relativistic chern simons higgs vortex equations an existence theorem is established for the solutions to the non abelian relativistic chern simons higgs vortex equations over a doubly periodic domain when the gauge group g assumes the most general and important prototype form g su n mathematics subject classification 2010 35c08 35j50 35q70 81e13

a quantum integrable supersymmetric multiple three wave interaction model a supersymmetric multiple three wave interaction model is proposed and its quantum integrability is demonstrated in a straightforward way

on growth rates of subadditive functions for semiflows abstract let x t x be a semiflow on a compact metric space x a function f x t x is subadditive with respect to if f x t s f x t f x t nbsp s we define the maximal growth rate of f to be sup x x lim sup t 1 t f x t this growth rate is shown to equal the maximal growth rate of the subadditive function restricted to the minimal center of attraction of the semiflow applications to birkhoff sums characteristic exponents of linear skew product semiflows on banach bundles and average lyapunov functions are developed in particular a relationship between the dynamical spectrum and the measurable spectrum of a linear skew product flow established by r a johnson k j palmer and g r sell siam j math anal 18 1987 1 33 is extended to semiflows in an infinite dimensional setting

tikhonov regularization and the l curve for large discrete ill posed problems discretization of linear inverse problems generally gives rise to very ill conditioned linear systems of algebraic equations typically the linear systems obtained have to be regularized to make the computation of a meaningful approximate solution possible tikhonov regularization is one of the most popular regularization methods a regularization parameter specifies the amount of regularization and in general an appropriate value of this parameter is not known a priori we review available iterative methods and present new ones for the determination of a suitable value of the regularization parameter by the l curve criterion and the solution of regularized systems of algebraic equations

robust permanence for interacting structured populations abstract the dynamics of interacting structured populations can be modeled by d x i d t a i x x i where x i r n i x x 1 x k and a i x are matrices with non negative off diagonal entries these models are permanent if there exists a positive global attractor and are robustly permanent if they remain permanent following perturbations of a i x necessary and sufficient conditions for robust permanence are derived using dominant lyapunov exponents i of the a i x with respect to invariant measures the necessary condition requires max i i 0 for all ergodic measures with support in the boundary of the non negative cone the sufficient condition requires that the boundary admits a morse decomposition such that max i i 0 for all invariant measures supported by a component of the morse decomposition when the morse components are axiom a uniquely ergodic or support all but one population the necessary and sufficient conditions are equivalent applications to spatial ecology epidemiology and gene networks are given

generalized arnoldi tikhonov method for sparse reconstruction this paper introduces two new algorithms belonging to the class of arnoldi tikhonov regularization methods which are particularly appropriate for sparse reconstruction the main idea is to consider suitable adaptively defined regularization matrices that allow the usual 2 norm regularization term to approximate a more general regularization term expressed in the p norm p geq 1 the regularization matrix can be updated both at each step and after some iterations have been performed leading to two different approaches the first one is based on the idea of the iteratively reweighted least squares method and can be obtained considering flexible krylov subspaces the second one is based on restarting the arnoldi algorithm numerical examples are given in order to show the effectiveness of these new methods and comparisons with some other already existing algorithms are made

limit cycles for competitor competitor mutualist lotka volterra systems abstract it is known that a limit cycle or periodic coexistence can occur in a competitor competitor mutualist lotka volterra system x 1 x 1 r 1 a 11 x 1 a 12 x 2 a 13 x 3 x 2 x 2 r 2 a 21 x 1 a 22 x 2 a 23 x 3 x 3 x 3 r 3 a 31 x 1 a 32 x 2 a 33 x 3 where r i a i j are positive real constants x liang j jiang the dynamical behavior of type k competitive kolmogorov systems and its applications to 3 dimensional type k competitive lotka volterra systems nonlinearity 16 2003 785 801 in this paper we shall construct an example with at least two limit cycles and furthermore we will show that the number of periodic orbits and hence a fortiori of limit cycles is finite it is also shown that contrary to three dimensional competitive lotka volterra systems nontrivial periodic coexistence does occur even if none of the three species can resist invasion from either of the others in this case new amenable conditions are given on the coefficients under which the system has no nontrivial periodic orbits these conditions imply that the positive equilibrium if it exists is globally asymptotically stable

approximation accuracy of the krylov subspaces for linear discrete ill posed problems abstract for the large scale linear discrete ill posed problem min a x b or a x b with b contaminated by gaussian white noise the lanczos bidiagonalization based krylov solver lsqr and its mathematically equivalent cgls the conjugate gradient cg method implicitly applied to a t a x a t b are most commonly used and cgme the cg method applied to min a a t y b or a a t y b with x a t y and lsmr which is equivalent to the minimal residual minres method applied to a t a x a t b have also been choices these methods exhibit typical semi convergence feature and the iteration number k plays the role of the regularization parameter however there has been no definitive answer to the long standing fundamental question can lsqr and cgls find 2 norm filtering best possible regularized solutions the same question is for cgme and lsmr too at iteration k lsqr cgme and lsmr compute different iterates from the same k dimensional krylov subspace a first and fundamental step towards answering the above question is to accurately estimate the accuracy of the underlying k dimensional krylov subspace approximating the k dimensional dominant right singular subspace of a assuming that the singular values of a are simple we present a general sin theorem for the 2 norm distances between these two subspaces and derive accurate estimates on them for severely moderately and mildly ill posed problems we also establish some relationships between the smallest ritz values and these distances numerical experiments justify the sharpness of our results

classical yang baxter equations and quantum integrable systems quantum integrable models associated with nondegenerate solutions of classical yang baxter equations related to the simple lie algebras are investigated these models are diagonalized for rational and trigonometric solutions in the cases of sl n gl n o n and sp n algebras the analogy with the quantum inverse scattering method is demonstrated

global stability and predator dynamics in a model of prey dispersal in a patchy environment on considere un systeme d equations differentielles autonomes non lineaires on determine l equilibre de ce systeme

on the quantization of the constrained akns flows it is shown that the quantum version of the constrained ablowitz kaup newell sogur akns flows from a completely integrable system and the corresponding lax pair can be constructed the quantum inverse problem for the system is then formulated following the technique of jurgo 1989 and gaunoulis 1987 finally the algebraic bethe ansatz is explicitly constructed thereby determining the energy eigenvalue of the excited states

criteria for cr robust permanence abstract let xi xifi x i 1 n be a cr vector field that generates a dissipative flow on the positive cone of rn is called permanent if the boundary of the positive cone is repelling is called crrobustly permanent if remains permanent for sufficiently small cr perturbations of the vector field a necessary condition and a sufficient condition for cr robust permanence involving the average per capita growth rates fi d with respect to invariant measures are derived the necessary condition requires that inf maxi fi d 0 where the infimum is taken over ergodic measures with compact support in the boundary of the positive cone the sufficient condition requires that the boundary flow admit a morse decomposition m1 mk such that every mj satisfies min maxi fi d 0 where the minimum is taken over invariant measures with support in mj as applications we provide a sufficient condition for cr robust permanence of lotka volterra models and a topological characterization of cr robust permanence for food chain models

robust uniform persistence in discrete and continuous nonautonomous systems abstract this is an extension of the work in salceanu 2011 14 to nonautonomous systems of difference and differential equations on the positive cone of r m that exhibit a positively invariant boundary hyperplane x it is shown that when a compact subset of x which attracts all orbits in x is a robust uniform weak repeller robust uniform persistence for the complementary dynamics i e the dynamics in r m x is obtained additional assumptions are made to deal with the nonautonomous nature of the systems some particular cases that often occur in applications are discussed and then sufficient conditions for the robust uniform persistence of the disease in two epidemic models from the literature are given

population dynamics under selection and mutation long time behavior for differential equations in measure spaces abstract we study the long time behavior of solutions to a measure valued selection mutation model that we formulated in 14 we establish permanence results for the full model and we study the limiting behavior even when there is more than one strategy of a given fitness a case that arises in applications we show that for the pure selection case the solution of the dynamical system converges to a dirac measure centered at the fittest strategy class provided that the support of the initial measure contains a fittest strategy thus we term this dirac measure an asymptotically stable strategy we also show that when the strategy space is discrete the selection mutation model with small mutation has a locally asymptotically stable equilibrium that attracts all initial conditions that are positive at the fittest strategy

arnoldi tikhonov regularization methods tikhonov regularization for large scale linear ill posed problems is commonly implemented by determining a partial lanczos bidiagonalization of the matrix of the given system of equations this paper explores the possibility of instead computing a partial arnoldi decomposition of the given matrix computed examples illustrate that this approach may require fewer matrix vector product evaluations and therefore less arithmetic work moreover the proposed range restricted arnoldi tikhonov regularization method does not require the adjoint matrix and hence is convenient to use for problems for which the adjoint is difficult to evaluate

quantum toda systems and lax pairs we describe a general method for constructing a lax pair representation of certain quantum mechanical systems that are integrable at the classical level this is then used to find conserved quantities at the quantum level for the toda systems

automatic parameter setting for arnoldi tikhonov methods in the framework of iterative regularization techniques for large scale linear ill posed problems this paper introduces a novel algorithm for the choice of the regularization parameter when performing the arnoldi tikhonov method assuming that we can apply the discrepancy principle this new strategy can work without restrictions on the choice of the regularization matrix moreover this method is also employed as a procedure to detect the noise level whenever it is just overestimated numerical experiments arising from the discretization of integral equations and image restoration are presented

discrete ill posed least squares problems with a solution norm constraint straightforward solution of discrete ill posed least squares problems with error contaminated data does not in general give meaningful results because propagated error destroys the computed solution error propagation can be reduced by imposing constraints on the computed solution a commonly used constraint is the discrepancy principle which bounds the norm of the computed solution when applied in conjunction with tikhonov regularization another approach which recently has received considerable attention is to explicitly impose a constraint on the norm of the computed solution for instance the computed solution may be required to have the same euclidean norm as the unknown solution of the error free least squares problem we compare these approaches and discuss numerical methods for their implementation among them a new implementation of the arnoldi tikhonov method also solution methods which use both the discrepancy principle and a solution norm constraint are considered

uniform persistence and chain recurrence soit 7b e d un espace metrique localement compact et e un sous ensemble clos de 7b e soit un systeme dynamique sur e on reconsidere la notion de persistance uniforme dans le cadre de la theorie de conley des ensembles invariants

how to find the lax pair from the yang baxter equation we show explicitly how to construct the quantum lax pair from the yang baxter equation we demonstrate the new method by applying it to the heisenberg xyz model

gmres type methods for inconsistent systems abstract the behavior of iterative methods of gmres type when applied to singular possibly inconsistent linear systems is discussed and conditions under which these methods converge to the least squares solution of minimal norm are presented error bounds for the computed iterates are shown this paper complements previous work by brown and walker p n brown h f walker siam j matrix anal appl 18 1997 37 51

classical and quantum mechanical systems of toda lattice type i solutions to the classical periodic and non periodic toda lattice type hamiltonian systems are expressed in terms of an iwasawa type factorization of a large lie group the scattering of these systems is determined in the non periodic case for the generalized periodic toda lattices a generalization of kostant s formula is obtained using standard representations of affine lie groups

uniform and strict persistence in monotone skew product semiflows with applications to non autonomous nicholson systems abstract we determine sufficient conditions for uniform and strict persistence in the case of skew product semiflows generated by solutions of non autonomous families of cooperative systems of odes or delay fdes in terms of the principal spectrums of some associated linear skew product semiflows which admit a continuous separation our conditions are also necessary in the linear case we apply our results to a noncooperative almost periodic nicholson system with a patch structure whose persistence turns out to be equivalent to the persistence of the linearized system along the null solution

kolmogorov vector fields with robustly permanent subsystems the following results are proven all subsystems of a dissipative kolmogorov vector field i xifi x are robustly permanent if and only if the external lyapunov exponents are positive for every ergodic probability measure with support in the boundary of the nonnegative orthant if the vector field is also totally competitive its carrying simplex is c1 applying these results to dissipative lotka volterra systems robust permanence of all subsystems is equivalent to every equilibrium x satisfying fi x 0 whenever xi 0 if in addition the lotka volterra system is totally competitive then its carrying simplex is c1

the stability under perturbations of repulsive sets on considere le systeme suivant sur r n x f x ou f f 1 f n x x 1 x n on demontre qu un theoreme de fonction de lyapunov inverse est verifie garantissant l existence d une fonction de lyapunov u et que l on peut choisir u de lipschitz

square smoothing regularization matrices with accurate boundary conditions this paper is concerned with the solution of large scale linear discrete ill posed problems the determination of a meaningful approximate solution of these problems requires regularization we discuss regularization by the tikhonov method and by truncated iteration the choice of regularization matrix in tikhonov regularization may significantly affect the quality of the computed approximate solution the present paper describes the construction of square regularization matrices from finite difference equations with a focus on the boundary conditions the regularization matrices considered have a structure that makes them easy to apply in iterative methods including methods based on the arnoldi process numerical examples illustrate the properties and effectiveness of the regularization matrices described

algebraic structure of the gradient holonomic algorithm for lax integrable nonlinear dynamical systems ii the reduction via dirac and canonical quantization procedure the generalized theory of the r structure on affine operator lie algebras is used to construct a complete theory of lax integrable nonlinear dynamical systems in multidimensions the operator bi hamiltonian structures and their functional reductions are discussed in great detail in the examples of operator korteweg de vries and benney kaup dynamical systems as an important by product of the developed algebraic theory the dirac canonical quantization problem is solved almost completely for the neumann bogoliubov type oscillatory dynamical system on spheres associated via moser with the spectral moment map on an affine associative metrized lie coalgebra with a one parameter gauge two cocycle some remarks are given on the problem of extending the developed algebraic theory to the case of lax integrable dynamical systems on discrete manifolds

regularization matrices determined by matrix nearness problems abstract this paper is concerned with the solution of large scale linear discrete ill posed problems with error contaminated data tikhonov regularization is a popular approach to determine meaningful approximate solutions of such problems the choice of regularization matrix in tikhonov regularization may significantly affect the quality of the computed approximate solution this matrix should be chosen to promote the recovery of known important features of the desired solution such as smoothness and monotonicity we describe a novel approach to determine regularization matrices with desired properties by solving a matrix nearness problem the constructed regularization matrix is the closest matrix in the frobenius norm with a prescribed null space to a given matrix numerical examples illustrate the performance of the regularization matrices so obtained

a predictor corrector iterated tikhonov regularization for linear ill posed inverse problems many questions in science and engineering often give rise to linear ill posed inverse problems to enable meaningful approximate solutions of the inverse problems various regularization methods have subsequently been proposed to make these problems less sensitive to perturbations one of the most popular regularization techniques is iterated tikhonov regularization which has attracted considerable attention due to its interesting applications in practical however this regularization often suffers from inaccurate results and low computational efficiency in some situations in this paper we proposed an accelerated predictor corrector iterated tikhonov regularization this method combined the classical iterated tikhonov regularization with modified euler method which could improve computational efficiency without sacrificing numerical accuracy the convergence rate of the accelerated regularization was investigated theoretically when the right hand side was corrupted by noise in particular we derived an error estimate of optimal order for the convergence of the accelerated regularization both one and two dimensional numerical experiments were implemented to illustrate the accuracy and efficiency of the accelerated version of iterated tikhonov regularization

arnoldi methods for image deblurring with anti reflective boundary conditions image deblurring with anti reflective boundary conditions and a non symmetric point spread function is considered several iterative methods based on krylov subspace projections as well as arnoldi tikhonov regularization methods with reblurring right or left preconditioners are compared the aim of the preconditioner is not to accelerate the convergence but to improve the quality of the computed solution and to increase the robustness of the regularization method right preconditioning in conjunction with methods based on the arnoldi process are found to be robust and give high quality restorations in particular when the observed image is contaminated by motion blur our new method is much more effective than other approaches described in the literature such as range restricted arnoldi methods and the conjugate gradient method applied to the normal equations implemented with the reblurring approach

implementations of range restricted iterative methods for linear discrete ill posed problems abstract this paper is concerned with iterative solution methods for large linear systems of equations with a matrix of ill determined rank and an error contaminated right hand side the numerical solution is delicate because the matrix is very ill conditioned and may be singular it is natural to require that the computed iterates live in the range of the matrix when the latter is symmetric because then the iterates are orthogonal to the null space computational experience indicates that it can be beneficial to require that the iterates live in the range of the matrix also when the latter is nonsymmetric we discuss the design and implementation of iterative methods that determine iterates with this property new implementations that are particularly well suited for use with the discrepancy principle are described

uniform persistence for nonautonomous and random parabolic kolmogorov systems abstract the purpose of this paper is to investigate uniform persistence for nonautonomous and random parabolic kolmogorov systems via the skew product semiflows approach it is first shown that the uniform persistence of the skew product semiflow associated with a nonautonomous random parabolic kolmogorov system implies that of the system various sufficient conditions in terms of the so called unsaturatedness and or lyapunov exponents for uniform persistence of the skew product semiflows are then provided among others it is shown that if the associated skew product semiflow has a global attractor and its restriction to the boundary of the state space has a morse decomposition which is unsaturated or whose external lyapunov exponents are positive then it is uniformly persistent more specific conditions are discussed for uniform persistence in n species particularly 3 species random competitive systems

on the regularizing properties of the gmres method the gmres method is a popular iterative method for the solution of large linear systems of equations with a nonsymmetric nonsingular matrix however little is known about the behavior of this method when it is applied to the solution of nonsymmetric linear ill posed problems with a right hand side that is contaminated by errors we show that when the associated error free right hand side lies in a finite dimensional krylov subspace the gmres method is a regularization method the iterations are terminated by a stopping rule based on the discrepancy principle

on thec1stability conjecture for flows we give a proof of thec1stability conjecture of palis and smale for flows which has reduced to proving thatc1structural stability implies axiom a the proof is based on the fundamental work of liao and mane and on the recent powerfulc1connecting lemma of hayashi

persistence in dynamical systems soit un espace metrique localement compact de metrique d et soit e un sous ensemble clos de a frontiere e et interieur e on suppose que l on a un flot continu 7b f defini sur e tel que e est invariant par 7b f on considere la notion de persistance et on donne un critere de persistance

uniform persistence and hopf bifurcations in r n we consider parameterized families of flows in locally compact metrizable spaces and give a characterization of those parameterized families of flows for which uniform persistence continues on the other hand we study the generalized poincare andronov hopf bifurcations of parameterized families of flows at boundary points of r n or more generally of an n dimensional manifold and show that this kind of bifurcations produce a whole family of attractors evolving from the bifurcation point and having interesting topological properties in particular in some cases the bifurcation transforms a system with extreme non permanence properties into a uniformly persistent one we study in the paper when this phenomenon happens and provide an example constructed by combining a holling type interaction with a pitchfork bifurcation