the center problem for z2 symmetric nilpotent vector fields abstract we say that a polynomial differential system x p x y y q x y having the origin as a singular point is z 2 symmetric if p x y p x y and q x y q x y it is known that there are nilpotent centers having a local analytic first integral and others which only have a c first integral however these two kinds of nilpotent centers are not characterized for different families of differential systems here we prove that the origin of any z 2 symmetric system is a nilpotent center if and only if there is a local analytic first integral of the form h x y y 2 where the dots denote terms of degree higher than two

orbitally universal centers abstract in this paper we define when a polynomial differential system is orbitally universal and we show the relevance of this notion in the classical center problem i e in the problem of distinguishing between a focus and a center

reversible nilpotent centers with cubic homogeneous nonlinearities abstract we provide 13 non topological equivalent classes of global phase portraits in the poincare disk of reversible cubic homogeneous systems with a nilpotent center at origin which complete the classification of the phase portraits of the nilpotent centers with cubic homogeneous nonlinearities

computational methods for inverse finite elastostatics abstract in the inverse motion problem in finite hyper elasticity the classical formulation relies on conservation laws based on eshelby s energy momentum tensor this formulation is shown to be lacking in several regards for a particular class of inverse motion problems where the deformed configuration and cauchy traction are given and the undeformed configuration must be calculated it is shown that for finite element calculations a simple re examination of the equilibrium equations provides a more suitable finite element formulation this formulation is also shown to involve only minor changes to existing elements designed for forward motion calculations examples illustrating the method in simple and complex situations involving a neo hookean material are presented

a space time finite element method for the wave equation a numerical method is introduced which uses finite elements in time and space simultaneously to solve the wave equation an error analysis for this scheme is presented and the results of several computations this scheme is accurate for time slabs of arbitrary thickness without introducing extra least squares or stabilization terms

analytic nilpotent centers with analytic first integral abstract in this paper a necessary condition to have local analytic integrability in an analytic nilpotent center is given using the normal form theory it is possible to verify if this necessary condition is satisfied the method is applied to several examples

a unified set of single step algorithms part 2 theory part 1 of this paper1 presents a very general single step algorithm sspj for the numerical integration of first and second order time dependent differential equations in part 2 we present and discuss results of the accuracy and stability analysis for ss11 ss21 ss31 ss22 and ss32 there is also a detailed comparison of ss22 and the newmark algorithm

counting real zeros of analytic functions satisfying linear ordinary differential equations abstract we suggest an explicit procedure to establish upper bounds for the number of real zeros of analytic functions satisfying linear ordinary differential equations with meromorphic coefficients if the equation formula has no singular points in a small neighborhooduof a real segmentk all the coefficientsaj t have absolute value aonuanda0 t 1 then any solution of this equation may have no more than a zeros onk where u k is a geometric constant depending only onkandu if the principal coefficienta0 t is nonconstant but its modulus is at leasta 0 somewhere onk then the number of real zeros onkof any solution analytic inu does not exceed a a with some u k

generating limit cycles from a nilpotent critical point via normal forms abstract it is well known that the normal form theory can be applied to solve the center focus problem for monodromic planar nilpotent singularities in this paper we see how this theory can also be applied to generate limit cycles from this type of singularities

monodromy and stability of a class of degenerate planar critical points abstract necessary and also sufficient monodromy conditions for a large class of degenerate singular points of planar differential systems are given for these systems we also find a computable expression of the principal term of the asymptotic expansion of the return map which gives the stability of the point

on the centers of the weight homogeneous polynomial vector fields on the plane we classify all centers of a planar weight homogeneous polynomial vector field of weight degree 1 2 3 and 4

mixed formulation and locking in path following nonlinear analysis abstract the arc length riks strategy has rapidly become a standard tool for path following analysis of nonlinear structures due to its theoretical ability to surpass limit points the aim of this paper is to show that the failures in convergence that are occasionally experienced are not related to proper defects of the algorithm but come from a subtle locking effect intrinsic to the nonlinear nature of the problem as a consequence its sanitization has to be pursued within a reformulation of the structural model the use of a mixed stress displacement variant of the algorithm in particular appears very promising in this respect the topic is discussed with reference to the analysis of nonlinear frames using a mixed version of the nonlinear beam model discussed in 39 it is shown that with no extra computational cost and only a minor modification in coding with respect to a purely compatible formulation it is possible to achieve a noticeable improvement in convergence and a real gain in both computational time and overall robustness of the algorithm

gradient enhanced damage for quasi brittle materials summary conventional continuum damage descriptions of material degeneration suffer from loss of well posedness beyond a certain level of accumulated damage as a consequence numerical solutions are obtained which are unacceptable from a physical point of view the introduction of higher order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models a consistent numerical solution procedure of the governing partial differential equations is presented which is shown to be capable of properly simulating localization phenomena

integrability degenerate centers and limit cycles for a class of polynomial differential systems we consider the class of polynomial differential equations email protected p n x y p n 1 x y p n 2 x y email protected q n x y q n 1 x y q n 2 x y for n 1 and where p i and q i are homogeneous polynomials of degree i these systems have a linearly zero singular point at the origin if n 2 inside this class we identify a new subclass of darboux integrable systems and some of them having a degenerate center i e a center with linear part identically zero moreover under additional conditions such darboux integrable systems can have at most one limit cycle we provide the explicit expression of this limit cycle

the center focus problem and reversibility in this paper we discuss the relation between time reversibility and the center focus problem we show the following for any analytic planar system x if j1x the one jet of x is conjugated to y x then x is analytically time reversible if and only if it is a center if j1x is conjugated to y 0 then some sufficient and necessary conditions for x to have a center are given in particular the reversibility of certain types of polynomial vector fields is studied

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

a method for characterizing nilpotent centers to characterize when a nilpotent singular point of an analytic differential system is a center is of particular interest first for the problem of distinguishing between a focus and a center and after for studying the bifurcation of limit cycles from it or from its period annulus we give an effective algorithm in the search of necessary conditions for detecting nilpotent centers based in recent developments moreover we survey the last results on this problem and illustrate our approach by means of examples

numerical null controllability of the 1d linear schrodinger equation abstract this paper deals with the numerical approximation to boundary controls that drive the solution to the 1 d linear schrodinger equation to a prescribed state at a final time using ideas from fursikov and imanuvilov we consider the control that minimizes over the class of admissible controls a functional that involves weighted integrals with weights that blow up at t we will see that this extremal problem is equivalent to a differential problem that is fourth order in space and second order in time adapting some numerical techniques applied by the first author and munch to the heat equation we approximate the variational formulation by introducing appropriate space time finite elements that are c 1 in space and c 0 in time we present two approaches the second one relies on a change of variable which leads to a lower condition number for the stiffness matrix the results of some experiments show the efficiency of these methods

finite elements in space and time for the analysis of generalised visco elastic materials numerical analysis of linear visco elastic materials requires robust and stable methods to integrate partial differential equations in both space and time in this paper symmetric space time finite element operators are derived for the first time for elementary linear elastic spring and linear viscous dashpot these can thereafter be assembled in parallel and in series to simulate an arbitrarily complex linear visco elastic behaviour the flexibility of the proposed method allows the formulation of the behaviour which closely reflects physical processes an efficient algorithm is proposed to use the generated elementary matrices in a way that is comparable with finite difference schemes in terms of both processor and memory costs this unconditionally stable and convergent procedure is equally valid for space domains in which geometry or material properties evolve with time copyright c 2013 john wiley sons ltd

divergence and poincare liapunov constants for analytic differential systems abstract we consider a planar autonomous real analytic differential system with a monodromic singular point p we deal with the center problem for the singular point p our aim is to highlight some relations between the divergence of the system and the poincare liapunov constants of p when these are defined

structural stability of multi folding structures with contact problem this paper presents the theoretical basis for both static and dynamic numerical approaches to the elastic stability of a folding multi layered truss both analyses are based on bifurcation theory and include geometrical nonlinearity the dynamic analysis includes an allowance for contact between nodes comparisons are made between published experimental folding patterns and the patterns obtained from both numerical methods in which bifurcations are demonstrated as elastic unstable snap through behaviour several folding patterns are identified during the elastic instability where the folding behaviour of the truss is shown to be a function of the initial geometry and velocity of the dynamic loading the authors suggest that the understanding of the behaviour will be very useful for the development of light weight structures subject to dynamic loading based on the bifurcation static analysis and dynamic analysis using both the displacement control method and the load control method

nine limit cycles around a singular point by perturbing a cubic hamiltonian system with a nilpotent center in this paper we study bifurcation of limit cycles in planar cubic near hamiltonian systems with a nilpotent center we use normal form theory to compute the generalized lyapunov constants and show that there exist at least 9 limit cycles around the nilpotent center this is a new lower bound on the number of limit cycles in planar cubic near hamiltonian systems with a nilpotent center

performance measures for optimal constrained beamformers in this paper the closed form expression is derived which relates the output signal to interference plus noise ratio to the minimum mean square error of constrained beamformers for narrowband and wideband signal environments

analytic normalization of analytic integrable systems and the embedding flows abstract this paper provides the normal forms of analytic integrable differential systems and diffeomorphisms via analytic normalizations furthermore we consider the existence of embedding flows of an analytic integrable diffeomorphism

the analytic and formal normal form for the nilpotent singularity abstract we study orbital normal forms for analytic planar vector fields with nilpotent singularity we show that the takens normal form is analytic in the case of generalized cusp we present the complete formal orbital normal form it contains functional moduli we interprete the coefficients of these moduli in terms of the hidden holonomy group

the center problem via averaging method the averaging method has been used to study the problem of the determination of the number of hyperbolic limit cycles that can bifurcate from the period annulus of a center in this paper we use the averaging method up to any order in the perturbation parameter to determine the center conditions of monodromic singular points of analytic planar vector fields

a simple fast adaptive algorithm for broad band null steering arrays a simple algorithm for adaptively steering the broadband null in a two element power inversion array which uses a tapped delay line filter as the processing element is presented and investigated by performing a simple signal transformation the algorithm constrains some of the filter weights so that a variable length delay line is approximated in the maximally flat sense by using the least mean square lms algorithm to adjust the weights controlling the length and gain of the delay line a broadband null is then adaptively formed to track and reject the broadband jammer as studied analytically and by using simulation results the convergence behavior of the algorithm is fast and depends only on the tolerable level of misadjustment noise its implementation complexity is comparable to that of using the lms algorithm directly

finite element modelling of spatially chaotic structures a simple non linear mechanical system comprising a pin jointed string of finite length links supported by elastic springs at the pins and compressed by an axial load is viewed from two perspectives when seen as an initial value problem equilibrium equations provide an iterative non linear mapping when seen as a boundary value problem it becomes a simple finite element model at loads less than the critical buckling load a preferred buckling configuration is found that is localized along the length in the limit of infinite length this is described as a homoclinic connection in phase space joining the flat equilibrium state to itself the infinite sequence of homoclinic points thus defined embeds within the complex topological structure of a homoclinic tangle within which also appear periodic quasi periodic and chaotic spatial solutions implications in the finite element setting are discussed 1997 john wiley sons ltd

a fast null steering algorithm for linearly constrained adaptive arrays a fast null steering algorithm for adaptive arrays with a look direction constraint is investigated in this algorithm the least mean square lms algorithm is used to adaptively adjust the positions of the array response zeros one after another in a time multiplexed manner to track unknown jammers to ensure that the look direction response and the other zeros remain unchanged when a particular null is being updated the element signals are suitably transformed before the lms updating despite this signal transformation the new algorithm has almost the same implementation complexity as when the lms algorithm is employed directly as only one zero is being adaptively updated at any instant however with each null being independently steered the convergence behavior of the new algorithm is significantly faster and is almost independent of the external noise environment

algorithmically imposed thermodynamic compliance for material models in mechanical simulations using the aim method thermodynamic irreversibility can be imposed on empirical material behaviour by using an appropriate algorithm which takes the path dependence of the degradation process into account this new algorithm algorithmically imposed mechanics aim for algorithmically irreversible mechanics is described and the convergence and unicity of the solutions obtained are proven aim is applicable to a range of mechanical behaviour and is demonstrated to work in conjunction with non local damage with rotating cracks as well as a mixed plastic and damage behaviour copyright c 2015 john wiley sons ltd

the center problem a view from the normal form theory abstract in this work we analyze some aspects of the center problem from the perspective of the normal form theory we provide alternative proofs of some well known results in the case of non vanishing linear part nondegenerate and nilpotent centers moreover some new results are also derived in particular we show that the unique characterization for centers in this situation is the orbital reversibility also we include some examples illustrating that this characterization is no longer valid for the case of null linear part

adaptive zero tracking complemented by lms weight update for guaranteed convergence a low complexity zero tracking algorithm with fast and guaranteed convergence behavior is proposed and investigated the algorithm implements a zero tracking algorithm and a least mean square lms weight update algorithm in parallel with the former adjusting the zeros of the array in a time multiplexed manner to achieve fast asymptotic and tracking behavior while the latter improves the initial transient behavior of the algorithm and guarantees its convergence to the global optimum by comparing their output powers the relative performances of the two component algorithms are monitored and re initialization of one algorithm by the other may occur periodically this gives the algorithm both fast and guaranteed convergence behavior even though the zeros are directly available and the implementation complexity is only two times that for the conventional lms algorithm

performance analysis of a wavelet based generalized sidelobe canceller in this paper we carry out a detailed performance analysis of the recently addressed wavelet based generalized sidelobe canceller gsc which employs a set of p regular m band wavelet filters in the design of the blocking matrix involved we begin our analysis by developing a closed form expression of the output signal to interference plus noise ratio sinr of partially adaptive beamformers with the gsc as the underlying structure under a one jammer or multiple jammer environment this new expression is shown to encompass several previous works as special cases we then examine the relationship between the choices of the parameters p and m in the wavelet based gsc and the corresponding output sinr based on this expression some guidelines for the choices of these parameters can thus be induced to achieve superior performance simulation results are also furnished to justify these suggestions

analytic integrability around a nilpotent singularity abstract in this work it is characterized the analytic integrability problem around a nilpotent singularity of a differential system in the plane under generic conditions

solution method for nonlinear problems with multiple critical points a generalized displacement control method has been proposed for geometrically nonlinear analysis and has been proven to be bery effective by several problems with multiple limit points and snap back points this method can be implemented easily in a general purpose finite element program

a unified set of single step algorithms part 1 general formulation and applications a general algorithm for a single step time marching scheme for use in dynamic or diffusion equations is presented this algorithm is easily programmed in its universal form for all orders of approximation and covers most of the currently used schemes as well as presenting many new possibilities in many cases it presents a computationally advantageous form over conventional procedures this is particularly so when compared with the newmark algorighm and its variants

cyclicity of some symmetric nilpotent centers in this work we present techniques for bounding the cyclicity of a wide class of monodromic nilpotent singularities of symmetric polynomial planar vector fields the starting point is identifying a broad family of nilpotent symmetric fields for which existence of a center is equivalent to existence of a local analytic first integral which unlike the degenerate case is not true in general for nilpotent singularities we are able to relate so called focus quantities to the poincare lyapunov quantities arising from the poincare first return map when we apply the method to concrete examples we show in some cases that the upper bound is sharp our approach is based on computational algebra methods for determining a minimal basis constructed by focus quantities instead of by poincare lyapunov quantities because of the easier computability of the former of the associated polynomial bautin ideal in the parameter space of the family the case in which the bautin ideal is not radical is also treated

a three dimensional finite element formulation for thermoviscoelastic orthotropic media summary this paper is concerned with the development of a numerical algorithm for the solution of the uncoupled quasistatic initial boundary value problem involving orthotropic linear viscoelastic media undergoing thermal and or mechanical deformation the constitutive equations expressed in integral form involving the relaxation moduli are transformed into an incremental algebraic form prior to development of the nite element formulation this incrementalization is accomplished in closed form and results in a recursive relationship which leads to the need of solving a simple set of linear algebraic equations only for the extraction of the nite element solution use is made of a dirichlet prony series representation of the relaxation moduli in order to derive the recursive relationship and thereby eliminate the storage problem that arises when dealing with materials possessing memory three illustrative example problems are included to demonstrate the method 1997 by john wiley sons ltd

bi center problem and bifurcation of limit cycles from nilpotent singular points in z2 equivariant cubic vector fields abstract in this paper bi center problem and bifurcation of limit cycles from nilpotent singular points in z 2 equivariant cubic vector fields are studied first the system is simplified by using some proper transformations and the first five lyapunov constants at a nilpotent singular point are calculated by applying the inverse integrating factor method then sufficient and necessary conditions are obtained for two nilpotent singular points of the system being centers a new perturbation scheme is present to prove the existence of 12 small amplitude limit cycles in cubic z 2 equivariant vector fields which bifurcate from two nilpotent singular points this is a new lower bound of the number of limit cycles bifurcating in such systems

analytic integrable systems analytic normalization and embedding flows abstract in this paper we mainly study the existence of analytic normalization and the normal form of finite dimensional complete analytic integrable dynamical systems more details we will prove that any complete analytic integrable diffeomorphism f x b x f x in c n 0 with b having eigenvalues not modulus 1 and f x o x 2 is locally analytically conjugate to its normal form meanwhile we also prove that any complete analytic integrable differential system x a x f x in c n 0 with a having nonzero eigenvalues and f x o x 2 is locally analytically conjugate to its normal form furthermore we will prove that any complete analytic integrable diffeomorphism defined on an analytic manifold can be embedded in a complete analytic integrable flow we note that parts of our results are the improvement of moser s one in j moser the analytic invariants of an area preserving mapping near a hyperbolic fixed point comm pure appl math 9 1956 673 692 and of poincare s one in h poincare sur l integration des equations differentielles du premier order et du premier degre ii rend circ mat palermo 11 1897 193 239 these results also improve the ones in xiang zhang analytic normalization of analytic integrable systems and the embedding flows j differential equations 244 2008 1080 1092 in the sense that the linear part of the systems can be nonhyperbolic and the one in n t zung convergence versus integrability in poincare dulac normal form math res lett 9 2002 217 228 in the way that our paper presents the concrete expression of the normal form in a restricted case

hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields we provide normal forms and the global phase portraits in the poincare disk for all hamiltonian nilpotent centers of linear plus cubic homogeneous planar polynomial vector fields

invariant algebraic curves of large degree for quadratic system in this paper we present for the first time examples of algebraic limit cycles and saddle loops of degree greater than 4 for planar quadratic systems in particular we give examples of algebraic limit cycles of degree 5 and 6 and algebraic saddle loops of degree 3 and 5 surrounding a strong focus we also give an example of an invariant algebraic curve of degree 12 for which the quadratic system has no darboux integrating factors or first integrals

tracing post limit point paths with reduced basis technique abstract a reduced basis technique and a problem adaptive computational algorithm are presented for predicting the post limit point paths of structures in the proposed approach the structure is discretized by using displacement finite element models the nodal displacement vector is expressed as a linear combination of a small number of vectors and a rayleigh ritz technique is used to approximate the finite element equations by a small system of nonlinear algebraic equations to circumvent the difficulties associated with the singularity of the stiffness matrix at limit points a constraint equation defining a generalized arc length in the solution space is added to the system of nonlinear algebraic equations and the rayleigh ritz approximation functions or basis vectors are chosen to consist of a nonlinear solution of the discretized structure and its various order derivatives with respect to the generalized arc length the potential of the proposed approach and its advantages over the reduced basis load control technique are outlined the effectiveness of the proposed approach is demonstrated by means of numerical examples of structural problems with snap through and snap back phenomena

a characterization of centres via first integrals on considere l existence d une integrale premiere lisse et l existence d une mesure invariante equivalente a la mesure de lebesgue pour des systemes differentiels dans le plan

an adaptive sub incremental strategy for the solution of homogenization based multi scale problems abstract in this contribution several schemes for the solution of homogenization based multi scale constitutive problems undergoing finite strains with inelastic material behavior are investigated these schemes are aimed at improving the robustness and efficiency of the newton raphson method in the multilevel finite element ml fem framework an adaptive sub incremental strategy is proposed for the discrete representative volume element rve boundary value problem the procedure is able to ensure the convergence of the solution algorithm in the presence of several sources of non linearity and obtains improved initial guesses for the newton raphson scheme in the ml fem framework the enlargement of the convergence bowl of the newton raphson procedure at the micro scale allows larger macroscopic deformation gradients to be prescribed and significantly reduces the overall computational cost of ml fem analyses the proposed strategy preserves the quadratic rates of asymptotic convergence that characterize the newton raphson scheme at the macroscopic level numerical examples of both micro scale and two scale finite element simulations are presented to demonstrate the improved robustness and efficiency of the solution procedures proposed

solution of linear elastodynamics problems with space time finite elements on structured and unstructured meshes abstract a new implicit approach for the solution of linear elastodynamics problems on structured and unstructured meshes with space time finite elements is suggested new weak formulations are based on time continuous tcg and discontinuous tdg galerkin methods it was shown that for structured meshes the new tcg method has a higher order of accuracy by a factor of two than that of the standard tcg method at the same number of degrees of freedom the accuracy of the new tcg method is one order higher than the accuracy of the standard tdg method the introduction of new weighting functions for the weak formulations of the tcg and tdg methods allows control of the high frequency behavior without degradation of accuracy of the methods a variable number of elements in the time direction as well as a variable order of polynomial time approximations of finite elements for time slabs allows the implementation of a coupled space time adaptive procedure using structured or unstructured meshes numerical examples for 1 d problems demonstrate the effectiveness of the technique

analytic nilpotent centers as limits of nondegenerate centers revisited abstract we prove that all the nilpotent centers of planar analytic differential systems are limit of centers with purely imaginary eigenvalues and consequently the poincare liapunov method to detect centers with purely imaginary eigenvalues can be used to detect nilpotent centers

analytic integrability for some degenerate planar vector fields abstract in this paper we study the analytic integrability of degenerate vector fields of the form y 3 2 a x 3 y x 5 3 a x 2 y 2 around the origin for these vector fields it is proved that integrability does not imply formal orbital equivalence to the hamiltonian leading part moreover it is shown the existence of a system in this class which has a center but is neither analytically integrable nor formal orbital reversible

algebraic and topological classification of the homogeneous cubic vector fields in the plane tsutomu date and masao iri in di gave an algebraic classification of systems i p x y i q x y where p and q are homogeneous polynomials of degree 2 for this they used the classification of the binary cubic forms and also the simultaneous classification of a linear binary form and a cubic binary form given by the algebraic invariant theory we begin by doing a similar study for systems p x y q x y where p and q are homogeneous polynomials of degree three i e cubic systems the classification s theorem of such systems is based on the classification of fourth order binary forms gurevich in gu did the classification of fourth order binary forms on the field of complex numbers since we did not find the classification on the real domain we adapt gurevich s proof to obtain it in section 1 we give some definitions and preliminary results while in section 2 we give the theorem of classification of fourth order binary forms on the real domain the method used in the proof caley s method let us obtain canonical forms of the fourth order binary forms and the algebraic characteristics section 3 is devoted to obtaining the algebraic classification of systems p x y j q x y where p and q are homogeneous polynomials of degree 3 given an arbitrary system x p q with p and q homogeneous polynomials of degree 3 we can know the equivalence class at which it belongs through the algebraic characteristics in section 4 we study the phase portraits of systems 1 p x y j q x y where p and q are homogeneous polynomials of degree n and p and q have no common factor such systems have been studied by j argemi in a here we give a shorter new proof of his results by using

existence of inverse integrating factors and lie symmetries for degenerate planar centers abstract we prove that any possibly degenerate center of an analytic planar system admits a c inverse integrating factor and a c lie symmetry in a neighborhood of the singularity we also show that there exists an analytic degenerate center for which any c inverse integrating factor is flat at the singular point and that a sufficient condition for the existence of an analytic inverse integrating factor is the existence of an analytic first integral

algebraic particular integrals integrability and the problem of the center in this work we clarify the global geometrical phenomena corresponding to the notion of center for plane quadratic vector fields we first show the key role played by the algebraic particular integrals of degrees less than or equal to three in the theory of the center these curves control the changes in the systems as parameters vary the bifurcation diagram used to prove this result is realized in the natural topological space for the situation considered namely the real four dimensional projective space next we consider the known four algebraic conditions for the center for quadratic vector fields one of them says that the system is hamiltonian a condition which has a clear geometric meaning we determine the geometric meaning of the remaining other three algebraic conditions i ii iii

continuous and discontinuous galerkin methods with finite elements in space and time for parallel computing of viscoelastic deformation abstract new non symmetric variational and discretized formulations with space time finite elements are proposed for viscoelastic problems based on the continuous galerkin method cgm and discontinuous galerkin method dgm viscoelastic behaviour is described by the three parameter malvern model which is represented by means of internal variables it allows to use only differential equations for the constitutive equations instead of integrodifferential ones the variational formulation reduces to two types of equations for total displacements and internal displacements internal variables namely to the equilibrium equation and the evolution equation for the internal displacements which are fulfilled in the weak form using continuous trial functions a continuous space time finite element formulation is obtained with simultaneous discretization in space and time subdividing the total observation time interval into time slabs and introducing discontinuous trial functions being continuous within time slabs and allowing jumps across interfaces a more general discontinuous finite element formulation is obtained the difference between these two formulations for one time slab consists in the satisfaction of initial conditions which are fulfilled exactly for the continuous formulation and in a weak form for the discontinuous case the proposed approach has some very attractive advantages with respect to semidiscretization methods regarding the possibility of adaptive space time refinements and parallel processing on mimd parallel computers the considered numerical examples show the effectiveness of simultaneous space time finite element calculations and a high convergence rate for adaptive refinement numerical efficiency is an advantage of dgm in comparison with cgm for discontinuously changing e g piecewise constant boundary conditions in time

on the performance of the generalized sidelobe canceller in coherent situations the convergence rate for the adaptive weights to reach the optimum value in an adaptive array system depends on the eigenvalue spread ratio of the autocovariance matrix how the eigenvalue spread ratio in a generalized sidelobe canceller gsc is affected by the various parameters is studied expressions for the output power of the gsc in coherent situations are derived and numerical results are included

z2 equivariant linear type bi center cubic polynomial hamiltonian vector fields abstract we study the global dynamical behavior of z 2 equivariant cubic hamiltonian vector fields with a linear type bi center at 1 0 by using a series of symbolic computation tools we obtain all possible phase portraits of these z 2 equivariant hamiltonian systems

the problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems abstract in this work we study the centers of planar analytic vector fields which are limit of linear type centers it is proved that all the nilpotent centers are limit of linear type centers and consequently the poincare liapunov method to find linear type centers can be also used to find the nilpotent centers moreover we show that the degenerate centers which are limit of linear type centers are also detectable with the poincare liapunov method

a critical comparison of nonlocal and gradient enhanced softening continua continuous models of material degradation may cease to produced meaningful results in the presence of high strain gradients these gradients may occur for instance in the propagation of waves with high wave numbers and at stress concentrators adding nonlocal or gradient terms to the constitutive modelling may enhance the ability of the models to describe such situations the effect of adding nonlocal or gradient terms and the relation between these enhancements are examined in a continuum damage setting a nonlocal damage model and two different gradient damage models are considered in one of the gradient models higher order deformation gradients enter the equilibrium equations explicitly while in the other model the gradient influence follows in a more implicit way from an additional partial differential equation the latter implicit gradient formulation can be rewritten in the integral format of the nonlocal model and can therefore be regarded as truly nonlocal this is not true for the explicit formulation in which the nonlocality is limited to an infinitesimal volume this fundamental difference between the formulations results in quite different behaviour in wave propagation localisation and at crack tips this is shown for the propagation of waves in the models their localisation properties and the behaviour at a crack tip the responses of the nonlocal model and the implicit gradient model agree remarkably well in these situations while the explicit gradient formulation shows an entirely different and sometimes nonphysical response

gradient damage models toward full scale computations abstract the description of localisation and structural failure through local damage constitutive laws leads to ill posed problems to retrieve a well posed problem the material state is described through the gradients of damage in addition to the strain and the damage under some assumptions it is shown that these gradient laws can be cast into a variational formulation its numerical treatment is reduced to the design of a mixed finite element so that algorithms such as newton s method and path following techniques are still available possible convergence difficulties related to the reduction of the damage band width and the appearance of micro instabilities are removed thanks to the design of a new class of brittle laws finally numerical applications show the convergence with mesh refinement the compatibility with coarser approaches such as griffith s theory and cohesive crack models the robustness in case of unstable multi cracking the applicability to full scale 3d situations and the physical relevance compared to experimental data

the output sinr of the linearly constrained beamformer the authors derive expressions of the output signal to interference plus noise ratio sinr of the linearly constrained narrowband beamformer in noncoherent situations using a vector approach numerical results are included

hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields abstract we provide normal forms and the global phase portraits in the poincare disk for all the hamiltonian linear type centers of linear plus cubic homogeneous planar polynomial vector fields

weierstrass integrability in lienard differential systems in this work we study the lienard differential systems that admit a weierstrass first integral or a weierstrass inverse integrating factor

bifurcation diagrams for hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields as a natural continuation of the work done in 7 we provide the bifurcation diagrams for the global phase portraits in the poincare disk of all the hamiltonian linear type centers of linear plus cubic homogeneous planar polynomial vector fields

an arc length method including line searches and accelerations this paper describes a method for introducing line searches into the arc length solution procedure such line searches may be used at each iteration to calculate an optimum scalar step length which scales the normal iterative vector in practice a loose tolerance is provided so that on many iterations the line searches are avoided however on difficult iterations the line searches are shown to lead to a substantial improvement in the convergence characteristics a simple single parameter acceleration is also developed using line search concepts the new arc length method is applied to both the geometrically nonlinear analysis of shallow shells and the materially nonlinear analysis of reinforced concrete beams and slabs significant improvements are demonstrated in relation to the standard arc length method

local bifurcation of limit cycles and integrability of a class of nilpotent systems of differential equations we study the analytic system of differential equations in the plane which can be written in a suitable coordinates system as email protected email protected email protected i 0 f q p 2 i s where p email protected n p 0 email protected n and f i p i q i t are quasi homogeneous vector fields of type t p q and degree i with f q p y 0 t and q q p 2 s 1 0 0 the origin of this system is a nilpotent and monodromic isolated singular point we show the taylor expansion of the return map near the origin for this system which allow us to generate small amplitude limit cycles bifurcating from the critical point also as an application of the theoretical procedure we characterize the centers and we generate limit cycles of small amplitude from the origin of several families finally we give a new family integrable analytically which includes the centers of the systems studied

a new algorithm for determining the monodromy of a planar differential system abstract we give a new algorithmic criterium that determines wether an isolated degenerate singular point of a system of differential equations on the plane is monodromic this criterium involves the conservative and dissipative parts associated to the edges and vertices of the newton diagram of the vector field

adaptive beam forming using a cascade configuration a new technique for adaptive beam forming based on the davies cascade array configuration 11 is presented first of all it is shown that an n element linear array can be reconfigured as a number of subarrays of two elements each this two element array is capable of steering one null in an arbitrary direction while maintaining a desired gain in some other prespecified look direction to adaptively perform this function at any cascade stage the inverse of a 2 2 correlation matrix of the signal vector at a subarray is computed and substituted in the expression for the constrained optimum weight vector similar processing is performed at subsequent stages of the cascade configuration at each stage of adaptation a noise source contributing maximum power at that stage is nulled out simulation studies carried out verify the validity of this approach and demonstrate the fast convergence property of the proposed technique