on the critical periods of perturbed isochronous centers abstract consider a family of planar systems x x x e having a center at the origin and assume that for e 0 they have an isochronous center firstly we give an explicit formula for the first order term in e of the derivative of the period function we apply this formula to prove that up to first order in e at most one critical period bifurcates from the periodic orbits of isochronous quadratic systems when we perturb them inside the class of quadratic reversible centers moreover necessary and sufficient conditions for the existence of this critical period are explicitly given from the tools developed in this paper we also provide a new characterization of planar isochronous centers

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

the monotonicity of the period function for planar hamiltonian vector fields if the hamiltonian system with hamiltonian h x y 12y2 v x has a center at the origin it is shown that the period function for the family of periodic trajectories surrounding the center is monotone when the function v v 2 is convex this theorem is applied to determine existence and uniqueness of solutions for the neumann boundary value problem x a x 2 bx c x 0 x 1 0

large deviations of the maximum eigenvalue in wishart random matrices we analytically compute the probability of large fluctuations to the left of the mean of the largest eigenvalue in the wishart laguerre ensemble of positive definite random matrices we show that the probability that all the eigenvalues of a n n wishart matrix w xtx where x is a rectangular m n matrix with independent gaussian entries are smaller than the mean value n c decreases for large n as where 1 2 corresponds respectively to real and complex wishart matrices c n m 1 and x c is a rate sometimes also called large deviation function that we compute explicitly the result for the anti wishart case m n simply follows by exchanging m and n we also analytically determine the average spectral density of an ensemble of wishart matrices whose eigenvalues are constrained to be smaller than a fixed barrier numerical simulations are in excellent agreement with the analytical predictions

a new zero crossing based discontinuity detector general zero crossing based discontinuity detectors in two dimensions which include marr hildreth 1980 residual difference of gaussians and other detectors as special cases are discussed mathematical justification for this class of detectors is presented an optimal detector that maximizes the signal to noise ratio is derived preliminary experimental results for real images are reported

derivation of optimal filters for the detection of coronary arteries optimal filters for the detection of coronary arteries with a diameter range of 0 5 6 0 mm in digital x ray images are derived using a computational approach this approach is based on the two requirements for optimal detection first the filter should maximize the number of detected true edges and minimize the number of detected false edges second if an edge has been detected its position should be as close as possible to the true edge position in the image since the grey value profile in a digital x ray image associated with an arterial vessel is asymmetric the theory on edge detection derived by canny has been expanded with two additional boundary constraints to make it suitable for the derivation of filters for asymmetric edges it is demonstrated that it is possible to derive optimal filters for coronary segments the localization error defined by the square root of the sum of the squared systematic and random errors in the assessment of the arterial diameter depends on the size of the coronary artery and the amount of noise in the image here an evaluation study is described to assess the relationship between localization error and the amount of noise upon the vessel profile for that purpose an analytical description of the vessel profile in an angiographic image was derived for the larger arteries the relation between noise and localization error was found to be linear and no systematic over or underestimations were observed even if the noise level was very high however it can be shown that the smallest diameter that can be measured depends on the amount of noise present in the data even for images that contain only a low amount of noise arterial diameters below 0 7 mm cannot be measured accurately if the noise in the image increases the lowest measurable arterial diameter value also increases also the random error increases rapidly for vessel diameters below 1 2 mm but with a limited amount of noise and a diameter value above 0 7 mm the random error is still acceptable 0 15 mm 21 for 0 7 mm vessels 0 06 mm 6 for 1 mm vessels

a few remarks on colour flavour transformations truncations of random unitary matrices berezin reproducing kernels and selberg type integrals we investigate diverse relations of the colour flavour transformations cft introduced by zirnbauer in supersymmetry for systems with unitary disorder circular ensembles 1996 j phys a math gen 29 7113 36 to various topics in random matrix theory and multivariate analysis such as measures on truncations of unitary random matrices jacobi ensembles of random matrices berezin reproducing kernels and a generalization of the selberg integral due to kaneko kadell and yan involving the schur functions apart from suggesting explicit formulae for bosonic cft for the unitary group in the range of parameters beyond that in zirnbauer s paper we also suggest an alternative variant of the transformation with integration going over an unbounded domain of a pair of hermitian matrices the latter makes possible the evaluation of certain averages in random matrix theory

complex wishart matrices and conductance in mesoscopic systems exact results it is noted that the hypothesis of independent random complex elements for the off diagonal blocks say m2 and m3 of the transfer matrix describing conductance in a mesoscopic wire allows the eigenvalue distribution of the matrix product m3 m3 or m2 m2 to be computed exactly exact expressions in terms of double wronskian and toeplitz determinants are derived for the distribution of the smallest and second smallest eigenvalue of this and similar random matrix products

bifurcation of critical periods from the reversible rigidly isochronous centers abstract in this paper we study bifurcation of critical periods by perturbing a nonlinear vector field containing m th degree homogeneous terms with a rigidly isochronous center at the origin first we give expressions of period bifurcation functions in the form of integrals and then study the number of critical periods for cases of m 1 2 3 respectively

renormalization group flow of the two dimensional hierarchical coulomb gas we consider a quasilinear parabolic differential equation associated with the renormalization group transformation of the two dimensional hierarchical coulomb system in the limit as the size of the block l darr 1 we show that the initial value problem is well defined in a suitable function space and the solution converges as t to one of the countably infinite equilibrium solutions the j th nontrivial equilibrium solution bifurcates from the trivial one at these solutions are fully described and we provide a complete analysis of their local and global stability for all values of inverse temperature 0 gallavotti and nicolo s conjecture on infinite sequence of phases transitions is also addressed our results rule out an intermediate phase between the plasma and the kosterlitz thouless phases at least in the hierarchical model we consider

spectral and modulational stability of periodic wavetrains for the nonlinear klein gordon equation abstract this paper is a detailed and self contained study of the stability properties of periodic traveling wave solutions of the nonlinear klein gordon equation u t t u x x v u 0 where u is a scalar valued function of x and t and the potential v u is of class c 2 and periodic stability is considered both from the point of view of spectral analysis of the linearized problem spectral stability analysis and from the point of view of wave modulation theory the strongly nonlinear theory due to whitham as well as the weakly nonlinear theory of wave packets the aim is to develop and present new spectral stability results for periodic traveling waves and to make a solid connection between these results and predictions of the formal modulation theory which has been developed by others but which we review for completeness

non hermitean wishart random matrices i a non hermitean extension of paradigmatic wishart random matrices is introduced to set up a theoretical framework for statistical analysis of real complex and real quaternion stochastic time series representing two remote complex systems the first paper in a series provides a detailed spectral theory of non hermitean wishart random matrices composed of complex valued entries the great emphasis is placed on an asymptotic analysis of the mean eigenvalue density for which we derive among other results a complex plane analog of the marcenko pastur law a surprising connection with a class of matrix models previously invented in the context of quantum chromodynamics is pointed out

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

on the period function of x f x x 2 g x 0 abstract we study the period function t of a center o of the title s equation a sufficient condition for the monotonicity of t or for the isochronicity of o is given such a condition is also necessary when f and g are odd and analytic in this case a characterization of isochronous centers is given some classes of plane systems equivalent to such equation are considered including some kukles systems

non ergodicity of the nose hoover thermostatted harmonic oscillator the nose hoover thermostat is a deterministic dynamical system designed for computing phase space integrals for the canonical gibbs distribution newton s equations are modified by coupling an additional reservoir variable to the physical variables the correct sampling of the phase space according to the gibbs measure is dependent on the nose hoover dynamics being ergodic hoover presented numerical experiments to show that the nose hoover dynamics are non ergodic when applied to the harmonic oscillator in this article we prove that the nose hoover thermostat does not give an ergodynamical system for the one dimensional harmonic oscillator when the mass of the reservoir is large our proof of non ergodicity uses kam theory to demonstrate the existence of invariant tori for the nose hoover dynamical system that separate phase space into invariant regions we present numerical experiments motivated by our analysis that seem to show that the dynamical system is not ergodic even for a moderate thermostat mass

monotonicity of the period of a non linear oscillator abstract we revisit the problem of monotonicity of the period function for the differential equation u u u p 0 and give a simple proof of recent results of miyamoto and yagasaki

on the period function of lienard systems abstract we study the period functiontof a centeroof a lienard system a sufficient condition for the monotonicity oft or for the isochronicity ofo is given such a condition is also necessary whenfandgare analytic andgis odd in this case a characterization of isochronous centers of lienard systems is given strict monotonicity and global monotonicity oftare also investigated

on the period function for a family of complex differential equations abstract we consider planar differential equations of the form z f z g z being f z and g z holomorphic functions and prove that if g z is not constant then for any continuum of period orbits the period function has at most one isolated critical period which is a minimum among other implications the paper extends a well known result for meromorphic equations z h z that says that any continuum of periodic orbits has a constant period function

on the upper bound of the criticality of potential systems at the outer boundary using the roussarie ecalle compensator abstract this paper is concerned with the study of the criticality of families of planar centers more precisely we study sufficient conditions to bound the number of critical periodic orbits that bifurcate from the outer boundary of the period annulus of potential centers in the recent years the new approach of embedding the derivative of the period function into a collection of functions that form a chebyshev system near the outer boundary has shown to be fruitful in this issue in this work we tackle with a remaining case that was not taken into account in the previous studies in which the roussarie ecalle compensator plays an essential role the theoretical results we develop are applied to study the bifurcation diagram of the period function of two different families of centers the power like family x x q x p p q r with p q and the family of dehomogenized loud s centers

on the period function in a class of generalized lotka volterra systems in this note motivated by the recent results of wang et al wang et al local bifurcations of critical periods in a generalized 2d lv system appl math comput 214 2009 17 25 we study the behaviour of the period function of the center at the point 1 1 of the planar differential systemu u p 1 v q v email protected q u p 1 where p q email protected r with pq 0 and m 0 our aim is twofold firstly we determine regions in the parameter space for which the corresponding system has a center with a monotonic period function secondly by taking advantage of the results of wang et al we show some properties of the bifurcation diagram of the period function and we make some comments for further research the differential system under consideration is a generalization proposed by farkas and noszticzius of the lotka volterra model

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

coping with discontinuities in computer vision their detection classification and measurement the general principles of detection classification and measurement of discontinuities are studied the following issues are discussed detecting the location of discontinuities classifying discontinuities by their degrees measuring the size of discontinuities and coping with the random noise and designing optimal discontinuity detectors an algorithm is proposed for discontinuity detection from an input signal s for degree k discontinuity detection and measurement a detector p phi is used where p is the pattern and phi is the corresponding filter if there is a degree k discontinuity at location t sub 0 then in the filter response there is a scaled pattern alpha p at t sub 0 where alpha is the size of the discontinuity this reduces the problem to searching for the scaled pattern in the filter response a statistical method is proposed for the approximate pattern matching to cope with the random noise a study is made of optimal detectors which minimize the effects of noise

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

monotonicity of the period function for u u up 0 with p r and p 1 abstract for p r and p 1 we consider the second order ordinary differential equation u u u p 0 which has a one parameter family of periodic solutions satisfying u 0 u 0 u 1 0 with u 1 0 1 we prove that the so called period function t u 1 which represents the period of the periodic solution is strictly decreasing on 0 1 this result is also applied to completely determine the global bifurcation diagram of interior single peak solutions in the neumann boundary value problem of u u u p 0 in 1 1 with u 1 0 where is a control parameter

newtonian scattering in hilbert space abstract we consider the scattering theory for a classical particle moving on the line in the context of l 2 of the phase space we establish the absence of a singular continuous spectrum and determine the bound states of the system also we show that in general the corresponding wave operators are not complete

robust extrema features for time series data analysis the extraction of robust features for comparing and analyzing time series is a fundamentally important problem research efforts in this area encompass dimensionality reduction using popular signal analysis tools such as the discrete fourier and wavelet transforms various distance metrics and the extraction of interest points from time series recently extrema features for analysis of time series data have assumed increasing significance because of their natural robustness under a variety of practical distortions their economy of representation and their computational benefits invariably the process of encoding extrema features is preceded by filtering of the time series with an intuitively motivated filter e g for smoothing and subsequent thresholding to identify robust extrema we define the properties of robustness uniqueness and cardinality as a means to identify the design choices available in each step of the feature generation process unlike existing methods which utilize filters x201c inspired x201d from either domain knowledge or intuition we explicitly optimize the filter based on training time series to optimize robustness of the extracted extrema features we demonstrate further that the underlying filter optimization problem reduces to an eigenvalue problem and has a tractable solution an encoding technique that enhances control over cardinality and uniqueness is also presented experimental results obtained for the problem of time series subsequence matching establish the merits of the proposed algorithm

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

optimal edge detectors for ramp edges it is argued that the best way to model an edge is by assuming all ideal mathematical function passed through a low pass filter and and immersed in noise using techniques similar to those developed by j canny 1983 1986 and l a spacek 1986 optimal filters are derived for ramp edges of various slopes the optimal nonrecursive filter for ideal step edges is then derived as a limiting case of the filters for ramp edges because there are no step edges in images edge detection is improved when the ramp filter is used instead of the filters developed for step edges for practical purposes some convolution masks are given which can be used directly for edge detection without the need to go into the details of the subject

using canny s criteria to derive a recursively implemented optimal edge detector a highly efficient recursive algorithm for edge detection is presented using canny s design 1 we show that a solution to his precise formulation of detection and localization for an infinite extent filter leads to an optimal operator in one dimension which can be efficiently implemented by two recursive filters moving in opposite directions in addition to the noise truncature immunity which results the recursive nature of the filtering operations leads with sequential machines to a substantial saving in computational effort five multiplications and five additions for one pixel independent of the size of the neighborhood the extension to the two dimensional case is considered and the resulting filtering structures are implemented as two dimensional recursive filters hence the filter size can be varied by simply changing the value of one parameter without affecting the time execution of the algorithm performance measures of this new edge detector are given and compared to canny s filters various experimental results are shown

average coherence and its typicality for random mixed quantum states the wishart ensemble is a useful and important random matrix model used in diverse fields by realizing induced random mixed quantum states as a wishart ensemble with fixed unit trace using matrix integral technique we give a fast track to the average coherence for random mixed quantum states induced via partial tracing of the haar distributed bipartite pure states as a direct consequence of this result we get a compact formula for the average subentropy of random mixed states these compact formulae extend our previous work

emerging spectra of singular correlation matrices under small power map deformations correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular yet most analysis assume stationarity of the underlying time series this tends to be an assumption of varying and often dubious validity the validity of the assumption improves as shorter time series are used if many time series are used this implies an analysis of highly singular correlation matrices we attack this problem by using the so called power map which was introduced to reduce noise its nonlinearity breaks the degeneracy of the zero eigenvalues and we analyze the sensitivity of the so emerging spectra to correlations this sensitivity will be demonstrated for uncorrelated and correlated wishart ensembles

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

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

abelian integrals and bifurcation theory abstract conditions are given for uniqueness of limit cycles for autonomous equations in the plane the results are applicable to codimension two bifurcations near equilibrium points for vector fields

on the largest singular values of random matrices with independent cauchy entries we apply the method of determinants to study the distribution of the largest singular values of large m n real rectangular random matrices with independent cauchy entries we show that for a special one parametric class of statistics the properties of the largest singular values rescaled by a factor 1 m2n2 agree in the limit with the statistical properties of the poisson random point process with the intensity 1 x 3 2 and therefore are different from the tracy widom law among other corollaries of our method we show an interesting connection between the mathematical expectations of the determinants of the complex rectangular m n standard wishart ensemble and the real rectangular 2m 2n standard wishart ensemble

global bifurcation of steady state solutions in this paper we study the bifurcation of steady state solutions of a reaction diffusion equation in one space variable the steady state solutions satisfy the equation a f u 0 on the interval l 0 or 0 for some nonzero function c c a for the neumann problem we use entirely different techniques to prove that s is never critical for any cubic polynomial j this implies at once that the neumann problem can have at most one nonconstant solution having a given number of maxima or minima this solution is necessarily strongly nondegenerate in the sense that zero is not contained in the spectrum of the linearized operator see 2 for the dirichlet problem the situation is far more complicated and the bifurcation diagrams undergo qualitative changes depending on the positions of the roots off for example fig 1 shows the bifurcation diagram for the positive solutions for two different cubic functions of the form f u a u u b u c it is interesting to note however that in every case we study there are at most three solutions to the dirichlet problem for each

bifurcations of limit cycles from quintic hamiltonian systems with an eye figure loop abstract in this paper we consider lienard equations of the form x y y x 2 x 3 x 5 e x 2 x 4 y where 0 e 1 r 3 and is bounded we prove that the least upper bound for the number of zeros of the related abelian integrals i h h x 2 x 4 y d x is 2 taking into account their multiplicities for h 0 1 6 and this upper bound is a sharp one this implies that the number of limit cycles bifurcated from periodic orbits in the vicinity of the center of the unperturbed system for e 0 inside an eye figure loop is less than or equal to 2

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

maximal and minimal eigenvalues and their associated nonlinear equations the spectral theory of uniformly elliptic operators a under perturbations v giving rise to operators of the form hv a v x on a bounded or unbounded region such as schrodinger operators are considered suppose that v p is constrained but v is otherwise unspecified the theory of the potentials v that maximize or minimize the eigenvalues of hv is presented the optimizing potentials are typically determined by equations of the form u w x u cu u the optimization of eigenvalues also turns out to be related to the determination of the best constants in sobolev s inequality and in its one dimensional simplification to a classical oscillator problem with instanton properties

critical periods of perturbations of reversible rigidly isochronous centers abstract in this paper we discuss bifurcation of critical periods in an m th degree time reversible system which is a perturbation of an n th degree homogeneous vector field with a rigidly isochronous center at the origin we present period bifurcation functions as integrals of analytic functions which depend on perturbation coefficients and reduce the problem of critical periods to finding zeros of a judging function this procedure gives not only the number of critical periods bifurcating from the period annulus but also the location of these critical periods applying our procedure to the case n m 2 we determine the maximum number of critical periods and their location to the case n m 3 we investigate the bifurcation of critical periods up to the first order in e and obtain the expression of the second period bifurcation function when the first one vanishes

on the number of critical periods for planar polynomial systems abstract in this paper we get some lower bounds for the number of critical periods of families of centers which are perturbations of the linear one we give a method which lets us prove that there are planar polynomial centers of degree l with at least 2 l 2 2 critical periods as well as study concrete families of potential reversible and lienard centers this last case is studied in more detail and we prove that the number of critical periods obtained with our approach does not increases with the order of the perturbation

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

on the number of critical periods for planar polynomial systems of arbitrary degree we construct a class of planar systems of arbitrary degree n having a reversible center at the origin and such that the number of critical periods on its period annulus grows quadratically with n as far as we know the previous results on this subject gave systems having linear growth

period function monotonicity of planar vector fields in this paper we study planar differential systems possessing a center at the origin we introduce functional conditions for centers and obtain sufficient conditions for monotonicity of period function and isochronicity of the center of systems of ode reducible to the equation email protected email protected f x email protected these criteria are applied to obtain sufficient conditions for isochronicity of some special important systems

orbital stability of periodic traveling wave solutions for the log kdv equation abstract in this paper we establish the orbital stability of periodic waves related to the logarithmic korteweg de vries equation our motivation is inspired in the recent work 3 in which the authors established the well posedness and the linear stability of gaussian solitary waves by using the approach put forward recently in 20 to construct a smooth branch of periodic waves as well as to get the spectral properties of the associated linearized operator we apply the abstract theories in 13 and 25 to deduce the orbital stability of the periodic traveling waves in the energy space

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

perturbed rigidly isochronous centers and their critical periods abstract this paper investigates the bifurcation of critical periods from a cubic rigidly isochronous center under any small polynomial perturbations of degree n it proves that for n 3 4 and 5 there are at most 2 and 4 critical periods induced by periodic orbits of the unperturbed cubic system respectively and in each case this upper bound is sharp moreover for any n 5 there are at most n 1 2 critical periods induced by periodic orbits of the unperturbed cubic system an example is given to show that the upper bound in the case of n 11 can be reached

a remark on the period of the periodic solution in the lotka volterra system abstract an important consideration in the nonlinear predator prey problem of lotka volterra type is the determination of the period this paper gives a general expression for the period in terms of the given parameters in the lotka volterra system we also discuss the qualitative behavior of the period related to the energy level of the lotka volterra system

an example of chaotic dynamics for the motion of a charged particle in a magnetic field abstract in this paper we discuss the presence of chaotic dynamics of charged particles inside an idealized magnetic field suggested by a tokamak type configuration our model is based on a periodically perturbed hamiltonian system in a half plane r 0 we propose a simple mechanism producing complex dynamics based on the theory of linked twist maps jointly with the method of stretching along the paths a key step in our argument relies on the monotonicity of the period map associated with the unperturbed planar system

the criticality of centers of potential systems at the outer boundary abstract the number of critical periodic orbits that bifurcate from the outer boundary of a potential center is studied we call this number the criticality at the outer boundary our main results provide sufficient conditions in order to ensure that this number is exactly 0 and 1 we apply them to study the bifurcation diagram of the period function of x y x x 1 p x 1 q y with q p this family was previously studied for q 1 by y miyamoto and k yagasaki

random matrices close to hermitian or unitary overview of methods and results the paper discusses recent progress in understanding statistical properties of eigenvalues of weakly non hermitian and non unitary random matrices the first type of ensembles is of the form i with being a large random n n hermitian matrix with independent entries deformed by a certain anti hermitian n n matrix i satisfying in the limit of large dimension n the condition tr 2 n tr 2 here can be either a random or just a fixed given hermitian matrix ensembles of such a type with 0 emerge naturally when describing quantum scattering in systems with chaotic dynamics and serve to describe resonance statistics related models are used to mimic complex spectra of the dirac operator with chemical potential in the context of quantum chromodynamics ensembles of the second type arising naturally in scattering theory of discrete time systems are formed by n n matrices with complex entries such that i for 0 this coincides with the circular unitary ensemble and 0 i describes deviation from unitarity our result amounts to answering statistically the following old question given the singular values of a matrix describe the locus of its eigenvalues we systematically show that the obtained expressions for the correlation functions of complex eigenvalues describe a non trivial crossover from wigner dyson statistics of real unimodular eigenvalues typical of hermitian unitary matrices to ginibre statistics in the complex plane typical of ensembles with strong non hermiticity tr 2 tr 2 when n finally we discuss scarce results available on eigenvector statistics for weakly non hermitian random matrices

close form solution and parameter selection for convex minimization based edge preserving smoothing this work presents a new approach for the analysis of convex minimization based edge preserving image smoothing and the parameter selection therein the global solution that is the response of a convex smoothing model to the ideal step edge is derived in close form by analyzing the close form solution insights are drawn into how the optimal solution responds to edges in the data and how the parameter values affect resultant edges in the solution based on this a scheme is proposed for selecting parameters to achieve desirable responses at edges the theoretic results are substantiated by experiments

on detecting edges an edge in an image corresponds to a discontinuity in the intensity surface of the underlying scene it can be approximated by a piecewise straight curve composed of edgels i e short linear edge elements each characterized by a direction and a position the approach to edgel detection here is to fit a series of one dimensional surfaces to each window kernel of the operator and accept the surface description which is adequate in the least squares sense and has the fewest parameters a one dimensional surface is one which is constant along some direction the tanh is an adequate basis for the stepedge and its combinations are adequate for the roofedge and the line edge the proposed method of step edgel detection is robust with respect to noise for step size noise 2 5 it has subpixel position localization position and an angular localization better than 10 further it is designed to be insensitive to smooth shading these results are demonstrated by some simple analysis statistical data and edgelimages also included is a comparison of performance on a real image with a typical operator difference of gaussians the results indicate that the proposed operator is superior with respect to detection localization and resolution

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

monotonicity of the first eigenvalue and the global bifurcation diagram for the branch of interior peak solutions abstract let b r n n 1 be a unit ball and d r m be a bounded domain we study the global branch consisting of interior single peak solutions of the elliptic neumann problem u u u p 0 in b u 0 on b and the monotonicity of the first eigenvalue along the branch for large where 1 p p s n 2 n 2 n 3 n 1 2 when the domain is replaced with b d using this monotonicity we show that the branch of solutions concentrating on 0 d has secondary bifurcation points for n 1 and p 2 an integer we determine the global bifurcation diagram by showing the monotonicity of the time map the period function the monotonicity of the first eigenvalue along the whole branch is also proved for n 1 and p 3

order estimation and discrimination between stationary and time varying tvar autoregressive models for a set of t independent observations of the same n variate correlated gaussian process we derive a method of estimating the order of an autoregressive ar model of this process regardless of its stationary or time varying nature we also derive a test to discriminate between stationary ar models of order m ar m and time varying autoregressive models of order m tvar m we demonstrate that within this technique the number t of independent identically distributed data samples required for order estimation and discrimination just exceeds the maximum possible order mmax which in many cases is significantly fewer than the dimension of the problem n

developments in random matrix theory in this introduction to the journal of physics a special issue on random matrix theory we give a review of the main historical developments in random matrix theory a short summary of the papers that appear in this special issue is also given

finiteness for critical periods of planar analytic vector fields limburgs univ centrum dept math b 3610 diepenbeek belgium chicone c univ missouri dept math columbia mo 65211

wishart and anti wishart random matrices we provide a compact exact representation for the distribution of the matrix elements of the wishart type random matrices for any finite number of rows and columns of without any large n approximations in particular we treat the case when the wishart type random matrix contains redundant non random information which is a new result this representation is of interest for a procedure for reconstructing the redundant information hidden in wishart matrices with potential applications to numerous models based on biological social and artificial intelligence networks

edge and line feature extraction based on covariance models image segmentation based on contour extraction usually involves three stages of image operations feature extraction edge detection and edge linking this paper is devoted to the first stage a method to design feature extractors used to detect edges from noisy and or blurred images the method relies on a model that describes the existence of image discontinuities e g edges in terms of covariance functions the feature extractor transforms the input image into a log likelihood ratio image such an image is a good starting point of the edge detection stage since it represents a balanced trade off between signal to noise ratio and the ability to resolve detailed structures for 1 d signals the performance of the edge detector based on this feature extractor is quantitatively assessed by the so called average risk measure the results are compared with the performances of 1 d edge detectors known from literature generalizations to 2 d operators are given applications on real world images are presented showing the capability of the covariance model to build edge and line feature extractors finally it is shown that the covariance model can be coupled to a mrf model of edge configurations so as to arrive at a maximum a posteriori estimate of the edges or lines in the image

a new generalised α scale spaces quadrature filters abstract the scale spaces is a recent theory that open new possibilities of phase based image processing it is a parameterised class 0 1 of linear scale space representations which allows a continuous connection beyond the well known gaussian scale space 1 in this paper we make use of this unified representation to derive new families of band pass quadrature filters built from derivatives and difference of the scale space generating kernels this construction leads to generalised kernel filters including the commonly known families derived from the gaussian and the poisson kernels the properties of each family are first studied and then experiments on one and two dimensional signals are shown to exemplify how the suggested filters can be used for edge detection this work is complemented by an experimental evaluation which demonstrates that the new proposed filters are a good alternative to the commonly used log gabor filter

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

period function and normalizers of vector fields in rn with n 1 first integrals we extend the theory that relates period function normalizers and first integrals which has been widely developed in r2 to any dimension in particular we show how to find n 1 independent normalizers of vector fields in rn with n 1 independent first integrals a formula for the derivatives of the period function is obtained and a necessary and sufficient condition for isochronicity is also proved these results generalize previous works of freire gasull and guillamon sabatini and villarini

detection localization and estimation of edges a method to detect locate and estimate edges in a one dimensional signal is presented it is inherently more accurate than all previous schemes as it explicitly models and corrects interaction between nearby edges the method is iterative with initial estimation of edges provided by the zero crossings of the signal convolved with laplacian of gaussian log filter the necessary computations necessitate knowledge of this convolved output only in a neighborhood around each zero crossing and in most cases could be performed locally by independent parallel processors results on one dimensional slices extracted from real images and on images which have been proposed independently in the row and column directions are shown an analysis of the method is provided including issues of complexity and convergence and directions of future research are outlined

the period function of generalized loudʼs centers abstract in this paper a three parameter family of planar differential systems with homogeneous nonlinearities of arbitrary odd degree is studied this family is an extension to higher degree of loud s systems the origin is a nondegenerate center for all values of the parameter and we are interested in the qualitative properties of its period function we study the bifurcation diagram of this function focusing our attention on the bifurcations occurring at the polycycle that bounds the period annulus of the center moreover we determine some regions in the parameter space for which the corresponding period function is monotonous or it has at least one critical period giving also its character maximum or minimum finally we propose a complete conjectural bifurcation diagram of the period function of these generalized loud s centers

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

first derivative of the period function with applications abstract given a centre of a planar differential system we extend the use of the lie bracket to the determination of the monotonicity character of the period function as far as we know there are no general methods to study this function and the use of commutators and lie bracket was restricted to prove isochronicity we give several examples and a special method which simplifies the computations when a first integral is known

study of the period function of a two parameter family of centers abstract in this paper we study the period function of x 1 x p 1 x q with p q r and p q we prove three independent results the first one establishes some regions in the parameter space where the corresponding center has a monotonous period function this result extends the previous ones by miyamoto and yagasaki for the case q 1 the second one deals with the bifurcation of critical periodic orbits from the center the third one is addressed to the critical periodic orbits that bifurcate from the period annulus of each one of the three isochronous centers in the family when perturbed by means of a one parameter deformation these three results together with the ones that we obtained previously on the issue lead us to propose a conjectural bifurcation diagram for the global behaviour of the period function of the family

two different approaches for iris recognition using gabor filters and multiscale zero crossing representation abstract importance of biometric user identification is increasing everyday one of the most promising techniques is the one based on the human iris the authors in this work describe different approaches to develop this biometric technique based on the works carried out by daugman the authors have worked using gabor filters and hamming distance but in addition they have also worked in zero crossing representation of the dyadic wavelet transform applied to two different iris signatures one based on a single virtual circle of the iris the other one based on an annular region also other metrics have been applied to be compared with the results obtained with the hamming distance in this work euclidean distance and d z will be shown the last proposed approach is translation rotation and scale invariant results will show a classification success up to 99 6 achieving an equal error rate down to 0 12 and the possibility of having null false acceptance rates with very low false rejection rates

glrt based detection estimation for undersampled training conditions for sensors where the number of available independent identically distributed training samples t is less than the number of antenna array elements m we propose nondegenerate properly normalized likelihood ratio lr tests both standard and scale invariant to support detection estimation of m point sources m t in white noise based on a generalized likelihood ratio test glrt approach we demonstrate that these tests can detect music specific ldquooutliersrdquo in the direction of arrival doa estimation of closely spaced independent sources caused by insufficient training volume and or signal to noise ratio snr we then compare the performance of the introduced lrs to other test statistics available in this undersampled regime we show that a search for solutions that increase the introduced lr allows us to replace the detected outliers by proper doa estimates this ldquopredict and curerdquo process leverages the snr ldquogaprdquo between music breakdown and breakdown of maximum likelihood estimation itself the resultant lr maximization makes the associated covariance model statistically ldquoas likelyrdquo as the true covariance matrix and removes the vast percentage of outliers in certain scenarios

the period in the lotka volterra system is monotonic abstract periodic solutions in a class of hamiltonian systems with one degree of freedom containing the lotka volterra system are considered their period is represented as an integral appropriate for numerical evaluation as well as for theoretical investigations the monotonicity of the period in the lotka volterra system follows as a simple consequence

global behaviour of the period function of the sum of two quasi homogeneous vector fields abstract we study the global behaviour of the period function on the period annulus of degenerate centres for two families of planar polynomial vector fields these families are the quasi homogeneous vector fields and the vector fields given by the sum of two quasi homogeneous hamiltonian ones in the first case we prove that the period function is globally decreasing extending previous results that deal either with the hamiltonian quasi homogeneous case or with the general homogeneous situation in the second family and after adding some more additional hypotheses we show that the period function of the origin is either decreasing or has at most one critical period and that both possibilities may happen this result also extends some previous results that deal with the situation where both vector fields are homogeneous and the origin is a non degenerate centre

exact results and universal asymptotics in the laguerre random matrix ensemble for various values of the parameters in the laguerre random matrix ensemble the distribution of the smallest eigenvalue and the scaled n level distribution function are calculated exactly in terms of generalized hypergeometric functions in certain cases these functions are expressed as multidimensional integrals from which asymptotic formulas are calculated and predictions of universal behavior verified

bifurcation of critical periods of polynomial systems abstract we describe a general approach to studying bifurcations of critical periods based on a complexification of the system and algorithms of computational algebra using this approach we obtain upper bounds on the number of critical periods of several families of cubic systems in some cases we overcome the problem of nonradicality of a relevant ideal by moving it to a subalgebra generated by invariants of a group of linear transformations

nonexistence of isochronous centers in planar polynomial hamiltonian systems of degree four abstract in this paper we study centers of planar polynomial hamiltonian systems and we are interested in the isochronous ones we prove that every center of a polynomial hamiltonian system of degree four that is with its homogeneous part of degree four not identically zero is nonisochronous the proof uses the geometric properties of the period annulus and it requires the study of the hamiltonian systems associated to a hamiltonian function of the form h x y a x b x y c x y 2 d x y 3