nonlinear eigenvalues for anisotropic quasilinear degenerate elliptic equations abstract we consider the dirichlet problem for a class of anisotropic degenerate elliptic equations

resolution of a system of the max product fuzzy relation equations using lou factorization in this paper the lu factorization is extended to the fuzzy square matrix with respect to the max product composition operator called l u factorization equivalently we will find two fuzzy lower and upper triangular matrices l and u for a fuzzy square matrix a such that a l u where is the max product composition an algorithm is presented to find the matrices l and u furthermore some necessary and sufficient conditions are proposed for the existence and uniqueness of the l u factorization for a given fuzzy square matrix a an algorithm is also proposed to find the solution set of a square system of fuzzy relation equations fre using the l u factorization the algorithm finds the solution set without finding its minimal solutions and maximum solution it is shown that the two algorithms have a polynomial time complexity as o n 3 since the determination of the minimal solutions is an np hard problem the algorithm can be very important from the practical point of view

a novel scheme for the solution of the time domain integral equations of electromagnetics a new method to numerically solve time domain integral equations pertinent to electromagnetic surface scattering phenomena is presented the method uses approximate prolate spheroidal wave functions and standard rao wilton glisson basis functions to effect the temporal and spatial discretization of the integral equations respectively because the temporal basis functions are noncausal an extrapolation scheme is used to construct a system of equations that can be solved by marching on in time numerical results show that the proposed method is stable and that its solutions converge exponentially fast with the time bandwidth product of the approximate prolate spheroidal wave functions to results from a frequency domain method of moments solver that uses spatial basis functions and integration rules identical to those in the time domain solver

quasilinear elliptic problems interacting with its asymptotic spectrum under suitable assumptions on the coefficients of the matrix a x u and on the nonlinear term f x u we study the quasilinear problem in bounded domains rn div a x u u f x u x u 0 x we extend the semilinear results of landesman lazer j math mech 19 1970 609 and of ambrosetti prodi in a primer on nonlinear analysis cambridge university press cambridge 1993 for resonant problems the existence of positive solution is also considered extending to the quasilinear case the classical result by ambrosetti rabinowitz j funct anal 14 1973 349 in this case the result is obtained as a corollary of the previous multiplicity result in the ambrosetti prodi framework

interpolation of fuzzy data analytical approach and overview we propose a general framework for the interpolation problem our framework stems from the classical elaboration of the problem we introduce the notion of an interpolating fuzzy function and show how this function can be characterized we examine and analyze previously published fuzzy interpolation algorithms to choose those algorithms that can be represented analytically we also propose an analytic solution of the interpolation problem that unifies various algorithmic approaches

a method of moments approach for the efficient and accurate modeling of moderately thick cylindrical wire antennas this paper introduces a moment method formulation which is capable of accurately modeling moderately thick cylindrical wire antennas new algorithms are presented for the efficient computation of the cylindrical wire kernel and related impedance matrix integrals these algorithms make use of exact series representations as well as efficient numerical procedures and lead to a significant reduction in overall computation time for thicker wires another major advantage of this moment method technique is that it is no longer restricted by the segment length to radius ratio limitations inherent in past formulations thereby making it possible to achieve solution convergence for a much wider class of wire antenna structures several examples illustrating the superior convergence properties of this new moment method formulation are presented and discussed

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

solvability and unique solvability of max min fuzzy equations abstract the problem of solvability and the problem of unique solvability of a fuzzy relation equation in an arbitrary max min algebra are considered and corresponding necessary and sufficient conditions are presented the results allow to solve both problems by an o mnp algorithm where m n p are the dimensions of the corresponding relations in the equation the existence of the greatest and of the least solution is also considered

convergence properties of higher order modeling of the cylindrical wire kernel extensive analysis of wire antennas using method of moments mom has been performed over the past decades despite the thorough understanding and widespread use of the wire antennas higher order modeling of wire structures has received little to no attention over the years this may be because the inaccuracies associated with the classic reduced kernel approach used to analyze wire antennas have precluded the use of higher order basis functions this paper combines a new method for computing integrating the cylindrical wire kernel with higher order basis functions for the accurate modeling of wire antennas numerical results demonstrate the higher order convergence of the approach

on the multiplicity of the solution set of some nonlinear boundary value problems ii on considere le probleme non lineaire lu f u s 1 h dans u 0 sur soit h l 2 f est de classe c et que f 1 et n f n 1 n 1 alors il existe s 0 tel que pour tout s s 0 l equation a au moins 2 solutions si n est impair et 3 solutions si n est pair

singularity evaluation of the straight wire mixed potential integral equation in the method of moments procedure a rigorous treatment on the computation of the various integrals that arise in the method of moments mom formulation of the straight wire electric field integral equation is provided for triangle basis functions along with delta function pulse or triangle weights particular attention is given to integrals whose integrands are weakly singular a singularity extraction technique is employed that splits the integral under question into two parts one that is numerically integrable and one that is analytically integrable closed form approximations based on taylor series techniques are also provided for the former these approximations are very robust resulting in errors less than 0 1 when 2 1 here is the length of a single mom segment and is the wire radius results are compared with data from the literature to demonstrate the robustness of the presented approach for fat wires

logical structure of fuzzy if then rules abstract this paper provides a logical basis for manipulation with fuzzy if then rules our theory is wide enough and it encompasses not only finding a conclusion by means of the compositional rule of inference due to lotfi a zadeh but also other kinds of approximate reasoning methods e g perception based deduction provided that there exists a possibility to characterize them within a formal logical system in contrast with other approaches employing variants of multiple valued first order logic the approach presented here employs fuzzy type theory of v novak which has sufficient expressive power to present the essential concepts and results in a compact elegant and justifiable form within the effectively formalized representation developed here based on a complete logical system it is possible to reconstruct numerous well known properties of cri related fuzzy inference methods albeit not from the analytic point of view as usually presented but as formal derivations of the logical system employed the authors are confident that eventually all relevant knowledge about fuzzy inference methods based on fuzzy if then rule bases will be represented formalized and backed up by proof within the well founded logical representation presented here an immediate positive consequence of this approach is that suddenly all elements of a fuzzy inference method based on fuzzy if then rules are first class citizens of the representation there are clear logically founded definitions for fuzzy if then rule bases to be consistent complete or independent

finitary solvability conditions for systems of fuzzy relation equations in this paper we consider the problem of solving systems of fuzzy relation equations two types of these systems with different compositions are considered and processed simultaneously a new sufficient condition and new solvability criteria are proposed for systems of both types all these conditions are finitary and thus can be easily verified the sufficient condition and criteria of solvability characterize a relationship between a skeleton nxn matrix n is a number of equations and a vector of the right hand side

higher order interpolatory vector bases for computational electromagnetics low order vector basis functions compatible with the nedelec 1980 representations are widely used for electromagnetic field problems higher order functions are receiving wider application but their development is hampered by the complex procedures used to generate them and lack of a consistent notation for both elements and bases in this paper fully interpolatory higher order vector basis functions of the nedelec type are defined in a unified and consistent manner for the most common element shapes it is shown that these functions can be obtained as the product of zeroth order nedelec representations and interpolatory polynomials with specially arranged arrays of interpolation points the completeness properties of the vector functions are discussed and expressions for the vector functions of arbitrary polynomial order are presented sample numerical results confirm the faster convergence of the higher order functions

on the ambrosetti prodi problem for non variational elliptic systems we study the ambrosetti prodi problem for nonlinear elliptic equations and systems with uniformly elliptic operators in non divergence form and non smooth coefficients and with non linearities with linear or power growth

application of curvilinear basis functions and mlfma for radiation and scattering problems involving curved pec structures the curvilinear surface and wire basis functions have been applied to solve radiation and scattering problems of various shapes of curved metallic structures with the method of moments however a suitable form of junction basis function that can connect the curvilinear wire and the curvilinear rao wilton glisson rwg surface basis functions has not been found we present a novel curvilinear junction basis function that can fill the gap the convergence tests reveal that the curvilinear junction basis function in conjunction with curvilinear wire and surface basis functions can reduce the radar cross section rcs error by one order of magnitude more than their reduced linear forms for a curved structure the curvilinear basis functions are applied to solve the radiation from wire antennas attached to curved surfaces we will demonstrate that the curvilinear basis functions with the multilevel fast multipole algorithm can significantly reduce the computational resources for simulating electrically large objects with curved features

evaluation of potential and impedance integrals in analysis of axially symmetric metallic structures to prescribed accuracy up to machine precision this paper presents a novel method for evaluating potential and impedance integrals appearing in the method of moment analysis of arbitrary axially symmetric metallic structures based on exact wire kernel and higher order bases due to new variable transforms proposed for singularity cancellation and smoothing the integrands high accuracy up to machine precision is achieved using relatively small number of integration points simple formulas are determined for predicting a number of integration points needed for prescribed accuracy benefits of high precision evaluation of impedance integrals are illustrated on a number of numerical examples

fuzzy rule base ensemble generated from data by linguistic associations mining as there are many various methods for time series prediction developed but none of them generally outperforms all the others there always exists a danger of choosing a method that is inappropriate for a given time series to overcome such a problem distinct ensemble techniques that combine several individual forecasts are being proposed in this contribution we employ the so called fuzzy rule based ensemble this method is constructed as a linear combination of a small number of forecasting methods where the weights of the combination are determined by fuzzy rule bases based on time series features such as trend seasonality or stationarity for identification of fuzzy rule bases we use the linguistic association mining a huge experimental justification is provided

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

higher order frequency domain computational electromagnetics a review of the higher order computational electromagnetics cem for antenna wireless and microwave engineering applications is presented higher order cem techniques use current field basis functions of higher orders defined on large e g on the order of a wavelength in each dimension curvilinear geometrical elements which greatly reduces the number of unknowns for a given problem the paper reviews all major surface volume integral and differential equation electromagnetic formulations within a higher order computational framework focusing on frequency domain solutions with a systematic and unified review of generalized curved parametric quadrilateral triangular hexahedral and tetrahedral elements and various types of higher order hierarchical and interpolatory vector basis functions in both divergence and curl conforming arrangements a large number of actual higher order techniques representing various combinations of formulations elements bases and solution procedures are identified and discussed the examples demonstrate the accuracy efficiency and versatility of higher order techniques and their advantages over low order discretizations the most important one being a much faster higher order convergence of the solution it is demonstrated that both components of the higher order modeling namely higher order geometrical modeling and higher order current field modeling are essential for accurate and efficient cem analysis of general antenna scattering and microwave structures

techniques for evaluating the uniform current vector potential at the isolated singularity of the cylindrical wire kernel the cylindrical wire kernel possesses a singularity which must be properly treated in order to evaluate the uniform current vector potential traditionally the singular part of the kernel is extracted resulting in a slowly varying function which is convenient for numerical integration this paper provides some new accurate and computationally efficient methods for evaluating the remaining singular integral it is shown that this double integral may be converted to a single integral which no longer possesses a singular integrand and consequently may be efficiently evaluated numerically this form of the integral is independent of the restrictions involving wire length and radius which are inherent in various approximations also presented is a highly convergent exact series representation of the integral which is valid except in the immediate vicinity of the singularity finally a new approximation is derived which is found to be an improvement over the classical thin wire approximation it is demonstrated that each of these methods provides extremely accurate as well as efficient results for a wide range of wire radii and field point locations

fuzzy relation equations and inequalities with two unknowns and their applications abstract in this paper we study several types of systems of fuzzy relation equations and inequalities composed of a given family of fuzzy relations between two sets and two unknown fuzzy relations on these sets solutions to these systems are pairs of fuzzy relations on the underlying sets and can be ordered coordinatewise we show that solutions to each of these systems form a complete lattice and provide procedures for computing the greatest solution which is less than or equal to a given pair of fuzzy relations we also demonstrate the application of solutions to these systems in data reduction

necessary and sufficient conditions for the existence of solution of generalized fuzzy relation equations a x b abstract in 2013 li and jin studied a particular type of fuzzy relational equations on finite sets where the introduced min bi implication composition is based on ukasiewicz equivalence in this paper such fuzzy relation equations are studied on a more general level namely complete residuated lattice valued fuzzy relation equations of type y y a x y x y b x are analyzed and the existence of solutions s is studied first a necessary condition for the existence of solution is established then conditions for lower and upper limits of solutions are given and finally sufficient conditions for the existence of the smallest and largest solutions respectively are characterized if such general or global solutions do not exist there might still be partial or point wise solutions this is a novel way to study fuzzy relation equations such point wise solutions are studied on ukasiewicz product and godel t norm based residuated lattices on the real unit interval

weakly linear systems of fuzzy relation inequalities the heterogeneous case new types of systems of fuzzy relation inequalities and equations called weakly linear have been recently introduced in j ignjatovic et al on the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations fuzzy sets syst 161 2010 3081 3113 the mentioned paper dealt with homogeneous weakly linear systems composed of fuzzy relations on a single set and a method for computing their greatest solutions has been provided this method is based on the computing of the greatest post fixed point contained in a given fuzzy relation of an isotone function on the lattice of fuzzy relations here we adapt this method for computing the greatest solutions of heterogeneous weakly linear systems where the unknown fuzzy relation relates two possibly different sets we also introduce and study quotient fuzzy relational systems and establish relationships between solutions to heterogeneous and homogeneous weakly linear systems besides we point out to applications of the obtained results in the state reduction of fuzzy automata and computing the greatest simulations and bisimulations between fuzzy automata as well as in the positional analysis of fuzzy social networks

on the suitability of the bandler kohout subproduct as an inference mechanism fuzzy relational inference fri systems form an important part of approximate reasoning schemes using fuzzy sets the compositional rule of inference cri which was introduced by zadeh has attracted the most attention so far in this paper we show that the fri scheme that is based on the bandler kohout bk subproduct along with a suitable realization of the fuzzy rules possesses all the important properties that are cited in favor of using cri viz equivalent and reasonable conditions for their solvability their interpolative properties and the preservation of the indistinguishability that may be inherent in the input fuzzy sets moreover we show that under certain conditions the equivalence of first infer then aggregate fita and first aggregate then infer fati inference strategies can be shown for the bk subproduct much like in the case of cri finally by addressing the computational complexity that may exist in the bk subproduct we suggest a hierarchical inferencing scheme thus this paper shows that the bk subproduct based fri is as effective and efficient as the cri itself

on the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations in this paper we study systems of fuzzy relation inequalities and equations of the form u v i v i u i i where u is an unknown and v i i i are given fuzzy relations the dual systems v i u u v i i i their conjunctions the systems of the form u v i v i u i i and certain special types of these systems we call them weakly linear systems for each weakly linear system with a complete residuated lattice as the underlying structure of truth values we prove the existence of the greatest solution and we provide an algorithm for computing the greatest solution which works whenever the underlying complete residuated lattice is locally finite otherwise we determine some sufficient conditions under which the algorithm works the algorithm is iterative and each its single step can be viewed as solving of a particular linear system weakly linear systems emerged from the fuzzy automata theory but we show that they also have important applications in other fields e g in the concurrency theory and social network analysis

a new formulation of pocklington s equation for thin wires using the exact kernel pocklington s integro differential equation for thin wires with the exact kernel is reformulated using a second derivative formula for improper integrals this allows for analytical evaluation of the second derivatives resulting in a pure integral equation in a similar manner to what is done when using the approximate kernel however as opposed to using the approximate kernel the resulting integral equation developed here is numerically stable even with a simple pulse function point matching solution good convergence for the current is obtained using pulse functions and the severe unphysical oscillations of the current that are encountered when using pulse functions with the approximate kernel are avoided

conditions for the existence of the least solution and minimal solutions to fuzzy relation equations over complete brouwerian lattices this paper discusses properties and existence conditions of minimal solutions to sup inf fuzzy relation equations over complete brouwerian lattices the relationship between minimal solutions to a system of fuzzy relation equations and minimal solutions to a fuzzy relation equation in the system is illustrated by two examples necessary and sufficient conditions for the existence of the least solution and minimal solutions to a system of fuzzy relation equations are given

system of fuzzy relation equations as a continuous model of if then rules we claim that a fuzzy relation which models a system of fuzzy if then rules has the property of continuity only if the underlying system of fuzzy relation equations is solvable in view of this connection it is important to consider the problem of solvability of a system of fuzzy relation equations with respect to an unknown fuzzy relation this problem is analyzed in the present paper we propose several new necessary and sufficient criteria for the so called mamdani relation to be a solution to the system we prove that in the general case these same criteria are sufficient but not always necessary for the solvability of the system a new easy to check criterion is proposed for the solvability of the system with special fuzzy parameters

infinite fuzzy relation equations with continuous t norms this study develops a concept of infinite fuzzy relation equations with a continuous t norm it extends the work by xiong and wang q q xiong x p wang some properties of sup min fuzzy relational equations on infinite domains fuzzy sets and systems 151 2005 393 402 we describe attainable respectively unattainable solutions which are closely related to minimal solutions to the equations it is shown that a solution set comprises both attainable and unattainable solutions the study offers a characterization of these solutions under some assumptions the solution set is presented and discussed two applications are also given