wavelet like bases for the fast solutions of second kind integral equations a class of vector space bases is introduced for the sparse representation of discretizations of integral operators an operator with a smooth nonoscillatory kernel possessing a finite number of singularities in each row or column is represented in these bases as a sparse matrix to high precision a method is presented that employs these bases for the numerical solution of second kind integral equations in time bounded by o n log 2 n where n is the number of points in the discretization numerical results are given which demonstrate the effectiveness of the approach and several generalizations and applications of the method are discussed

ray analysis of modal reflection for three dimensional open ended waveguides an efficient high frequency ray analysis which combines the geometrical theory of diffraction gtd with the equivalent current method is used for evaluating modal reflection at the open ends of three dimensional waveguides after reviewing a method used for the two dimensional case and introducing some extensions necessary for evaluating modal reflection of open ended three dimensional waveguides the modal reflection coefficients are then given for open ended circular and rectangular waveguides numerical results calculated using these expressions agree favorably with those obtained by a different analytical technique and by experiment

a study of wavelets for the solution of electromagnetic integral equations the use of wavelet basis functions for the efficient solution of electromagnetic integral equations is studied it has previously been demonstrated that the use of wavelets for expansion and testing functions produces a sparse moment method matrix here this effect is examined and analyzed in terms of the radiation receiving characteristics of the wavelet basis functions the limitations of wavelets as an efficient solution technique are discussed and a comparison is made to other fast algorithms

on the use of coifman intervallic wavelets in the method of moments for fast construction of wavelet sparsified matrices orthonormal wavelets have been successfully used as basis and testing functions for the integral equations and extremely sparse impedance matrices have been obtained however in many practical problems the solution domain is confined in a bounded interval while the wavelets are originally defined on the entire real line to overcome this problem periodic wavelets have been described in the literature nonetheless the unknown functions must take on equal values at the endpoints of the bounded interval in order to apply periodic wavelets as the basis functions we present the intervallic coifman wavelets coiflets for the method of moments mom the intervallic wavelets release the endpoints restrictions imposed on the periodic wavelets the intervallic wavelets form an orthonormal basis and preserve the same multiresolution analysis mra of other usual unbounded wavelets the coiflets possesses a special property that their scaling functions have many vanishing moments as a result the zero entries of the matrices are identified directly without using a truncation scheme with an artificially established threshold further the majority of matrix elements are evaluated directly without performing numerical integration procedures such as gaussian quadrature for an n spl times n matrix the number of actual numerical integrations is reduced from n sup 2 to the order of 3n 2l 1 when the coiflets of order l is employed the construction of intervallic wavelets is presented numerical examples of scattering problems are discussed and the relative error of this method is studied analytically

the monotone iterative technique for a parabolic boundary value problem with discontinuous nonlinearity let be a bounded lebesgue measurable domain of r n with a lipschitz boundary the following initial boundary value problem is considered u t lu f u h in q bu o on u 0 where q o t o t and 0 0 l is a uniformly elliptic operator b a boundary operator defined by bu u v bu in which v denotes the outer normal derivative on and f represents a discontinuous non linearity

on a choice of wavelet bases in the wavelet transform approach the daubechies orthogonal wavelet dow is compared with the nonorthogonal cardinal spline wavelet ncsw in the wavelet transform approach and it is shown that the dow is better than the ncsw in view of the computation cost first the computation cost required for the wavelet transform based on the dow is less than that based on the ncsw because the dow has smaller support provided the same number of vanishing moments of wavelets is used second in contrast with the fact that the wavelet transform based on the dow does not affect the condition number of the impedance matrix that based on the ncsw has an effect to make it very large as a result even though the ncsw results in a sparser impedance matrix it requires more computation cost for solving the resultant matrix equation in comparison with the dow because the cost depends not only on the sparsity but also on the condition number of the matrix

on the attainable set of differential inclusions and control systems in several cases problems in optimal control mathematical economics and mechanics involving various types of ambiguity indeterminancy or shortage of information hysteresis stochastic problems dynamical price decentralization etc lead to the study of differential inclusions in a differential inclusion the tangent at each point is prescribed by a multifunction set valued function and the direction field is usually called an orientor field in this paper we consider the differential inclusion

harmonic oscillator with multiplicative noise nonmonotonic dependence on the strength and the rate of dichotomous noise the output signal of a undamped linear oscillator with a random frequency subject to a periodic force shows nonmonotonic dependence on the strength and the rate of color noise stochastic resonance the effect is absent for white noise

arbitrary high order c0 tensor product galerkin finite element methods for the electromagnetic scattering from a large cavity the paper is concerned with the electromagnetic scattering from a large cavity embedded in an infinite ground plane the electromagnetic cavity problem is described by the helmholtz equation with a nonlocal boundary condition on the aperture of the cavity and dirichlet or neumann boundary conditions on the walls of the cavity a tensor product galerkin finite element method fem is proposed in which spaces of c 0 piecewise polynomials of degree k 1 are employed by the fast fourier transform and the toeplitz type structure of the approximation to the nonlocal operator in the nonlocal boundary condition a fast algorithm is designed for solving the linear system arising from the cavity problem with vertically layered media which requires o n 2logn operations on an nxn uniform partition numerical results for model problems illustrate the efficiency of the fast algorithm and exhibit the expected optimal global convergence rates of the finite element methods moreover our numerical results also show that the high order approximations are especially effective for problems with large wave numbers

on the convergence in distribution of measurable multifunctions random sets normal integrands stochastic processes and stochastic infima the concept of the distribution function of a closed valued measurable multifunction is introduced and used to study the convergence in distribution of sequences of multifunctions and the epi convergence in distribution of normal integrands and stochastic processes in particular various compactness criteria are exhibited the connections with the classical convergence theory for stochastic processes are analyzed and for purposes of illustration we apply the theory to sketch out a modified derivation of donsker s theorem brownian motion as a limit of normalized random walks we also suggest the potential application of the theory to the study of the convergence of stochastic infima

on a new class of differential variational inequalities and a stability result this paper addresses a new class of differential variational inequalities that have recently been introduced and investigated in finite dimensions as a new modeling paradigm of variational analysis to treat many applied problems in engineering operations research and physical sciences this new subclass of general differential inclusions unifies ordinary differential equations with possibly discontinuous right hand sides differential algebraic systems with constraints dynamic complementarity systems and evolutionary variational systems the purpose of this paper is two fold firstly we show that these differential variational inequalities when considering slow solutions and the more general level of a hilbert space contain projected dynamical systems another recent subclass of general differential inclusions this relation follows from a precise geometric description of the directional derivative of the metric projection in hilbert space which is based on the notion of the quasi relative interior secondly we are concerned with stability of the solution set to this class of differential variational inequalities here we present a novel upper set convergence result with respect to perturbations in the data including perturbations of the associated set valued maps and the constraint set here we impose weak convergence assumptions on the perturbed set valued maps use the monotonicity method of browder and minty and employ mosco convergence as set convergence also as a consequence we obtain a stability result for linear complementarity systems

a sixth order fast algorithm for the electromagnetic scattering from large open cavities in this paper a sixth order fast algorithm is presented for solving the electromagnetic scattering problem from a rectangular open cavity embedded in an infinite ground plane firstly a sixth order compact finite difference scheme is employed to discretize the scattering problem described by the helmholtz equation with a nonlocal boundary condition then exploiting the discrete fourier transformation in the horizontal and a gaussian elimination in the vertical direction presented by 2 the discrete system reduces to a much smaller interface system an effective preconditioner is developed for the krylov subspace iterative solver to solve this interface system numerical results show the remarkable efficiency and accuracy of the new algorithm

legendre spectral galerkin method for electromagnetic scattering from large cavities the paper is concerned with the electromagnetic scattering from a large cavity embedded in an infinite ground plane which is governed by a helmholtz type equation with nonlocal hypersingular transparent boundary condition on the aperture we first present some stability estimates with the explicit dependency of wavenumber for the helmholtz type cavity problem then a legendre spectral galerkin method is proposed in which the legendre gauss interpolatory approximation is applicable to the hypersingular integral and a legendre galerkin scheme is used for the approximation to the helmholtz equation the existence and the uniqueness of the approximation solution are established for large wavenumbers the stability and the spectral convergence of the numerical method are then proved illustrative numerical results presented confirm our theoretical estimates and show that the proposed spectral method compared with low order finite difference methods is especially effective for problems with large wavenumbers

sparsity and conditioning of impedance matrices obtained with semi orthogonal and bi orthogonal wavelet bases wavelet and wavelet packet transforms are often used to sparsify dense matrices arising in the discretization of cem integral equations this paper compares orthogonal semi orthogonal and bi orthogonal wavelet and wavelet packet transforms with respect to the condition numbers matrix sparsity and number of iterations for the transformed systems the best overall results are obtained with the orthogonal wavelet packet transforms that produce highly sparse matrices requiring fewest iterations among wavelet transforms the semi orthogonal wavelet transforms lead to the sparsest matrices but require too many iterations due to high condition numbers the bi orthogonal wavelets produce very poor sparsity and require many iterations and should not be used in these applications

on the existence of solutions for random differential inclusions in a banach space abstract we prove two existence theorems for random differential inclusions defined in a separable banach space one is about differential inclusions defined on all of the banach space x and the other for differential inclusion defined on a closed convex subset k both theorems are proved through the use of analogous deterministic results which we also include and techniques from the theory of measurable multifunctions

distributional properties of correspondences on loeb spaces abstract we present some regularity properties for the set of distributions induced by the measurable selections of a correspondence over a loeb space which include closedness convexity compactness purification and semicontinuity we also note that all the properties reported in the main theorems are not satisfied by some correspondences on the unit lebesgue interval

on a paper by khan and majumdar abstract in this paper we generalize two results of khan and majumdar on the weak sequential convergence of functions in the lebesgue bochner space l x 1 and on a fatou like convergence theorem

stochastic resonance in chaotic systems the phenomenon of stochastic resonance sr is investigated for chaotic systems perturbed by white noise and a harmonic force the bistable discrete map and the lorenz system are considered as models it is shown that sr in chaotic systems can be realized via both parameter variation in the absence of noise and by variation of the noise intensity with fixed values of the other parameters

a hybrid bem wtm approach for analysis of the em scattering from large open ended cavities an effective hybrid boundary element method bem and wavelet transform method wtm is proposed to analyze electromagnetic scattering from three dimensional 3 d open ended cavities with arbitrary shapes this hybrid technique formulates the original cavity problems by a magnetic field integral equation the bem is employed to establish the mapping between the original complex integral surface and the unit square the wtm is used to reduce the density of the moment matrix since a surface integral equation has to be solved the wtm requires a two dimensional 2 d wavelet basis to implement the numerical computation the previous fast iterative algorithm for 2 d wavelets has been extended for efficiently constructing various 2 d wavelet basis functions by a tensorial product from two one dimensional 1 d regular multiresolution analyses unlike the conventional method of moments the proposed hybrid technique can always obtain sparse moment matrix equations which can be efficiently solved by sparse solvers as the level scales for numerical discretization of cavities increase larger compression rates can be obtained which makes it possible for the hybrid bem wtm technique to efficiently solve scattering from large open ended cavities with complex terminations numerical results are presented to demonstrate the merits of the proposed method

on compactly supported spline wavelets and a duality principle let v 1 v 0 v 1 be a multiresolution analysis of l 2 generated by the mth order b spline n m x we exhibit a compactly supported basic wavelet m x that generates the corresponding orthogonal complementary wavelet subspaces w 1 w 0 w 1 consequently the two finite sequences that describe the two scale relations of n m x and m x in terms of n m 2x j j z yield an efficient reconstruction algorithm to give an efficient wavelet decomposition algorithm based on these two finite sequences we derive a duality principle which also happens to yield the dual bases n m x j and 59 m x j relative to n m x j and m x j respectively

two transparent boundary conditions for the electromagnetic scattering from two dimensional overfilled cavities we consider electromagnetic scattering from two dimensional 2d overfilled cavities embedded in an infinite ground plane the unbounded computational domain is truncated to a bounded one by using a transparent boundary condition tbc proposed on a semi ellipse for overfilled rectangular cavities with homogeneous media another tbc is introduced on the cavity apertures which produces a smaller computational domain the existence and uniqueness of the solutions of the variational formulations for the transverse magnetic and transverse electric polarizations are established in the exterior domain the 2d scattering problem is solved in the elliptic coordinate system using the mathieu functions in the interior domain the problem is solved by a finite element method numerical experiments show the efficiency and accuracy of the new boundary conditions

an effective wavelet matrix transform approach for efficient solutions of electromagnetic integral equations an effective numerical method based on wavelet matrix transforms for efficient solution of electromagnetic em integral equations is proposed using the wavelet matrix transform produces highly sparse moment matrices which can be solved efficiently a fast construction method for various orthonormal or nonorthonormal wavelet basis matrices is also given it has been found that using nonsimilarity wavelet matrix transforms such as nonsimilarity nonorthonormal cardinal spline wavelet nsncsw transform one can obtain a much higher compression rate and much better accuracy of the approximate solutions than using similarity wavelet transforms such as daubechies 1992 orthonormal wavelet dow transform numerical examples are given to show the validity and effectiveness of the method

convergence of multivalued mappings via approximable measurable selectors we investigate the convergence of measurable selectors for the limit of measurable multivalued maps the relationship between the convergence of measurable selectors and lower and upper limits of measurable multivalued mappings with closed images is also derived

a stability result for differential inclusions in banach spaces on etablit un resultat de stabilite pour les inclusions differentielles definies sur un espace de banach separable

stochastic resonance in overdamped two coupled anharmonic oscillators abstract we consider the overdamped version of two coupled anharmonic oscillators with the external periodic force f sin t and gaussian noise term t added to one of the two state variables of the system linear stability analysis is carried out in the absence of external periodic force and noise then the system with external periodic force only and noise term only are studied in the noise free system four period t orbits are found to co exist one in each of the four wells for small values of forcing amplitude f for fixed values of other parameters at a critical value of f f c cross well periodic orbit appears f c is found to increase with increase in the coupling strength in the absence of forcing the system is found to exhibit intermittent jumping motion between two wells above a particular value of noise strength d d c the noise induced jumping behaviour is characterized by first passage time and residence time distributions next the influence of noise in the presence of the external periodic force is numerically studied the system is found to exhibit stochastic resonance behaviour the observed stochastic resonance dynamics is characterized using power spectrum signal to noise ratio and residence time distribution the plot of maximal lyapunov exponent versus noise strength has shown a stochastic resonance profile the occurrence of stochastic resonance is studied by varying the forcing frequency and the coupling strength finally the influence of addition of external periodic force and noise term to different state variables is also presented

asymptotic stochastic programs consider a stochastic program with unique solution by the notion of epi convergence in distribution in local coordinates we define the asymptotic stochastic program associated to it stochastic programs may be classified according to the type of the pertaining asymptotic program in particular three such types are studied in detail the normal shift program the wiener type program and the poisson hyperplane program conditions for the convergence to each of the three types are given

impedance matrix compression imc using iteratively selected wavelet basis we present a novel approach for the incorporation of wavelets into the solution of frequency domain integral equations arising in scattering problems in this approach we utilize the fact that when the basis functions used are wavelet type functions only a few terms in a series expansion are needed to represent the unknown quantity to determine these dominant expansion functions an iterative procedure is devised the new approach combined with the iterative procedure yields a new algorithm that has many advantages over the presently used methods for incorporating wavelets numerical results which illustrate the approach are presented for three scattering problems

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed

contributions to the theory of set valued functions and set valued measures measurable multifunctions and multimeasures with values in a banach space are studied we start by proving a variation of the known dunford theorem for weak compactness in l1 x with a similar technique we prove that the range of certain vector valued integrals that appear in applications is w compact and convex also we obtain dunford pettis type theorems for sequences of integrably bounded multifunctions some pointwise w compactness theorems are also obtained for certain families of measurable multifunctions then we prove a representation theorem for additive set valued operators defined on l1 x finally in the last section a detailed study of transition multimeasures is conducted and several representation theorems are proved

electromagnetic scattering from three dimensional cavities via a connection scheme the electromagnetic scattering from arbitrary three dimensional cavities is presented to alleviate computational constraints for three dimensional problems a connection scheme is developed based on microwave network theory this scheme allows the cavity to be divided into sections and each section to be analyzed independently of the rest of the cavity each section of the cavity is represented by a generalized admittance matrix which if formulated via a boundary integral equation approach using the concept of input and load admittance the aperture admittance matrix of the cavity can be derived by cascading the admittance matrices of individual sections once the cavity aperture admittance matrix is obtained the aperture electric field and the backscattered field are found by the standard generalized network formulation numerical results are compared against modal solutions of regularly shaped cavities with good agreement this connection scheme leads to a reduction in computational resources especially for cavities with one dimension much larger than the other two

a fixed point approach in the study of the solution sets of lipschitzian functional differential inclusions abstract this paper deals with applications of general results on fixed point sets of set valued contraction mappings to the study of solution sets of functional differential inclusions with lipschitz type right hand side in separable banach spaces

on the use of wavelet expansions in the method of moments em scattering an approach which incorporates the theory of wavelet transforms in method of moments solutions for electromagnetic wave interaction problems is presented the unknown field or response is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function which is often referred to as the mother wavelet the wavelet expansion can adaptively fit itself to the various length scales associated with the scatterer by distributing the localized functions near the discontinuities and the more spatially diffused ones over the smooth expanses of the scatterer the approach is thus best suited for the analysis of scatterers which contain a broad spectrum of length scales ranging from a subwavelength to several wavelengths using a galerkin method and subsequently applying a threshold procedure the moment method matrix is rendered sparsely populated the structure of the matrix reveals the localized scale fitting distribution long before the matrix equation is solved the performance of the proposed discretization scheme is illustrated by a numerical study of electromagnetic coupling through a double slot aperture

a hybrid wavelet expansion and boundary element analysis of electromagnetic scattering from conducting objects a new wavelet approach is presented for treating the two dimensional electromagnetic scattering problems over curved computation domains the wavelet expansion method in combination with the boundary element method bem is applied to solve the integral equation for the unknown surface current the unknown surface current is expanded in terms of a basis derived from a periodic orthogonal wavelet in interval 0 1 the geometrical representation of the bem is employed to establish the map between the curved computation domain and the interval 0 1 this technique exhibits the advantages of both the wavelet expansion method and the boundary element method sparse matrix system and accurately modeling of curved surfaces comparisons of the results from the new technique with the moment method solutions the analytical solutions or the data in previous publications are provided good agreements are observed

a fast algorithm for the electromagnetic scattering from a large cavity a fast algorithm is presented for solving electromagnetic scattering from a rectangular open cavity embedded in an infinite ground plane the medium inside the cavity is assumed to be vertically layered by introducing a transparent artificial boundary condition the problem in the open cavity is reduced to a bounded domain problem a simple finite difference method is then applied to solve the model helmholtz equation the fast algorithm is designed for solving the resulting discrete system in terms of the discrete fourier transform in the horizontal direction a gaussian elimination in the vertical direction and a preconditioning conjugate gradient method with a complex diagonal preconditioner for the indefinite interface system the existence and uniqueness of the finite difference solution are established for arbitrary wave numbers our numerical experiments for large numbers of mesh points up to 16 million unknowns and for large wave numbers e g between 100 and 200 wavelengths show that the algorithm is extremely efficient the cost for calculating the radar cross section which is of significant interest in practice is o m2 for an m times m mesh the proposed algorithm may be extended easily to solve discrete systems from other discretization methods of the model problem

product type block preconditioners for electromagnetic cavity problems in a radar detecting system the radar cross section rcs of a target is an important application in electromagnetics computation cavity prediction is usually required in the computation process when wavelengths of electromagnetic field are large cavity calculation is a challenging problem the main aim of this paper is to employ the preconditioned gmres method to solve linear systems arising in cavity calculation of the transverse magnetic and transverse electric problems we develop new preconditioners based on fast transforms and toeplitz solvers our numerical results show that the proposed preconditioners are quite efficient and effective especially when the wavelength is large

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

improving the performance of the boundary element method with time dependent fundamental solutions by the use of a wavelet expansion in the time domain the object of this paper is a wavelet based formulation of the boundary element method bem for diffusion problems characterized by time dependent fundamental solution while the bem is a well known and often used technique its time dependent formulation for diffusion problems is very rarely used in practical applications due to the high computational cost which characterizes it here a new formulation is proposed which through the use of the wavelet expansion of the time behaviour of the boundary elements is characterized by a lower cpu time consumption when compared with the standard bem diffusion formulation the problem to be solved is transformed into an algebraic system of higher dimension and its solution gives the time domain behaviour of the desired quantities in this way the time stepping procedure is avoided together with the formulation the analysis of the computational cost and two examples are given in the paper copyright 2006 john wiley sons ltd

convergence of set valued sub and supermartingales in the kuratowski mosco sense the purpose of this paper is to prove some convergence theorems of closed and convex set valued sub and supermartingales in the kuratowski mosco sense to get submartingale convergence theorems we give sufficient conditions for the kudo aumann integral and hiai umegaki conditional expectation to be closed both for compact convex set valued random variables and for closed convex set valued random variables we also give an example of a bounded closed convex set valued random variable whose kudo aumann integral is not closed

multivalued perturbations of subdifferential type evolution equations in hilbert spaces in this paper we study the multivalued evolution equation x t x t f t x t x 0 x0 where x r is a proper convex lower semicontinuous l s c function f is a multivalued perturbation and x is an infinite dimensional separable hilbert space we have an existence result for f being nonconvex valued and another for f being convex valued but not closed valued when k indicator function of a compact convex set k we obtain some extensions of earlier results by moreau and henry then using the kuratowski mosco convergence of sets and the convergence of functions we prove a well posedness result for the evolution inclusion we are studying also we consider a random version of it and prove the existence of a random solution finally we present applications to problems in partial differential equations

an application of the continuous selection theorem to the study of the fixed points of multivalued mappings abstract applying the continuous selection theorem given by k przestawski and l rybinski michael selection theorem under weak lower semicontinuity assumption proc amer math soc in press we state the result on continuous dependence of the fixed points of set valued contractions and the krasnoselski type fixed point theorem for multivalued mappings

deterministic stochastic resonance in a piecewise linear chaotic map the phenomenon of stochastic resonance sr is observed in a completely deterministic setting with thermal noise being replaced by one dimensional chaos the piecewise linear map investigated in the paper shows a transition from symmetry broken to symmetric chaos on increasing a system parameter in the latter state the chaotic trajectory switches between the two formerly disjoint attractors driven by the map s inherent dynamics this chaotic switching rate is found to resonate with the frequency of an externally applied periodic perturbation multiplicative or additive by periodically modulating the parameter at a specific frequency omega we observe the existence of resonance where the response of the system in terms of the residence time distribution is maximum this is a clear indication of sr like behavior in a chaotic system

continuous selections and retractive representations for the fixed points sets of set valued reich s contractions abstract we refine a continuous selection approach adopted earlier to fixed points of set valued banach s contractions an extension of selection and representation results to continuous set valued reich s contractions is given a new krasnoselskii melvin type fixed point theorem is stated as a corollary

on the dependence of the solutions and optimal solutions of control problems on the control constraint set abstract in this paper we examine the dependence of the solutions and optimal solutions of a class of linear infinite dimensional control systems on the control constraint set this is done using the weak and the kuratowski mosco convergence of sets first we establish some general facts about weakly convergent multifunctions then we prove some convergence theorems for the trajectories of certain control systems we also derive a general relaxation theorem subsequently we pass to optimal control problems and prove various convergence results we conclude with an example from parabolic control systems

a hybrid bem wtm dft technique for analysis of the em scattering from open ended circular cavities with cylindrically periodic terminations the cavity problem formulated using a magnetic field integral equation mfie can be solved by the iterative physical optics ipo method the progressive physical optics ppo method or the hybrid boundary element method wavelet transform method bem wtm in this paper we focus on open ended circular cavities with cylindrically periodic terminations the cavity problem is formulated using an electric field integral equation efie based on the dyadic green function technique instead of an mfie the discrete fourier transform dft technique is applied by exploiting the periodicity of the termination to reduce the original computational size by a factor of n sub s with corresponding computational savings of a factor of n sub s sup 2 where n sub s denotes the number of blades in the cylindrically periodic termination two kinds of dyadic green functions are derived to reduce the integral range in the efie thus accelerating the scattering solutions for different cavity applications the bem wtm method is combined with the dft to obtain sparse impedance matrices that can be efficiently solved using sparse solvers the proposed hybrid bem wtm dft technique provides an alternative means of effectively analyzing the electromagnetic em scattering from large size circular cavities with cylindrically periodic terminations numerical results are presented to demonstrate the merits of the method

stochastic integrals of set valued processes and fuzzy processes we define the stochastic integrals of a set valued process and a fuzzy process with respect to a cylindrical brownian motion on a hilbert space we also give their properties which are useful for the study of fuzzy stochastic differential equations and stochastic differential inclusions with a set valued diffusion term

classical harmonic oscillator with multiplicative noise abstract the first two moments of an underdamped harmonic oscillator were found for additive and multiplicative noises a detailed analysis is performed of the case of a random damping which supplements the case of a random frequency which has received the most study in both cases the second moments are unstable for the sufficient large noise strength the difference appears in the stability conditions of the first moments which can diverge already for white noise for the random damping and only for color noise for the random frequency the difference between these two types of multiplicative noises shows up also in the response to an external periodic force namely white noise influences the first moment only in the case of a random damping however the second moments in both cases show the non monotonic dependence on the noise strength and correlation rate stochastic resonance in linear systems

on cournot nash equilibria in generalized qualitative games with a continuum of players in recent years the nash debreu theorem 28 8 of 1951 52 has been the subject of two particularly far reaching generalizations the first is a neglected contribution of ma 24 and is a result on the existence of cournot nash equilibria in games with an arbitrary set of players each of whom has strategy sets in an arbitrary hausdorff topological vector space the second is a result of toussaint 32 and it can be viewed as a generalization of ma s theorem to a setting where each player s pay off is generated by a nonordered relation both of these results are elegant and simple enough that they can be fully stated the following result was proved in 1969

noise free stochastic resonance in simple chaotic systems abstract the phenomenon of stochastic resonance sr is reported in a completely noise free situation with the role of thermal noise being taken by low dimensional chaos a one dimensional piecewise linear map and a pair of coupled excitatory inhibitory neurons are the systems used for the investigation both systems show a transition from symmetry broken to symmetric chaos on varying a system parameter in the latter state the systems switch between the formerly disjoint attractors due to the inherent chaotic dynamics this switching rate is found to resonate with the frequency of an externally applied periodic perturbation either parametric or additive the existence of a resonance in the response of the system is characterized in terms of the residence time distributions the results are an unambiguous indicator of the presence of sr like behavior in these systems analytical investigations supporting the observations are also presented the results have implications in the area of information processing in biological systems

on the convergence of closed valued measurable multifunctions in this paper we study the convergence almost everywhere and in measure of sequences of closed valued multifunctions we first give a number of criteria for the convergence of sequences of closed subsets these results are used to obtain various characterizations for the convergence of measurable multifunctions in particular we are interested in the convergence properties of measurable selections

multiresolution analysis of printed antennas and circuits a dual isoscalar approach a new approach is presented for the integral equation analysis of multilayer printed circuits antennas and arrays it is based on the introduction of new multiresolution vector functions with properties similar to those of the scalar wavelets and flexible enough to accommodate for general shapes the resulting method of moments mom impedance matrix shows a good conditioning that allows its safe sparsification and the efficient use of iterative methods for the solution of the linear system the results of the analysis of various real life structures show the advantage of the method

survey of numerical methods for solution of large systems of linear equations for electromagnetic field problems many of the popular methods for the solution of large matrix equations are surveyed with the hope of finding an efficient method suitable for both electromagnetic scattering and radiation problems and system identification problems

numerical solution of electromagnetic scattering from a large partly covered cavity the paper focuses on the numerical study of electromagnetic scattering from two dimensional 2d large partly covered cavities which is described by the helmholtz equation with a nonlocal boundary condition on the aperture the classical five point finite difference method is applied for the discretization of the helmholtz equation and a linear approximation is used for the nonlocal boundary condition we prove the existence and uniqueness of the numerical solution when the medium in the cavity is y direction layered or the number of the mesh points on the aperture is large enough the fast algorithm proposed in bao and sun 2005 2 for open cavity models is extended to solving the partly covered cavity problem with vertically layered media a preconditioned krylov subspace method is proposed to solve the partly covered cavity problem with a general medium in which a layered medium model is used as a preconditioner of the general model numerical results for several types of partly covered cavities with different wave numbers are reported and compared with those by ilu type preconditioning algorithms our numerical experiments show that the proposed preconditioning algorithm is more efficient for partly covered cavity problems particularly with large wave numbers

semi orthogonal versus orthogonal wavelet basis sets for solving integral equations the two categories of wavelets orthogonal and semi orthogonal are compared and it is shown that the semi orthogonal wavelet is best suited for integral equation applications the battle lemarie orthogonal wavelet and the spline generated semi orthogonal wavelet are each used to solve for the current distribution on an infinite strip illuminated by a transverse magnetic tm plane wave and a straight thin wire illuminated by a normally incident plane wave the grounds for comparison are accuracy in characterizing the current matrix sparsity computation time and singularity extraction capability the limitations and advantages of solving integral equations with each of the two wavelet categories are discussed