an efficient closed form derivation of spatial green s function for finite dielectric structures using characteristic green s function rational function fitting method a uniform and closed form spatial green s function for finite dielectric structures is derived by using a combination of the characteristic green s function cgf and rational function fitting method rffm employing the concept of quasi leaky waves cgf rffm represents both of the discrete and continuous spectrum contributions efficiently by using the modified vectfit algorithm the method is examined for 2 d truncated dielectric slab while it can be implemented for 3 d structure straightforwardly an error of less than 0 2 is achieved compared with the direct numerical integration of the spectral integral the derived green s function is exact for separable structures while it is approximate for nonseparable structures like truncated dielectric substrates where the corner regions are replaced with fictitious materials to obtain more accurate results mode conversions due to the surface waves sws incident on the end facet are considered by employing the scattering matrix in the formulation for structures supporting several guided modes the main advantage of this method lies in its speed as well as accuracy excellent agreements with the rigorous method of moments mom are shown in several examples

extending fuzzy logics with many hedges abstract fuzzy logic aims at modeling logical reasoning with vague or imprecise statements which may contain linguistic hedges in fact many hedges e g very highly rather and slightly can be used simultaneously to express different levels of emphasis moreover each hedge might have a dual one e g slightly can be seen as a dual hedge of very thus it is necessary to extend systems of fuzzy logic with multiple hedges this work proposes two axiomatizations for multiple hedges as an expansion of a core fuzzy logic in one axiomatization hedges do not have any dual one while in the other each hedge can have its own dual one it is shown that the proposed logics not only cover a large class of hedge functions but also have all completeness properties as the underlying logic w r t the class of their chains as well as distinguished subclasses of their chains including standard completeness the axiomatizations are also extended to the first order level furthermore we present a method to build linguistic fuzzy logics based on the axiomatizations and a hedge algebra whose corresponding algebras use a linguistic truth domain taken from the hedge algebra for representing and reasoning with linguistically expressed human knowledge where truth values of vague sentences are given in linguistic terms

truth depressing hedges and bl logic abstract we show a complete axiomatization of unary connectives interpreted by monotone and superdiagonal truth functions so called truth depressing hedges these connectives formalize linguistic hedges like slightly true and more or less we follow ideas of p hajek on very true fuzzy sets and systems 124 2001 329 333 and show that bl vt logic can be enriched by a unary connective for which we can establish strong completeness with respect to the desired interpretation

derivation digraphs for dependencies in ordinal and similarity based data we present graph based method of reasoning with if then rules describing dependencies between attributes in ordinal and similarity based data the rules we consider have two basic interpretations as attribute implications in object attribute incidence data where objects are allowed to have attributes features to degrees and as similarity based functional dependencies in an extension of the codd model of data main results in this paper show that degrees to which if then rules are semantically entailed from sets or graded sets of other if then rules can be characterized by existence of particular directed acyclic graphs with vertices labeled by attributes and degrees coming from complete residuated lattices in addition we show that the construction of directed acyclic graphs can be used to compute closures of sets of attributes and normalized proofs

a general mass conservative numerical solution for the unsaturated flow equation numerical approximations based on different forms of the governing partial differential equation can lead to significantly different results for unsaturated flow problems numerical solution based on the standard h based form of richards equation generally yields poor results characterized by large mass balance errors and erroneous estimates of infiltration depth conversely numerical solutions based on the mixed form of richards equation can be shown to possess the conservative property so that mass is perfectly conserved this leads to significant improvement in numerical solution performance while requiring no additional computational effort however use of the mass conservative method does not guarantee good solutions accurate solution of the unsaturated flow equation also requires use of a diagonal time or mass matrix only when diagonal time matrices are used can the solution be shown to obey a maximum principle which guarantees smooth nonoscillatory infiltration profiles this highlights the fact that proper treatment of the time derivative is critical in the numerical solution of unsaturated flow

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

efficient algorithms for computing sommerfeld integral tails sommerfeld integrals sis are ubiquitous in the analysis of problems involving antennas and scatterers embedded in planar multilayered media it is well known that the oscillating and slowly decaying nature of their integrands makes the numerical evaluation of the si real axis tail segment a very time consuming and computationally expensive task therefore si tails have to be specially treated in this paper we compare two recently developed techniques for their efficient numerical evaluation first a partition extrapolation method in which the integration then summation procedure is combined with a new version of the weighted averages wa extrapolation technique is summarized the previous variants of wa technique are also discussed then a review of double exponential de quadrature formulas for direct integration of the si tails is presented the efficient way of implementing the algorithms their pros and cons as well as comparisons of their performance are discussed in detail

direct rational function fitting method for accurate evaluation of sommerfeld integrals in stratified media the current work proposes a direct rational function fitting method employing cylindrical waves alone for the accurate evaluation of sommerfeld integrals for planar multilayered structures three are the key points of the effort 1 until now relative works require the extraction of the quasi static asymptotic terms and branch cut continuous wave contribution explicitly in the current one the explicit treatment of those terms is avoided the proposed methodology is based on the direct fitting of the spectrum of the green s function by rational functions thus it provides the spatial green s function solely in terms of cylindrical waves 2 the effectiveness robustness and accuracy improvement of the rational function fit rely upon the proper sampling of the spectrum this accurate fitting is possible because instead of avoiding large variations of the spectral kernel we introduce proper paths to include more variation and thus more spectrum information before we apply the modified vectfit algorithm 3 furthermore proper weighting of the vectfit is proposed in order to guide the algorithm in providing increased accuracy in specific desired areas of the horizontal distance between the source and observation points armed with the above the direct rational function fitting method provides accurate results both for the near and far field regions various examples among them the correct treatment of a two branch case are given that prove the excellent performance and robustness of the proposed approach

accurate approximation of green s functions in planar stratified media in terms of a finite sum of spherical and cylindrical waves a robust and computationally expedient methodology is presented for accurate closed form approximation of the green s functions used in the mixed potential integral equation statement of the electromagnetic boundary value problem in planar stratified media the proposed methodology is based on the fitting of the spectrum of the green s function after the extraction of the quasistatic part making use of rational functions the effectiveness and robustness of the proposed methodology rely upon the proper sampling of the spectrum in order to improve the accuracy of the rational function fit the resulting closed form approximation is in terms of both spherical and cylindrical waves thus high accuracy is obtained in the approximation of the green s function irrespective of the distance of the observation point from the source the methodology is validated through its application to the approximation of the green s function for a multi layered planar dielectric stack

algebraic and proof theoretic characterizations of truth stressers for mtl and its extensions extensions of monoidal t norm logic mtl and related fuzzy logics with truth stresser modalities such as globalization and very true are presented here both algebraically in the framework of residuated lattices and proof theoretically as hypersequent calculi completeness with respect to standard algebras based on t norms embeddings between logics decidability and the finite embedding property are then investigated for these logics

numerical integration of related hankel transforms by quadrature and continued fraction expansion an algorithm is presented for the accurate evaluation of hankel or bessel transforms of algebraically related kernel functions defined here as the non bessel function portion of the integrand that is more widely applicable than the standard digital filter methods without enormous increases in computational burden the algorithm performs the automatic integration of the product of the kernel and bessel functions between the asymptotic zero crossings of the latter and sums the series of partial integrations using a continued fraction expansion equivalent to an analytic continuation of the series the integrands may be saved to allow the rapid computation of related transforms without recalculating the kernel or bessel functions and the integration steps use interlacing quadrature formulas so that no function evaluations are wasted when it is necessary to increase the order of the quadrature rule the continued fraction algorithm allows very slowly divergent or even formally divergent integrals to be computed quite easily the local error is controlled at each step in the algorithm and accuracy is limited largely by machine resolution the algorithm is written in fortran and is listed in an appendix along with a driver program that illustrates its features the driver program and subroutine are available from the seg business offtce

an efficient approach for the computation of 2 d green s functions with 1 d and 2 d periodicities in homogeneous media this paper presents an algorithm for the acceleration of the series involved in the computation of 2 d homogeneous green s functions with 1 d and 2 d periodicities the algorithm is based on an original implementation of the spectral kummer poisson s method and it can be applied to the efficient computation of a wide class of infinite series in the algorithm the number of asymptotic terms retained in kummer s transformation is externally controlled so that any of the series that has to be accelerated is split into one series with exponential convergence and another series with algebraic convergence of arbitrarily large order numerical simulations have shown that there is an ldquooptimumrdquo number of asymptotic terms retained in kummer s transformation for which the cpu time needed in the summation of the series is minimized the cpu times required by ewald s method for the evaluation of 2 d green s functions with 1 d and 2 d periodicities have been compared with those required by the present algorithm and the algorithm has been found to be between 1 2 and 3 times faster than ewald s method when working in ldquooptimumrdquo operation conditions

monotonicity considerations for saturated unsaturated subsurface flow it is demonstrated that monotonicity is a sufficient condition to ensure that no new nonphysical local maxima and minima can be produced in the discrete nonlinear unsaturated flow equation monotonicity conditions are derived for various types of weighting for the mobility term the basic discretization is of finite element type but the results can be extended to finite volume discretizations central weightings are only conditionally monotone while upstream weightings are unconditionally monotone sample computations are given for highly heterogeneous problems

fast computation of sommerfeld integral tails via direct integration based on double exponential type quadrature formulas a direct integration algorithm based on double exponential type quadrature rules is presented for the efficient computation of the sommerfeld integral tails arising in the evaluation of multilayered green s functions the proposed scheme maintains the error controllable nature of the so called partition extrapolation methods often used to tackle this problem whereas it requires substantially reduced computational time moreover the proposed method is very easy to implement since the associated weights and abscissas can be precomputed the overall behavior of the proposed method both in terms of accuracy and efficiency is demonstrated through a series of representative numerical experiments where compared with one of the most proven methods available in the literature

an efficient numerical evaluation of the green s function for the helmholtz operator on periodic structures abstract numerical methods which are based on boundary integral formulations require the numerical evaluation of the green s function associated with the problem in the case of periodic structures the green s function is often an infinite series this infinite series may converge slowly making numerical evaluation expensive here we present a practical computer implementation of a technique which dramatically speeds up the convergence of the infinite series green s function associated with the helmholtz operator to show the consequences of using this technique we include some numerical examples

the weighted averages algorithm revisited the classic weighted averages wa algorithm for the evaluation of sommerfeld like integrals is reviewed and reappraised as a result a new version of the wa algorithm called generalized wa is introduced the new version can be considered as a generalization of the well established holder and cesaro means used to sum divergent series generalized wa exhibits a more compact formulation devoid of iterative and recursive steps and a wider range of applications it is more robust as it provides a unique formulation valid for monotonic and oscillating functions the implementation of the new version is easier and more economical in terms of basic operations preliminary numerical examples show that generalized wa also outperforms in terms of accuracy the classic wa algorithm which is currently recognized as the most competitive algorithm to evaluate sommerfeld integral tails

an explicit unconditionally stable numerical solution of the advection problem in irrotational flow fields 1 a new methodology for the eulerian numerical solution of the advection problem is proposed the methodology is based on the conservation of both the zero and the first order spatial moments inside each element of the computational domain and leads to the solution of several small systems of ordinary differential equations since the systems are solved sequentially one element after the other the method can be classified as explicit the proposed methodology has the following properties 1 it guarantees local and global mass conservation 2 it is unconditionally stable and 3 it applies second order approximation of the concentration and its fluxes inside each element limitation of the procedure to irrotational flow fields for the 2 d and 3 d cases is discussed the results of three 1 d and 2 d literature tests are compared with those obtained using other techniques a new 2 d test with radially symmetric flow is also carried out

an asymptotic closed form representation for the grounded double layer surface green s function an efficient closed form asymptotic representation for the grounded double layer substrate superstrate green s function is presented the formulation is valid for both source a horizontal electric dipole and observation points anywhere inside the superstate or at the interfaces the asymptotic expressions are developed via a steepest descent evaluation of the original sommerfeld type integral representation of the green s function and the large parameter in this asymptotic development is proportional to the lateral separation between source and observation points the asymptotic solution is shown to agree with the exact green s function for lateral distances even as small as a few tenths of the free space wavelengths thus constituting a very efficient tool for analyzing printed circuits antennas since the asymptotic approximation gives separate contributions pertaining to the different wave phenomena it provides physical insight into the field behavior as shown by examples

finite element approximation of the diffusion operator on tetrahedra linear galerkin finite element discretizations of the laplace operator produce nonpositive stiffness coefficients for internal element edges of two dimensional delaunay triangulations this property also called the positive transmissibility pt condition is a prerequisite for the existence of an m matrix and ensures that nonphysical local extrema are not present in the solution for tetrahedral elements it has already been shown that the linear galerkin approach does not in general satisfy the pt condition we propose a modification of the three dimensional galerkin scheme that if a delaunay triangulation is used satisfies the pt condition for internal edges and if further conditions on the boundary are specified yields an m matrix the proposed approach can also be extended to the general diffusion operator with nonconstant or anisotropic coefficients

a mixed form thin stratified medium fast multipole algorithm for both low and mid frequency problems a mixed form thin stratified medium fast multipole algorithm is proposed for fast simulation of general microstrip structures at both low and mid frequencies the newly developed matrix friendly formula of layered medium green s function is applied in this algorithm for well separated interactions the path deformation technique is implemented to achieve a smoother and exponentially convergent integral the two dimensional addition theorem is then incorporated into the integrand to expedite the matrix vector product in our approach multipole expansion low frequency fast multiple algorithm as well as the plane wave expansion mid frequency fast multipole algorithm of the translational addition theorem are combined into a single multilevel tree to capture quasi static physics and wave physics simultaneously the outgoing wave is represented first in terms of multipole expansion at leafy levels and then switched to plane wave expansion automatically at higher levels this seamless connection makes the algorithm applicable in simulations where subwavelength interaction and wave physics both exist

an accurate derivation of spatial green s function for finite dielectric structures using characteristic green s function perfectly matched layer method a closed form spatial green s function for a truncated dielectric slab is derived by using a combination of the characteristic green s function cgf and perfectly matched layer pml method the original structure is terminated by pml that is backed by perfect electric conductor pec in semi infinite layer at the top and or bottom the eigenmodes of the closed structure by pml construct the continuous spectrum contribution of the original structure efficiently derived green s function is exact for separable finite structure while it is approximate for nonseparable one especially in the corners generalized scattering matrix gsm of truncating surface which contains possible conversions between all modes is computed with mode matching method it is demonstrated that by importing gsm in cgf formulation more exact results for nonseparable structures can be obtained the source and observation points dependence is analytically available in derived expression and allows very efficient computation and storage of the spatial green s function very close to the source where the large number of modes must be considered shank s transform is used to preserve the efficiency of the method the main advantage of the method lies in its accuracy and low dependency of the result to the pml parameters excellent agreements with the rigorous method of moments mom are shown in several examples

green s functions in lossy layered media integration along the imaginary axis and asymptotic behavior this paper presents an efficient technique for evaluating green s functions associated to layered media when formulated as sommerfeld integrals in the space domain the key step in the formulation is that sommerfeld integrals are computed choosing a suitable integration path which is closed through the imaginary axis of the complex spectral plane it is shown that with this original choice of the integration contour the numerical effort usually involved in the evaluation of sommerfeld integrals can be greatly reduced specially when large source observer distances are involved one asset of this technique is that it can be easily incorporated into integral equation based cad packages for the efficient analysis of complex printed microwave circuit and antennas in addition the theoretical developments needed to set up the numerical algorithm throw a new light on the asymptotic behavior of the layered media green s functions for large source observer distances

accelerating the convergence of series representing the free space periodic green s function a method for improving the convergence of the series representing the doubly periodic free space green s function is presented the method consists of successively applying three different transformations to the green s function spectral representation kummer s transformation is first applied to convert the slowly converging spectral representation into the sum of a rapidly converging series and a slowly converging series the latter series is recognized as the spectral representation of the original periodic source distribution radiating in a medium with an imaginary wavenumber application of the poisson transformation to this series renders it exponentially convergent since it effectively represents propagation of point source contributions through a medium with imaginary wavenumber finally shanks transform is plotted versus the number of terms taken in the series numerical results confirm that an improvement in the convergence rate of the series is achieved for a particular convergence criterion

the mast fv fe scheme for the simulation of two dimensional thermohaline processes in variable density saturated porous media a novel methodology for the simulation of 2d thermohaline double diffusive processes driven by heterogeneous temperature and concentration fields in variable density saturated porous media is presented the stream function is used to describe the flow field and it is defined in terms of mass flux the partial differential equations governing system is given by the mass conservation equation of the fluid phase written in terms of the mass based stream function as well as by the advection diffusion transport equations of the contaminant concentration and of the heat the unknown variables are the stream function the contaminant concentration and the temperature the governing equations system is solved using a fractional time step procedure splitting the convective components from the diffusive ones in the case of existing scalar potential of the flow field the convective components are solved using a finite volume marching in space and time mast procedure this solves a sequence of small systems of ordinary differential equations one for each computational cell according to the decreasing value of the scalar potential in the case of variable density groundwater transport problem where a scalar potential of the flow field does not exist a second mast procedure has to be applied to solve again the odes according to the increasing value of a new function called approximated potential the diffusive components are solved using a standard galerkin finite element method the numerical scheme is validated using literature tests

gaussian ring basis functions for the analysis of modulated metasurface antennas this paper presents a novel type of basis functions whose spectral and space domain properties can be exploited for the efficient method of moments mom analysis of planar metasurface mts antennas the effect of the homogenized mts is introduced in the integral equation as an impedance boundary condition ibc the proposed basis functions are shaped as gaussian type rings with small width and linear azimuthal phase the analytical form of the spectrum of the gaussian ring basis allows for a closed form evaluation of the mom impedance matrix s entries moreover these basis functions account for the global evolution of the surface current density in an effective manner reducing the size of the mom system of equations with respect to the case of subdomain basis functions these features allow one to carry out a direct solution for problems with a diameter of up to 15 wavelengths in less than 1 min using a conventional laptop the applicability on practical antennas has been tested through the full wave analysis of mts antennas implemented with small printed elements

electromagnetic modeling of three dimensional bodies in layered earths using integral equations we have developed an algorithm based on the method of integral equations to simulate the electromagnetic responses of three dimensional bodies in layered earths the inhomogeneities are replaced by an equivalent current distribution which is approximated by pulse basis functions a matrix equation is constructed using the electric tensor green s function appropriate to a layered earth and it is solved for the vector current in each cell subsequently scattered fields are found by integrating electric and magnetic tensor green s functions over the scattering currents efficient evaluation of the tensor green s functions is a major consideration in reducing computation time we find that tabulation and interpolation of the six electric and five magnetic hankel transforms defining the secondary green s functions is preferable to any direct hankel transform calculation using linear filters a comparison of responses over elongate three dimensional 3 d bodies with responses over two dimensional 2 d bodie

a new approach to dyadic green s function in spectral domain a new method is proposed to derive the dyadic green s function for stratified dielectric layers from the wave equation in spectral domain the result is a clear equivalent circuit of the whole structure which combines the te and tm modes by hybrid block matrices it is simple to apply and evaluate the relation to the conventional immittance approach is shown by means of a similarity transform which diagonalizes the submatrices the simplicity of the method is demonstrated in the application to the well known example of a single microstrip patch on a grounded dielectric layer as well as structures with multiple layers and metallizations in arbitrary interfaces

techniques for making finite elements competitve in modeling flow in variably saturated porous media a galerkin finite element formulation is developed for the numerical simulation of water flow in variably saturated soil systems included in this formulation is a solution strategy based on picard and newton raphson algorithms both algorithms are designed especially to cope with severely nonlinear field problems the two algorithms are formulated for both rectangular and triangular elements the element matrices are evaluated in a simple and efficient manner using a technique referred to as the influence coefficient technique this technique avoids numerical integration and leads to a substantial saving of computational cost four examples are presented to demonstrate the effectiveness of the present finite element approach these examples show that the nonlinear solution schemes are capable of accomodating cases involving large variations in the saturated hydraulic conductivity as well as highly nonlinear soil moisture characteristics a comparative study of the picard and the newton raphson algorithms is also provided the study indicates that despite the higher cost per iteration of the newton raphson scheme it usually requires a substantially smaller number of iterations than the picard scheme in some instances where convergence difficulties are experienced with the latter scheme it is desirable to use the newton raphson scheme in order to obtain a cost effective solution to the problem

regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions the boundary integral equations bies in their original forms which govern the electromagnetic em wave scattering in three dimensional space contain at least a hypersingularity 1 r sup 3 or a cauchy singularity 1 r sup 2 usually both thus obtaining reliable numerical solutions using such equations requires considerable care especially when developing systematic numerical integration procedures for realistic problems regularized bies for the numerical computation of time harmonic em scattering fields due to arbitrarily shaped scatterers are introduced two regularization approaches utilizing an isolation method plus a mapping are presented to remove all singularities prior to numerical integration both approaches differ from all existing approaches to em scattering problems both work for integral equations initially containing either hypersingularities or cauchy singularities without the need to introduce surface divergences or other derivatives of the em fields on the boundary also neither approach is limited to flat surfaces nor flat element models of curved surfaces the muller linear combination of the electric and magnetic field integral equations efie and mfie is used to avoid the resonance difficulty that is usually associated with integral equation based formulations some preliminary numerical results for em scattering due to single and multiple dielectric spheres are presented and compared with analytical solutions

on minimal sets of graded attribute implications we explore the structure of non redundant and minimal sets consisting of graded if then rules the rules serve as graded attribute implications in object attribute incidence data and as similarity based functional dependencies in a similarity based generalization of the relational model of data based on our observations we derive a polynomial time algorithm which transforms a given finite set of rules into an equivalent one which has the least size in terms of the number of rules

a comprehensive theory of trichotomous evaluative linguistic expressions in this paper a logical theory of the so called trichotomous evaluative linguistic expressions tev expressions is presented these are frequent expressions of natural language such as small very small roughly medium extremely big etc the theory is developed using the formal system of higher order fuzzy logic namely the fuzzy type theory generalization of classical type theory first we discuss informally what are properties of the meaning of tev expressions then we construct step by step axioms of a formal logical theory t e v of tev expressions and prove various properties of t e v all the proofs are syntactical and so our theory is very general we also outline construction of a canonical model of t e v the main elegancy of our theory consists in the fact that semantics of all kinds of evaluative expressions is modeled in a unified way we also prove theorems demonstrating that essential properties of the vagueness phenomenon can be captured within our theory

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

new expansions of bessel functions of first kind and complex argument we present accurate trigonometric expansions of bessel functions of first kind and integer order for complex arguments of the form j v z sum k alpha k s beta k z where alpha k and beta k are constants and s is a sinusoidal function using the new expansions varying levels of accuracy and range of applicability can be achieved by varying the number of terms in the expansions for example a four term expansion of j 0 z yields an average relative error of for vert z vert leq 2 pi and same accuracy is achieved for an eight term expansion for an extended range vert z vert leq 5 pi further a phase and amplitude corrected large argument asymptotic formula is studied such that the lower limit of its usage is reduced to medium magnitude ranges of arguments the new set of formulas can not only be incorporated into math libraries very easily but also be useful for treatment of radiation and scattering problems involving bessel functions

on expansions of wnm t norm based logics with truth constants this paper focuses on completeness results about generic expansions of propositional weak nilpotent minimum wnm logics with truth constants indeed we consider algebraic semantics for expansions of these logics with a set of truth constants r r c for a suitable countable c 0 1 and provide a full description of completeness results when i the t norm is a weak nilpotent minimum satisfying the finite partition property and ii the set of truth constants covers all the unit interval in the sense that each interval of the partition contains values of c in its interior

the continuous galerkin method is locally conservative we examine the conservation law structure of the continuous galerkin method we employ the scalar advection diffusion equation as a model problem for this purpose but our results are quite general and apply to time dependent nonlinear systems as well in addition to global conservation laws we establish local conservation laws which pertain to subdomains consisting of a union of elements as well as individual elements these results are somewhat surprising and contradict the widely held opinion that the continuous galerkin method is not locally conservative

closed form green s function of a 2 d rectangular room closed form enough accurate green s function for wave propagation modeling in a rectangular 2 d room is presented using the characteristic green s function technique this green s function is first developed in an integral form then its spatial domain closed form is obtained using three fast methods in the first method the integral is computed by the stationary phase method in the second one the integral is computed analytically by expanding the integrand into a complex exponential series in the third method the integrand is approximated by a series of rational functions and the integral is computed using cauchy s residue theorem the results of these three methods are studied and compared in an example the results show that the methods are fast while preserving accuracy

efficient evaluation of the finite part of pole free sommerfeld integrals in half space problems with predefined accuracy this communication presents a novel simple and robust approach for the computation of the finite part of pole free sommerfeld integrals sis in half space problems with high and controllable accuracy over a large range of source observer distances the approach includes the following techniques 1 cancellation of the branch point singularities based on the square root change of variables for numerical integration 2 approximation of real axis integration path in order to enhance the singularity cancellation for arbitrary low loss dielectrics 3 thresholds for truncation of the interval of integration for given accuracy which improve the efficiency of computation and 4 prediction formulas that estimate the required number of integration points for a given accuracy up to 1000 wavelengths of source observer distance the proposed approach is verified through numerical examples and comparison to reference methods

constraint heterogeneous concept lattices and concept lattices with heterogeneous hedges the paper deals with the isomorphism between the constraint heterogeneous concept lattices and concept lattices with heterogeneous hedges the essential point of the former approach encompasses the full diversification of data structures within a formal context in particular we use a different complete lattice for diverse objects a different complete lattice for diverse attributes and a different poset for diverse matrix fields the latter framework with heterogeneous hedges results in a reduction in the size of the corresponding concept lattice we present the properties of constraint heterogeneous approach that is associated with the fixpoints of hedges and we add remarks to the related studies

clarification of issues on the closed form green s functions in stratified media the closed form green s functions cfgf derived for the vector and scalar potentials in planar multilayer media have been revisited to clarify some issues and misunderstandings on the derivation of these green s functions in addition the range of validity of these green s functions is assessed with and without explicit evaluation of the surface wave contributions as it is well known the derivation of the cfgf begins with the approximation of the spectral domain green s functions by complex exponentials and continues with applying the sommerfeld identity to cast these approximated spectral domain green s functions into the space domain in closed forms questions and misunderstandings of this derivation which have mainly originated from the approximation process of the spectral domain green s functions in terms of complex exponentials can be categorized and discussed under the topics of 1 branch point contributions 2 surface wave pole contributions and 3 the accuracy of the obtained cfgf when these issues are clarified the region of validity of the cfgf so obtained may be defined better therefore in this paper these issues will be addressed first and then their origins and possible remedies will be provided with solid analysis and numerical demonstrations

mixed finite elements and newton type linearizations for the solution of richards equation we present the development of a two dimensional mixed hybrid finite element mhfe model for the solution of the non linear equation of variably saturated flow in groundwater on unstructured triangular meshes by this approach the darcy velocity is approximated using lowest order raviart thomas rt0 elements and is exactly mass conserving hybridization is used to overcome the ill conditioning of the mixed system the scheme is globally first order in space nevertheless numerical results employing non uniform meshes show second order accuracy of the pressure head and normal fluxes on specific grid points the non linear systems of algebraic equations resulting from the mhfe discretization are solved using picard or newton iterations realistic sample tests show that the mhfe newton approach achieves fast convergence in many situations in particular when a good initial guess is provided by either the picard scheme or relaxation techniques copyright 1999 john wiley sons ltd

multilayered media green s functions in integral equation formulations a compact representation is given of the electric and magnetic type dyadic green s functions for plane stratified multilayered uniaxial media based on the transmission line network analog along the aids normal to the stratification furthermore mixed potential integral equations are derived within the framework of this transmission line formalism for arbitrarily shaped conducting or penetrable objects embedded in the multilayered medium the development emphasizes laterally unbounded environments but an extension to the case of a medium enclosed by a rectangular shield is also included

a new mass lumping scheme for the mixed hybrid finite element method diffusion type partial differential equation is a common mathematical model in physics solved by mixed finite elements it leads to a system matrix which is not always an m matrix therefore the numerical solution may exhibit unphysical results due to oscillations the criterion necessary to obtain an m matrix is discussed in details for triangular rectangular and tetrahedral elements it is shown that the system matrix is never an m matrix for rectangular elements and can be an m matrix for triangular an tetrahedral elements if criteria on the element s shape and on the time step length are fulfilled a new mass lumping scheme is developed which leads to a less restrictive criterion the discretization must be weakly acute all angles less than 2 and there is no constraint on the time step length the lumped formulation of mixed hybrid finite element can be applied not only to triangular meshes but also to more general shape elements in two and three dimensions numerical experiments show that compared to the standard mixed hybrid formulation the lumping scheme avoids or strongly reduce oscillations and does not create additional numerical errors copyright 2006 john wiley sons ltd

development and evaluation of closed form expressions for hysteretic soil hydraulic properties a concise representation of hysteretic soil hydraulic properties is given based on a combination of m t van genuchten s 1980 parametric k h model and p s scott et al s 1983 empirical hysteresis model modified to account for air entrapment the resulting model yields compact closed form expressions for the hysteretic water retention curve h and soil water capacity c h as well as for the hydraulic conductivity function k h depending on the degree of simplification involved the model entails a total of 6 9 parameters which can be calibrated from direct measurements of h and saturated conductivity or by an inverse solution approach from transient flow experiments comparison of model predicted and measured k h relations for eight soils revealed one case in which model predictions were very poor model accuracy was judged to be acceptably good in the other cases mualern s modified y mualem 1984 dependent domain model was found to be more accurate for soils with very narrow pore size distributions use of a simplified version of the proposed model with two parameters eliminated provided overall accuracy very similar to that of the more complex model numerical simulations of flow during transient infiltration and drainage using the proposed model and a variant of y mualem s 1984 modified dependent domain model did not differ greatly and agreed reasonably well with experimental water content distributions even when scanning curves were not described very accurately by contrast simulations without consideration of hysteresis produced highly unacceptable results it is concluded that the proposed model provides a convenient and simple means of incorporating hysteretic effects into numerical flow models to provide significant improvement in prediction accuracy with little additional effort and with minimal data requirements

generalized pencil of function method for extracting poles of an em system from its transient response a generalized pencil of function gpof method is developed for extracting the poles of an electromagnetic system from its transient response the gpof method needs the solution of a generalized eigenvalue problem to find the poles subspace decomposition is also used to optimize the performance of the gpof method the gpof method has advantages over the prony method in both computation and noise sensitivity and approaches the cramer rao bound when the signal to noise ratio snr is above threshold an application of the gpof method to a thin wire target is presented

the maximum principle violations of the mixed hybrid finite element method applied to diffusion equations the affluent literature of finite element methods applied to linear parabolic problems generally produces numerical procedures with satisfactory properties from a numerical approximation point of view however some initial boundary conditions or abrupt sink source terms may cause large gradients at some points and consequently jumps in the solution that usually needs a certain period of time to become more and more smooth this intuitive fact of the diffusion process necessitates when applying numerical methods varying the mesh size in time and space according to the smoothness of the solution in this work the numerical behavior of the time dependent solutions for such problems during small time duration obtained by using the mixed hybrid finite element method mhfem is investigated numerical comparisons with the standard galerkin finite element fe as well as the finite difference fd methods are checked up on due to the fact that the mixed methods violate the discrete maximum principle some numerical experiments showed that the mhfem leads sometimes to non physical peaks in the solution a diffusivity criterion relating the mesh steps for an artificial initial boundary value problem will be presented one of the propositions given to avoid any non physical oscillations is to use the mass lumping techniques

algorithms for solving richards equation for variably saturated soils previous work has shown that a one dimensional water content based finite difference algorithm can offer improved cpu efficiency in modeling infiltration into very dry heterogeneous soil when compared to similar pressure based algorithms the usefulness of the water content based method is limited however since it cannot be applied to saturated soils in this paper we develop two new methods which retain the advantages of water content based methods while still permitting fully saturated conditions in the first method we define a new variable for the transformed richards equation which has the characteristics of water content when soil is unsaturated and of pressure when soil is at or near saturation in addition to the transformed richards equation method an improved pressure based method which uses flux updating is presented both methods are implemented in algorithms using a preconditioned conjugate gradient method equation solver the performance of the algorithms is compared to that of an algorithm based on a mixed form of richards equation using modified picard iteration two test cases are examined the first test case examines two dimensional infiltration into very dry heterogeneous soil which remains unsaturated throughout the simulation period the second test case examines a two dimensional developing perched water table results indicate that the new methods retain the advantages of the water content based method for fully unsaturated heterogeneous problems while allowing for fully saturated conditions for the unsaturated problem the new algorithms were from 16 to 59 times faster than the algorithm based on the mixed form of richards equation using modified picard iteration for the saturated problem the new algorithms were from 6 to 25 times faster than the mixed base algorithm results also indicate that the performance of the mixed base algorithm could be significantly improved if a more effective adaptive time step were developed

complex plane generalization of scalar levin transforms a robust rapidly convergent method to compute potentials and fields in multi layered media abstract we propose the complex plane generalization of a powerful algebraic sequence acceleration algorithm the method of weighted averages mwa to guarantee exponential cum algebraic convergence of fourier and fourier hankel f h integral transforms this complex plane mwa effected via a linear path detour in the complex plane results in rapid absolute convergence of field and potential solutions in multi layered environments regardless of the source observer geometry and anisotropy loss of the media present in this work we first introduce a new integration path used to evaluate the field contribution arising from the radiation spectra subsequently we 1 exhibit the foundational relations behind the complex plane extension to a general levin type sequence convergence accelerator 2 specialize this analysis to one member of the levin transform family the mwa 3 address and circumvent restrictions arising for two dimensional integrals associated with wave dynamics problems through minimal complex plane detour restrictions and a novel partition of the integration domain 4 develop and compare two formulations based on standard real axis mwa variants and 5 present validation results and convergence characteristics for one of these two formulations

extension and optimization of the axisymmetric 2 5 d eigensolver toward far field calculations in stratified backgrounds we extend and optimize the axisymmetric 2 5 d eigensolver to calculate the far field results of axisymmetric structures in stratified backgrounds sbs which is useful and practical for optical design and engineering two kinds of near field to far field transformations nfffts are proposed one is called closed surface transformation which is based on the dipole radiations in sbs the other is called open surface transformation which is based on the analytic continuation this transformation can provide the far field results of any axisymmetric structure including backgrounds the far field results achieved by these two transformations are in good agreement with each other and with analytical ones moreover in order to obtain accurate near field results we optimize the perfectly matched layer pml setting of the 2 5 d eigensolver corresponding optimization rules are proposed and discussed

variety theorem for algebras with fuzzy orders abstract we present generalization of the bloom variety theorem of ordered algebras in fuzzy setting algebras with fuzzy orders consist of sets of functions which are compatible with fuzzy orders fuzzy orders are defined on universe sets of algebras using complete residuated lattices as structures of degrees in this setting we show that classes of models of fuzzy sets of inequalities are closed under suitably defined formations of subalgebras homomorphic images and direct products conversely we prove that classes having these closure properties are definable by fuzzy sets of inequalities

analytical expressions for spatial domain green s functions in layered media accurate and efficient formulas for computing spatial domain green s functions are presented in this paper to apply the formulas we only require a set of sample points of the spectral domain green s function sdgf on an integration path avoiding its singularities and an infinite domain tail path since the sampling is carried out for the integrand excluding the bessel function the number of sample points required is much smaller than the numerical integration method this aspect of the proposed method proves to be very advantageous for evaluating closed form green s functions at large source observer distances it is shown that the proposed formulas provide accurate results for both the near and far field regions as well as a wide range of material parameters such as lossless lossy left handed materials as well as multilayered substrates

time domain integral equation solver for planar circuits over layered media using finite difference generated green s functions a simple highly accurate and efficient 2d finite difference technique for computing the direct convolution of time domain green s functions tdgfs of layered media with temporal interpolators is presented the proposed tdgfs are incorporated into a recently developed marching on in time mot based time domain integral equation tdie solver based on noncausal high order b spline temporal interpolators without requiring the prediction of future unknowns numerical results demonstrating the applicability of the technique to the analysis of various microwave structures are presented

conservative p 1 conforming and nonconforming galerkin fems effective flux evaluation via a nonmixed method approach given a p1 conforming or nonconforming galerkin finite element method gfem solution ph which approximates the exact solution p of the diffusion reaction equation nabla cdot mathcal k nabla p alpha p f with full tensor variable coefficient mathcal k we evaluate the approximate flux uh to the exact flux bf u mathcal k nabla p by a simple but physically intuitive formula over each finite element the flux is sought in the continuous in normal component or the discontinuous raviart thomas space a systematic way of deriving such a formula is introduced this direct method retains local conservation property at the element level typical of mixed methods finite element or finite volume type but avoids solving an indefinite linear system in short the present method retains the best of the gfem and the mixed method but without their shortcomings thus we view our method as a conservative gfem and demonstrate its equivalence to a certain mixed finite volume box method the equivalence theorems explain how the pressure can decouple basically cost free from the mixed formulation the accuracy in the flux is of first order in the h dive omega norm numerical results are provided to support the theory

contour fft based spectral domain mbf analysis of large printed antenna arrays a fast spectral domain method is proposed to evaluate the reaction terms between the macro basis functions in regular and non regular arrays made of identical printed antennas the presented technique first exploits the filtering capabilities of the macro basis functions in the spectral domain the method is then strongly accelerated with the help of a newly formulated fast fourier transform fft based technique which is applicable to a contour integration in the complex plane we name the method as contour fft c fft besides an effective homogeneous medium term treated with multipoles a computational complexity of order n log2 n is achieved for the tabulation of substrate related reaction terms for any possible relative positions the complexity of the proposed method is independent from the complexity of the elements numerical results obtained with the proposed method are compared with those from a pre validated reference solution based on the traditional macro basis functions technique an excellent agreement is observed

godel logics with monotone operators we consider the extension of godel logic by a unary operator interpreted by functions on the unit interval with certain monotonicity properties we prove that validity of propositional formulas is decidable by giving a sound and complete proof system with finitely many axioms we show also how to transfer the deduction theorem the lifting lemma and the agreement of entailment and 1 entailment from godel logic to the propositional fragment of our extension finally we prove an enumerability result for a ring normal prenex fragment

spectral domain iterative analysis of single and double layered microstrip antennas using the conjugate gradient algorithm an analysis for single and double layered microstrip antennas is described the planarity of these structures makes it possible to construct a general spectral representation for any number of layers and to derive the spectral green s dyad in a compact fashion using a transmission line analogy a formulation of the antenna problem in the spectral domain incorporating this dyad is coupled with the conjugate gradient algorithm whose applicability as an efficient way of analyzing a number of microstrip antennas is studied results are quite accurate conclusions pertaining to the applicability of the method including effects of problem parameters on convergence rates are drawn

fuzzy logic programming reduced to reasoning with attribute implications abstract we present a link between two types of logic systems for reasoning with graded if then rules the system of fuzzy logic programming flp in sense of vojtas and the system of fuzzy attribute logic fal in sense of belohlavek and vychodil we show that each finite theory consisting of formulas of fal can be represented by a definite program so that the semantic entailment in fal can be characterized by correct answers for the program conversely we show that for each definite program there is a collection of formulas of fal so that the correct answers can be represented by the entailment in fal using the link we can transport results from fal to flp and vice versa which gives us e g a syntactic characterization of correct answers based on pavelka style armstrong like axiomatization of fal we further show that entailment in flp is reducible to reasoning with boolean attribute implications and elaborate on related issues including properties of least models

a comparison of picard and newton iteration in the numerical solution of multidimensional variably saturated flow problems picard iteration is a widely used procedure for solving the nonlinear equation governing flow in variably saturated porous media the method is simple to code and computationally cheap but has been known to fail or converge slowly the newton method is more complex and expensive on a per iteration basis than picard and as such has not received very much attention its robustness and higher rate of convergence however make it an attractive alternative to the picard method particularly for strongly nonlinear problems in this paper the picard and newton schemes are implemented and compared in one two and three dimensional finite element simulations involving both steady state and transient flow the eight test cases presented highlight different aspects of the performance of the two iterative methods and the different factors that can affect their convergence and efficiency including problem size spatial and temporal discretization initial solution estimates convergence error norm mass lumping time weighting conductivity and moisture content characteristics boundary conditions seepage faces and the extent of fully saturated zones in the soil previous strategies for enhancing the performance of the picard and newton schemes are revisited and new ones are suggested the strategies include chord slope approximations for the derivatives of the characteristic equations relaxing convergence requirements along seepage faces dynamic time step control nonlinear relaxation and a mixed picard newton approach the tests show that the picard or relaxed picard schemes are often adequate for solving richards equation but that in cases where these fail to converge or converge slowly the newton method should be used the mixed picard newton approach can effectively overcome the newton scheme s sensitivity to initial solution estimates while comparatively poor performance is reported for the various chord slope approximations finally given the reliability and efficiency of current conjugate gradient like methods for solving linear nonsymmetric systems the only real drawback of using newton rather than picard iteration is the algebraic complexity and computational cost of assembling the derivative terms of the jacobian matrix and it is suggested that both methods can be effectively implemented and used in numerical models of richards equation

complex time representation of the sommerfeld type integrals and its application to 1 d periodic structures the concept of complex time is employed to derive the time domain representation of the green s function of a periodic structure for the first time the spatial domain green s function of the periodic structure in the frequency domain is separated into singular and nonsingular terms the nonsingular terms are approximated by using exponential functions resulting in the well known complex time representation of the time domain green s function in order to find a closed form expression for the singular terms a novel time domain representation of the sommerfeld type integrals is derived the proposed procedure is applied to the computation of the time domain green s function of a one dimensional periodic structure numerical experiments demonstrate the high accuracy of this method

two dimensional exponential fitting and applications to drift diffusion models a class of methods is introduced that generalizes the so called exponential fitting method to two dimensional problems and more specifically to equations of the type operatorname div underset raise0 3em hbox smash scriptscriptstyle nabla u u underset raise0 3em hbox smash scriptscriptstyle nabla psi f with psi given and underset raise0 3em hbox smash scriptscriptstyle nabla psi big in a part of the domain the basic idea is the following i write the equation as operatorname div e psi underset raise0 3em hbox smash scriptscriptstyle nabla rho f through the change of variables u rho e psi ii discretize the symmetric equation by means of a method that uses some kind of harmonic average for the coefficient e psi mixed hybrid etc iii write the discrete scheme in terms of the nodal values of u e psi rho this produces an m matrix

analysis of stacked microstrip patches with a mixed potential integral equation a method based on the mixed potential integral equation for the analysis of flat microstrip antennas in a double layer substrate is presented the method is used to compute the input impedance of a stacked patch configuration this structure permits a larger bandwidth and may also provide dual frequency operation the green s functions are discussed in detail and numerical results are obtained for the propagation constant of the dominant surface wave theoretical and experimental results are compared for a dual frequency and a broadband stacked patch antenna theoretical results for the input impedance are in good agreement with measurements the difference between theoretical and experimental results for the resonant frequency is less than 4 5 in all cases

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 analysis of arbitrarily shaped aperture coupled patch antennas via a mixed potential integral equation a mixed potential integral equation mpie is formulated for the electric and magnetic currents on a multilayered aperture coupled patch antenna the integral equation is solved via the method of moments mom using subsectional basis functions that allow the analysis of nonrectangular aperture and patch shapes the input impedance and radiation efficiency of various aperture coupled elements are calculated using the proposed technique and compared to measured results the advantages and disadvantages of several aperture and patch configurations are discussed and six methods of numerically de embedding the element s input impedance are compared

spectral dyadic green s function formulation for planar integrated structures the problem of the complete determination of the dyadic spectral green s function for an integrated planar structure with a grounded dielectric slab has been considered and solved in a rigorous way by using the spectral theory of the electromagnetic field the reciprocity theorem and the geometrical symmetry of the structure have demonstrated the different roles played by the independent terms of the spectral green s function in the evaluation of the electromagnetic characteristics of the grounded slab excited with a general source furthermore an equivalent circuit representation of the structure allowing a noteworthy simplification in the determination of the total power has been obtained these equivalent circuits and the derived spectral green s function presented here can be used to analyze and design microstrip antennas of arbitrary shape with a general type of loading such as matched or unmatched loads parasitic and shorting pins

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

a logical approach to fuzzy truth hedges the starting point of this paper are the works of hajek and vychodil on the axiomatization of truth stressing and depressing hedges as expansions of hajek s bl logic by new unary connectives they showed that their logics are chain complete but standard completeness was only proved for the expansions over godel logic we propose weaker axiomatizations over an arbitrary core fuzzy logic which have two main advantages i they preserve the standard completeness properties of the original logic and ii any subdiagonal resp superdiagonal non decreasing function on 0 1 preserving 0 and 1 is a sound interpretation of the truth stresser resp depresser connectives hence these logics accommodate most of the truth hedge functions used in the literature about of fuzzy logic in a broader sense

parameterizing the semantics of fuzzy attribute implications by systems of isotone galois connections we study the semantics of fuzzy if then rules called fuzzy attribute implications parameterized by systems of isotone galois connections the rules express dependences between fuzzy attributes in object attribute incidence data the proposed parameterizations are general and include as special cases the parameterizations by linguistic hedges used in earlier approaches we formalize the general parameterizations propose bivalent and graded notions of semantic entailment of fuzzy attribute implications show their characterization in terms of least models and complete axiomatization and provide characterization of bases of fuzzy attribute implications derived from data

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

a robust method for the computation of green s functions in cylindrically stratified media closed form green s functions for cylindrically stratified media are derived in terms of spherical waves and surface wave contributions the methodology is based on a two level approximation of the spectral domain green s functions in the first step the large argument behavior of the zeroth order hankel functions is used for the extraction of the quasistatic images from the spectral domain green s functions with the use of the sommerfeld identity in the second step the remaining part of the green s functions are approximated in terms of pole residue expressions via the rational function fitting method this robust efficient and fully numerical approach does not call for an analytical cumbersome extraction of the surface wave poles prior to the spectrum fitting moreover it can be applied in both the near and far field numerical results for the green s functions of one layer and two layer structures are presented to verify the accuracy and efficiency of this approach

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

the mast edge centred lumped scheme for the flow simulation in variably saturated heterogeneous porous media a novel methodology is proposed for the solution of the flow equation in a variably saturated heterogeneous porous medium the computational domain is descretized using triangular meshes and the governing pdes are discretized using a lumped in the edge centres numerical technique the dependent unknown variable of the problem is the piezometric head a fractional time step methodology is applied for the solution of the original system solving consecutively a prediction and a correction problem a scalar potential of the flow field exists and in the prediction step a marching in space and time mast formulation is applied for the sequential solution of the ordinary differential equation of the cells ordered according to their potential value computed at the beginning of the time step in the correction step the solution of a large linear system with order equal to the number of edges is required a semi analytical procedure is also proposed for the solution of the prediction step the computational performance the order of convergence and the mass balance error have been estimated in several tests and compared with the results of other literature models

resonance frequency of a rectangular microstrip patch the microstrip patch resonant frequency problem is formulated in terms of an integral equation using vector fourier transforms using galerkins s method in solving the integral equation the resonant frequency of the microstrip patch is studied with both chebyshev polynomials and sinusoidal functions as basis functions in the case of the chebyshev polynomials the edge singularity is included but it is not important for convergence furthermore the resonant frequency of the microstrip patch is ascertained with a perturbation calculation the results for galerkin s method and experiments are in good agreement the perturbation calculation agrees asymptotically with galerkin s method with the aim of developing a computer aided design formula the solutions obtained by galerkin s method are interpolated with a three variable polynomial

computing sets of graded attribute implications with witnessed non redundancy in this paper we extend our previous results on sets of graded attribute implications with witnessed non redundancy we assume finite residuated lattices as structures of truth degrees and use arbitrary idempotent truth stressing linguistic hedges as parameters which influence the semantics of graded attribute implications in this setting we introduce algorithm which transforms any set of graded attribute implications into an equivalent non redundant set of graded attribute implications with saturated consequents whose non redundancy is witnessed by antecedents of the formulas as a consequence we solve the open problem regarding the existence of general systems of pseudo intents which appear in formal concept analysis of object attribute data with graded attributes and linguistic hedges furthermore we show a polynomial time procedure for determining bases given by general systems of pseudo intents from sets of graded attribute implications which are complete in data

robust solution of richards equation for nonuniform porous media capillary pressure saturation relative permeability relations described using the van genuchten 1980 and mualem 1976 models for nonuniform porous media lead to numerical convergence difficulties when used with richards equation for certain auxiliary conditions these difficulties arise because of discontinuities in the derivative of specific moisture capacity and relative permeability as a function of capillary pressure convergence difficulties are illustrated using standard numerical approaches to simulate such problems we investigate constitutive relations interblock permeability nonlinear algebraic system approximation methods and two time integration approaches an integral permeability approach approximated by hermite polynomials is recommended and shown to be robust and economical for a set of test problems which correspond to sand loam and clay loam media