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

a possibilistic regression based on gradual interval b splines application for hyperspectral imaging lake sediments abstract according to an epistemic view of intervals this paper proposes a possibilistic regression based on gradual interval b splines to represent the input output data mapping in this context an improvement of the parametric fuzzy regression through the notion of gradual interval b splines is proposed the proposed gradual regression based on b splines can be regarded as an extension of the nonparametric interval based regression where an uncertain dimension is integrated the proposed method is validated through illustrative and comparative examples moreover it is applied for modeling the input output behavior between reflectance and wavelengths in an application for hyperspectral imaging for lake sediments

application of the iterative approach to modal methods for the solution of maxwell s equations in this work we discuss the possibility to reduce the computational complexity of modal methods i e methods based on eigenmodes expansion from the third power to the second power of the number of eigenmodes by applying the iterative technique the proposed approach is based on the calculation of the eigenmodes part by part by using shift and invert iterative procedure and by utilizing the iterative approach to solve linear equations to compute eigenmodes expansion coefficients as practical implementation the iterative modal methods based on polynomials and trigonometric functions as well as on finite difference scheme are developed alternatives to the scattering matrix s matrix technique which are based on pure iterative or mixed direct iterative approaches allowing to markedly reduce the number of required numerical operations are discussed additionally the possibility of diminishing the memory demand of the whole algorithm from second to first power of the number of modes by implementing the iterative approach is demonstrated this allows to carry out calculations up to hundreds of thousands eigenmodes without using a supercomputer modal methods computational complexity reduced to 2nd power of eigenmodes number memory demand reduced to the 1st power of the number of eigenmodes eigenmodes are found by batches using arnoldi method and shift and invert technique an iterative procedure is used instead of s or r matrix formalism calculations up to hundreds of thousands eigenmodes without using supercomputers

alpha bounds of fuzzy numbers applications of operators of contrast modification of fuzzy sets to fuzzy numbers are studied it is shown that for a fuzzy number a and for 0 1 an upper bound and an lower bound of a can be created cardinality of the boundary region will be called flexibility of a relationship among bounds strong bounds and ultimate bounds of a is discussed when bounds are trapezoidal fuzzy numbers then flexibility of a can be used to assess roughness of approximation of a in the knowledge base consisting of trapezoidal fuzzy numbers

difference equations and pseudo differential operators on zn abstract in this paper we develop the calculus of pseudo differential operators on the lattice z n which we can call pseudo difference operators an interesting feature of this calculus is that the global frequency space t n is compact so the symbol classes are defined in terms of the behaviour with respect to the lattice variable we establish formulae for composition adjoint transpose and for parametrix for the elliptic operators we also give conditions for the l 2 weighted l 2 and l p boundedness of operators and for their compactness on l p we describe a link to the toroidal quantization on the torus t n and apply it to give conditions for the membership in schatten classes on l 2 z n furthermore we discuss a version of fourier integral operators on the lattice and give conditions for their l 2 boundedness the results are applied to give estimates for solutions to difference equations on the lattice z n moreover we establish garding and sharp garding inequalities with an application to the unique solvability of parabolic equations on the lattice z n

on the complexity of aperiodic fourier modal methods for finite periodic structures the fourier modal method fmm is based on fourier expansions of the electromagnetic field and is inherently built for infinitely periodic structures when the infinite periodicity assumption is not realistic the finiteness of the structure has to be incorporated into the model in this paper we discuss the recent extensions of the fmm for finite periodic structures and analyze their complexity both with respect to the main discretization parameter email protected as well as with respect to the number of periods r we show that among the three fmm based approaches able to represent finiteness the aperiodic fourier modal method with alternative discretization has the lowest computational cost given by either o email protected 3log 2r or o email protected 2r depending on the values of email protected and r this result demonstrates that the method is highly suited for rigorous modeling of scattering from large periodic structures for instance for email protected 100 and r 1000 the complexity of the aperiodic fourier modal method with alternative discretization is comparable to the complexity of the standard fmm

a weak form of the conjugate gradient fft method for plate problems a number of electromagnetic field problems for planar structures can be formulated in terms of a hypersingular integral equation in which a grad div operator acts on a vector potential the vector potential is a convolution of the free space green s function and some surface current density over the domain of interest a weak form of this integral equation is obtained by testing it with subdomain basis functions defined over the plate domain only as a next step the vector potential is expanded in a sequence of subdomain basis functions and the grad div operator is integrated analytically over the plate domain only for the problem of electromagnetic scattering by a plate the method shows excellent numerical performance the numerical difficulties encountered in some previous conjugate gradient fast fourier transform cgfft methods have been eliminated

asymmetry of convolution norms on lie groups abstract we prove that on most connected non commutative lie groups there exists a convolution operator which is bounded on l p but unbounded on l q for every q not belonging to the interval with endpoints 2 and p furthermore the kernel of such an operator can be supported on an arbitrary neighbourhood of the identity

lp lq multipliers on locally compact groups abstract in this paper we discuss the l p l q boundedness of both spectral and fourier multipliers on general locally compact separable unimodular groups g for the range 1 p 2 q as a consequence of the established fourier multiplier theorem we also derive a spectral multiplier theorem on general locally compact separable unimodular groups we then apply it to obtain embedding theorems as well as time asymptotics for the l p l q norms of the heat kernels for general positive unbounded invariant operators on g we illustrate the obtained results for sub laplacians on compact lie groups and on the heisenberg group as well as for higher order operators we show that our results imply the known results for l p l q multipliers such as hormander s fourier multiplier theorem on r n or known results for fourier multipliers on compact lie groups the new approach developed in this paper relies on advancing the analysis in the group von neumann algebra and its application to the derivation of the desired multiplier theorems

possibilistic linear regression analysis for fuzzy data abstract fuzzy data given by expert knowledge can be regarded as a possibility distribution by which possibilistic linear systems are defined recently it has become important to deal with fuzzy data in connection with expert knowledge three formulations of possibilistic linear regression analysis are proposed here to deal with fuzzy data since our formulations can be reduced to linear programming problems the merit of our formulations is to be able to obtain easily fuzzy parameters in possibilistic linear models and to add other constraint conditions which might be obtained from expert knowledge of fuzzy parameters this approach can be regarded as a fuzzy interval analysis in a fuzzy environment

coupling of finite element and boundary integral methods for electromagnetic scattering in a two layered medium consider a time harmonic electromagnetic plane wave incident on an inhomogeneity embedded in a two layered medium in this paper a method of coupling of finite element and boundary integral equation methods is presented for the solutions of electromagnetic scattering in both transverse electric and magnetic polarization cases the well posedness of the continuous and discrete problems as well as optimal error estimates for the coupled variational approximations are obtained numerical results are included to illustrate the accuracy with the optimal convergence property of the proposed method and to show the wave features in a two layered medium

on reduction theory and brown measure for closed unbounded operators abstract the theory of direct integral decompositions of both bounded and unbounded operators is further developed in particular results about spectral projections functional calculus and affiliation to von neumann algebras are proved for operators belonging to or affiliated to a tracial von neumann algebra that is a direct integral von neumann algebra the brown measure is shown to be given by the corresponding integral of brown measures

efficient solution of maxwell s equations for geometries with repeating patterns by an exchange of discretization directions in the aperiodic fourier modal method the aperiodic fourier modal method in contrast field formulation is a numerical discretization and solution technique for solving scattering problems in electromagnetics typically spectral discretization is used in the finite periodic direction and spatial discretization in the orthogonal direction in the light of the fact that the structures of interest often have a large width to height ratio and that the two discretization approaches have different computational complexities we propose exchanging the directions for spatial and spectral discretization moreover if the scatterer has repeating patterns swapping the discretization directions facilitates the reuse of previous computations therefore the new method is suited for scattering from objects with a finite number of periods such as gratings memory arrays metamaterials etc numerical experiments demonstrate a considerable reduction of the computational costs in terms of time and memory for a specific test case considered in this paper the new method based on alternative discretization is 40 times faster and requires 100 times less memory than the method based on classical discretization

interval regression analysis using support vector networks support vector machines svms have been very successful in pattern classification and function estimation problems for crisp data in this paper the v support vector interval regression network v svirn is proposed to evaluate interval linear and nonlinear regression models for crisp input and output data as it is difficult to select an appropriate value of the insensitive tube width in e support vector regression network the proposed v svirn alleviates this problem by utilizing a new parametric insensitive loss function the proposed v svirn automatically adjusts a flexible parametric insensitive zone of arbitrary shape and minimal size to include the given data besides the proposed method can achieve automatic accuracy control in the interval regression analysis task for a priori chosen v at most a fraction v of the data points lie outside the interval model constructed by the proposed v svirn to be more precise v is an upper bound on the fraction of training errors and a lower bound on the fraction of support vectors hence the selection of v is more intuitive moreover the proposed algorithm here is a model free method in the sense that we do not have to assume the underlying model function experimental results are then presented which show the proposed v svirn is useful in practice especially when the noise is heteroscedastic that is the noise strongly depends on the input value x

hardy littlewood hausdorff young paley inequalities and lp lq fourier multipliers on compact homogeneous manifolds abstract in this paper we prove new inequalities describing the relationship between the size of a function on a compact homogeneous manifold and the size of its fourier coefficients these inequalities can be viewed as noncommutative versions of the hardy littlewood inequalities obtained by hardy and littlewood 17 on the circle for the example case of the group su 2 we show that the obtained hardy littlewood inequalities are sharp yielding a criterion for a function to be in l p su 2 in terms of its fourier coefficients we also establish paley and hausdorff young paley inequalities on general compact homogeneous manifolds the latter is applied to obtain conditions for the l p l q boundedness of fourier multipliers for 1 p 2 q on compact homogeneous manifolds as well as the l p l q boundedness of general non invariant operators on compact lie groups we also record an abstract version of the marcinkiewicz interpolation theorem on totally ordered discrete sets to be used in the proofs with different plancherel measures on the unitary duals

an orderwise polynomial regression procedure for fuzzy data a procedure for polynomial fit with fuzzy data is presented as in real case studies there is often dependence between modes and spreads we propose a regression polynomial model capable to take into account possible interactions between the estimated spreads and modes this method finds applications in several fields such as reliability quality control psychometrics marketing image processing etc an application to a software reliability problem is also presented

extended fuzzy regression models using regularization method regularization approach to regression can be easily found in statistics and information science literatures the technique of regularization was introduced as a way of controlling the smoothness properties of regression function the main purpose of this paper is to extend the models of diamond inform sci 46 1988 141 to fuzzy multiple linear regression models and to extend the model f3 with numerical input of diamond inform sci 46 1988 141 to fuzzy nonlinear model here all extensions are based on regularization technique

l p fourier multipliers on compact lie groups in this paper we prove l p fourier multiplier theorems for invariant and also non invariantoperatorsoncompactliegroupsinthespiritofthewell knownhormander mikhlin theorem on r n and its variants on tori t n we also give applications to a priori estimates for non hypoelliptic operators already in the case of tori we get an interesting refinement of the classical multiplier theorem

fuzzy least squares abstract several models for simple least squares fitting of fuzzy valued data are developed criteria are given for when fuzzy data sets can be fitted to the models and analogues of the normal equations are derived