual basis function is ideal to represent the magnetic current because it is similar to the rwg basis function in properties but approximately orthogonal to it in space with a simple testing scheme the resultant system matrix is well conditioned and the mlfma acceleration can be rapidly convergent numerical examples for em scattering by large composite objects are presented to demonstrate the robustness of the scheme

an interpretation of fuzzy measures and the choquet integral as an integral with respect to a fuzzy measure abstract in this paper the non additivity of sugeno s fuzzy measures is interpreted in terms of addition and the rationality of the choquet integral is discussed it is pointed out that a fuzzy measure on a set x expresses the interaction between the subsets of x and can be represented by an additive measure it is shown through concrete examples that the choquet integral is reasonable as an integral with respect to a fuzzy measure it is also found that the choquet integral is closely related with the representation of a fuzzy measure

a novel meshless scheme for solving surface integral equations with flat integral domains numerical solutions for electromagnetic em integral equations rely on the discretization of integral domains and the use of meshes for geometric description meshing geometries is very tedious especially for complicated structures with many details tiny parts and geometric discontinuities corners or edges and remeshing could be required in many scenarios to reduce the costs of generating quality meshes meshless or mesh free methods were developed and they have been extensively studied in mechanical engineering though there are less obvious interests in em community the meshless methods employ discrete nodes to replace meshes in the description of geometries but the background meshes for integrations are still needed traditionally in this work we first address the traditional meshless scheme for solving em integral equations based on the moving least square mls approximation for unknown currents and the use of background meshes for integrations and then develop a novel meshless scheme by applying the green s lemma to the em surface integral equations with flat domains the novel scheme transforms a surface integral over a flat domain into a line integral along its boundaries when excluding a singular patch in the domain since only the domain boundaries are discretized and no background meshes are needed the scheme is truly meshless numerical examples for em scattering by flat surface objects are presented to demonstrate the effectiveness of the novel scheme

fuzzy number fuzzy measures and fuzzy integrals ii fuzzy integrals of fuzzy valued functions with respect to fuzzy number fuzzy measures on fuzzy sets this is a subsequent paper of 9 by using the concepts of fuzzy number fuzzy measures 9 and fuzzy valued functions 10 a theory of fuzzy integrals of fuzzy valued functions with respect to fuzzy number fuzzy measures is built up so far it is a more general one following sugeno s 5

transformation theorems of abstract integrals on fuzzy sets abstract the concept of abstract integrals on fuzzy sets is introduced and some elementary properties for such type of integrals are given this paper also proves some transformation theorems for abstract integrals on fuzzy sets and presents some convergence theorems of a sequence of abstract integrals

a theory of fuzzy measures representations the choquet integral and null sets abstract some theorems of t murofushi and m sugeno fuzzy sets and systems 29 1989 201 227 concerning representation of fuzzy measures and the choquet integral are generalized it is shown that if there is a certain relation between two measurable functions then the choquet integral is additive for these two functions in addition this article discusses null sets with respect to fuzzy measures and also fuzzy measures defined on a class which is not a algebra