on the number of limit cycles for a class of discontinuous quadratic differential systems abstract the present paper is devoted to the study of the maximum number of limit cycles bifurcated from the periodic orbits of the quadratic isochronous center x y 16 3 x 2 4 3 y 2 y x 8 3 x y by the averaging method of first order when it is perturbed inside a class of discontinuous quadratic polynomial differential systems the chebyshev criterion is used to show that this maximum number is 5 and can be realizable in some sense the result and that in paper 6 also answer the questions left in the paper 9

homoclinic loop and multiple limit cycle bifurcation surfaces this paper establishes the existence and analyticity of homoclinic loop bifurcation surfaces z and multiplicity two limit cycle bifurcation surfaces f for planar systems depending on two or more parameters it determines the side of or f on which limit cycles occur and it shows that if x and intersect then typically they do so at a flat contact

invariant pattern recognition using radon dual tree complex wavelet and fourier transforms an invariant pattern recognition descriptor is proposed in this paper by using the radon transform the dual tree complex wavelet transform and the fourier transform the radon transform can capture the directional features of the pattern image by projecting the pattern onto different orientation slices the dual tree complex wavelet transform can select shift invariant features in a multiresolution way the fourier transform can extract features that are invariant to rotation of the patterns standard normalization techniques are used to normalize the input pattern image so that it is translation and scale invariant experiments conducted in this paper show that the proposed descriptor achieves high recognition rates for different combinations of rotation angles and noise levels the descriptor is very robust to gaussian white noise even when the noise level is very high

contour based handwritten numeral recognition using multiwavelets and neural networks abstract in this paper we develop a handwritten numeral recognition descriptor using multiwavelets and neural networks we first trace the contour of the numeral then normalize and resample the contour so that it is translation and scale invariant we then perform multiwavelet orthonormal shell expansion on the contour to get several resolution levels and the average finally we use the shell coefficients as features to input into a feed forward neural network to recognize the handwritten numerals the main advantage of the orthonormal shell decomposition is that it decomposes a signal into multiresolution levels but without down sampling wavelet transforms with down sampling can give very different coefficients when the input signal is shifted this is the main limitation of wavelet transforms in pattern recognition for the shell expansion we prefer multiwavelets to scalar wavelets because we have two coordinates x and y for each point on the contour if we extract features from x and y separately just as wunsch et al did pattern recognition 28 1995 1237 then we may not get the best features in addition we know that multiwavelets have advantages over scalar wavelets such as short support orthogonality symmetry and higher order of vanishing moments these properties allow multiwavelets to outperform scalar wavelets in some applications e g signal denoising ieee trans signal process 46 12 1998 3414 we conducted experiments and found that it is feasible to use multiwavelet features in handwritten numeral recognition

rotation invariant pattern recognition using ridgelets wavelet cycle spinning and fourier features in this paper we propose a rotation invariant descriptor for pattern recognition by using ridgelets wavelet cycle spinning and the fourier transform ridgelets have been developed recently and have many advantages over wavelets in applications to image processing however the current implementation of ridgelets cannot be applied to pattern recognition directly in order to overcome this problem we have successfully extracted ridgelet features within the circle surrounding the pattern we are trying to recognize wavelet cycle spinning and fourier spectrum magnitudes are used to achieve rotation invariance the main motivation of using ridgelets is that we have a much better tool for the extraction of features based on line singularities as compared to point singularities as in the case of wavelets based on this observation important features can be extracted our experiments show that our proposed descriptor is very robust to gaussian noise and it achieves high recognition rates

a hierarchical domain decomposition preconditioner for h p finite element approximation on locally refined meshes a domain decomposition preconditioner suitable for h p finite element approximation on locally refined meshes with nonuniform polynomial degree is proposed and analysed the preconditioner is highly suited for parallel computation the algorithm generalizes methods proposed by smith domain decomposition algorithms for the partial differential equations of linear elasticity ph d thesis mathematics department new york university new york 1991 for the h version finite element method with piecewise linear basis functions and by mandel comput methods appl mech engrg 80 1990 pp 117 128 for the p version finite element method the analysis shows that the condition number of the preconditioned system grows at most as min h h 1 log 2p 1 log 2 hp h this result generalizes the known estimates in each of the special cases mentioned above numerical examples are given confirming the theoretical analysis

efficient preconditioning for the p version finite element method in two dimensions parallel preconditioners are formulated and analyzed for systems of equations arising from the p version finite element method applied to second order self adjoint elliptic boundary value problems in two dimensions by using new theoretical results for polynomial spaces it is proved that the condition number of the preconditioned system grows as log 2 p where p is the degree of the polynomial space numerical results are presented showing that the condition number indeed grows very slowly with p

limit cycles bifurcated from a class of quadratic reversible center of genus one abstract we investigate the bifurcation of limit cycles in a class of planar quadratic reversible non hamiltonian systems this systems has a center of genus one the exact upper bound of the number of limit cycles is given

invariant algebraic curves and conditions for a centre conditions for the existence of a centre in two dimensional systems are considered along the lines of darboux we show how these methods can be used in the search for maximal numbers of bifurcating limit cycles we also extend the method to include more degenerate cases such as are encountered in less generic systems these lead to new classes of integrals in particular the kukles system is considered and new centre conditions for this system are obtained

on weak dirichlet boundary conditions for elliptic problems in the continuous galerkin method abstract we combine continuous and discontinuous galerkin methods in the setting of a model diffusion problem starting from a hybrid discontinuous formulation we replace element interiors by more general subsets of the computational domain groups of elements that support a piecewise polynomial continuous expansion this step allows us to identify a new weak formulation of dirichlet boundary condition in the continuous framework we show that the boundary condition leads to a stable discretization with a single parameter insensitive to mesh size and polynomial order of the expansion the robustness of the approach is demonstrated on several numerical examples

coexistence of limit cycles and invariant algebraic curves for a kukles system abstract we consider a kukles system of the form x y y f x y where f x y is a polynomial with real coefficients of degree d without y as a divisor we study the maximum number of small amplitude limit cycles for these kind of systems which can coexist with invariant algebraic curves we give all the possible distributions of invariant straight lines for a kukles system and we give some bounds for the number of limit cycles we also give some necessary conditions for the existence of an invariant algebraic curve of degree 2 and we study the possible coexistence of this curve and a limit cycle finally we give two examples of cubic kukles systems both with an invariant hyperbola in the first example the hyperbola coexists with a center and in the second one it coexists with two small amplitude limit cycles these two examples contradict a previous result given in ann differential equations 7 3 1991 323

bifurcation of limit cycles from centers and separatrix cycles of planar analytic systems this paper presents a survey of results on the bifurcation of limit cycles from centers and separatrix cycles of perturbed planar analytic systems and contributes some new results on the bifurcation of multiple limit cycles from centers and on the multiplicity of separatrix cycles of such systems the basic theme throughout the paper is that the number positions and multiplicities of the limit cycles that bifurcate under perturbations are related to the number positions and multiplicities of the zeros of the melnikov function for the system the general theory is illustrated by a number of examples from the literature some of which are extended to include new results

invariant fourier wavelet descriptor for pattern recognition abstract we present a novel set of descriptors for recognizing complex patterns such as roadsigns keys aircrafts characters etc given a pattern we first transform it to polar coordinate r using the centre of mass of the pattern as origin we then apply the fourier transform along the axis of polar angle and the wavelet transform along the axis of radius r the features thus obtained are invariant to translation rotation and scaling as an example we apply the method to a database of 85 printed chinese characters the result shows that the fourier wavelet descriptor is an efficient representation which can provide for reliable recognition

wavelet descriptors for multiresolution recognition of handprinted characters we present a novel set of shape descriptors that represents a digitized pattern in a concise way and that is particularly well suited for the recognition of handprinted characters the descriptor set is derived from the wavelet transform of a pattern s contour the approach is closely related to feature extraction methods by fourier series expansion the motivation to use an orthonormal wavelet basis rather than the fourier basis is that wavelet coefficients provide localized frequency information and that wavelets allow us to decompose a function into a multiresolution hierarchy of localized frequency bands we describe a character recognition system that relies upon wavelet descriptors to simultaneously analyze character shape at multiple levels of resolution the system was trained and tested on a large database of more than 6000 samples of handprinted alphanumeric characters the results show that wavelet descriptors are an efficient representation that can provide for reliable recognition in problems with large input variability

on the limit cycles of a class of kukles type differential systems abstract in this paper we study the limit cycles of two families of differential systems in the plane these systems are obtained by polynomial perturbations with arbitrary degree on the second component of the standard linear center the classes under consideration are polynomial generalizations of certain canonical form of a kukles system with an invariant ellipse previously studied in the literature we provide in both cases an accurate upper bound of the maximum number of limit cycles that the perturbed system can have bifurcating from the periodic orbits of the linear center using the averaging theory of first second and third order these upper bounds are presented in terms of the degree of the respective systems moreover the existence of a weak focus with the highest order is also studied

the fast discrete radon transform i theory an inversion scheme for reconstruction of images from projections based on the slope intercept form of the discrete radon transform is presented a seminal algorithm for the forward and the inverse transforms proposed by g beylkin 1987 demonstrated poor dispersion characteristics for steep slopes and could not invert transforms based on nonlinear slope variations by formulating the computation of a discrete computation of the continuous radon transform formula the authors explicitly derive fast generalized inversion methods that overcome the original shortcomings the generalized forward frt and inverse ifrt algorithms proposed are fast eliminate interpolation calculations and convert directly between a raster scan grid and a rectangular polar grid in one step

an optimal preconditioner for a class of saddle point problems with a penalty term iterative methods are considered for a class of saddle point problems with a penalty term arising from finite element discretizations of certain elliptic problems an optimal preconditioner which is independent of the discretization and the penalty parameter is constructed this approach is then used to design an iterative method with a convergence rate bounded independently of the lame parameters occurring in the equations of linear elasticity

balancing neumann neumann methods for incompressible stokes equations this paper describes the unerlying mathematical model and the balancing neumann neumann methods are introduced and studied for incompressible stokes equations discretized with mixed finite or spectral elements with discontinuous pressures after decomposing the original domain of the problem into nonoverlapping subdomains the interior unknowns which are the interior velocity component and all except the constant pressure component of each subdomain problem are implicitly eliminated the resulting saddle point schur complement is solved with a krylov space method with a balancing neumann neumann preconditioner based on the solution of a coarse stokes problem with a few degrees of freedom per subdomain and on the solution of local stokes problems with natural neumann velocity and essential boundary conditions on the subdomains this preconditioner is of hybrid form in which the coarse problem is treated multiplicatively while the local problems are treated additively the condition number of the preconditioned operator is independent of the number of subdomains and is bounded from above by the product of the square of the logarithm of the local number of unknowns in each subdomain and the inverse of the inf sup constants of the discrete problem and of the coarse subproblem numerical results show that the method is quite fast they are also fully consistent with the theory

an extension of the feti domain decomposition method for incompressible and nearly incompressible problems incompressible and nearly incompressible problems are treated herein with a mixed finite element formulation in order to avoid ill conditioning that prevents accuracy in pressure estimation and can lead to a lack of convergence for iterative solution algorithms a multilevel dual domain decomposition method is then chosen as an iterative algorithm the original feti and feti dp methods are extended to deal with such problems when the discretization of the pressure field is discontinuous throughout the elements a dedicated augmentation of the algorithms is proposed and the different methods are compared with several preconditioners for bidimensional test cases the resulting approaches are both optimal and numerically scalable and their costs are estimated with a complexity analysis

a fast discrete approximation algorithm for the radon transform this paper addresses fast parallel methods for the computation of the radon or hough transform the radon transform of an image is a set of projections of the image taken at different angles its computation is important in image processing and computer vision for problems such as pattern recognition and reconstruction of medical images a unique new method for combining partial results is presented from which an algorithm is constructed that computes a provably good approximation to the discrete radon transform the approximate discrete radon transform adrt algorithm computes 4 n 4 projections through an n times n image in time o n 2 mathrm lg n the majority of previous algorithms are o n 3 the method is quite simple and easy to parallelize a parallel version of the adrt requires only o mathrm lg n parallel steps on o n 2 processors ignoring communication time an additional property of the algorithm is that it can be applied directly to compute the backprojection step of the inverse rt

non overlapping domain decomposition methods for adaptive hp approximations of the stokes problem with discontinuous pressure fields abstract this paper proposes a framework for non overlapping domain decomposition methods applied to viscous incompressible flows governed by stokes equations modelled by the hp version of the finite element method preconditioning methods developed earlier for elliptic problems are extended to this case suitable condition number bounds are obtained for both the hierarchical hp preconditioners of the type proposed in 9 and neumann neumann preconditioners proposed in 10 systematic procedures for constructing compatible hp approximations for incompressible flow are also described

fast iterative solution of stabilised stokes systems part ii using general block preconditioners mixed finite element approximation of the classical stokes problem describing slow viscous incompressible flow gives rise to symmetric indefinite systems for the discrete velocity and pressure variables iterative solution of such indefinite systems is feasible and is an attractive approach for large problems part i of this work described a conjugate gradient like method the method of preconditioned conjugate residuals which is applicable to symmetric indefinite problems a j wathen and d j silvester siam j numer anal 30 1993 pp 630 649 using simple arguments estimates for the eigenvalue distribution of the discrete stokes operator on which the convergence rate of the iteration depends are easily derived part i discussed the important case of diagonal preconditioning scaling this paper considers the more general class of block preconditioners where the partitioning into blocks corresponds to the natural partitioning into the velocity and pressure variables it is shown that provid

the monotonicity of period function for codimension four quadratic system q4 abstract in this paper we study the codimension four quadratic system q 4 z iz 4 z 2 2 z 2 b ic z 2 where b and c are real constants i 2 1 z x iy b ic 2 it is proved that the period function of periodic trajectories for q 4 is monotone the content of this paper can be viewed as a contribution to the proof of chicone s conjecture cf mr 94h 58072

a class of iterative methods for solving saddle point problems we consider the numerical solution of indefinite systems of linear equations arising in the calculation of saddle points we are mainly concerned with sparse systems of this type resulting from certain discretizations of partial differential equations we present an iterative method involving two levels of iteration similar in some respects to the uzawa algorithm we relate the rates of convergence of the outer and inner iterations proving that under natural hypotheses the outer iteration achieves the rate of convergence of the inner iteration the technique is applied to finite element approximations of the stokes equations

bifurcation of limit cycles from quadratic isochrones abstract for a one parameter family of plane quadratic vector fields x e depending analytically on a small real parameter e we determine the number and position of the local families of limit cycles which emerge from the periodic trajectories surrounding an isochronous or linearizable center techniques are developed for treating the bifurcations of all orders and these are applied to prove the following results for the linear isochrone the maximum number of continuous families of limit cycles which can emerge is three for one class of nonlinear isochrones at most one continuous family of limit cycles can emerge whereas for all other nonlinear isochrones at most two continuous families of limit cycles can emerge moreover for each isochrone in one of these classes there are small perturbations such that the indicated maximum number of continuous families of limit cycles can be made to emerge from a corresponding number of arbitrarily prescribed periodic orbits within the period annulus of the isochronous center

on the enforcement of the zero mean pressure condition in the spectral element approximation of the stokes problem this paper considers the spectral element approximation of the stokes problem and the conditioning of the resulting discrete problem the well posedness of the variational formulation of the stokes problem and in particular the uniqueness of the pressure has been demonstrated when the subspace of square integrable functions having vanishing mean is chosen for the pressure space in the discrete setting a conforming subspace is chosen for the discrete pressure space and the analysis of the discrete problem is based on this choice however this space is not used in practical implementations of finite or spectral element methods for the stokes problem in this paper it is shown how the zero volume condition on the pressure may be accommodated within the trial space by modifying the continuity equation in a consistent manner the dependence of the condition number of the uzawa operator and the accuracy of the spectral element approximation on the weighting factor is investigated

image representation via a finite radon transform a model of finite radon transforms composed of radon projections is presented the model generalizes to finite group projections in the classical radon transform theory the radon projector averages a function on a group over cosets of a subgroup reconstruction formulae that were formally similar to the convolved backprojection ones are derived and an iterative reconstruction technique is found to converge after a finite number of steps applying these results to the group z sub 2 sup p new computationally favorable image representations have been obtained a numerical study of the transform coding aspects is attached

analysis of iterative methods for the steady and unsteady stokes problem application to spectral element discretizations a new and detailed analysis of the basic uzawa algorithm for decoupling of the pressure and the velocity in the steady and unsteady stokes operator is presented the paper focuses on the following new aspects explicit construction of the uzawa pressure operator spectrum for a semiperiodic model problem general relationship of the convergence rate of the uzawa procedure to classical inf sup discretization analysis and application of the method to high order variational discretization

similarity transformation parameters recovery based on radon transform application in image registration and object recognition the radon transform since its introduction in the beginning of the last century has been studied deeply and applied by researchers in a great number of applications especially in the biomedical imaging fields by using the radon transform properties the issue is to recover the transformation parameters regarding the rotation scaling and translation by handling only the image projections assuming no access to the spatial domain of the image this paper proposes an algorithm using an extended version of the radon transform to recover such parameters relating to two unknown images directly from their projection data especially our approach deals with the problem of the estimation accuracy of the rotation angle and its finding in one step instead of two steps as it is reported in the literature this method may be applied in image registration as well in object recognition the results are for the first time exploited in object recognition where comparison with powerful descriptors shows the outstanding performance of the proposed paradigm moreover the influence of additive noise on registration and recognition experiments is discussed and shows the efficiency of the method to reduce the effect of the noise highlightswe define 2 based radon transform rt and motivate its use we propose an algorithm to recover rst transforms using only rt the algorithm is tested on images in real world application e g ct mri etc this rst parameter recovery method is newly applied in object recognition a new confusion matrix is designed to identify also a mislabeled class element

constraint interface preconditioning for the incompressible stokes equations we introduce a novel substructuring approach for solving the incompressible stokes equations for the case of enclosed flows we employ a simple distribution of the global pressure constraint to subdomains which allows for a natural decomposition into stokes subdomain problems with dirichlet data which are well posed and inf sup stable this approach yields a saddle point problem on the interface gamma involving an operator which is continuous and coercive on h 1 2 gamma and which is restricted to the interface trace space of functions satisfying the incompressibility constraint we derive the form of the constraints explicitly both for the continuous and for the discrete case this allows us to design directly a class of interface preconditioners of constraint type thus avoiding the need to formulate a coarse level problem our analysis indicates that the resulting solution method has performance independent of the mesh size while numerical results point to a mild dependence on the number of s

asymptotics and stability of the delayed duffing equation abstract we examine how insertion of a delay in a system of ordinary differential equations can change the asymptotic dynamics and stabilize the structure of the system under further change

a multiscale darcy brinkman model for fluid flow in fractured porous media the aim of this work is to present a reduced mathematical model for describing fluid flow in porous media featuring open channels or fractures the darcy s law is assumed in the porous domain while the stokes brinkman equations are considered in the fractures we address the case of fractures whose thickness is very small compared to the characteristic diameter of the computational domain and describe the fracture as if it were an interface between porous regions we derive the corresponding interface model governing the fluid flow in the fracture and in the porous media and establish the well posedness of the coupled problem further we introduce a finite element scheme for the approximation of the coupled problem and discuss solution strategies we conclude by showing the numerical results related to several test cases and compare the accuracy of the reduced model compared with the non reduced one

higher order bifurcations of limit cycles abstract this paper shows that asymmetrically perturbed symmetric hamiltonian systems of the formx y y x x3 1y 2x2 3xy 4x2y with analytic j e o e have at most two limit cycles that bifurcate for smalle 0 from any period annulus of the unperturbed system this fact agrees with previous results of petrov dangelmayr and guckenheimer and chicone and iliev but shows that the result of three limit cycles for the asymmetrically perturbed exterior duffing oscillator recently obtained by jebrane and oladek is incorrect the proofs follow by deriving an explicit formula for thekth order melnikov function mk h and using a picard fuchs analysis to show that in each case mk h has at most two zeros moreover the method developed in this paper for determining the higher order melnikov functions also applies to more general perturbations of these systems

preconditioned conjugate residual methods for mixed spectral discretizations of elasticity and stokes problems abstract mixed spectral methods applied to elasticity and stokes problems in three dimensions produce large symmetric indefinite systems of equations these systems are sparse and more ill conditioned than those produced by h version finite element methods these stiffness matrices have the structure of saddle point problems with a penalty term in this paper preconditioned iterative methods of conjugate residual type are introduced for these systems the convergence rates of the resulting algorithms are proven to be independent of the penalty parameter and mildly dependent on the spectral degree n several numerical experiments on three dimensional model problems confirm the results obtained

domain decomposition preconditioners for p and hp finite element approximation of stokes equations abstract domain decomposition preconditioning techniques are developed in the context of hp finite element approximation of the stokes problem two basic types of preconditioner are considered a block diagonal scheme based on decoupling the velocity and pressure components and a scheme based on an indefinite system similar to the original stokes system for each type of scheme theoretical estimates are obtained for the location of the eigenvalues of the preconditioned operators in terms of the polynomial degree the mesh sizes on the coarse and fine grids and the inf sup constant for the method theoretical estimates show that the growth of the bounds is modest as the mesh is refined and the polynomial order is increased the preconditioners are shown to be applicable to various iterative schemes for the stokes systems the theoretical bounds are compared with actual quantities obtained in practical computations for several representative problems

on the number of critical points of the period in the study of subharmonic bifurcations from a planar hamiltonian system it is often assumed that the period of a one parameter family of periodic orbits of the unperturbed system is a monotone function of the parameter see e g hale and taboas s chow and hale es however this hypothesis is in many instances difficult to verify for example it is well known that every orbit in the first quadrant of the vollterra lotka equation is periodic it is only in recent years that the monotonicity of the periods of these periodic orbits has been shown hsu 9 and waldvogel 151 such problems also occur in the study of bifurcation of steady state solutions of a reaction diffusion equation in one space variable the steady state solutions satisfy the equation u f u o uer 1 1 on some interval in 14 smoller and wasserman showed that if f u u u u u cc

mixed hp finite element methods for problems in elasticity and stokes flow we consider the mixed formulation for the elasticity problem and the limiting stokes problem in bbb r d d 2 3 we derive a set of sufficient conditions under which families of mixed finite element spaces are simultaneously stable with respect to the mesh size h and subject to a maximum loss of o k frac d 1 2 with respect to the polynomial degree k we obtain asymptotic rates of convergence that are optimal up to o k epsilon in the displacement velocity and up to o k frac d 1 2 epsilon in the pressure with epsilon 0 arbitrary both rates being optimal with respect to h several choices of elements are discussed with reference to properties desirable in the context of the hp version

a preconditioner based on domain decomposition for h p finite element approximation on quasi uniform meshes the problem of solving the algebraic systems arising from the discretization of a symmetric elliptic boundary value problem using h p finite element methods in two dimensions is addressed a preconditioning technique similar to those of bramble pasciak and schatz math comp 47 1986 pp 103 135 based on domain decomposition also known as substructuring is developed the method is applicable to problems on general domains involving differential operators with quite general coefficients the algorithm reduces to that of bramble pasciak and schatz if linear elements are used it is shown that the condition number of the preconditioned system which determines the rate of convergence of the iterative method grows at most as 1 log 2 p 1 log 2 hp h where p is the polynomial degree h is the size of the elements and h is the size of the subdomains

the discrete periodic radon transform in this correspondence a discrete periodic radon transform and its inversion are developed the new discrete periodic radon transform possesses many properties similar to the continuous radon transform such as the fourier slice theorem and the convolution property etc with the convolution property a 2 d circular convolution can be decomposed into 1 d circular convolutions hence improving the computational efficiency based on the proposed discrete periodic radon transform we further develop the inversion formula using the discrete fourier slice theorem it is interesting to note that the inverse transform is multiplication free this important characteristic not only enables fast inversion but also eliminates the finite word length error that may be generated in performing the multiplications

deriving a new domain decomposition method for the stokes equations using the smith factorization in this paper the smith factorization is used systematically to derive a new domain decomposition method for the stokes problem in two dimensions the key idea is the transformation of the stokes problem into a scalar bi harmonic problem we show how a proposed domain decomposition method for the bi harmonic problem leads to a domain decomposition method for the stokes equations which inherits the convergence behavior of the scalar problem thus it is sufficient to study the convergence of the scalar algorithm the same procedure can also be applied to the three dimensional stokes problem as transmission conditions for the resulting domain decomposition method of the stokes problem we obtain natural boundary conditions therefore it can be implemented easily a fourier analysis and some numerical experiments show very fast convergence of the proposed algorithm our algorithm shows a more robust behavior than neumann neumann or feti type methods

bifurcation of critical periods for plane vector fields on etudie un probleme de bifurcation dans des familles de champs de vecteurs analytiques plans qui ont un centre non degenere a l origine pour toutes les valeurs d un parametre r n on definit la fonction periode p on determine les points critiques de cette fonction pres du centre avec comme parametre de bifurcation

analysis of the inexact uzawa algorithm for saddle point problems in this paper we consider the so called inexact uzawa algorithm for iteratively solving linear block saddle point problems such saddle point problems arise for example in finite element and finite difference discretizations of stokes equations the equations of elasticity and mixed finite element discretization of second order problems we consider both the linear and nonlinear variants of the inexact uzawa iteration we show that the linear method always converges as long as the preconditioners defining the algorithm are properly scaled bounds for the rate of convergence are provided in terms of the rate of convergence for the preconditioned uzawa algorithm and the reduction factor corresponding to the preconditioner for the upper left hand block in the case of nonlinear iteration the inexact uzawa algorithm is shown to converge provided that the nonlinear process approximating the inverse of the upper left hand block is of sufficient accuracy bounds for the nonlinear iteration are given in terms of this accuracy parameter and the rate of convergence of the preconditioned linear uzawa algorithm applications to the stokes equations and mixed finite element discretization of second order elliptic problems are discussed and finally the results of numerical experiments involving the algorithms are presented

a dual primal feti method for incompressible stokes equations in this paper a dual primal feti method is developed for incompressible stokes equations approximated by mixed finite elements with discontinuous pressures the domain of the problem is decomposed into nonoverlapping subdomains and the continuity of the velocity across the subdomain interface is enforced by introducing lagrange multipliers by a schur complement procedure the solution of an indefinite stokes problem is reduced to solving a symmetric positive definite problem for the dual variables i e the lagrange multipliers this dual problem is solved by the conjugate gradient method with a dirichlet preconditioner in each iteration step both subdomain problems and a coarse level problem are solved by a direct method it is proved that the condition number of this preconditioned dual problem is independent of the number of subdomains and bounded from above by the square of the product of the inverse of the inf sup constant of the discrete problem and the logarithm of the number of unknowns in the individual subdomains numerical experiments demonstrate the scalability of this new method

limit cycles for generalized kukles polynomial differential systems abstract we study the limit cycles of generalized kukles polynomial differential systems using averaging theory of first and second order

bounding the number of limit cycles of discontinuous differential systems by using picard fuchs equations abstract in this paper by using picard fuchs equations and chebyshev criterion we study the upper bounds of the number of limit cycles given by the first order melnikov function for discontinuous differential systems which can bifurcate from the periodic orbits of quadratic reversible centers of genus one r19 x y 12 x 2 16 y 2 y x 16 x y and r20 x y 4 x 2 y x 16 x y and the periodic orbits of the quadratic isochronous centers s 1 x y x 2 y 2 y x 2 x y and s 2 x y x 2 y x x y the systems r19 and r20 are perturbed inside the class of polynomial differential systems of degree n and the system s 1 and s 2 are perturbed inside the class of quadratic polynomial differential systems the discontinuity is the line y 0 it is proved that the upper bounds of the number of limit cycles for systems r19 and r20 are respectively 4 n 3 n 4 and 4 n 3 n 3 counting the multiplicity and the maximum numbers of limit cycles bifurcating from the period annuluses of the isochronous centers s 1 and s 2 are exactly 5 and 6 counting the multiplicity on each period annulus respectively

a codimension two bifurcation with a third order picard fuchs equation abstract using a third order picard fuchs equation we show that a certain two parameter family of planar vectorfields for parameter values in a certain cone has a unique limit cycle which is born from a hopf bifurcation and dies in a saddle connection this removes a superfluous hypothesis in theorem 3 2 chapter 13 of s n chow and j k hale methods of bifurcation theory springer verlag new york 1982

spiral aggregation map splam this paper describes a robust template matching algorithm undergoing rotation scaling translation rst variations via our proposed spiral aggregation map splam which is a novel image warping scheme it not only provides an efficient method for generating the desired projection profiles for matching it also enables us to determine the rotation angle and is invariant to scale changes compared to other model based methods the proposed spiral projection model spm provides the structural and statistical information about the template in a more general and easier to comprehend format the spm is a model based texture description scheme that enables the simultaneous representation for each value of projection profile the profile a set of parametric projection values functions by angular indexing is the aggregate from a group of spiral sampling pixels the experimental evaluation shows that the properties of the algorithm achieved very attractive results this paper describes a robust and fast template matching algorithm we introduced a novel image warping scheme called the spiral aggregation map splam this descriptor is capable of expressing the template with high order texture characteristics

schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems part i algorithms and numerical results we describe sequential and parallel algorithms based on the schwarz alternating method for the solution of mixed finite element discretizations of elliptic problems using the raviart thomas finite element spaces these lead to symmetric indefinite linear systems and the algorithms have some similarities with the traditional block gauss seidel or block jacobi methods with overlapping blocks the indefiniteness requires special treatment the sub blocks used in the algorithm correspond to problems on a coarse grid and some overlapping subdomains and is based on a similar partition used in an algorithm of dryja and widlund for standard elliptic problems if there is sufficient overlap between the subdomains the algorithm converges with a rate independent of the mesh size the number of subdomains and discontinuities of the coefficients extensions of the above algorithms to the case of local grid refinement is also described convergence theory for these algorithms will be presented in a subsequent paper

limit cycle bifurcations by perturbing piecewise smooth hamiltonian systems with multiple parameters abstract this paper is concerned with the problem of limit cycle bifurcation for piecewise smooth near hamiltonian systems with multiple parameters by the first melnikov function some novel criteria have been established for the existence of multiple limit cycles furthermore an example is included to validate the obtained results by considering the maximum number of limit cycles for a piecewise quadratic system studied in llibre and mereu 2014 12 compared with the result in the above reference one more limit cycle is found by our method

a preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems this paper provides a preconditioned iterative technique for the solution of saddle point problems these problems typically arise in the numerical approximation of partial differential equations by lagrange multiplier techniques and or mixed methods the saddle point problem is reformulated as a symmetric positive definite system which is then solved by conjugate gradient iteration applications to the equations of elasticity and stokes are discussed and the results of numerical experiments are given

limit cycles by perturbing quadratic isochronous centers inside piecewise polynomial differential systems abstract in this paper we consider the quadratic isochronous centers perturbed inside piecewise polynomial differential systems of arbitrary degree n with the straight line of discontinuity x 0 the main concerns are the number of zeros of the first order melnikov functions and the estimate of the number of limit cycles bifurcating from the period annuli for quadratic isochronous centers s 1 s 2 and s 3 we will provide a sharp upper bound for the number of zeros of the first order melnikov functions for quadratic isochronous center s 4 we give a rough estimate however when the problem is reduced to perturbations inside polynomial differential systems our result for s 4 will improve that in li et al 2000 12 significantly moreover we will reveal out some equivalence between the first order melnikov function method and the first order averaging method for investigating the number of limit cycles of piecewise polynomial differential systems

wavelet based affine invariant representation a tool for recognizing planar objects in 3d space a technique is developed to construct a representation of planar objects undergoing a general affine transformation the representation can be used to describe planar or nearly planar objects in a three dimensional space observed by a camera under arbitrary orientations the technique is based upon object contours parameterized by an affine invariant parameter and the dyadic wavelet transform the role of the wavelet transform is the extraction of multiresolution affine invariant features from the affine invariant contour representation a dissimilarity function is also developed and used to distinguish among different object representations this function makes use of the extrema on the representations thus making its computation very efficient a study of the effect of using different wavelet functions and their order or vanishing moments is also carried out experimental results show that the performance of the proposed representation is better than that of other existing methods particularly when objects are heavily corrupted with noise

balancing neumann neumann preconditioners for mixed approximations of heterogeneous problems in linear elasticity balancing neumann neumann methods are extented to mixed formulations of the linear elasticity system with discontinuous coefficients discretized with mixed finite or spectral elements with discontinuous pressures these domain decomposition methods implicitly eliminate the degrees of freedom associated with the interior of each subdomain and solve iteratively the resulting saddle point schur complement using a hybrid preconditioner based on a coarse mixed elasticity problem and local mixed elasticity problems with natural and essential boundary conditions a polylogarithmic bound in the local number of degrees of freedom is proven for the condition number of the preconditioned operator in the constant coefficient case parallel and serial numerical experiments confirm the theoretical results indicate that they still hold for systems with discontinuous coefficients and show that our algorithm is scalable parallel and robust with respect to material heterogeneities the results on heterogeneous general problems are also supported in part by our theory

positive definite balancing neumann neumann preconditioners for nearly incompressible elasticity in this paper a positive definite balancing neumann neumann bnn solver for the linear elasticity system is constructed and analyzed the solver implicitly eliminates the interior degrees of freedom in each subdomain and solves iteratively the resulting schur complement involving only interface displacements using a bnn preconditioner based on the solution of a coarse elasticity problem and local elasticity problems with natural and essential boundary conditions while the schur complement becomes increasingly ill conditioned as the materials becomes almost incompressible the bnn preconditioned operator remains well conditioned the main theoretical result of the paper shows that the proposed bnn method is scalable and quasi optimal in the constant coefficient case this bound holds for material parameters arbitrarily close to the incompressible limit while this result is due to an underlying mixed formulation of the problem both the interface problem and the preconditioner are positive definite numerical results in two and three dimensions confirm these good convergence properties and the robustness of the methods with respect to the almost incompressibility of the material

invariant pattern recognition using the rfm descriptor a pattern descriptor invariant to rotation scaling translation rst and robust to additive noise is proposed by using the radon fourier and mellin transforms the radon transform converts the rst transformations applied on a pattern image into transformations in the radial and angular coordinates of the pattern s radon image these beneficial properties of the radon transform make it an useful intermediate representation for the extraction of invariant features from pattern images for the purpose of indexing matching in this paper invariance to rst is obtained by applying the 1d fourier mellin and discrete fourier transforms on the radial and angular coordinates of the pattern s radon image respectively the implementation of the proposed descriptor is reasonably fast and correct based mainly on the fusion of the radon and fourier transforms and on a modification of the mellin transform theoretical arguments validate the robustness of the proposed descriptor to additive noise and empirical evidence on both occlusion deformation and noisy datasets shows its effectiveness

a nonoverlapping domain decomposition method for stabilized finite element approximations of the oseen equations abstract a nonoverlapping domain decomposition algorithm of robin robin type is applied to the discretized oseen equations using stabilized finite element approximations of velocity and pressure thus allowing in particular equal order interpolation as a crucial result we have to inspect the proof of a modified inf sup condition in particular the dependence of the stability constant with respect to the reynolds number cf appendix after proving coercivity and strong convergence of the method we derive an a posteriori estimate which controls convergence of the discrete subdomain solutions to the global discrete solution provided that jumps of the discrete solution converge at the interface furthermore we obtain information on the design of some free parameters within the robin type interface condition which essentially influence the convergence speed some numerical results confirm the theoretical ones

on the number of algebraically independent poincare liapunov constants abstract in this paper an upper bound for the number of algebraically independent poincare liapunov constants in a certain basis for planar polynomial differential systems is given finally it is conjectured that an upper bound for the number of functionally independent poincare liapunov quantities would be m 2 3 m 7 where m is the degree of the polynomial differential system moreover the computational problems which appear in the computation of the poincare liapunov constants and in the determination of the center cases are also discussed

schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems part ii convergence theory in this paper we discuss bounds for the convergence rates of several domain decomposition algorithms to solve symmetric indefinite linear systems arising from mixed finite element discretizations of elliptic problems the algorithms include schwarz methods and iterative refinement methods on locally refined grids the implementation of schwarz and iterative refinement algorithms have been discussed in part i a discussion on the stability of mixed discretizations on locally refined grids is included and quantiative estimates for the convergence rates of some iterative refinement algorithms are also derived

limit cycles of polynomial differential systems with homogeneous nonlinearities of degree 4 via the averaging method by using the averaging method we study the limit cycles for a class of quartic polynomial differential systems as well as their global shape in the plane more specifically we analyze the global shape of limit cycles bifurcating from a hopf bifurcation and also from periodic orbits with linear center x y y x the perturbation of these systems is made inside the class of quartic polynomial differential systems without quadratic and cubic terms

simultaneous bifurcation of limit cycles from two nests of periodic orbits abstract let z f z be an holomorphic differential equation having a center at p and consider the following perturbation z f z e r z z we give an integral expression similar to an abelian integral whose zeroes control the limit cycles that bifurcate from the periodic orbits of the period annulus of p this expression is given in terms of the linearizing map of z f z at p the result is applied to control the simultaneous bifurcation of limit cycles from the two period annuli of z i z z 2 after a polynomial perturbation

higher order limit cycle bifurcations from non degenerate centers abstract the computational problems which appear in the computation of the poincare liapunov constants and the determination of their functionally independent number has led in recent works to consider only the lowest terms of these constants in this work we improve the results obtained in this direction for polynomials systems of the form x y p n x y y x q n x y where p n and q n are a homogeneous polynomial of degree n we use center bifurcation to estimate the cyclicity of a unique singular point of focus center type for different values of n and compare with the results given by the conjecture presented in 15