a direct branching algorithm for checking the equivalence of two deterministic pushdown transducers one of which is real time strict abstract a new direct branching algorithm is presented for checking the equivalence of deterministic pushdown transducers one of whose associated deterministic pushdown automata dpdas is real time strict it is a straightforward extension of the corresponding algorithm for dpdas tomita 1982 and then proves the general applicability of our approach

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

an extended direct branching algorithm for checking equivalence of deterministic pushdown automata abstract this paper extends the direct branching algorithm of 25 for checking equivalence of deterministic pushdown automata it does so by providing a technique called halting for dealing with nodes with unbounded degree in the comparison tree this may occur when a skipping step may be applied infinitely many times to a certain node as a result of infinite sequences of e moves this extension allows the algorithm to check equivalence of two deterministic pushdown automata when none of them is real time but in a certain condition that properly contains a case where one of them is real time strict

stable gfem sgfem improved conditioning and accuracy of gfem xfem for three dimensional fracture mechanics abstract in this paper we present an extension of the stable generalized fem sgfem for 3 d fracture mechanics problems numerical experiments show that the use of available singular enrichment bases derived from the 2 d asymptotic crack tip solution leads to a severe loss of accuracy in the sgfem an enrichment scheme based on singular bases and linear polynomials is shown to recover the optimal convergence of the sgfem the proposed sgfem for 3 d fractures delivers the same rate of growth in condition number as the standard fem for proper choice of singular enrichment functions the accuracy and conditioning obtained with the sgfem is compared with the generalized fem gfem for different types of singular enrichment bases a fully 3 d fracture mechanics problem is considered to highlight issues that arise only in 3 d problems the convergence of stress intensity factors sifs extracted from gfem and sgfem solutions and the effect of the size of enrichment sub domains on the accuracy of extracted sifs are also studied it is shown that the accuracy of sifs may deteriorate with mesh refinement when the topological enrichment strategy is adopted the proposed sgfem delivers much better accuracy than the gfem for both geometrical and topological enrichment strategies

a penalty method for the vorticity velocity formulation we present a new vorticity velocity formulation and implementation for the unsteady three dimensional navier stokes equations based on a penalty method it relies on an equivalence theorem that employs exact boundary conditions and the vorticity definition on the domain boundary this approach is particularly attractive for high order methods for which the often used influence matrix method fails to converge for t 0 the accuracy and the robustness of the new method is demonstrated in the context of several spectral element simulations of unsteady two and three dimensional internal and external flows in particular the flow past a finite span cylinder attached to end plates is studied in some detail in order to evaluate the effects of the aspect ratio on the formation length

meshless formulation using nurbs basis functions for eigenfrequency changes of beam having multiple open cracks abstract this paper presents a meshless formulation using non uniform rational b spline nurbs basis functions and its applications to evaluate natural frequencies of a beam having multiple open cracks node based nurbs basis functions are used to construct the approximation function the characteristic differentiability of the nurbs basis functions allows it to represent a function having specific degrees of smoothness and or discontinuity the discontinuity can be incorporated simply by assigning multiple knots at those locations hence it can yield exact solutions having interior discontinuous derivatives these advantages of nurbs are well known and have been used extensively in graphical approximation of geometrical surfaces however it is seldom used in other engineering applications to model the multiple open cracks in a beam quartic nurbs basis functions are employed and quadruplicate knots are assigned at the crack locations hence it is capable to model the abrupt changes of slope the first derivative of displacement across a crack in the present applications additional equivalent massless rotational springs are inserted at the crack locations to represent the local flexibility caused by the cracks as such the cracked beam can be treated in the usual manner as a continuous beam by adopting the meshless petrov galerkin formulation a generalized stiffness matrix for the cracked beam can be derived compared to the conventional finite element method the present method does not require a finite element mesh for the purposes of interpolation and numerical integration the advantages and effectiveness of the present method is illustrated in solving the eigenfrequencies of a beam having multiple open cracks of different depths

thermal generalized stress intensity factors in 2 d domains lately methods that are capable of predicting failure initiation and propagation in structural components subjected to thermal loads have been sought it is postulated as in the theory of linear elastic fracture mechanics that the methods should correlate experimental observed failures to parameters characterizing the thermoelastic stress field in the vicinity of failure initiation points failures due to thermal loading occur for example in integrated circuits which are assemblages of dissimilar materials with different thermal and mechanical properties addressed in chapter 9 the mismatch of elastic constants and thermal expansion coefficients causes stress intensification at corners of interfaces and may lead to mechanical failure

multidimensional directional filter banks and surfacelets in 1992 bamberger and smith proposed the directional filter bank dfb for an efficient directional decomposition of 2 d signals due to the nonseparable nature of the system extending the dfb to higher dimensions while still retaining its attractive features is a challenging and previously unsolved problem we propose a new family of filter banks named ndfb that can achieve the directional decomposition of arbitrary n dimensional nges2 signals with a simple and efficient tree structured construction in 3 d the ideal passbands of the proposed ndfb are rectangular based pyramids radiating out from the origin at different orientations and tiling the entire frequency space the proposed ndfb achieves perfect reconstruction via an iterated filter bank with a redundancy factor of n in n d the angular resolution of the proposed ndfb can be iteratively refined by invoking more levels of decomposition through a simple expansion rule by combining the ndfb with a new multiscale pyramid we propose the surfacelet transform which can be used to efficiently capture and represent surface like singularities in multidimensional data

stress distribution at sharp and rounded v notches in quasi orthotropic plane abstract the eigensolution of the quasi orthotropic wedge problem is presented the degenerate orthotropic material of the wedge is characterized by doubled roots of the characteristic equation using the method of singular integral equations the distribution of the stress field in the quasi orthotropic plane weakened by semi infinite rounded v notch was obtained the edge of the notch was free of load and the asymptotic stress field defined by a stress intensity factor was set at the infinity on this basis the relationship between stress intensity factor at the sharp notch vertex and the normal stress at the vertex of corresponding rounded v notch with the same opening angle was established as it was shown in the example this relationship is asymptotic for finite notched bodies and it can be used to calculate a notch stress intensity factor based on a stress concentration results obtained for a notch rounded with small radius of curvature

sparse geometric image representations with bandelets this paper introduces a new class of bases called bandelet bases which decompose the image along multiscale vectors that are elongated in the direction of a geometric flow this geometric flow indicates directions in which the image gray levels have regular variations the image decomposition in a bandelet basis is implemented with a fast subband filtering algorithm bandelet bases lead to optimal approximation rates for geometrically regular images for image compression and noise removal applications the geometric flow is optimized with fast algorithms so that the resulting bandelet basis produces minimum distortion comparisons are made with wavelet image compression and noise removal algorithms

the contourlet transform an efficient directional multiresolution image representation the limitations of commonly used separable extensions of one dimensional transforms such as the fourier and wavelet transforms in capturing the geometry of image edges are well known in this paper we pursue a true two dimensional transform that can capture the intrinsic geometrical structure that is key in visual information the main challenge in exploring geometry in images comes from the discrete nature of the data thus unlike other approaches such as curvelets that first develop a transform in the continuous domain and then discretize for sampled data our approach starts with a discrete domain construction and then studies its convergence to an expansion in the continuous domain specifically we construct a discrete domain multiresolution and multidirection expansion using nonseparable filter banks in much the same way that wavelets were derived from filter banks this construction results in a flexible multiresolution local and directional image expansion using contour segments and thus it is named the contourlet transform the discrete contourlet transform has a fast iterated filter bank algorithm that requires an order n operations for n pixel images furthermore we establish a precise link between the developed filter bank and the associated continuous domain contourlet expansion via a directional multiresolution analysis framework we show that with parabolic scaling and sufficient directional vanishing moments contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves finally we show some numerical experiments demonstrating the potential of contourlets in several image processing applications

a direct branching algorithm for checking equivalence of some classes of deterministic pushdown automata a new direct algorithm is presented for checking equivalence of some classes of deterministic pushdown automata dpda s after korenjak and hopcroft s branching algorithm it is not only powerful enough to be applicable to two dpda s accepting by empty stack one of which is real time but also simple even for dpda s in lower subclasses this is the first time the branching algorithm has been used to give such a general decision procedure without ever mixing the two languages in question in other words it deals with only the equivalence equation whose left hand side consists of a pure reachable configuration of one dpda and whose right hand side that of the other

directionlets anisotropic multidirectional representation with separable filtering in spite of the success of the standard wavelet transform wt in image processing in recent years the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions one dimensional 1 d discontinuities in images edges and contours that are very important elements in visual perception intersect too many wavelet basis functions and lead to a nonsparse representation to efficiently capture these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions a more complex multidirectional m dir and anisotropic transform is required we present a new lattice based perfect reconstruction and critically sampled anisotropic m dir wt the transform retains the separable filtering and subsampling and the simplicity of computations and filter design from the standard two dimensional wt unlike in the case of some other directional transform constructions e g curvelets contourlets or edgelets the corresponding anisotropic basis functions directionlets have directional vanishing moments along any two directions with rational slopes furthermore we show that this novel transform provides an efficient tool for nonlinear approximation of images achieving the approximation power o n sup 1 55 which while slower than the optimal rate o n sup 2 is much better than o n sup 1 achieved with wavelets but at similar complexity

non conforming finite element methods for transmission eigenvalue problem abstract the transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering theory in this paper for the helmholtz transmission eigenvalue problem we give a weak formulation which is a nonselfadjoint linear eigenvalue problem based on the weak formulation we first discuss the non conforming finite element approximation and prove the error estimates of the discrete eigenvalues obtained by the adini element the morley zienkiewicz element the modified zienkiewicz element et al and we report some numerical examples to validate the efficiency of our approach for solving transmission eigenvalue problem

mixed hp finite element method for linear elasticity with weakly imposed symmetry abstract the paper presents a generalization of arnold falk winther elements to meshes with elements of variable order the formulation is straightforward but the stability analysis involves a non trivial modification of interpolation operators the analysis addresses only h convergence but the presented numerical results indicate p convergence as well

a chebyshev rational chebyshev spectral method for the helmholtz equation in a sector on the surface of a sphere defeating corner singularities when the boundaries of a domain meet at an angle the solutions to an elliptic partial differential equation will usually be singular at the corner using the example of the helmholtz equation on the surface of a sphere in a domain bounded by meridians we show how corner singularities can be defeated by mapping the corner to infinity by applying a chebyshev series in longitude and a rational chebyshev series in the mercator coordinate y arctanh cos colatitude we obtain an exponential rate of convergence despite the corner singularities

regularity and numerical solution of eigenvalue problems with piecewise analytic data this paper discusses the regularity of the eigenfunctions of eigenvalue problems with piecewise analytic data and the approximation of the eigenvalues and eigenfunctions of such problems a detailed and systematic numerical study of these approximations is presented together with an analysis of the numerical results in light of the theoretical results the specific aim is to assess the reliability of the theoretical results which are of an asymptotic nature as a guide to practical computations which may take place in the pre asymptotic phase and to look for characteristic features of the numerical results that are not completely explained by known theoretical results

fast semi analytic computation of elastic edge singularities abstract the singularities that we consider are the characteristic non smooth solutions of the equations of linear elasticity in piecewise homogeneous media near two dimensional corners or three dimensional edges we describe here a method to compute their singularity exponents and the associated angular singular functions we present the implementation of this method in a program whose input data are geometrical data the elasticity coefficients of each material involved and the type of boundary conditions dirichlet neumann or mixed conditions our method is particularly useful with anisotropic materials and allows to follow the dependency of singularity exponents along a curved edge

a c0ipg method and its error estimates for the helmholtz transmission eigenvalue problem abstract the interior penalty methods using c 0 lagrange elements c 0 ipg developed in the last decade for the fourth order problems are an interesting topic in academia at present in this paper we apply the methods to the helmholtz transmission eigenvalue problem which is quadratic and non self adjoint and has important applications in the inverse scattering theory we propose a discrete scheme present a complete error analysis and first prove the c 0 ipg method can capture smooth eigenpairs efficiently using the argument in this paper we can prove that the c 0 ipg methods for the fourth order eigenvalue problems in the existing literature can also capture smooth eigenpairs efficiently numerical examples confirm our theoretical analysis

a direct branching algorithm for checking equivalence of strict deterministic vs ll k grammars abstract we present here an equivalence checking algorithm which operates directly on a pair of strict deterministic vs ll k grammars it is also straightforwardly applicable to a pair of ll k grammars though an ll k grammar is not necessarily strict deterministic the basic idea is from korenjak and hopcroft s branching algorithm for simple deterministic grammars but ours is so distinguished that it is throughout free from mixing the nonterminals of the respective grammars in question and then very simple

multigrid methods for the computation of singular solutions and stress intensity factors i corner singularities we consider the poisson equation u f with homogeneous dirichlet boundary condition on a two dimensional polygonal domain with cracks multigrid methods for the computation of singular solutions and stress intensity factors using piecewise linear functions are analyzed the convergence rate for the stress intensity factors is mathcal o h 3 2 in whenfel2 and mathcal o h 2 in whenfeh1 the convergence rate in the energy norm is mathcal o h 1 in in the first case and mathcal o h in the second case the costs of these multigrid methods are proportional to the number of elements in the triangulation the general case wherefehm is also discussed

the lifting factorization and construction of wavelet bi frames with arbitrary generators and scaling in this paper we present the lifting factorization and construction of wavelet bi frames with arbitrary generators and scaling we show that an arbitrary polyphase matrix of a wavelet bi frame can be factorized into a series of lifting steps based on the proposed factorization we present a general construction of bi frames especially we give an explicit formula to construct the bi frames of two scaling and two generators with symmetry and one vanishing moment this paper does not involve many theories of wavelet frames in mathematics but focuses on the algebraic issues related to laurent polynomials which are efficient expressions in redundant filter banks associated with wavelet frames as an extension of the classical two channel filter bank the redundant filter bank is more complicated but also more flexible furthermore we present an algorithm to increase the number of vanishing moments to arbitrary order by lifting which is iterated and is straightforward in implementation

image denoising using scale mixtures of gaussians in the wavelet domain we describe a method for removing noise from digital images based on a statistical model of the coefficients of an overcomplete multiscale oriented basis neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables a gaussian vector and a hidden positive scalar multiplier the latter modulates the local variance of the coefficients in the neighborhood and is thus able to account for the empirically observed correlation between the coefficient amplitudes under this model the bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable we demonstrate through simulations with images contaminated by additive white gaussian noise that the performance of this method substantially surpasses that of previously published methods both visually and in terms of mean squared error

computation of the stress intensity factors of sharp notched plates by the fractal like finite element method the fractal like finite element method ffem is an accurate and efficient method to compute the stress intensity factors sifs of different crack configurations in the ffem the cracked notched body is divided into singular and regular regions both regions are modelled using conventional finite elements a self similar fractal mesh of an infinite number of conventional finite elements is used to model the singular region the corresponding large number of local variables in the singular region around the crack tip is transformed to a small set of global co ordinates after performing a global transformation by using global interpolation functions in this paper we extend this method to analyse the singularity problems of sharp notched plates the exact stress and displacement fields of a plate with a notch of general angle are derived for plane stress strain conditions these exact analytical solutions which are eigenfunction expansion series are used to perform the global transformation and to determine the sifs the use of the global interpolation functions reduces the computational cost significantly and neither post processing technique to extract sifs nor special singular elements to model the singular region are needed the numerical examples demonstrate the accuracy and efficiency of the ffem for sharp notched problems copyright 2008 john wiley sons ltd

singular solutions of a transmission problem in plane linear elasticity for wedge shaped regions in plane elasticity when two different wedge shaped elastic materials isotropic homogeneous are bonded together along a common edge and subject to tractions on the boundary the stress field will become infinite at the apex in fact asymptotically the displacementu satisfies u approx sum limits j 1 n r i lambda j sum limits k 0 eta j 1 ln k r phi jk theta asr to 0 where r are the polar coordinates with origin at the wedge apex and the complex numbers j are the roots with positive imaginary part and multiplicity j of an explicitly given transcendental equation g 0 for applications it is desirable to understand how the number of terms that give rise to unbounded stresses in the above expansion depends on the elasticity constants and on the wedge angles setting n q sum limits 0 operatorname im lambda j q eta j the problem is then to studyn 1 as a function of the material constants and wedge angles a rigorous analysis is presented here for the case in which the wedge angles are equal symmetric domains using the fact thatg is an entire function of which depends continuously on the parameters of the problem we develop a continuity method which enables us to evaluate the functions n left frac pi a right and n left frac pi 2a right wherea is the measure of each wedge angle this yields bounds onn 1 as well as some information on the zeros ofg that correspond to higher order singularities

the lifting scheme for wavelet bi frames theory structure and algorithm in this paper we present the lifting scheme of wavelet bi frames along with theory analysis structure and algorithm we show how any wavelet bi frame can be decomposed into a finite sequence of simple filtering steps this decomposition corresponds to a factorization of a polyphase matrix of a wavelet bi frame based on this concept we present a new idea for constructing wavelet bi frames for the construction of symmetric bi frames we use generalized bernstein basis functions which enable us to design symmetric prediction and update filters the construction allows more efficient implementation and provides tools for custom design of wavelet bi frames by combining the different designed filters for the prediction and update steps we can devise practically unlimited forms of wavelet bi frames moreover we present an algorithm of increasing the number of vanishing moments of bi framelets to arbitrary order via the presented lifting scheme which adopts an iterative algorithm and ensures the shortest lifting scheme several construction examples are given to illustrate the results

solving laplacian problems with boundary singularities a comparison of a singular function boundary integral method with the p hp version of the finite element method we solve a laplacian problem over an l shaped domain using a singular function boundary integral method as well as the p hp finite element method in the former method the solution is approximated by the leading terms of the local asymptotic solution expansion and the unknown singular coefficients are calculated directly in the latter method these coefficients are computed by post processing the finite element solution the predictions of the two methods are discussed and compared with recent numerical results in the literature

analysis of bonded and fastened repairs by the p version of the finite element method abstract the development of efficient and reliable methods for the design and analysis of fastened structural connections and bonded joints is among the most important and most challenging problems in aerospace applications because these connections are common sites of failure initiation and there is a complicated nonlinear interaction between the fasteners and the connected plates realistic representations of fastened connections must account for the diameter of fastener holes the stiffness of the fasteners the effects of interference fitting or looseness of fit contact between the fasteners and the connected plates and yielding of the plates similarly the treatment of bonded joints is complicated by the fact that bonded patches are typically composed of several thin layers of orthotropic material and the adhesive material may yield under load requiring a nonlinear analysis consequently the complexity of the models is such that it is difficult and time consuming to treat them using conventional finite element or boundary element procedures fortunately these problems lend themselves to standardization in fea based handbook libraries structural connections can be described in a parametric form therefore topologically similar families of connections need to be meshed only once the fea based handbook library provides for the archival and recall of entries for analysis users need only enter the parameters the finite element mesh being associative is adjusted automatically therefore users need not be concerned with meshing or other details of the analysis process the finite element solution and the computation of all data of interest are performed automatically and the results are displayed in tabular and graphical forms automatic quality control tests are performed and reported for purposes of documentation there are provisions for the computation of margins of safety the advanced fea based handbook library produces results of sufficient reliability to permit certification of repairs and joints based on computed information this will be demonstrated by examples

the dpg methodology applied to different variational formulations of linear elasticity abstract the flexibility of the dpg methodology is exposed by solving the linear elasticity equations under different variational formulations including some with non symmetric functional settings different infinite dimensional trial and test spaces the family of formulations presented is proved to be mutually ill or well posed when using traditional energy spaces on the whole domain moreover they are shown to remain well posed when using broken energy spaces and interface variables four variational formulations are solved in 3d using the dpg methodology numerical evidence is given for both smooth and singular solutions and the expected convergence rates are observed

unsupervised texture segmentation using gabor filters abstract this paper presents a texture segmentation algorithm inspired by the multi channel filtering theory for visual information processing in the early stages of human visual system the channels are characterized by a bank of gabor filters that nearly uniformly covers the spatial frequency domain and a systematic filter selection scheme is proposed which is based on reconstruction of the input image from the filtered images texture features are obtained by subjecting each selected filtered image to a nonlinear transformation and computing a measure of energy in a window around each pixel a square error clustering algorithm is then used to integrate the feature images and produce a segmentation a simple procedure to incorporate spatial information in the clustering process is proposed a relative index is used to estimate the true number of texture categories

asymptotic description of the logarithmic singular stress field and its application abstract in a joint of two dissimilar materials under mechanical or thermal loading the stresses at the intersection of the edges and the interface are very high or singular for elastic materials behaviour for most joint geometries and material combinations there is a type of r singularity however for some joint geometries and material combinations there is a type of ln r singularity in this paper the type of ln r stress singularity for a two dissimilar materials joint under thermal loading is treated by the mellin transform method emphasis is placed on the asymptotical description of the stress distribution near the singular point the angular functions used to describe the stresses are given in a general form which are different to those of the same joint under edge tractions for a quarter planes joint angular functions are given in an explicit form finally examples are presented to show when the asymptotical solution for the type of ln r stress singularity can be used to describe stresses near the singular point in the practical relevant joints for a finite joint the unknown factor k used to describe the stress is given as well

adaptive directional lifting based wavelet transform for image coding we present a novel 2 d wavelet transform scheme of adaptive directional lifting adl in image coding instead of alternately applying horizontal and vertical lifting as in present practice adl performs lifting based prediction in local windows in the direction of high pixel correlation hence it adapts far better to the image orientation features in local windows the adl transform is achieved by existing 1 d wavelets and is seamlessly integrated into the global wavelet transform the predicting and updating signals of adl can be derived even at the fractional pixel precision level to achieve high directional resolution while still maintaining perfect reconstruction to enhance the adl performance a rate distortion optimized directional segmentation scheme is also proposed to form and code a hierarchical image partition adapting to local features experimental results show that the proposed adl based image coding technique outperforms jpeg 2000 in both psnr and visual quality with the improvement up to 2 0 db on images with rich orientation features

propagation of cracks in elastic media throughout this paper the normal n denotes the interior normal direction i e n f x1 1 p 1 jf x1 j when x approaches from above denoted by and n f x1 1 p 1 jf x1 j from below denoted by in a recent paper 2 the present authors studied the asymptotic behavior of any solution of 1 2 1 4 in a neighborhood of the tip x t taking for simplicity t 0 and assuming that

a fast semi analytic method for the computation of elastic edge singularities the singularities that we consider are the characteristic non smooth solutions of the equations of linear elasticity in piecewise homogeneous media near two dimensional corners or three dimensional edges we describe here a method to compute their singularity exponents and the associated angular singular functions we present the implementation of this method in a program whose input data are geometrical data the elasticity coefficients of each material involved and the type of boundary conditions dirichlet neumann or mixed conditions our method is particularly useful with anisotropic materials and allows to follow the dependency of singularity exponents along a curved edge

a locking free hp dpg method for linear elasticity with symmetric stresses we present two new methods for linear elasticity that simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree p this is achieved within the recently developed discontinuous petrov galerkin dpg framework in this framework both the stress and the displacement approximations are discontinuous across element interfaces we study locking free convergence properties and the interrelationships between the two dpg methods

numerical analysis of singularities in two dimensions part 2 computation of generalized flux stress intensity factors summary a numerical method for the computation of the generalized flux stress intensity factors gfifs gsifs for the asymptotic solution of linear second order elliptic partial differential equations in two dimensions in the vicinity of singular points is described special attention is given to heat transfer and elasticity problems the singularities may be caused by re entrant corners and abrupt changes in material properties such singularities are of great interest from the point of view of failure initiation the eigenpairs computed in a companion paper characterize the straining modes and their amplitudes the gfifs gsifs quantify the amount of energy residing in particular straining modes for this reason failure theories directly or indirectly involve the gfifs gsifs this paper addresses a general method based on the complementary weak formulation for determining the gfifs gsifs numerically as a post solution operation on the finite element solution vector importantly the method is applicable to anisotropic materials multi material interfaces and cases where the singularities are characterized by complex eigenpairs an error analysis is sketched and numerical examples are presented to illustrate the effectiveness of the technique

the idude framework for grayscale image denoising we present an extension of the discrete universal denoiser dude specialized for the denoising of grayscale images the original dude is a low complexity algorithm aimed at recovering discrete sequences corrupted by discrete memoryless noise of known statistical characteristics it is universal in the sense of asymptotically achieving without access to any information on the statistics of the clean sequence the same performance as the best denoiser that does have access to such information the dude however is not effective on grayscale images of practical size the difficulty lies in the fact that one of the dude s key components is the determination of conditional empirical probability distributions of image samples given the sample values in their neighborhood when the alphabet is relatively large as is the case with grayscale images even for a small sized neighborhood the required distributions would be estimated from a large collection of sparse statistics resulting in poor estimates that would not enable effective denoising the present work enhances the basic dude scheme by incorporating statistical modeling tools that have proven successful in addressing similar issues in lossless image compression instantiations of the enhanced framework which is referred to as idude are described for examples of additive and nonadditive noise the resulting denoisers significantly surpass the state of the art in the case of salt and pepper s p and ary symmetric noise and perform well for gaussian noise

stress singularities in a dissimilar materials joint with edge tractions under mechanical and thermal loadings in a two dissimilar materials joint the stresses at the intersection of the edges and the interface are singular for elastic material behaviour for a joint with edge tractions the stresses near the singular point are the sum of singular terms and regular terms earlier investigations have shown that the singular stress exponents are the same for a joint with free edge and edges with tractions in the literatures only the singular term has been studied the emphasis in this paper is placed on giving an explicit form of the regular stress terms as a function of the edge tractions the material properties and the geometry of the joint it is shown that the regular terms are important also for the stress distribution near the singular point

lossless image compression based on optimal prediction adaptive lifting and conditional arithmetic coding the optimal predictors of a lifting scheme in the general n dimensional case are obtained and applied for the lossless compression of still images using first quincunx sampling and then simple row column sampling in each case the efficiency of the linear predictors is enhanced nonlinearly directional postprocessing is used in the quincunx case and adaptive length postprocessing in the row column case both methods are seen to perform well the resulting nonlinear interpolation schemes achieve extremely efficient image decorrelation we further investigate context modeling and adaptive arithmetic coding of wavelet coefficients in a lossless compression framework special attention is given to the modeling contexts and the adaptation of the arithmetic coder to the actual data experimental evaluation shows that the best of the resulting coders produces better results than other known algorithms for multiresolution based lossless image coding

oriented wavelet transform for image compression and denoising in this paper we introduce a new transform for image processing based on wavelets and the lifting paradigm the lifting steps of a unidimensional wavelet are applied along a local orientation defined on a quincunx sampling grid to maximize energy compaction the orientation minimizing the prediction error is chosen adaptively a fine grained multiscale analysis is provided by iterating the decomposition on the low frequency band in the context of image compression the multiresolution orientation map is coded using a quad tree the rate allocation between the orientation map and wavelet coefficients is jointly optimized in a rate distortion sense for image denoising a markov model is used to extract the orientations from the noisy image as long as the map is sufficiently homogeneous interesting properties of the original wavelet are preserved such as regularity and orthogonality perfect reconstruction is ensured by the reversibility of the lifting scheme the mutual information between the wavelet coefficients is studied and compared to the one observed with a separable wavelet transform the rate distortion performance of this new transform is evaluated for image coding using state of the art subband coders its performance in a denoising application is also assessed against the performance obtained with other transforms or denoising methods

multiscale computations with a combination of the h and p versions of the finite element method the numerical treatment of structural problems is often difficult if the global system behavior is affected by phenomena on different length scales when simulating multiscale problems it is essential to find a discretization that equally reflects all aspects of the problem with sufficient accuracy the present paper is concerned with the formulation of a finite element procedure which combines the p method to resolve global features of a problem with an h method to resolve local features thus the advantageous properties of both standard procedures can be optimally exploited the implementation provides the further advantage that the numerical treatment of the problems on the different length scales can be done with independent finite element discretizations to solve the overall problem an iteration scheme with an adaptive solution strategy is developed benchmark problems and an example with relevance to soil mechanics are presented

finite element stress extraction by the complementary energy principle this paper presents a new method for accurate pointwise stress extraction from finite element solutions applied to two dimensional linear elastostatic problem shaving bounded value stresses the method denoted by sec stress extraction by complementary principle is based on the complementary energy principle applied overalocal domain in thepost processing phase detailed formulation of the sec method is provided and numerical experiments with the h and p versions of the finite element method are presented for a family of exact solutions characterized by varying degree of smoothness it is shown that on the boundaries of the domain as well as in the interior accurate pointwise stresses are obtained and the relative error in the pointwise stresses converges with a rate which is as fast as the relative error measured in energy norm or faster importantly the sec method in conjunction with the p version of the finite element method is virtually independent of the poisson s ratio and is equally applicable to nearly in compressible materials 1997 by john wiley sons ltd

extracting edge flux intensity functions for the laplacian the solution to the laplace operator in three dimensional domains in the vicinity of straight edges is presented as an asymptotic expansion involving eigenpairs with their coefficients called edge flux intensity functions efifs the eigenpairs are identical to their two dimensional counterparts over a plane perpendicular to the edge extraction of efifs however cannot be obtained in a straightforward manner over this two dimensional plane a method based on l 2 projection and richardson extrapolation is presented for point wise extraction of efifs from p finite element solutions and illustrated by examples a similar but more efficient method based on energy projection for extracting efifs is proposed

singularities in 2d anisotropic potential problems in multi material corners real variable approach an analysis of singular solutions at corners consisting of several different homogeneous wedges is presented for anisotropic potential theory in plane the concept of transfer matrix is applied for a singularity analysis first of single wedge problems and then of multi material corner problems explicit forms of eigenequations for evaluation of singularity exponent in the case of multi material corners are derived both for all combinations of homogeneous neumann and dirichlet boundary conditions at faces of open corners and for multi material planes with singular interior points perfect transmission conditions at wedge interfaces are considered in both cases it is proved that singularity exponents are real for open anisotropic multi material corners and a sufficient condition for the singularity exponents to be real for anisotropic multi material planes is deduced a case of a complex singularity exponent for an anisotropic multi material plane is reported apparently for the first time in potential theory simple expressions of eigenequations are presented first for open bi material corners and bi material planes and second for a crack terminating at a bi material interface as examples of application of the theory developed here analytical solutions of these eigenequations are presented for interface cracks with any combination of homogeneous boundary conditions along the interface crack faces and also for a special case of a crack perpendicular to a bi material interface a numerical study of variation of the singularity exponent as a function of inclination of a crack terminating at a bi material interface is presented

the estimation of laplace random vectors in additive white gaussian noise this paper develops and compares the maximum a posteriori map and minimum mean square error mmse estimators for spherically contoured multivariate laplace random vectors in additive white gaussian noise the mmse estimator is expressed in closed form using the generalized incomplete gamma function we also find a computationally efficient yet accurate approximation for the mmse estimator in addition this paper develops an expression for the mse for any estimator of spherically contoured multivariate laplace random vectors in additive white gaussian noise awgn the development of which again depends on the generalized incomplete gamma function the estimators are motivated and tested on the problem of wavelet based image denoising

numerical analysis of singularities in two dimensions part 1 computation of eigenpairs a numerical method is described for the computation of eigenpairs which characterize the exact solution of linear second order elliptic partial differential equations in two dimensions in the vicinity of singular points the singularities may be caused by re entrant corners and abrupt changes in boundary conditions or material properties such singularities are of great interest from the point of view of failure initiation the eigenpairs characterize the straining modes and their amplitudes quantify the amount of energy residing in particular straining modes for this reason failure theories directly or indirectly involve the eigenpairs and their amplitudes this paper addresses the problem of determining the eigenpairs numerically on the basis of the steklov formulation numerical results are presented for several cases importantly the method is applicable to three dimensional cases

fracture analysis of v notched components effects of first non singular stress term the effect of the first non singular stress term on the fracture behavior of notched structures was investigated under symmetric geometry and loading conditions according to the williams series expansion for a large domain of notch angles the non singular stress terms of sharp notches are functions of complex eigenvalues and their corresponding complex coefficients hence a new representation of stress field near the notch tip was developed in which the higher order terms are expressed as several explicit functions of real and imaginary parts of both the complex eigenvalues and their complex coefficients a critical stress criterion was then applied to the new stress formulations to assess the influence of the first non singular stress term on the apparent fracture toughness several finite element analyses were also performed on two laboratory specimens in order to show the effects of first non singular term on the near field stress distribution of notched specimens the results demonstrated that neglecting the first non singular stress term could lead to significant errors in predicting the apparent fracture toughness of notched components

layer potentials for elastostatics and hydrostatics in curvilinear polygonal domains the symbolic calculus of pseudodifferential operators of mellin type is applied to study layer potentials on a plane domain q whose boundary 9q is a curvilinear polygon a singularity type is a zero of the determinant of the matrix of symbols of the mellin operators and can be used to calculate the bad values of p for which the system is not fredholm on lp 9q using the method of layer potentials we study the singularity types of the system of elastostatics lu uau au vdivu 0 in a plane domain q whose boundary 9k2 is a curvilinear polygon here u 0 and u a oo when a oo the system is the stokes system of hydrostatics for the traction double layer potential we show that all singularity types in the strip 0 re z i lie in the interval 1 1 so that the system of integral equations is a fredholm operator of index 0 on lp aq for all p 2 p oo the explicit dependence of the singularity types on a and the interior angles 0 of aq is calculated the singularity type of each corner is independent of a if the corner is nonconvex introduction recently there has been considerable interest in using layer potentials to solve lp boundary value problems for elliptic operators and systems on a lipschitz domain q in r for the systems of elastostatics dkv and hydrostatics fkv dahlberg fabes kenig and verchota have used rellich type identities to prove that the double layer potential integral equations yield a fredholm operator of index 0 on l 2 q for p 2 only limited information is available on the boundary integral equations for general lipschitz domains in rn the general problem of the notion of symbol on the boundary of a general lipschitz domain is still very much open in this paper we treat a very special case a curvilinear polygonal domain in r in this 2 dimensional case a precise symbolic calculus of pseudodifferential operators of mellin type is available we show that certain double layer boundary integral equations yield operators which for all p 2 p 00 are received by the editors december 14 1988 1980 mathematics subject classification 1985 revision primary 35j25 45e05 research partially supported by the italian cnr 1990 american mathematical society 0002 9947 90 1 00 25 per page

the finite ridgelet transform for image representation the ridgelet transform was introduced as a sparse expansion for functions on continuous spaces that are smooth away from discontinuities along lines we propose an orthonormal version of the ridgelet transform for discrete and finite size images our construction uses the finite radon transform frat as a building block to overcome the periodization effect of a finite transform we introduce a novel ordering of the frat coefficients we also analyze the frat as a frame operator and derive the exact frame bounds the resulting finite ridgelet transform frit is invertible nonredundant and computed via fast algorithms furthermore this construction leads to a family of directional and orthonormal bases for images numerical results show that the frit is more effective than the wavelet transform in approximating and denoising images with straight edges

adaptive sequential prediction of multidimensional signals with applications to lossless image coding we investigate the problem of designing adaptive sequential linear predictors for the class of piecewise autoregressive multidimensional signals and adopt an approach of minimum description length mdl to determine the order of the predictor and the support on which the predictor operates the design objective is to strike a balance between the bias and variance of the prediction errors in the mdl criterion the predictor design problem is particularly interesting and challenging for multidimensional signals e g images and videos because of the increased degree of freedom in choosing the predictor support our main result is a new technique of sequentializing a multidimensional signal into a sequence of nested contexts of increasing order to facilitate the mdl search for the order and the support shape of the predictor and the sequentialization is made adaptive on a sample by sample basis the proposed mdl based adaptive predictor is applied to lossless image coding and its performance is empirically established to be the best among all the results that have been published till present

the nonsubsampled contourlet transform theory design and applications in this paper we develop the nonsubsampled contourlet transform nsct and study its applications the construction proposed in this paper is based on a nonsubsampled pyramid structure and nonsubsampled directional filter banks the result is a flexible multiscale multidirection and shift invariant image decomposition that can be efficiently implemented via the a trous algorithm at the core of the proposed scheme is the nonseparable two channel nonsubsampled filter bank nsfb we exploit the less stringent design condition of the nsfb to design filters that lead to a nsct with better frequency selectivity and regularity when compared to the contourlet transform we propose a design framework based on the mapping approach that allows for a fast implementation based on a lifting or ladder structure and only uses one dimensional filtering in some cases in addition our design ensures that the corresponding frame elements are regular symmetric and the frame is close to a tight one we assess the performance of the nsct in image denoising and enhancement applications in both applications the nsct compares favorably to other existing methods in the literature

multiresolution direction filterbanks theory design and applications this paper presents new developments of directional filterbanks dfbs the motivation for the paper is the existence of multiresolution and multidirection orthogonal transform for two dimensional 2 d discrete signals based on the frequency supports of the ideal transform a new uniformly maximally decimated dfb with six highpass directional subbands and two lowpass subands is introduced the uniform dfb udfb can be implemented by a binary tree structure of two channel filterbanks the filterbank employed in the tree is shown to be alias free decimation and permissible the udfb is then extended to a nonuniform case nudfb which is still maximally decimated by combining the two lowpass subbands the nudfb yields nonuniform frequency division which composes of one lowpass filter with a decimation factor of one fourth and six highpass directional filters with a decimation factor of one eighth the new dfbs offer alternative image decompositions which overcome the limited directional selectivity of the separable wavelets and the limited multiresolution of the conventional dfb the lowpass subband of the nudfb can be used to obtain a multiresolution representation by simply reiterating the same nudfb decomposition on the other hand the directional subbands can also be further refined by simply applying a two channel conventional dfb at each highpass component a simple design method yielding near orthogonal uniform and nonuniform multidimensional filterbanks is presented finally the performances of the newly proposed nudfb are compared with other conventional transforms in nonlinear approximation image denoising and texture classification to demonstrate its potential

directional filtering transform for image intra frame compression while directional adaption is introduced into traditional transforms different orders of two 1 d transforms will result in different results of one 2 d transform based upon an anisotropic image model this paper analyzes the effect of transform orders in terms of theoretical coding gain our results reveal that the transform orders have little effect on the coding gain with full decomposition good directional modes and good interpolation however in practical compression schemes since high pass bands are not decomposed fully because of the consideration on complexity different transform orders have different coding performances which can be solved by an adaptive transform order motivated by our analyzed results a directional filtering transform dft in order to distinguish from the common usage on dft is proposed in this paper to better exploit correlations among samples in h 264 intraframe coding it provides an evenly distributed set of prediction modes with an adaptive transform order both interblock and intrablock correlations are exploited in this scheme experimental results in h 264 intraframe coding demonstrate its superiority both objectively and subjectively

the equivalence problem for real time dpdas the equivalence problem for deterministic real time pushdown automata is shown to be decidable this result is obtained by showing that valiant s parallel stacking technique using a replacement function introduced in this paper succeeds for deterministic real time pushdown automata equivalence is also decidable for two deterministic pushdown automata one of which is real time

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

wavelet based statistical signal processing using hidden markov models wavelet based statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly gaussian these models are unrealistic for many real world signals we develop a new framework for statistical signal processing based on wavelet domain hidden markov models hmms that concisely models the statistical dependencies and non gaussian statistics encountered in real world signals wavelet domain hmms are designed with the intrinsic properties of the wavelet transform in mind and provide powerful yet tractable probabilistic signal models efficient expectation maximization algorithms are developed for fitting the hmms to observational signal data the new framework is suitable for a wide range of applications including signal estimation detection classification prediction and even synthesis to demonstrate the utility of wavelet domain hmms we develop novel algorithms for signal denoising classification and detection

direction adaptive discrete wavelet transform for image compression we propose a direction adaptive dwt da dwt that locally adapts the filtering directions to image content based on directional lifting with the adaptive transform energy compaction is improved for sharp image features a mathematical analysis based on an anisotropic statistical image model is presented to quantify the theoretical gain achieved by adapting the filtering directions the analysis indicates that the proposed da dwt is more effective than other lifting based approaches experimental results report a gain of up to 2 5 db in psnr over the conventional dwt for typical test images subjectively the reconstruction from the da dwt better represents the structure in the image and is visually more pleasing

efficient boundary element analysis of sharp notched plates the present paper further develops the boundary element singularity subtraction technique to provide an efficient and accurate method of analysing the general mixed mode deformation of two dimensional linear elastic structures containing sharp notches the elastic field around sharp notches is singular because of the convergence difficulties that arise in numerical modelling of elastostatic problems with singular fields these singularities are subtracted out of the original elastic field using the first term of the williams series expansion this regularization procedure introduces the stress intensity factors as additional unknowns in the problem hence extra conditions are required to obtain a solution extra conditions are defined such that the local solution in the neighbourhood of the notch tip is identical to the williams solution the procedure can take into account any number of terms of the series expansion the standard boundary element method is modified to handle additional unknowns and extra boundary conditions analysis of plates with symmetry boundary conditions is shown to be straightforward with the modified boundary element method in the case of non symmetrical plates the singular tip tractions are not primary boundary element unknowns the boundary element method must be further modified to introduce the boundary integral stress equations of an internal point approaching the notch tip as primary unknowns in the formulation the accuracy and efficiency of the method is demonstrated with some benchmark tests of mixed mode problems new results are presented for the mixed mode analysis of a non symmetrical configuration of a single edge notched plate

adaptive wavelet thresholding for image denoising and compression the first part of this paper proposes an adaptive data driven threshold for image denoising via wavelet soft thresholding the threshold is derived in a bayesian framework and the prior used on the wavelet coefficients is the generalized gaussian distribution ggd widely used in image processing applications the proposed threshold is simple and closed form and it is adaptive to each subband because it depends on data driven estimates of the parameters experimental results show that the proposed method called bayesshrink is typically within 5 of the mse of the best soft thresholding benchmark with the image assumed known it also outperforms sureshrink donoho and johnstone 1994 1995 donoho 1995 most of the time the second part of the paper attempts to further validate claims that lossy compression can be used for denoising the bayesshrink threshold can aid in the parameter selection of a coder designed with the intention of denoising and thus achieving simultaneous denoising and compression specifically the zero zone in the quantization step of compression is analogous to the threshold value in the thresholding function the remaining coder design parameters are chosen based on a criterion derived from rissanen s minimum description length mdl principle experiments show that this compression method does indeed remove noise significantly especially for large noise power however it introduces quantization noise and should be used only if bitrate were an additional concern to denoising

a 2 d orientation adaptive prediction filter in lifting structures for image coding lifting style implementations of wavelets are widely used in image coders a two dimensional 2 d edge adaptive lifting structure which is similar to daubechies 5 3 wavelet is presented the 2 d prediction filter predicts the value of the next polyphase component according to an edge orientation estimator of the image consequently the prediction domain is allowed to rotate spl plusmn 45 spl deg in regions with diagonal gradient the gradient estimator is computationally inexpensive with additional costs of only six subtractions per lifting instruction and no multiplications are required

the post processing approach in the finite element method part 2 the calculation of stress intensity factors abstract in the context of a model problem the authors describe post processing techniques for the calculation of generalized stress intensity factors they discuss two broad classes of methods one involving an influence function and the other related to the well known energy release principle of fracture mechanics an error analysis is sketched and two numerical examples are given to illustrate the effectivity of the techniques this is the second in a series of three papers author

translation invariant directional framelet transform combined with gabor filters for image denoising this paper is devoted to the study of a directional lifting transform for wavelet frames a nonsubsampled lifting structure is developed to maintain the translation invariance as it is an important property in image denoising then the directionality of the lifting based tight frame is explicitly discussed followed by a specific translation invariant directional framelet transform tidft the tidft has two framelets 1 2 with vanishing moments of order two and one respectively which are able to detect singularities in a given direction set it provides an efficient and sparse representation for images containing rich textures along with properties of fast implementation and perfect reconstruction in addition an adaptive block wise orientation estimation method based on gabor filters is presented instead of the conventional minimization of residuals furthermore the tidft is utilized to exploit the capability of image denoising incorporating the map estimator for multivariate exponential distribution consequently the tidft is able to eliminate the noise effectively while preserving the textures simultaneously experimental results show that the tidft outperforms some other frame based denoising methods such as contourlet and shearlet and is competitive to the state of the art denoising approaches

the discrete shearlet transform a new directional transform and compactly supported shearlet frames it is now widely acknowledged that analyzing the intrinsic geometrical features of the underlying image is essential in many applications including image processing in order to achieve this several directional image representation schemes have been proposed in this paper we develop the discrete shearlet transform dst which provides efficient multiscale directional representation and show that the implementation of the transform is built in the discrete framework based on a multiresolution analysis mra we assess the performance of the dst in image denoising and approximation applications in image approximations our approximation scheme using the dst outperforms the discrete wavelet transform dwt while the computational cost of our scheme is comparable to the dwt also in image denoising the dst compares favorably with other existing transforms in the literature

a domain independent integral for computation of stress intensity factors along three dimensional crack fronts and edges by bem the present work deals with an evaluation of stress intensity factors sifs along straight crack fronts and edges in three dimensional isotropic elastic solids a new numerical approach is developed for extraction from a solution obtained by the boundary element method bem of those sifs which are relevant for a failure assessment of mechanical components in particular the generalized sifs associated to eigensolutions characterized by unbounded stresses at a neighbourhood of the crack front or a reentrant edge and also that associated to t stress at the crack front can be extracted the method introduced is based on a conservation integral called h integral which leads to a new domain independent integral represented by a scalar product of the sif times some element shape function defined along the crack front or edge for sufficiently small element lengths these weighted averages of sifs give reasonable pointwise estimation of the sifs a proof of the domain integral independency based on the bi orthogonality of the classical two dimensional eigensolutions associated to a corner problem is presented numerical solutions of two three dimensional problems a crack problem and a reentrant edge problem are presented the accuracy and convergence of the new approach for sif extraction being analysed

numerical methods for extracting edge stress intensity functions in anisotropic three dimensional domains the solution to elasticity problems in three dimensional 3 d polyhedral domains in the vicinity of an edge is represented by a family of eigen functions similar to 2 d domains complemented by shadow functions and their associated edge stress intensity functions esifs which are functions along the edge these are of major engineering importance because failure theories directly or indirectly involve them in isotropic materials one may compute analytically the eigen functions and their shadows z yosibash n omer m costabel m dauge edge stress intensity functions in polyhedral domains and their extraction by a quasi dual function method int j fract 136 2005 37 73 used in conjunction with the quasi dual function method m costabel m dauge z yosibash a quasi dual function method for extracting edge stress intensity functions siam j math anal 35 5 2004 1177 1202 for extracting esifs from finite element solutions however in anisotropic materials and multi material interfaces the analytical derivation becomes intractable and numerical methods are mandatory herein we use p finite element methods p fem for the computation of the eigen pairs and shadow functions together with their duals having computed these the p fem is used again to obtain a fe solution from which we extract approximations of the esifs based on a family of adaptive hierarchical jacobi polynomials of increasing order numerical examples for 3 d isotropic and anisotropic materials are provided for which the eigen pairs and shadow functions are numerically computed and esifs extracted these examples show the efficiency and high accuracy of the numerical approximations 2007 elsevier b v all rights reserved

local sparse structure denoising for low light level image sparse and redundant representations perform well in image denoising however sparsity based methods fail to denoise low light level lll images because of heavy and complex noise they consider sparsity on image patches independently and tend to lose the texture structures to suppress noises and maintain textures simultaneously it is necessary to embed noise invariant features into the sparse decomposition process we therefore used a local structure preserving sparse coding lspsc formulation to explore the local sparse structures both the sparsity and local structure in image it was found that with the introduction of spatial local structure constraint into the general sparse coding algorithm lspsc could improve the robustness of sparse representation for patches in serious noise we further used a kernel lspsc k lspsc formulation which extends lspsc into the kernel space to weaken the influence of linear structure constraint in nonlinear data based on the robust lspsc and k lspsc algorithms we constructed a local sparse structure denoising lssd model for lll images which was demonstrated to give high performance in the natural lll images denoising indicating that both the lspsc and k lspsc based lssd models have the stable property of noise inhibition and texture details preservation

on the determination of higher order terms of singular elastic stress fields near corners in two dimensional elasticity stresses at reentrant corners exhibit singular behavior the stress field is of the form sigma sigma rm k iota r lambda 2 1 f i theta lambda i where r are polar coordinates centered at the tip of the corner andf i i are smooth functions for practical use of this series the eigenvalues i which are generally complex numbers are required in order of ascending real part the problem then is to find the roots of a transcendental equation eigenequation in the complex plane and arranged in order of ascending real part a theorem is proved on the number location and nature of the roots of this equation with the real part in fixed intervals of length excellent initial estimates of the real part of the complex roots become available and so are bounds within which single real roots exist this enables the determination of any number of roots in ascending order of real part the critical angles at which the eigenvalues change nature are also determined it is shown that for certain cases and for the symmetric mode of deformation the eigenvalue 1 does not represent a rigid body rotation therefore it has to be included in the series representation of the stresses the coefficientsk i can be determined by recently developed extraction techniques thus allowing complete determination of the elastic field and enabling its correlation with experimental data on brittle fracture crack initiation plastic zone estimation etc

h p spectral element methods for three dimensional elliptic problems on non smooth domains this paper is devoted to the study of non conforming h p spectral element methods for three dimensional elliptic problems on non smooth domains using parallel computers to overcome the singularities which arise in the neighbourhoods of vertices edges and vertex edges we use local systems of coordinates together with geometric meshes which become finer near corners and edges we provide estimates for the error and the computational complexity of our method and present results of numerical simulations that have been performed to validate the theoretical estimates obtained in 22

a finite element approach for computing edge singularities in piezoelectric materials by using the eigenfunction expansion technique and the weak form of the governing equations for prismatic sectorial domains composed of piezoelectrics and air an one dimensional finite element procedure is formulated for computing the eigensolutions of the electromechanical field problem generalized displacement and electric potential are taken to be the nodal variables the resulting global equation is a second order characteristic matrix equation validity of the formulation is verified by comparing the computed results with the existing solutions for impermeable cracks and interfacial cracks configurations which are of practical interest including conducting cracks permeable and impermeable notches are studied

a numerical procedure for the determination of certain quantities related to the stress intensity factors in two dimensional elasticity abstract this work is devoted to the investigation of corner and interface singularities in linear elasticity and to the development of a numerical code that computes certain quantities associated with those singularities we compute several terms of the asymptotic expansion of the solution of the elasticity system near the corner or interface which is of the form knr nfn in particular the n and fn we treat our problem as a non linear eigenvalue problem and we use an approach based on the shooting method for boundary value problems to create an analytic function whose zeros are the n above the zeros of this function are then found using an iteration method and a global method to make sure that no zero was overlooked the program works for the general case of anisotropic non homogeneous wedge with general boundary conditions as well as in the case of crossing interfaces in an internal point we test the convergence accuracy robustness efficiency and reliability of the code from those tests it can be seen that the code works quite well for the majority of the applications

translation invariant contourlet transform and its application to image denoising most subsampled filter banks lack the feature of translation invariance which is an important characteristic in denoising applications in this paper we study and develop new methods to convert a general multichannel multidimensional filter bank to a corresponding translation invariant ti framework in particular we propose a generalized algorithme agrave trous which is an extension of the algorithme agrave trous introduced for 1 d wavelet transforms using the proposed algorithm as well as incorporating modified versions of directional filter banks we construct the ti contourlet transform tict to reduce the high redundancy and complexity of the tict we also introduce semi translation invariant contourlet transform stict then we employ an adapted bivariate shrinkage scheme to the stict to achieve an efficient image denoising approach our experimental results demonstrate the benefits and potential of the proposed denoising approach complexity analysis and efficient realization of the proposed ti schemes are also presented

weighted adaptive lifting based wavelet transform for image coding in this paper a new weighted adaptive lifting wal based wavelet transform is presented the proposed wal approach is designed to solve the problems existing in the previous adaptive directional lifting adl approach such as mismatch between the predict and update steps interpolation favoring only horizontal or vertical direction and invariant interpolation filter coefficients for all images the main contribution of the proposed approach consists of two parts one is the improved weighted lifting which maintains the consistency between the predict and update steps as far as possible and preserves the perfect reconstruction at the same time another is the directional adaptive interpolation which improves the orientation property of the interpolated image and adapts to statistical property of each image experimental results show that the proposed wal based wavelet transform for image coding outperforms the conventional lifting based wavelet transform up to 3 06 db in psnr and significant improvement in subjective quality is also observed compared with the adl based wavelet transform up to 1 22 db improvement in psnr is reported

superconvergent extraction of flux intensity factors and first derivatives from finite element solutions a superconvergent method for the computation of the derivatives of the solution and the coefficients of the asymptotic expansion at singular points is presented for the laplace problem in two dimensions the algorithm utilizes the complementary weak form on a localized small domain mathematical analysis demonstrates the superconvergent behavior and numerical experiments support our analysis this method is well suited for anisotropic multi material singular interface problems

crack tip interpolation revisited it is well known that the near tip displacement eld on a crack surface can be represented in a power series in the variable p r where r is the distance to the tip it is shown herein that the coecients of the linear terms on the two sides of the crack are equal equivalently the linear term in the crack opening displacement vanishes the proof is a completely general argument valid for an arbitrary e g multiple nonplanar crack conguration and applied boundary conditions moreover the argument holds for other equations such as laplace a limit procedure for calculating the surface stress in the form of a hypersingular boundary integral equation is employed to enforce the boundary conditions along the crack faces evaluation of the nite surface stress and examination of potentially singular terms lead to the result inclusion of this constraint in numerical calculations should result in a more accurate approximation of the displacement and stress elds in the tip region and thus a more accurate evaluation of stress intensity factors