the mixed order bcgs fft method for the scattering of three dimensional inhomogeneous anisotropic magnetodielectric objects this paper presents the first fft based fast volume integral equation solver for inhomogeneous anisotropic magnetodielectric objects the volume integral equations are formulated by employing mixed order basis functions that expand the flux densities and vector potentials in the coupled field integral equations in terms of different sets of basis functions with different orders volumetric roof top basis functions are used for flux densities whereas second order curl conforming basis functions are used for vector potentials a fast volume integral equations solver namely the bcgs fft method is then applied to accelerate the solution of this mixed order weak form formulation examples show that the mixed order bcgs fft method has high accuracy compared to both analytical and numerical solutions examples also show the mixed order bcgs fft method has high computational efficiency compared to commercial software

electromagnetic scattering by radially inhomogeneous dielectric spheres a method to determine the electric field scattered by a dielectric sphere with a permittivity and conductivity varying only in the radial direction is presented in order to take advantage of the spherically symmetrical geometry the interior electric field is expanded in terms of vector spherical harmonics which are orthogonal over a spherical surface using the orthogonality of those functions with the vector wave functions in the expanded form of the free space dyadic green s function one can reduce the three dimensional 3 d electric field integral equation into a system of one dimensional 1 d integral equations the scalar coefficients of the series expansion for the interior electric field are then obtained by solving this system of equations for the medium outside the sphere the scattered field is evaluated through the same procedure comparisons with alternative methods for specific cases demonstrate that the method is reliable in determining the interior field and the scattered field for spherical objects with layered or continuously varying radial profile

closed form uniform asymptotic expansions of green s functions in layered media far field closed form expressions are derived for spatial domain multilayered green s functions gf for the derivation of these far field expressions the spectral domain multilayered gf are approximated by means of the total least square algorithm tlsa in terms of the spectral variable u0 k 2 k02 1 2 and uniform asymptotic expansions are determined for the sommerfeld integrals of the resulting tlsa approximations numerical results show that the far field asymptotic expressions are accurate within 0 1 for distances between source and field points larger than one free space wavelength also it is shown that the hybrid use of the discrete complex image method and the tlsa in terms of the spectral variable k leads to near field closed form expressions of multilayered gf that are typically accurate within 0 1 for distances between source and field points smaller than one free space wavelength therefore the combination of the novel far field asymptotic expressions and the well known near field expressions makes it possible to compute multilayered gf with a great accuracy in the whole range of distances between source and field points and in a wide range of frequencies

on box totally dual integral polyhedra edmonds and giles introduced the class of box totally dual integral polyhedra as a generalization of submodular flow polyhedra in this paper a geometric characterization of these polyhedra is given this geometric result is used to show that each tdi defining system for a box tdi polyhedron is in fact a box tdi system that the class of box tdi polyhedra is in co np and is closed under taking projections and dominants that the class of box perfect graphs is in co np and a result of edmonds and giles which is related to the facets of box tdi polyhdera

a characterization of box mengerian matroid ports let m be a matroid on e l where l e is a distinguished element of m the l port of m is the set p p p e with p l a circuit of m let a be the p e incidence matrix let u2 4 be the uniform matroid on four elements of rank two let f7 be the fano matroid let f7 be the dual of f7 and let f7 be the unique series extension of f7 in this paper we prove that the system ax 1 x 0 is box totally dual integral box tdi if and only if m has no u2 4 minor using l no f7 minor using l and no f7 minor using l as a series element our characterization yields a number of interesting results in combinatorial optimization

an improved discrete complex image method based on a special sampling path a special sampling path is proposed to improve the accuracy of the discrete complex image method dcim in evaluating the lateral wave different from all the previous dcim implementations the proposed sampling path goes through the branch point directly which helps to evaluate its contribution to the lateral wave more accurately in this communication different sampling paths of dcim have been implemented and compared it is found that in the situations where the lateral wave dominates the far field region dcim with the new path gives more accurate and stable results

trapezoidal approximations of fuzzy numbers the problem of the trapezoidal approximation of fuzzy numbers is discussed a set of criteria for approximation operators is formulated these constraints can be used for direct operator derivation a new nearest trapezoidal approximation operator preserving expected interval is suggested

an efficient approach for extracting poles of green s functions in general multilayered media a fast approach of closed form green s functions for mixed potential integral equation analysis of both near field and far field in planar multilayered media is presented in this paper since all components of the green s functions in spectral domain are restructured concisely by four elementary functions the surface wave pole extraction is very effective in terms of a function related to the generalized reflection coefficients meanwhile the number of required two level discrete complex image method dcim with high order sommerfeld identities is also minimized under this scheme the numerical results show that this approach is more efficient and accurate for the electromagnetic scattering by and radiation in the presence of electrically large three dimensional 3 d objects in multilayered media although lossless examples are considered in the numerical examples the method presented here works also for the lossy materials where the poles move away from the real axis in the complex plane

box total dual integrality box integrality and equimodular matrices box totally dual integral box tdi polyhedra are polyhedra described by systems which yield strong min max relations we characterize them in several ways involving the notions of principal box integer polyhedra and equimodular matrices a polyhedron is box integer if its intersection with any integer box ell le x le u is integer we define principally box integer polyhedra to be the polyhedra p such that kp is box integer whenever kp is integer a rational r times n matrix is equimodular if it has full row rank and its nonzero r times r determinants all have the same absolute value a face defining matrix is a full row rank matrix describing the affine hull of a face of the polyhedron our main result is that the following statements are equivalent along our proof we show that a polyhedral cone is box tdi if and only if it is box integer and that these properties are carried over to its polar we illustrate these charaterizations by reviewing well known results about box tdi polyhedra we also provide several applications the first one is a new perspective on the equivalence between two results about binary clutters secondly we refute a conjecture of ding zang and zhao about box perfect graphs thirdly we discuss connections with an abstract class of polyhedra having the integer caratheodory property finally we characterize the box tdiness of the cone of conservative functions of a graph and provide a corresponding box tdi system

discrete models of electromagnetic wave scatterers in a frequency range we investigate the spatial and frequency characteristics of electromagnetic fields scattered by some object frequency functions that allow the expression of all elements of the object scatter matrix are introduced the sampling theorems that are proved for the introduced functions make it possible to characterize the scatterer by a set of discrete parameters the application of the proved theorems provides for the creation of a versatile scatterer discrete model that determines the dependence of scattered fields both on spatial coordinates and frequency a random scatterer is considered and the conditions under which the discrete parameters are statistically independent normalized random variables are stated the article presents the results of a random scatterer modeling

efficient calculation of the electromagnetic dyadic green s function in spherical layered media a numerical methodology is proposed for the evaluation of the electromagnetic fields of an electric or magnetic dipole of arbitrary orientation in spherical stratified media the proposed methodology is based on the numerical solution of the differential equation in the radial coordinate that is satisfied by each coefficient in the spherical harmonics expansion of the governing helmholtz equation more specifically the finite difference solution of this equation may be cast in a pole residue form that allows the analytic evaluation of the spherical harmonics series by means of the watson transformation thus a closed form expression is obtained for the electromagnetic fields in terms of a short series of associated legendre functions p sup m sub spl nu cos spl theta of integer order m and complex degree spl nu the number of terms in the series is strongly dependent on the angle spl theta and decreases very fast when the point of observation moves away from the source the method allows for arbitrary variation in the permittivity and permeability profiles in the radial directions

acoustic field induced in spheres with inhomogeneous density by external sources acoustic or electromagnetic fields induced in the interior of inhomogeneous penetrable bodies by external sources can be evaluated via well known volume integral equations for bodies of arbitrary shape and or composition for which separation of variables fails a direct attack for the solution of these integral equations is the only available approach in a previous paper by the same authors the scalar acoustic field in inhomogeneous spheres of arbitrary compressibility but with constant density was considered in the present one the direct hybrid analytical numerical method applied to the much simpler integral equation for spheres with constant density is generalized to densities that vary with r or even this extension is by no means trivial owing to the appearance of the derivatives of both the density and the unknown function in the volume integral a fact necessitating a more subtle and accuracy sensitive approach again the spherical shape allows use of the orthogonal spherical harmonics and of dini s expansions of a general type for the radial functions the convergence of the latter shown to be superior to other possible sets of orthogonal expansions can be further optimized by the proper selection of a crucial parameter in their eigenvalue equation

asymptotic extraction approach for antennas in a multilayered spherical media an efficient algorithm is introduced to enhance the convergence of dyadic green s functions dgf in a layered spherical media where asymptotic expressions have been developed the formulated expressions involve an infinite series of spherical eigenmodes that can be reduced to the simple homogenous media green s function using the addition theorem of spherical hankel functions substantial improvements in the convergence speed have been attained by subtracting the asymptotic series representation from the original dgf the subtracted components are then added to the solution using the homogenous media green s function format

trapezoidal approximation and aggregation trapezoidal approximation of fuzzy numbers is discussed in relation to data aggregation an important problem whether it is better to simplify initial data before using an aggregation operator or conversely to aggregate original fuzzy values and then to simplify the output is addressed

trapezoidal approximations of fuzzy numbers revisited fuzzy number approximation by trapezoidal fuzzy numbers which preserve expected interval is discussed the previously proposed approximation operator is improved so as to always produce a well formed trapezoidal fuzzy number

numerical analysis of single microstrip antenna and antennas array in spherically layered media this communication presents a comprehensive numerical analysis of single microstrip antenna and antennas array in spherically layered media using the method of moments mom the curvilinear rao wilton glisson crwg triangular basis functions are employed to simulate the equivalent current on the antenna surface first the dyadic green s functions using debye potential are deduced then their efficient computation procedures are carried out to improve calculation efficiency finally the characteristic basis function method is employed to save memory and calculation time by reducing dimension of the impedance matrix the results of this study are in good agreement with those of the feko software and they show that the method proposed in this communication is more efficient than feko in the analysis process

a generalized asymptotic extraction solution for antennas in multilayered spherical media an efficient model is developed to accelerate the convergence of the dyadic green s function s dgf infinite summation when the source and observation points are placed in different layers of a dielectric sphere thereby expediting computational analysis the proposed procedure is based on asymptotic extraction principles in which the quasi static images are extracted from the spectral domain dgf the effectiveness of the approach is demonstrated in a method of moment model where a microstrip antenna as well as a conformal dipole array have been studied

modified spherical wave functions with anisotropy ratio application to the analysis of scattering by multilayered anisotropic shells we describe a novel and rigorous vector eigenfunction expansion of electric type green s dyadics for radially multi layered uniaxial anisotropic media in terms of the modified spherical vector wave functions which can take into account the effects of anisotropy ratio systematically in each layer the material constitutions e and epsiv macrmu macr are tensors and distribution of sources is arbitrary both the unbounded and scattering dyadic green s functions dgfs for rotationally uniaxial anisotropic media are derived in spherical coordinates r thetas phi the coefficients of scattering dgfs based on the coupling recursive algorithm satisfied by the coefficient matrix are derived and expressed in a compact form with these dgfs obtained the electromagnetic fields in each layer are straightforward once the current source is known a specific model is proposed for the scattering and absorption characteristics of multilayered uniaxial anisotropic spheres and some novel performance regarding anisotropy effects is revealed

an acoustic inverse scattering problem for spheres with radially inhomogeneous compressibility an inverse acoustic scattering problem the main aim of which is to reconstruct the one dimensional variation of the acoustical parameters of a spherical object is investigated the problem is first formulated conventionally through a coupled system of integral equations and then this system is reduced to one dimensional form by using the orthogonality properties of spherical harmonics the inverse problem is solved in an iterative fashion via classical newton algorithm some numerical simulations are carried out to test the feasibility of the method as well as to see the effects of some parameters on the solution it is shown that the method is very effective for the profiles having smooth variations provided that an appropriate initial guess is chosen however some of the classical disadvantages of the newton type algorithms are also observed in numerical experiments which may limit the applicability of the method to a certain extent

trapezoidal and triangular approximations preserving the expected interval in this paper an improvement of the nearest trapezoidal approximation operator preserving the expected interval is studied which is proposed by grzegorzewski and mrowka a formula for computing the improved approximation is presented moreover the nearest triangular approximation operator preserving the expected interval is also investigated

a new technique for the derivation of closed form electromagnetic green s functions for unbounded planar layered media a closed form electromagnetic green s function for unbounded planar layered media is derived in terms of a finite sum of hankel functions the derivation is based on the direct inverse hankel transform of a pole residue representation of the spectral domain form of the green s function such a pole residue form is obtained through the solution of the spectral domain form of the governing green s function equation numerically through a finite difference approximation rather than analytically the proposed methodology can handle any number of layers including the general case where the planar media exhibit arbitrary variation in their electrical properties in the vertical direction the numerical implementation of the proposed methodology is straightforward and robust and does not require any preprocessing of the spectrum of the green s function for the extraction of surface wave poles or its quasi static part the number of terms in the derived closed form expression is chosen adaptively with the distance between source and observation point as parameter the development of the closed form green s function is presented for both vertical and horizontal dipoles its accuracy is verified through a series of numerical examples and comparisons with results from other established methods

response of a source on top of a vertically stratified half space the solution of the response of a source on top of a horizontally stratified half space is well known however when the half space is vertically stratified the problem can only be solved with numerical methods like the finite element method here a semi analytic approach to solve such a problem is presented the three dimensional variation of the problem is reduced to two dimensional variation by fourier transform in one coordinate variable the remaining two dimensional problem is solved by finding the eigensolution in each of the half spaces the eigensolutions of each region are found from the partial differential equation directly using the same basis set of expansion functions this makes the calculation of the reflection and transmission operators very efficient the reflection and transmission operators account for the mode conversion reflection and transmission of the waves with the reflection and transmission operators the field everywhere can be calculated the solution reduces to that of the sommerfeld s half space problem when the two half spaces are homogeneous

integral equation based analysis of scattering from 3 d inhomogeneous anisotropic bodies this paper presents an integral equation based scheme to analyze scattering from inhomogeneous bodies with anisotropic electromagnetic properties both the permittivity and permeability are assumed to be generalized tensors requisite integral equations are derived using volume equivalence theorem with the electric and magnetic flux densities being the unknown quantities matrix equations are derived by discretizing these unknowns using three dimensional rao wilton glisson basis functions reduction of the integral equation to a corresponding matrix equation is considerably more involved due to the presence of anisotropy and the use of vector basis function methods for evaluation of the integrals involved in the construction of this matrix is elucidated in detail the method of moments technique is augmented with the fast multipole method and a compression scheme the latter two enable large scale analysis finally several numerical results are presented and compared against analytical solutions to validate the proposed scheme an appendix provides analytical derivations for the formulae that are used to validate numerical method and the necessary formulae that extends the approach presented herein to the analysis of scattering bianisotropic bodies

a numerical methodology for efficient evaluation of 2d sommerfeld integrals in the dielectric half space problem the analysis of 2d scattering in the presence of a dielectric half space by integral equation formulations involves repeated evaluation of sommerfeld integrals deformation of the contour to the steepest descent path results in a well behaved integrand that can be readily integrated a well known drawback of this method is that an analytical expression for the path is available only for evaluation of the reflected fields but not for the evaluation of the transmitted fields a simple scheme for numerical determination of the steepest descent path valid for both cases is presented the computational cost of the numerical determination is comparable to that of evaluating the analytical expression for the steepest descent path for reflected fields when necessary contributions from branch cut integrals and a second saddle point are taken into account certain ranges of the input parameters which result in integrands that vary rapidly in the neighborhood of the saddle point require special treatment alternative paths and specialized gaussian quadrature rules for these cases are also proposed an implementation of the proposed numerically determined steepest descent path nd sdp method is freely available for download

one third integrality in the max cut problem given a graphg v e the metric polytopes g is defined by the inequalitiesx f x c f f 1 for f subseteq c f odd c cycle ofg and 0 xe 1 fore e optimization overs g provides an approximation for the max cut problem the graphg is called 1 d integral if all the vertices ofs g have their coordinates in i d 0 i d we prove that the class of 1 d integral graphs is closed under minors and we present several minimal forbidden minors for 1 3 integrality in particular we characterize the 1 3 integral graphs on seven nodes we study several operations preserving 1 d integrality in particular thek sum operation for 0 k 3 we prove that series parallel graphs are characterized by the following stronger property all vertices of the polytopes g x l x u are 1 3 integral for every choice of 1 3 integral boundsl u on the edges ofg

the model based parameter estimation of antenna radiation patterns using windowed interpolation and spherical harmonics techniques previously reported for interpolating antenna radiation patterns simultaneously in both the spatial and frequency domains are reexamined here in order to develop new algorithms with improved efficiency and speed while maintaining comparable accuracy to this end interpolation in the frequency domain is constrained to a windowed scheme whereby a series of reduced order pade spl acute rational function fitting models of only three or four sampling frequencies are used to interpolate over a relatively large bandwidth the use of this piece wise technique is shown to reduce the complexity of determining the unknown coefficients without any significant loss in the resulting interpolation accuracy or increase in the required number of sampling frequencies in this paper exact analytical expressions are found for the unknown coefficients that allow the spatial domain interpolation to be performed entirely separate from the frequency domain interpolation the technique is applied to the case of a 0 5 meter dipole modeled from 150 to 950 mhz and for spl theta from 0 spl deg to 90 spl deg using fitting windows with three and four sampling frequencies the results are compared to those obtained using a previously developed generalized simultaneous interpolation procedure in the spatial domain spherical harmonics are introduced as model based fitting functions for antenna radiation patterns specifically interpolation procedures are developed using zonal harmonics and tesseral harmonics to model one and two dimensional far field radiation patterns respectively the case of a z oriented 0 5 meter dipole is considered to demonstrate the efficiency and accuracy obtained by applying these physically based fitting models in the spatial domain zonal harmonics are used to interpolate far field radiation patterns of this antenna for spl theta from 0 spl deg to 180 spl deg for several different frequencies over the range from 150 to 950 mhz this example demonstrates the attractiveness of using spherical harmonics functions to accurately and efficiently interpolate radiation patterns in the spatial domain

natural trapezoidal approximations of fuzzy numbers fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is considered new operators that fulfill additional requirements for the core and support of the fuzzy number are suggested these supplementary conditions guarantee the proper interpretation of the solution even for very skew input fuzzy numbers moreover the trapezoidal approximation without expected interval invariance is also examined and the relationship between these two approximations is discussed

a unified approach to box mengerian hypergraphs a hypergraph is called box mengerian if the linear system ax 1 x 0 is box totally dual integral box tdi where a is the edge vertex incidence matrix of the hypergraph because it is np hard in general to recognize box mengerian hypergraphs a basic theme in combinatorial optimization is to identify such objects associated with various problems in this paper we show that the so called equitably subpartitionable esp property first introduced by ding and zang ding g w zang 2002 packing cycles in graphs j combin theory ser b 86 381 407 in their characterization of all graphs with the min max relation on packing and covering cycles turns out to be even sufficient for box mengerian hypergraphs we also establish several new classes of box mengerian hypergraphs based on esp property this approach is of transparent combinatorial nature and is hence fairly easy to work with

the reflection of electromagnetic waves from stratified anisotropic media a direct approach to the investigation of the reflection of electromagnetic waves from a plane interface separating a vacuum half space and a stratified anisotropic layer is presented the formulation involves the generation of a riccati differential equation for a certain 2 2 reflection matrix the approach is already well established for scalar problems but its implementation in cases which allow mode conversion is believed to be new the reflection matrix concerned is unitary when the anisotropic layer is nondissipative and an efficient numerical method to solve the equation is outlined sample results are presented to illustrate the theory

nearest interval approximation of a fuzzy number the problem of the interval approximation of fuzzy numbers is discussed a new interval approximation operator which is the best one with respect to a certain measure of distance between fuzzy numbers is suggested

trapezoidal approximations of fuzzy numbers preserving the expected interval algorithms and properties fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is discussed algorithms for calculating the proper approximations are proposed and some properties of the approximation operators are discussed it is shown that an adequate approximation operator might be chosen through the comparisons of some characteristics of the fuzzy number like its ambiguity width its value and weighted expected value

best lipschitz constant of the trapezoidal approximation operator preserving the expected interval in this paper we prove new distance properties between a fuzzy number and its trapezoidal approximation preserving the expected interval then we find the best lipschitz constant of the trapezoidal approximation operator preserving the expected interval finally we use this result in finding within a reasonable error the trapezoidal approximation of a fuzzy number preserving the expected interval in the case when the direct formula leads to complex calculations

em field induced in inhomogeneous dielectric spheres by external sources the electromagnetic field induced in the interior of inhomogeneous dielectric bodies by external sources can be evaluated by solving the well known electric field integrodifferential equation efide for spheres with constant magnetic permeability but variable dielectric constant a direct mainly analytical solution can be used even in case when the inhomogeneity in renders separation of variables inapplicable this approach constitutes a generalization of the hybrid analytical numerical scalar method developed by the authors in two recent papers for the corresponding acoustic scalar field induced in spheres with variable density and or compressibility this extension by no means trivial owing to the vector and integrodifferential nature of the equation is based on field vector expansions using the set of three harmonic surface vectors orthogonal and complete over the surface of the sphere for their angular dependence and dini s expansions of a general type for their radial functions the use of the latter has been shown to be superior to other possible sets of orthogonal expansions and as far as its convergence is concerned it may further be improved by properly choosing a crucial parameter in their eigenvalue equation the restriction to the spherical shape is imposed here to allow use of the well known expansion of green s dyadic in spherical eigenvectors of the vector wave equation

metrics and orders in space of fuzzy numbers abstract two classes of metrics p q and p where 1 p 0 q 1 in space of fuzzy numbers are introduced then a method of ranking fuzzy numbers based on these metrics is proposed and investigated not only fuzzy numbers but also the left sided and right sided fuzzy numbers are considered applications in making decisions and statistics are suggested

fast calculations of dyadic green s functions for electromagnetic scattering in a multilayered medium abstract in this paper we introduce a novel acceleration method for the calculation of dyadic green s functions for the mixed potential integral equation formulation of electromagnetic scattering of scatterers embedded in a multilayered medium numerical results are provided to demonstrate the efficiency and accuracy of the proposed method

stripline fed arbitrarily shaped printed aperture antennas a full wave analysis method is presented for modeling the radiation properties of a stripline fed planar printed aperture antenna element in this formulation both the finite length of stripline and the finite aperture may be of any arbitrary shape since their equivalent electric and magnetic currents are modeled with triangular patch basis functions galerkin s method is applied to numerically solve the coupled mixed potential integral equation mpie exact spatial domain green s functions are used to account for all radiation surface wave and mutual coupling effects interactions between the stripline feed and the radiating aperture are rigorously included numerical analysis is presented for the following nonrectangular shapes an exponentially tapered slot an annular slot an annular slot with opposing stubs and a monofilar archimedean spiral slot element results are shown for input return loss radiation patterns and axial ratio for the circularly polarized elements

discontinuity of the trapezoidal fuzzy number valued operators preserving core we prove that any trapezoidal fuzzy number valued operator preserving core is discontinuous with respect to any weighted metric on the space of fuzzy numbers as an application we obtain the discontinuity of the weighted trapezoidal approximation operator preserving core

the resonance mode theory for exterior problems of electrodynamics and its application to discrete antenna modeling in a frequency range the problem under consideration here is that of building a versatile discrete antenna model in a frequency range the eigenfunction mode expansion or singularity expansion method sem is used in working out the problem a detailed substantiation of sem is provided and an expression determining the dependence of mode amplitudes on exterior source fields is derived a simple example is provided in support of the theory the sem is used in inquiring into the frequency dependence of antenna generalized matrix entries it is intimated that all of the matrix entries contain resonance factors and factors that are hankel transforms of radial coordinate functions a sampling theorem which is a generalized extension of the classic sampling theorem is used for the hankel transform the application of the generalized sampling theorem completes the process of building a versatile discrete antenna model in a frequency range

weighted trapezoidal and triangular approximations of fuzzy numbers in 2007 zeng and li proposed a weighted triangular approximation of a fuzzy number unfortunately this approximation may fail to be a fuzzy number in this paper we improve this approximation and propose a generalization by the name of weighted trapezoidal approximation their algorithms are also presented finally some examples and relevant properties are discussed

field induced in inhomogeneous spheres by external sources i the scalar case the evaluation of acoustic or electromagnetic fields induced in the interior of inhomogeneous penetrable bodies by external sources is based on well known volume integral equations this is particularly true for bodies of arbitrary shape and or composition for which separation of variables fails in this paper the investigation focuses on acoustic scalar fields in inhomogeneous spheres of arbitrary composition i e with r or even dependent medium parameters the volume integral equation is solved by a hybrid analytical numerical method which takes advantage of the orthogonal properties of spherical harmonics and in particular of the so called dini s expansions of the radial functions whose convergence is optimized the numerical part comes at the end it involves the evaluation of certain definite integrals and the matrix inversion for the expansion coefficients of the solution the scalar case treated here serves as a steppingstone for the solution of the more difficult electromagnetic problem

packing circuits in matroids the purpose of this paper is to characterize all matroids m that satisfy the following minimax relation for any nonnegative integral weight function w defined on e m begin aligned rm maximum k m rm has k rm circuits repetition allowed such that each element e rm of m quad quad quad quad quad rm is used at most 2w e rm times by these circuits rm minimum left sum nolimits x in x w x x rm is a collection of elements repetition allowed of m right quad quad quad quad quad left vphantom sum x in x rm such that every circuit in m rm meets x rm at least twice right end aligned our characterization contains a complete solution to a research problem on 2 edge connected subgraph polyhedra posed by cornuejols fonlupt and naddef in 1985 which was independently solved by vandenbussche and nemhauser in vandenbussche and nemhauser j comb optim 9 357 379 2005

nearest piecewise linear approximation of fuzzy numbers abstract the problem of the nearest approximation of fuzzy numbers by piecewise linear 1 knot fuzzy numbers is discussed by using 1 knot fuzzy numbers one may obtain approximations which are simple enough and flexible to reconstruct the input fuzzy concepts under study they might be also perceived as a generalization of the trapezoidal approximations moreover these approximations possess some desirable properties apart from theoretical considerations approximation algorithms that can be applied in practice are also given

weighted trapezoidal approximation preserving cores of a fuzzy number recently various researchers have proved that approximations of fuzzy numbers may fail to be fuzzy numbers in this contribution we suggest a new weighted trapezoidal approximation of an arbitrary fuzzy number which preserves its cores we prove that the weighted trapezoidal approximation preserving core is always a fuzzy number we then discuss properties of the approximation strategy including translation invariance scale invariance identity and continuity the advantage is that the method presented here is simpler than other methods computationally

a hypothesis testing based discussion on the sensitivity of means of fuzzy data with respect to data shape abstract in assessing fuzzy numbers to model imprecise data associated with random experiments trapezoidal fuzzy numbers are often considered such an assessment is mainly due to easing both interpretation and computation this becomes especially noticeable when those assessing fuzzy numbers to data have a weak knowledge low background and little or no expertise in using fuzzy sets as it happens when questionnaires whose responses involve a free fuzzy rating are conducted since the required training to explain the meaning and use of trapezoidal fuzzy numbers is definitely lower than that associated with other shapes nevertheless a question that constantly arises in connection with this trapezoidal assessment is whether it can importantly affect the conclusions of the study involving such data this paper aims to answer the last question from a statistical perspective more concretely the analysis of the influence of the choice of trapezoidal fuzzy numbers to model data is to be based on the conclusions from statistical hypothesis testing about the mean values of the involved fuzzy datasets for this purpose the p values of tests have been compared for trapezoidal assessment vs other frequently used ones like some lu assessments the analysis is first performed by developing simulation based pairwise comparisons and it is later illustrated and corroborated to some extent with a real life example the analysis indicates that the shape of the fuzzy assessment scarcely affects statistical conclusions

approximations of fuzzy numbers by trapezoidal fuzzy numbers preserving the ambiguity and value value and ambiguity are two parameters which were introduced to represent fuzzy numbers in this paper we find the nearest trapezoidal approximation and the nearest symmetric trapezoidal approximation to a given fuzzy number with respect to the average euclidean distance preserving the value and ambiguity to avoid the laborious calculus associated with the karush kuhn tucker theorem the working tool in some recent papers a less sophisticated method is proposed algorithms for computing the approximations many examples proofs of continuity and two applications to ranking of fuzzy numbers and estimations of the defect of additivity for approximations are given

on the nearest parametric approximation of a fuzzy number many nearest parametric approximation methods of fuzzy sets are proposed in the literature it is clear that the specific approximations may lead to the loss of information about fuzziness to overcome this problem most of these methods rely on the minimization of the distance between the original fuzzy set and its approximation but these approximations mostly are not flexible to the decision maker s choice hence in this paper we offer a parametric fuzzy approximation method based on the decision maker s strategy as an extension of trapezoidal approximation of a fuzzy number this method comprises the selection of the form of the parametric membership function and its evaluation

the nearest approximation of a fuzzy quantity in parametric form applications of fuzzy logic and fuzzy mathematics are increasing widely all around the world thus working with fuzzy numbers are very important in many applications of fuzzy mathematics we need or it is better to work with the same fuzzy numbers in this work we approximate parametric fuzzy numbers with polynomial parametric fuzzy numbers

approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval the problem to find the nearest trapezoidal approximation of a fuzzy number with respect to a well known metric which preserves the expected interval of the fuzzy number is completely solved the previously proposed approximation operators are improved so as to always obtain a trapezoidal fuzzy number properties of this new trapezoidal approximation operator are studied

weighted pseudometric approximation of 2 dimensional fuzzy numbers by fuzzy 2 cell prismoid numbers preserving the centroid abstract up to now there have been many research results about approximations of fuzzy numbers by specific fuzzy numbers under preservation of some operators however there are few investigations about approximations of n dimensional fuzzy numbers the main reason is that the structure of n dimensional fuzzy numbers are more complex this paper devotes to seek an approximation operator that produces a special kind of 2 dimensional fuzzy number which is the nearest one to the given 2 dimensional fuzzy number along the direction k the concept of four edges approximation for 2 dimensional fuzzy numbers is defined which is a special kind of 2 dimensional fuzzy numbers at the same time the concept of fuzzy 2 cell prismoid numbers is introduced and the nearest fuzzy 2 cell prismoid numbers of 2 dimensional fuzzy numbers which preserve the centroid of the core for the 2 dimensional fuzzy numbers with respect to the weighted pseudometric are discussed finally with respect to the criteria scale invariance identity criterion and nearness criterion some properties of the approximation operator are presented

a robust method for the computation of green s functions in stratified media closed form green s functions for unbounded planar stratified media are derived in terms of cylindrical and spherical waves the methodology is based on a two level approximation of the spectral domain representation of green s functions this robust efficient and fully numerical approach does not call for an analytical extraction of ldquoproblematicrdquo behaviors such as the quasi static terms and the surface wave poles prior to the spectrum fitting instead the spatial domain green s functions derived in this paper provide an accurate description of both the near field singularity in the vicinity of the source and the far field dominant behavior of the surface waves

the mean value of a fuzzy number abstract the notion of expectation is defined for fuzzy numbers of intervals viewing them as consonant random sets this expectation is interval valued and remains additive in the sense of fuzzy interval addition as a by product some light is shed on the debate between probability and possibility theory and the problem of how to carry measure theoretic notions into the field of possibility theory

extrapolation methods for sommerfeld integral tails a review is presented of the extrapolation methods for accelerating the convergence of sommerfeld type integrals i e semi infinite range integrals with bessel function kernels which arise in problems involving antennas or scatterers embedded in planar multilayered media attention is limited to partition extrapolation procedures in which the sommerfeld integral is evaluated as a sum of a series of partial integrals over finite subintervals and is accelerated by an extrapolation method applied over the real axis tail segment spl alpha spl infin of the integration path where spl alpha 0 is selected to ensure that the integrand is well behaved an analytical form of the asymptotic truncation error or the remainder which characterizes the convergence properties of the sequence of partial sums and serves as a basis for some of the most efficient extrapolation methods is derived several extrapolation algorithms deemed to be the most suitable for the sommerfeld integrals are described and their performance is compared it is demonstrated that the performance of these methods is strongly affected by the horizontal displacement of the source and field points spl rho and by the choice of the subinterval break points furthermore it is found that some well known extrapolation techniques may fail for a number of values of spl rho and ways to remedy this are suggested finally the most effective extrapolation methods for accelerating sommerfeld integral tails are recommended

fast volumetric integral equation solver for acoustic wave propagation through inhomogeneous media elements are described of a volumetric integral equation based algorithm applicable to accurate large scale simulations of scattering and propagation of sound waves through inhomogeneous media the considered algorithm makes possible simulations involving realistic geometries characterized by highly subwavelength details large density contrasts and described in terms of several million unknowns the algorithm achieves its competitive performance characterized by o nlogn solution complexity and o n memory requirements where n is the number of unknowns through a fast and nonlossy fast fourier transform based matrix compression technique the adaptive integral method previously developed for solving large scale electromagnetic problems because of its ability of handling large problems with complex geometries the developed solver may constitute an efficient and high fidelity numerical simulation tool for calculating acoustic field distributions in anatomically realistic models e g in investigatin

the nearest trapezoidal fuzzy number to a fuzzy quantity in this paper we introduce a fuzzy trapezoidal approximation using the metric distance between two fuzzy numbers an application of this approximation is also investigated

on a canonical representation of fuzzy numbers abstract fuzzy numbers and more generally linguistic values are approximate assessments given by experts and accepted by decision makers when obtaining more accurate values is impossible or unnecessary to simplify the task of representing and handling fuzzy numbers several authors have introduced real indices in order to capture the information contained in a fuzzy number in this paper we propose two parameters value and ambiguity for this purpose we use these parameters to obtain canonical representations and to deal with fuzzy numbers in decision making problems several examples illustrate these ideas

dyadic green s function for a multilayered planar medium a dyadic eigenfunction approach a new formulation of the dyadic green s function for a planarly layered medium is presented based on dyadic eigenfunctions of the green s function operator the general development of the dyadic green s function is shown resulting in a three dimensional purely spectral representation the spectral form is converted to a hankel function form using standard techniques analogous to the sum of residues plus branch cut representation often obtained from the sommerfeld green s function advantages and disadvantages of both the eigenfunction and hankel function forms are outlined and compared to other green s function representations examples of the green s dyadic for free space and for a grounded dielectric slab environment are provided and the role of the continuous and discrete spectrum is discussed

analysis of the zonal and rectangular slots on a conducting spherical cavity the zonal slot cut on a conducting spherical cavity is analyzed rigorously the slot is excited asymmetrically which excites higher order azimuthal modes the green s function approach is used to formulate an integral equation for the magnetic current in the slot which is solved using the moment method mom new recurrence formulas are derived so that within their stable region the admittance integrals can be evaluated without the need for any numerical integration in this case the solution is very easy to implement with extremely short computation time the effects of the latitude angle on the peak resistance and percentage bandwidth are investigated furthermore the cavity resonance modes and their degeneracy are examined by plotting the expansion coefficients of the magnetic current in addition the problem of a rectangular slot in the nonequatorial plane is also studied measurements are carried out and good agreement between theory and experiment is obtained

on the nearest parametric approximation of a fuzzy number revisited the problem of finding the nearest parametric approximation of a fuzzy number with respect to the average euclidean distance is completely solved properties of translation invariance scale invariance additivity preservation of expected value value and ambiguity of this new approximation operator are studied and an algorithm for computing it is provided

a full vectorial contrast source inversion scheme for three dimensional acoustic imaging of both compressibility and density profiles imaging the two acoustic medium parameters density and compressibility requires the use of both the acoustic pressure and velocity wave fields described via integral equations imaging is based on solving for the unknown medium parameters using known measured scattered wave fields and it is difficult to solve this ill posed inverse problem directly using a conjugate gradient inversion scheme here a contrast source inversion method is used in which the contrast sources defined via the product of changes in compressibility and density with the pressure and velocity wave fields respectively are computed iteratively after each update of the contrast sources an update of the medium parameters is obtained total variation as multiplicative regularization is used to minimize blurring in the reconstructed contrasts the method successfully reconstructed three dimensional contrast profiles based on changes in both density and compressibility using synthetic data both with and without 50 white noise the results were compared with imaging based only on the pressure wave field where speed of sound profiles were solely based on changes in compressibility it was found that the results improved significantly by using the full vectorial method when changes in speed of sound depended on changes in both compressibility and density

further improvement for fast computation of mixed potential green s functions for cylindrically stratified media a method of fast computation of the mixed potential green s functions mpgfs in spatial domain for cylindrically stratified media has been developed based on the convergence behavior of the mpgfs in spectral domain the discrete complex image method dcim and the extrapolation technique are employed to perform the inverse fourier transform which is different from that of planarly stratified media in order to evaluate the summation of cylindrical eigenmode from order of negative infinity to order of positive infinity the green s functions in spectral domain are rearranged so that acceleration technique can be well applied to speed up the convergence of summation process for the integral along the deformed sommerfeld integral path with respect to k sub z dcim is used to speed up the computation after the quasistatic components are completely subtracted from the spectral domain green s functions the inverse transform of the remaining parts has an approximated analytical form the proposed method can be used to accurately and efficiently calculate the spatial domain mpgfs which are useful for characterizing conformal patch structures mounted on cylindrically stratified media

the expected value of a fuzzy number abstract the notions of expected interval and expected value of fuzzy number are introduced the expected interval is defined as the expected value of an interval random set generated by the fuzzy number and the expected value of this number is defined as the centre of the expected interval the linearity of the expected interval is studied

an asymptotic extraction technique for evaluating sommerfeld type integrals an asymptotic extraction process is developed which leads to an efficient method for the evaluation of the electric field from a hertzian dipole in a layered geometry this technique allows for a rapidly converging expression for the electric field which remains well behaved as the source and observation heights z z coincide a useful application of this method is in the calculation of mutual impedance between printed dipoles

weighted semi trapezoidal approximations of fuzzy numbers recently many scholars investigated interval triangular and trapezoidal approximations of fuzzy numbers these publications can be grouped into two classes euclidean distance class and non euclidean distance class most approximations in euclidean distance class can be calculated by formulas but calculating approximations in the other class is more complicated in the present paper we study a special class of non linear approximations with respect to a weighted euclidean distance we call it weighted semi trapezoidal approximations the proposed approximations generalize all recent approximations in euclidean distance class first we embed fuzzy numbers into a hilbert space then compute weighted semi trapezoidal approximations by means of best approximations in a closed convex subset of the hilbert space finally we propose formulas of matrix type which is more clear than the previous contributions

on the interval approximation of a fuzzy number the notion of an approximation interval of a fuzzy number is introduced it is the interval which fulfills two conditions in the first its width is equal to the width of a fuzzy number being approximated in the second the hamming distance between this interval and the approximated number is minimal the introduced notion is compared with the notion of expected interval of a fuzzy number known in literature