the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

large scale tikhonov regularization via reduction by orthogonal projection abstract this paper presents a new approach to computing an approximate solution of tikhonov regularized large scale ill posed least squares problems with a general regularization matrix the iterative method applies a sequence of projections onto generalized krylov subspaces a suitable value of the regularization parameter is determined by the discrepancy principle

exact closed form solution for the vibration modes of the euler bernoulli beam with multiple open cracks abstract in this study exact closed form expressions for the vibration modes of the euler bernoulli beam in the presence of multiple concentrated cracks are presented the proposed expressions are provided explicitly as functions of four integration constants only to be determined by the standard boundary conditions the enforcement of the boundary conditions leads to explicit expressions of the natural frequency equations besides the evaluation of the natural frequencies neither computational work nor recurrence expressions for the vibration modes are required the cracks that are not subjected to the closing phenomenon are modelled as a sequence of dirac s delta generalised functions in the flexural stiffness the eigen mode governing equation is formulated over the entire domain of the beam without enforcement of any continuity conditions which are already accounted for in the adopted flexural stiffness model the vibration modes of beams with different numbers of cracks under different boundary conditions have been analysed by means of the proposed closed form expressions in order to show their efficiency

a posteriori parameter choice with an efficient discretization scheme for solving ill posed problems abstract recently rajan m p rajan an efficient discretization scheme for solving the ill posed problems journal of mathematical analysis and applications 313 2 2006 654 677 considered a discretization scheme for solving ill posed problems and obtained optimal error estimates under an a priori parameter choice strategy with a particular smoothness assumption on the solution it is shown that the computational information for solving the system is far less than the traditional projection schemes neubauer a neubauer an a posteriori parameter choice for tikhonov regularization in the presence of modeling error applied numerical mathematics 4 1988 507 519 and engl and gfrerer h w engl h gfrerer a posteriori parameter choice for general regularization methods for solving ill posed problems applied numerical mathematics 4 1988 395 417 suggested an a posteriori method for choosing the regularization parameter which does not require any knowledge about the exact solution respectively under finite dimensional as well as general setting in this paper we consider an a posteriori parameter choice for finite dimensional approximation which does not require any information about the smoothness of the exact solution and apply to the discretization scheme considered by rajan the computational efficiency of the scheme is illustrated through numerical examples

a geometric interpretation of prolongation by means of connections a geometric interpretation of prolongation can be formulated by using the theory of connections a fiber bundle can be established which is composed of a base manifold and variables which span a prolongation space a particular connection is introduced in terms of these coordinates this provides a very different way of viewing the technique and for introducing prolongation algebras as well as generating integrable equations in a novel way

a new gradient regularization algorithm for source term inversion in 1d solute transportation with final observations abstract in this paper a new gradient regularization algorithm is introduced and applied to solve an inverse problem of determining source terms in one dimensional advection dispersion equation with final observations by functional approximations the algorithm is reduced to find an optimal perturbation for a given source parameter involving computations of gradient vectors in the case of using accurate data the optimal perturbation can be directly worked out by the least square method in the case of with random noisy data regularization strategy may be useful to the realization of the algorithm as compared with ordinary gradient regularization algorithm the new gradient regularization algorithm gives a possible approach to the precise choices of optimal regularization parameters several numerical simulations under different conditions are carried out showing that the algorithm is feasible and efficient furthermore the algorithm is successfully applied to solve a real life example of determining an average magnitude of groundwater pollution sources

a regularization parameter for nonsmooth tikhonov regularization in this paper we develop a novel rule for choosing regularization parameters in nonsmooth tikhonov functionals it is solely based on the value function and applicable to a broad range of nonsmooth models and it extends one known criterion a posteriori error estimates of the approximations are derived an efficient numerical algorithm for computing the minimizer is developed and its convergence properties are discussed numerical results for several common nonsmooth models are presented including deblurring natural images the numerical results indicate the rule can yield results comparable with those achieved with the discrepancy principle and the optimal choice and the algorithm merits a fast and steady convergence

regularization parameter determination for discrete ill posed problems the straightforward solution of discrete ill posed linear systems of equations or least squares problems with error contaminated data does not in general give meaningful results because the propagated error destroys the computed solution the problems have to be modified to reduce their sensitivity to the error in the data the amount of modification is determined by a regularization parameter it can be difficult to determine a suitable value of the regularization parameter when no knowledge of the norm of error in the data is available this paper proposes a new simple technique for determining a value of the regularization parameter that can be applied in this situation it is based on comparing computed solutions determined by tikhonov regularization and truncated singular value decomposition analogous comparisons are proposed for large scale problems the technique for determining the regularization parameter implicity provides an estimate for the norm of the error in the data

using the linear sampling method and an improved maximum product criterion for the solution of the electromagnetic inverse medium problem we present a tikhonov parameter choice approach for three dimensional reconstructions based on a maximum product criterion mpc which provides a regularization parameter located in the concave part of the l curve in log log scale our method baptized improved maximum product criterion impc is an extension of the mpc method developed by bazan et al for two dimensional reconstructions in the 3d framework impc computes the regularization parameter via a fast iterative algorithm and requires no a priori knowledge of the noise level in the data it is applied on the linear sampling method for solving the electromagnetic inverse medium problem in the 3d framework the effectiveness of impc is illustrated with numerical examples involving more than one scatterer

gauge transformation between the first order nonisospectral and isospectral heisenberg hierarchies abstract by means of the ablowitz kaup newell segur system with symbolic computation the gauge transformation between the first order nonisospectral and isospectral heisenberg spectral problems is obtained correspondingly the equivalence relation between the first order nonisospectral and isospectral heisenberg hierarchies is given in addition further applications and potential research directions of our method are discussed

regularization tools and robust optimization for ill conditioned least squares problem a computational comparison least squares problems arise frequently in many disciplines such as image restorations in these areas for the given least squares problem usually the coefficient matrix is ill conditioned thus if the problem data are available with certain error then after solving least squares problem with classical approaches we might end up with a meaningless solution tikhonov regularization is one of the most widely used approaches to deal with such situations in this paper first we briefly describe these approaches then the robust optimization framework which includes the errors in problem data is presented finally our computational experiments on several ill conditioned standard test problems using the regularization tools a matlab package for least squares problem and the robust optimization framework show that the latter approach may be the right choice

tikhonov regularization and the l curve for large discrete ill posed problems discretization of linear inverse problems generally gives rise to very ill conditioned linear systems of algebraic equations typically the linear systems obtained have to be regularized to make the computation of a meaningful approximate solution possible tikhonov regularization is one of the most popular regularization methods a regularization parameter specifies the amount of regularization and in general an appropriate value of this parameter is not known a priori we review available iterative methods and present new ones for the determination of a suitable value of the regularization parameter by the l curve criterion and the solution of regularized systems of algebraic equations

rational solutions for a 2 1 dimensional nonlinear model in water waves generated by the jaulent miodek hierarchy abstract this paper deals with a 2 1 dimensional nonlinear evolution equation nlee generated by the jaulent miodek hierarchy for nonlinear water waves via the hirota s bilinear method and pfaffian first we construct rational solutions for general bilinear equations and then convert the target bilinear equations to the general ones to obtain their rational solutions the pfaffian plays a role to simplifying the computations compared with the determinant way in the existing literatures once the first and second order rational solutions have been obtained the higher order solutions can be derived by the same token figures for the first and second order rational solutions are plotted and analyzed as an application the rational solutions for the modified kadomtsev petviashvili equation have also been constructed the method might be used for some other nlees to construct their rational solutions

a regularization parameter in discrete ill posed problems the tikhonov regularization method for discrete ill posed problems is considered for the practical choice of the regularization parameter alpha some authors use a plot of the norm of the regularized solution versus the norm of the residual vector for all alpha considered this paper contains an analysis of the shape of this plot and gives a theoretical justification for choosing the regularization parameter so it is related to the l corner of the plot considered in the logarithmic scale moreover a new criterion for choosing alpha is introduced independent of the shape of the plot which gives a new interpretation of the corner criterion mentioned above the existence of l corner is discussed

on single integral equations for the transmission problem of acoustics the transmission problem namely scattering of time harmonic waves in a compressible fluid by a fluid inclusion with different material properties is usually formulated as a pair of coupled boundary integral equations over the interface s between the inclusion and the exterior fluid in this paper however we consider methods for solving the transmission problem using a single integral equation over s for a single unknown function in fact we derive four different integral equations using a hybrid of the direct green s theorem and indirect layer ansatz methods and give conditions for the unique solvability of each and for the subsequent construction of the solution to the transmission problem some of our single integral equations are fredholm integral equations of the second kind with weakly singular kernels thus these equations all of which appear to be new are attractive computationally

the gauge equivalence of the nls and the schrodinger flow of maps in 2 1 dimensions the gauge equivalence of the analogues of the nonlinear schrodinger equation nls and those of the schrodinger flow of maps into h2 the minkowski hf model in 2 1 dimensions are proved respectively combining these with the already known results we obtain a complete understanding of the gauge equivalence of the analogous models of the nonlinear schrodinger equation for 1 or 1 and those of the heisenberg ferromagnet model for euclidean or minkowski in 2 1 dimensions

fixed point iterations in determining a tikhonov regularization parameter in kirsch s factorization method kirsch s factorization method is a fast inversion technique for visualizing the profile of a scatterer from measurements of the far field pattern the mathematical basis of this method is given by the far field equation which is a fredholm integral equation of the first kind in which the data function is a known analytic function and the integral kernel is the measured and therefore noisy far field pattern we present a tikhonov parameter choice approach based on a fast fixed point iteration method which constructs a regularization parameter associated with the corner of the l curve in log log scale the performance of the method is evaluated by comparing our reconstructions with those obtained via the l curve and we conclude that our method yields reliable reconstructions at a lower computational cost

z index parameterization for volumetric ct image reconstruction via 3 d dictionary learning despite the rapid developments of x ray cone beam ct cbct image noise still remains a major issue for the low dose cbct to suppress the noise effectively while retain the structures well for low dose cbct image in this paper a sparse constraint based on the 3 d dictionary is incorporated into a regularized iterative reconstruction framework defining the 3 d dictionary learning 3 ddl method in addition by analyzing the sparsity level curve associated with different regularization parameters a new adaptive parameter selection strategy is proposed to facilitate our 3 ddl method to justify the proposed method we first analyze the distributions of the representation coefficients associated with the 3 d dictionary and the conventional 2 d dictionary to compare their efficiencies in representing volumetric images then multiple real data experiments are conducted for performance validation based on these results we found 1 the 3 d dictionary based sparse coefficients have three orders narrower laplacian distribution compared with the 2 d dictionary suggesting the higher representation efficiencies of the 3 d dictionary 2 the sparsity level curve demonstrates a clear z shape and hence referred to as z curve in this paper 3 the parameter associated with the maximum curvature point of the z curve suggests a nice parameter choice which could be adaptively located with the proposed z index parameterization zip method 4 the proposed 3 ddl algorithm equipped with the zip method could deliver reconstructions with the lowest root mean squared errors and the highest structural similarity index compared with the competing methods 5 similar noise performance as the regular dose fdk reconstruction regarding the standard deviation metric could be achieved with the proposed method using 1 2 1 4 1 8 dose level projections the contrast noise ratio is improved by 2 5 3 5 times with respect to two different cases under the 1 8 dose level compared with the low dose fdk reconstruction the proposed method is expected to reduce the radiation dose by a factor of 8 for cbct considering the voted strongly discriminated low contrast tissues

soliton fusion and fission in a generalized variable coefficient fifth order korteweg de vries equation in fluids under investigation in this paper is a generalized variable coefficient fifth order korteweg de vries equation which describes the interaction between a water wave and a floating ice cover or the gravity capillary waves via the hirota method bell polynomial approach and symbolic computation bilinear forms n soliton solutions backlund transformation and lax pair are derived infinitely many conservation laws are obtained based on the bell polynomial typed backlund transformation soliton fusion and fission and influence of the variable coefficients from the equation are analyzed both variable coefficients c t and n t are in direct proportion to the soliton velocities but have no effect on the amplitudes while another constant coefficient can affect the types of the interactions in the sense of the elastic or inelastic elastic inelastic interactions among the three solitons are presented as well

an improved perturbation method for stochastic finite element model updating in this paper an improved perturbation method is developed for the statistical identification of structural parameters by using the measured modal parameters with randomness on the basis of the first order perturbation method and sensitivity based finite element fe model updating two recursive systems of equations are derived for estimating the first two moments of random structural parameters from the statistics of the measured modal parameters regularization technique is introduced to alleviate the ill conditioning in solving the equations the numerical studies of stochastic fe model updating of a truss bridge are presented to verify the improved perturbation method under three different types of uncertainties namely natural randomness measurement noise and the combination of the two the results obtained using the perturbation method are in good agreement with although less accurate than those obtained using the monte carlo simulation mcs method it is also revealed that neglecting the correlation of the measured modal parameters may result in an unreliable estimation of the covariance matrix of updating parameters the statistically updated fe model enables structural design and analysis damage detection condition assessment and evaluation in the framework of probability and statistics copyright 2007 john wiley sons ltd

the use of regularization methods in computing radon nikodým derivatives application to grain size distributions let a probability law nu on a b be absolutely continuous with respect to another probability law mu specified equivalent to the lebesgue measure lambda on a b we seek to approximate the density frac d nu d mu assumed to be in l mu 2 a b in the least square sense given the values of the distribution function nu a t at fixed points t j 1 leq j leq p we obtain a convenient solution of this ill posed problem via a hilbert space embedding and the associated discretized problem is solved by using regularization methods this problem is connected with sedimentological topics such as sediment transport and changes of scale as an example a weight frequency cumulative curve is processed

preconditioner based on the sherman morrison formula for regularized least squares problems we propose a sparse approximate inverse preconditioner based on the sherman morrison formula for tikhonov regularized least square problems theoretical analysis shows that the factorization method can take the advantage of the symmetric property of the coefficient matrix and be implemented cheaply combined with dropping rules the incomplete factorization leads to a preconditioner for krylov iterative methods to solve regularized least squares problems numerical experiments show that our preconditioner is competitive compared to existing methods especially for ill conditioned and rank deficient least squares problems

solitons and rouge waves for a generalized 3 1 dimensional variable coefficient kadomtsev petviashvili equation in fluid mechanics evolution of the long water waves and small amplitude surface waves with the weak nonlinearity weak dispersion and weak perturbation in fluid mechanics in three spatial dimensions can be described by a generalized 3 1 dimensional variable coefficient kadomtsev petviashvili equation which is studied in this paper with symbolic computation via the truncated painleve expansion an auto backlund transformation is derived based on which under certain variable coefficient constraints one soliton two soliton homoclinic breather wave and rouge wave solutions are respectively obtained via the hirota method graphic analysis shows that the soliton propagates with the varying soliton direction change of the value of any one of g t m t n t h t q t and l t in the equation can cause the change of the soliton shape while the soliton amplitude cannot be affected by that change where g t represents the dispersion m t and n t respectively stand for the disturbed wave velocities along the y and z directions h t q t and l t are the perturbed effects y and z are the scaled spatial coordinates and t is the temporal coordinate soliton direction and type of the interaction between the two solitons can vary with the change of the value of g t while they cannot be affected by m t n t h t q t and l t homoclinic breather wave and rouge wave are respectively displayed where the rouge wave comes from the extreme behaviour of the homoclinic breather wave

lax pair darboux transformation and nth order rogue wave solutions for a 2 1 dimensional heisenberg ferromagnetic spin chain equation abstract a new 2 1 dimensional heisenberg ferromagnetic spin chain equation is investigated which can be used to describe magnetic soliton excitations in two dimensional space fields and a time field the lax pair of the equation is first constructed based on the lax pair initial seed solution and darboux transformation the analytic first second and third order rogue wave solutions are obtained and a general expression of the n th order n 3 rogue wave solutions is presented the impacts of the system parameters on the rogue waves are demonstrated through numerical visualization method

a maximum product criterion as a tikhonov parameter choice rule for kirsch s factorization method kirsch s factorization method is a fast inversion technique for visualizing the profile of a scatterer from measurements of the far field pattern we present a tikhonov parameter choice approach based on a maximum product criterion mpc which provides a regularization parameter located in the concave part of the l curve on a log log scale the performance of the method is evaluated by comparing our reconstructions with those obtained via the l curve morozov s discrepancy principle and the svd tail numerical results that illustrate the effectiveness of the mpc in reconstruction problems involving both simulated and real data are reported and analyzed

on computing first and second order derivative spectra enhancing resolution in spectral response and an ability to differentiate spectral mixing in delineating the endmembers from the spectral response are central to the spectral data analysis first and higher order derivatives analysis of absorbance and reflectance spectral data is commonly used techniques in differentiating the spectral mixing but high sensitivity of derivative to the noise in data is a major problem in the robust estimation of derivative of spectral data an algorithm of robust estimation of first and second order derivative spectra from evenly spaced noisy normal spectral data is proposed the algorithm is formalized in the framework of an inverse problem where based on the fundamental theorem of calculus a matrix equation is formed using a volterra type integral equation of first kind a regularization technique where the balancing principle is used in selecting a posteriori optimal regularization parameter is designed to solve the inverse problem for robust estimation of first order derivative spectra the higher order derivative spectra are obtained while using the algorithm in sequel the algorithm is tested successfully with synthetically generated spectral data contaminated with additive white gaussian noise and also with real absorbance and reflectance spectral data for fresh and sea water respectively robust and efficient algorithm of computing first and second orders derivative spectra is designed the algorithm is based on the premise of inverse problem where a robust solution is achieved via regularization it couples discrepancy and balancing principles to determine regularization parameter and implement stopping rule respectively numerical experiments on noisy data suggest superiority of the method over finite difference and fourier transform based techniques the proposed method is applied on absorbance and reflectance spectral data for fresh and sea water

force reconstruction analysis and regularization of a deconvolution problem the reconstruction of force is considered by means of indirect measurements this necessitates taking measurements from the impacted structure and then to deconvolve those signals from the impulse response function more precisely the purpose of the work described here is to analyze a deconvolution technique and to solve the problems which occur thus it is highlighted that the associated deconvolution problem depends on the location of the measurement points is it possible or not to reconstruct the impact force versus the location of this point numerical predictions are compared and validated with experiment but the deconvolution is a well known ill posed problem the results are often unstable this is why it is necessary to regularize the problem which consists of adding a condition to the solution which does not appear in the initial problem some regularization methods are presented nevertheless they necessitate the determination of a parameter the difficulty is to calculate an appropriate value of this regularization parameter the methods are successfully used to recover an experimental force

some properties of the arnoldi based methods for linear ill posed problems in this paper we study some properties of the classical arnoldi based methods for solving infinite dimensional linear equations involving compact operators these problems are intrinsically ill posed since a compact operator does not admit a bounded inverse we study the convergence properties and the ability of these algorithms to estimate the dominant singular values of the operator

orthogonal laurent polynomials on the unit circle extended cmv ordering and 2d toda type integrable hierarchies abstract we connect the theory of orthogonal laurent polynomials on the unit circle and the theory of toda like integrable systems using the gauss borel factorization of a cantero moral velazquez moment matrix that we construct in terms of a complex quasi definite measure supported on the unit circle the factorization of the moment matrix leads to orthogonal laurent polynomials on the unit circle and the corresponding second kind functions we obtain jacobi operators 5 term recursion relations christoffel darboux kernels and corresponding christoffel darboux formulas from this point of view in a completely algebraic way we generalize the cantero moral velazquez sequence of laurent monomials recursion relations christoffel darboux kernels and corresponding christoffel darboux formulas in this extended context we introduce continuous deformations of the moment matrix and we show how they induce a time dependent orthogonality problem related to a toda type integrable system which is connected with the well known toeplitz lattice we obtain the lax and zakharov shabat equations using the classical integrability theory tools we explicitly derive the dynamical system associated with the coefficients of the orthogonal laurent polynomials and we compare it with the classical toeplitz lattice dynamical system for the verblunsky coefficients of szeg polynomials for a positive measure discrete flows are introduced and related to darboux transformations finally we obtain the representation of the orthogonal laurent polynomials and their second kind functions using the formalism of miwa shifts in terms of functions and the subsequent bilinear equations

flutter and divergence instability of the multi cracked cantilever beam column for conservative systems instability can occur only by divergence and the presence of damage can produce both a reduction of the buckling loads and modification of the corresponding mode shapes depending on the positions and intensities of the damage distribution for nonconservative systems instability is found to occur by divergence flutter or both characterised by multiple stable and unstable ranges of the loads whose boundary can be altered by the damage distribution this paper focuses on the stability behaviour of multi cracked cantilever euler beam column subjected to conservative or nonconservative axial loads the exact flutter and divergence critical loads are obtained by means of the exact closed form solution of the multi cracked beam column derived by the authors in a previous paper the extensive numerical applications reported in the paper aimed at evaluating the influence of several damage scenarios for different values of the degree of nonconservativeness it is shown how the presence of damage can strongly modify the ranges of divergence and flutter critical loads of the corresponding undamaged cantilever column which has been the subject of several papers starting from the pfluger paradoxical results

an analysis of the zero crossing method for choosing regularization parameters solving discrete ill posed problems via tikhonov regularization introduces the problem of determining a regularization parameter there are several methods available for choosing such a parameter yet in general the uniqueness of this choice is an open question two empirical methods for determining a regularization parameter which appear in the biomedical engineering literature are the composite residual and smoothing operator and the zero crossing method an equivalence is established between the zero crossing method and a minimum product criterion which has previously been linked with the l curve method finally the uniqueness of a choice of regularization parameter is established under certain restrictions on the fourier coefficients of the data in the ill posed problem

parameter identification with weightless regularization although the regularization increased the popularity of parameter identification due to its capability of deriving a stable solution the significant problem is that the solution depends upon the regularization parameters chosen this paper presents a technique for deriving solutions without the use of the parameters and further an optimization method which can work efficiently for problems of concern numerical examples show that the technique can efficiently search for appropriate solutions copyright 2001 john wiley sons ltd

subset selection in noise based on diversity measure minimization we develop robust methods for subset selection based on the minimization of diversity measures a bayesian framework is used to account for noise in the data and a maximum a posteriori map estimation procedure leads to an iterative procedure which is a regularized version of the focal underdetermined system solver focuss algorithm the convergence of the regularized focuss algorithm is established and it is shown that the stable fixed points of the algorithm are sparse we investigate three different criteria for choosing the regularization parameter quality of fit sparsity criterion l curve the l curve method as applied to the problem of subset selection is found not to be robust and we propose a novel modified l curve procedure that solves this problem each of the regularized focuss algorithms is evaluated through simulation of a detection problem and the results are compared with those obtained using a sequential forward selection algorithm termed orthogonal matching pursuit omp in each case the regularized focuss algorithm is shown to be superior to the omp in noisy environments

on a generalization of reginska s parameter choice rule and its numerical realization in large scale multi parameter tikhonov regularization abstract a crucial problem concerning tikhonov regularization is the proper choice of the regularization parameter this paper deals with a generalization of a parameter choice rule due to reginska 1996 31 analyzed and algorithmically realized through a fast fixed point method in bazan 2008 3 which results in a fixed point method for multi parameter tikhonov regularization called mfp like the single parameter case the algorithm does not require any information on the noise level further combining projection over the krylov subspace generated by the golub kahan bidiagonalization gkb algorithm and the mfp method at each iteration we derive a new algorithm for large scale multi parameter tikhonov regularization problems the performance of mfp when applied to well known discrete ill posed problems is evaluated and compared with results obtained by the discrepancy principle the results indicate that mfp is efficient and competitive the efficiency of the new algorithm on a super resolution problem is also illustrated

interpreting potential field anomaly of an isolated source of regular geometry revisited abstracti have developed an improved practical method for interpreting a symmetrical shaped potential field anomaly due to an isolated source body of regular geometric configuration the method uses the first order horizontal derivative of the logarithmically transformed absolute value of the anomaly in estimating the source body parameters such as the location depth of burial and shape factor to tackle noise in data a regularization technique is designed which ensures a robust estimate of the first order derivative of logarithmically transformed data the regularization technique uses an optimal value of regularization parameter that although noise dependent requires no a priori knowledge of the noise level in the data a graphical method is designed to determine an optimal value of the regularization parameter from the position of the local minimum of a specially defined functional with respect to the regularization parameters numerical tests have been conducted on the noise contaminated synthe

complete integrability of the kadomtsev petviashvili equation abstract the total hierarchy of the kadomtsev petviashvili kp equation is transformed to the system of linear partial differential equations with constant coefficients the complete integrability of the kp equation is proved by using this linear system the existence and uniqueness theorem of the cauchy problem of the kp hierarchy is obtained

integrability of the coupled kdv equations derived from two layer fluids prolongation structures and miura transformations abstract the lax integrability of the coupled kdv equations derived from two layer fluids s y lou b tong h c hu x y tang coupled kdv equations derived from two layer fluids j phys a math gen 39 2006 513 527 is investigated by means of prolongation technique as a result the lax pairs of some painleve integrable coupled kdv equations and several new coupled kdv equations are obtained finally the miura transformations and some coupled modified kdv equations associated with the lax integrable coupled kdv equations are derived by an easy way

closed form solutions of a multi cracked circular arch under static loads abstract generalised functions have been widely adopted in structural mechanics to treat singularities of beam like structures however due to the curved geometry that couples axial and transversal displacements their use has never been explored for curved beams in this paper the capability of distributions of leading to closed form exact solutions for multi cracked circular arch is shown the exact closed form solution of a circular euler arch in presence of any number of discontinuities due to concentrated damage and subjected to an arbitrary distribution of static loads is obtained damage under the form of concentrated cracks has been modeled through the widely adopted and validated equivalent elastic hinge concept and has been introduced in the governing differential equations by making use of dirac s delta functions the resulting nontrivial generalised six order differential equations have been derived and solved in closed form independently of the number of along arch concentrated cracks the solution is expressed as a function of six integration constants only in which the damage positions and intensities are given data appearing explicitly in the solution expression this latter aspect constitutes a fundamental aid towards the resolution of the static damage inverse identification problem the results have been validated through some comparisons with finite element numerical simulations examples referred to multi cracked euler arches with different boundary conditions damage and load scenarios are presented

a convergent algorithm for orthogonal nonnegative matrix factorization this paper proposes a convergent algorithm for nonnegative matrix factorization nmf with orthogonality constraint on the factors we design the algorithm based on the additive update rule algorithm for the standard nmf proposed by lee and seung and derive the convergent version by generalizing the convergence proof of the algorithm developed by lin further we use the proposed algorithms to improve clustering capability of the standard nmf using the reuter document corpus a standard dataset in clustering research

multi parameter regularization techniques for ill conditioned linear systems when a system of linear equations is ill conditioned regularization techniques provide a quite useful tool for trying to overcome the numerical inherent difficulties the ill conditioned system is replaced by another one whose solution depends on a regularization term formed by a scalar and a matrix which are to be chosen in this paper we consider the case of several regularizations terms added simultaneously thus overcoming the problem of the best choice of the regularization matrix the error of this procedure is analyzed and numerical results prove its efficiency

multi parameter regularization and its numerical realization in this paper we propose and analyse a choice of parameters in the multi parameter regularization of tikhonov type a modified discrepancy principle is presented within the multi parameter regularization framework an order optimal error bound is obtained under the standard smoothness assumptions we also propose a numerical realization of the multi parameter discrepancy principle based on the model function approximation numerical experiments on a series of test problems support theoretical results finally we show how the proposed approach can be successfully implemented in laplacian regularized least squares for learning from labeled and unlabeled examples

generalized darboux transformation and rational soliton solutions for chen lee liu equation in this paper the chen lee liu c l l equation is investigated by the darboux transformation dt method a specific construction of the n fold dt for c l l equation is derived in a simple way the form of the n fold dt is a matrix polynomial and each element of the matrix can be expressed by a ratio of two determinants furthermore by choosing suitable eigenvalues and eigenfunctions under the reduction conditions we can obtain the determinant solution of the reduced c l l equation moreover the generalized dt gdt for c l l equation is also constructed through the limiting technique as applications of the gdt method the first and the second order rational solitons with vanished background vbc and non vanished background nvbc from different seeds are calculated for c l l equation we hope our results can be realized by experiments in plasma physics and optical fibers

analytic study on a 2 1 dimensional nonlinear schrodinger equation in the heisenberg ferromagnetism in this paper a 2 1 dimensional nonlinear schrodinger equation for a 2 1 dimensional heisenberg ferromagnetic spin chain with the bilinear and anisotropic interactions is investigated via the hirota method and symbolic computation bilinear forms and multi soliton solutions are derived the one two and three solitons are analyzed graphically and we find the amplitudes and widths of the two and three solitons keep invariant after each interaction the bell shape one soliton as well as parallel crossed two and three solitons are respectively observed through the asymptotic analysis expressions which denote the two solitons before and after the interactions are obtained and interactions between the two solitons are proved to be elastic

multiple orthogonal polynomials of mixed type gauss borel factorization and the multi component 2d toda hierarchy multiple orthogonality is considered in the realm of a gauss borel factorization problem for a semi infinite moment matrix perfect combinations of weights and a finite borel measure are constructed in terms of m nikishin systems these perfect combinations ensure that the problem of mixed multiple orthogonality has a unique solution that can be obtained from the solution of a gauss borel factorization problem for a semi infinite matrix which plays the role of a moment matrix this leads to sequences of multiple orthogonal polynomials their duals and second kind functions it also gives the corresponding linear forms that are bi orthogonal to the dual linear forms expressions for these objects in terms of determinants from the moment matrix are given recursion relations are found which imply a multi diagonal jacobi type matrix with snake shape and results like the abc theorem or the christoffel darboux formula are re derived in this context using the factorization problem and the generalized hankel symmetry of the moment matrix the connection between this description of multiple orthogonality and the multi component 2d toda hierarchy which can be also understood and studied through a gauss borel factorization problem is discussed deformations of the weights natural for m nikishin systems are considered and the correspondence with solutions to the integrable hierarchy represented as a collection of lax equations is explored corresponding lax and zakharov shabat matrices as well as wave functions and their adjoints are determined the construction of discrete flows is discussed in terms of miwa transformations which involve darboux transformations for the multiple orthogonality conditions the bilinear equations are derived and the tau function representation of the multiple orthogonality is given

inferring perceptual saliency fields from viewpoint dependent recognition data we present an algorithm for computing the relative perceptual saliencies of the features of a three dimensional object using either goodness of view scores measured at several viewpoints or perceptual similarities among several object views this technique addresses the inverse illposed version of the direct problem of predicting goodness of view scores or view point similarities when the object features are known on the basis of a linear model for the direct problem we solve the inverse problem using the method of regularization the critical assumption we make to regularize the solution is that perceptual salience varies slowly on the surface of the object the salient regions derived using this assumption empirically indicate what object structures are important in human three dimensional object perception a domain where theories typically have been based on somewhat ad hoc features

the linear sampling method for solving the electromagnetic inverse scattering problem we consider the inverse scattering problem of determining the shape of an obstacle in mathbb r from knowledge of the time harmonic incident electromagnetic wave and the far field pattern of the scattered wave with frequency in the resonance region the approach used is the linear sampling method which does not require a priori knowledge of either the boundary condition or the connectivity of the scattering obstacle numerical examples are given for the case of both a simply connected perfect conductor and multiply connected obstacles satisfying an impedance boundary condition on the boundary of one component and satisfying a perfect conducting boundary condition on the boundary of another component

exact solution of the multi cracked euler bernoulli column abstract the use of distributions generalized functions is a powerful tool to treat singularities in structural mechanics and besides providing a mathematical modelling their capability of leading to closed form exact solutions is shown in this paper in particular the problem of stability of the uniform euler bernoulli column in presence of multiple concentrated cracks subjected to an axial compression load under general boundary conditions is tackled concentrated cracks are modelled by means of dirac s delta distributions an integration procedure of the fourth order differential governing equation which is not allowed by the classical distribution theory is proposed the exact buckling mode solution of the column as functions of four integration constants and the corresponding exact buckling load equation for any number position and intensity of the cracks are presented as an example a parametric study of the multi cracked simply supported and clamped clamped euler bernoulli columns is presented

an adaptive iterative method for downward continuation of potential field data from a horizontal plane we have developed an improved adaptive iterative method based on the nonstationary iterative tikhonov regularization method for performing a downward continuation of the potential field data from a horizontal plane our method uses the tikhonov regularization result as initial value and has an incremental geometric choice of the regularization parameter we compared our method with previous methods tikhonov regularization landweber iteration and integral iteration method the downwardcontinuation performance of these methods in spatial and wavenumber domains were compared with the aspects of their iterative schemes filter functions and downwardcontinuation operators applications to synthetic gravity and real aeromagnetic data showed that our iterative method yields a better downward continuation of the data than other methods our method shows fast computation times and a stable convergence in addition the l curve criterion for choosing the regularization parameter is expressed here in the wavenumber domain and used to speed up computations and to adapt the wavenumber domain iterative method

the exact explicit dynamic stiffness matrix of multi cracked euler bernoulli beam and applications to damaged frame structures abstract in this paper the closed form expression of the exact dynamic stiffness matrix of an euler bernoulli beam in the presence of an arbitrary number of concentrated cracks is derived the procedure adopted for the evaluation of the dynamic stiffness matrix is based on the availability of the exact closed form solution of the vibration modes of the multi cracked beam derived by the same authors in a previous paper the knowledge of the exact explicit dynamic stiffness matrix of the multi cracked beam makes the direct evaluation of the exact global dynamic stiffness matrix of damaged frame structures possible furthermore it allows the exact evaluation of the frequencies and the corresponding vibration modes consistent with the distributed parameter model through the application of the well known wittrick williams algorithm some numerical applications relative to the evaluation of frequencies and the corresponding mode shapes of multi cracked framed structure are reported furthermore the closed form solution has been validated by comparing with some exact results available in the literature for a simple single cracked frame finally further new results for a multi cracked frame have been compared with those obtained by a finite element simulation

monte carlo sure a black box optimization of regularization parameters for general denoising algorithms we consider the problem of optimizing the parameters of a given denoising algorithm for restoration of a signal corrupted by white gaussian noise to achieve this we propose to minimize stein s unbiased risk estimate sure which provides a means of assessing the true mean squared error mse purely from the measured data without need for any knowledge about the noise free signal specifically we present a novel monte carlo technique which enables the user to calculate sure for an arbitrary denoising algorithm characterized by some specific parameter setting our method is a black box approach which solely uses the response of the denoising operator to additional input noise and does not ask for any information about its functional form this therefore permits the use of sure for optimization of a wide variety of denoising algorithms we justify our claims by presenting experimental results for sure based optimization of a series of popular image denoising algorithms such as total variation denoising wavelet soft thresholding and wiener filtering smoothing splines in the process we also compare the performance of these methods we demonstrate numerically that sure computed using the new approach accurately predicts the true mse for all the considered algorithms we also show that sure uncovers the optimal values of the parameters in all cases

on robust estimation of discrete hilbert transform of noisy data abstractwe developed a novel technique of robust estimation of the discrete hilbert transform dht of noisy geophysical data the technique used the sinc method in which the data were transformed via conformal mapping and the sinc bases were determined by solving a linear matrix equation a transformation rule was presented for selecting a suitable conformal mapping function that would transform the class of geophysical data set in an appropriate interval range a novel regularization technique was designed to obtain a robust solution of sinc bases when the data contained noise in which an optimal regularization parameter was obtained in an automated way using a 1d optimization scheme the technique of selecting the optimal value of the regularization parameter required no a priori knowledge about the level of noise contamination in the data numerical experiments were conducted on synthetically generated and published field data sets with a varying level of noise contamination to test the performance

n fold darboux transformation and solitonic interactions of a variable coefficient generalized boussinesq system in shallow water abstract under consideration in this paper is a variable coefficient generalized boussinesq system for the long weakly nonlinear and weakly dispersive surface waves in shallow water with the aid of symbolic computation n fold darboux transformation n dt is constructed for that system analytic solutions of the system are obtained via the n dt elastic interactions of three bell shaped and periodic bell shaped solitons are obtained fusion interactions and periodic fusion fission interactions of the solitary waves are graphically analyzed which are inelastic

a new method for solving linear ill posed problems abstract in this paper we propose a new method for solving large scale ill posed problems this method is based on the karush kuhn tucker conditions fisher burmeister function and the discrepancy principle the main difference from the majority of existing methods for solving ill posed problems is that we do not need to choose a regularization parameter in advance experimental results show that the proposed method is effective and promising for many practical problems

parameter determination for tikhonov regularization problems in general form abstract tikhonov regularization is one of the most popular methods for computing an approximate solution of linear discrete ill posed problems with error contaminated data a regularization parameter 0 balances the influence of a fidelity term which measures how well the data are approximated and of a regularization term which dampens the propagation of the data error into the computed approximate solution the value of the regularization parameter is important for the quality of the computed solution a too large value of 0 gives an over smoothed solution that lacks details that the desired solution may have while a too small value yields a computed solution that is unnecessarily and possibly severely contaminated by propagated error when a fairly accurate estimate of the norm of the error in the data is known a suitable value of often can be determined with the aid of the discrepancy principle this paper is concerned with the situation when the discrepancy principle cannot be applied it then can be quite difficult to determine a suitable value of we consider the situation when the tikhonov regularization problem is in general form i e when the regularization term is determined by a regularization matrix different from the identity and describe an extension of the cose method for determining the regularization parameter in this situation this method has previously been discussed for tikhonov regularization in standard form i e for the situation when the regularization matrix is the identity it is well known that tikhonov regularization in general form with a suitably chosen regularization matrix can give a computed solution of higher quality than tikhonov regularization in standard form

regularization parameter estimation for non negative hyperspectral image deconvolution this paper aims at studying a method to automatically estimate the regularization parameters of non negative hyperspectral image deconvolution methods the deconvolution problem is formulated as a multi objective optimization problem and the properties of the corresponding response surface are studied based on these properties the minimum distance criterion mdc and the maximum curvature criterion mcc are proposed to estimate regularization parameters especially for the non negativity constrained deconvolution problem mdc has good theoretical properties convexity and uniqueness but requires to choose a reference point on the contrary mcc does not need to choose any reference point but does not have interesting theoretical properties a grid search based approach to minimize the computational cost of mdc and mcc is proposed it results in fast approaches to estimate the regularization parameters based on simulated 2d images the proposed approaches are compared with the state of the art methods confirming the effectiveness of the mdc and mcc for the non negativity constrained image deconvolution problem in the case of non negative hyperpsectral image deconvolution the fast mdc yields better performances than the fast mcc an application to real world hyperspectral fluorescence microscopy images is also provided it confirms the superiority of mdc

nonclassical symmetry reductions for the kadomtsev petviashvili equation abstract in this paper we discuss dimensional reductions of the physically and mathematically significant kadomtsev petviashvili equation in particular we exhibit some new reductions of the kadomtsev petviashvili equation which are obtained by a generalization of the direct method for determining similarity reductions recently developed by clarkson and kruskal j math phys 30 1989 2201 new solutions of the kadomtsev petviashvili equation are obtained in terms of weierstrass elliptic functions solutions of the lame equations and the first second and fourth painleve transcendents a group theoretical explanation of the new solutions is provided in terms of conditional symmetries leaving only specific subsets of solutions of the kadomtsev petviashvili equation invariant

sampling method based projection approach for the reconstruction of 3d acoustically penetrable scatterers abstract we present a projection based regularization parameter choice approach within the framework of the linear sampling method for the reconstruction of acoustically penetrable objects using the golub kahan bidiagonalization algorithm and the lanczos tridiagonalization process we form appropriate subspaces which generate a sequence of regularized solutions as a result two new and efficient methods are developed and used for the solution of problems that involve large linear systems of equations the effectiveness of our approach is illustrated with reconstructions of three dimensional objects

flutter and divergence instability of nonconservative beams and plates for a conservative system the only possible instability is of divergence type for a nonconservative system however instability can be of divergence flutter or both depending on the amount of nonconservativeness in this paper we study the instability of a cantilevered beam and a simply supported plate subjected to a combination of fixed and follower forces a nonconservative parameter is introduced to provide all possible combinations of these forces for the beam instability changes from divergence to flutter at a critical value of this parameter for values of the parameter above the critical value the flutter instability remains as the only instability pattern in contrast to implications in the literature for the plate the instability is governed by flutter for a certain range of the nonconservative parameter even though divergence instability still exists the range depends on the geometry aspect ratio and material property poisson s ratio of the plate

mixed type soliton solutions for the n coupled hirota system in an optical fiber under investigation in this paper is the n coupled hirota system which describes the ultrashort pulse simultaneous propagation of the n field components in an optical fiber through the hirota method and symbolic computation using some auxiliary functions we obtain the improved bilinear forms and two mixed type soliton solutions for the 3 coupled hirota system while the system admits two mixed type solitons for all the cases of 1 2 and 3 which the represent the defocusing or focusing nonlinearities of the 3 components with the help the analytic and graphic analysis we study the properties and interactions for the two mixed type solitons for the 3 coupled hirota system amplitudes for the two mixed type one solitons are not affected by but their velocities are linearly related to with as the higher order effect which represents the relative width of the spectrum that arises due to the quasi monochromocity for the 2 bright 1 dark two solitons there exist the elastic and inelastic interactions while for the 1 bright 2 dark two solitons there is only the elastic interaction the 2 bright 1 dark and 1 bright 2 dark bound state two solitons are also presented finally we extend those results to the n coupled hirota system

pfaffian solutions to a 3 1 dimensional generalized b type kadomtsev petviashvili equation and its modified counterpart abstract a class of exact pfaffian solutions to a 3 1 dimensional generalized b type kadomtsev petviashvili equation is obtained a set of sufficient conditions consisting of systems of linear partial differential equations involving free parameters is generated to guarantee that the pfaffian solves the equation a backlund transformation of the equation is presented the equation is transformed into a set of bilinear equations and a few classes of traveling wave solutions rational solutions and pfaffian solutions to the extended bilinear equations are furnished examples of the pfaffian solutions are explicitly computed and a few solutions are plotted

regularization parameter selection for nonlinear iterative image restoration and mri reconstruction using gcv and sure based methods regularized iterative reconstruction algorithms for imaging inverse problems require selection of appropriate regularization parameter values we focus on the challenging problem of tuning regularization parameters for nonlinear algorithms for the case of additive possibly complex gaussian noise generalized cross validation gcv and weighted mean squared error mse approaches based on stein s unbiased risk estimate sure need the jacobian matrix of the nonlinear reconstruction operator representative of the iterative algorithm with respect to the data we derive the desired jacobian matrix for two types of nonlinear iterative algorithms a fast variant of the standard iterative reweighted least squares method and the contemporary split bregman algorithm both of which can accommodate a wide variety of analysis and synthesis type regularizers the proposed approach iteratively computes two weighted sure type measures predicted sure and projected sure which require knowledge of noise variance 2 and gcv which does not need 2 for these algorithms we apply the methods to image restoration and to magnetic resonance image mri reconstruction using total variation and an analysis type l1 regularization we demonstrate through simulations and experiments with real data that minimizing predicted sure and projected sure consistently lead to near mse optimal reconstructions we also observe that minimizing gcv yields reconstruction results that are near mse optimal for image restoration and slightly suboptimal for mri theoretical derivations in this paper related to jacobian matrix evaluations can be extended in principle to other types of regularizers and reconstruction algorithms

on a family of solutions of the kadomtsev petviashvili equation which also satisfy the toda lattice hierarchy we describe the interaction pattern in the x y plane for a family of soliton solutions of the kadomtsev petviashvili kp equation the solutions considered also satisfy the finite toda lattice hierarchy we determine completely their asymptotic patterns for y and we show that all the solutions except the 1 soliton solution are of resonant type consisting of arbitrary numbers of line solitons in both asymptotics that is arbitrary n incoming solitons for y interact to form arbitrary n outgoing solitons for y we also discuss the interaction process of those solitons and show that the resonant interaction creates a web like structure having n 1 n 1 holes

convergence analysis of tikhonov type regularization algorithms for multiobjective optimization problems in this paper we introduce a vector valued tikhonov type regularization algorithm for an extended valued multiobjective optimization problem under some mild conditions we prove that any sequence generated by this algorithm converges to a weak pareto optimal solution of the multiobjective optimization problem our results improve and generalize some known results

exterior differential expression of the 1 1 dimensional nonlinear evolution equation with lax integrability abstract a 1 1 dimensional nonlinear evolution equation with lax integrability is investigated in this paper with the aid of differential forms and exterior differentials equivalent definition of the lax integrability is given relation between the lax integrability and complete integrability is discussed geometric interpretation of the lax equation is presented gauge transformation and darboux transformation are restated in terms of the differential forms and exterior differentials if i s is a darboux transformation between two lax equations the system that the matrix s should satisfy is given where is the spectral parameter and i is the identity matrix the completely integrable condition of that system is obtained according to the frobenius theorem and it is shown that s h h 1 satisfies that completely integrable condition with h and as two matrices