finite element methods for active contour models and balloons for 2 d and 3 d images the use of energy minimizing curves known as snakes to extract features of interest in images has been introduced by kass witkin and terzopoulos 1987 a balloon model was introduced by cohen 1991 as a way to generalize and solve some of the problems encountered with the original method a 3 d generalization of the balloon model as a 3 d deformable surface which evolves in 3 d images is presented it is deformed under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential we also show properties of energy minimizing surfaces concerning their relationship with 3 d edge points to solve the minimization problem for a surface two simplified approaches are shown first defining a 3 d surface as a series of 2 d planar curves then after comparing finite element method and finite difference method in the 2 d problem we solve the 3 d model using the finite element method yielding greater stability and faster convergence this model is applied for segmenting magnetic resonance images

tracking deformable objects in the plane using an active contour model the problems of segmenting a noisy intensity image and tracking a nonrigid object in the plane are discussed in evaluating these problems a technique based on an active contour model commonly called a snake is examined the technique is applied to cell locomotion and tracking studies the snake permits both the segmentation and tracking problems to be simultaneously solved in constrained cases a detailed analysis of the snake model emphasizing its limitations and shortcomings is presented and improvements to the original description of the model are proposed problems of convergence of the optimization scheme are considered in particular an improved terminating criterion for the optimization scheme that is based on topographic features of the graph of the intensity image is proposed hierarchical filtering methods as well as a continuation method based on a discrete sale space representation are discussed results for both segmentation and tracking are presented possible failures of the method are discussed

difference formulas for the surface laplacian on a triangulated surface abstract different approximating expressions for the surface laplacian operator on a triangulated surface are derived they are evaluated on a triangulated spherical surface for which the analytical expression of the surface laplacian is known it is shown that in order to obtain accurate results due care has to be taken of irregularities present in the triangulation grid if this is done the approximation will equal the performance of an expression based on least squares which can be derived next the different approximations obtained are used as a regularization operator in the solution of an ill posed inverse problem in electrical volume conduction it is shown that in this application a crude approximation to the surface laplacian suffices

a melnikov method for homoclinic orbits with many pulses we present an extension of the melnikov method which can be used for ascertaining the existence of homoclinic and heteroclinic orbits with many pulses in a class of near integrable systems the melnikov function in this situation is the sum of the usual melnikov functions evaluated with some appropriate phase delays we show that a nonfolding condition which involves the logarithmic derivative of the melnikov function must be satisfied in addition to the usual transversality conditions in order for homoclinic orbits with more than one pulse to exist

geometry and chaos near resonant equilibria of 3 dof hamiltonian systems in this paper we study the dynamics near resonant elliptic equilibria in three degree of freedom hamiltonian systems the resonances we consider have multiplicity two and the corresponding local normal form for the equilibrium is integrable at cubic order we prove the existence of families of 3 tori and whiskered 2 tori with nearby chaotic dynamics in the quartic normal form the whiskers of the 2 tori intersect in a non trivial way giving rise to multi pulse homoclinic and heteroclinic connections these connections survive in the full system as orbits homoclinic to invariant 3 spheres

dynamics of 4d symplectic maps near a double resonance abstract we study the dynamics of a family of 4 d symplectic mappings near a doubly resonant elliptic fixed point we derive and discuss algebraic properties of the resonances required for the analysis of a takens type normal form in particular we propose a classification of the double resonances adapted to this problem including cases of both strong and weak resonances around a weak double resonance a junction of two resonances of two different orders both being larger than 4 the dynamics can be described in terms of a simple in general non integrable hamiltonian model the non integrability of the normal form is a consequence of the splitting of the invariant manifolds associated with a normally hyperbolic invariant cylinder we use a 4 d generalisation of the standard map in order to illustrate the difference between a truncated normal form and a full 4 d symplectic map we evaluate numerically the volume of a 4 d parallelotope defined by 4 vectors tangent to the stable and unstable manifolds respectively in good agreement with the general theory this volume is exponentially small with respect to a small parameter and we derive an empirical asymptotic formula which suggests amazing similarity to its 2 d analog different numerical studies point out that double resonances play a key role to understand arnold diffusion this paper has to be seen also as a first step in this direction

continuous preference logic for system evaluation in this paper we investigate mathematical models that are suitable for modeling decisions in the area of system evaluation comparison and selection our interest is focused on soft computing models that can be directly related to observable properties of human reasoning and have a record of use in system evaluation practice we analyze various approaches to defining andness and orness and use a generalized conjunction disjunction gcd to build compound preference logic functions and logic models for system evaluation we also present applications of the continuous preference logic in decision models based on the lsp method

geometric phases reduction and lie poisson structure for the resonant three wave interaction hamiltonian lie poisson structures of the three wave equations associated with the lie algebras su 3 and su 2 1 are derived and shown to be compatible poisson reduction is performed using the method of invariants and geometric phases associated with the reconstruction are calculated these results can be applied to applications of nonlinear waves in for instance nonlinear optics some of the general structures presented in the latter part of this paper are implicit in the literature our purpose is to put the three wave interaction in the modern setting of geometric mechanics and to explore some new things such as explicit geometric phase formulas as well as some old things such as integrability in this context

horseshoes in two degree of freedom hamiltonian systems with saddle centers we consider a class of two degree of freedom hamiltonian systems which have saddle centers with homoclinic orbits and do not take the form of small perturbations of integrable systems using a melnikov type global perturbation technique we present a condition under which orbits transversely homoclinic to periodic orbits exist and horseshoes are created on surfaces of energy level near the saddle centers we apply the theory to systems with potentials and give concrete examples in particular we can detect the presence of horseshoes in a class of systems to which previous results did not apply

on reduction of two degrees of freedom hamiltonian systems by an s1 action and so0 1 2 as a dynamical group reduction by an s1 action is a method of finding periodic solutions in hamiltonian systems which is known rather as the method of averaging such periodic solutions can be reconstructed as s1 orbits by pulling back the critical points of an associated reduced hamiltonian on a reduced phase space along the reduction for hamiltonian systems of two degrees of freedom a geometric setting of the reduction is already accomplished in the case where the reduced phase space is a two sphere in the euclidean space r3 and the reduced hamilton s equations of motion are euler s equations this article deals with the case where the reduced phase space will be a two hyperboloid in the three minkowski space and the reduced hamilton s equations of motion will be euler s equations with respect to the lorentz metric this reduction is associated with su 1 1 symplectic action on the phase space r4 as a consequence of this association the reduced hamiltonian system proves to admit a dynamical group so0 1 2 a w

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

orbits homoclinic to resonances with an application to chaos in a model of the forced and damped sine gordon equation abstract in this paper we develop new global perturbation techniques for detecting homoclinic and heteroclinic orbits in a class of four dimensional ordinary differential equations that are perturbations of completely integrable two degree of freedom hamiltonian systems our methods are fundamentally different than other global perturbation methods e g standard melnikov theory in that we are seeking orbits homoclinic and heteroclinic to fixed points that are created in a resonance resulting from the perturbation our methods combine the higher dimensional melnikov theory with geometrical singular perturbation theory and the theory of foliations of invariant manifolds we apply our methods to a modified model of the forced and damped sine gordon equation developed by bishop et al we give explicit conditions in terms of the system parameters for the model to possess a symmetric pair of homoclinic orbits to a fixed point of saddle focus type chaotic dynamics follow from a theorem of silnikov this provides a mechanism for chaotic dynamics geometrically similar to that observed by bishop et al namely a random jumping between two spatially dependent states with an intermediate passage through a spatially independent state however in order for this type of silnikov dynamics to exist we require a different and unphysical type of damping compared to that used by bishop et al

reduction of the semisimple 1 1 resonance the method of averaging is often used in hamiltonian systems of two degrees of freedom to find periodic orbits such periodic orbits can be reconstructed from the critical points of an associated reduced hamiltonian on a reduced space this paper details the construction of the reduced space and the reduced hamiltonian for the semisimple 1 1 resonance case the reduced space will be a 2 sphere in r3 and the reduced differential equations will be euler s equations restricted to this sphere the orbit projection from the energy surface in phase space to this sphere will be the hopf map the results of the paper are related to problems in physics on degeneracies due to symmetries of classical two dimensional harmonic oscillators and their quantum analogues for the hydrogen atom

multi dimensional homoclinic jumping and the discretized nls equation we consider a class of dynamical systems that arise frequently in multi mode truncations and discretizations of partial differential equations including the perturbed nls we develop a general method to detect the existence of multi pulse solutions that are doubly asymptotic to an invariant manifold with two different time scales we use our method together with some recent results of li and mclaughlin to show the existence of several families of multi pulse orbits for the ablowitz ladik discretization of the perturbed nls these orbits include n pulse heteroclinic orbits and n pulse silnikov type orbits for arbitrarily large n

orbits homoclinic to resonances the hamiltonian case abstract in this paper we develop methods to show the existence of orbits homoclinic or heteroclinic to periodic orbits hyperbolic fixed points or combinations of hyperbolic fixed points and or periodic orbits in a class of two degree of freedom integrable hamiltonian systems subject to arbitrary hamiltonian perturbations our methods differ from previous methods in that the invariant sets periodic orbits fixed points are created and become hyperbolic as a result of the interaction of the perturbation with a resonance in the unperturbed system this results in a very degenerate situation that requires a combination of geometric singular perturbation theory higher dimensional melnikov type methods and transversality theory we establish a simple energy phase criterion which gives a fairly complete picture of the complex dynamics associated with orbits homoclinic to the resonance we apply our methods to a two mode truncation of the driven nonlinear schrodinger equation first studied by bishop et al in this example we show that as the energy is increased at resonance orbits homoclinic to hyperbolic periodic orbits are created in pairs in a global bifurcation that is best described as a saddle node bifurcation of homoclinic orbits

geometry of the bifurcations of the normalized reduced henon heiles family this paper deals with the global geometry of the bifurcations of a family of hamiltonian functions that arises from normalizing the henon heiles family to fourth degree terms and then performing a reduction this gives a geometric explanation of the bifurcation diagram for the main resonance in the model of axisymmetric galaxies of braun and verhulst

universal homoclinic bifurcations and chaos near double resonances we study the dynamics near the intersection of a weaker and a stronger resonance inn degree of freedom nearly integrable hamiltonian systems for a truncated normal form we show the existence of n 2 dimensional hyperbolic invariant tori whose whiskers intersect inmultipulse homoclinic orbits with large splitting angles the homoclinic obits are doubly asymptotic to solutions that diffuse across the weak resonance along the strong resonance we derive a universalhomoclinic tree that describes the bifurcations of these orbits which are shown to survive in the full normal form we illustrate our results on a three degree of freedom mechanical system

normal forms for driven surface waves boundary conditions symmetry and genericity abstract the parametric excitation of standing waves in a vertically oscillated fluid can be studied by analyzing the period doubling bifurcation in the associated stroboscopic map when the fluid container has symmetry the stroboscopic map will exhibit this symmetry and this in turn significantly affects the structure of the bifurcation problem for both square and circular containers the normal forms appropriate to the reduced maps for the critical mode amplitudes are discussed the experiments of simonelli and gollub with square containers strongly suggest that the effective symmetry of the problem is larger than the obvious geometric symmetry of the boundaries for the ideal fluid model of benjamin and ursell with neumann boundary conditions nbc one can show that the problem does indeed have a larger symmetry because it embeds in a model on a larger domain with periodic boundary conditions pbc the original nbc are then realized as a symmetry constraint on the solutions of this extended model the additional symmetries introduced in this way lead to a large number of effects that would otherwise be non generic including critical eigenspaces carrying reducible representations of and reduced maps on these eigenspaces that have symmetries larger than these extra symmetries relate in phase and out of phase mixed modes and lead to new branches to pure modes the case of circular geometry is also discussed as it does not allow this extension to pbc and thus provides an instructive contrast with the subtleties found for square geometry

weak monotonicity of lehmer and gini means we analyze directional monotonicity of several mixture functions in the direction 1 1 1 called weak monotonicity our particular focus is on power weighting functions and the special cases of lehmer and gini means we establish limits on the number of arguments of these means for which they are weakly monotone these bounds significantly improve the earlier results and hence increase the range of applicability of gini and lehmer means we also discuss the case of affine weighting functions and find the smallest constant which ensures weak monotonicity of such mixture functions

multi bump orbits homoclinic to resonance bands we establish the existence of several classes of multi bump orbits homoclinic to resonance bands for completely integrable hamiltonian systems subject to small amplitude hamiltonian or dissipative perturbations each bump is a fast excursion away from the resonance band and the bumps are interspersed with slow segments near the resonance band the homoclinic orbits which include multi bump silnikov orbits connect equilibria and periodic orbits in the resonance band the main tools we use in the existence proofs are the exchange lemma with exponentially small error and the existence theory of orbits homoclinic to resonance bands which make only one fast excursion away from the resonance bands

multi pulse jumping orbits and homoclinic trees in a modal truncation of the damped forced nonlinear schro dinger equation abstract in this paper we prove the existence of multi pulse orbits homoclinic to a slow manifold in a two mode truncation of the damped forced nonlinear schrodinger equation first suggested by bishop et al these orbits are jumping i e the corresponding solutions keep switching in time between neighborhoods of the two charateristic breathers of the integrable limit in the case of no damping we find multi pulse smale horseshoes in the two mode model while in the dissipative case we establish the existence of structurally stable multi pulse heterolinic connections between two unstable equilibria the orbits we construct are not amenable to melnikov type perturbation methods in both the hamiltonian and the dissipative case we find homoclinic trees which describe the repeated bifurcations of multi pulse solutions to illustrate the theoretical predictions we also present visualizations of these complicated structures

weighted compensative logic with adjustable threshold andness and orness the threshold andness is a border between soft and hard partial conjunction similarly the threshold orness is a border between soft and hard partial disjunction this paper presents a weighted compensative logic based on aggregators that use adjustable threshold andness and orness the adjustability of threshold andness orness is a new degree of freedom in weighted logics which is suitable for increasing the precision of evaluation criteria developed by evaluation experts we investigate the distribution of threshold andness and present a new form of interpolative aggregators that provide adjustable threshold andness and orness our goal is to use a new verbalized approach based on decomposing the perception of overall importance for designing the generalized conjunction disjunction gcd aggregators the verbalized approach helps specify parameters that affect both the formal logic properties and the semantic properties of gcd facilitating the use of soft computing evaluation logic and corresponding evaluation methods

using the extended melnikov method to study the multi pulse global bifurcations and chaos of a cantilever beam the aim of this paper is to investigate the multi pulse global bifurcations and chaotic dynamics for the nonlinear non planar oscillations of a cantilever beam subjected to a harmonic axial excitation and two transverse excitations at the free end by using an extended melnikov method in the resonant case first the extended melnikov method for studying the shilnikov type multi pulse homoclinic orbits and chaos in high dimensional nonlinear systems is briefly introduced in the theoretical frame then this method is utilized to investigate the shilnikov type multi pulse homoclinic bifurcations and chaotic dynamics for the nonlinear non planar oscillations of the cantilever beam how to employ this method to analyze the shilnikov type multi pulse homoclinic bifurcations and chaotic dynamics of high dimensional nonlinear systems in engineering applications is demonstrated through this example finally the results of numerical simulation are given and also show that the shilnikov type multi pulse chaotic motions can occur for the nonlinear non planar oscillations of the cantilever beam which verifies the analytical prediction

deformable triangular surfaces using fast 1 d radial lagrangian dynamics segmentation of 3 d mr and ct images of the wrist we developed a new triangulated deformable surface model which is used to detect the boundary of the bones in three dimensional magnetic resonance mr and computed tomography ct images of the wrist this surface model is robust to initialization and provides wide geometrical coverage and quantitative power the surface is deformed by applying one dimensional 1 d radial lagrangian dynamics for initialization a tetrahedron is placed within the bone to be segmented this initial surface is inflated to a binary approximation of the boundary during inflation the surface is refined by the addition of vertices after the surface is fully inflated a detailed accurate boundary detection is obtained by the application of radial scale space relaxation in this optimization stage the image intensity is filtered with a series of 1 d second order gaussian filters the resolution of the triangulated mesh is adapted to the width of the gaussian filter to maintain the coherence between the vertices a resampling technique is applied which is based on collapsing and splitting of edges we regularized the triangulated mesh by a combination of volume preserving vertex averaging and equi angulation of edges in this paper we present both qualitative and quantitative results of the surface segmentations in eight mr and ten ct images

dynamics near a symmetric hopf bifurcation on considere les effets d une petite perturbation de rupture de symetrie sur un systeme d equations differentielles pres d un point de bifurcation de hopf ou le systeme non perturbe a une symetrie o 2 on montre qu il existe des bifurcations secondaires des 2 tores invariants des solutions et que les flots sur les tores peuvent etre quasi periodiques ou faiblement resonnants dependant de la taille de la perturbation

model based deformable surface finding for medical images describes a new global shape parameterization for smoothly deformable three dimensional 3 d objects such as those found in biomedical images whose diversity and irregularity make them difficult to represent in terms of fixed features or parts this representation is used for geometric surface matching to 3 d medical image data such as from magnetic resonance imaging mri the parameterization decomposes the surface into sinusoidal basis functions four types of surfaces are modeled tori open surfaces closed surfaces and tubes this parameterization allows a wide variety of smooth surfaces to be described with a small number of parameters extrinsic model based information is incorporated by introducing prior probabilities on the parameters surface finding is formulated as an optimization problem results of the method applied to synthetic images and 3 d medical images of the heart and brain are presented

heteroclinic dynamics in the nonlocal parametrically driven nonlinear schrodinger equation faraday waves are described under appropriate conditions by a damped nonlocal parametrically driven nonlinear schrodinger equation as the strength of the applied forcing increases this equation undergoes a sequence of transitions to chaotic dynamics the origin of these transitions is explained using a careful study of a two mode galerkin truncation and linked to the presence of heteroclinic connections between the trivial state and spatially periodic standing waves these connections are associated with cascades of gluing and symmetry switching bifurcations such bifurcations are located in the partial differential equations as well

mel nikov analysis of numerically induced chaos in the nonlinear schro dinger equation abstract certain hamiltonian discretizations of the periodic focusing nonlinear schrodinger equation nls have been shown to be responsible for the generation of numerical instabilities and chaos in this paper we undertake a dynamical systems type of approach to modeling the observed irregular behavior of a conservative discretization of the nls using heuristic mel nikov methods the existence of a pair of isolated homoclinic orbits is indicated for the perturbed system the structure of the persistent homoclinic orbits that are predicted by the mel nikov theory possesses the same features as the wave form observed numerically in the perturbed system after the onset of chaotic behavior and appears to be the main structurally stable feature of this type of chaos the mel nikov analysis implemented in the pde context appears to provide relevant qualitative information about the behavior of the pde in agreement with the numerical experiments in a neighborhood of the persistent homoclinic orbits the existence of a horseshoe is investigated and related with the onset of chaos in the numerical study

oscillatory convection in a rotating layer abstract the stability of travelling and standing rolls in oscillatory rotating convection is considered from the point of view of equivariant bifurcation theory to study stability with respect to oblique perturbations the problem is formulated on a rotating rhombic lattice all primary solution branches with maximal isotropy are determined together with their stability properties using a truncation of the most general equivariant vector field at third order in addition as many as seven branches of temporally periodic or quasiperiodic solutions with submaximal isotropy may be present instabilities analogous to the kuppers lortz instability of steady rolls in rotating convection are uncovered for both travelling rolls and for standing rolls these instabilities are triggered by the formation of a heteroclinic orbit connecting two travelling roll states or two sets of standing rolls with different wave vectors conditions are given for the formation and asymptotic stability of a structurally stable heteroclinic cycle connecting four travelling roll states the results are compared with recent studies of oscillatory patterns on a rotating square lattice and on a nonrotating rhombic lattice

homoclinic orbits for a perturbed nonlinear schrodinger equation in recent years there have been extensive studies on the existence of homoclinic orbits for nearly integrable hamiltonian pdes which are closely related to chaos in this work we consider a perturbed nonlinear schrodinger equation for u even and periodic in x the diffusion ieuxx is an unbounded perturbation term when the diffusion is replaced by its bounded fourier truncation li mclaughlin shatah and wiggins 26 proved the existence of homoclinic orbits for the perturbed equation the method was based on invariant manifolds foliations and melnikov analysis the unboundedness of the diffusion prevents the equation from being solved for t 0 for general initial values and destroys some geometric structures however we overcome these difficulties and prove the existence of homoclinic orbits for the diffusively perturbed nls 2000 john wiley sons inc

extension of bivariate means to weighted means of several arguments by using binary trees averaging aggregation functions are valuable in building decision making and fuzzy logic systems and in handling uncertainty some interesting classes of averages are bivariate and not easily extended to the multivariate case we propose a generic method for extending bivariate symmetric means to n variate weighted means by recursively applying the specified bivariate mean in a binary tree construction we prove that the resulting extension inherits many desirable properties of the base mean and design an efficient numerical algorithm by pruning the binary tree we show that the proposed method is numerically competitive to the explicit analytical formulas and hence can be used in various computational intelligence systems which rely on aggregation functions

computation of normal forms for high dimensional non linear systems and application to non planar non linear oscillations of a cantilever beam a new and efficient computation of the normal forms is developed in this paper for high dimensional non linear systems and the computational method is applied to non planar non linear oscillations of a cantilever beam the method developed here has the advantage of directly calculating the coefficients of the normal forms and the associated near identity non linear transformations for three different cases that is 1 the case of two pairs of pure imaginary eigenvalues 2 the case of one non semisimple double zero and a pair of pure imaginary eigenvalues and 3 the case of two non semisimple double zero eigenvalues the final partial differential equations of various resonant cases appear in a canonical form whose solutions can be conveniently obtained using polynomial equations with the aid of the maple software a symbolic program for computing the normal forms of high dimensional non linear systems is given comparing the method developed here with other methods of computing the normal forms it is understood that we may respectively obtain the normal forms the coefficients of the normal forms and the associated near identity non linear transformations for three resonant cases by using a same main maple symbolic program moreover the method is easy to apply to engineering problems the normal forms of the averaged equations and their coefficients for non planar non linear oscillations of the cantilever beam under combined parametric and forcing excitations are calculated for two resonant cases

on averaging reduction and symmetry in hamiltonian systems abstract the existence of periodic orbits for hamiltonian systems at low positive energies can be deduced from the existence of nondegenerate critical points of an averaged hamiltonian on an associated reduced space alternatively in classical kinetic plus potential energy hamiltonians the existence of such orbits can often be established by elementary geometrical arguments the present paper unifies the two approaches by exploiting discrete symmetries including reversing diffeomorphisms that occur in a given system the symmetries are used to locate the periodic orbits in the averaged hamiltonian and thence in the original hamiltonian when the periodic orbits are continued under perturbations admitting the same symmetries in applications to the henon heiles hamiltonian it is illustrated how higher order averaging can sometimes be used to overcome degeneracies encountered at first order

importance weighting and andness control in de morgan dual power means and owa operators abstract importance weighted aggregation plays a central role in utilization of information resources for information retrieval and fusion pattern and object recognition decision making etc a class of aggregation operators of particular interest is formed by the aggregation operators between the min minimum and the max maximum the so called averaging operators two key issues in the choice of such an operator for a given application are the kind of importance weighting and the andness minness of the operator two main kinds of importance weighting for such operators namely multiplicative and implicative are proposed and discussed the purpose of this paper is to facilitate the choice and application of such operators through providing a systematization of their classes according to their behavior and equipping some classical averaging operators namely the power means and the owa operators with importance weighting schemes and direct parametric andness control for both kinds of importance weighting for increased efficacy and for symmetric behavior by andness and orness 1 andness at the same degree of both measures the two classes of averaging operators are applied in a de morgan dual form the main issue in the choice of underlying the classical averaging operator appears to be the computational cost of its application

normal forms for three dimensional parametric instabilities in ideal hydrodynamics we derive and analyze several low dimensional hamiltonian normal forms describing system symmetry breaking in ideal hydrodynamics the equations depend on two parameters where is the strength of a system symmetry breaking perturbation and is a detuning parameter in many cases the resulting equations are completely integrable and have an interesting hamiltonian structure our work is motivated by three dimensional instabilities of rotating columnar fluid flows with circular streamlines such as the burger vortex subjected to precession elliptical distortion or off center displacement

n pulse homoclinic orbits in perturbations of resonant hamiltonian systems in this paper we develop an analytical method to detect orbits doubly asymptotic to slow manifolds in perturbations of integrable two degree of freedom resonant hamiltonian systems our energy phase method applies to both hamiltonian and dissipative perturbations and reveals families of multi pulse solutions which are not amenable to melnikov type methods as an example we study a two mode approximation of the nonlinear nonplanar oscillations of a parametrically forced inextensional beam in this problem we find unusually complicated mechanisms for chaotic motions and verify their existence numerically

algorithms for refining triangular grids suitable for adaptive and multigrid techniques two general algorithms for refining triangular computational meshes based on the bisection of triangles by the longest side are presented and discussed the algorithms can be applied globally or locally for selective refinement of any conforming triangulation and always generate a new conforming triangulation after a finite number of interactions even when locally used the algorithms also ensure that all angles in subsequent refined triangulations are greater than or equal to half the smallest angle in the original triangulation the shape regularity of all triangles is maintained and the transition between small and large triangles is smooth in a natural way proofs of the above properties are presented the second algorithm is a simpler improved version of the first which retains most of the properties of the latter the algorithms can be used either for constructing irregular computational meshes or for locally refining any given triangulation in this sense they can be adequately combined with adaptive and or multigrid techniques for solving finite element systems examples of the application of the algorithms are given and two possible generalizations are pointed out

general object reconstruction based on simplex meshes in this paper we propose a general tridimensional reconstruction algorithm of range and volumetric images based on deformable simplex meshes simplex meshes are topologically dual of triangulations and have the advantage of permitting smooth deformations in a simple and efficient manner our reconstruction algorithm can handle surfaces without any restriction on their shape or topology the different tasks performed during the reconstruction include the segmentation of given objects in the scene the extrapolation of missing data and the control of smoothness density and geometric quality of the reconstructed meshes the reconstruction takes place in two stages first the initialization stage creates a simplex mesh in the vicinity of the data model either manually or using an automatic procedure then after a few iterations the mesh topology can be modified by creating holes or by increasing its genus finally an iterative refinement algorithm decreases the distance of the mesh from the data while preserving high geometric and topological quality several reconstruction examples are provided with quantitative and qualitative results

on the origin and nature of finite amplitude instabilities in physical systems finite amplitude instabilities are ubiquitous but their theory and precise definitions require clarification in this work we discuss the interrelation of various notions connected with finite amplitude instabilities and offer a precise context for these phenomena then we establish a connection between non normality of linear operators energy conservation by nonlinear operators and the existence of finite amplitude instabilities in finite and infinite dimensional dynamical systems both in the conservative and dissipative cases such a connection may at first appear counter intuitive since it relates intrinsically linear and nonlinear phenomena but it follows naturally from the properties of linear and nonlinear operators when they appear together in a dynamical system in particular the main theorem of this communication proves that non normality is a necessary condition for a finite amplitude instability it is demonstrated that this phenomenon is relevant to a wide class of physical systems with energy conserving nonlinearities