the approximation for the boundary optimal control problem of burgers fisher equation with constraints this paper deals with the numerical approximation with meshless method for the boundary optimal control problem with some control and state constraints governed by the burgers fisher equation which is a nonlinear evolution equation and is the prototype model for the reaction convection and diffusion phenomena arising in many spatial temporal processes by making use of the element free galerkin efg method the original optimal control problem is discretized spatially to a semi discrete optimal control problem governed by a system of nonlinear ordinary differential equations then by using the control parameterization method the original problem can be reduced to an optimal parameter selection problem governed by a lumped parameter system which can be solved as a nonlinear optimization problems by using the sequential quadratic programming sqp algorithm the numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method

distributional chaos revisited in their famous paper schweizer and smital introduced the definition of a distributionally chaotic pair and proved that the existence of such a pair implies positive topological entropy for continuous mappings of a compact interval further their approach was extended to the general compact metric space case in this article we provide an example which shows that the definition of distributional chaos and as a result li yorke chaos may be fulfilled by a dynamical system with intuitively regular dynamics embedded in 3 next we state strengthened versions of distributional chaos which as we show are present in systems commonly considered to have complex dynamics we also prove that any interval map with positive topological entropy contains two invariant subsets x y c i such that f x has positive topological entropy and f y displays distributional chaos of type 1 but not conversely

quasi factors of zero entropy systems for minimal systems x t of zero topological entropy we demon strate the sharp difference between the behavior regarding entropy of the sys tems m x t and 2x t induced by t on the spaces m x of prob ability measures on x and 2x of closed subsets of x it is shown that the system m x t has itself zero topological entropy two proofs of this the orem are given the first uses ergodic theoretic ideas the second relies on the different behavior of the banach spaces ln and ln with respect to the existence of almost hilbertian central sections of the unit ball in contrast to this theorem we construct a minimal system x t of zero entropy with a minimal subsystem y t of 2 t whose entropy is positive school of mathematics tel aviv university ramat aviv israel e mail address glasner0math tau ac il institute of mathematics hebrew university jerusalem israel e mail address weissfmath huji ac il this content downloaded from 207 46 13 117 on sun 23 oct 2016 04 35 33 utc all use subject to http about jstor org terms

positive topological entropy and δ weakly mixing sets abstract the notion of weakly mixing set is introduced and studied it is proved that weakly mixing sets share many properties with weakly mixing sets in particular if a dynamical system has positive topological entropy then the collection of weakly mixing sets is residual in the closure of the collection of entropy sets in the hyperspace the existence of weakly mixing sets in a topological dynamical system admitting an ergodic invariant measure which is not measurable distal is obtained these results generalize several well known results and also answer several open questions

optimal control computation for nonlinear systems with state dependent stopping criteria in this paper we consider a challenging optimal control problem in which the terminal time is determined by a stopping criterion this stopping criterion is defined by a smooth surface in the state space when the state trajectory hits this surface the governing dynamic system stops by restricting the controls to piecewise constant functions we derive a finite dimensional approximation of the optimal control problem we then develop an efficient computational method based on nonlinear programming for solving the approximate problem we conclude the paper with four numerical examples

independence in topological and c dynamics we develop a systematic approach to the study of independence in topological dynamics with an emphasis on combinatorial methods one of our principal aims is to combinatorialize the local analysis of topological entropy and related mixing properties we also reframe our theory of dynamical independence in terms of tensor products and thereby expand its scope to c dynamics

on li yorke pairs the li yorke definition of chaos proved its value for interval maps in this paper it is considered in the setting of general topological dynamics we adopt two opposite points of view on the one hand sufficient conditions for li yorke chaos in a topological dynamical system are given we solve a long standing open question by proving that positive entropy implies li yorke chaos on the other hand properties of dynamical systems without li yorke pairs are investigated in addition to having entropy 0 they are minimal when transitive and the property is stable under factor maps arbitrary products and inverse limits finally it is proved that minimal systems without li yorke pairs are disjoint from scattering systems

on the lifting of elliptic cusp forms to siegel cusp forms of degree 2n i 1 cf 8 in this paper we will prove that their conjecture is true moreover we obtain a simple fourier coefficient formula for f z ibukiyama 23 also made a similar conjecture which was formulated in terms of the koecher maass series which we will not consider here let us describe our results throughout this paper we fix positive integers k and n such that k n mod 2 and put e 1 k 1 n for any positive rational number n we denote the absolute value of the discriminant of q vn q by dn the primitive dirichlet character corresponding to q v n q is denoted by xn let fn be the positive rational number such that n nf2nlet b e m2n q be a positive definite half integral symmetric matrix put db det 2b db d db fb f db and xb x db note that edb 0 1 mod 4 and that fb is an integer for each prime p let p qp cx be the unique additive character such that bp x exp 27ir ltx for x e z p 1 recall that the siegel series for b is defined by

runge kutta methods in optimal control and the transformed adjoint system the convergence rate is determined for runge kutta discretizations of nonlinear control problems the analysis utilizes a connection between the kuhn tucker multipliers for the discrete problem and the adjoint variables associated with the continuous minimum principle this connection can also be exploited in numerical solution techniques that require the gradient of the discrete cost function

on minimum time paths of bounded curvature with position dependent constraints we consider the problem of a particle traveling from an initial configuration to a final configuration given by a point in the plane along with a prescribed velocity vector in minimum time with non homogeneous velocity and with constraints on the minimum turning radius of the particle over multiple regions of the state space necessary conditions for optimality of these paths are derived to characterize the nature of optimal paths both when the particle is inside a region and when it crosses boundaries between neighboring regions these conditions are used to characterize families of optimal and nonoptimal paths among the optimality conditions we derive a refraction law at the boundary of the regions that generalizes the so called snell s law of refraction in optics to the case of paths with bounded curvature tools employed to deduce our results include recent principles of optimality for hybrid systems a numerical example is given to demonstrate the derived results

time optimal zermelo s navigation problem with moving and fixed obstacles in this paper we consider a time optimal zermelo s navigation problem znp with moving and fixed obstacles this problem can be formulated as an optimal control problem with continuous inequality constraints and terminal state constraints by using the control parametrization technique together with the time scaling transform the problem is transformed into a sequence of optimal parameters selection problems with continuous inequality constraints and terminal state constraints for each problem an exact penalty function method is used to append all the constraints to the objective function yielding a new unconstrained optimal parameters selection problem it is solved as a nonlinear optimization problem different scenarios are considered in the simulation and the results obtained show that the proposed method is effective

brief paper optimal control problems with multiple characteristic time points in the objective and constraints in this paper we develop a computational method for a class of optimal control problems where the objective and constraint functionals depend on two or more discrete time points these time points can be either fixed or variable using the control parametrization technique and a time scaling transformation this type of optimal control problem is approximated by a sequence of approximate optimal parameter selection problems each of these approximate problems can be viewed as a finite dimensional optimization problem new gradient formulae for the cost and constraint functions are derived with these gradient formulae standard gradient based optimization methods can be applied to solve each approximate optimal parameter selection problem for illustration two numerical examples are solved

the weak specification property and distributional chaos abstract in this paper we first discuss almost periodic points in a compact dynamical system with the weak specification property on the basis of this discussion we draw two conclusions i the weak specification property implies a dense mycielski uniform distributionally scrambled set ii the weak specification property and a fixed point imply a dense mycielski uniform invariant distributionally scrambled set these conclusions improve on some of the latest results concerning the specification property and give a final positive answer to an open problem posed in p oprocha invariant scrambled sets and distributional chaos dyn syst 24 2009 31 43

distributionally scrambled invariant sets in a compact metric space abstract the paper solves a question posed by oprocha on the existence of invariant distributionally chaotic scrambled sets we show among other things that a continuous map f acting on compact metric space x d with a weak specification property fixed point and infinitely many mutually distinct periods has a dense mycielski i e c dense set of type f invariant distributionally scrambled set as a consequence we describe a class of maps with a distributionally scrambled invariant set of full lebesgue measure in the case when x is a k dimensional cube

specification on the interval we study the consequences of discontinuities on the specification property for interval maps after giving a necessary and sufficient condition for a piecewise monotonic piecewise continuous map to have this property we show that for a large and natural class of families of such maps including the 3 transformations the set of parameters for which the specification property holds though dense has zero lebesgue measure thus regarding the specification property the general case is at the opposite of the continuous case solved by a m blokh russian math surveys 38 1983 133 134 for which we give a proof

optimal boundary control for water hammer suppression in fluid transmission pipelines when fluid flow in a pipeline is suddenly halted a pressure surge or wave is created within the pipeline this phenomenon called water hammer can cause major damage to pipelines including pipeline ruptures in this paper we model the problem of mitigating water hammer during valve closure by an optimal boundary control problem involving a nonlinear hyperbolic pde system that describes the fluid flow along the pipeline the control variable in this system represents the valve boundary actuation implemented at the pipeline terminus to solve the boundary control problem we first use the method of lines to obtain a finite dimensional ode model based on the original pde system then for the boundary control design we apply the control parameterization method to obtain an approximate optimal parameter selection problem that can be solved using nonlinear optimization techniques such as sequential quadratic programming sqp we conclude the paper with simulation results demonstrating the capability of optimal boundary control to significantly reduce flow fluctuation

measures of chaos and a spectral decomposition of dynamical systems on the interval let f 0 1 0 1 be continuous for x y e 0 1 the upper and lower distance distribution functions fx y and fxy are defined for any t 0 as the lim sup and lim inf as n oc of the average number of times that the distance ifi x fi y i between the trajectories of x and y is less than t during the first n iterations the spectrum of f is the system f of lower distribution functions which is characterized by the following properties 1 the elements of f are mutually incomparable 2 for any f e f there is a perfect set pf 8 0 such that fuv f and fuv 1 for any distinct u v e pf 3 if s is a scrambled set for f then there are f g in f and a decomposition s sf u sg sg may be empty such that fuv f if u v e sf and fuv g if u v e sg our principal results are 1 if f has positive topological entropy then f is nonempty and finite and any f e f is zero on an interval 0 e where e 0 and hence any pf is a scrambled set in the sense of li and yorke 2 if f has zero topological entropy then f f where f 1 it follows that the spectrum of f provides a measure of the degree of chaos of f in addition a useful numerical measure is the largest of the numbers fo 1 f t dt where f e f

a chaotic function with a distributively scrambled set of full lebesgue measure abstract misiurewicz proved that there exists a continuous map of the interval 0 1 onto itself for which there exists a scrambled set of full lebesgue measure in this paper we form a continuous interval map which has a distributively scrambled set of full lebesgue measure in which each point has dense orbit this contains misiurewicz s result since any distributively scrambled set must be scrambled but the converse is not generally true

δ weakly mixing subset in positive entropy actions of a nilpotent group abstract the notion of weakly mixing subsets is introduced for countable torsion free discrete group actions it is shown that for a finitely generated torsion free discrete nilpotent group action positive topological entropy implies the existence of weakly mixing subsets and while there exists a finitely generated torsion free discrete solvable group action which has positive topological entropy but without any weakly mixing subsets

controller design and value function approximation for nonlinear dynamical systems this work considers the infinite time discounted optimal control problem for continuous time input affine polynomial dynamical systems subject to polynomial state and box input constraints we propose a sequence of sum of squares sos approximations of this problem obtained by first lifting the original problem into the space of measures with continuous densities and then restricting these densities to polynomials these approximations are tightenings rather than relaxations of the original problem and provide a sequence of rational controllers with value functions associated to these controllers converging under some technical assumptions to the value function of the original problem in addition we describe a method to obtain polynomial approximations from above and from below to the value function of the extracted rational controllers and a method to obtain approximations from below to the optimal value function of the original problem thereby obtaining a sequence of asymptotically optimal rational controllers with explicit estimates of suboptimality numerical examples demonstrate the approach

optimal shortcuts to adiabaticity for a quantum piston abstract in this paper we use optimal control to design minimum time adiabatic like paths for the expansion of a quantum piston under realistic experimental constraints we calculate the minimum expansion time and compare it with that obtained from a state of the art inverse engineering method we use this result to rederive the known upper bound for the cooling rate of a refrigerator which provides a quantitative description for the unattainability of absolute zero the third law of thermodynamics we finally point out the relation of the present work to the fast adiabatic like expansion of an accordion optical lattice a system which can be used to magnify the initial quantum state quantum microscope

pullback of the lifting of elliptic cusp forms and miyawaki s conjecture we construct a lifting from siegel cusp forms of degree r to siegel cusp forms of degree r 2n for r n 1 our result is a partial solution of a conjecture made by miyawaki 27 page 307 in 1992 in particular we can calculate the standard l function of a cusp form of degree 3 and weight 12 which is in accordance with miyawaki s conjecture we give a conjecture on the petersson inner product of the lifting in terms of certain l values

distributional chaos on compact metric spaces via specification properties abstract in this paper we show that a continuous function on a compact metric space exhibits distributional chaos as introduced in b schweizer and j smital trans amer math soc 344 1994 737 754 and elucidated in b schweizer a sklar and j smital to appear if the function has either a weaker form of the specification property see m denker c grillenberger and k sigmund springer lecture notes in mathematics vol 527 springer verlag new york heidelberg berlin 1976 or the generalized specification property introduced in f balibrea b schweizer a sklar and j smital to appear in particular any anosov diffeomorphism is distributionally chaotic regardless of the fact that in this case the trajectories of a e pair of points exhibit regular non chaotic behavior

a computational method for solving time delay optimal control problems with free terminal time abstract this paper considers a class of optimal control problems for general nonlinear time delay systems with free terminal time we first show that for this class of problems the well known time scaling transformation for mapping the free time horizon into a fixed time interval yields a new time delay system in which the time delays are variable then we introduce a control parameterization scheme to approximate the control variables in the new system by piecewise constant functions this yields an approximate finite dimensional optimization problem with three types of decision variables the control heights the control switching times and the terminal time in the original system which influences the variable time delays in the new system we develop a gradient based optimization approach for solving this approximate problem simulation results are also provided to demonstrate the effectiveness of the proposed approach

generalized specification property and distributionally scrambled sets abstract suppose the dynamical system x f has generalized specification property in this paper we research the existence of the invariant mycielski distributionally scrambled sets for dynamical system x f moreover some properties about measure center are discussed and a dichotomy theorem is proved

a mass formula for unimodular lattices with no roots we derive a mass formula for n dimensional unimodular lattices having any prescribed root system we use katsurada s formula for the fourier coefficients of siegel eisenstein series to compute these masses for all root systems of even unimodular 32 dimensional lattices and odd unimodular lattices of dimension n 30 in particular we find the mass of even unimodular 32 dimensional lattices with no roots and the mass of odd unimodular lattices with no roots in dimension n 30 verifying bacher and venkov s enumerations in dimensions 27 and 28 we also compute better lower bounds on the number of inequivalent unimodular lattices in dimensions 26 to 30 than those afforded by the minkowski siegel mass constants