meromorphic functions sharing values in an angular domain in this paper we study the problems of meromorphic functions sharing values in an angular domain and obtain some uniqueness results which are the improvement of the well known five value theorem and four value theorem given by nevanlinna

integrability of the 2d lotka volterra system via polynomial first integrals and polynomial inverse integrating factors we present new first integrals of the two dimensional lotka volterra systems which have a polynomial inverse integrating factor moreover we characterize all the polynomial first integrals of the two dimensional lotka volterra systems

optimal multireservoir network control by the discrete maximum principle an optimal control algorithm based on the discrete maximum principle is applied to multireservoir network control variable metric techniques are used for direct solution of the resulting two point boundary value problem state variable constraints are considered by use of penalty functions computer time and storage requirements are moderate and increase roughly linearly with the problem dimension application to a 10 reservoir network demonstrates efficacy of the proposed algorithm

integrable hamiltonians with higher transcendental invariants a new family of integrable two dimensional hamiltonians is found the corresponding potentials v x y are determined by the relation phi v y x a1v a2 0 where phi is an arbitrary function and a1 a2 are arbitrary parameters the second constants of motion are higher transcendental functions in momenta these results are found by deriving non separable solutions of the hamilton jacobi equation

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

utilization of soma and differential evolution for robust stabilization of chaotic logistic equation this paper deals with the utilization of two evolutionary algorithms self organizing migrating algorithm soma and differential evolution de for the optimization of the control of chaos this paper is aimed at an explanation on how to use evolutionary algorithms eas and how to properly define the advanced targeting cost function cf securing fast precise and mainly robust stabilization of selected chaotic system on a desired state for any initial conditions the role of ea here is as a powerful tool for an optimal tuning of control technique input parameters as a model of deterministic chaotic system the one dimensional discrete logistic equation was used the four canonical strategies of soma and six canonical strategies of de were utilized for each ea strategy repeated simulations were conducted to outline the effectiveness and robustness of used method and targeting cf securing robust solution satisfactory results obtained by both heuristic and the two proposed cost functions are compared with previous research given by different cost function designs

meromorphic functions in the unit disc that share values in an angular domain in this paper we investigate the uniqueness of meromorphic functions in the unit disc and consider the relation between the borel points and shared values of meromorphic functions in an angular domain

kowalevski s analysis of the swinging atwood s machine we study the kowalevski expansions near singularities of the swinging atwood s machine we show that there is an infinite number of mass ratios m m where such expansions exist with the maximal number of arbitrary constants these expansions are of the so called weak painleve type however in view of these expansions it is not possible to distinguish between integrable and nonintegrable cases

on the nonintegrability of yang mils potentials the nonintegrability of three hamiltonian systems obtained by simplifications of the yang mills classical field theory is proved by application of two theorems of yoshida 1987 1988 it is also shown that for the two four degree of freedom systems there exists a set of three independent integrals of motion in involution

non integrability of the truncated toda lattice hamiltonian at any order two sufficient conditions for the non existence of an additional analytic integral are given for hamiltonian systems with non homogeneous polynomial potential of an arbitrary degree an application is made to the truncated three particle toda lattice which is proved to be non integrable at any order

optimal short term hydro scheduling from the principle of progressive optimality this paper presents an algorithm based on the principle of progressive optimality for determining the optimal short term scheduling of multireservoir power systems the method takes into account water head variations spilling and time delays between upstream and downstream reservoirs the method is computationally efficient and has minimal storage requirements the convergence is monotonic and a global solution is reached contrary to dynamic programing the state variables do not have to be discretized with this method an example consisting of four hydroplants in series is solved and the results are presented

darboux points and integrability of hamiltonian systems with homogeneous polynomial potential in this paper we study the integrability of natural hamiltonian systems with a homogeneous polynomial potential the strongest necessary conditions for their integrability in the liouville sense have been obtained by a study of the differential galois group of variational equations along straight line solutions these particular solutions can be viewed as points of a projective space of dimension smaller by one than the number of degrees of freedom we call them darboux points we analyze in detail the case of two degrees of freedom we show that except for a radial potential the number of darboux points is finite and it is not greater than the degree of the potential moreover we analyze cases when the number of darboux points is smaller than maximal for two degrees of freedom the above mentioned necessary condition for integrability can be expressed in terms of one nontrivial eigenvalue of the hessian of potential calculated at a darboux point we prove that for a given potential these nontrivial eigenvalues calculated for all darboux points cannot be arbitrary because they satisfy a certain relation which we give in an explicit form we use this fact to strengthen maximally the necessary conditions for integrability and we show that in a generic case for a given degree of the potential there is only a finite number of potentials which satisfy these conditions we also describe the nongeneric cases as an example we give a full list of potentials of degree four satisfying these conditions then investigating the differential galois group of higher order variational equations we prove that except for one discrete family among these potentials only those which are already known to be integrable are integrable we check that a finite number of potentials from the exceptional discrete family are not integrable and we conjecture that all of them are not integrable

on the non integrability of some generalized toda lattices abstract we consider a one parameter family of two degrees of freedom generalized toda hamiltonians using ziglin s theorem with some extensions we prove the non existence of an additional single valued analytic integral except for special values of the parameter

an enhanced differential evolution algorithm for daily optimal hydro generation scheduling the daily optimal hydro generation scheduling problem dohgsb is a complicated nonlinear dynamic constrained optimization problem which plays an important role in the economic operation of electric power systems this paper proposes a new enhanced differential evolution algorithm to solve dohgsb in the proposed method chaos theory was applied to obtain self adaptive parameter settings in differential evolution de in order to handle constraints effectively three simple feasibility based selection comparison techniques embedded into de are devised to guide the process toward the feasible region of the search space the feasibility of the proposed method is demonstrated for the daily generation scheduling of a hydro system with four interconnected cascade hydro plants and the test results are compared with those obtained by the conjugate gradient and two phase neural network method in terms of solution quality the simulation results show that the proposed method is able to obtain higher quality solutions

existence of exponentially unstable periodic solutions and the non integrability of homogeneous hamiltonian systems abstract in hamiltonian systems with polynomial potential of homogeneous degree characteristic multipliers floquet multipliers permit an explicit expression for straight line periodic solutions by use of ziglin s theorem it is shown that the existence of an exponentially unstable straight line periodic solution implies the non integrability of the system

meromorphic functions in the unit disc that share slowly growing functions in an angular domain in this paper we investigate the uniqueness of meromorphic functions in the unit disc that share five distinct meromorphic functions of slow growth in an angular domain

lie symmetries and invariants of the lotka volterra system in this paper we use the lie symmetry method for finding rational and transcendental symmetry transformations and invariants for the 3d lotka volterra system

lie symmetries for the reduced three wave interaction problem the authors show how the method of lie symmetries can be used to obtain first integrals and for the identification of completely or partially integrable cases of the reduced three wave interaction problem

nonintegrability of nonhomogeneous nonlinear lattices we study the integrability of nonlinear lattices with nonhomogeneous polynomial potentials we prove a nonintegrability theorem for these dynamical systems

on the integrability of bianchi cosmological models in this paper we investigate the problem of the integrability of bianchi class a cosmological models this class of systems is reduced to the form of hamiltonian systems with exponential potential forms the dynamics of bianchi class a models is investigated through the euler lagrange equations and geodesic equations in the jacobi metric on this basis we have come to some general conclusions concerning the evolution of the volume of 3 space of constant time the general form of this function has been found it can serve as a controller during numerical calculations of the dynamics of cosmological models the integrability of cosmological models is also discussed from the points of view of different integrability criteria we show that the dimension of the phase space of bianchi class a hamiltonian systems can be reduced by two we prove that the vector field of the reduced system is polynomial and that it does not admit any analytic or even formal first integral

differential galois obstructions for integrability of homogeneous newton equations in this paper we formulate necessary conditions for the integrability in the jacobi sense of newton equations q f q where q cn and all components of f are polynomial and homogeneous of the same degree l these conditions are derived from an analysis of the differential galois group of variational equations along special particular solutions of the newton equations we show that taking all admissible particular solutions we restrict considerably the set of newton s equations satisfying the necessary conditions for the integrability moreover we apply the obtained conditions for a detailed analysis of the newton equations with two degrees of freedom i e n 2 we demonstrate the strength of the obtained results analyzing general cases with degfi l 4 for l 3 we have found an integrable case when the newton equations have two polynomial first integrals and both of them are of degree 4 in the momenta p1 q1 and p2 q2 moreover for an arbitrary l we found a particular family of newton equations d

a list of all integrable two dimensional homogeneous polynomial potentials with a polynomial integral of order at most four in the momenta we searched for integrable two dimensional homogeneous polynomial potentials with a polynomial first integral by using the so called direct method of searching for first integrals we proved that there exist no polynomial first integrals which are genuinely cubic or quartic in the momenta if the degree of homogeneous polynomial potentials is greater than four

a criterion for the non existence of an additional integral in hamiltonian systems with a homogeneous potential abstract a non integrability criterion on the basis of ziglin s theorem is given for two degrees of freedom hamiltonians with a homogeneous potential of integer degree as simple examples the anisotropic kepler problem and the one dimensional newtonian three body problem are proved to be non integrable a self contained proof of ziglin s theorem n dimensional homogeneous potential version is also given

non integrability criteria for hamiltonians in the case of lame normal variational equations abstract we consider complex analytic classical hamiltonian systems with two degrees of freedom and an invariant plane furthermore we assume that the normal variational equations nve are of lame type we describe the possible potentials giving rise to this kind of problems and non integrability criteria based on the differential galois approach to the ziglin theorem some examples are included

non integrable character of hamiltonian systems with global and symmetric coupling abstract a new sufficient condition to prove non integrability of hamiltonian systems with symmetric variational equations is proposed though the present condition is taken as an extension of ziglin and yoshida s non resonant condition the algorithmic bottle neck proving non integrability in high dimensional cases can be removed here as a result the non existence of additional integrals of various symmetric hamiltonian systems with an arbitrary number of degrees of freedom is proven

integrability partial integrability and nonintegrability for systems of ordinary differential equations the integrability of systems of ordinary differential equations with polynomial vector fields is investigated by using the singularity analysis methods three types of results are obtained first a general relationship between the degrees of first integrals and the so called kowalevskaya exponents is derived second it is shown that all solutions of algebraically integrable systems can be expanded in puiseux series third a new method to study partially integrable systems is studied these different aspects allow us to study algorithmically the integrability partial integrability and nonintegrability of differential systems

a new necessary condition for the integrability of hamiltonian systems with a two dimensional homogeneous potential abstract recently morales ruiz and ramis obtained a strong necessary condition for the integrability of hamiltonian systems with a homogeneous potential based on their own theorem on the differential galois theory picard vessiot theory for hamiltonian systems the theorem claims that if the original hamiltonian system is integrable then the variational equation around a particular solution is solvable in the sense of the differential galois theory i e the solution is obtained only by a combination of quadratures exponential of quadratures and algebraic functions in this paper a direct and independent proof of this statement is given for hamiltonian systems with a two dimensional homogeneous potential which leads to the new necessary condition for integrability this new necessary condition well justifies the so called weak painleve conjecture of ramani et al for the first time

nonintegrability of the suslov problem in this paper we investigate the suslov problem in the case when the vector of nonholonomic constraint coincides with the third principal axis of the body and the fixed point of the body lies in the principal plane defined by the third and the first principal axes but is out of these axes we called this version of the suslov problem the generalized kozlov case and we prove that in this case a third real meromorphic first integral functionally independent together with the energy and geometrical integrals does not exist

darboux integrability for 3d lotka volterra systems we describe the improved darboux theory of integrability for polynomial ordinary differential equations in three dimensions using this theory and computer algebra we study the existence of first integrals for the three dimensional lotka volterra systems only working up to degree two with the invariant algebraic surfaces and the exponential factors we find the major part of the known first integrals for such systems and in addition we find three new classes of integrability the method used is of general interest and can be applied to any polynomial ordinary differential equations in arbitrary dimension

global integrability of cosmological scalar fields we investigate the liouvillian integrability of hamiltonian systems describing a universe filled with a scalar field possibly complex the tool used is the differential galois group approach as introduced by morales ruiz and ramis the main result is that the generic systems with minimal coupling are non integrable although there still exist some values of parameters for which integrability remains undecided the conformally coupled systems are only integrable in four known cases we also draw a connection with the chaos present in such cosmological models and the issues of the integrability restricted to the real domain