on continuous dependence for an inverse initial boundary value problem for the wave equation abstract we show that the bounded coefficient q x of the wave equation u tt u qu x t 0 t u x 0 u t x 0 0 x u v x x x t 0 t can be continuously determined by its neumann to dirichlet map in certain function spaces

algebraic graph theory without orientation abstract let g be an undirected graph with vertices v 1 v 2 v and edges e1 e2 e let m be the matrix whose ijth entry is 1 if ej is a link incident with vi 2 if ej is a loop at vi and 0 otherwise the matrix obtained by orienting the edges of a loopless graph g i e changing one of the 1 s to a 1 in each column of m has been studied extensively in the literature the purpose of this paper is to explore the substructures of g and the vector spaces associated with the matrix m without imposing such an orientation we describe explicitly bases for the kernel and range of the linear transformation from r to r defined by m our main results are determinantal formulas using the unoriented laplacian matrix mmt to count certain spanning substructures of g these formulas may be viewed as generalizations of the matrix tree theorem the point of view adopted in this paper also gives rise to a matroid structure on the edges of g analogous to the cycle matroid and its dual in this setting the analogue of a spanning forest can have components with one odd cycle and the analogue of an edge cut has the property that its removal creates a new bipartite component

on spectral integral variations of mixed graphs in this paper we characterize the mixed graphs with exactly one laplacian eigenvalue moving up by an integer and other laplacian eigenvalues remaining invariant when an edge is added the results extend those of fan linear and multilinear algebra 50 2002 133 for general graphs and so linear and multilinear algebra 46 1999 193 for simple graphs

a novel technique for inverse identification of distributed stiffness factor in structures abstract a computational inverse technique for identifying stiffness distribution in structures is proposed in this paper using structural dynamics response in the frequency domain in the present technique element stiffness factors of the finite element model of a structure are taken to be the parameters and explicitly expressed in a linear form in the system equation for forward analysis of the harmonic response of the structure this offers great convenience in applying newton s method to search for the parameters of stiffness factor inversely as the jacobian matrix can be obtained simply by solving sets of linear algebraic equation derived from the system equation examples of identifying stiffness factor distribution which is often related to damage in the elements of the structure are presented to demonstrate the present technique the advantages of the present technique for inverse parameter identification problem are 1 the number of the parameters can be very large 2 the identification process is very fast and 3 the accuracy is very high the efficiency of the proposed technique is compared with genetic algorithms

dead beat control of simple hammerstein models dead beat controllers for simple hammerstein systems are investigated several designs for nonminimum time state dead beat controllers are given for certain classes of simple hammerstein systems a general minimum time state dead beat controller is presented for a class of simple hammerstein systems a design for a family of minimum time control laws is provided this enables to a certain extent shaping of transient response via choosing an appropriate control law finally the authors design an output dead beat controller for a class of hammerstein systems that are not necessarily state dead beat controllable

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

an operator marching method for inverse problems in range dependent waveguides abstract for large scale inverse problems in acoustics and electromagnetics numerical schemes based on direct methods e g fem and meshless methods often result in huge linear systems and thus are not feasible in terms of computing speed and memory storage this work proposes the inverse fundamental operator marching method based on the dirichlet to neumann map for solving large scale inverse boundary value problems in range dependent waveguides truncated singular value decomposition is employed to solve ill conditioned linear systems arising in marching process and the number of propagating modes in the waveguide assumes the role of a regularization parameter numerical results show that the method is computationally efficient highly accurate stable with respect to data noise for retrieving the propagating part of the starting field it particularly suits to long range wave propagation in slowly varying stratified waveguide

finding a control parameter in one dimensional parabolic equations an inverse problem concerning diffusion equation with source control parameter is considered several finite difference schemes are presented for identifying the control parameter which produces at each time a desired temperature at a given point in a spatial domain these schemes are based on the second order 3 point forward time centred space ftcs explicit formula and the fourth order 5 point ftcs explicit scheme and the second order 3 point backward time centred space btcs implicit technique and the fourth order 3 3 crandall s implicit formula the 5 point ftcs scheme has a bounded range of stability but its fourth order accuracy is significant the 3 point btcs method uses less central processor cpu time than the 3 3 crandall s technique but it is only second order accurate the basis of analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach developed from the 1974 work of warming and hyett this allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes the results of a numerical experiment are presented and accuracy and the cpu time needed for the parabolic inverse problem are discussed

the least eigenvalue of signless laplacian of graphs under perturbation abstract we investigate how the least eigenvalue of the signless laplacian of a graph changes by relocating a bipartite branch from one vertex to another vertex and minimize the least eigenvalue of the signless laplacian among the class of connected graphs with fixed order which contains a given non bipartite graph as an induced subgraph

a quadratic layer element for analyzing stress waves in fgms and its application in material characterization abstract a novel method is presented for investigating elastic waves in functionally graded material fgm plates excited by plane pressure waves the fgm plate is first divided into quadratic layer elements qles a general solution for the equation of motion governing the qle has been derived the general solution is then used together with the boundary and continuity conditions to obtain the displacement and stress in the frequency domain for an arbitrary fgm plate the response of the plate to an incident pressure wave is obtained using the fourier transform techniques results obtained by the present method are compared with an existing method using homogeneous layer elements numerical examples are presented to investigate stress waves in fgm plates the relationship between the surface displacement response and the material property of quadratic fgm plates has been analytically obtained for the material characterization a computational inverse technique is also presented for characterizing material property of an arbitrary fgm plate from the surface displacement response data using present qle method as forward solver and genetic algorithm as the inverse operator this technique is utilized to reconstruct the material property of an actual sic c fgm

simple sufficient conditions for reachability of discrete time polynomial systems we consider reachability of discrete time polynomial systems the reachability of such systems can be interpreted as the surjectivity of the polynomial mappings defined by the systems for a polynomial mapping between suitable spaces of the same dimensions it has been shown that the injectivity of the mapping also implies the surjectivity by utilizing this fact we derive sufficient conditions for the reachability of the polynomial systems which essentially check the injectivity of the polynomial mappings

a new iterative method for solving the coefficient inverse problem of the wave equation on donne la definition de l equation operateur non lineaire du probleme inverse coefficient de l equation d onde dans le domaine des variables d espace et de temps sans les transformees de laplace et de fourier

a combined genetic algorithm and nonlinear least squares method for material characterization using elastic waves abstract the inverse problem of material characterization is formulated as a parameter identification problem in which a set of parameters corresponding to the material property can be found by minimizing error functions formulated using the measured displacement response and the one computed by a forward solver based on projected candidates of parameters a hybrid numerical method is employed as the forward solver to calculate the dynamic displacement response on the surface of the composite plate for given material property a combined method is used as the inverse operator to determine the material property of composite plate in this method genetic algorithm is first used to select a set of better solutions close to the optima then the nonlinear least squares method is applied using these better solutions as the initial guesses finally the identification results can be determined from the solutions of nonlinear least squares method by comparing their corresponding error function values actual material characterizations of composites demonstrate the higher efficiency of the present method

rapid inverse parameter estimation using reduced basis approximation with asymptotic error estimation this paper presents a rapid and reliable approach to solve inverse problems of parameter estimation for structural systems using reduced basis method rbm a reduced basis model is first developed with asymptotic error estimation and is used for fast computation of solving forward mechanics problems of solids and structures a genetic algorithm ga is then used in the inverse search procedure for parameter estimation the approach is applied to a typical inverse problem of estimating the crack location length and orientation inside a cantilever beam the displacements measured at five points on the lower surface of the beam which can also be evaluated by our fast rbm solver are used as inputs for constructing objective functions of error the genetic algorithm is used to search these parameters of the crack inside cantilever beam that minimize the objective function an example has been presented it is found that the estimated results are very accurate and reliable due to the use of rbm forward model with an effective and robust error estimation and detailed sensitivity analysis the present procedure is 460 times faster than the full fem model used inverse procedure

first eigenvalue of nonsingular mixed graphs with given number of pendant vertices abstract let g be a mixed graph and l g be the laplacian matrix of the mixed graph g the first eigenvalue of g is referred to the least nonzero eigenvalue of l g let mg n k be the set of nonsingular mixed graphs with n vertices and k pendant vertices where n 4 in this paper up to a signature matrix we determine the unique graph with the minimal first eigenvalue among all graphs in m g n k thus we obtain a lower bound for the first eigenvalue of a mixed graph in terms of the number of pendant vertices

commutative algebraic methods for controllability of discrete time polynomial systems abstractin this paper we consider controllability of discrete time polynomial systems first we present a forward accessibility local reachability condition that can be verified in finite time in contrast to conventional conditions second we give a backward accessibility local controllability condition for an invertible system and a condition to verify invertibility finally we derive sufficient conditions to test whether the forward accessible system is reachable and to test the backward accessible system is controllable

an isogeometric collocation method using superconvergent points abstract we develop an iga collocation method modified by collocating at points other than the standard greville abscissae the method is related to orthogonal collocation used for solving differential equations and to the superconvergence theory therefore we refer to this method as super collocation iga sc by carefully choosing the collocation points it can be seen that the iga sc converges in the first derivative energy norms at rates similar to that of the galerkin solution this is different from the collocation at greville abscissae iga c where the convergence in energy norm for odd polynomial degrees is typically suboptimal the method is tested on 1d 2d and 3d numerical examples in which it is compared to iga c and galerkin s method iga g the comparison includes a detailed cost vs accuracy analysis which shows an improved efficiency of the proposed method in particular for odd polynomial degrees

on integrability of observable space for discrete time polynomial control systems the goal of the technical note is to extend the results on the observability decomposition of continuous time nonlinear systems into the discrete time polynomial systems in general the observable space related to the concept of single experiment observability of the discrete time nonlinear systems cannot always be locally spanned by exact one forms whose integrals would define the observable state coordinates in this technical note we show that for the special subclass of reversible polynomial systems the observable space is integrable like in the continuous time case

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

detection of multiple flaws in piezoelectric structures using xfem and level sets abstract an iterative procedure to solve the inverse problem of detecting multiple voids in piezoelectric structure is proposed in each iteration the forward problem is solved for various void configurations and at each iteration the mechanical and electrical responses of a piezoelectric structure is minimized at known specific points along the boundary to match the measured data the extended finite element method xfem is employed for determining the responses as it allows the use of a fixed mesh for varying void geometries the numerical method based on combination of classical shape derivative and of the level set method for front propagation used in structural optimization is utilized to minimize the cost function the results obtained show that this method is effectively able to determine the number of voids in a piezoelectric structure and its corresponding locations and shapes

observability of linear systems with saturated outputs we present necessary and sufficient conditions for observability of the class of output saturated systems these are linear systems whose output passes through a saturation function before it can be measured

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

output feedback stabilization of a class of wiener systems a globally stabilizing output feedback controller is designed for a class of continuous time wiener systems the wiener systems we consider consist of a linear dynamical block and an output polynomial nonlinearity connected in series the hybrid controller consists of three modes of operation which are periodically applied to the system the controller achieves a dead beat response of the closed loop system

a note on observability tests for general polynomial and simple wiener hammerstein systems we propose an algorithm based on symbolic computation packages for testing observability conditions of general polynomial systems which were formulated in sontag siam j control optim 17 1979 139 151 computational complexity of the observability test can be reduced and the test simplified for classes of polynomial systems we illustrate this by considering the class of simple wiener hammerstein systems which consist of a series of two linear dynamic blocks between which a static nonlinearity is sandwiched we consider the case when the nonlinearity is a monomial n q q 1 simple necessary and sufficient conditions for observability are given and they resemble but are subtly different from the well known result on observability for the series connection of two linear systems c 1998 elsevier science b v all rights reserved

radial point interpolation collocation method rpicm for partial differential equations this paper presents a truly meshfree method referred to as radial point interpolation collocation method rpicm for solving partial differential equations this method is different from the existing point interpolation method pim that is based on the galerkin weak form because it is based on the collocation scheme no background cells are required for numerical integration radial basis functions are used in the work to create shape functions a series of test examples were numerically analysed using the present method including 1 d and 2 d partial differential equations in order to test the accuracy and efficiency of the proposed schemes several aspects have been numerically investigated including the choice of shape parameter c with can greatly affect the accuracy of the approximation the enforcement of additional polynomial terms and the application of the hermite type interpolation which makes use of the normal gradient on neumann boundary for the solution of pdes with neumann boundary conditions particular emphasis was on an efficient scheme namely hermite type interpolation for dealing with neumann boundary conditions the numerical results demonstrate that good improvement on accuracy can be obtained after using hermite type interpolation the h convergence rates are also studied for rpicm with different forms of basis functions and different additional terms

controllability for a class of simple wiener hammerstein systems abstract controllability for a class of simple wiener hammerstein systems is considered necessary and sufficient conditions for dead beat and complete controllability for these systems are presented the controllability tests consist of two easy to check tests for the subsystems

linear systems with sign observations this paper deals with systems that are obtained from linear time invariant continuous or discrete time devices followed by a function that just provides the sign of each output such systems appear naturally in the study of quantized observations as well as in signal processing and neural network theory results are given on observability minimal realizations and other system theoretic concepts certain major differences exist with the linear case and other results generalize in a surprisingly straightforward manner

observability at an initial state for polynomial systems we consider observability at an initial state for polynomial systems when testing for local observability for nonlinear systems the observability rank condition based on the inverse function theorem is commonly used however the rank condition is a sufficient condition and we cannot test for global observability using the rank condition in this paper first we derive necessary and sufficient conditions for global observability at an initial state for continuous time polynomial systems then necessary and sufficient conditions for local observability are derived from one of the global observability conditions using the localization of a polynomial ring using the same procedure we derive both global and local observability conditions for discrete time polynomial systems each condition is characterized by a finite set of equations since polynomial rings are noetherian finally examples demonstrate the proposed criteria for testing for observability

an inverse procedure for determination of material constants of composite laminates using elastic waves a procedure is proposed to determine the material constants of composite laminates from dynamic displacement responses wave response obtained at only one receiving point of laminate surfaces a hybrid numerical method is used for forward computation that relates the material constants to the displacement responses a uniform micro genetic algorithm is adopted to develop an inverse procedure and its effectiveness to the present type of applications is shown the robustness of the procedure to the effect of measurement noise is investigated by adding gauss noise to the input displacement response numerical simulations are performed on laminates with different composite materials layer orientations layer number and thickness the satisfactory identification results for all cases demonstrate the effectiveness of the present procedure as well as its robustness to the noises effects

a note on dead beat controllability of generalised hammerstein systems necessary and sufficient conditions for dead beat and complete controllability for a class of generalised hammerstein systems are presented since the system s structure is very close to linear only linear algebra is used for the controllability test the test is very simple and easy to use a closed loop minimum time dead beat controller can be designed for a subclass of generalised hammerstein systems using the grobner basis method

structure identification of nonlinear dynamic systems a survey on input output approaches abstract in the past several methods have been elaborated for the identification of nonlinear dynamic systems most of the methods assume that the structure of the system is given a priori therefore they are in reality parameter estimation algorithms and structure identification is thus usually performed by repeated parameter estimation however in nonlinear system theory several methods are known to determine the structure of a system in this paper structure identification of block oriented especially cascade models of semi linear dynamic models with signal dependent parameters and of nonlinear dynamic models being linear in the parameters will be considered different structure selection methods are summarized based on step and impulse tests frequency response measurements correlation analysis repeated reproducible tests and normal operating data

subdomain radial basis collocation method for fracture mechanics the direct approximation of strong form using radial basis functions rbfs commonly called the radial basis collocation method rbcm has been recognized as an effective means for solving boundary value problems nevertheless the non compactness of the rbfs precludes its application to problems with local features such as fracture problems among others this work attempts to apply rbcm to fracture mechanics by introducing a domain decomposition technique with proper interface conditions the proposed method allows 1 natural representation of discontinuity across the crack surfaces and 2 enrichment of crack tip solution in a local subdomain with the proper domain decomposition and interface conditions exponential convergence rate can be achieved while keeping the discrete system well conditioned the analytical prediction and numerical results demonstrate that an optimal dimension of the near tip subdomain exists the effectiveness of the proposed method is justified by the mathematical analysis and demonstrated by the numerical examples copyright 2010 john wiley sons ltd

a functional optimization formulation and implementation of an inverse natural convection problem abstract a formulation and a fem implementation for the solution of an ill posed inverse design natural convection problem is proposed in particular we consider an incompressible viscous liquid material occupying a given domain where convection is driven by buoyancy thermal boundary conditions are only prescribed in the part h 0 of the boundary in addition the temperature distribution is also prescribed in the part i of the boundary h 1 where the heat flux is known i e i is a boundary with over specified thermal boundary conditions the inverse convection problem is posed as an optimization problem in l 2 i 0 t max for the calculation of the boundary heat flux q o x t with x t h 0 0 t max the optimization scheme minimizes the discrepancy m x t x t q o l 2 1 0 t max between the temperature x t q o calculated from the solution of a direct problem for each flux q 0 and the measured or desired temperature m x t at the boundary i the gradient of the cost functional is obtained from the adjoint fields the adjoint problem is defined from the sensitivity operators obtained by linearization of the equations governing the direct problem the conjugate gradient method is employed to perform the optimization process the fem is used for the calculation of the direct adjoint and sensitivity thermal and fluid flow fields finally the method is demonstrated with the solution of some two dimensional inverse problems with known solutions the numerical results are discussed and future work with potential applications is addressed

extremizing first eigenvalue of 3 colored digraphs made with given blocks abstract this article describes the structure of the non singular connected 3 colored digraphs extremizing the first eigenvalue among all such graphs made with some given blocks as an application we determine the non singular unicyclic 3 colored digraph which minimizes the first eigenvalue over all such graphs with fixed order and girth