transformation optics based local mesh refinement for solving maxwell s equations in this paper a novel local mesh refinement algorithm based on transformation optics to has been developed for solving the maxwell s equations of electrodynamics the new algorithm applies transformation optics to enlarge a small region so that it can be resolved by larger grid cells the transformed anisotropic maxwell s equations can be stably solved by an anisotropic fdtd method while other subgridding or adaptive mesh refinement fdtd methods require time space field interpolations and often suffer from the late time instability problem to avoid small time steps introduced by the transformation optics approach an additional application of the mapping of the material matrix to a dispersive material model is employed numerical examples on scattering problems of dielectric and dispersive objects illustrate the performance and the efficiency of the transformation optics based fdtd method

fuzzy number valued fuzzy measure and fuzzy number valued fuzzy integral on the fuzzy set abstract in this paper some new concepts the fuzzy number valued fuzzy measure autocontinuity and null additivity of fuzzy number valued fuzzy measures on the fuzzy algebra and the fuzzy number valued fuzzy integral on the fuzzy set are introduced some properties of fuzzy number valued fuzzy integrals and some convergence theorems for sequences of fuzzy number valued fuzzy integrals on a fuzzy set are discussed

type fuzzy quantifiers determined by fuzzy measures defined on residuated lattices part ii permutation and isomorphism invariances abstract we study the properties of permutation invariance and isomorphism invariance of fuzzy quantifiers of type 1 1 defined using fuzzy measures and integrals these properties hold if fuzzy quantifiers are invariant with respect to permutations bijective mappings on the universe of discourse permutation invariance and with respect to bijections between different universes of discourse isomorphism invariance in other words fuzzy quantifiers with these properties are sensitive only to the cardinality of subsets of the universe of discourse and not to the individual nature of the elements of these subsets we characterize these properties by means of the corresponding properties of functionals used in the definition of the fuzzy quantifiers

mesa type patterns in the one dimensional brusselator and their stability the brusselator is a generic reaction diffusion model for a tri molecular chemical reaction we consider the case when the input and output reactions are slow in this limit we show the existence of k periodic spatially bi stable structures mesas and study their stability using singular perturbation techniques we find a threshold for the stability of k mesas this threshold occurs in the regime where the exponentially small tails of the localized structures start to interact by comparing our results with turing analysis we show that in the generic case a turing instability is followed by a slow coarsening process whereby logarithmically many mesas are annihilated before the system reaches a steady equilibrium state we also study a breather type instability of a mesa which occurs due to a hopf bifurcation full numerical simulations are shown to confirm the analytical results in 1952 turing proposed that the formation of spatial patterns during morphogenesis could be explained in terms of the instability of a homogeneous steady state solution of a reaction diffusion network describing the evolution of a set of morphogens 31 turing himself illustrated his ideas on two chemical models turing s original work is primarily concerned with the stability analysis of the homogeneous steady state solution of the rate equations for the interacting morphogens 22 the main point of biological interest however is whether stable spatial structures may be generated beyond the instability i e whether the rate equations admit stable and positive inhomogeneous solutions exhibiting the most characteristic features of morphogenetic patterns this point has been taken up seriously in the early seventies more systematic numerical studies of turing s model have been performed showing irregular spatial structures 4 this led to serious reservations about the relevance of turing s theory in developmental biology particularly its ability to generate regular patterns but these criticisms originate from a somewhat unfortunate choice of turing s example and they do not touch the essential points of turing s theory more specifically the obvious requirement that the rate equations must admit positive and bounded solutions is not satisfied in turing s example 11

linguistic quantifiers modeled by sugeno integrals since quantifiers have the ability of summarizing the properties of a class of objects without enumerating them linguistic quantification is a very important topic in the field of high level knowledge representation and reasoning this paper introduces a new framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures and the truth value of a quantified proposition is evaluated by using sugeno s integral this framework allows us to have some elegant logical properties of linguistic quantifiers we compare carefully our new model of quantification and other approaches to linguistic quantifiers a set of criteria for linguistic quantification was proposed in the previous literature the relationship between these criteria and the results obtained in the present paper is clarified some simple applications of the sugeno s integral semantics of quantifiers are presented

finite difference on grids with nearly uniform cell area and line spacing for the wave equation on complex domains a finite difference time dependent numerical method for the wave equation supported by recently derived novel elliptic grids is analyzed the method is successfully applied to single and multiple two dimensional acoustic scattering problems including soft and hard obstacles with complexly shaped boundaries the new grids have nearly uniform cell area j grids and nearly uniform grid line spacing email protected numerical experiments reveal the positive impact of these two grid properties on the scattered field convergence to its harmonic steady state the restriction imposed by stability conditions on the time step size is relaxed due to the near uniformity cell areas and grid line spacing as a consequence moderately large time steps can be used for relatively fine spatial grids resulting in greater accuracy at a lower computational cost also numerical solutions for wave problems inside annular regions of complex shapes are obtained the use of the new grids results in late time stability in contrast with other classical finite difference time dependent methods

a high order accurate parallel solver for maxwell s equations on overlapping grids a scheme for the solution of the time dependent maxwell s equations on composite overlapping grids is described the method uses high order accurate approximations in space and time for maxwell s equations written as a second order vector wave equation high order accurate symmetric difference approximations to the generalized laplace operator are constructed for curvilinear component grids the modified equation approach is used to develop high order accurate approximations that use only three time levels and have the same time stepping restriction as the second order scheme discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed the implementation is optimized for component grids that are cartesian resulting in a fast and efficient method the solver runs on parallel machines with each component grid distributed across one or more processors numerical results in two and three dimensions are presented for the fourth order accurate version of the method these results demonstrate the accuracy and efficiency of the approach

a novel 3 d cpfdtd scheme for modeling grid nonconformally aligned transmitter structures in this paper a novel three dimensional 3 d subcell algorithm for modeling metallic objects which are nonconformally oriented within the finite difference time domain fdtd grid is proposed the generally applicable algorithm is based on the contour path cp technique and enables in combination with an enhanced nonconformally aligned source model a more accurate spatial representation of antenna structures than the common staircase approach to evaluate the performance of the new algorithm the simulation results are compared with the classical staircase approach for dipole antennas as well as for a generic phone significant improvements were achieved for all antenna parameters from the near and far field i e feedpoint impedance radiation pattern and field distributions

time dependent numerical method with boundary conforming curvilinear coordinates applied to wave interactions with prototypical antennas a new unstaggered finite difference time dependent technique to accurately model scattring from prototypical 2d antenna structures is devised the unbounded boundary value problems defining these phenomena are redefined over bounded domains using appropriate radiation operators over finite artificial boundaries generalized curvilinear coordinates are generated such that physical boundaries correspond to coordinate lines a numerical procedure to generate almost orthogonal boundary conforming fine grids over these bounded regions is developed once the governing equations are written in terms of the new curvilinear coordinates a time dependent numerical method is applied to obtain time harmonic steady state solutions to these problems the electric field wave amplitude as well as the wave pattern inside the waveguide and the scattered field from the prototypical antennas are obtained accuracy and computational cost are compared when almost orthogonal and nonorthogonal grids are in use an optical theorem for a flanged waveguide antenna with perfect electrical conductor walls is derived it is verified that the approximate solutions obtained by application of the time dependent numerical method with boundary conforming curvilinear coordinates satisfy the optical theorem

self replication of mesa patterns in reaction diffusion systems abstract certain two component reaction diffusion systems on a finite interval are known to possess mesa box like steady state patterns in the singularly perturbed limit of small diffusivity for one of the two solution components as the diffusivity d of the second component is decreased below some critical value d c with d c o 1 the existence of a steady state mesa pattern is lost triggering the onset of a mesa self replication event that ultimately leads to the creation of additional mesas the initiation of this phenomena is studied in detail for a particular scaling limit of the brusselator model near the existence threshold d c of a single steady state mesa it is shown that an internal layer forms in the centre of the mesa the structure of the solution within this internal layer is shown to be governed by a certain core problem comprised of a single nonautonomous second order ode by analysing this core problem using rigorous and formal asymptotic methods and by using the singular limit eigenvalue problem slep method to asymptotically calculate small eigenvalues an analytical verification of the conditions of nishiura and ueyama y nishiura d ueyama a skeleton structure of self replicating dynamics physica d 130 1 1999 73 104 believed to be responsible for self replication is given these conditions include 1 the existence of a saddle node threshold at which the steady state mesa pattern disappears 2 the dimple shaped eigenfunction at the threshold believed to be responsible for the initiation of the replication process and 3 the stability of the mesa pattern above the existence threshold finally we show that the core problem is universal in the sense that it pertains to a class of reaction diffusion systems including the gierer meinhardt model with saturation where mesa self replication also occurs

on fuzzy type theory this paper is a generalization of classical simple type theory we have developed a formal system of fuzzy type theory which differs from the classical one essentially in extension of truth values from two to infinitely many the structure of truth values is assumed to be an imtl algebra residuated lattice with prelinearity and double negation extended by the baaz delta operation various properties of fuzzy type theory are proved including its completeness

a high order mixed vector finite element method for solving the time dependent maxwell equations on unstructured grids we present a mixed vector finite element method for solving the time dependent coupled ampere and faraday laws of maxwell s equations on unstructured hexahedral grids that employs high order discretization in both space and time the method is of arbitrary order accuracy in space and up to 4th order accurate in time making it well suited for electrically large problems where grid anisotropy and numerical dispersion have plagued other methods in addition the method correctly models both the jump discontinuities and the divergence free properties of the electric and magnetic fields is charge and energy conserving conditionally stable and free of spurious modes several computational experiments are performed to demonstrate the accuracy efficiency and benefits of the method

an explicit fourth order orthogonal curvilinear staggered grid fdtd method for maxwell s equations the explicit fourth order staggered finite difference time domain scheme previously proposed for a cartesian grid is extended to maxwell s equations in an orthogonal curvilinear coordinate system and applied to electromagnetic wave problems a simple technique is also presented for generating orthogonal curvilinear grids that conform to the material boundaries and interfaces of the problem numerical experiments are presented to illustrate the efficiency and accuracy of the method

three dimensional contour fdtd modeling of scattering from single and multiple bodies this paper introduces a generalization of the three dimensional finite difference time domain fdtd method the three dimensional contour fdtd cfdtd method is introduced the fdtd method represents curved media boundaries as stepped edges through the use of subcell modeling the cfdtd method conformably models bodies with curved surfaces yet retains the ability to model corners and edges electromagnetic scattering from single and multiple bodies is presented

second order procedure for modeling dielectric material interfaces in structured nonorthogonal finite difference discretizations of maxwell s equations structured nonorthogonal finite difference discretizations of maxwell s equations are often employed to incorporate curved dielectric material interfaces as part of this process it is necessary to employ an adequate procedure to enforce the tangential field continuity conditions at the locations of the interfaces where the components of the permittivity tensor are discontinuous this contribution proposes a second order domain splitting procedure that can accomplish this task without assuming that the permittivity tensor components are piecewise constant or diagonal as explained this feature is needed to exploit the full geometrical flexibility of structured grid generation the proposed domain splitting procedure consistently yields a global error that is second order accurate even in extreme cases where the components of the permittivity tensor have a change of sign or a sharp jump

time domain method having a naturally diagonal mass matrix independent of element shape for general electromagnetic analysis 2 d formulations in this paper we present a new time domain method that has a naturally diagonal mass matrix and thereby a strict linear computational complexity per time step regardless of whether the discretization is a structured grid or an unstructured mesh this property is obtained independent of the element shape used for discretization no interpolations projections and mass lumping are required the accuracy and stability of the proposed method are both theoretically guaranteed in addition no dual mesh is needed and the tangential continuity of the fields is satisfied across the element interface the flexible framework of the proposed method also allows for a straightforward extension to higher order accuracy in both electric and magnetic fields numerical experiments have been conducted on a variety of unstructured triangular element meshes correlations with analytical solutions and the time domain finite element method have validated the accuracy and generality of the proposed new time domain method

the convergence for a sequence of fuzzy integrals of fuzzy number valued functions on the fuzzy set abstract in this paper a new concept of fuzzy number valued fuzzy integral of fuzzy number valued function with respect to fuzzy number valued fuzzy measure on the fuzzy set is introduced and some equivalent definitions of the above mentioned concept are given and its elementary properties are discussed and a series of the convergent theorems of fuzzy number valued fuzzy integrals on the fuzzy set are obtained

linguistic characterization of time series the goal of this paper is to provide an overview of applications of special soft computing theories the fuzzy transform and fuzzy natural logic to analysis forecasting and mining information from time series the focus is especially placed on the ability of methods of fuzzy natural logic to provide information in sentences of natural language our approach is based on the decomposition of time series into three components the trend cycle seasonal component and noise the trend cycle is extracted using the f transform and its course is characterized by automatically generated linguistic description the latter is then used to forecast the trend cycle the trend cycle can be furthermore decomposed into trend general tendency and cycle the former is computed again using the f transform moreover the f1 transform makes it possible to estimate the direction of the trend which can then be characterized by expressions of natural language stagnating slightly increasing sharply decreasing etc finally we focus on selected problems of mining information from time series first we suggest an algorithm for finding intervals of monotonous behavior and then show how the theory of intermediate quantifiers a constituent of fuzzy natural logic and generalized aristotle s syllogisms can be applied to automatic summarization of information on time series

an analysis of finite volume finite element and finite difference methods using some concepts from algebraic topology in this paper we apply the ideas of algebraic topology to the analysis of the finite volume and finite element methods illuminating the similarity between the discretization strategies adopted by the two methods in the light of a geometric interpretation proposed for the role played by the weighting functions in finite elements we discuss the intrinsic discrete nature of some of the factors appearing in the field equations underlining the exception represented by the constitutive term the discretization of which is maintained as the key issue for numerical methods devoted to field problems we propose a systematic technique to perform this task present a rationale for the adoption of two dual discretization grids and point out some optimization opportunities in the combined selection of interpolation functions and cell geometry for the finite volume method finally we suggest an explanation for the intrinsic limitations of the classical finite difference method in the construction of accurate high order formulas for field problems

instability and localisation of patterns due to a conserved quantity abstract we describe the influence of a conserved quantity on the stability properties of roll square and hexagonal patterns near stationary onset the appropriate systems of amplitude equations are analysed they comprise equations for the amplitudes of the pattern modes together with an additional coupled equation governing the evolution of a large scale mode associated with the conserved quantity we find that the presence of this large scale mode may result in the destabilisation of all regular roll square or hexagonal patterns leading to amplitude modulation and strong localisation of the pattern our analytical results are complemented throughout by numerical simulations of a model partial differential equation to illustrate the modulational instabilities and their nonlinear development

dynamics of an epidemic model with spatial diffusion mathematical models are very useful in analyzing the spread and control of infectious diseases which can be used to predict the developing tendency of the infectious disease determine the key factors and to seek the optimum strategies of disease control as a result we investigated the pattern dynamics of a spatial epidemic model with logistic growth by using amplitude equation we found that there were different types of stationary patterns including spotted mixed and stripe patterns which mean that spatial motion of individuals can form high density of diseases the obtained results can be extended in other related fields such as vegetation patterns in ecosystems

l fuzzy quantifiers of type determined by fuzzy measures the aim of this paper is first to introduce two new types of fuzzy integrals namely fuzzy integral and fuzzy integral the first integral is based on a fuzzy measure of l fuzzy sets and the second one on a complementary fuzzy measure of l fuzzy sets where l is a complete residuated lattice some of their properties and a relation to the fuzzy sugeno integral are investigated second using these integrals two classes of monadic l fuzzy quantifiers of type are defined these l fuzzy quantifiers can be used for modeling the semantics of natural language quantifiers like all some many none at most half etc several semantic properties of these l fuzzy quantifiers are studied

pattern formation by super diffusion in fitzhugh nagumo model abstract the aim of this paper is to examine the turing instability and pattern formation in the fitzhugh nagumo model with super diffusion in two dimensional numerical simulation we also studied the effects of the super diffusive exponent on pattern formation concluding that with the presence of super diffusion the stable homogenous steady state becomes unstable by using the stability analysis of local equilibrium point we procure the conditions which ensure that the turing and hopf bifurcations occur for pattern selection the weak nonlinear multi scale analysis is used to derive the amplitude equations of the stationary patterns we then apply amplitude equations and observe that this model has very rich dynamical behaviors such as stripes spots and hexagon patterns the complexity of the dynamics in this system is theoretically discussed and graphically displayed in numerical simulation the simulation helps us to show the effectiveness of theoretical analysis and patterns which appear numerically

pattern formation in a general two cell brusselator model abstract in this article we are concerned with the following general coupled two cell brusselator type system d 1 u a b 1 u f u v c w u in d 2 v b u f u v in d 1 w a b 1 w f w z c u w in d 2 z b w f w z in u v w z 0 on here r n n 1 is a smooth and bounded domain a b c d 1 d 2 are positive constants and f c 1 0 c 0 is a nonnegative and nondecreasing function such that f 0 in 0 when f u u 2 this system corresponds to the coupled two cell brusselator model in the present work we exhibit the crucial role played by the nonlinearity f in generating the stationary patterns our conclusions show that if f has a sublinear growth then no stationary patterns occur while if f has a superlinear growth stationary patterns may exist

fuzzy measures and integrals defined on algebras of fuzzy subsets over complete residuated lattices this paper presents basic notions about fuzzy measures over algebras of fuzzy subsets of a fuzzy set it also presents basic ideas on fuzzy integrals defined using these fuzzy measures definitions of new types of fuzzy measures and integrals are motivated by our research on generalized quantifiers several useful properties of fuzzy measures and fuzzy integrals are stated and proved definitions presented in this paper and its results will be employed in subsequent papers on generalized quantifiers defined using this type of fuzzy integral

monadic l fuzzy quantifiers of the type the aim of this paper is to introduce monadic l fuzzy quantifiers of the type and investigate some of their semantic properties that are well known in generalized quantifier theory relationships between the properties of generalized quantifiers are also studied for monadic l fuzzy quantifiers finally a property to be extensional with respect to a given l permutation equivalence is proposed and some properties are shown

accuracy of staircase approximations in finite difference methods for wave propagation while a number of increasingly sophisticated numerical methods have been developed for time dependent problems in electromagnetics the yee scheme is still widely used in the applied fields mainly due to its simplicity and computational efficiency a fundamental drawback of the method is the use of staircase boundary approximations giving inconsistent results usually experience of numerical experiments provides guidance of the impact of these errors on the final simulation result in this paper we derive exact discrete solutions to the yee scheme close to the staircase approximated boundary enabling a detailed theoretical study of the amplitude phase and frequency errors created furthermore we show how evanescent waves of amplitude o 1 o 1 occur along the boundary these characterize the inconsistencies observed in electromagnetic simulations and the locality of the waves explain why in practice the yee scheme works as well as it does the analysis is supported by detailed proofs and numerical examples

fdtd algorithm in curvilinear coordinates em scattering the finite difference time domain fdtd algorithm for the solution of electromagnetic scattering problems is formulated in generalized coordinates in two dimensions and implemented in a code with the lowest order bayliss turkel radiation boundary condition expressed in cylindrical coordinates it is shown that for a perfect conductor such a formulation leads to a stable well posed algorithm and that in regions where the curvature of the coordinate lines is not great the dispersion and anisotropy effects are negligible such effects become more pronounced in regions of high curvature leading to unphysical phase shifts the magnitude of such shifts and the amount of wavefront distortion is studied via numerical experiments using a cylindrical mesh near field results are given for two canonical shapes for each polarization the circular cylinder and cylinders of square and rectangular cross sections these results are compared with those obtained by exact eigenfunction expansion techniques with method of moments mm solutions and with solutions obtained from an alternate fdtd approach in each case agreement is excellent the propagation of a plane wave through a polar space in the absence of a scatterer is also examined and it is shown that the fdtd algorithm is capable of tracking the incident wave closely

fuzzy quantifiers defined over fuzzy domains abstract in this paper we introduce a generalization of the concept of fuzzy quantifier called fuzzy quantifiers over fuzzy domains the development of this generalization is motivated by the impossibility to satisfactorily define the important operation of relativization for standard fuzzy quantifiers we provide basic examples of these quantifiers and define and investigate also several semantic properties of them finally we prove a theorem saying among other things that all these two argument fuzzy quantifiers that possess properties of extension and conservativity are relativizations of one argument fuzzy quantifiers of this kind

a formal theory of generalized intermediate syllogisms in this paper we continue developing the formal theory of intermediate quantifiers expressions such as most few almost all a lot of many a great deal of a large part of a small part of the theory is a fuzzy logic formalization of the concept introduced by peterson in his book we will syntactically prove that 105 generalized aristotle s syllogisms introduced in this book are valid in our theory at the same time we will also prove that syllogisms listed there as invalid are invalid also in our theory therefore we believe that our theory provides a reasonable mathematical model of the generalized syllogistics

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

diffusive stability of spatially periodic solutions of the brusselator model applying the lyapunov schmidt reduction approach introduced by mielke and schneider in their analysis of the fourth order scalar swift hohenberg equation we carry out a rigorous small amplitude stability analysis of turing patterns for the canonical second order system of reaction diffusion equations given by the brusselator model our results confirm that stability is accurately predicted in the small amplitude limit by the formal ginzburg landau amplitude equations rigorously validating the standard weakly unstable approximation and the eckhaus criterion

numerical stability of nonorthogonal fdtd methods in this paper a sufficient test for the numerical stability of generalized grid finite difference time domain fdtd schemes is presented it is shown that the projection operators of such schemes must be symmetric positive definite without this property such schemes can exhibit late time instabilities the origin and the characteristics of these late time instabilities are also uncovered based on this study nonorthogonal grid fdtd schemes nfdtd and the generalized yee gy methods are proposed that are numerically stable in the late time for quadrilateral prism elements allowing these methods to be extended to problems requiring very long time simulations the study of numerical stability that is presented is very general and can be applied to most solutions of maxwell s equations based on explicit time domain schemes

a finite volume method for the approximation of maxwell s equations in two space dimensions on arbitrary meshes a new finite volume method is presented for discretizing the two dimensional maxwell equations this method may be seen as an extension of the covolume type methods to arbitrary possibly non conforming or even non convex n sided polygonal meshes thanks to an appropriate choice of degrees of freedom an equivalent formulation of the scheme is given in terms of discrete differential operators obeying discrete duality principles the main properties of the scheme are its energy conservation its stability under a cfl like condition and the fact that it preserves gauss law and divergence free magnetic fields second order convergence is demonstrated numerically on non conforming and distorted meshes

fuzzy valued measure abstract the main purpose of this paper is to introduce and develop the notion of a fuzzy valued measure in separable banach space this definition of fuzzy valued measure is a natural generalization of the set valued measure radon nikod m theorems for fuzzy valued measure are established

amplitude equations for reaction diffusion systems with cross diffusion using taylor series expansion multiscaling and further expansion in powers of a small parameter we develop general amplitude equations for two variable reaction diffusion systems with cross diffusion terms in the cases of hopf and turing instabilities we apply this analysis to the oregonator and brusselator models and find that inhibitor cross diffusion induced by the activator and activator cross diffusion induced by the inhibitor have opposite effects in the two models as a result of the different structure of their community matrices our analysis facilitates finding regions of supercritical and subcritical bifurcations as well as wave and antiwave domains and domains of turbulent waves in the case of hopf instability

algorithm for some anomalously diffusive hyperbolic systems in molecular dynamics theoretical analysis and pattern formation abstract departing from a two dimensional hyperbolic system that describes the interaction between some activator and inhibitor substances in chemical reactions we investigate a general form of that model using a finite difference approach the model under investigation is a nonlinear system consisting of two coupled partial differential equations with generalized reaction terms the presence of two dimensional diffusive terms consisting of fractional operators of the riesz type is considered here using spatial differentiation orders in the set 0 1 1 2 we impose initial conditions on a closed and bounded rectangle and a finite difference methodology based on the use of fractional centered differences is proposed among the most important results of this work we prove the existence and the uniqueness of the solutions of the numerical method and establish analytically the second order consistency of our scheme moreover the discrete energy method is employed to prove the stability and the quadratic convergence of the technique some numerical simulations obtained through our method show the presence of turing patterns and wave instabilities in agreement with some reports found in the literature on superdiffusive hyperbolic activator inhibitor systems we show numerically that the presence of turing patterns is independent of the size of the spatial domain as a new application we show that turing patterns are also present in subdiffusive scenarios

three dimensional computer modeling of electromagnetic fields a global lookback lattice truncation scheme abstract a new lattice truncation scheme for the finite difference time domain approach to the solution of maxwell s equations has been developed the problem space is truncated near the sources and the field components on its boundary are generated from those field values known at retarded times on an interior surface one cell from it with an integral representation of the electromagnetic field the numerical implementation of this global lookback scheme is discussed examples which have been used to determine its characteristics and its validity are given

a stitching method for the generation of unstructured meshes for use with co volume solution techniques abstract the successful implementation of co volume time domain solution techniques requires the use of high quality smooth dual meshes the generation of delaunay voronoi diagrams with these properties for two dimensional domains of complicated geometrical shape is considered in the adopted approach near boundary regions are discretised according to prescribed criteria and the remainder of the computational domain is discretised using an ideal mesh the two meshes are stitched together to provide a consistent mesh for the complete domain after smoothing the resulting mesh is found to be of a quality which exceeds that of meshes produced by standard automatic unstructured mesh generation methods examples involving electromagnetic wave scattering are included to demonstrate the computational performance that can be achieved with a co volume time domain solution algorithm on these meshes

the finite difference time domain fdtd and the finite volume time domain fvtd methods in solving maxwell s equations the finite difference time domain fdtd and its current generalizations have been demonstrated to be useful and powerful tools for the calculation of the radar cross section rcs of complicated objects the radiation of antennas in the presence of other structures and other applications the mathematical techniques for conformal fdtd have matured the primary impediments to its implementation are the complex geometries and material properties associated with the problem even under these circumstances fdtd is more flexible to implement because it is based on first principles instead of a clever mathematical trick this paper gives an account of some new results on conformal fdtd obtained by the authors and their associates at lockheed martin space company since 1988 the emphasis is on nonsmooth boundary condition simulation

the theory of intermediate quantifiers in fuzzy natural logic revisited and the model of many abstract the fuzzy natural logic fnl is a formal theory whose goal is to provide a mathematical model of natural human reasoning whose typical feature is the use of natural language one of its tasks is to develop a mathematical model of a special class of linguistic quantifiers called intermediate ones in our previous papers we introduced a general principle of how intermediate quantifiers can be formed and suggested generalized definitions of the relations of contrary contradictory subcontrary and subalterns between these quantifiers based on these relations and following peterson s book 62 we were able to suggest a formal model of the 5 square of opposition with intermediate quantifiers this paper picks up the threads of this work and has the following goals it contributes to the development of the theory of fuzzy natural logic first it gets back to some concepts of the theory of evaluative linguistic expressions introduces slight modifications and proves some not yet presented properties furthermore it improves the formal theory of intermediate quantifiers some definitions are made more precise and some new theorems are proved finally it contributes to the theory of the intermediate quantifier many and the analysis of its position in the mentioned 5 square we will show that many manifests an ambiguous relation towards the other quantifiers

pattern formation in a predator prey model with spatial effect abstract in this paper spatial dynamics in the beddington deangelis predator prey model with self diffusion and cross diffusion is investigated we analyze the linear stability and obtain the condition of turing instability of this model moreover we deduce the amplitude equations and determine the stability of different patterns numerical simulations show that this system exhibits complex dynamical behaviors in the turing space we find three types of typical patterns one is the coexistence of hexagon patterns and stripe patterns the other two are hexagon patterns of different types the obtained results well enrich the finding in predator prey models with beddington deangelis functional response

a stable and consistent generalization of the fdtd technique to nonorthogonal unstructured grids a new way to extend the finite difference time domain fdtd technique to nonorthogonal grids is described in this paper the method whose theoretical foundations are based on the finite integration technique and on recently extended affine theories can be proven to be both stable and consistent in order to show its benefits the nonorthogonal fdtd is applied to the analysis of a cylindrical cavity and to the characterization of biconical antennas for ultrawideband applications

cardinality quantifiers and the aggregation of fuzzy criteria abstract in this paper we are interested in counting the number of elements of a fuzzy set we study two concepts of fuzzy cardinality one which gives the answer as a fuzzy set or fuzzy number and the other which gives an ordinary integer relationships between these concepts and others which have been studied in the literature e g sigma count are also investigated some properties of the new concepts are studied such as fuzzy convexity monotonicity and additivity the concepts of fuzzy cardinality are important for a better understanding of fuzzy quantified rules of the form qx s are a or qa s are b where q is a fuzzy quantifier and a b are fuzzy sets we study such rules as well as aggregation rules of the form q of a1 ap contain x

stability of turing patterns in the brusselator model the selection and competition of turing patterns in the brusselator model are reviewed the stability of stripes and hexagons towards spatial perturbations is studied using the amplitude equation formalism for hexagonal patterns these equations include both linear and nonpotential spatial terms enabling distorted solutions the latter modify substantially the stability diagrams and select patterns with wave numbers quite different from the critical value the analytical results from the amplitude formalism agree with direct simulations of the model moreover we show that slightly squeezed hexagons are locally stable in a full range of distortion angles the stability regions resulting from the phase equation are similar to those obtained numerically by other authors and to those observed in experiments

disclinations in square and hexagonal patterns we report the observation of defects with fractional topological charges disclinations in square and hexagonal patterns as numerical solutions of several generic equations describing many pattern forming systems swift hohenberg equation damped kuramoto sivashinsky equation as well as nonlinear evolution equations describing large scale rayleigh benard and marangoni convection in systems with thermally nearly insulated boundaries it is found that disclinations in square and hexagonal patterns can be stable when nucleated from special initial conditions the structure of the disclinations is analyzed by means of generalized cross newell equations

a discontinuous galerkin finite element time domain method modeling of dispersive media a method is proposed for solving the time dependent maxwell s equations via the discontinuous galerkin finite element time domain dgfetd method with dispersive media an auxiliary differential equation ade method is used to represent the constitutive relations the method is applied to drude materials as well as to multiple pole debye and lorentz materials an efficient implementation for high order runge kutta time integration schemes is presented the method is validated and is shown to exhibit high order convergence

fdtd simulations of tem horns and the implications for staircased representations two dimensional 2 d tem horns are modeled using the finite difference time domain fdtd method the boundary walls are perfect electric conductors and one wall which does not align with the cartesian grid is approximated using a staircased representation by carefully comparing the fdtd results to those of the analytic solution one can make conclusions about the coarseness with which a boundary can be represented it is found that staircasing errors are small when the staircase diagonal the hypotenuse of the right triangle created by the stairstep is smaller than half a wavelength at the highest significant frequency in the excitation this rule of thumb is put forward as a necessary condition for the discretization of general problems results are also provided for some simple fdtd schemes that are designed to reduce staircasing errors by using large aspect ratio cells a grid can be constructed that satisfies the rule of thumb given above while this approach eliminates general staircasing errors some errors persist owing to the presence of step discontinuities immediately adjacent to the horn feed these errors can be further reduced by using a cell splitting approach it is shown that the contour path fdtd technique can be used to eliminate nearly all staircasing errors while some additional improvement is shown to be provided by using a stabilized contour path fdtd approach finally a recently proposed conformal technique that permits simple implementation is shown to provide results comparable with those of the stabilized contour path approach

type 1 1 fuzzy quantifiers determined by fuzzy measures on residuated lattices part iii extension conservativity and extensionality we study the properties of extension conservativity and extensionality of fuzzy quantifiers of type 1 1 defined using fuzzy measures and integrals the property of extension states that truth values of quantifier applications are invariant with respect to possible extensions of the universe conservativity expresses the property that quantifiers are sensitive in their second argument only to objects that lie in the intersection of their arguments extensionality represents a form of the smoothness of quantifiers we characterize these properties by the corresponding properties of functionals used in the definition of fuzzy quantifiers

convergence analysis of a covolume scheme for maxwell s equations in three dimensions this paper contains error estimates for covolume discretizations of maxwell s equations in three space dimensions several estimates are proved first an estimate for a semi discrete scheme is given second the estimate is extended to cover the classical interlaced time marching technique third some of our unstructured mesh results are specialized to rectangular meshes both uniform and nonuniform by means of some additional analysis it is shown that the spatial convergence rate is one order higher than for the unstructured case

convergence analysis of fully discrete finite volume methods for maxwell s equations in nonhomogeneous media we will consider both explicit and implicit fully discrete finite volume schemes for solving three dimensional maxwell s equations with discontinuous physical coefficients on general polyhedral domains stability and convergence for both schemes are analyzed we prove that the schemes are second order accurate in time both schemes are proved to be first order accurate in space for the voronoi delaunay grids and second order accurate for nonuniform rectangular grids we also derive explicit expressions for the dependence on the physical parameters in all estimates

a simple mesh generator in matlab creating a mesh is the first step in a wide range of applications including scientific computing and computer graphics an unstructured simplex mesh requires a choice of meshpoints vertex nodes

pattern formation in the fitzhugh nagumo model in this paper we investigate the effect of diffusion on pattern formation in fitzhugh nagumo model through the linear stability analysis of local equilibrium we obtain the condition how the turing bifurcation hopf bifurcation and the oscillatory instability boundaries arise by using the method of the weak nonlinear multiple scales analysis and taylor series expansion we derive the amplitude equations of the stationary patterns the analysis of amplitude equations shows the occurrence of different complex phenomena including turing instability eckhaus instability and zigzag instability in addition we apply this analysis to fitzhugh nagumo model and find that this model has very rich dynamical behaviors such as spotted stripe and hexagon patterns finally the numerical simulation shows that the analytical results agree with numerical simulation

divergence preserving discrete surface integral methods for maxwell s curl equations using non orthogonal unstructured grids abstract several new discrete surface integral methods for solving maxwell s equations in the time domain are presented these methods which allow the use of general non orthogonal mixed polyhedral unstructured grids are direct generalizations of the canonical staggered grid finite difference method these methods are conservative in that they locally preserve divergence or charge employing mixed polyhedral cells hexahedral tetrahedral etc these methods allow more accurate modeling of non rectangular structures and objects because the traditional stair stepped boundary approximations associated with the orthogonal grid based finite difference methods can be avoided numerical results demonstrating the accuracy of these new methods are presented

extensions of fuzzy relational compositions based on generalized quantifiers abstract the aim of this paper is to extend the fuzzy relational compositions motivated by their applications to medical diagnosis problem by bandler and kohout these compositions employ two quantifiers the universal quantifier and the existential quantifier as there exists a big gap between these two quantifiers that may be appropriately filled in by intermediate generalized quantifiers we take this as a motivation for our study in particular we introduce the concept of fuzzy relational compositions based on generalized quantifiers furthermore we show that the properties that are typically valid for standard fuzzy relational compositions are also valid for the compositions based on generalized quantifiers yet sometimes in a weaken form apart from fuzzy relational compositions the use of generalized quantifiers is also applied to images and preimages of fuzzy sets under fuzzy relations

an overview of fuzzy quantifiers i interpretations quantification is an important topic in fuzzy theory and its applications an overview is presented for quantification in fuzzy theory after a brief review of quantifiers in first order logic two approaches of generalizing quantifiers are given the algebraic method and the substitution method by distinguishing the fuzziness of predicates and quantifiers various approaches to quantification in fuzzy logic can be organized quantifiers in first order logic can be generalized in crisp sense and these generalized quantifiers can also be applied to fuzzy sets moreover quantifiers themselves can be fuzzy i e they can only be represented by a fuzzy set these different kinds of quantifications are identified quantifiers relate close to the concept of the cardinality of a fuzzy set which is summarized before investigating fuzzy quantifications different to classical logic various semantics of propositions in fuzzy logic fall into different frameworks which are known as the possibility distribution based reasoning system and the many valued fuzzy logics accordingly numerical and possibilistic interpretation explored in literature are reviewed conforming to these two frameworks

an overview of fuzzy quantifiers ii reasoning and applications abstract in the second part of the overview reasoning with fuzzily defined quantifiers and applications are presented possibility based reasoning is summarized in detail the widely used quantifier extension principle and various reasoning schemas derived from it are discussed some disadvantages of the quantifier extension principle are pointed out although intervalvalued quantifiers are only a special case of general quantifiers some specific properties and results arise from them furthermore they suggest another approach to interence with fuzzy quantifiers reasoning with quantification and several kinds of qualification is introduced this kind of reasoning requires a seamless synthesis of probability theory possibility theory fuzzy logic and belief theory at last the applications of fuzzily defined quantifiers in decision making and fuzzy database systems are introduced

type fuzzy quantifiers determined by fuzzy measures on residuated lattices part i basic definitions and examples abstract we study fuzzy quantifiers of type 1 1 defined using fuzzy measures and integrals residuated lattices are considered as structures of truth values we present basic notions on fuzzy measures over algebras of fuzzy subsets of a given fuzzy set and the definition and necessary properties of so called fuzzy integrals residuated lattice operations are established to derive operations between fuzzy sets describing degrees in which formulas expressing relations between fuzzy sets are true finally a general definition of type 1 1 fuzzy quantifiers determined by fuzzy measures and integrals is introduced and several examples of important natural language quantifiers are modeled using this approach

reasoning about mathematical fuzzy logic and its future this paper is devoted to reasoning about fuzzy logic which is based on various personal observations of the author our goal is to think of the state of the art in mathematical fuzzy logic mfl and to outline some of the tasks on which in the author s opinion mfl should focus in the future in our discussion we will mention not only the basic theory but also its extension called fuzzy logic in broader sense flb the paradigm of the latter is to be the logic of natural human reasoning whose most essential characteristic is the use of natural language besides brief description of flb we will also mention some of its applications on the basis of that we will ponder on other possible directions for research namely the possibility of using fln as a metatheory of fuzzy mathematics as a proper tool for modeling of the main manifestations of the phenomenon of vagueness and as a reasonable tool for developing models of linguistic semantics

explicit time domain finite element method stabilized for an arbitrarily large time step the root cause of the instability is quantitatively identified for the explicit time domain finite element method that employs a time step beyond that allowed by the stability criterion with the identification of the root cause an unconditionally stable explicit time domain finite element method is successfully created which is stable and accurate for a time step solely determined by accuracy regardless of how large the time step is the proposed method retains the strength of an explicit time domain method in avoiding solving a matrix equation while eliminating its shortcoming in time step numerical experiments have demonstrated its superior performance in computational efficiency as well as stability compared with the conditionally stable explicit method and the unconditionally stable implicit method the essential idea of the proposed method for making an explicit method stable for an arbitrarily large time step irrespective of space step is also applicable to other time domain methods

three dimensional orthogonal vector basis functions for time domain finite element solution of vector wave equations three dimensional 3 d orthogonal vector basis functions are developed for the time domain finite element solution of vector wave equations these basis functions enforce both the tangential continuity of the electric field and the normal continuity of the electric flux the stability of the resulting time domain finite element schemes is investigated and demonstrated to be guaranteed the use of the proposed basis functions completely eliminates the matrix solution at each time step required by the time domain finite element solution of vector wave equations the computational cost thereby scales as o n sub t n with n sub t and n denoting the number of time steps and the number of unknowns respectively defined over tetrahedral elements the proposed basis functions increase the solution efficiency without compromising the geometry modeling flexibility both numerical results and comparison with traditional vector basis functions demonstrate the accuracy as well as the efficiency of the proposed three dimensional orthogonal vector bases

bifurcation and stability analysis of steady states to a brusselator model abstract in this paper we consider the structure of the nonnegative steady state solutions of a brusselator model we prove the existence and boundedness of continua of the steady state solutions by applying the theorems of global bifurcation theory the concentration of one intermediary reactant is treated as a bifurcation parameter through the asymptotic bifurcation analysis we derive an explicit formula for the non constant steady states i e stationary patterns using it as a base we establish the stability criteria and find a selection mechanism of the wave modes for the stable patterns by computing the leading term of the principal eigenvalue our results demonstrate that all of the bifurcations other than the one at the first bifurcation location are unstable and if the pattern is stable then its mode must be a positive integer which minimizes the bifurcation parameter a specific example is presented to illustrate our analytical results

numerical dispersion and stability characteristics of time domain methods on nonorthogonal meshes the familiar finite difference time domain method for discretizing maxwell s curl equations on orthogonal grids has been extended to nonorthogonal grids by a number of researchers while it is difficult to determine the dispersion and stability characteristics of these methods when applied on arbitrary grids analysis of the idealized but representative case of a uniform skewed mesh proves to be quite tractable in 2 d this analysis demonstrates that numerical dispersion errors are small for well resolved spatial wavelengths and that these methods converge to the continuous space solution in the limit as the cell and time step sizes vanish grid anisotropy variations in wave propagation speed as a function of the propagation angle relative to the mesh coordinates increases as the mesh is skewed in spite of this there exist some angles where waves propagate through the skewed mesh with virtually no dispersion this analysis also provides a stability limit for the time step size in terms of geometrical mesh quantities

antonyms and linguistic quantifiers in fuzzy logic abstract the paper is a contribution to the theory of fuzzy logic in broader sense flb namely the discussion of linguistic expressions fundamental for it the evaluating linguistic predications the pairs nominal syntagm antonym and the theory of linguistic quantifiers the aim is to develop a theory of natural human reasoning whose characteristic feature is the use of natural language formalism of flb is based on the theory of fuzzy logic in narrow sense with evaluated syntax which provides us means for modelling of the concepts of intension possible world and extension characterization of some of the main properties of the above expressions is provided we also propose a modified definition of the linguistic variable