mixed integer programming model formulations for dynamic multi item multi level capacitated lotsizing abstract recently there have been two new proposals to model the dynamic multi item multi level capacitated lotsizing problem by variable redefinitions based on either a shortest route or a simple plant location representation of the underlying decision problem here we will introduce an extended version of the well known inventory and lotsize model followed by a new model formulation based on modeling the changes of end of period inventory levels explicitly secondly we will compare the suitability of different model formulations when solving problem instances with up to 40 items and 16 periods utilizing state of the art standard mip software on a personal computer

on nonstability of the linear recurrence of order one abstract we show that under some assumptions the linear recurrence or difference equation of order one in a banach space is nonstable in the hyers ulam sense our results are also connected with the notion of shadowing in dynamical systems and computer sciences

a hybrid optimization approach for multi level capacitated lot sizing problems abstract solving multi level capacitated lot sizing problems is still a challenging task in spite of increasing computational power and faster algorithms in this paper a new approach combining an ant based algorithm with an exact solver for mixed integer linear programs is presented a max min ant system is developed to determine the principal production decisions a lp mip solver is used to calculate the corresponding production quantities and inventory levels two different local search methods and an improvement strategy based on reduced mixed integer problems are developed and integrated into the ant algorithm this hybrid approach provides superior results for small and medium sized problems in comparison to the existing approaches in the literature for large scale problems the performance of this method is among the best

understanding complex dynamics by means of an associated riemann surface we provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated riemann surface thanks to this geometric description an explicit formula for the period of the orbits can be derived which is shown to depend on the initial data and the continued fraction expansion of a simple ratio of the coupling constants of the problem for rational values of this ratio and generic values of the initial data all orbits are periodic and the system is isochronous for irrational values of the ratio there exist periodic and quasi periodic orbits for different initial data moreover the dependence of the period on the initial data shows a rich behavior and initial data can always be found with arbitrarily large periods

nonautonomous impulsive systems with unbounded nonlinear terms in fenner and pinto 1999 23 proved that if the linear impulsive system satisfies the is condition see definition 2 1 with bounded nonlinear term f t x then the perturbed nonlinear impulsive system has a unique bounded solution see theorem a the method used to prove theorem a cannot be applied to the unbounded case in this paper we prove that if f t x e t m then the perturbed nonlinear impulsive system has a unique solution

dirichlet series and the integrability of multilinear differential equations we explore the relationship between the integrability of nonsemilinear partial differential equations and formal dirichlet series solutions to this end we consider a variety of integrable and nonintegrable differential equations we also demonstrate that such series solutions are a natural extension to the nonlinear case of those obtained by basic solution techniques for linear ordinary differential equations

multilevel capacitated lotsizing complexity and lp based heuristics abstract this paper presents the first heuristics capable of solving multilevel lotsizing problems with capacity constraints on more than one level moreover the form of the heuristics is quite general so that they can easily be extended to solve a variety of problems if one wants to solve these problems on a routine basis in a real environment one needs to find fast and easy algorithms however we show that for certain problem classes this is a very difficult task far more difficult than has been suggested in the literature for problems with setup times we show that finding a feasible solution is np complete even without setup times testing for feasibility can be very difficult just how time consuming such heuristics must be is demonstrated this leaves little chance to build fast and easy heuristics except for the most simple cases our exploration of the complexity issues points to mathematical programming as a potential source of heuristics for these problems this paper presents a new and general approach based on rounding an lp solution for the problem without setup times the methods use different information and patterns evident in the lp solution are explored the approach is tested on a large set of problems the main contributions of this paper are the way in which we distinguish between the easy and hard lotsizing problems the lp based heuristics and the test set of capacitated multilevel lotsizing problems

investigation of painleve property under time singularities transformations in this paper the relation between the painleve property for ordinary differential equations and some coordinate transformations in the complex plane is investigated two sets of transformations are introduced for which the transformations of singularities structure in the complex plane are explicitly computed the first set acts only on the dependent variables while the second one acts also on the independent variables it allows for defining an extended painleve test which is coordinates invariant our results are applied on various problems arising in the singularity analysis such as the problem of negative resonances and the weak painleve conjecture the method for finding new first integrals for dynamical systems is also shown

factorization and painleve analysis of a class of nonlinear third order partial differential equations a class of fully nonlinear third order partial differential equations pdes is considered this class contains several examples which have recently appeared in the literature and for which rather unusual travelling wave solutions have been given these solutions consist essentially of sums of exponentials we trace the occurrence of these exponentials back to the existence of a linear subequation which appears as a factor in the travelling wave reduction in addition we consider the painleve analysis of this set of equations both for the original pde and also for reductions to ordinary differential equations odes no equation in the class considered survives the combination of pde and ode tests also an equation in the class considered which is known to be integrable is shown to possess only the weak painleve property our analysis therefore confirms the limitations of the painleve test as a test for complete integrability when applied to fully nonlinear pdes

integrability and the painleve property for low dimensional systems we examine a system described by two first order nonlinear differential equations from the point of view of integrability the singularity analysis in the complex time plane is used to investigate the painleve property which according to the ablowitz ramani segur conjecture is a prerequisite for integrability for infinite dimensional systems we show that for such low dimensional systems the painleve analysis is still a most useful guide but integrable cases also exist which do not possess the painleve property

on the connection between hyperelliptic separability and painleve integrability we consider systems of odes which are associated with some physically significant examples shallow water equilibrium solutions travelling waves of the harry dym equation a lotka volterra system of competing species and the geodesic flow on the triaxial ellipsoid the first three are shown to share the following properties i they are hyperelliptically separable systems hss and after a suitable nonlinear time transformation become algebraically completely integrable aci and ii they are of the weak painleve type and become full painleve after the application of this transformation the geodesic flow on the other hand although it passes the usual painleve test does not possess a full set of free constants and thus one may not conclude whether it has the painleve property or not this system is also hss and becomes aci after the application of a suitable nonlinear time transformation we also combine our geometric analytical investigation with a numerical analysis of the system in the complex plane and show that there is perfect correspondence between the results of the two approaches this correspondence strengthens the reliability of such numerical studies and helps us better understand their implication in cases where such nonlinear transformations to complete integrability are not available

on the non integrability of a family of duffing van der pol oscillators we investigate the non integrability of a family of duffing van der pol oscillators x alpha x x2 1 x beta x3 gamma cos omega t by studying the analytic properties of the dynamics in complex time we find that the solutions of have no worse than algebraic singularities at t with only t t 1 2 terms present in their series expansions unlike for example the alpha 0 duffing case where typically log t t terms arise still when integrating around long enough contours a remarkably intricate pattern of square root singularities emerges on different sheets which appears to prevent solutions from ever returning to the original sheet such evidence of infinitely sheeted solutions termed the iss property has also been observed in a number of hamiltonian systems and is illustrated here on a simple example of a single first order differential equation we suggest that the iss property is a necessary condition for non integrability i e non existence of a complete set of analytic single valued constants of the motion which would permit the complete integration of a dynamical system in terms of quadratures

the kowalewski and henon heiles motions as manakov geodesic flows on so 4 a two dimensional family of lax pairs the invariant surfaces for the kowalewski top the henon heiles system and the manakov geodesic flow onso 4 complete into abelian surfacesa by adjoining in each case a divisord of arithmetic genus 9 these divisors belong to the same linear system ona and they each define a polarization 2 4 therefore there are rational maps transforming the kowalewski top and the henon heiles system into manakov s geodesic flow onso 4 this paper deals with the precise geometric relationship between these three problems it is based on the splitting of the 8 dimensional space of sections ofd theta functions into an even and an odd part and also on a normal form for the six quadrics describinga as embedded in 7 as a byproduct we get a 2 dimensional family of lax pairs for both the kowalewski top and the henon heiles system

a new class of integrable systems we present a family of dynamical systems associated with the motion of a particle in two space dimensions these systems possess a second integral of motion quadratic in velocities apart from the hamiltonian and are thus completely integrable they were found through the derivation and subsequent resolution of the integrability condition in the form of a partial differential equation pde for the potential a most important point is that the same pde was derived through considerations on the analytic structure of the singularities of the solutions weak painleve property

nagumo type existence results of sturm liouville bvp for impulsive differential equations abstract in this paper the method of upper and lower solutions and the schauder degree theory are employed in the study of sturm liouville boundary value problems for second order impulsive differential equations we obtain the existence of at least three solutions to the problem under the assumption that the nonlinear term f satisfies a nagumo condition with respect to the first order derivative

dynamical systems on infinitely sheeted riemann surfaces this paper is part of a program that aims to understand the connection between the emergence of chaotic behaviour in dynamical systems in relation with the multi valuedness of the solutions as functions of complex time in this work we consider a family of systems whose solutions can be expressed as the inversion of a single hyperelliptic integral the associated riemann surface r c is known to be an infinitely sheeted covering of the complex time plane ramified at an infinite set of points whose projection in the plane is dense the main novelty of this paper is that the geometrical structure of these infinitely sheeted riemann surfaces is described in great detail which allows to study global properties of the flow such as asymptotic behaviour of the solutions periodic orbits and their stability or sensitive dependence on initial conditions the results are then compared with a numerical integration of the equations of motion following the recent approach of calogero the real time trajectories of the system are given by paths on r that are projected to a circle on the complex plane due to the branching of r the solutions may have different periods or may not be periodic at all

stability for time varying linear dynamic systems on time scales we study conditions under which the solutions of a time varying linear dynamic system of the form x t a t x t are stable on certain time scales we give sufficient conditions for various types of stability including lyapunov type stability criteria and eigenvalue conditions on slowly varying systems that ensure exponential stability finally perturbations of the unforced system are investigated and an instability criterion is also developed

hyers ulam stability of a first order partial differential equation abstract we prove that the existence of a global prime integral leads in appropriate conditions to the hyers ulam stability of a linear partial differential equation of first order

non integrable systems with algebraic singularities in complex time dynamical arguments are presented which suggest that there are non integrable systems without clustering of singularities without infinite singularities or singularities with an infinite number of branches in the complex t plane several examples with only algebraic singularities are studied for which strong numerical evidence is presented for non integrability and infinitely sheeted solutions weak painleve potentials are also analysed from this point of view and all integrable cases are found to possess only finitely sheeted solutions

the hyers ulam stability constants of first order linear differential operators let x be a complex banach space h a complex valued continuous function on the real line r and th c1 r x c r x the linear differential operator defined by thu u hu we completely determine the hyers ulam stability constant of th

laplace transform and hyers ulam stability of linear differential equations abstract in this paper we prove the hyers ulam stability of a linear differential equation of the n th order more precisely applying the laplace transform method we prove that the differential equation y n t k 0 n 1 k y k t f t has hyers ulam stability where k is a scalar y and f are n times continuously differentiable and of exponential order respectively

optimization problems for general simple population with n impulsive harvest in this paper n impulsive harvest problems of general simple population are discussed by models with dirac function the optimal impulsive harvest policies to protect the renewable resource better are obtained under conditions of fixed quantity per impulsive harvest then a concept of the sequence for optimal harvest moments for general simple population is presented which is beneficial to protect resource better and sustainable development finally we apply the conclusions to some special models

hyers ulam stability of a system of first order linear differential equations with constant coefficients abstract in this paper using matrix method we prove the hyers ulam stability of a system of first order linear differential equations with constant coefficients

hamiltonians with high order integrals and the weak painleve concept we examine the singularity structure of the equations of motion associated to integrable two dimensional hamiltonians with second integrals of order higher than 2 we show in these specific examples that the integrability is associated to a singularity expansion of the weak painleve type new cases of integrability are discovered with still higher order integrals which are explicitly computed

existence of mild solutions for fractional neutral evolution equations abstract in this paper by using the fractional power of operators and some fixed point theorems we discuss a class of fractional neutral evolution equations with nonlocal conditions and obtain various criteria on the existence and uniqueness of mild solutions in the end we give an example to illustrate the applications of the abstract results

investigating non integrability and chaos in complex time the question of integrability of systems of ordinary differential equations odes has been studied extensively for centuries recently however owing to an upsurge of interest in chaos a lot of studies have focused on the investigation of non integrable systems where chaos often manifests itself as extremely sensitive dependence on initial conditions of a dense set of real solutions in real time here we argue that non integrability can be efficiently investigated by solving odes in complex time and review recent results which strongly suggest that for a system of odes to be non integrable it is necessary that it possess a dense set of infinitely sheeted solutions in the complex domain

hyers ulam stability of non autonomous systems in terms of boundedness of cauchy problems in this paper the concepts of hyers ulam stability are generalized for non autonomous linear differential systems we prove that the k periodic linear differential matrix system z t a t z t t r is hyers ulam stable if and only if the matrix family l e k 0 has no eigenvalues on the unit circle i e we study the hyers ulam stability in terms of dichotomy of the differential matrix system z t a t z t t r furthermore we relate hyers ulam stability of the system z t a t z t t r to the boundedness of solution of the following cauchy problem y t a t y t t t 0 y 0 x x 0 where a t is a square matrix for any t r t is a bounded function and x x 0 c m

the integration of three dimensional lotka volterra systems the general solutions of many three dimensional lotka volterra systems previously known to be at least partially integrable are constructed with the aid of special functions examples include certain abc and may leonard systems the special functions used are elliptic and incomplete beta functions in some cases the solution is parametric with the independent and dependent variables expressed as functions of a new time variable this auxiliary variable satisfies a nonlinear third order differential equation of a generalized schwarzian type and results of carton lebrun on the equations of this type that have the painleve property are exploited so as to produce solutions in closed form for several especially difficult lotka volterra systems the solutions are expressed in terms of painleve transcendents an appendix on incomplete beta functions and closed form expressions for their inverses is included

explicit integrability for hamiltonian systems and the painleve conjecture we analyze a class of hamiltonian systems in two dimensions for which we proved that a second constant of motion exists it is shown that using the two first integrals the equations of motion can be written in a form which allows their integration by quadratures an analysis of the equations of motion in this reduced form establishes the behavior of the solutions in the complex time plane it is shown explicitly that the systems belonging to this class possess the weak painleve property i e their solutions in complex time can present singularities of a specific algebraic type

kowalewski s asymptotic method kac moody lie algebras and regularization we use an effective criterion based on the asymptotic analysis of a class of hamiltonian equations to determine whether they are linearizable on an abelian variety i e solvable by quadrature the criterion is applied to a system with hamiltonian h 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 sum limits i 1 l p i 2 sum limits i 1 l 1 exp left sum limits j 1 l n ij x j right parametrized by a real matrixn n ij of full rank it will be solvable by quadrature if and only if for alli j 2 n nt ij n n t jj 1 is a nonpositive integer i e the interactions correspond to the toda systems for the kac moody lie algebras the criterion is also applied to a system of gross neveu

solvability of second order hamiltonian systems with impulses via variational method in this paper a class of second order impulsive hamiltonian systems are considered some new existence results are obtained by using a variational method and critical point theorem due to tang and wu some recent results are extended three examples are presented to illustrate the feasibility and effectiveness of our results

on a class of physically important integrable equations abstract a methodology introduced by fuchssteiner and the author is used to derive a class of physically important integrable evolution equations among these equations are integrable generalizations of the korteweg devries kdv of the modified kdv of the nonlinear schrodinger nls and of the sine gordon equations the modeling of water waves as well as general asymptotic considerations are used to illustrate the occurrence of the generalized modified kdv and nls equations respectively

iterative improvement methods for a multiperiod network design problem we address an important problem in telecommunications planning the multiperiod network expansion problem our aim is to show that it can be efficiently solved using a new local search approach to achieve our goal we first show how to adapt the problem s formulation to meet our local search program s requirements we then describe glit generic local improvement template a new generic auto calibrating local search algorithm the different neighbouring strategies that we designed specifically for this problem as well as a genetic algorithm for this problem we compare and discuss the performance of these algorithms using extensive computational tests on a large range of instances with up to 7500 arcs these experiments show that glit clearly outperforms competitive approaches especially when it is coupled with genetic algorithms we also show that the hybrid algorithms genetic tabu genetic simulated annealing and finally genetic glit all outperform both pure genetic and pure local search algorithms

homogeneous polynomials as lyapunov functions in the stability research of solutions of difference equations the linear autonomous system of difference equations x n 1 ax n is considered where email protected r k a is a real nonsingular kxk matrix in this paper it has been proved that if w x is any homogeneous polynomial of m th degree in x then there exists a unique homogeneous polynomial v x of m th degree such that dv v ax v x w x if and only if l 1 i 1 l 2 i 2 l k i k 1 i 1 i 2 i k m i j 0 where l 1 l 2 l k are the eigenvalues of the matrix a the theorem on the instability has also been proved

the painleve property for partial differential equations ii backlund transformation lax pairs and the schwarzian derivative in this paper we investigate the painleve property for partial differential equations by application to several well known partial differential equations burgers kdv mkdv bousinesq higher order kdv and kp equations it is shown that consideration of the singular manifold leads to a formulation of these equations in terms of the schwarzian derivative this formulation is invariant under the moebius group acting on dependent variables and is shown to obtain the appropriate lax pair linearization for the underlying nonlinear pde

ulam hyers stability of dynamic equations on time scales via picard operators in this paper we study the ulam hyers stability of some linear and nonlinear dynamic equations and integral equations on time scales we use both direct and operatorial methods and we propose a unified approach to ulam hyers stability based on the theory of picard operators see 28 33 our results extend some recent results from 24 25 8 14 13 5 6 to dynamic equations and are more general than the results from 1 the operatorial point of view based on the theory of picard operators allows to discuss the ulam hyers stability of many types of differential and integral equations on time scales and also to obtain simple and structured proofs to the existing results but as we point out at our final remarks there are also a few disadvantages

hyers ulam stability of linear differential equations of first order iii abstract let x be a complex banach space and let i a b be an open interval in this paper we will prove the generalized hyers ulam stability of the differential equation t y t y t t r x 0 0 for the class of continuously differentiable functions f i x where and r are complex constants and x 0 is an element of x by applying this result we also prove the hyers ulam stability of the euler differential equation of second order

on the stability of invariant sets of systems with impulse effect abstract a system of differential equations with impulse effect is considered it is assumed that this system has an invariant set m by means of the direct lyapunov method the necessary and sufficient conditions of its uniform asymptotic stability are obtained the conditions on the perturbations of right hand sides of differential equations and impulse effects under which the uniform asymptotic stability of the invariant set m of the nonperturbed system implies the uniform asymptotic stability of the invariant set of the perturbed system are obtained the stability properties of invariant sets of periodic systems are also studied

new definitions of exponential hyperbolic and trigonometric functions on time scales abstract we propose two new definitions of the exponential function on time scales the first definition is based on the cayley transformation while the second one is a natural extension of exact discretizations our exponential functions map the imaginary axis into the unit circle therefore it is possible to define hyperbolic and trigonometric functions on time scales in a standard way the resulting functions preserve most of the qualitative properties of the corresponding continuous functions in particular pythagorean trigonometric identities hold exactly on any time scale dynamic equations satisfied by cayley motivated functions have a natural similarity to the corresponding differential equations the exact discretization is less convenient as far as dynamic equations and differentiation are concerned

equilibrium states for impulsive semiflows abstract we consider impulsive semiflows defined on compact metric spaces and give sufficient conditions both on the semiflows and the potential functions for the existence and uniqueness of equilibrium states we also generalize the classical notion of topological pressure to our setting of discontinuous semiflows and prove a variational principle

ulam s type stability of impulsive ordinary differential equations abstract in this paper we introduce four ulam s type stability concepts for impulsive ordinary differential equations by applying the integral inequality of gronwall type for piecewise continuous functions ulam s type stability results for impulsive ordinary differential equations are obtained an example is also provided to illustrate our results

ulam s type stability of higher order nonlinear delay differential equations via integral inequality of gronwall bellman bihari s type abstract in this paper we prove the hyers ulam stability and the hyers ulam rassias stability of a class of higher order nonlinear delay differential equations with multiple bounded variable delays on a compact interval result of existence and uniqueness of solution is obtained by fixed point approach meanwhile for the first time integral inequality of gronwall bellman bihari s type with delay is applied to prove the stability theorem which made our results more generalized and interesting

population dynamics control in regard to minimizing the time necessary for the regeneration of a biomass taken away from the population the dynamics of a population whose mathematical model is the equation of verhulst is considered from the population by discrete external effects in the form of impulses a certain quantity of biomass is taken away or added this process is described by means of differential equations with impulses at fixed moments the moments and the magnitudes of the impulses are determined so that the time of regeneration of the quantity of biomass taken away from the population be minimal

the transition from regular to irregular motions explained as travel on riemann surfaces we introduce and discuss a simple hamiltonian dynamical system interpretable as a three body problem in the complex plane and providing the prototype of a mechanism explaining the transition from regular to irregular motions as travel on riemann surfaces the interest of this phenomenology illustrating the onset in a deterministic context of irregular motions is underlined by its generality suggesting its eventual relevance to understand natural phenomena and experimental investigations here only some of our main findings are reported without detailing their proofs a more complete presentation will be published elsewhere

meta heuristics for dynamic lot sizing a review and comparison of solution approaches proofs from complexity theory as well as computational experiments indicate that most lot sizing problems are hard to solve because these problems are so difficult various solution techniques have been proposed to solve them in the past decade meta heuristics such as tabu search genetic algorithms and simulated annealing have become popular and efficient tools for solving hard combinatorial optimization problems we review the various meta heuristics that have been specifically developed to solve lot sizing problems discussing their main components such as representation evaluation neighborhood definition and genetic operators further we briefly review other solution approaches such as dynamic programming cutting planes dantzig wolfe decomposition lagrange relaxation and dedicated heuristics this allows us to compare these techniques understanding their respective advantages and disadvantages gives insight into how we can integrate elements from several solution approaches into more powerful hybrid algorithms finally we discuss general guidelines for computational experiments and illustrate these with several examples

a heuristic approach for big bucket multi level production planning problems multi level production planning problems in which multiple items compete for the same resources frequently occur in practice yet remain daunting in their difficulty to solve in this paper we propose a heuristic framework that can generate high quality feasible solutions quickly for various kinds of lot sizing problems in addition unlike many other heuristics it generates high quality lower bounds using strong formulations and its simple scheme allows it to be easily implemented in the xpress mosel modeling language extensive computational results from widely used test sets that include a variety of problems demonstrate the efficiency of the heuristic particularly for challenging problems

existence uniqueness and stability of solution to mixed integral dynamic systems with instantaneous and noninstantaneous impulses on time scales abstract in this paper we study the existence and uniqueness of solution and stability results of mixed integral dynamic system with instantaneous and noninstantaneous impulses on time scales by using the fixed point method the main tools to establish our results are the gronwall s inequality on time scales picard operator and abstract gronwall lemma some assumptions are made to overcome the hurdles in achieving our results at the end an example is given that shows the validity of our main results

on the complete and partial integrability of non hamiltonian systems abstract the methods of singularity analysis are applied to several third order non hamiltonian systems of physical significance including the lotka volterra equations the three wave interaction and the rikitake dynamo model complete integrability is defined and new completely integrable systems are discovered by means of the painleve property in all these cases we obtain integrals which reduce the equations either to a final quadrature or to an irreducible second order ordinary differential equation ode solved by painleve transcendents relaxing the painleve property we find many partially integrable cases whose movable singularities are poles at leading order with in t t 0 terms entering at higher orders in an n th order generalized rossler model a precise relation is established between the partial fulfillment of the painleve conditions and the existence of n 2 integrals of the motion

symplectic structures their backlund transformations and hereditary symmetries abstract it is shown that compatible symplectic structures lead in a natural way to hereditary symmetries we recall that a hereditary symmetry is an operator valued function which immediately yields a hierarchy of evolution equations each having infinitely many commuting symmetries all generated by this hereditary symmetry furthermore this hereditary symmetry usually describes completely the soliton structure and the conservation laws of these equations this result then provide us with a method for constructing hereditary symmetries and hence exactly solvable evolution equations in addition we show how symplectic structures transform under backlund transformations this leads to a method for generating a whole class of symplectic structures from a given one several examples and applications are given illustrating the above results also the connection of our results with those of gelfand and dikii and of magri is briefly pointed out

multilevel lot sizing with setup times and multiple constrained resources internally rolling schedules with lot sizing windows in this paper a new time oriented decomposition heuristic is proposed to solve the dynamic multi item multilevel lot sizing problem in general product structures with single and multiple constrained resources as well as setup times while lot sizing decisions are made sequentially within an internally rolling planning interval or lot sizing window capacities are always considered over the entire planning horizon for each submodel a model formulation based on the simple plant location representation is developed these mixed integer linear submodels are solved by standard mathematical programming software even for relatively large test instances extensive computational tests show that the heuristic proposed provides a better solution quality than a well known special purpose heuristic

hyers ulam rassias stability of cauchy equation in the space of schwartz distributions abstract we reformulate and prove the hyers ulam rassias stability of cauchy equation in the space of schwartz tempered distributions and fourier hyperfunctions

newtonian dynamics in the plane corresponding to straight and cyclic motions on the hyperelliptic curve μ2 νn 1 n z ergodicity isochrony and fractals we study the complexification of the one dimensional newtonian particle in a monomial potential we discuss two classes of motions on the associated riemann surface the rectilinear and the cyclic motions corresponding to two different classes of real and autonomous newtonian dynamics in the plane the rectilinear motion has been studied in a number of papers while the cyclic motion is much less understood for small data the cyclic time trajectories lead to isochronous dynamics for bigger data the situation is quite complicated computer experiments show that for sufficiently small degree of the monomial the motion is generically isochronous with integer period which depends in a quite sensitive way on the initial data if the degree of the monomial is sufficiently high computer experiments show essentially chaotic behavior we suggest a possible theoretical explanation of these different behaviors we also introduce a two parameter family of two dimensional mappings describing the motion of the center of the circle as a convenient representation of the cyclic dynamics we call such a mapping the center map computer experiments for the center map show a typical multifractal behavior with periodicity islands therefore the above complexification procedure generates dynamics amenable to analytic treatment and possessing a high degree of complexity

on the stability of the linear differential equation of higher order with constant coefficients abstract we obtain a result on stability of the linear differential equation of higher order with constant coefficients in aoki rassias sense as a consequence we obtain the hyers ulam stability of the above mentioned equation a connection with dynamical sytems perturbation is established

a lagrangean based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times in this paper a heuristic approach for the dynamic multilevel multiitem lotsizing problem in general product structures with multiple constrained resources and setup times is proposed with the help of lagrangean relaxation the capacitated multilevel multiitem lotsizing problem is decomposed into several uncapacitated single item lotsizing problems from the solutions of these single item problems lower bounds on the minimum objective function value are derived upper bounds are generated by means of a heuristic finite scheduling procedure the quality of the approach is tested with reference to various problem groups of differing sizes

painleve conjecture revisited the discovery of new integrable two dimensional hamiltonian systems is reported the analytic structure of the solutions makes necessary the generalization of the painlev e conjecture a widely used integrability criterion such a generalization is presented which the authors believe should replace the usual conjecture for two dimensional hamiltonian systems it is indeed compatible with all the systems already found and in addition leads to still new integrable cases

boundary value problems for nonlinear impulsive hamiltonian systems we study two point boundary value problems for nonlinear impulsive hamiltonian systems spectral analysis of the corresponding linear impulsive hamiltonian system and a fixed point theorem are employed to obtain an existence and uniqueness result for solutions of the nonlinear problem two examples are given in which the main condition is made explicit

varieties of local integrability of analytic differential systems and their applications abstract in this paper we provide a characterization of local integrability for analytic or formal differential systems in r n or c n via the integrability varieties our result generalizes the classical one of poincare and lyapunov on local integrability of planar analytic differential systems to any finitely dimensional analytic differential systems as an application of our theory we study the integrability of a family of four dimensional quadratic hamiltonian systems

a perturbative painleve approach to nonlinear differential equations abstract we further improve the painleve test so that negative indices resonances can be treated we demand single valuedness not only for any pole like expansion as in the usual painleve test but also for every solution close to it represented as a perturbation series in a small parameter e order zero is the usual test order one already treated in a preliminary paper reduces to a linear fuchs analysis near a regular singularity and allows the introduction of all missing arbitrary coefficients higher orders lead to the analysis of a linear fuchsian type inhomogeneous equation we obtain an infinite sequence of necessary conditions for the absence of movable logarithmic branch points arising at every integer index whether positive or negative and at every order those arising at negative indices including 1 are new while some conditions may not arise before some high perturbation order we present several illustrative examples we discuss the understanding of negative indices and conclude that they are indistinguishable from positive indices just as in the fuchs theory in particular negative indices give rise to doubly infinite laurent series