a fast combined field volume integral equation solution to em scattering by 3 d dielectric objects of arbitrary permittivity and permeability a fast solution to the combined field volume integral equation cfvie for electromagnetic scattering by large three dimensional dielectric bodies of arbitrary permittivity and permeability is presented the cfvie is formulated in the region of the scatterers by expressing the total fields as the sum of the incident wave and the radiated wave due to both the electric and magnetic polarization currents the resultant integral equation is solved using the method of moments mom then the precorrected fast fourier transform p fft method is applied to reduce the memory requirement and accelerate the matrix vector multiplication in the mom solution in the implementation of the p fft method two sets of projection operators are constructed respectively for the projections of the electric sources and magnetic sources in addition two sets of interpolation operators are also applied respectively for the computation of the vector scalar potentials and the curl of the vector potentials in the support of the testing functions the resultant method has a memory requirement of o n and a computational complexity of o nlogn respectively where n denotes the number of unknowns

a wide band equivalent source reconstruction method exploiting the stoer bulirsch algorithm with the adaptive frequency sampling conventional equivalent source reconstruction methods are only operating at a single frequency point each time however for wide band radiators their computation cost of the source reconstruction increases with the number of frequency points in this communication a wide band equivalent source reconstruction method wb srm based on the neville type stoer bulirsch sb algorithm is developed since the sb algorithm is a recursive tabular method it can perform the interpolation over a broadband using a single rational function without any singularity issue supported by the adaptive frequency sampling afs scheme the number of required sampling data is significantly reduced which leads to much better computational efficiency during the afs process three fitting models fm are considered two are triangle rules and another one is rhombus rule in this communication a bisection searching strategy is performed furthermore to achieve high order accuracy the nystrom method is implemented numerical examples are presented to validate the proposed wb srm and demonstrate its accuracy and applications

solving the volume integral equations of electromagnetic scattering time harmonic electromagnetic scattering by inhomogeneous three dimensional structures within a free space environment can be described by electric and magnetic field volume integral equations involving the free space green function a comprehensive set of galerkin projection formulations also known as moment methods for the numerical solution of these equations is presented together with comparative numerical results such formulations are widely used for particle scattering analysis optical near field calculation etc results are obtained with higher order divergence and curl conforming basis functions on iso parametric tetrahedral meshes the results demonstrate that all formulations converge with similar accuracy in the case of an analytically solvable test problem when modeling flux densities as solution variables it is argued that solenoidal function spaces should be used rather than the standard divergence conforming function spaces this assertion is supported by the results some of the formulations involve solving for curl conforming fields such fields can be discretized with fewer unknowns than divergence conforming ones implying lower computational costs additionally some formulations yield system matrices which are approximately halfway sparse meaning that computational costs will be down by a factor of 2 when iterative solvers are employed which is the case for the widely used fast methods

on deriving a locally corrected nystrom scheme from a quadrature sampled moment method a novel high order method of moment procedure with quadrature point based discretization is presented the scheme is equivalent to a moment method employing smooth basis and testing functions applying a fixed point numerical quadrature approximation for the outer integral mapping the current to the quadrature points then leads to a formulation that is equivalent to that derived via the locally corrected nystrom method the convergence properties of the current density and rcs for smooth and singular geometries in two and three dimensions are also studied

planar near field to far field transformation using an equivalent magnetic current approach an alternative method is presented for computing far field antenna patterns from near field measurements the method utilizes the near field data to determine equivalent magnetic current sources over a fictitious planar surface that encompasses the antenna and these currents are used to ascertain the far fields under certain approximations the currents should produce the correct far fields in all regions in front of the antenna regardless of the geometry over which the near field measurements are made an electric field integral equation efie is developed to relate the near fields to the equivalent magnetic currents the method of moments is used to transform the integral equation into a matrix one the matrix equation is solved with the conjugate gradient method and in the case of a rectangular matrix a least squares solution for the currents is found without explicitly computing the normal form of the equation near field to far field transformation for planar scanning may be efficiently performed under certain conditions numerical results are presented for several antenna configurations

on the existence and construction of t transitive closures in this paper it is shown that any fuzzy relation r on an arbitrary universe x has a t transitive closure the triangular norm t involved is not subject to any conditions this existential result can be turned into an explicit expression in the case of a left continuous triangular norm t furthermore this continuity restriction vanishes in the case of a finite universe x in that case the explicit expression can also be operationalized

effort associated with a class of random optimization methods when differentiability is not assumed random procedures can be successfully used to estimate the extreme values of a given function for a class of such algorithms we treat the problem of estimating the mean effort

reconstruction of equivalent currents distribution over arbitrary three dimensional surfaces based on integral equation algorithms a technique for the determination of the equivalent currents distribution from a known radiated field is described this inverse radiation problem is solved through an integral equation algorithm that allows the characterization of antennas of complex geometry both for near field to far field nf ff transformation purposes as well as for diagnostic tasks the algorithm is based on the representation of the radiating structure by means of a set of equivalent currents over a three dimensional 3d surface that can be fitted to the arbitrary geometry of the antenna the innovative formulation uses an integral equation involving the electric field due to the currents tangential components to the represented antenna 3d surface for that purpose both the magnetic and electric equivalent currents are considered in the integral equations regularization techniques are also introduced to improve the convergence of the proposed iterative solution the paper concludes with several results related to the practical verification of the equivalence principle and the characterization of a horn antenna

limiting distribution for random optimization methods let f be a function defined on some domain omega subset r d we consider the problem of finding the global minimum of f subjected to some constraints say g i x leqq 0 i 1 cdots m when differentiability is not assumed random optimization methods provide an alternative way to estimate the minimum for two such methods we study the existence of the limiting distribution and the estimation of the parameter of the limiting distribution

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

the relationships among several types of fuzzy automata we discuss the relationships among several types of fuzzy automata in which all fuzzy sets are defined by membership functions whose codomains are a lattice ordered monoid l these automata include nondeterministic l valued finite automata with l move nondeterministic l valued finite automata deterministic l valued finite automata and l valued finite state automata we consider all that come with fuzzy initial states and fuzzy final states or with crisp initial states or crisp final states some comparative results concerning the power of fuzzy automata used in the existing literature to recognize fuzzy languages are given systematically

construction of fuzzy automata from fuzzy regular expressions li and pedrycz have proved fundamental results that provide different equivalent ways to represent fuzzy languages with membership values in a lattice ordered monoid and generalize the well known results of the classical theory of formal languages in particular they have shown that a fuzzy language over an integral lattice ordered monoid can be represented by a fuzzy regular expression if and only if it can be recognized by a fuzzy finite automaton however they did not give any efficient method for constructing an equivalent fuzzy finite automaton from a given fuzzy regular expression in this paper we provide such an efficient method transforming scalars appearing in a fuzzy regular expression ainto letters of the new extended alphabet we convert the fuzzy regular expression ato an ordinary regular expression a r then starting from an arbitrary nondeterministic finite automaton a that recognizes the language a r represented by the regular expression a r we construct fuzzy finite automata a a and a a r with the same or even less number of states than the automaton a which recognize the fuzzy language a represented by the fuzzy regular expression a the starting nondeterministic finite automaton a can be obtained from a r using any of the well known constructions for converting regular expressions to nondeterministic finite automata such as glushkov mcnaughton yamada s position automaton brzozowski s derivative automaton antimirov s partial derivative automaton or ilie yu s follow automaton

multilevel fast multipole accelerated inverse equivalent current method employing rao wilton glisson discretization of electric and magnetic surface currents the radiation of any object in a homogeneous environment can be described by a set of equivalent sources different types of equivalent sources are feasible and all of them have their own benefits equivalent current methods are especially advantageous for irregular measurement grids of arbitrary shape and if a priori information about the object shall be used also they can immediately provide diagnostic information about the object in this paper a very flexible equivalent current method is presented which has been derived from a general purpose boundary integral equation solver as such the method works with arbitrary triangular surface meshes and rao wilton glisson basis functions where electric and or magnetic surface current densities can be assumed high efficiency is achieved since the multilevel fast multipole method has been adapted to speed up the inverse solution process results obtained from simulations and measurements are presented where large scale problems with dimensions up to 75 wavelengths are considered

dgtd analysis of electromagnetic scattering from penetrable conductive objects with ibc to avoid straightforward volumetric discretization a discontinuous galerkin time domain dgtd method integrated with the impedance boundary condition ibc is presented in this paper to analyze the scattering from objects with finite conductivity two situations are considered 1 the skin depth is smaller than the thickness of the conductive volume 2 the skin depth is larger than the thickness of a thin conductive sheet for the first situation a surface impedance boundary condition sibc is employed wherein the surface impedance usually exhibits a complex relation with the frequency to incorporate the sibc into dgtd the surface impedance is first approximated by rational functions in the laplace domain using the fast relaxation vector fitting frvf technique via inverse laplace transform the time domain dgtd matrix equations can be obtained conveniently in integral form with respect to time t for the second situation a transmission ibc tibc is used to include the transparent effects of the fields in the tibc the tangential magnetic field jump is related with the tangential electric field via the surface conductivity in this work a specifically designed dgtd algorithm with tibc is developed to model the graphene up to the terahertz thz band in order to incorporate the tibc into dgtd without involving the time domain convolution an auxiliary surface polarization current governed by a first order differential equation is introduced over the graphene for open region scattering problems the dgtd algorithm is further hybridized with the time domain boundary integral tdbi method to rigorously truncate the computational domain to demonstrate the accuracy and applicability of the proposed algorithm several representative examples are provided

high order numerical solutions of the mfie for the linear dipole the magnetic field integral equation mfie was applied to a dipole using three different discretization methods and high order basis functions for moderate order and higher basis functions it was found that the different discretization methods produced essentially the same results continuity of current and its first derivative was observed at cell boundaries even though continuity of current was not explicitly enforced there the mfie provided lower condition numbers than the hallen equation over the range of dipole radii examined in close proximity to surface discontinuities including hidden ones residual errors could not be significantly reduced by increasing the order of the basis functions implying the need for better modeling at discontinuities and calling into question the use of faceting to represent curved surfaces

near field to near far field transformation for arbitrary near field geometry utilizing an equivalent electric current and mom presented here is a method for computing near and far field patterns of an antenna from its near field measurements taken over an arbitrarily shaped geometry this method utilizes near field data to determine an equivalent electric current source over a fictitious surface which encompasses the antenna this electric current once determined can be used to ascertain the near and the far field this method demonstrates the concept of analytic continuity i e once the value of the electric field is known for one region in space from a theoretical perspective its value for any other region can be extrapolated it is shown that the equivalent electric current produces the correct fields in the regions in front of the antenna regardless of the geometry over which the near field measurements are made in this approach the measured data need not satisfy the nyquist sampling criteria an electric field integral equation is developed to relate the near field to the equivalent electric current a moment method procedure is employed to solve the integral equation by transforming it into a matrix equation a least squares solution via singular value decomposition is used to solve the matrix equation computations with both synthetic and experimental data where the near field of several antenna configurations are measured over various geometrical surfaces illustrate the accuracy of this method

a comment on construction of fuzzy automata from fuzzy regular expressions the aim of this comment is to point out that the fuzzy language recognized by a nondeterministic finite automaton which is associated with a fuzzy regular expression in the context of stamenkovic iric s method stamenkovic and iric 2012 11 is recognized by a fuzzy finite automaton with e moves every fuzzy automaton with e moves is also equivalent to a fuzzy automaton and there are effective methods for removing e moves in order to obtain the equivalent fuzzy automaton in this way our proposal to convert a fuzzy regular expression to a fuzzy finite automaton is based on the construction of a fuzzy automaton with e moves for the fuzzy regular expression and the construction of an equivalent fuzzy finite automaton by means of e removal operation

fast antenna diagnosis algorithm using oblate spheroidal nonuniform grids a fast algorithm for the diagnosis of large antennas is developed the algorithm is based on the rayleigh sommerfeld rs backpropagation method accelerated by a multilevel nonuniform grid algorithm comparison between the field distributions reconstructed from measurements and the desired ones can be used for the localization of antenna defects and geometrical distortions the optimal performance is obtained by using oblate spheroidal grids which are tailored to both the measurement and antenna surfaces further acceleration can be achieved for particular cases via optimal sampling on the antenna surface the algorithm s performance is demonstrated for the example of a parabolic reflector with a number of surface distortions and compared to that achieved with spherical grids the accuracy and error controllability are studied in comparison to the direct rs integral computation

numerical solution of the helmholtz equation in 2d and 3d using a high order nystrom discretization we show how to solve time harmonic scattering problems by means of a high order nystrom discretization of the boundary integral equations of wave scattering in 2d and 3d the novel aspect of our new method is its use of local corrections to the discretized kernel in the vicinity of the kernel singularity enhanced by local corrections the new algorithm has the simplicity and speed advantages of the traditional nystrom method but also enjoys the advantages of high order convergence for controlling solution error we explain the practical details of implementing a scattering code based on a high order nystrom discretization and demonstrate by numerical example that a scattering code based on this algorithm can achieve high order convergence to the correct answer we also demonstrate its performance advantages over a high order galerkin code

nystrom method solution of volume integral equations for electromagnetic scattering by 3d penetrable objects the volume integral equations vies for electromagnetic em scattering by three dimensional 3d penetrable objects are solved by nystrom method the vies are essential and cannot be replaced by surface integral equations sies for inhomogeneous problems but they are usually solved by the method of moments mom the nystrom method as an alternative for the mom has shown much promise and has been widely used to solve the sies but it is less frequently applied to the vies especially for 3d em problems in this work we implement the nystrom method for 3d vies by developing an efficient local correction scheme for singular and near singular integrals over tetrahedral elements the scheme first interpolates the unknown functions within the tetrahedral elements and then derives analytical solutions for the resultant singular or near singular integrals after singularity subtraction the scheme is simpler and more efficient in implementation compared with those based on the redesign of quadrature rules for the singular or near singular integrands numerical examples are presented to demonstrate the effectiveness of the proposed scheme and its convergence feature is also studied

fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids we study fuzzy finite automata in which all fuzzy sets are defined by membership functions whose codomain forms a lattice ordered monoid l for these l fuzzy finite automata l ffa for short we provide necessary and sufficient conditions for the extendability of the state transition function it is shown that nondeterministic l ffa nl ffa for short are more powerful than deterministic l ffa dl ffa for short then we give necessary and sufficient conditions for the simulation of an nl ffa by an equivalent dl ffa next we turn to the closure properties of languages defined by l ffas we establish closure under the regular operations and provide conditions for closure under intersection and reversal in particular we show that the family of fuzzy languages accepted by dl ffas is not closed under kleene closure operation and the family of fuzzy languages accepted by nl ffas is not closed under complement operation furthermore we introduce the notions of l fuzzy regular expressions and give the kleene theorem for nl ffas the description of dl ffas by l fuzzy regular expressions is also given finally we investigate the level structures of l ffas our results provide some insight as to what extend properties of l ffas and their languages depend on the algebraic properties of l

accurate and efficient nystrom volume integral equation method for the maxwell equations for multiple 3 d scatterers in this paper we develop an accurate and efficient nystrom volume integral equation vie method for the maxwell equations for a large number of 3 d scatterers the cauchy principal values that arise from the vie are computed accurately using a finite size exclusion volume together with explicit correction integrals consisting of removable singularities also the hyper singular integrals are computed using interpolated quadrature formulae with tensor product quadrature nodes for cubes spheres and cylinders that are frequently encountered in the design of meta materials the resulting nystrom vie method is shown to have high accuracy with a small number of collocation points and demonstrates p convergence for computing the electromagnetic scattering of these objects numerical calculations of multiple scatterers of cubic spherical and cylindrical shapes validate the efficiency and accuracy of the proposed method

estimation of the minimum of a function using order statistics abstract suppose a is a bounded set in d and f a real function defined on a suppose m min f x x a exists using a random sample x 1 x 2 x n from a uniform distribution over a we construct a confidence interval for m using asymptotic theory our results contain some statistical results valid in general extreme value theory estimation of the main parameter of extreme value distributions