denseness of the generalized eigenvectors of an h s discrete operator let t be a closed densely defined linear operator in a hilbert space h and assume there exists 0 p t such that r 0 t is a hilbert schmidt operator the operator t is a special type of discrete operator a so called h s discrete operator which is shown to be a fredholm operator in h with fredholm set equal to the whole complex plane let t i i 1 where the operator t i has ascent mi let pi i 1 2 be the projection of h onto the generalized eigenspace n t i mi along r t i mi and let s and m be the subspaces of h consisting of all x h such that x i 1 pix and such that pix 0 for i 1 2 respectively sufficient conditions are introduced which guarantee that s h and m 0 these conditions require that r t be bounded on certain rays in the complex plane and r t 0 as on at least one of the rays but specific decay rates for r t are not necessary

monotone methods for a finite difference system of reaction diffusion equation with time delay abstract the aim of this paper is to present some monotone iterative schemes for computing the solution of a system of nonlinear difference equations which arise from a class of nonlinear reaction diffusion equations with time delays the iterative schemes lead to computational algorithms as well as existence uniqueness and upper and lower bounds of the solution an application to a diffusive logistic equation with time delay is given

initial value methods for discrete boundary value problems motivated by the work of angel and kalaba s and golberg 8 on twopoint boundary value problems for difference equations in this paper we shall study several initial value methods for multipoint boundary value problems for linear and nonlinear difference systems we generalize method of adjoints goodman and lance 9 method of complementary functions tifford 17 d an method of particular solutions miele 111 proposed for two point continuous problems to linear multipoint problems for difference equations next we show that method of adjoint and method of complementary functions can be used in an iterative way to solve nonlinear problems to justify the results obtained here several examples are also given the methods discussed here are similar to our earlier work l 3 on continuous problems we will take up the initial adjusting method of ojika kasue and welsh 12 15 18 for the discrete case later throughout the paper we shall assume the existence uniqueness and stability properties of solutions of the problems discussed and refer to 4 for some of these questions

monotone enclosure for a class of discrete boundary value problems without monotone nonlinearities abstract a new concept of a pair of upper and lower solutions is introduced for a class of discrete boundary value problems without monotone nonlinearities some comparison results are established an existence and enclosing theorem for the solutions is given in terms of upper and lower solutions a new monotone iterative scheme is proposed the numerical example is given

global description of edge patterns using moments abstract shape recognition has traditionally been accomplished using well bounded segmented regions or their closed contours in this way the internal edge details of the objects are ignored there are cases such as in character recognition and in object recognition when patterns are not closed contours in this paper such patterns are defined as edge patterns and edge standard moments esm are developed which are invariant to location scale and rotation results of patterns matching with character recognition and polyhedral object recognition are presented

homogenization and bloch wave method for fluid tube bundle interaction the aim of this paper is to investigate the problem of the vibrations of large arrays of elastic rods immersed in a perfect incompressible fluid the case of an infinite spatially periodic bundle is firstly considered leading to use the bloch wave method in order to describe the resonance spectrum of the coupled system when the bundle is contained in a bounded domain the homogenization technique combined with the bloch wave method allows to obtain the eigenspectrum which is formed of two eigenfrequencies of infinite multiplicity and of a continuous spectrum

boundary value problems for general discrete systems on infinite intervals this paper continues the study of boundary value problems for a discrete system which in particular includes the prototype equation x k 1 f k x k equations with finite as well as infinite delays equations of neutral type and the discrete integral equations of volterra type while the finite discrete interval case regular as well as at resonance has been discussed in 1 2 in the present paper the infinite interval case will be addressed

classification of partially occluded objects using 3 point matching and distance transformation abstract recognition of partially occluded objects has been recently made possible by describing an object boundary with a sequence of local feature segments localized with control or dominant points and then matching the representations with those of a set of known reference shapes when part of the object boundary is being occluded contiguous intact feature segments will be used for identifying the object and distorted elements will be rejected in the matching process the main problem associated with this method is that the nature of occlusion may separate the object contour into discrete regions resulting in the degeneration of an individual representation into small isolated clusters reflecting only weak evidence on the object identity in this paper a new scheme capable of combining the isolated clusters for object classification is presented in essence curvature guided polygonal approximation is employed for detecting the dominant points of the boundaries a 3 point matching technique is developed for extracting cluster s of dominant points on an unknown boundary which matched against reference objects and to link up the scattered clusters to form a complete representation the chamfer 3 4 distance transform together with a quantitative measurement on the boundary covered by the matched dominant points is employed for calculating the similarity between the unknown and the reference contours the scheme has been successfully applied for recognizing multiple overlapped handtools in different sizes and orientations

robust hausdorff distance matching algorithms using pyramidal structures abstract this paper proposes two hausdorff distance hd matching algorithms in which robust hd measures are implemented in pyramidal structures by computer simulations the matching performance of the conventional hd measures and the proposed robust hd matching algorithms using pyramidal structures is compared with real images which are degraded by noise and occlusions

curvilinear immersed boundary method for simulating fluid structure interaction with complex 3d rigid bodies the sharp interface curvib approach of ge and sotiropoulos l ge f sotiropoulos a numerical method for solving the 3d unsteady incompressible navier stokes equations in curvilinear domains with complex immersed boundaries journal of computational physics 225 2007 1782 1809 is extended to simulate fluid structure interaction fsi problems involving complex 3d rigid bodies undergoing large structural displacements the fsi solver adopts the partitioned fsi solution approach and both loose and strong coupling strategies are implemented the interfaces between immersed bodies and the fluid are discretized with a lagrangian grid and tracked with an explicit front tracking approach an efficient ray tracing algorithm is developed to quickly identify the relationship between the background grid and the moving bodies numerical experiments are carried out for two fsi problems vortex induced vibration of elastically mounted cylinders and flow through a bileaflet mechanical heart valve at physiologic conditions for both cases the computed results are in excellent agreement with benchmark simulations and experimental measurements the numerical experiments suggest that both the properties of the structure mass geometry and the local flow conditions can play an important role in determining the stability of the fsi algorithm under certain conditions the fsi algorithm is unconditionally unstable even when strong coupling fsi is employed for such cases however combining the strong coupling iteration with under relaxation in conjunction with the aitken s acceleration technique is shown to effectively resolve the stability problems a theoretical analysis is presented to explain the findings of the numerical experiments it is shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the fsi algorithm the stabilizing role of under relaxation is also clarified and the upper bound of the under relaxation coefficient required for stability is derived

symmetric phase only matched filtering of fourier mellin transforms for image registration and recognition presents a new method to match a 2d image to a translated rotated and scaled reference image the approach consists of two steps the calculation of a fourier mellin invariant fmi descriptor for each image to be matched and the matching of the fmi descriptors the fmi descriptor is translation invariant and represents rotation and scaling as translations in parameter space the matching of the fmi descriptors is achieved using symmetric phase only matched filtering spomf the performance of the fmi spomf algorithm is the same or similar to that of phase only matched filtering when dealing with image translations the significant advantage of the new technique is its capability to match rotated and scaled images accurately and efficiently the innovation is the application of spomf to the fmi descriptors which guarantees high discriminating power and excellent robustness in the presence of noise this paper describes the principle of the new method and its discrete implementation for either image detection problems or image registration problems practical results are presented for various applications in medical imaging remote sensing fingerprint recognition and multiobject identification

piecewise approximation of contours through scale space selection of dominant points this paper describes a method of approximating a shape contour with a polygon the polygon vertices are extracted from the curvature extremes through a scale space description of the contour via linear diffusion these vertices are located on the contour points where the sharper changes of the contour directions occur using a proper strategy a set of extremes that result in a given approximation level is chosen by adding new vertices the approximation level can be improved and a scalable representation of the contour is identified this method results in an approximation that discriminates local from global geometric features and provides a good visual representation of the original contour this polygonal approximation method is used for scalable encoding of the shape contours in this regard an encoding technique suitable for scalable polygonal approximation has been developed we show that encoding the approximated polygons result in a good relation between the distortion and the bitrate finally we show that in addition to coding this method can be efficiently used for shape comparison and shape retrieval

some recent developments of numerov s method abstract this paper is a survey of some recent developments of numerov s method for solving nonlinear two point boundary value problems the survey consists of three different parts the existence uniqueness of a solution computational algorithm for computing a solution and some extensions of numerov s method the sufficient conditions for the existence and uniqueness of a solution are presented some of them are best possible various iterative methods are reviewed including picard s iterative method modified newton s iterative method monotone iterative method and accelerated monotone iterative method in particular two more direct monotone iterative methods are presented to save computational work each of these iterative methods not only gives a computational algorithm for computing a solution but also leads to an existence and uniqueness theorem the estimate on the rate of convergence of the iterative sequence is given the extensions of numerov s method to a coupled problem and a general problem are addressed the numerical results are presented to validate the theoretical analysis

a stable fluid structure interaction solver for low density rigid bodies using the immersed boundary projection method dispersion of low density rigid particles with complex geometries is ubiquitous in both natural and industrial environments we show that while explicit methods for coupling the incompressible navier stokes equations and newton s equations of motion are often sufficient to solve for the motion of cylindrical particles with low density ratios for more complex particles such as a body with a protrusion they become unstable we present an implicit formulation of the coupling between rigid body dynamics and fluid dynamics within the framework of the immersed boundary projection method similarly to previous work on this method the resulting matrix equation in the present approach is solved using a block lu decomposition each step of the block lu decomposition is modified to incorporate the rigid body dynamics we show that our method achieves second order accuracy in space and first order in time third order for practical settings only with a small additional computational cost to the original method our implicit coupling yields stable solution for density ratios as low as 10 4 we also consider the influence of fictitious fluid located inside the rigid bodies on the accuracy and stability of our method

a scale space filtering approach for visual feature extraction this paper presents a new integrated approach for detecting visual features which include corners ends arcs and lines the effect of scale space filtering on visual features is studied in detail as it forms the theoretical basis of our work in this approach the outline of the object is first extracted and it is then smoothed by scale space filtering at different scale levels subsequently the local extreme curvature points extracted from the smoothed curve and end candidates are determined to guide the termination of the filtering process information about the curvature of each point at the largest scale level is used to detect the different kinds of visual features several algorithms are proposed to determine corners ends arcs and lines experimental results show that our approach is robust to translation rotation and scaling of the object as well as noise corruption in addition efficient visual features can also be successfully extracted with this approach

finding contour based abstractions of planar patterns abstract an algorithm is described to detect a number of points on the contour of a planar shape which constitute the vertices of a schematic polygonal representation of the shape itself a set of points initially extracted from the chain coded representation of the contour is iteratively examined while removing some points and inserting new ones the number of selected points decreases in size from iteration to iteration and the selection process converges towards an expected perceptually significant set of points the polygon obtained by linking successive points approximates the contour in an intuitive way it is not constrained within a given tolerance and is likely to locally change from a coarse to a more faithful approximating shape in correspondence with contour regions increasing in details

monotone methods for a boundary value problem of second order discrete equation abstract the comparison and existence results of the upper and lower solutions are established for a boundary value problem of second order discrete equation a monotone iterative scheme is proposed the local as well as global existence and uniqueness of the solution are obtained the global convergence of the iteration is investigated the convergence rate of the iteration is analyzed and compared some examples are given

wavelet based approach to character skeleton character skeleton plays a significant role in character recognition the strokes of a character may consist of two regions i e singular and regular regions the intersections and junctions of the strokes belong to singular region while the straight and smooth parts of the strokes are categorized to regular region therefore a skeletonization method requires two different processes to treat the skeletons in theses two different regions all traditional skeletonization algorithms are based on the symmetry analysis technique the major problems of these methods are as follows 1 the computation of the primary skeleton in the regular region is indirect so that its implementation is sophisticated and costly 2 the extracted skeleton cannot be exactly located on the central line of the stroke 3 the captured skeleton in the singular region may be distorted by artifacts and branches to overcome these problems a novel scheme of extracting the skeleton of character based on wavelet transform is presented in this paper this scheme consists of two main steps namely a extraction of primary skeleton in the regular region and b amendment processing of the primary skeletons and connection of them in the singular region a direct technique is used in the first step where a new wavelet based symmetry analysis is developed for finding the central line of the stroke directly a novel method called smooth interpolation is designed in the second step where a smooth operation is applied to the primary skeleton and thereafter the interpolation compensation technique is proposed to link the primary skeleton so that the skeleton in the singular region can be produced experiments are conducted and positive results are achieved which show that the proposed skeletonization scheme is applicable to not only binary image but also gray level image and the skeleton is robust against noise and affine transform

asymptotic behavior of solutions for a lotka volterra mutualism reaction diffusion system with time delays this paper is to investigate the asymptotic behavior of solutions for a time delayed lotka volterra n species mutualism reaction diffusion system with homogeneous neumann boundary condition it is shown under a simple condition on the reaction rates that the system has a unique bounded time dependent solution and a unique constant positive steady state solution and for any nontrivial nonnegative initial function the corresponding time dependent solution converges to the constant positive steady state solution as time tends to infinity this convergence result implies that the trivial steady state solution and all forms of semitrivial steady state solutions are unstable and moreover the system has no nonconstant positive steady state solution a condition ensuring the convergence of the time dependent solution to one of nonnegative semitrivial steady state solutions is also given

hybrid symbiotic genetic optimisation for robust edge based stereo correspondence this work proposes a novel algorithm for performing robust feature based stereo matching without the ordering constraint the calculation of the disparity map is decomposed to a set of disjoint intra row subproblems each one having two objectives the search for a high confidence intra row matching and the enforcement of figural continuity at the inter row level a separate genetic algorithm ga is allocated at each epipolar to search the feasible solution space all gas evolve parallely in a symbiotic fashion and continuously exchange currently available solution information to enable optimisation of figural continuity to accelerate the search we adapt a deterministic solver to seed the gas and design problem specific genetic operators for greater efficiency

an hp finite element adaptive scheme to solve the laplace model for fluid solid vibrations abstract in this paper we introduce an hp finite element method to solve a two dimensional fluid structure spectral problem this problem arises from the computation of the vibration modes of a bundle of parallel tubes immersed in an incompressible fluid we prove the convergence of the method and a priori error estimates for the eigenfunctions and the eigenvalues we define an a posteriori error estimator of the residual type which can be computed locally from the approximate eigenpair we show its reliability and efficiency by proving that the estimator is equivalent to the energy norm of the error up to higher order terms the equivalence constant of the efficiency estimate being suboptimal in that it depends on the polynomial degree we present an hp adaptive algorithm and several numerical tests which show the performance of the scheme including some numerical evidence of exponential convergence

bloch wave homogenization for a spectral problem in fluid solid structures this paper is concerned with the study of the vibrations of a coupled fluid solid periodic structure as the period goes to zero an asymptotic analysis of the spectrum i e the set of eigenfrequencies is performed with the help of a new method the so called bloch wave homogenization method which is a blend of two scale convergence and bloch wave decomposition the limit spectrum is made of three parts the macroscopic or homogenized spectrum the microscopic or bloch spectrum and the boundary layer spectrum the two first parts are completely characterized the homogenized and the bloch spectra are purely essential and have a band structure the boundary layer spectrum is shown to be empty in the special case of periodic boundary condition

boundary based corner detection using neural networks abstract in this paper we present a novel boundary based corner detection approach using artificial neural networks anns two neural networks are proposed one for detecting corner points with high curvature and the other for detecting tangent points and inflection points that generally have low curvature for a given boundary point p i the first ann uses the normalized coordinates of points on the forward arm neighboring points succeeding p i or on the backward arm neighboring points preceding p i of the point p i as the input vector the output feature of the network is the angle of the forward arm or backward arm with respect to the x axis the boundary point with sufficiently small angle between the forward and backward arms is identified as a corner since the feature points of tangency and inflection have relatively low curvature the signs of curvature rather than the magnitude of curvature for points in the neighborhood of p i are used as the input vector to the second ann the curvature sign at each boundary point is derived from the outputs of the first ann the outputs of the second ann only respond to the sign patterns of tangent points and inflection points by using both anns all features of corners tangent points and inflection points can be extracted from the boundary of any arbitrary shape experimental results have shown that the proposed anns have good detection and localization for objects in random orientations and with moderate scale changes

accelerated monotone iterative methods for a boundary value problem of second order discrete equations abstract an accelerated monotone iterative method for a boundary value problem of second order discrete equations is presented this method leads to an existence comparison theorem as well as a computational algorithm for the solutions the monotone property of the iterations gives improved upper and lower bounds of the solution in each iteration and the rate of convergence of the iterations is either quadratic or nearly quadratic depending on the property of the nonlinear function some numerical results are presented to illustrate the monotone convergence of the iterative sequences and the rate of convergence of the iterations

matching invariant to translations rotations and scale changes abstract an optimization approach to invariant matching is proposed in this approach an object or a pattern is invariantly represented by an object centred description called an attributed relational structure ars embedding invariant properties and relations between the primitives of the pattern such as line segments and points noise effect is taken into account such that a scene can consist of noisy sub parts of a model the matching is then to find the optimal mapping between the arss of the scene and the model a gain functional is formulated to measure the goodness of fit and is to be maximized by using the relaxation labelling method experiments are shown to illustrate the matching algorithm and to demonstrate that the approach is truly invariant to arbitrary translations rotations and scale changes under noise

assessment of classical numerical models for the separate fluid structure modal analysis in the numerical analysis of the eigen behavior of huge liquid storage tanks treatment of large scale matrices becomes a burden owing to the hydrodynamic interaction between two different media structure and liquid in order to overcome such a problem it is classical to split the dynamic system into two separate problem regions the structure and the liquid by utilizing the mass adding technique in general the eigenbehavior of interior liquid is characterized by the sloshing mode while that of the structure by the bulging mode and furthermore the two modes exhibit a weak coupling based upon this weak coupling the structure deformation to the sloshing mode and the liquid free surface fluctuation to the bulging mode have been neglected in the classical added mass computation this paper is concerned with the refinement and the assessment of classical interaction modelling by including both neglected effects in order to estimate the accurate mass added to the structure we refine the classical procedure by reflecting the liquid free surface fluctuation on the other hand we qualitatively and quantitatively analyze the additional effect by the structure deformation onto the classical rigid tank sloshing model through the numerical experiments carried out with a representative cylindrical liquid storage tank we illustrate our theoretical results

invariant representation matching and pose estimation of 3d space curves under similarity transformations this paper presents a system for matching and pose estimation of 3d space curves under the similarity transformation composed of rotation translation and uniform scaling the system makes use of constraints not only on the feature points but also on curve segments a representation called the similarity invariant coordinate system sics is presented for deriving semi local invariants of 3d curves the sics also enables an efficient exploration of constraints on the shape of the entire curve model based curve matching is performed in the principle of maximum a posteriori map probability in which markov random fields mrfs are used to model the prior probability results are given to demonstrate the matching with missing and extra feature points the extensive exploration of the curve shape constraints in both the matching and the pose estimation stages are shown to significantly improve the quality of the recognition and pose estimation

a convergence study of a new partitioned fluid structure interaction algorithm based on fictitious mass and damping we develop analyze and validate a new method for simulating fluid structure interactions fsis which is based on fictitious mass and fictitious damping in the structure equation we employ a partitioned method for the fluid and structure motions in conjunction with sub iteration and aitken relaxation in particular the use of such fictitious parameters requires sub iterations in order to reduce the induced error in addition to the local temporal truncation error to this end proper levels of tolerance for terminating the sub iteration procedure have been obtained in order to recover the formal order of temporal accuracy for the coupled fsi problem these fictitious terms have a significant effect leading to better convergence rate and hence substantially smaller number of sub iterations through analysis we identify the proper range of these parameters which we then verify by corresponding numerical tests we implement the method in the context of spectral element discretization which is more sensitive than low order methods to numerical instabilities arising in the explicit fsi coupling however the method we present here is simple and general and hence applicable to fsi based on any other discretization we demonstrate the effectiveness of the method in applications involving 2d vortex induced vibrations viv and in 3d flexible arteries with structural density close to blood density we also present 3d results for a patient specific aneurysmal flow under pulsatile flow conditions examining in particular the sensitivity of the results on different values of the fictitious parameters

an efficient interface capturing method for a large collection of interacting bodies immersed in a fluid an efficient method to capture an arbitrary number of fluid structure interfaces in a level set framework is built following ideas introduced for contour capturing in image analysis using only three label maps and two distance functions we succeed in locating and evolving the bodies independently in the whole domain and get the distance between the closest bodies in order to apply a collision force whatever the number of cells is the method is applied to rigid solid bodies in order to compare to the results available in the literature in that case a global penalization model uses the label maps to follow the solid bodies all together without a separate computation of each body velocity numerical simulations are performed in two and three dimensions an application to immersed vesicles is also proposed and shows the capability and efficiency of the method to handle numerical contacts between elastic bodies at low resolution two dimensional simulations of vesicles under various flow conditions are presented

classification of temporal sequences via prediction using the simple recurrent neural network abstract an approach to classify temporal sequences using the simple recurrent neural network srnn is developed in this paper a classification problem is formulated as a component prediction problem and two training methods are described to train a single srnn to predict the components of temporal sequences belonging to multiple classes issues related to the selection of the dimension of the context vector and the influence of the context vector on classification are identified and investigated the use of a different initial context vector for each class is proposed as a means to improve classification and a classification rule which incorporates the different initial context vectors is formulated a systematic method in which the srnn is trained with noisy exemplars is developed to enhance the classification performance of the network a 4 class localized object classification problem is selected to demonstrate that a a single srnn can be trained to classify real multi class sequences via component prediction b the classification accuracy can be improved by using a distinguishing initial context vector for each class and c the classification accuracy of the srnn can be improved significantly by using the distinguishing initial context vector in conjunction with the systematic re training method it is concluded that through the approach developed in this paper the srnn can robustly classify temporal sequences which may have an unequal number of components

occluded objects recognition using multiscale features and hopfield neural network abstract a new method to recognize partially visible two dimensional objects by means of multiscale features and hopfield neural network was proposed the hopfield network was employed to perform global feature matching since the network only guarantees to converge to a local optimal state the matching results heavily depend on the initial network state determined by the extracted features to acquire more satisfactory initial matching results a new feature vector was developed which consists of the multiscale evolution of the extremal position and magnitude of the wavelet transformed contour orientation these features can even be used to discriminate dominant points hence good initial states can be obtained the good initiation enables our proposed method to recognize objects even heavily occluded that cannot be achieved by using the nasrabadi li s method in addition to make the matching results more insensitive to the threshold value selection of the network we replace the step like thresholding function by a ramp like one experimental results have shown that our method is effective even for noisy occluded objects

multiscale corner detection by using wavelet transform a multiscale corner detection algorithm based on the wavelet transform of contour orientation is proposed it can utilize both the information of the local extrema and modulus of transform results to detect corners and arcs effectively the ramp width of contour orientation profile which can be computed using the transformed modulus of two scales reveals the difference between corner and arc and is utilized in the determination of corner points the experimental results have shown that the detector is more effective than both the single and multiple scale detectors they also demonstrate that the detector is insensitive to boundary noise in addition the proposed method is more efficient than the other multiscale corner detector because it operates on fewer number of scales which can be implemented by a fast transform algorithm

matching of partially occluded planar curves abstract an algorithm for curves partial matching up to a similarity transformation is presented the matching is based on the total curvature graph which is the direction of the first derivative of the curve no higher derivatives are required the algorithm uses dynamic programming it is not dependent on reference or feature points the base step consists of a comparison of the total curvatures of neighborhoods the neighborhoods are dynamically chosen according to local characteristics of the curve in the recursive step ratios of lengths of matched curve segments are compared in order to extend the matches the matching is not sensitive to local deviations of the curves the algorithm is fast and simple its worst case time complexity is o mn where m and n are the number of points in the two digital curves experimental results are presented

on discrete boundary value problems arising in transport phenomena for the discrete boundary value problems arising in transport processes we provide comparison results these results are used to develop monotone iterative methods for the construction of the maximal and minimal solutions in a sector the advantage of this technique is that the successive approximations are the solutions of the initial and terminal value problems numerical illustration showing the sharpness as well the importance of the obtained results is also included

stability of a class of delay difference equations on montre que les proprietes de stabilite a la fois locales et globales de la solution d equilibre positive du systeme a retard n i 1 s i n i t 1 s i g i n t h i peuvent se deduire de celles du systeme sans retard associe n i t 1 g i n t

a modified accelerated monotone iterative method for finite difference reaction diffusion convection equations this paper is concerned with monotone algorithms for the finite difference solutions of a class of nonlinear reaction diffusion convection equations with nonlinear boundary conditions a modified accelerated monotone iterative method is presented to solve the finite difference systems for both the time dependent problem and its corresponding steady state problem this method leads to a simple and yet efficient linear iterative algorithm it yields two sequences of iterations that converge monotonically from above and below respectively to a unique solution of the system the monotone property of the iterations gives concurrently improving upper and lower bounds for the solution it is shown that the rate of convergence for the sum of the two sequences is quadratic under an additional requirement quadratic convergence is attained for one of these two sequences in contrast with the existing accelerated monotone iterative methods our new method avoids computing local maxima in the construction of these sequences an application using a model problem gives numerical results that illustrate the effectiveness of the proposed method

successive linear newton interpolation methods for solving the large scale nonlinear eigenvalue problems abstract we present the successive linear newton interpolation method for solving the large scale nonlinear eigenvalue problems establish locally linear convergence and give the corresponding convergence factor of the method in terms of the left and right eigenvectors in this paper to speed up the convergence rate we develop the modified successive linear newton interpolation method which updates the pole simultaneously in addition we propose the inexact versions of the modified successive linear newton interpolation method to reduce the computational cost and analyze the convergence properties numerical results demonstrate the effectiveness of our proposed methods

curve fitting approach for tangent angle and curvature measurements abstract the measures of tangent angle and curvature of a digital curve play an important role in image analysis such as corner detection 1d shape representation and shape signature in the generalized hough transform instead of using the discrete measurement approach the least squares method is employed to fit known digital points to two cubic polynomial functions one with y f x that minimizes the sum of the vertical distances and the other with x g y that minimizes the sum of the horizontal distances from the known points to the approximated curve the tangent angle and curvature are therefore directly computable from the first and second order derivatives of the continuous functions hybrid procedures are also proposed to select the better curve from f and g for accurate evaluation of tangent angle and curvature experimented results on both analytic curves and real world images are included

finite difference solutions of reaction diffusion equations with continuous time delays abstract this paper is an extension of the monotone iterative methods for finite difference equations with discrete time delays to a class of nonlinear finite difference system with continuous time delays the system under consideration is a finite difference approximation of a class of reaction diffusion equations with continuous time delays in the nonlinear reaction under either dirichlet or neumann robin boundary conditions various monotone iterative schemes which depend on the property of the nonlinear reaction mechanism are developed for the computation of numerical solutions it is shown by the method of upper and lower solutions that the two sequences obtained from each iterative scheme converge monotonically from above and below respectively to a unique solution of the finite difference system applications are given to two model problems known as the diffusive logistic equation and the fisher s diffusion equation in population genetics

classification of partial 2 d shapes using fourier descriptors we present a method for the classification of 2 d partial shapes using fourier descriptors we formulate the problem as one of estimating the fourier descriptors of the unknown complete shape from the observations derived from an arbitrarily rotated and scaled shape with missing segments the method used for obtaining the estimates of the fourier descriptors minimizes a sum of two terms the first term of which is a least square fit to the given data subject to the condition that the number of missing boundary points is not known and the second term is the perimeter2 area of the unknown shape experiments with synthetic and real boundaries show that estimates closer to the true values of fourier descriptors of complete boundaries are obtained also classification experiments performed using real boundaries indicate that reasonable classification accuracies are obtained even when 20 30 percent of the data is missing

monotone iterative methods for a general class of discrete boundary value problems abstract in this paper we shall offer comparison results as well as monotone iterative schemes for the construction of solutions to a very general class of discrete boundary value problems the discrete system we consider includes in particular the n th order prototype systems finite as well as infinite discrete delay equations and discrete integral equations further the boundary conditions we consider include the initial terminal periodic and transport type problems numerical examples illustrating the usefulness of the proposed schemes to a variety of boundary value problems are also included

a stable partitioned fsi algorithm for rigid bodies and incompressible flow part i model problem analysis a stable partitioned algorithm is developed for fluid structure interaction fsi problems involving viscous incompressible flow and rigid bodies this added mass partitioned amp algorithm remains stable without sub iterations for light and even zero mass rigid bodies when added mass and viscous added damping effects are large the scheme is based on a generalized robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body added mass effects are handled in the robin condition by inclusion of a boundary integral term that depends on the pressure added damping effects due to the viscous shear forces on the body are treated by inclusion of added damping tensors that are derived through a linearization of the integrals defining the force and torque added damping effects may be important at low reynolds number or for example in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small in this first part of a two part series the properties of the amp scheme are motivated and evaluated through the development and analysis of some model problems the analysis shows when and why the traditional partitioned scheme becomes unstable due to either added mass or added damping effects the analysis also identifies the proper form of the added damping which depends on the discrete time step and the grid spacing normal to the rigid body the results of the analysis are confirmed with numerical simulations that also demonstrate a second order accurate implementation of the amp scheme

parallel monotone iterative relaxation methods for a class of two dimensional discrete boundary value problems abstract a parallel monotone iterative relaxation method for a class of two dimensional discrete boundary value problems is established and the sequence of iterations is shown to converge monotonically either from above or below to a solution of the problem this monotone convergence results yields a parallel computational algorithm as well as an existence comparison result for the solutions to compute the sequence of iterations the thomas algorithm can be used in the same fashion as for one dimensional problem the existence and comparison results of the upper and lower solutions are given the local as well as global existence uniqueness of the solution are obtained the global convergence of the iterations is investigated and the influence of the parameters on the rate of convergence of the iterations is analyzed numerical results are given to corroborate the analytical results

integral invariants for shape matching for shapes represented as closed planar contours we introduce a class of functionals which are invariant with respect to the euclidean group and which are obtained by performing integral operations while such integral invariants enjoy some of the desirable properties of their differential counterparts such as locality of computation which allows matching under occlusions and uniqueness of representation asymptotically they do not exhibit the noise sensitivity associated with differential quantities and therefore do not require presmoothing of the input shape our formulation allows the analysis of shapes at multiple scales based on integral invariants we define a notion of distance between shapes the proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other its computation results in optimal point correspondence as an intermediate step numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts missing parts and noise as a quantitative analysis we report matching scores for shape retrieval from a database

exact wave based bloch analysis procedure for investigating wave propagation in two dimensional periodic lattices abstract this paper presents an exact wave based approach for determining bloch waves in two dimensional periodic lattices this is in contrast to existing methods which employ approximate approaches e g finite difference ritz finite element or plane wave expansion methods to compute bloch waves in general two dimensional lattices the analysis combines the recently introduced wave based vibration analysis technique with specialized bloch boundary conditions developed herein timoshenko beams with axial extension are used in modeling the lattice members the bloch boundary conditions incorporate a propagation constant capturing bloch wave propagation in a single direction but applied to all wave directions propagating in the lattice members this results in a unique and properly posed bloch analysis results are generated for the simple problem of a periodic bi material beam and then for the more complex examples of square diamond and hexagonal honeycomb lattices the bi material beam clearly introduces the concepts but also allows the bloch wave mode to be explored using insight from the technique the square diamond and hexagonal honeycomb lattices illustrate application of the developed technique to two dimensional periodic lattices and allow comparison to a finite element approach differences are noted in the predicted dispersion curves and therefore band gaps which are attributed to the exact procedure more faithfully modeling the finite nature of lattice connection points the exact method also differs from approximate methods in that the same number of solution degrees of freedom is needed to resolve low frequency and arbitrarily high frequency dispersion branches these advantageous features may make the method attractive to researchers studying dispersion characteristics band gap behavior and energy propagation in two dimensional periodic lattices

segmentation of vessel like patterns using mathematical morphology and curvature evaluation this paper presents an algorithm based on mathematical morphology and curvature evaluation for the detection of vessel like patterns in a noisy environment such patterns are very common in medical images vessel detection is interesting for the computation of parameters related to blood flow its tree like geometry makes it a usable feature for registration between images that can be of a different nature in order to define vessel like patterns segmentation is performed with respect to a precise model we define a vessel as a bright pattern piece wise connected and locally linear mathematical morphology is very well adapted to this description however other patterns fit such a morphological description in order to differentiate vessels from analogous background patterns a cross curvature evaluation is performed they are separated out as they have a specific gaussian like profile whose curvature varies smoothly along the vessel the detection algorithm that derives directly from this modeling is based on four steps 1 noise reduction 2 linear pattern with gaussian like profile improvement 3 cross curvature evaluation 4 linear filtering we present its theoretical background and illustrate it on real images of various natures then evaluate its robustness and its accuracy with respect to noise

reliable polygonal approximations of imaged real objects through dominant point detection abstract the problem of dominant point detection is posed taking into account what usually happens in practice the algorithms found in the literature often prove their performance with laboratory contours but the shapes in real images present noise quantization and high inter and intra shape variability these effects are analyzed and solutions to them are proposed we will also focus on the conditions for an efficient few points and precise low error dominant point extraction that preserves the original shape a measurement of the committed error optimization error e 0 that takes into account both aspects is defined for studying this feature

added mass and damping in fluid structure interaction abstract this paper is concerned with the added mass matrix for a mechanical structure vibrating in an incompressible liquid it is shown in particular that this matrix does not depend on viscosity and from this fact can be calculated as if the fluid is perfect the viscous effect on the mechanical system can then be represented by a damping term of type time convolution the presence of a flowing fluid around the structure leads to additional damping terms proportional to the fluid density

flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes curve matching is one instance of the fundamental correspondence problem our flexible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations a syntactic representation is constructed for both curves and an edit transformation which maps one curve to the other is found using dynamic programming we present extensive experiments where we apply the algorithm to silhouette matching in these experiments we examine partial occlusion viewpoint variation articulation and class matching where silhouettes of similar objects are matched based on the qualitative syntactic matching we define a dissimilarity measure and we compute it for every pair of images in a database of 121 images we use this experiment to objectively evaluate our algorithm first we compare our results to those reported by others second we use the dissimilarity values in order to organize the image database into shape categories the veridical hierarchical organization stands as evidence to the quality of our matching and similarity estimation

partial shape classification using contour matching in distance transformation an algorithm is presented to recognize and locate partially distorted 2d shapes without regard to their orientation location and size the algorithm first calculates the curvature function from the digitized image of an object the points of local maxima and minima extracted from the smooth curvature are used as control points to segment the boundary and to guide the boundary matching procedure the boundary matching procedure considers two shapes at a time one shape from the template databank and the other from the object being classified the procedure tries to match the control points in the unknown shape to those of a shape from the template databank and estimates the translation rotation and scaling factors to be used to normalize the boundary of the unknown shape the chamfer 3 4 distance transformation and a partial distance measurement scheme constitute the final step in measuring the similarity between the two shapes the unknown shape is assigned to the class corresponding to the minimum distance the algorithm has been successfully tested on partial shapes using two sets of data one with sharp corners and the other with curve segments this algorithm not only is computationally simple but also works reasonably well in the presence of a moderate amount of noise

non parametric planar shape representation based on adaptive curvature functions this paper presents a non parametric method to extract a very short feature vector from the curvature function of a planar shape curvature is adaptively calculated using a new procedure that removes noise from the contour without missing relevant points then its fourier transform is projected onto a set of vectors which have been chosen to be as representative as possible to obtain the similarity between the input object and each vector of the set these similarity values are the elements of the feature vector the proposed method is very fast and classification has proven that the representation is good

stability of a general class of difference systems abstract in this paper we shall investigate several notions of stability of a general ordinary difference system using the prolific second method of lyapunov

the detection of dominant points on digital curves by scale space filtering the detection of dominant points is an important preprocessing step for shape recognition an effective method of scale space filtering with a gaussian kernel is introduced to detect dominant points on digital curves the conventional polygonal approximation algorithms are time consuming and need input parameter tuning for gaussian smoothing the noise and quantization error also they are sensitive to scaling and rotation of the object curve the above dit culty can be overcome by finding out the dominant points at each scale by scale space filtering by tracing back the dominant point contours in the scale space image the stable cardinal curvature points can be detected very accurately this new method requires no input parameters and the resultant dominant points do not change under translation rotation and scaling meanwhile a fast convolution algorithm is proposed to detect the dominant points at each scale dominant points scale space gaussian smoothing curvature

object matching algorithms using robust hausdorff distance measures a hausdorff distance hd is one of commonly used measures for object matching this work analyzes the conventional hd measures and proposes two robust hd measures based on m estimation and least trimmed square lts which are more efficient than the conventional hd measures by computer simulation the matching performance of the conventional and proposed hd measures is compared with synthetic and real images

the bloch wave method and vibrations of elastic cylinder arrays in a fluid abstract it is shown that the added mass matrix of an infinite periodic tube bank immersed in a perfect fluid can be derived by means of the bloch wave technique with account taken of the repetitive structure of the mechanical system this method merely requires computations on the representative cell of the bundle the case of a tube array placed in a viscous cross flow is also considered from which a quadratic eigenvalue problem arises the technique so described can be used to determine the critical flow beyond which the tubes begin to oscillate

an algorithm for approximate solving of differential equations with maxima an algorithm for constructing two sequences of successive approximations of the solution of the initial value problem for nonlinear differential equations with maxima is given this algorithm is based on the monotone iterative technique it is proved that both sequences are monotonically convergent each term of the constructed sequences is a solution of an initial value problem for linear differential equations with maxima and it is a lower upper solution of the given problem both the scalar case and the multidimensional case are studied an example solved by computer realization of the suggested algorithm illustrates the practical application of the method

asymptotic analysis relating spectral models in fluid solid vibrations an asymptotic study of two spectral models which appear in fluid solid vibrations is presented in this paper these two models are derived under the assumption that the fluid is slightly compressible or viscous respectively in the first case min max estimations and a limit process in the variational formulation of the corresponding model are used to show that the spectrum of the compressible case tends to be a continuous set as the fluid becomes incompressible in the second case we use a suitable family of unbounded non self adjoint operators to prove that the spectrum of the viscous model tends to be continuous as the fluid becomes inviscid at the limit in both cases the spectrum of a perfect incompressible fluid model is found we also prove that the set of generalized eigenfunctions associated with the viscous model is dense for the l2 norm in the space of divergence free vector functions finally a numerical example to illustrate the convergence of the viscous model is presented

robust automatic target recognition using a localized boundary representation abstract a localized classification approach which includes a localized target boundary representation a set of local features to characterize parts of a target boundary and a feature matching method is developed to classify highly degraded targets each pixel on the target boundary is represented by the perpendicular euclidean distance between the boundary pixel and the chord connecting the end points of a window centered on the boundary pixel the resulting localized representation is quite robust with respect to noise and missing segments in the targets a local feature is the segment of the localized representation between two points selected on the target boundary the two points on the boundary may be specified or randomly selected the reference features of a hypothesized target class are compared with segments of the localized representation of the test target to determine a dissimilarity measure between the hypothesized target class and the test target segments of the test target may also be matched with the reference localized contour sequences of the targets the test target is assigned to a target class using a minimum mismatch rule results from a series of experiments conducted on three targets show that it is possible to classify targets experiencing high levels of noise and high percentages of missing segments in partial targets

an analysis of a new stable partitioned algorithm for fsi problems part i incompressible flow and elastic solids stable partitioned algorithms for fluid structure interaction fsi problems are developed and analyzed in this two part paper part i describes an algorithm for incompressible flow coupled with compressible elastic solids while part ii discusses an algorithm for incompressible flow coupled with structural shells importantly these new added mass partitioned amp schemes are stable and retain full accuracy with no sub iterations per time step even in the presence of strong added mass effects e g for light solids the numerical approach described here for bulk compressible solids extends the scheme of banks et al 1 2 for inviscid compressible flow and uses robin mixed boundary conditions with the fluid and solid solvers at the interface the basic amp robin conditions involving a linear combination of velocity and stress are determined from the outgoing solid characteristic relation normal to the fluid solid interface combined with the matching conditions on the velocity and traction two alternative forms of the amp conditions are then derived depending on whether the fluid equations are advanced with a fractional step method or not the stability and accuracy of the amp algorithm is evaluated for linearized fsi model problems the full nonlinear case being left for future consideration a normal mode analysis is performed to show that the new amp algorithm is stable for any ratio of the solid and fluid densities including the case of very light solids when added mass effects are large in contrast it is shown that a traditional partitioned algorithm involving a dirichlet neumann coupling for the same fsi problem is formally unconditionally unstable for any ratio of densities exact traveling wave solutions are derived for the fsi model problems and these solutions are used to verify the stability and accuracy of the corresponding numerical results obtained from the amp algorithm for the cases of light medium and heavy solids