on singular control problems with state constraints and regime switching this paper investigates a singular stochastic control problem for a multi dimensional regime switching diffusion process confined in an unbounded domain the objective is to maximize the total expected discounted rewards from exerting the singular control such a formulation stems from application areas such as optimal harvesting multiple species and optimal dividends payments schemes in random environments with the aid of weak dynamic programming principle and an exponential transformation we characterize the value function to be the unique constrained viscosity solution of a certain system of coupled nonlinear quasi variational inequalities several examples are analyzed in detail to demonstrate the main results

the use of pde centres in the local rbf hermitian method for 3d convective diffusion problems in this work an extension is proposed to the local hermitian interpolation lhi method a meshless numerical method based on interpolation with small and heavily overlapping radial basis function rbf systems this extension to the lhi method uses interpolation functions which themselves satisfy the partial differential equation pde to be solved in this way a much improved reconstruction of partial derivatives can be obtained resulting in significantly improved accuracy in many cases the implementation algorithm is described and is validated via three convection diffusion reaction problems for steady and transient situations a crank nicolson implicit time stepping technique is used for the time dependent problems in the proposed approach a form of analytical upwinding is implicitly implemented by the use of the partial differential operator of the governing equation in the interpolation function which includes the desired information about the convective velocity field the implicit upwinding scheme intrinsic to the proposed numerical approach is tested by solving a one dimensional travelling front problem at peclet numbers of 500 1000 2000 5000 and infinity which corresponds to a shock front in the case of infinity in addition the accuracy of the numerical scheme is validated against a one dimensional steady state solution exhibiting strong boundary layer effects and also against a steady and a transient three dimensional convection diffusion problem on irregular datasets all the test cases are validated against the corresponding analytical solutions finally the effect of various interpolation stencil configurations is investigated and some important limitations on local data centre distribution are identified

a numerical study of some radial basis function based solution methods for elliptic pdes abstract during the last decade three main variations have been proposed for solving elliptic pdes by means of collocation with radial basis functions rbfs in this study we have implemented them for infinitely smooth rbfs and then compared them across the full range of values for the shape parameter of the rbfs this was made possible by a recently discovered numerical procedure that bypasses the ill conditioning which has previously limited the range that could be used for this parameter we find that the best values for it often fall outside the range that was previously available we have also looked at piecewise smooth versus infinitely smooth rbfs and found that for pde applications with smooth solutions the infinitely smooth rbfs are preferable mainly because they lead to higher accuracy in a comparison of rbf based methods against two standard techniques a second order finite difference method and a pseudospectral method the former gave a much superior accuracy

dsc ritz method for the free vibration analysis of mindlin plates this paper introduces a novel method for the free vibration analysis of mindlin plates the proposed method takes the advantage of both the local bases of the discrete singular convolution dsc algorithm and the pb 2 ritz boundary functions to arrive at a new approach called dsc ritz method two basis functions are constructed by using dsc delta sequence kernels of the positive type the energy functional of the mindlin plate is represented by the newly constructed basis functions and is minimized under the ritz variational principle extensive numerical experiments are considered by different combinations of boundary conditions of mindlin plates of rectangular and triangular shapes the performance of the proposed method is carefully validated by convergence analysis the frequency parameters agree very well with those in the literature numerical experiments indicate that the proposed dsc ritz method is a very promising new method for vibration analysis of mindlin plates copyright 2004 john wiley sons ltd

moments in infinite channel queues we consider a new approach to the problem of evaluating the moments of the steady state number of customers in system b for an infinite channel queue having general input our new approach uses the rate conservation law as a consequence we show that for a variety of g gi queues var b as long as service times have finite first moment in addition we give some ordering relations for the variance of b when comparing two alternative systems with convex ordered inter arrival time distributions

imposing various boundary conditions on positive definite kernels abstract this work is motivated by the frequent occurrence of boundary value problems with various boundary conditions in the modeling of some problems in engineering and physical science here we propose a new technique to force the positive definite kernels such as some radial basis functions to satisfy the boundary conditions exactly it can improve the applications of existing methods based on positive definite kernels and radial basis functions especially the kernel based pseudospectral method for handling the differential equations with more complicated boundary conditions in the proposed technique some new kernels are constructed using the positive definite kernels in a manner that they satisfy the required conditions in addition we prove the positive definiteness of the newly constructed kernel and also the non singularity of the collocation matrix is proved under some conditions the proposed method is verified through the numerical solution of some benchmark problems such as a singularly perturbed steady state convection diffusion problem two and three dimensional poissons equations with various boundary conditions

exact closed form frequency equations for thick circular plates using a third order shear deformation theory abstract this paper presents for the first time exact closed form frequency equations and transverse displacement for thick circular plates with free soft simply supported hard simply supported and clamped boundary conditions based on reddy s third order shear deformation theory hamiltonian and minimum potential energy principles are used to extract the equations of dynamic equilibrium and natural boundary conditions of the plate the new formulation is verified by comparing the results with their counterparts reported in open literature natural frequencies of circular plates with different boundary conditions are tabulated in dimensionless form for various values of thickness radius ratios the results presented on the basis of exact closed form frequency equations are expected to serve as reliable benchmarks

the runge phenomenon and spatially variable shape parameters in rbf interpolation many studies mostly empirical have been devoted to finding an optimal shape parameter for radial basis functions rbf when exploring the underlying factors that determine what is a good such choice we are led to consider the runge phenomenon rp best known in cases of high order polynomial interpolation as a key error mechanism this observation suggests that it can be advantageous to let the shape parameter vary spatially rather than assigning a single value to it benefits typically include improvements in both accuracy and numerical conditioning still another benefit arises if one wishes to improve local accuracy by clustering nodes in selected areas this idea is routinely used when working with splines or finite element methods however local refinement with rbfs may cause rp type errors unless we use a spatially variable shape paremeter with this enhancement rbf approximations combine freedom from meshes with spectral accuracy on irregular domains and furthermore permit local node clustering to improve the resolution wherever this might be needed

locking free finite element method for a bending moment formulation of timoshenko beams in this paper we study a finite element formulation for timoshenko beams it is known that standard finite elements applied to this model lead to wrong results when the thickness of the beam is small here we consider a mixed formulation in terms of the transverse displacement rotation shear stress and bending moment by using the classical babuska brezzi theory it is proved that the resulting variational formulation is well posed we discretize it by continuous piecewise linear finite elements for the shear stress and bending moment and discontinuous piecewise constant finite elements for the displacement and rotation we prove an optimal linear order of convergence in terms of the mesh size for the natural norms and a double order quadratic in l 2 norms for the shear stress and the bending moment these estimates involve constants and norms of the solution that are proved to be bounded independently of the beam thickness which ensures the locking free character of the method numerical tests are reported in order to support our theoretical results

vibration analysis of circular mindlin plates using the differential quadrature method abstract axisymmetric free vibrations of moderately thick circular plates described by the linear shear deformation mindlin theory are analyzed by the differential quadrature dq method the first fifteen natural frequencies of vibration are calculated for uniform circular plates with free simply supported and clamped edges through these computations the capability and simplicity of the differential quadrature method for moderately thick plate eigenvalue analysis is demonstrated and convergence and accuracy are thoughtfully examined the case of rigid point support at the plate centre is also considered in the present paper for which special attention is paid to the capability and convergence of the current method

axisymmetric vibrations of polar orthotropic mindlin annular plates of variable thickness abstract analysis and numerical results are presented for the axisymmetric vibrations of polar orthotropic annular plates with linear variation in thickness according to mindlin s shear theory of plates a chebyshev collocation technique has been employed to obtain the frequency equations for the transverse motion of such plates for three different boundary conditions frequencies mode shapes and moments for the first three modes of vibration have been computed for different plate parameters a comparison of frequencies with the corresponding values obtained by classical plate theory leads to some interesting conclusions

a new stable basis for radial basis function interpolation it is well known that radial basis function interpolants suffer from bad conditioning if the basis of translates is used in the recent work by pazouki and schaback 2011 5 the authors gave a quite general way to build stable and orthonormal bases for the native space n f w associated to a kernel f on a domain w r s the method is simply based on the factorization of the corresponding kernel matrix starting from that setting we describe a particular basis which turns out to be orthonormal in n f w and in 2 w x where x is a set of data sites of the domain w the basis arises from a weighted singular value decomposition of the kernel matrix this basis is also related to a discretization of the compact operator t f n f w n f w t f f x w f x y f y dy x w and provides a connection with the continuous basis that arises from an eigendecomposition of t f finally using the eigenvalues of this operator we provide convergence estimates and stability bounds for interpolation and discrete least squares approximation

application of the rbf meshless method to the solution of the radiative transport equation in this paper we introduce a radial basis function collocation method for computing solutions to the time dependent radiative transfer equation for these computations we use finite differences to discretize the time coordinate a discrete ordinate method to discretize the directional variable and an expansion in radial basis functions to approximate the spatial dependence of the solution the main advantages of the rbf method are that it does not require any mesh or grid achieves spectral accuracy in multi dimensions for arbitrary node layouts and it is extremely simple to implement

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

adaptive residual subsampling methods for radial basis function interpolation and collocation problems we construct a new adaptive algorithm for radial basis functions rbfs method applied to interpolation boundary value and initial boundary value problems with localized features nodes can be added and removed based on residuals evaluated at a finer point set we also adapt the shape parameters of rbfs based on the node spacings to prevent the growth of the conditioning of the interpolation matrix the performance of the method is shown in numerical examples in one and two space dimensions with nontrivial domains

variational derivation of governing differential equations for truncated version of bresse timoshenko beams abstract in this paper we provide a variational derivation of modified bresse timoshenko equations this process leads to the additional term to so called truncated set of bresse timoshenko equations this new term is associated with the modified slope inertia the two sets of truncated versions of the bresse timoshenko equations are contrasted with each other as well as with the original bresse timoshenko equations on the example of the a beam that is simply supported at its both ends and b the cantilever beam with end mass it is concluded that application of either truncated sets of equations is advantageous over the original bresse timoshenko equations as far as two truncated sets of equations are concerned the variationally derived set appears to be preferable

a study on multivariate interpolation by increasingly flat kernel functions abstract in this paper we improve upon some observations made in recent papers on the subject of increasingly flat interpolation we shall establish that the corresponding lagrange functions converge both for a finite set of functions collocation matrix and also for kernels fredholm matrix in our analysis we use a finite maclaurin expansion of a multivariate function with remainder and some additional matrix theoretic facts

exact vibration solutions for circular mindlin plates with multiple concentric ring supports this paper presents an analytical approach to investigate the vibration behaviour of circular mindlin plates with multiple concentric ring supports a circular plate is first divided into multiple annular segments and a circular segment at the locations of the ring supports the governing differential equations and the solutions of these equations for the annular and circular segments based on the mindlin plate theory are presented a homogenous equation system governing the vibration of circular mindlin plates with ring supports is derived by imposing the essential and natural boundary and segment interface conditions the first known exact vibration frequencies for circular mindlin plates with multiple concentric ring supports are obtained and the modal shapes of displacement fields and stress resultants for several selected cases are presented the influence of the ring support locations plate boundary conditions and plate thickness ratios on the vibration behaviour of circular plates is discussed

natural frequencies of thick plates made of orthotropic monoclinic and hexagonal materials by a meshless method abstract we use the first order shear deformation theory and a meshless method based on radial basis functions in a pseudospectral framework for predicting the free vibration behavior of thick orthotropic monoclinic and hexagonal plates the shape parameter is obtained by an optimization procedure the three translational and two rotational degrees of freedom of a point of the laminate are independently approximated through numerical experiments the capability and efficiency of the radial basis functions pseudospectral method for eigenvalue problems are demonstrated and the numerical accuracy and convergence are examined

finite horizon cal h _ infty control for discrete time varying systems with randomly occurring nonlinearities and fading measurements this technical note deals with the cal h infty control problem for a class of discrete time varying nonlinear systems with both randomly occurring nonlinearities and fading measurements over a finite horizon the system measurements are transmitted through fading channels described by a modified stochastic rice fading model the purpose of the addressed problem is to design a set of time varying controllers such that in the presence of channel fading and randomly occurring nonlinearities the cal h infty performance is guaranteed over a given finite horizon the model transformation technique is first employed to simplify the addressed problem and then the stochastic analysis in combination with the completing squares method are carried out to obtain necessary and sufficient conditions of an auxiliary index which is closely related to the finite horizon cal h infty performance moreover the time varying controller parameters are characterized via solving coupled backward recursive riccati difference equations rdes a simulation example is utilized to illustrate the usefulness of the proposed controller design scheme

integrated multiquadric radial basis function approximation methods promising numerical results using once and twice integrated radial basis functions have been recently presented in this work we investigate the integrated radial basis function irbf concept in greater detail connect to the existing rbf theory and make conjectures about the properties of irbf approximation methods the irbf methods are used to solve pdes

vibration analysis of symmetrically laminated plates based on fsdt using the moving least squares differential quadrature method in this paper we adopt the first order shear deformation theory in the moving least squares differential quadrature mlsdq procedure for predicting the free vibration behavior of moderately thick symmetrically laminated composite plates the transverse deflection and two rotations of the laminate are independently approximated with the moving least squares mls approximation the weighting coefficients used in the mlsdq approximation are obtained through the fast computation of the mls shape functions and their partial derivatives the natural frequencies of vibration are computed for various laminated plates and compared with the available published results through numerical experiments the capability and efficiency of the mlsdq method for eigenvalue problems are demonstrated and the numerical accuracy and convergence are thoughtfully examined effects of the size of support order of completeness of the basis functions and node irregularity on the numerical accuracy are also investigated

the parameter r2 in multiquadric interpolation the multiquadric mq method is an effective bivariate interpolant to three dimensional data xi yi zi where the xi yi are arbitrarily located in the plane the accuracy of the mq method is dependent on a user defined parameter r2 and most practitioners select r2 based upon the number of data points and the locations of the xi yi in the plane we observe that the optimal value of r2 is a strong function of the zi and that it is essentially independent of both the number and the locationsof the xi yi points contrary to some opinions we observe that the mq method can effectively interpolate to track data that is data sampled densely along tracks in the plane together with several other observations we present an algorithm that generally yields an effective value for r2

effect of built in edges on 3 d vibrational characteristics of thick circular plates the vibrational characteristics of thick circular plates built into a rigid medium in the vicinity of the circumference are studied the analysis procedure is based on the exact small strain three dimensional linear elasticity theory in the analysis the plate is considered as comprising an inner circular disc with free upper and lower surfaces connected to an outer annulus that is built into the rigid medium the chebyshev polynomials multiplied by suitable boundary characteristic functions are selected as the admissible functions of the displacement functions and the three dimensional displacement fields in each part can be expressed accordingly through the ritz method the eigenvalue equations can be established for the inner disc and the outer annulus respectively utilizing the displacement continuity conditions at the interface between the two parts the eigenvalue equation for the whole plate is derived convergence and comparison studies demonstrate the correctness and accuracy of the present method the effect of structural parameters such as plate thickness built in length and the end condition on eigenfrequencies of circular plate is investigated in detail it is shown that with the increase of plate thickness the effect of the built in annulus on eigenfrequencies significantly increases therefore for a thick plate the flexibility of the built in part should be considered in the dynamic analysis

adaptive estimation for a class of nonlinearly parameterized dynamical systems the technical note presents a new technique for the adaptive parameter estimation in nonlinear parameterized dynamical systems the technique proposes an uncertainty set update approach that guarantees forward invariance of the true value of the parameters in addition it is shown that in the presence of sufficiently exciting state trajectories the parameter estimates converge to the true values and the uncertainty set vanishes around the true value of the parameters the set based approach is also shown to identify when the parameter estimates are biased two simulation examples are presented that demonstrate the effectiveness of the technique

filtering for a class of nonlinear discrete time stochastic systems with state delays in this paper the filtering problem is investigated for a class of nonlinear discrete time stochastic systems with state delays we aim at designing a full order filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially ultimately bounded in the mean square for all admissible nonlinearities and time delays first an algebraic matrix inequality approach is developed to deal with the filter analysis problem and sufficient conditions are derived for the existence of the desired filters then based on the generalized inverse theory the filter design problem is tackled and a set of the desired filters is explicitly characterized a simulation example is provided to demonstrate the usefulness of the proposed design method

eigenvalue analysis of timoshenko beams and axisymmetric mindlin plates by the pseudospectral method a study of the free vibration of timoshenko beams and axisymmetric mindlin plates is presented the analysis is based on the chebyshev pseudospectral method which has been widely used in the solution of fluid mechanics problems clamped simply supported free and sliding boundary conditions of timoshenko beams are treated and numerical results are presented for different thickness to length ratios eigenvalues of the axisymmetric vibration of mindlin plates with clamped simply supported and free boundary conditions are presented for various thickness to radius ratios

free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first order shear deformation theory in this study free vibration of laminated skew plates was investigated discrete singular convolution dsc method is used for numerical solution of vibration problems the straight sided quadrilateral domain is mapped into a square domain in the computational space using a four node element by using the geometric transformation typical results are presented for different geometric parameters and boundary conditions it is concluded from the results that the skew angle have considerable influence on the variations of the frequencies with fibre orientation angle and number of layers in the laminate the results obtained by dsc method are compared with those obtained by analytical and numerical approaches it is shown that reasonable accurate results are obtained present work also indicates that the method of dsc is a promising and potential approach for computational mechanics copyright 2009 john wiley sons ltd

vibration analysis of non homogeneous circular plate of nonlinear thickness variation by differential quadrature method free axisymmetric vibrations of non homogeneous isotropic circular plates of nonlinear thickness variation have been analyzed on the basis of classical plate theory employing the differential quadrature dq method the non homogeneity is assumed to arise due to the variation in young s modulus and also the density of the plate material the first three natural frequencies have been obtained for clamped simply supported and free edge conditions taking grid points as zeros of chebyshev polynomials the effect of non homogeneity and thickness variation on natural frequencies of vibration has been investigated for the first three modes of vibration the results for linear as well as parabolic thickness variations have been obtained as special cases comparison studies have been carried out to establish the accuracy and versatility of the present dq method

vibration of mindlin plates using boundary characteristic orthogonal polynomials abstract the vibration analysis of shear deformable plates formulated on the basis of first order mindlin theory is presented the displacement and rotational functions of the plates are approximated by sets of boundary characteristic orthogonal polynomials the ease of generation and manipulation of these polynomial functions greatly enhances the computational efficiency of the numerical method the energy functional of the shear deformable plates derived from the mindlin plate theory is minimized in the ritz procedure to arrive at the governing eigenvalue equation corresponding natural frequencies and mode shapes can be obtained by solving the eigenvalue equation computed frequency results for various boundary conditions aspect ratios a b and thickness ratios t b are presented to demonstrate the effects of each factor on the vibration frequencies of moderately thick plates vibration mode shapes in the form of contour plots are presented for a thickness ratio of t b 0 1 these plots are believed to be the first known in the open literature

exponential synchronization of hybrid coupled networks with delayed coupling this paper investigates exponential synchronization of coupled networks with hybrid coupling which is composed of constant coupling and discrete delay coupling there is only one transmittal delay in the delayed coupling the fact is that in the signal transmission process the time delay affects only the variable that is being transmitted from one system to another then it makes sense to assume that there is only one single delay contributing to the dynamics some sufficient conditions for synchronization are derived based on lyapunov functional and linear matrix inequality lmi in particular the coupling matrix may be asymmetric or nondiagonal moreover the transmittal delay can be different from the one in the isolated system a distinctive feature of this work is that the synchronized state will vary in comparison with the conventional synchronized solution especially the degree of the nodes and the inner delayed coupling matrix heavily influence the synchronized state finally a chaotic neural network is used as the node in two regular networks to show the effectiveness of the proposed criteria

interpolation in the limit of increasingly flat radial basis functions abstract many types of radial basis functions such as multiquadrics contain a free parameter in the limit where the basis functions become increasingly flat the linear system to solve becomes highly ill conditioned and the expansion coefficients diverge nevertheless we find in this study that limiting interpolants often exist and take the form of polynomials in the 1 d case we prove that with simple conditions on the basis function the interpolants converge to the lagrange interpolating polynomial hence differentiation of this limit is equivalent to the standard finite difference method we also summarize some preliminary observations regarding the limit in 2 d

convergence guarantees for moving horizon estimation based on the real time iteration scheme in this note conditions are proven under which a real time implementable moving horizon estimation mhe scheme is locally convergent specifically the real time iteration scheme of is studied in which a single gauss newton iteration is applied to approximate the solution to the respective mhe optimization problem at each time step convergence is illustrated by a challenging small scale example the lorenz attractor with an unknown parameter it is shown that the performance of the proposed real time mhe algorithm is nearly identical to a fully converged mhe solution while its fixed execution time per sample would allow one to solve 30 000 mhe problems per second on current hardware

a meshfree method for inverse wave propagation using collocation and radial basis functions abstract a stable and highly accurate meshfree scheme based on strong form collocation associated with radial basis functions and explicit time integration is proposed to solve ill posed inverse wave propagation problems tikhonov regularization technique and the l curve criterion are employed to deal with the noise measurement data before solving the governing equation to get a stable solution appropriate weights are first derived for imposing boundary conditions and known conditions from the measurement data to yield the optimal convergence for inverse problems compared to the required iterative procedures in common methods no iteration is needed in the proposed method which leads to the time saving computation and avoids the instability resulting from the iterative methods dispersion analysis describes that this method has much less dispersion error than the classical finite element method fem and popular weak form meshfree methods and stability analysis is performed to predict the critical time step for the explicit time integration another outstanding advantage of this method is that it is effortless to extend the solution scheme of one dimensional inverse problem to high dimensional inverse problems furthermore the influences of the high noise into measurement data are evaluated which demonstrate that even handling with very high noise in the input data the proposed algorithm can achieve stable and high accuracy solutions

h_ infty state estimation for discrete time nonlinear singularly perturbed complex networks under the round robin protocol this paper investigates the h infty state estimation problem for a class of discrete time nonlinear singularly perturbed complex networks spcns under the round robin rr protocol a discrete time nonlinear spcn model is first devised on two time scales with their discrepancies reflected by a singular perturbation parameter spp the network measurement outputs are transmitted via a communication network where the data transmissions are scheduled by the rr protocol with hope to avoid the undesired data collision the error dynamics of the state estimation is governed by a switched system with a periodic switching parameter a novel lyapunov function is constructed that is dependent on both the transmission order and the spp by establishing a key lemma specifically tackling the spp sufficient conditions are obtained such that for any spp less than or equal to a predefined upper bound the error dynamics of the state estimation is asymptotically stable and satisfies a prescribed h infty performance requirement furthermore the explicit parameterization of the desired state estimator is given by means of the solution to a set of matrix inequalities and the upper bound of the spp is then evaluated in the feasibility of these matrix inequalities moreover the corresponding results for linear discrete time spcns are derived as corollaries a numerical example is given to illustrate the effectiveness of the proposed state estimator design scheme

limit problems for interpolation by analytic radial basis functions interpolation problems for analytic radial basis functions like the gaussian and inverse multiquadrics can degenerate in two ways the radial basis functions can be scaled to become increasingly flat or the data points coalesce in the limit while the radial basis functions stay fixed both cases call for a careful regularization which if carried out explicitly yields a preconditioning technique for the degenerating linear systems behind these interpolation problems this paper deals with both cases for the increasingly flat limit we recover results by larsson and fornberg together with lee yoon and yoon concerning convergence of interpolants towards polynomials with slight modifications the same technique can also handle scenarios with coalescing data points for fixed radial basis functions the results show that the degenerating local lagrange interpolation problems converge towards certain hermite birkhoff problems this is an important prerequisite for dealing with approximation by radial basis functions adaptively using freely varying data sites

a new approach based on the genetic algorithm for finding a good shape parameter in solving partial differential equations by kansa s method many radial basis function rbf methods contain a free shape parameter that plays an important role for the accuracy of the method in most papers the authors end up choosing this shape parameter by trial and error or some other ad hoc means in this paper we propose applying the genetic algorithm to determine a good shape parameter of radial basis functions for the solution of partial differential equations we use meshless collocation method based on the radial basis function kansa s method to solve partial differential equations due to the severely ill conditioned matrix arising from using rbf we also consider the truncated singular value decomposition method tsvd for solving system of linear equations which is obtained from kansa s method numerical results show that the proposed algorithm based on the genetic optimization is effective and provides a reasonable shape parameter along with acceptable accuracy of the solution

event triggered consensus control for discrete time stochastic multi agent systems this paper is concerned with the event triggered consensus control problem for a class of discrete time stochastic multi agent systems with state dependent noises a novel definition of consensus in probability is proposed to better describe the dynamics of the consensus process of the addressed stochastic multi agent systems the measurement output available for the controller is not only from the individual agent but also from its neighboring ones according to the given topology an event triggered mechanism is adopted with hope to reduce the communication burden where the control input on each agent is updated only when a certain triggering condition is violated the purpose of the problem under consideration is to design both the output feedback controller and the threshold of the triggering condition such that the closed loop system achieves the desired consensus in probability first of all a theoretical framework is established for analyzing the so called input to state stability in probability issip for general discrete time nonlinear stochastic systems within such a theoretical framework some sufficient conditions on event triggered control protocol are derived under which the consensus in probability is reached furthermore both the controller parameter and the triggering threshold are obtained in terms of the solution to certain matrix inequalities involving the topology information and the desired consensus probability finally a simulation example is utilized to illustrate the usefulness of the proposed control protocol

optimal dividend strategies of two collaborating businesses in the diffusion approximation model in this paper we consider the optimal dividend payment strategy for an insurance company that has two collaborating business lines the surpluses of the business lines are modeled by diffusion processes the collaboration between the two business lines permits that money can be transferred from one line to another with or without proportional transaction costs while money must be transferred from one line to another to help both business lines keep running before simultaneous ruin of the two lines eventually occurs

fast calculation of laurent expansions for matrix inverses previously described algorithms for calculating the laurent expansion of the inverse of a matrix valued analytic function become impractical already for singularity orders as low as around p 6 since they require over o 28p matrix multiplications and correspondingly large amounts of memory in place of using mathematically exact recursions we show that for floating point calculations a rational approximation approach can avoid this cost barrier without any significant loss in accuracy

analysis of laminated plates by trigonometric theory radial basis and unified formulation a study using the radial basis function rbf collocation method to analyze static deformations free vibrations and buckling loads of square cross ply laminated plates using a sinus based shear and normal deformation theory is presented allowing for through the thickness deformations the principle of virtual displacements is used to obtain the equations of motions and boundary conditions and the governing equations in strong form for the rbf method are observed a simply supported square laminated plate of side a and thickness h composed of four equally layers oriented at 0 90 90 0 is considered it is found that the present mesh less results are in very close agreement with the mesh free results the laminated plate is supported along the edges parallel to the x axis while the other two edges may be simply supported s or clamped c an excellent agreement is achieved for all edge conditions when comparing the results obtained by the present rbf approach with those found earlier

theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions multivariate interpolation of smooth data using smooth radial basis functions is considered the behavior of the interpolants in the limit of nearly flat radial basis functions is studied both theoretically and numerically explicit criteria for different types of limits are given using the results for the limits the dependence of the error on the shape parameter of the radial basis function is investigated the mechanisms that determine the optimal shape parameter value are studied and explained through approximate expansions of the interpolation error

seismic modeling with radial basis function generated finite differences abstractseismic exploration is the primary tool for finding and mapping out hydrocarbon deposits we have considered the 2d forward modeling problem the subsurface structures were assumed to be known and the task was to simulate elastic wave propagation throughout the medium many traditional approaches to solving this problem account for material interfaces by allowing model parameter values such as wave speed and density to vary either sharply or smoothly between adjacent data points although simple to implement these strategies typically produce solutions that feature a suboptimal first order convergence to the true solution spatial discretization based on radial basis function generated finite differences rbf fds has previously been shown to offer high accuracy and algebraic simplicity when using scattered layouts of computational nodes we have now developed this method further to provide third order accuracy not only throughout smooth regions but also for wave reflections and transmission

a new method for evaluating options based on multiquadric rbf fd method abstract in this paper a new local meshless approach based on radial basis functions rbfs is presented to price the options under the black scholes model the global rbf approximations derived from the conventional global collocation method usually lead to ill conditioned matrices employing the idea of local approximants of the finite difference fd method and combining it with the radial basis function rbf method can result in a local meshless approach such as rbf fd it removes the difficulty of ill conditionness of the original method the new proposed approach is unconditionally stable as it is shown by von neumann stability analysis it is fast and produces high accurate results as shown in numerical experiments moreover we took into account the variation of shape parameter and analyzed numerically the behavior of the rbf fd method

rbf ps scheme for solving the equal width equation the equal width equation is solved by a rbf ps scheme this technique is meshless and there is no need to linearize the nonlinear terms the radial kernels are used to transform the pde into a system of odes a higher order ode solver is used to solve the ode system the method is tested for single solitary wave interaction of two and three solitary waves the development of an undular bore and the interaction of two solitary waves the results are compared with earlier work and other methods

comparative accuracy of dq and hdq methods for three dimensional vibration analysis of rectangular plates an accuracy study between the differential quadrature dq and harmonic differential quadrature hdq methods for three dimensional elasticity solutions of free vibration of rectangular plates is carried out the solution capability of the dq and hdq methods is first studied then the numerical performance of both the methods is compared it is found that the dq method displays more superior convergence characteristics over the hdq method for the lower modes of vibration however the hdq method is advantageous over the dq method for computing higher modes of vibration it is also discovered that the dq and hdq methods produce better convergent solutions than the finite element method fem when a similar number of discrete points nodes are used copyright 1999 john wiley sons ltd

free vibration analyses of thin sector plates by the new version of differential quadrature method abstract the new version of differential quadrature dq method is extended to analyze the free vibration of thin sector plates with various sector angles and six combinations of boundary conditions detailed formulations are given various numerical examples are studied comparisons are made with existing analytical and or numerical data numerical results indicate that convergence can be achieved with increasing in number of grid points and accurate results could be obtained with 9 9 gird or even higher grid by using the extended dq method for the cases considered

free vibration of circular and annular plates with variable thickness and different combinations of boundary conditions in this paper the first nine frequency parameters of circular and annular plates with variable thickness and combined boundary conditions are computed for different thickness to radius ratios several combined boundary conditions are considered for inner and outer edges these are free soft and hard simply supported and clamped boundary conditions three dimensional elasticity theory is used results of this paper are compared with works of other authors and the results of finite element method analysis which are in agreement data for thick circular and annular plates with linear and parabolic thickness variation and different combinations are presented for the first time

bounded h_ infty synchronization and state estimation for discrete time varying stochastic complex networks over a finite horizon in this paper new synchronization and state estimation problems are considered for an array of coupled discrete time varying stochastic complex networks over a finite horizon a novel concept of bounded h synchronization is proposed to handle the time varying nature of the complex networks such a concept captures the transient behavior of the time varying complex network over a finite horizon where the degree of bounded synchronization is quantified in terms of the h norm a general sector like nonlinear function is employed to describe the nonlinearities existing in the network by utilizing a timevarying real valued function and the kronecker product criteria are established that ensure the bounded h synchronization in terms of a set of recursive linear matrix inequalities rlmis where the rlmis can be computed recursively by employing available matlab toolboxes the bounded h state estimation problem is then studied for the same complex network where the purpose is to design a state estimator to estimate the network states through available output measurements such that over a finite horizon the dynamics of the estimation error is guaranteed to be bounded with a given disturbance attenuation level again an rlmi approach is developed for the state estimation problem finally two simulation examples are exploited to show the effectiveness of the results derived in this paper

static analysis of mindlin plates the differential quadrature element method dqem abstract the differential quadrature method dqm is a new numerical method for fast solving linear and nonlinear differential equations based on global basis functions in the present study a discrete approximate method based on the dqm the differential quadrature element method dqem is developed for the axisymmetric static analysis of moderately thick circular and annular plates described by the mindlin shear deformable theory the basic idea of the dqem is 1 to divide the whole variable domain into several sub domains elements 2 to form discretized element governing equations by applying the dqm to each element and 3 to assemble all the discretized element governing equations into the overall characteristic equations with the consideration of displacement and stress compatibility conditions between adjacent elements the annular and circular mindlin plate elements of differential quadrature dq are established the convergence characteristics of the proposed method are carefully investigated from the view points of element refinement and element grid refinement and some general regulations and suggestions on element division and element grid selection are provided a number of numerical examples are calculated and the results are compared with the corresponding exact solutions which exhibits high accuracy simplicity and applicability of the present method

impossibility of fast stable approximation of analytic functions from equispaced samples it is shown that no stable procedure for approximating functions from equally spaced samples can converge exponentially for analytic functions to avoid instability one must settle for root exponential convergence the proof combines a bernstein inequality of 1912 with an estimate due to coppersmith and rivlin in 1992

local rbf fd technique for solving the two dimensional modified anomalous sub diffusion equation abstract the main aim of this paper is to propose an efficient and suitable numerical procedure based on the local meshless collocation method for solving the two dimensional modified anomalous sub diffusion equation the fractional derivative is based on the riemann liouville fractional integral firstly a finite difference scheme with o has been employed to discrete the time variable and also the local radial basis finite difference lrbf fd method is used to discrete the spatial direction for the presented numerical technique we prove the unconditional stability and also obtain an error bound we employ a test problem to show the accuracy of the proposed technique also we solve the mentioned model on irregular domain to show the efficincy of the developed technique

event based h_ infty filter design for a class of nonlinear time varying systems with fading channels and multiplicative noises in this paper a general event triggered framework is developed to deal with the finite horizon h infty filtering problem for discrete time varying systems with fading channels randomly occurring nonlinearities and multiplicative noises an event indicator variable is constructed and the corresponding event triggered scheme is proposed such a scheme is based on the relative error with respect to the measurement signal in order to determine whether the measurement output should be transmitted to the filter or not the fading channels are described by modified stochastic rice fading models some uncorrelated random variables are introduced respectively to govern the phenomena of state multiplicative noises randomly occurring nonlinearities as well as fading measurements the purpose of the addressed problem is to design a set of time varying filter such that the influence from the exogenous disturbances onto the filtering errors is attenuated at the given level quantified by a h infty norm in the mean square sense by utilizing stochastic analysis techniques sufficient conditions are established to ensure that the dynamic system under consideration satisfies the h infty filtering performance constraint and then a recursive linear matrix inequality rlmi approach is employed to design the desired filter gains simulation results demonstrate the effectiveness of the developed filter design scheme

time space domain mesh free finite difference based on least squares for 2d acoustic wave modeling abstractfinite difference fd methods approximate derivatives through a weighted summation of function values from neighboring nodes traditionally these neighboring nodes are assumed to be distributed regularly such as in square or rectangular lattices to improve geometric flexibility one option is to develop fd in a mesh free discretization in which scattered nodes can be placed suitably with respect to irregular boundaries or arbitrarily shaped anomalies without coordinate transformation or forming any triangles or tetrahedra etc these mesh free fds have had successful applications especially in computational geoscience however they are all space domain fd schemes in which fd coefficients are derived by approximating spatial derivatives individually in the space domain for acoustic wave modeling it has been proven that space domain fd methods normally have higher dispersion error than time space domain fd methods which determine fd coefficients by approximating the time space domain disp

free vibration and buckling analyses of shear deformable plates based on fsdt meshfree method abstract a meshfree method based on the reproducing kernel particle approximate is employed for the free vibration and buckling analyses of shear deformable plates in this approach the first order mindlin reissner plate theory fsdt is used and the displacement shape functions are constructed using the reproducing kernel approximation satisfying the consistency condition the essential boundary conditions are enforced by a transformation method numerical examples considering various aspect ratios skew angles and boundary conditions are demonstrated to show the validity of the proposed method and satisfactory results were obtained when comparisons are made with the exact and other available numerical results existing in the literature

an augmented rbf method for solving fractional sturm liouville eigenvalue problems in this work we construct numerical schemes using radial basis functions rbfs to solve sturm liouville eigenvalue problems in which the so called fractional derivatives are involved we take into account the fact that the solutions to such problems might be nonsmooth and consequently we augment the space generated by rbf base functions with some fractional polynomials to overcome this problem we show through some examples the effectiveness of our method

analysis of thick isotropic and cross ply laminated plates by radial basis functions and a unified formulation in this paper we combine carrera s unified formulation and a radial basis function collocation technique for predicting the static deformations and free vibration behavior of thin and thick isotropic and cross ply laminated plates through numerical experiments the capability and efficiency of this collocation technique for static and vibration problems are demonstrated and the numerical accuracy and convergence are thoughtfully examined

meshless methods for two dimensional oscillatory fredholm integral equations abstract in this paper a meshless solution procedure incorporating delaminating quadrature method for two dimensional highly oscillatory fredholm integral equation is put forward the proposed method is an extension of our earlier findings of meshless methods for two dimensional oscillatory fredholm integral equation having kernel function free of stationary phase point s siraj ul islam et al 2015 the current method deals not only with the kernels having no stationary phase point s but also with the kernels having stationary phase point s in the context of highly oscillatory integral equations the new method is numerically stable and computationally fast numerical experiments are presented to testify the robustness and efficiency of the proposed method

robust state estimation for uncertain neural networks with time varying delay the robust state estimation problem for a class of uncertain neural networks with time varying delay is studied in this paper the parameter uncertainties are assumed to be norm bounded based on a new bounding technique a sufficient condition is presented to guarantee the existence of the desired state estimator for the uncertain delayed neural networks the criterion is dependent on the size of the time varying delay and on the size of the time derivative of the time varying delay it is shown that the design of the robust state estimator for such neural networks can be achieved by solving a linear matrix inequality lmi which can be easily facilitated by using some standard numerical packages finally two simulation examples are given to demonstrate the effectiveness of the developed approach

vibration analysis of annular like plates abstract the existence of eccentricity of the central hole for an annular plate results in a significant change in the natural frequencies and mode shapes of the structure in this paper the vibration analysis of annular like plates is presented based on numerical and experimental approaches using the finite element analysis code nastran the effects of the eccentricity hole size and boundary condition on vibration modes are investigated systematically through both global and local analyses the results show that analyses for perfect symmetric conditions can still roughly predict the mode shapes of recessive modes of the plate with a slightly eccentric hole they will however lead to erroneous results for dominant modes in addition the residual displacement mode shape is verified as an effective parameter for identifying damage occurring in plate like structures experimental modal analysis on a clamped free annular like plate is performed and the results obtained reveal good agreement with those obtained by numerical analysis this study provides guidance on modal analysis vibration measurement and damage detection of plate like structures

free vibration analysis of cylindrical helical springs by the pseudospectral method abstract the pseudospectral method is applied to the free vibration analysis of cylindrical helical springs the displacements and the rotations are approximated by the series expansions of chebyshev polynomials and the governing equations are collocated the number of collocation points is chosen to be less than the number of the expansion terms to handle the boundary condition numerical examples are provided for fixed fixed free free fixed free and hinged hinged boundary conditions the results show good agreement with those of the transfer matrix method and the dynamic stiffness method the formulation of the pseudospectral method is straightforward and shows an exponential rate of convergence with mesh refinement

an innovative eigenvalue problem solver for free vibration of uniform timoshenko beams by using the adomian modified decomposition method this paper deals with free vibration problems of uniform timoshenko beams under various supporting boundary conditions the technique we have used is based on applying the adomian modified decomposition method amdm to our vibration problems doing some simple mathematical operations on the method we can obtain ith natural frequencies and mode shapes one at a time the computed results agree well with those analytical and numerical results given in the literature these results indicate that the present analysis is accurate and provides a unified and systematic procedure which is simpler and more straightforward than the other modal analysis

stable computation of multiquadric interpolants for all values of the shape parameter abstract spectrally accurate interpolation and approximation of derivatives used to be practical only on highly regular grids in very simple geometries since radial basis function rbf approxima ions permit this even for multivariate scattered data there has been much recent interest in practical algorithms to compute these approximations effectively several types of rbfs feature a free parameter e g c in the multiquadric mq case f r r 2 c 2 the limit of c increasingly flat basis functions has not received much attention because it leads to a severely ill conditioned problem we present here an algorithm which avoids this difficulty and which allows numerically stable computations of mq rbf interpolants for all parameter values we then find that the accuracy of the resulting approximations in some cases becomes orders of magnitude higher than was the case within the previously available parameter range our new method provides the first tool for the numerical exploration of mq rbf interpolants in the limit of c the method is in no way specific to mq basis functions and can without any change be applied to many other cases as well

observations on the behavior of radial basis function approximations near boundaries abstract rbf approximations would appear to be very attractive for approximating spatial derivatives in numerical simulations of pdes rbfs allow arbitrarily scattered data generalize easily to several space dimensions and can be spectrally accurate however accuracy degradations near boundaries in many cases severely limit the utility of this approach with that as motivation this study aims at gaining a better understanding of the properties of rbf approximations near the ends of an interval in 1 d and towards edges in 2 d

stability analysis and dynamic output feedback controller design of t s fuzzy systems with time varying delays and external disturbances abstract this paper investigates the stability analysis and takagi sugeno t s fuzzy dynamic output feedback control for a class of t s fuzzy systems with multiple time varying delays and unmatched disturbances firstly the t s fuzzy model is employed to represent the system based on the system input matrix and output matrix secondly the t s fuzzy dynamic output feedback controller is designed based on the t s fuzzy model thirdly the line integral fuzzy lyapunov functional is employed and the boundary information of membership functions is considered in the stability analysis compared with previous works the multiple time varying delays and unmatched disturbances are considered in the t s fuzzy system the t s fuzzy dynamic output feedback controller and t s fuzzy system employ the same number of fuzzy rules but different membership functions to relax the control design conditions the line integral fuzzy lyapunov functional is employed and the boundary information of membership functions is considered to obtain the less conservative stability conditions finally two simulation examples are performed and some comparison figures results are presented to show the effectiveness and advantage of proposed method respectively

the use of proper orthogonal decomposition pod meshless rbf fd technique to simulate the shallow water equations abstract the main aim of this paper is to develop a fast and efficient local meshless method for solving shallow water equations in one and two dimensional cases the mentioned equation has been classified in category of advection equations the solutions of advection equations have some shock thus especial numerical methods should be employed for example discontinuous galerkin and finite volume methods here based on the proper orthogonal decomposition approach we want to construct a fast meshless method to this end we consider shallow water models and obtain a suitable time discrete scheme based on the predictor corrector technique then by applying the proper orthogonal decomposition technique a new set of basis functions can be built for the solution space in which the size of new solution space is less than the original problem thus by employing the new bases the cpu time will be reduced some examples have been studied to show the efficiency of the present numerical technique

laurent expansion of the inverse of perturbed singular matrices in this paper we describe a numerical algorithm to compute the laurent expansion of the inverse of singularly perturbed matrices the algorithm is based on the resolvent formalism used in complex analysis to study the spectrum of matrices the input of the algorithm are the matrix coefficients of the power series expansion of the perturbed matrix the matrix coefficients of the laurent expansion of the inverse are computed using recursive analytical formulae we show that the computational complexity of the proposed algorithm grows algebraically with the size of the matrix but exponentially with the order of the singularity we apply this algorithm to several matrices that arise in applications we make special emphasis to interpolation problems with radial basis functions

delay dependent state estimation for delayed neural networks in this letter the delay dependent state estimation problem for neural networks with time varying delay is investigated a delay dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable the proposed method is based on the free weighting matrix approach and is applicable to the case that the derivative of a time varying delay takes any value an algorithm is presented to compute the state estimator finally a numerical example is given to demonstrate the effectiveness of this approach and the improvement over existing ones

computation of natural frequencies of shear deformable beams and plates by an rbf pseudospectral method a study of free vibration of timoshenko beams and mindlin plates is presented the analysis is based on a new numerical scheme where collocation by radial basis functions and pseudospectral methods are combined to produce highly accurate results numerical results are presented and discussed for various thickness to length ratios

free vibration analysis of mindlin sector plates numerical solutions by differential quadrature method abstract in this paper the free vibration analysis of moderately thick sector plates based on mindlin s first order shear deformation theory is examined the solutions to this problem are determined using the differential quadrature dq method for numerical evaluation the dq formulations for free vibration of the mindlin sector plates in two dimensional polar co ordinate system are derived to demonstrate the accuracy of the dq method convergence and comparison studies are carried out in parametric study the first eight frequency parameters are computed for sector plates with different boundary conditions relative thickness ratios and sector angles 30 360 the effects of sector angle and relative thickness ratio on the frequency parameters are discussed

ultimate boundedness control for networked systems with try once discard protocol and uniform quantization effects this paper is concerned with the ultimate boundedness control problem for a class of networked nonlinear systems subject to the try once discard tod protocol scheduling and uniform quantization effects to prevent the transmission data from collisions the communication between sensor nodes and the controller is implemented via a constrained communication channel where only one sensor node is permitted to transmit data at each time instant the tod protocol is utilized to regulate the signal transmission over the communication network under which the scheduling behavior is described by a special switching function on the other hand the uniform quantization effects of the network are characterized by a round function i e the nearest integer function the purpose of the addressed problem is to design an observer based controller for the networked nonlinear systems such that in the presence of tod protocol and uniform quantization effects the closed loop system is ultimately bounded and the controlled output is locally minimized sufficient conditions are established to guarantee the ultimate boundedness of the dynamics of the closed loop system in mean square by applying the stochastic analysis approach furthermore the desired controller gains are derived by solving a convex optimization problem finally a numerical example is given to illustrate the effectiveness of the proposed controller design scheme

h_ infty state estimation for complex networks with uncertain inner coupling and incomplete measurements in this paper the h state estimation problem is investigated for a class of complex networks with uncertain coupling strength and incomplete measurements with the aid of the interval matrix approach we make the first attempt to characterize the uncertainties entering into the inner coupling matrix the incomplete measurements under consideration include sensor saturations quantization and missing measurements all of which are assumed to occur randomly by introducing a stochastic kronecker delta function these incomplete measurements are described in a unified way and a novel measurement model is proposed to account for these phenomena occurring with individual probability with the measurement model a set of h state estimators is designed such that for all admissible incomplete measurements as well as the uncertain coupling strength the estimation error dynamics is exponentially mean square stable and the h performance requirement is satisfied the characterization of the desired estimator gains is derived in terms of the solution to a convex optimization problem that can be easily solved using the semidefinite program method finally a numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach

vibration of non homogeneous circular mindlin plates with variable thickness free vibration analysis of non homogeneous circular plates of variable thickness has been presented using the first order shear deformation plate theory of mindlin chebyshev collocation technique has been employed to obtain the first three natural frequencies and mode shapes for clamped simply supported and free plate with four digit exactitude the effect of structural parameters such as taper non homogeneity and density and that of edge conditions on the natural frequencies has been investigated comparison of results for some special cases with published results obtained from other approximate methods has been presented which shows an excellent agreement

a spectral tchebychev technique for solving linear and nonlinear beam equations abstract this paper presents a spectral tchebychev technique for solving linear and nonlinear beam problems the technique uses tchebychev polynomials as spatial basis functions and applies galerkin s method to obtain the spatially discretized equations of motion unlike alternative techniques that require different admissible functions for each different set of boundary conditions the spectral tchebychev technique incorporates the boundary conditions into the derivation and thereby enables the utilization of the solution for any linear boundary conditions without re derivation furthermore the proposed technique produces symmetric system matrices for self adjoint problems in this work the spectral tchebychev solutions for euler bernoulli and timoshenko beams are derived the convergence and accuracy characteristics of the spectral tchebychev technique is studied by solving eigenvalue problems with different boundary conditions it is found that the convergence is exponential and a small number of polynomials is sufficient to obtain machine precision accuracy the application of the technique is demonstrated by solving 1 eigenvalue problems for tapered timoshenko beams with different boundary conditions taper ratios and beam lengths 2 an euler bernoulli beam problem with spatially and temporally varying forcing elastic boundary and damping 3 large deflection nonlinear euler bernoulli beam problems with different boundary conditions and 4 a micro beam problem with nonlinear electrostatic excitation the results obtained from the spectral tchebychev solutions are seen to be in excellent agreement with those presented in the literature

recovery of elastic parameters of cellular materials by inversion of vibrational data abstract this investigation addresses the inverse problem of the retrieval of the macroscopic young s modulus and poisson ratio of light fluid saturated cellular materials from the measured resonance frequencies of their vibrational response the latter is shown to be generally nonlinear for all except very small excitations in order to remain in the linear regime and thus avoid ambiguities in the characterization of the material we employ lightweight piezoelectric transducers and sensors and a low noise amplifier for the acquisition of dynamic response data the cellular materials under investigation polyurethane melamine are shown to behave as isotropic equivalent homogeneous elastic solids with rayleigh damping equivalent to a rheological model having the same dependence of attenuation on frequency in the frequency band of interest our viscoelastic model is validated by comparing its predictions of the dynamic response of the specimens to the predictions of the more complete biot interaction model the computations with both of these models are carried out by means of 3d finite element fe codes for a variety of specimen shapes and sizes once the simpler viscoelastic model is validated it is then employed to compute the trial resonance frequencies which are the solutions of an eigenvalue problem associated with this model during the inversion process the cost function which is a measure of the discrepancy between the trial and measured resonance frequencies for a number of vibrational modes is constructed and then minimized by the levenberg marquardt optimization algorithm in order to recover the sought for moduli finally a discussion is presented concerning the influence of the size and shape of the specimens as well as the number of employed modes on the uniqueness and quality of the inversion

eigenvalue stability of radial basis function discretizations for time dependent problems differentiation matrices obtained with infinitely smooth radial basis function rbf collocation methods have under many conditions eigenvalues with positive real part preventing the use of such methods for time dependent problems we explore this difficulty at theoretical and practical levels theoretically we prove that differentiation matrices for conditionally positive definite rbfs are stable for periodic domains we also show that for gaussian rbfs special node distributions can achieve stability in 1 d and tensor product nonperiodic domains as a more practical approach for bounded domains we consider differentiation matrices based on least squares rbf approximations and show that such schemes can lead to stable methods on less regular nodes by separating centers and nodes least squares techniques open the possibility of the separation of accuracy and stability characteristics

state estimation for discrete time dynamical networks with time varying delays and stochastic disturbances under the round robin protocol this paper is concerned with the state estimation problem for a class of nonlinear dynamical networks with time varying delays subject to the round robin protocol the communication between the state estimator and the nodes of the dynamical networks is implemented through a shared constrained network in which only one node is allowed to send data at each time instant the round robin protocol is utilized to orchestrate the transmission order of nodes by using a switch based approach the dynamics of the estimation error is modeled by a periodic parameter switching system with time varying delays the purpose of the problem addressed is to design an estimator such that the estimation error is exponentially ultimately bounded with a certain asymptotic upper bound in mean square subject to the process noise and exogenous disturbance furthermore such a bound is subsequently minimized by the designed estimator parameters a novel lyapunov like functional is employed to deal with the dynamics analysis issue of the estimation error sufficient conditions are established to guarantee the ultimate boundedness of the estimation error in mean square by applying the stochastic analysis approach then the desired estimator gains are characterized by solving a convex problem finally a numerical example is given to illustrate the effectiveness of the estimator design scheme

mixed h_2 h_ infty state estimation for discrete time switched complex networks with random coupling strengths through redundant channels this article investigates the mixed h 2 h infty state estimation problem for a class of discrete time switched complex networks with random coupling strengths through redundant communication channels a sequence of random variables satisfying certain probability distributions is employed to describe the stochasticity of the coupling strengths a redundant channel based data transmission mechanism is adopted to enhance the reliability of the transmission channel from the sensor to the estimator the purpose of the addressed problem is to design a state estimator for each node such that the error dynamics achieves both the stochastic stability with probability 1 and the prespecified mixed h 2 h infty performance requirement by using the switched system theory an extensive stochastic analysis is carried out to derive the sufficient conditions ensuring the stochastic stability as well as the mixed h 2 h infty performance index the desired state estimator is also parameterized by resorting to the solutions to certain convex optimization problems a numerical example is provided to illustrate the validity of the proposed estimation scheme