algebraic and analytical tools for the study of the period function abstract in this paper we consider analytic planar differential systems having a first integral of the form h x y a x b x y c x y 2 and an integrating factor x not depending on y our aim is to provide tools to study the period function of the centers of this type of differential system and to this end we prove three results theorem a gives a characterization of isochronicity a criterion to bound the number of critical periods and a necessary condition for the period function to be monotone theorem b is intended for being applied in combination with theorem a in an algebraic setting that we shall specify finally theorem c is devoted to study the number of critical periods bifurcating from the period annulus of an isochrone perturbed linearly inside a family of centers four different applications are given to illustrate these results

stability of two soliton collision for nonintegrable gkdv equations we continue our study of the collision of two solitons for the subcritical generalized kdv equations label kdvabs partial t u partial x partial x 2 u f u 0 quad quad 0 1 solitons are solutions of the type u t x q c 0 x x 0 c 0 t where c0 0 in 21 mainly devoted to the case f u u4 we have introduced a new framework to understand the collision of two solitons q c 1 q c 2 for 0 1 in the case c 2 ll c 1 or equivalently q c 2 h 1 ll q c 1 h 1 in this paper we consider the case of a general nonlinearity f u for which q c 1 q c 2 are nonlinearly stable in particular since f is general and c1 can be large the results are not perturbations of the ones for the power case in 21

instability of spatially quasi periodic states of the ginzburg landau equation the ginzburg landau gl equation with real coefficients is a model equation appearing in superconductor physics and near critical hydrodynamic stability problems the stationary gl equation has a two parameter i 1 i 2 family of spatially quasi periodic qp states with frequencies omega 1 omega 2 and frequency map with determinant delta k partial omega 1 omega 2 partial i 1 i 2 in this paper the linear stability of these qp states is studied and an expression for the stability exponent is obtained which has a novel geometric interpretation in terms of delta k when delta k 0 is a necessary but not sufficient condition for linear stability there is an interesting relation between delta k and the kam persistence theorem for invariant toroids

stability and instability of solitary waves of korteweg de vries type considered herein are the stability and instability properties of solitary wave solutions of a general class of equations that arise as mathematical models for the unidirectional propagation of weakly nonlinear dispersive long waves special cases for which our analysis is decisive include equations of the korteweg de vries and benjamin ono type necessary and sufficient conditions are formulated in terms of the linearized dispersion relation and the nonlinearity for the solitary waves to be stable

a class of hamiltonian systems with increasing periods on considere un systeme hamiltonien de la forme x g y y f x ou h f et h g satisfont certaines hypotheses on montre qu il y a un intervalle maximal 0 a a 0 tel que chaque solution x t y t avec x 0 a 0 a y 0 0 est periodique avec son orbite enfermant 0 0 soit p a la plus petite periode de cette solution alors p 0 a r est differentiable avec p a 0

global existence and asymptotic convergence of weak solutions for the one dimensional navier stokes equations with capillarity and nonmonotonic pressure abstract we construct global weak solution of the navier stokes equations with capillarity and nonmonotonic pressure the volume variable v 0 is initially assumed to be in h 1 and the velocity variable u 0 to be in l 2 on a finite interval 0 1 we show that both variables become smooth in positive time and that asymptotically in time u 0 strongly in l 2 0 1 and v approaches the set of stationary solutions in h 1 0 1

protein classification by matching and clustering surface graphs in this paper we address the problem of comparing and classifying protein surfaces with graph based methods comparison relies on matching surface graphs extracted from the surfaces by considering concave and convex patches through a kernelized version of the softassign graph matching algorithm on the other hand classification is performed by clustering the surface graphs with an em like algorithm also relying on kernelized softassign and then calculating the distance of an input surface graph to the closest prototype we present experiments showing the suitability of kernelized softassign for both comparing and classifying surface graphs

period function for a class of hamiltonian systems abstract this paper studies the period function of the class of hamiltonian systems x h y y h x where h x y has the special form h x y f x g y and the origin is a non degenerate center more concretely if t h denotes the period of the periodic orbit contained in h x y h we solve the inverse problem of characterizing all systems with a given function t h we also characterize the limiting behaviour of t at infinity when the origin is a global center and apply this result to prove among other results that there are no nonlinear polynomial isochronous centers in this family

from isochronous potentials to isochronous systems abstract there is a wide literature involving the study of isochronous equations of the type x t v x t 0 where v is a c 2 function in this paper we show how the kinetic energy t y 1 2 y 2 can be modified still preserving the isochronicity property of the corresponding system more generally we provide estimates for the periods and show an application to the steen s equation and other systems related to the anharmonic potential v x a x 2 b x 2

traveling waves for a model of gravity driven film flows in cylindrical domains abstract traveling wave solutions are studied for a recently derived model of a falling viscous film on the interior of a vertical rigid tube by identifying a hopf bifurcation and using numerical continuation software families of non trivial traveling wave solutions may be traced out in parameter space these families all contain a single solution at a turnaround point with larger film thickness than all others in the family in an earlier paper it was conjectured that this turnaround point may represent a critical thickness separating two distinct flow regimes observed in physical experiments as well as two distinct types of behavior in transient solutions to the model here these hypotheses are verified over a range of parameter values using a combination of numerical and analytical techniques the linear stability of these solutions is also discussed both large and small amplitude solutions are shown to be unstable though the instability mechanisms are different for each wave type specifically for small amplitude waves the region of relatively flat film away from the localized wave crest is subject to the same instability that makes the trivial flat film solution unstable for large amplitude waves this mechanism is present but dwarfed by a much stronger tendency to relax to a regime close to that followed by small amplitude waves

spectral stability of periodic wave trains of the korteweg de vries kuramoto sivashinsky equation in the korteweg de vries limit we study the spectral stability of a family of periodic wave trains of the korteweg de vries kuramoto sivashinsky equation tv v xv 3v 2 xv 4 xv 0 0 in the korteweg de vries limit 0 a canonical limit describing small amplitude weakly unstable thin lm ow more precisely we carry out a rigorous singular perturbation analysis reducing the problem of spectral stability in this limit to the validation of a set of three conditions each of which have been numerically analyzed in previous studies and shown to hold simultaneously on a non empty set of parameter space the main technical diculty

geometric methods for two point nonlinear boundary value problems on considere une classe d equations differentielles de la forme x f x g x avec des conditions aux limites soit de dirichlet soit de neumann on etudie l existence de la solution triviale

asymptotic expansion of the period function abstract let p be a not necessarily bounded polycycle of an analytic vector field on an open set of the plane suppose that the singularities which appear after desingularization of the vertices of p are formally linearizable consider the function t defined by the return time near p it is shown that the function t and its derivative t have asymptotic expansions in x r and x log x r it is also shown that under some other conditions imposed on the polycycle vertices the asymptotic expansions of t and t converge absolutely and uniformly to these functions respectively these results are applied to the polycycles of the analytic vector fields which have a darboux first integral in particular it is obtained that if p is a polycycle of a hamiltonian vector field with an analytic polynomial if p is unbounded hamiltonian function t is a nonoscillating function another application concerns the nilpotent centers or focus since the singularities which appear after desingularization of such a singularity have analytic first integrals

asymptotic stability of solitary waves we show that the family of solitary waves 1 solitons of the korteweg de vries equation partial t u u partial x u partial x 3 u 0 is asymptotically stable our methods also apply for the solitary waves of a class of generalized korteweg de vries equations partial t u partial x f u partial x 3 u 0 in particular we study the case wheref u up 1 p 1 p 1 2 3 and 3 0 withf c4 the same asymptotic stability result for kdv is also proved for the casep 2 the modified korteweg de vries equation we also prove asymptotic stability for the family of solitary waves for all but a finite number of values ofp between 3 and 4 the solitary waves are known to undergo a transition from stability to instability as the parameterp increases beyond the critical valuep 4 the solution is decomposed into a modulating solitary wave with time varying speedc t and phase t bound state part and an infinite dimensional perturbation radiating part the perturbation is shown to decay exponentially in time in a local sense relative to a frame moving with the solitary wave asp 4 the local decay or radiation rate decreases due to the presence of aresonance pole associated with the linearized evolution equation for solitary wave perturbations

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

criteria to bound the number of critical periods in the present paper we study the period function of centers of potential systems we obtain criteria to bound the number of critical periods in case that the system is polynomial our result enables to tackle the problem from a purely algebraic point of view since it allows to bound the number of critical periods by counting the zeros of a polynomial to illustrate its applicability some new and old results are proved

sufficient conditions for orbital stability of periodic traveling waves abstract the present paper deals with sufficient conditions for orbital stability of periodic waves of a general class of evolution equations supporting nonlinear dispersive waves our method can be seen as an extension to spatially periodic waves of the theory of solitary waves recently developed in 25 firstly our main result do not depend on the parametrization of the periodic wave itself secondly motived by the well known orbital stability criterion for solitary waves we show that the same criterion holds for periodic waves in addition we show that the positiveness of the principal entries of the hessian matrix related to the energy surface function are also sufficient to obtain the stability consequently we establish the orbital stability of periodic waves for several nonlinear dispersive models we believe our method can be applied in a wide class of evolution equations in particular it can be extended to regularized dispersive wave equations

on the return time function around monodromic polycycles abstract in this paper we study the period function of centers of planar polynomial differential systems with a convenient compactification of the phase portrait the boundary of the period annulus of the center has two connected components the center itself and a polycycle we are interested in the behaviour of the period function near the polycycle the desingularization of its critical points gives rise to a new polycycle monodromic as well with hyperbolic saddles or saddle nodes at the vertices in this paper we compute the first terms in the asymptotic development of the time function around any orbitally linearizable saddle that may come from this desingularization process in addition we use these developments to study the bifurcation diagram of the period function of the dehomogenized loud s centers more generally the tools developed here can be used to study the return time function around a monodromic polycycle this work is a continuation of the results in p mardesic d marin j villadelprat on the time function of the dulac map for families of meromorphic vector fields nonlinearity 16 2003 855 881 p mardesic d marin j villadelprat the period function of reversible quadratic centers j differential equations 224 2006 120 171

properties of the period function for some hamiltonian systems and homogeneous solutions of a semilinear elliptic equation abstract in this work we study the period function t of solutions to the conservative equation x t f x t 0 we present conditions on f that imply the monotonicity and convexity of t as a consequence we obtain the criterium established by c chicone and find conditions easier to apply we also get a condition obtained by cima gasull and manosas about monotonicity and following some of their calculations present results on the period function of hamiltonian systems where h x y f x n 1 y n using the monotonicity of t we count the homogeneous solutions to the semilinear elliptic equation u u 1 in two dimensions

nondegeneracy and stability of antiperiodic bound states for fractional nonlinear schrodinger equations abstract we consider the existence and stability of real valued spatially antiperiodic standing wave solutions to a family of nonlinear schrodinger equations with fractional dispersion and power law nonlinearity as a key technical result we demonstrate that the associated linearized operator is nondegenerate when restricted to antiperiodic perturbations i e that its kernel is generated by the translational and gauge symmetries of the governing evolution equation in the process we provide a characterization of the antiperiodic ground state eigenfunctions for linear fractional schrodinger operators on r with real valued periodic potentials as well as a sturm liouville type oscillation theory for the higher antiperiodic eigenfunctions

clustering techniques for protein surfaces though most approaches to protein comparison are based on their structure several studies produced evidence of a strict correlation between the surface characteristics of proteins and the way they interact surface based techniques for protein comparison typically require applying clustering algorithms to the punctual 3d description of the surface in order to produce a compact surface representation capable of effectively condensing its description in this paper we propose a formalization of the requirements for surface clustering in the biochemical context and present two different clustering techniques that meet them based respectively on region growing and on an original template matching algorithm we discuss the validity of these techniques with the support of tests performed on a set of about one hundred protein models generated by punctual mutations of four structurally characterized proteins finally an analysis is made of how different factors impact on the effectiveness of clustering in capturing surface similarities

orbital stability of one parameter periodic traveling waves for dispersive equations and applications abstract this paper establishes sufficient conditions for the orbital stability of one parameter spatially periodic traveling wave solutions for one dimensional dispersive equations our method of proof combines known techniques with some new ideas as a consequence of our result we give several applications for well known dispersive equations extension of the theory to regularized equations is also established

stability of periodic solutions of conservation laws with viscosity analysis of the evans function nonclassical conservation laws with viscosity arising in multiphase fluid and solid mechanics exhibit a rich variety of traveling wave phenomena including homoclinic pulse type and periodic solutions along with the standard heteroclinic shock or front type solutions here we investigate stability of periodic traveling waves within the abstract evans function framework established by r a gardner our main result is to derive a useful stability index analogous to that developed by gardner and zumbrun in the traveling front or pulse context giving necessary conditions for stability with respect to initial perturbations that are periodic on the same period t as the traveling wave moreover we show that the periodic stability index has an interpretation analogous to that of the traveling front or pulse index in terms of well posedness of an associated riemann problem for an inviscid medium now to be interpreted as allowing a wider class of measure valued solutions or alternatively in terms of existence and nonsingularity of a local mass map from perturbation mass to potential time asymptotic t periodic states a closely related calculation yields also a complementary long wave stability criterion necessary for stability with respect to periodic perturbations of arbitrarily large period nt n we augment these analytical results with numerical investigations analogous to those carried out by brin in the traveling front or pulse case approximating the spectrum of the linearized operator about the wave

the period function of the generalized lotka volterra centers abstract the present paper deals with the period function of the quadratic centers in the literature different terminologies are used to classify these centers but essentially there are four families hamiltonian reversible q 3 r codimension four q 4 and generalized lotka volterra systems q 3 lv chicone c chicone review in mathscinet ref 94h 58072 conjectured that the reversible centers have at most two critical periods and that the centers of the three other families have a monotonic period function with regard to the second part of this conjecture only the monotonicity of the hamiltonian and q 4 families w a coppel l gavrilov the period function of a hamiltonian quadratic system differential integral equations 6 1993 1357 1365 y zhao the monotonicity of period function for codimension four quadratic system q 4 j differential equations 185 2002 370 387 has been proved concerning the q 3 lv family no substantial progress has been made since the middle 80s when several authors showed independently the monotonicity of the classical lotka volterra centers f rothe the periods of the volterra lokta system j reine angew math 355 1985 129 138 r schaaf global behaviour of solution branches for some neumann problems depending on one or several parameters j reine angew math 346 1984 1 31 j waldvogel the period in the lotka volterra system is monotonic j math anal appl 114 1986 178 184 by means of the first period constant one can easily conclude that the period function of the centers in the q 3 lv family is monotone increasing near the inner boundary of its period annulus i e the center itself thus according to chicone s conjecture it should be also monotone increasing near the outer boundary which in the poincare disc is a polycycle in this paper we show that this is true in addition we prove that except for a zero measure subset of the parameter plane there is no bifurcation of critical periods from the outer boundary finally we show that the period function is globally i e in the whole period annulus monotone increasing in two other cases different from the classical one

the period function for quadratic integrable systems with cubic orbits this paper is concerned with the monotonicity of the period function for families of quadratic systems with centers whose orbits lie on cubic planar curves it is proved that each such system has a period function with at most one critical point

3d part segmentation using simulated electrical charge distributions a novel approach to 3d part segmentation is presented it is a well known physical fact that electrical charge on the surface of a conductor tends to accumulate at a sharp convexity and vanish at a sharp concavity thus object part boundaries which are usually denoted by a sharp surface concavity can be detected by simulating the electrical charge density over the object surface and locating surface points which exhibit local charge density minima beginning with single or multiview range data of a 3d object we simulate the charge density distribution over an object s surface which has been tessellated by a triangular mesh we detect the deep surface concavities by tracing local charge density minima and then decompose the object into parts at these points the charge density computation does not require an assumption on surface smoothness and uses weighted global data to produce robust local surface features for part segmentation

algebraic simplex initialization combined with the nonfeasible basis method we propose in this paper a new method to initialize the simplex algorithm this approach does not involve any artificial variables it can detect also the redundant constraints or infeasibility if any generally the basis found by this approach is not feasible to achieve feasibility this algorithm appeals to the nonfeasible basis method nfb furthermore we propose a new pivoting rule for nfb method which shows to be beneficial in both numerical and time complexity when solving a linear program we develop an efficient criterion to decide in advance which algorithm between nfb and formal nonfeasible basis method seems to be more rapid comparative analysis is carried out with a set of standard test problems from netlib our computational results indicate that the proposed algorithm is more advantageous than two phase and perturbation algorithm in terms of number of iterations number of involved variables and also computational time

direct dynamical energy cascade in the modified kdv equation in this study we examine the energy transfer mechanism during the nonlinear stage of the modulational instability mi in the modified korteweg de vries equation the particularity of this study consists in considering the problem essentially in the fourier space a dynamical energy cascade model of this process originally proposed for the focusing nls type equations is transposed to the mkdv setting using the existing connections between the kdv type and nls type equations the main predictions of the d cascade model are outlined and thoroughly discussed finally the obtained theoretical results are validated by direct numerical simulations of the mkdv equation using the pseudo spectral methods a general good agreement is reported in this study the nonlinear stages of the mi evolution are also investigated for the mkdv equation

high multiplicity of positive solutions for superlinear indefinite problems with homogeneous neumann boundary conditions abstract we prove that a class of superlinear indefinite problems with homogeneous neumann boundary conditions admits an arbitrarily high number of positive solutions provided that the parameters of the problem are adequately chosen the sign changing weight in front of the nonlinearity is taken to be piecewise constant which allows us to perform a sharp phase plane analysis firstly to study the sets of points reached at the end of the regions where the weight is negative and then to connect such sets through the flow in the positive part moreover we study how the number of solutions depends on the amplitude of the region in which the weight is positive using the latter as the main bifurcation parameter and constructing the corresponding global bifurcation diagrams

isochronous centers of lienard type equations and applications abstract in this work we study eq e x f x x 2 g x 0 with a center at 0 and investigate conditions of its isochronicity when f and g are analytic not necessary odd a necessary and sufficient condition for the isochronicity of 0 is given this approach allows us to present an algorithm for obtained conditions for a point of e to be an isochronous center in particular we find again by another way the isochrones of the quadratic loud systems l d f we also classify a 5 parameters family of reversible cubic systems with isochronous centers

an overview on the simplex algorithm in this paper the simplex algorithm and its variants are investigated first we define a new concept called formal tableau which leads to derive easily the dual solution from the latest primal table without any distinction between the original variables and the slack ones second we propose a new method for initializing the simplex algorithm unlike the two phase and the big m methods our technique does not involve artificial variables the computational results reveal that this new method is very favorable especially when the number of artificial variables is significant finally this method will be combined with the notion of formal tableau leading naturally to a second new approach

the many facets of linear programming we examine the history of linear programming from computational geometric and complexity points of view looking at simplex ellipsoid interior point and other methods

an index theorem for the stability of periodic travelling waves of korteweg de vries type we consider the stability of periodic travelling wave solutions to a generalized korteweg de vries gkdv equation and prove an index theorem relating the number of unstable and potentially unstable eigenvalues to geometric information on the classical mechanics of the travelling wave ordinary differential equation we illustrate this result with several examples including the integrable kdv and modified kdv equations the l 2 critical kdv 4 equation that arises in the study of blow up and the kdv equation which is an idealized model for plasmas

an instability index theory for quadratic pencils and applications primarily motivated by the stability analysis of nonlinear waves in second order in time hamiltonian systems in this paper we develop an instability index theory for quadratic operator pencils acting on a hilbert space in an extension of the known theory for linear pencils explicit connections are made between the number of eigenvalues of a given quadratic operator pencil with positive real parts to spectral information about the individual operators comprising the coefficients of the spectral parameter in the pencil as an application we apply the general theory developed here to yield spectral and nonlinear stability instability results for abstract second order in time wave equations more specifically we consider the problem of the existence and stability of spatially periodic waves for the good boussinesq equation in the analysis our instability index theory provides an explicit and somewhat surprising connection between the stability of a given periodic traveling wave solution of the good boussinesq equation and the stability of the same periodic profile but with different wavespeed in the nonlinear dynamics of a related generalized korteweg de vries equation