cone valued lyapunov functions and stability for impulsive functional differential equations abstract the stability criteria in terms of two measures for impulsive functional differential equations are established via cone valued lyapunov functions and razumikhin technique the stability can be deduced from the q 0 q stability of comparison impulsive differential equations an example is given to illustrate the advantages of the results obtained

asymptotic stability for impulsive differential systems employing piecewise continuous lyapunov functions results of stability in terms of two different measures for impulsive differential systems are derived an example is worked out

an example of a gas system which can be destabilized by an integrable perturbation a construction of a globally asymptotically stable time invariant system which can be destabilized by some integrable perturbation is given besides its intrinsic interest this serves to provide counterexamples to an open question regarding lyapunov functions

unbounded and scattered field representations of the dyadic green s functions for planar stratified bianisotropic media this paper presents a rigorous formulation of the spectral domain dyadic green s functions for planar stratified bianisotropic media the media may consist of any number of layers bounded by optional impedance admittance walls both electric and magnetic dyadic green s functions for arbitrary field and source locations are derived simultaneously based on the principle of scattering superposition these dyadics are decomposed into unbounded and scattered parts the scattered dyadic green s functions are determined without cumbersome operations using the concepts of effective reflection and transmission of outward bounded and inward bounded waves the scattering coefficient matrices are expressed in compact and convenient forms involving global reflection and transmission matrices corresponding to the impedance admittance boundary walls the global reflection matrices are related directly to the wall impedance admittance dyadics for illustration the general expressions of dyadic green s functions are applied to the configuration of a grounded bianisotropic slab embedded in isotropic halfspace

scattering from an impedance object at the edge of a perfectly conducting wedge in this study scattering from impedance bodies positioned at the edge of a perfectly electrically conducting wedge is investigated in the treatment of the problem eigenfunction expansion in terms of spherical vector wave functions is employed a complete dyadic green s function for the spherical impedance boss at the edge is developed it is observed that the scattering is highly enhanced by the edge guided waves additionally using t matrix method the solution is extended to the general case of irregularly shaped scatterers the t matrix solution is verified by applying it to the case of a spherical scatterer and results are compared with the dyadic green s function solution

on the φ0 stability of comparison differential systems for many years now the variety of problems of the qualitative properties of differential equations in the context of lyaponov second method has been successfully investigated in a unified way using the comparison principle s in this method the qualitative properties of the system of differential equations are inferred from the corresponding properties of the solutions of the system of comparison equations in order to successfully employ this method it is generally required that the comparison systems possess some special properties the conditions under which the scalar comparison equations possess positivity and stability behaviour have been investigated using scalar lyapunov function method by brauer l siljak and grujic 9 and others ladde 3 gave suficient conditions for nonnegativity and stability of solutions of systems of comparison equations in his investigation of stability of comparison differential systems ladde 3 considered the asymptotic stability and exponential asymptotic stability of the comparison differential system using the method of vector lyapunov functions however imbedded in the method of vector lyapunov function is the requirement of quasimonotone nondecreasing property of the comparison system but quasimonotonicity of the comparison system is not a necessary condition for the system to be stable thus the limitation of the application potential of this general and effective method is due to the fact that

perturbing lyapunov functions and stability criteria for initial time difference stability criteria for differential equations where the initial time for each solution is different is developed using the method of perturbing lyapunov functions

green s function for an unbounded biaxial medium in cylindrical coordinates the dyadic green s function for an unbounded biaxial medium is treated analytically in the fourier domain the green s function is initially expressed as a triple fourier integral which is next reduced to a double one by performing the integration over the longitudinal fourier variable a delta type source term is extracted which is dependent on the particular coordinate system

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

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

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

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

ϕ0 stability of hybrid impulsive dynamic systems on time scales abstract in this paper we shall employ the method of cone valued lyapunov functions and comparison principle to investigate the 0 stability of impulsive hybrid systems on time scales

an efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures an efficient multilevel fast multipole algorithm mlfma formalism to model radiation and scattering by from large planar microwave structures is presented the technique relies on an electric field integral equation efie formulation and a series expansion for the green dyadic based on the use of perfectly matched layers pml in this way a new pml mlfma is developed to efficiently evaluate matrix vector multiplications arising in the iterative solution of the scattering problem the computational complexity of the new algorithm scales down to o n for electrically large structures the theory is validated by means of several illustrative numerical examples

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

on 0 stability for nonlinear volterra integrodifferential systems 0 stability and lipschitz 0 stability notions of ordinary differential equations odes are introduced in this paper we extend these notions to systems of integro differential equations ides and give some criteria of these notions our technique depends on liapunov s direct method

analysis of an infinite periodic array of slot radiators with dielectric loading an efficient numerical procedure for determining the radiation characteristics of an infinite periodic array of slots in a conducting screen is presented the procedure employs a novel mixed potential integral equation formulation and is solved by the method of moments subdomain type basis functions are used to provide the flexibility to model arbitrarily shaped slots analysis is carried out to account for dielectric layers ground planes or cavities placed on either side of the slot series acceleration techniques are employed to reduce significantly the computation time required to sum the series representing the periodic green s function the numerical scheme developed is applied to obtain quantities such as the slot field distribution and input admittance as a function of the array scan angle where possible numerical results obtained are compared with data available in the literature data for the half space case are found to agree with those of a y grinev et al 1978 except for the case of multilayer dielectric loading

stability and boundedness criteria of nonlinear impulsive systems employing perturbing lyapunov functions this paper develops a new comparison principle for nonlinear impulsive differential systems then the stability practical stability and boundedness of impulsive differential systems are proved by using the method of perturbing lyapunov functions the notion of perturbing lyapunov functions enables us to discuss stability properties of impulsive systems under much weaker assumptions the reported novel results complement the existing results it may provide a greater prospect for solving problems which exhibit impulsive effects

semantics of dyadic and mixed potential field representation for 3 d current distributions in planar stratified media the full spectral electric dyadic green s function for three dimensional current distributions in planar stratified media can be obtained straight from maxwell s equations by following a physical reasoning analogous with the free space case but using general derivative relations for multilayered green s functions we derive a basic mixed potential form with a simple vector potential kernel but multiple scalar potential kernels and also obtain the well established single scalar potential formulations with a dyadic vector potential kernel mixed potential forms are thus arrived at without the a priori introduction of scalar and vector potential or choice of gauge condition the nonuniqueness of the scalar potential kernel and the dyadic nature of the scalar and or vector potentials are believed to be clarified by the proposed approach a discussion of the different formulations focuses on physical meaning and numerical consequences for the solution of integral equations

spectral electromagnetic modeling of a planar integrated structure with a general grounded anisotropic slab a formulation for the solution of the electromagnetic field in vertically stratified structures with a general anisotropic grounded slab under planar electric excitation conditions is presented the development of the solution is obtained by using the two dimensional fourier transform applied to the partial differential equations describing the electromagnetic field which can be expressed in terms of dyadic electric green s functions moreover a spectral equivalent circuit representation of the solution separated into its spectral transverse electric te and transverse magnetic tm components with respect to the vertical direction is given it is demonstrated that such a spectral circuit representation is always possible when the constitutive epsilon and mu tensors are reduced to their diagonal form the transmission line representation for an unbounded gyrotropic medium with vertical preferred axis is presented this theory is applied to a planar structure with an anisotropic biaxial grounded slab and an electric horizontal point source embedded in it numerical examples of evaluation of the radiated pattern and noteworthy information about the radiation on the horizon plane are given

stability and boundedness of differential equations relative to initial time difference by employing vector lyapunov functions the existing stability results relative to initial time difference are not easy to be applied into practice since it is too hard to find a lyapunov function satisfying all the conditions this paper presents several quasi stability criteria for nonlinear differential dynamical systems relative to initial time difference by employing vector lyapunov functions these new results might be more fruitful since it can satisfy less rigid requirements as an application the results are applied into a nonlinear dynamical system to get the quasi stability properties

properties of the dyadic green s function for an unbounded anisotropic medium radiation in an unbounded anisotropic medium is treated analytically by studying the dyadic green s function of the problem initially expressed as a triple fourier integral which is next reduced to a double one under certain conditions the existence of incoming waves is verified it is also found that exponentially decaying waves are possible in such media finally the existence of branch points in the remaining integrand function is investigated and appropriate branch cuts are proposed

a unified and consistent view on the singularities of the electric dyadic green s function in the source region ambiguities associated with the singularity of the electric dyadic green s function are clarified the numerical advantages of finite and infinitesimal principal volumes are dependent on the particular problem being treated it is shown that apparent discrepancies are nonexistent and that either the method of potential or the theory of distribution can be used in this problem and a unified and consistent view can be formed

critical distance for grating lobe series estimating a transition or critical distance above a planar periodic array of point sources radiating into an unbounded medium is considered it is shown that as an observation point approaches a periodic planar phased array of point sources the corresponding spectral domain green s function or grating lobe series converges much more slowly than an equivalent mixed domain representation exhibiting gaussian convergence for a given argument of the green s function the critical transition distance above the array for which both representations take the same time to compute can be estimated numerically since phased array antenna structures with cavity or waveguide type backings often have dimensions that fall well below the critical distance investigations of such structures would seem to benefit significantly from formulations incorporating such hybrid green s functions

exponential and global stability of nonlinear dynamical systems relative to initial time difference specialized research fund for the doctoral program of higher education 20100121120018 natural science foundation of fujian province of china 2010j05013 fundamental research funds for the central universities 2010121004

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

ϕ0 stability of an impulsive system obtained from perturbing lyapunov functions abstract this paper focuses on the stability of the zero solution for the impulsive differential system at fixed times using the method of perturbing lyapunov functions on the basis of the method some sufficient conditions for the above stability to hold are given

on the eigenfunction expansion of electromagnetic dyadic green s functions a relatively simple approach is described for developing the complete eigenfunction expansion of time harmonic electric bar e and magnetic bar h fields within exterior or interior regions containing an arbitrarily oriented electric current point source in particular these results yield directly the complete eigenfunction expansion of the electric and magnetic dyadic green s functions bar bar g e and bar bar g m that are associated with bar e and bar h respectively this expansion of bar bar g e and bar bar g m contains only the solenoidal type eigenfunctions in addition the expansion of bar bar g e also contains an explicit dyadic delta function term which is required for making that expansion complete at the source point the explicit dyadic delta function term in bar bar g e is found readily from a simple condition governing the behavior of the eigenfunction expansion at the source point provided one views that condition in the light of distribution theory these general expressions for the eigenfunction expansion of bar bar g e and bar bar g m reduce properly to those obtained previously for special geometries by tai

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

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

waveguide excited microstrip patch antenna theory and experiment an arbitrarily shaped microstrip patch antenna excited through an arbitrarily shaped aperture in the mouth of a rectangular waveguide is investigated theoretically and experimentally the metallic patch resides on a dielectric substrate grounded by the waveguide flange and may be covered by a dielectric superstrate the substrate and superstrate if present consists of one or more planar homogeneous layers which may exhibit uniaxial anisotropy the analysis is based on the space domain integral equation approach more specifically the green s functions for the layered medium and the waveguide are used to formulate a coupled set of integral equations for the patch current and the aperture electric field the layered medium green s function is expressed in terms of sommerfeld type integrals and the waveguide green s function in terms of floquet series which are both accelerated to reduce the computational effort the coupled integral equations are solved by the method of moments using vector basis functions defined over triangular subdomains the dominant mode reflection coefficient in the waveguide and the far field radiation patterns are then found from the computed aperture field and patch current distributions the radar cross section rcs of a plane wave excited structure is obtained in a like manner sample numerical results are presented and are found to be in good agreement with measurements and with published data

on perturbing liapunov functional perturbing liapunov function method was introduced for systems of ordinary differential equations in this paper we will extend this method to systems of functional differential equations and discuss stability and boundedness properties via the concept of perturbing liapunov function

stability for impulsive differential systems in terms of two measures stability properties of impulsive differential systems are investigated using two different measures and employing piecewise continuous lyapunov functions

φ 0 boundedness and practical φ 0 stability of difference equations in this paper we develop the notions of f 0 boundedness and practical f 0 stability for difference equations via perturbing cone valued lyapunov functions and obtain sufficient conditions of f 0 boundedness and practical f 0 stability

application of dcim to mpie mom analysis of 3d pec objects in multilayered media the formulation c green s functions for multilayered media are reformulated in this paper to extract z dependent part when the source and observation points are in different layers the discrete complex image method dcim is applied to obtain complex images independent on z but dependent on z spl acute for simulation of three dimensional 3 d perfectly electrical conduction pec objects penetrating two or more layers tables of complex images are built in a z spl acute grid during the matrix filling stage of the mixed potential integral equation together with method of moments mpie mom the spatial domain green s functions are interpolated from values in the z spl acute grid while these values are calculated from complex images in the z spl acute grid this interpolation scheme is more efficient than those directly storing the spatial domain green s functions numerical examples are given for analyzing a dipole in a two layered media

computation of the sommerfeld integral tails using the matrix pencil method the oscillating infinite domain sommerfeld integrals si are difficult to integrate using a numerical procedure when dealing with structures in a layered media even though several researchers have attempted to do that generally integration along the real axis is used to compute the si however significant computational effort is required to integrate the oscillating and slowly decaying function along the tail extrapolation methods are generally applied to accelerate the rate of convergence of these integrals however there are difficulties with the extrapolation methods such as locations for the breakpoints in this paper we illustrate a simplified approach for accurate and efficient calculation of the integrals dealing with the tails of the si in this paper we fit the tail by a sum of finite usually 10 to 20 complex exponentials using the matrix pencil method mpm the integral of the tail of the si is then simply calculated by summing some complex numbers no numerical integration is needed in this process as the integrals can be done analytically good accuracy is achieved with a small number of evaluations for the integral kernel 60 points for the mpm as compared with hundreds or thousands of functional evaluations using the traditional extrapolation methods along the tails of the si simulation results show that to obtain the similar accuracy in the evaluation of the si the mpm is approximately 10 times faster than the traditional extrapolation methods moreover since the mpm is robust to the effects of noise this method is more stable especially for large values of the horizontal distances the method proposed in this paper is thus a new and better technique to obtain accurate results for the computation of the green s function for a layered media in the spatial domain

fuzzy rule based classification with featureselector and modified threshold accepting abstract this paper highlights the need to reduce the dimension of the feature space in classification problems of high dimensions without sacrificing the classification power considerably we propose a methodology for classification tasks which comprises three phases i feature selection ii automatic generation of fuzzy if then rules and iii reduction of the rule base while retaining its high classification power the first phase is executed by using featureselector a software developed solely for feature extraction in pattern recognition and classification problems this is for the first time that the featureselector is used as a preprocessor for rule based classification systems in the second phase a standard fuzzy rule based classification system is modified and invoked with the most important features extracted by the featureselector as the new set of features in the third phase a modified threshold accepting algorithm mta proposed elsewhere by the authors ravi et al fuzzy sets and systems forthcoming is used for minimizing the number of rules in the classification system while guaranteeing high classification power the number of rules used and the classification power are taken as the objectives for this multi objective combinatorial global optimization problem the methodology proposed here has been successfully demonstrated for two well known problems i the wine classification problem which includes 13 feature variables in its original form and ii the wisconsin breast cancer determination problem which has 9 feature variables in conclusion the results are encouraging as there is no remarkable reduction in the classification power in both the problems despite the fact that some features have been deleted from the study by resorting to feature selection also the mta outperformed the original threshold accepting algorithm for the test problems considered here the authors suggest that classification problems having higher feature dimensions can be solved successfully within the framework of the methodology presented here the high classification powers obtained for both the problems when working with less feature variables than the original number is the significant achievement of this study

a novel efficient technique for the calculation of the green s functions in rectangular waveguides based on accelerated series decomposition a new efficient technique for computing the green s functions inside rectangular waveguides is presented after a summary of the classical approaches and their difficulties a new strategy is proposed based on the decomposition of the main spectral series into simpler terms although the resulting series present better convergence rate several acceleration techniques are combined to further improve the efficiency several results are presented to demonstrate the improvements in convergence rates obtained using the new decomposition

mining axiomatic fuzzy set association rules for classification problems abstract in this paper we propose a novel method to mine association rules for classification problems namely afsrc afs association rules for classification realized in the framework of the axiomatic fuzzy set afs theory this model provides a simple and efficient rule generation mechanism it can also retain meaningful rules for imbalanced classes by fuzzifying the concept of the class support of a rule in addition afsrc can handle different data types occurring simultaneously furthermore the new model can produce membership functions automatically by processing available data an extensive suite of experiments are reported which offer a comprehensive comparison of the performance of the method with the performance of some other methods available in the literature the experimental result shows that afsrc outperforms most of other methods when being quantified in terms of accuracy and interpretability afsrc forms a classifier with high accuracy and more interpretable rule base of smaller size while retaining a sound balance between these two characteristics

analysis of a circular microstrip disk antenna with a thick dielectric substrate the problem of a circular microstrip disk excited by a probe is solved using rigorous analysis the disk is assumed to have zero thickness and the current on the probe is taken to be uniform using vector hankel transforms the problem is formulated in terms of vector dual integral equations from which the unknown current can be solved for due to the singular nature of the current distribution arising from probe excitation the direct application of galerkin s basis function expansion method gives a slowly convergent result therefore the singular part of the current is removed since the singularity is known a priori the unknown current to be solved for is then regular and tenable to galerkin s method of analysis it is shown that this analysis agrees with the single mode approximation when the dielectric substrate layer is thin and that it deviates from the single mode approximation when the substrate layer is thick excellent agreement of both the computed real and imaginary parts of the input impedance with experimental data is noted the radiation patterns and the current distributions on the disk are also presented

on practical stability of perturbed differential systems the notions of practical stability of systems of ordinary differential equations ode was introduced in this paper we will extend practical stability notion to a new type of stability called practical f 0 stability of perturbed systems of ordinary differential equations and given some criteria and results our technique depends on cone vector liapunov function method

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

stability and boundedness of nonlinear impulsive systems in terms of two measures via perturbing lyapunov functions this paper develops the concepts of stability practical stability and boundedness in terms of two measures for nonlinear impulsive differential systems using the method of perturbing lyapunov functions the notion of perturbing lyapunov functions enables us to discuss stability properties of solutions of nonlinear impulsive differential systems in terms of two measures under much weaker assumptions the novel results offer a way to unify a variety of stability results found in the relative literature

on lipschitz stability for comparison systems of differential equations via limiting equation lipschitz f 0 stability notion was introduced in this paper we will discuss the notion of lipschitz f 0 stability of comparison systems of differential equations our technique depends on limiting equation method

on total φ 0 stability of nonlinear systems of differential equations the notions of f 0 stability of systems of ordinary differential equations odes were introduced in this paper we will extend the f 0 stability notion to a new type of stability called total f 0 stability and give some criteria and results our technique depends on liapunov s direct method

uniform eventual lipschitz stability of impulsive systems on time scales in this paper we discuss the uniform eventual lipschitz stability of impulsive system on time scales by using comparison method lyapunov function and analysis technology some criteria of such stability for system with impulses on time scales are obtained an example is presented to illustrate the efficiency of proposed results

a hybrid three dimensional electromagnetic modeling scheme we present an efficient numerical method for computing electromagnetic em scattering of arbitrary three dimensional 3 d local inhomogeneities buried in a uniform or two layered earth in this scheme the inhomogeneity is enclosed by a volume whose conductivity is discretized by a finite element mesh and whose boundary is only a slight distance away from the inhomogeneity the scheme uses two sets of independent equations the first is a set of finite element equations derived from a variational integral and the second is a mathematical expression for the fields at the boundany in terms of electric fields inside the boundary the green s function is used to derive the second set of equations an iterative algorithm has been developed to solve these two sets of equations the solutions are the electric fields at nodes inside the finite element mesh the scattered fields anywhere may then be obtained by performing volume integrations over the inhomogeneous region the scheme is used for modeling 3 d inho

on the asymptotic stability by nondecrescent ljapunov function on donne des conditions suffisantes pour la stabilite asymptotique partielle de la solution nulle d un systeme non autonome en utilisant une fonction auxiliaire additionnelle au lieu de la decrescence de la fonction de ljapunov

some observations on the spatial and eigenfunction representations of dyadic green s functions electromagnetic theory the principal volume method of expressing the spatial representation of the dyadic green s function in free space is reviewed followed by the eigenfunction expansion method of deriving the dyadic green s function in free space and an arbitrarily shaped waveguide in both cases there are dirac delta function singularities it is shown that dirac delta function in the eigenfunction representation has the same physical interpretation as the dirac delta function singularity in the principal volume method however in the eigenfunction representation there is no need to specify a principal volume this study shows some relationships between the principal volume method and the eigenfunction expansion method and reasserts that the dyadic green s function should be regarded as a distribution or a generalized function

rigorous and efficient full wave analysis of trapezoidal patch antennas a rigorous full wave analysis in the spectral domain for trapezoidal patch antennas is presented particularly a new set of entire domain basis functions for an efficient implementation of the method of moments mom is carried out by properly imposing the boundary conditions the simulated results obtained through the presented method are compared to the measurements showing a good agreement finally a parametric analysis of the main antenna features matching radiation pattern cross polarization levels is also carried out

parametric analysis of slot loaded trapezoidal patch antennas slot loaded trapezoidal patch antennas are analyzed in order to achieve a multifrequency operation a moment method formulation based on new analytical entire domain basis functions is developed and compared to the one involving the rao wilton glisson 1982 rwg triangular discretization the numerical results obtained through the new efficient implemented code are compared to the measurements showing a good agreement a parametric analysis of such antennas is also presented leading to useful design graphs showing the main antenna properties resonance frequencies cross polarization levels matching etc as a function of the patch geometrical dimensions symmetric collocation of the slots on the patch and slot dimensions

vector lyapunov functions and the technique in perturbation theory in l a new comparison theorem is developed that connects the solution of perturbed and unperturbed differential systems in a manner useful in the theory of perturbations this comparison result blends in a sense the two approaches namely the method of lyapunov functions and the method of variation of parameters and consequently provides a flexible mechanism to preserve the nature of perturbations the results that are given in l show that the usual comparison theorem in terms of a lyapunov function is included as a special case and that perturbation theory could be studied in a more fruitful way in the study of large scale dynamic systems s by the method of decomposition and aggregation several lyapunov functions result in a natural way this is because one assumes that the given large scale system is decomposed into isolated subsystems and interconnections between them if the solution of these subsystems possesses good behavior like uniform asymptotic stability then one can construct a lyapunov function relative to each subsystem which can then be utilized to investigate the stability properties of the given large scale dynamic system as a perturbed system by employing the method of vector lyapunov functions in this

perturbing families of lyapunov functions and stability in terms of two measures on considere les proprietes de stabilite non uniforme en termes de deux mesures en employant des familles perturbantes de fonctions de lyapunov

on stability for impulsive perturbed systems via cone valued lyapunov function method the notion of f 0 stability recently was introduced in this paper we will extend this notion to the so called eventual f 0 stability for impulsive systems of differential equations under more relax conditions our technique depends on lyapunov s direct method

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

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 pattern recognition for automatic detection of different teeth substances abstract a method for characterizing the surface of a test object on the basis of its oscillatory behaviour is presented the basic principle of the method is the excitation of oscillations in a small surface element on the elastic solid under investigation and the appropriate measurement of the reaction to this excitation after calculation of the fourier transform a total of 400 magnitude values of the oscillation are available as characteristic features for the classification of an unkown surface for testing the measuring system experiments were conducted on various test objects and the results of measurements performed on different tooth surface are presented the automatic classification of tooth surface is important for the detection of the cementoenamel junction in parodontological practice and the soft removal of dental calculus because in this application the spectra are subject to severe fluctuations by variations in the test object a fuzzy classifier with weighted distance function is employed for the automatic classification for solving the essential problem of selecting from a total of 400 spectral features those which appear to be suited for the respective classification problem a new feature selection algorithm is presented the highly successful result of these experiments indicates possibilities of applying new diagnostic and therapeutic instruments in the field of periodontology

on cone perturbing liapunov function for impulsive differential systems the concept of f 0 stability and f 0 boundedness recently were introduced for systems of ordinary differential equations odes perturbing liapunov function method was discussed for systems of odes and extend to systems of functional differential equations fdes in this paper we extend these notions to impulsive systems of differential equations via cone perturbing liapunov function method

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

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

practical stability of nonlinear differential equation with initial time difference this paper develops the concept of practical stability to nonlinear differential equations with solutions starting with different initial times several practical stability criteria of nonlinear dynamical systems relative to initial time difference are presented by employing two lyapunov like functions the method of two lyapunov like functions enables us to obtain results under weaker assumptions

on the asymptotic stability of systems with impulses by the direct method of lyapunov abstract in the present paper the asymptotic and globally asymptotic stability of the zero solution of systems with impulses is investigated for this purpose piecewise continuous auxiliary functions are used which are an analogue of lyapunov s functions the theorem of marachkov on the asymptotic stability of systems without impulses is generalized the results obtained are formulated in six theorems

practical stabilization of control systems with impulse effects abstract in this paper we investigate practical stabilization of control systems with impulse effects utilizing piecewise continuous lyapunov functions and impulsive differential inequalities we prove some general comparison results through which we establish some sufficient conditions for practical stabilization of control systems with impulse effects we also use two different measures which gives a unified approach and include many interesting special cases

on stability of nonlinear systems of functional differential equations the aim of this paper is to extend some results of f 0 stability for systems of functional differential equations f d e and to give results via razumikhin s method

equivalent layers of surface charge current sheet and polarization in the eigenfunction expansions of green s functions in electromagnetic theory the discontinuous behavior of the eigenfunction expansion of various green s functions commonly used in electromagnetic theory is discussed with the aid of equivalent layers of surface charge current sheet and surface polarization green s function pertaining to the potential function in electrostatics is discussed first followed by a detailed analysis of an eigenfunction representation of a typical dyadic green s function for time varying harmonic fields

a spherical wave representation of the dyadic green s function for a wedge a new expansion for the dyadic green s function of a perfectly conducting wedge is derived it is expressed in terms of a discrete series of spherical vector wave functions this expansion converges well except near a spherical surface which passes through the source point the convergence is particularly rapid in the paraxial region this results in the identification of an edge wave which can play an important role in the radiation from sources and scatterers at the edge of the wedge

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

stability criteria for impulsive differential equations in terms of two measures in general the stability notions of a given solution d t of an impulsive differential system cannot be transferred to the stability notions of the trivial solution by change of variables this is because of the fact that moments of impulse effects of 4 t need not be the same as that of a different solution x t and therefore demanding that the difference lx t d t 1 be small for all future time seems unnatural see 4 73 as a result the definitions of stability require suitable changes in the general situations and the corresponding theory has not yet been developed however in the case of impulsive differential systems with fixed moments of impulse effects such a problem does not arise and hence the standard definitions of stability will suffice employing suitable discontinuous lyapunov functions stability theory has recently been developed for such systems 1 2 3 51 in this paper we shall discuss stabiliy theory of impulsive differential systems with fixed moments of impulse effects in terms of two measures since such a theory enables us to unify a variety of stability results found in the literature we shall employ theory of impulsive differential inequalities as well as a direct approach to bring out the advantages of each approach

on relative ϕ0 stability of impulsive hybrid systems via perturbing lyapunov functions abstract this paper obtains some sufficient conditions for the relative 0 stability of the two impulsive hybrid systems by using the method of perturbing lyapunov functions

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

on stability of nonlinear differential systems via cone valued liapunov function method the notions of partial relative and f 0 stability of ordinary differential equations odes are introduced in e p akpan o akinyele j math anal appl 164 1992 307 324 v lakshmikantham s leela differential and integral inequalities vol 1 academic press new york 1969 in this paper we extend these notions to new types of stability namely f 0 relative and f 0 partial stability of odes using cone valued liapunov function method and comparison technique

lyapunov functions on product spaces and stability theory of delay differential equations if we examine the lyapunov functionals constructed for all the examples that have been discussed so far in the literature we find that the investigators inadvertently employ a combination of a lyapunov function and a functional in such a way that the corresponding derivative can be estimated suitably without demanding minimal classes of functions or the knowledge of solutions as in the case of lyapunov functions or lyapunov functionals respectively 3 61 the method of lyapunov functionals however demands the knowledge of solutions of delay differential equations considered and consequently the discussion of examples is not really in the spirit of the method this observation leads us to develop the method of lyapunov functions on product spaces for studying stability properties of equations with delay where except conceptually the knowledge of solutions is not demanded we shall also develop stability theory in terms of two measures which unifies several known stability concepts our presentation demonstrates the advantage of utilizing lyapunov functions on product spaces 391 0022 247x 91 3 00

on stability of nonlinear systems of ordinary differential equations the notions of f 0 stability h 0 h stability integral and eventual stability of nonlinear systems of ordinary differential equations ode s are introduced our aim in this paper is to improve and extend these notions to new types of stability namely f 0 l p stability h 0 h integral stability and h 0 h eventual stability of systems of ode s respectively and given some criteria our technique depends on liapunov direct method