global solutions for a semilinear two dimensional klein gordon equation with exponential type nonlinearity we prove the existence and uniqueness of global solutions for a cauchy problem associated to a semilinear klein gordon equation in two space dimensions our result is based on an interpolation estimate with a sharp constant obtained by a standard variational method 2006 wiley periodicals inc

on tracking control of a class of complementary slackness hybrid mechanical systems abstract in this note we consider the problem of feedback control of n dof degree of freedom rigid manipulators subject to a scalar frictionless unilateral constraint f x 0 x r n is the vector of generalized coordinates the stability analysis relies on a stability concept that incorporates the hybrid and nonsmooth dynamical feature of the overall system it is shown that stability of the closed loop system can be obtained this work generalizes the results in brogliato et al ieee trans automat control 42 2 1997 200 215 which were mainly restricted to the 1 dof case it also clarifies some concepts related to the hybrid nature of closed loop complementary slackness mechanical systems

global well posedness and scattering for the defocusing l 2 critical nonlinear schrodinger equation when d 2 in this article we prove that the defocusing cubic nonlinear schrodinger initial value problem is globally well posed and scattering for u0 l2 r2 the proof uses the bilinear estimates of planchon and vega and a frequency localized interaction morawetz estimate similar to the high frequency estimate of colliander keel staffilani takaoka and tao and especially the low frequency estimate of dodson

hybrid zero dynamics of planar biped walkers planar underactuated biped walkers form an important domain of applications for hybrid dynamical systems this paper presents the design of exponentially stable walking controllers for general planar bipedal systems that have one degree of freedom greater than the number of available actuators the within step control action creates an attracting invariant set a two dimensional zero dynamics submanifold of the full hybrid model whose restriction dynamics admits a scalar linear time invariant return map exponentially stable periodic orbits of the zero dynamics correspond to exponentially stabilizable orbits of the full model a convenient parameterization of the hybrid zero dynamics is imposed through the choice of a class of output functions parameter optimization is used to tune the hybrid zero dynamics in order to achieve closed loop exponentially stable walking with low energy consumption while meeting natural kinematic and dynamic constraints the general theory developed in the paper is illustrated on a five link walker consisting of a torso and two legs with knees

robust trajectory tracking for a class of hybrid systems an internal model principle approach this paper deals with the asymptotic tracking of periodic trajectories for hybrid systems having linear dynamics in each operating mode and isolated discrete switching events switching systems parametric uncertainties are considered and the dimension of the state vector is allowed to vary among modes to deal with the hybrid nature of the system and the possible discontinuities of its solutions at switching times a properly amended tracking control problem is defined and a feedback control law based on a discontinuous version of the classical internal model principle is proposed the innovative design of the discrete time dynamics of the compensator guarantees the robust existence of a steady state response giving zero tracking error in the controlled output and local convergence to it

long time dynamics of defocusing energy critical 3 1 dimensional wave equation with potential in the radial case using the channel of energy inequalities developed by t duyckaerts c kenig and f merle we prove that modulo a free radiation any finite energy radial solution to the defocusing energy critical wave equation with radial potential in 3 1 dimensions converges to the set of steady states as time goes to infinity for generic potentials we prove there are only finitely many steady states and in this case modulo some free radiation the solution converges to one steady state as time goes to infinity

asymptotic behaviour and attractors for a semilinear damped wave equation with supercritical exponent we prove the existence of a global attractor for the problem where f is coercive at infinity and satisfies the growth condition while g l 2 r 3

dynamics for the energy critical nonlinear wave equation in high dimensions t duyckaerts and f merle 2008 studied the variational structure near the ground state solution w of the energy critical wave equation and classified the solutions with the threshold energy e w 0 in dimensions d 3 4 5 in this paper we extend the results to all dimensions d 6 the main issue in high dimensions is the non lipschitz continuity of the nonlinearity which we get around by making full use of the decay property of w

k means type algorithms a generalized convergence theorem and characterization of local optimality the k means algorithm is a commonly used technique in cluster analysis in this paper several questions about the algorithm are addressed the clustering problem is first cast as a nonconvex mathematical program then a rigorous proof of the finite convergence of the k means type algorithm is given for any metric it is shown that under certain conditions the algorithm may fail to converge to a local minimum and that it converges under differentiability conditions to a kuhn tucker point finally a method for obtaining a local minimum solution is given

iterated maxima search for the maximally diverse grouping problem the maximally diverse grouping problem mdgp is to partition the vertices of an edge weighted and undirected complete graph into m groups such that the total weight of the groups is maximized subject to some group size constraints mdgp is a np hard combinatorial problem with a number of relevant applications in this paper we present an innovative heuristic algorithm called iterated maxima search ims algorithm for solving mdgp the proposed approach employs a maxima search procedure that integrates organically an efficient local optimization method and a weak perturbation operator to reinforce the intensification of the search and a strong perturbation operator to diversify the search extensive experiments on five sets of 500 mdgp benchmark instances of the literature show that ims competes favorably with the state of the art algorithms we provide additional experiments to shed light on the rationality of the proposed algorithm and investigate the role of the key ingredients

an elementary proof of the blow up for semilinear wave equation in high space dimensions abstract this paper concerns the blow up of solutions to u tt u u p in high dimensions for n 4 and 1 p p 0 n where p 0 n is a critical exponent we proved that the solutions blow up in finite time by estimating the solutions near the wave front using elementary inequalities

variable neighborhood search principles and applications abstract systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization called variable neighborhood search vns we present a basic scheme for this purpose which can easily be implemented using any local search algorithm as a subroutine its effectiveness is illustrated by solving several classical combinatorial or global optimization problems moreover several extensions are proposed for solving large problem instances using vns within the successive approximation method yields a two level vns called variable neighborhood decomposition search vnds modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed vns svns heuristic finally we show how to stabilize column generation algorithms with help of vns and discuss various ways to use vns in graph theory i e to suggest disprove or give hints on how to prove conjectures an area where metaheuristics do not appear to have been applied before

brief paper passivity based switching control of flexible joint complementarity mechanical systems in this study one considers the tracking control problem of a class of nonsmooth lagrangian systems with flexible joints and subject to frictionless unilateral constraints the task under consideration consists of a succession of free motion and constrained motion phases particular attention is paid to impacting and detachment phases a passivity based switching controller that allows one to extend the stability analysis described in our previous works to the case of systems with lumped flexibilities is proposed numerical tests show the effectiveness of the controller

global classical solutions of nonlinear wave equations is a formally selfadjoint positive elliptic operator and f is a real c2 function with non negative primitive function we treat both the homogeneous initialboundary value problem over ir x f2 for a smooth open set 2clr and the cauchy problem over ir x 1r for the initial boundary value problem we show that any strong solution of 0 1 known to exist according to heinz and yon wahl 4 if 2rn f j u2 o lul 2j j 0 1 u oo

tracking control for hybrid systems with state triggered jumps this paper addresses the tracking problem in which the controller should stabilize time varying reference trajectories of hybrid systems despite the fact that discrete events or jumps in hybrid systems can often not be controlled directly as e g is the case in impacting mechanical systems the controller should still stabilize the desired trajectory a major complication in the analysis of this hybrid tracking problem is that in general the jump times of the plant do not coincide with those of the reference trajectory consequently the conventional euclidean tracking error does not converge to zero even if trajectories converge to the reference trajectory in between jumps and the jump times converge to those of the reference trajectory hence standard control approaches can not be applied we propose a novel definition of the tracking error that overcomes this problem and formulate lyapunov based conditions for the global asymptotic stability of the hybrid reference trajectory using these conditions we design hysteresis based controllers that solve the hybrid tracking problem for two exemplary systems including the well known bouncing ball problem

deformations for linear periodic discrete time systems the adjoint normal form following the technique proposed by arnold for matrices time invariant autonomous systems and extended by tannenbaum to time invariant linear control systems with inputs and outputs a normal form for linear periodic discrete time systems depending on physical parameters is proposed the considered actions are deformations i e linear periodic transformations depending on the parameters being identity at the nominal values of them

quantum classical correspondence in polygonal billiards we show that wave functions in planar rational polygonal billiards all angles rationally related to ensuremath pi can be expanded in a basis of quasistationary and spatially regular states unlike the energy eigenstates these states are directly related to the classical invariant surfaces in the semiclassical limit this is illustrated for the barrier billiard we expect that these states are also present in integrable billiards with point scatterers or magnetic flux lines

follow the bouncing ball global results on tracking and state estimation with impacts in this paper we formulate tracking and state estimation problems of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set due to the discontinuous trajectories arising from the impacts we use hybrid systems stability analysis tools to establish the results using a novel concept of mirrored images of the target mass we prove that 1 a tracking control algorithm and 2 an observer algorithm guarantee global exponential stability results for specific classes of polyhedral billiards including rectangles moreover we combine these two algorithms within dynamic controllers that guarantee global output feedback tracking the results are illustrated via simulations

the global cauchy problem for the non linear klein gordon equation on demontre l unicite de solutions faibles et l existence et l unicite de solutions globales fortement continues dans l espace energie

the p median problem for cluster analysis a comparative test using the mixture model approach recently mulvey and crowder mulvey j h crowder 1979 cluster analysis an application of lagrangian relaxation management sci 25 329 340 suggested that the p median problem might be useful for cluster analysis problems where the goal is to group objects described by a vector of characteristics in such a way that objects in the same group are somehow more alike than objects in different groups the intent of this paper is to test mulvey and crowder s proposal using the mixture model approach i e by applying a number of algorithms including one for the p median problem to a set of objects randomly sampled from a number of known multivariate populations and comparing the ability of each algorithm to detect the original populations in order to evaluate the results a generalized partition comparison measure and its distribution are developed using this measure results from various algorithms are compared

record breaking optimization results using the ruin and recreate principle a new optimization principle is presented solutions of problems are partly but significantly ruined and rebuilt or recreated afterwards performing this type of change frequently one can obtain astounding results for classical optimization problems the new method is particularly suited for more complex optimization problems discontinuous ones problems with hard to find admissible solutions problems with complex objectives or many constraints the method is an all purpose heuristic numerical results are given for the traveling salesman problem for the vehicle routing problem with time windows and for network optimization numerical evidence for the quality of the proposed principle is given for most of the instances of a research library of problems the ruin and recreate r r implementation achieved the best published results for many instances better or much better solutions could be found

a simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem over the last decade many metaheuristics have been applied to the flowshop scheduling problem ranging from simulated annealing or tabu search to complex hybrid techniques some of these methods provide excellent effectiveness and efficiency at the expense of being utterly complicated in fact several published methods require substantial implementation efforts exploit problem specific speed up techniques that cannot be applied to slight variations of the original problem and often re implementations of these methods by other researchers produce results that are quite different from the original ones in this work we present a new iterated greedy algorithm that applies two phases iteratively named destruction were some jobs are eliminated from the incumbent solution and construction where the eliminated jobs are reinserted into the sequence using the well known neh construction heuristic optionally a local search can be applied after the construction phase our iterated greedy algorithm is both very simple to implement and as shown by experimental results highly effective when compared to state of the art methods

on periodical trajectories of the billiard systems within an ellipsoid in rd and generalized cayley s condition the analytical condition for a trajectory of the billiard system within an ellipsoid of any dimension is given an interesting property is obtained every periodical trajectory with the period less than the dimension of the space is placed in a coordinate hyperplane

trajectory tracking for a particle in elliptical billiards an infinitely rigid unitary mass particle is considered moving on a planar region delimited by a rigid elliptical barrier elliptical billiards under the action of proper control forces a class of periodic trajectories involving an infinite sequence of non smooth impacts between the mass and the barrier at fixed times is found by using an lmis based procedure the jumps in the velocities at the impact times render difficult if not impossible to obtain the classical stability and attractivity properties for the dynamic system describing the tracking error behaviour hence the tracking control problem is properly stated using notions similar to the quasi stability concept in v lakshmikantham d d bainov and p s simeonov theory of impulsive differential equations 6 world scientific 1989 a controller whose state is subject to discontinuities based on the internal model principle is shown to solve the proposed tracking problem giving rise to control forces that are piecewise continuous fun

on the control of complementary slackness juggling mechanical systems studies the feedback control of a class of complementary slackness hybrid mechanical systems roughly the systems we study are composed of an uncontrollable part the object and a controlled one the robot linked by a unilateral constraint and an impact rule a systematic and general control design method for this class of systems is proposed the approach is a nontrivial extension of the one degree of freedom dof juggler control design in addition to the robot control it is also useful to study some intermediate controllability properties of the object s impact poincare mapping which generally takes the form of a nonlinear discrete time system the force input mainly consists of a family of dead beat feedback control laws introduced via a recursive procedure and exploiting the underlying discrete time structure of the system the main goal of the paper is to highlight the role of various physical and control properties characteristic of the system on its stabilizability properties and to propose solutions in certain cases

control of contact problem in constrained euler lagrange systems stabilization of an euler lagrange system onto a constraint surface when the system makes contact with a nonzero impact velocity is an important problem in systems interacting with external environments potential applications include robotic surface following and surface finishing operations in manufacturing industry in the paper the constrained dynamic equations are modeled as a set of nonsmooth differential equations depending on whether the system lies on the constraint surface or the system repeatedly makes and loses contact with the constraint surface the focus is on the initial condition problem i e the system hits the constraint with a nonzero impact velocity a new discontinuous control scheme is proposed that ensures stable regulation of the system onto the constraint surface

an iterated greedy heuristic for the sequence dependent setup times flowshop problem with makespan and weighted tardiness objectives iterated greedy ig algorithms are based on a very simple principle are easy to implement and can show excellent performance in this paper we propose two new ig algorithms for a complex flowshop problem that results from the consideration of sequence dependent setup times on machines a characteristic that is often found in industrial settings the first ig algorithm is a straightforward adaption of the ig principle while the second incorporates a simple descent local search furthermore we consider two different optimization objectives the minimization of the maximum completion time or makespan and the minimization of the total weighted tardiness extensive experiments and statistical analyses demonstrate that despite their simplicity the ig algorithms are new state of the art methods for both objectives

strichartz type estimates and the well posedness of an energy critical 2d wave equation in a bounded domain abstract we study the well posedness of the cauchy problem with dirichlet or neumann boundary conditions associated to an h 1 critical semilinear wave equation on a smooth bounded domain r 2 first we prove an appropriate strichartz type estimate using the l q spectral projector estimates of the laplace operator our proof follows burq lebeau and planchon 2008 4 then we show the global well posedness when the energy is below or at the threshold given by the sharp moser trudinger inequality finally in the supercritical case we prove an instability result using the finite speed of propagation and a quantitative study of the associated ode with oscillatory data

hybrid output regulation for linear systems with periodic jumps solvability conditions structural implications and semi classical solutions the problem of output regulation for a class of hybrid linear systems characterized by periodic jumps is considered in this paper necessary and sufficient conditions for its solution are provided both in the full information and error feedback case by a detailed analysis of such conditions several interesting properties are derived including the fact that the regulator must contain a suitably defined copy of the flow zero dynamics of the plant in addition to the usual copy of the exosystem dynamics and the fact that the output regulation problem is generically solvable for fat plants having more inputs than outputs and generically not solvable for square plants in addition semi classical solutions to the hybrid output regulation problem are introduced and discussed such solutions are characterized by the property that the required steady state input can be generated as a simple linear function of the state of the exosystem as in the non hybrid case although the associated steady state response has a genuinely hybrid structure

an iterated greedy heuristic for a market segmentation problem with multiple attributes this research has been supported by the mexican national council for science and technology conacyt through grants cb2005 01 48499y and cb2011 01 166397 and a scholarship for graduate studies and by the universidad autonoma de nuevo leon through its scientific and technological research support program paicyt grants ca1478 07 ce012 09 it511 10 and ce331 15 ruben ruiz is partially supported by the spanish ministry of economy and competitiveness under the project scheyard optimization of scheduling problems in container yards no dpi2015 65895 r financed by feder funds we would like to thank rafael frinhani richard fuchshuber and their corresponding research teams for providing us the source code of their algorithms to carry out the corresponding tests furthermore we are grateful to the editor and the four anonymous reviewers for their careful reading of our manuscript and their constructive comments and suggestions which helped us improve its quality

on the control of finite dimensional mechanical systems with unilateral constraints this paper focuses on the problem of the control of a class of mechanical systems with a finite number of degrees of freedom subject to unilateral constraints on the position roughly speaking those systems are described by a set of ordinary differential equations that represent smooth dynamics together with an algebraic inequality condition f q spl ges 0 where q is the vector of generalized coordinates and an impact rule relating the interaction impulse and the velocity nonsmooth dynamics is at the core of the study of such systems this implies that one can suitably define solutions and stability concepts that fit with the considered model we then discuss the closed loop control problem and analyze various switching control strategies

trajectory tracking control of multiconstraint complementarity lagrangian systems in this study one considers the tracking control problem of a class of nonsmooth fully actuated lagrangian systems subject to frictionless unilateral constraints the task under consideration contains both free motion and constraint motion phases a switching controller that guarantees an approximate tracking is designed particular attention is paid to transition impacting and detachment between different phases of motion the exogenous signals that assure the stabilization on take off from some constraints are explicitly defined this paper extends previous works on the topic as it considers more than one constraint for n degree of freedom systems numerical examples illustrate the main results

modeling and control of impact in mechanical systems theory and experimental results considers the equations of motion of mechanical systems subject to inequality constraints which can be obtained by looking for the stationary value of the action integral two different methods are used to take into account the inequality constraints in the computation of the stationary value of the action integral the valentine variables method and the penalty functions method the equations of motion resulting from the application of the valentine variables method which introduces the concept of nonsmooth impacts constitute the exact model of the constrained mechanical system such a model is suitable to be employed when the impacting parts of the actual mechanical system are very stiff the equations of motion resulting from the application of the penalty functions method which introduces the concept of smooth impacts constitute an approximate model of the constrained mechanical system such a model is suitable to be employed when the impacting parts of the actual mechanical system show some flexibility various feedback control laws from the natural outputs and from their time derivatives are studied with reference to both models of impact the closed loop systems resulting from the application of the same control law to both models show pretty much the same global asymptotic stability properties the proposed control laws are only concerned with regulation problems in the presence of possible contacts and impacts among parts of the mechanical system or with the external environment the effectiveness of the proposed control structure has been tested experimentally with reference to a single link robot arm showing a valuable behavior

elliptical billiards and hyperelliptic functions the geometrical properties of the elliptical billiard system are related to poncelet s theorem this theorem states that if a polygon is inscribed in a conic and circumscribed about a second conic every point of the former conic is a vertex of a polygon with the same number of sides and the same perimeter chang and friedberg have extended this theorem to three and higher dimensions they have shown that the geometrical properties of the hyperelliptic billiard system are related to the algebraic character of a poincare map in the phase space the geometrical and algebraic properties of the system can be understood in terms of the analytical structure of the equations of motion these equations form a complete system of abelian integrals the integrability of the physical system is reflected by the topology of the riemann surfaces associated to these integrals the algebraic properties are connected with the existence of addition formulas for hyperelliptic functions the main purpose of this study is to establish such a connection and to provide an algebraic proof of poncelet s theorem in three and higher dimensions

distance function design and lyapunov techniques for the stability of hybrid trajectories the comparison between time varying hybrid trajectories is crucial for tracking observer design and synchronisation problems for hybrid systems with state triggered jumps in this paper a generic distance function is designed that can be used for this purpose the so called peaking phenomenon which occurs when using the euclidean distance to compare two hybrid trajectories is circumvented by taking the hybrid nature of the system explicitly into account based on the proposed distance function we define the stability of a trajectory and present sufficient lyapunov type conditions for hybrid system with state triggered jumps a constructive lyapunov function design is presented for hybrid systems with affine flow and jump maps and a jump set that is a hyperplane the stability conditions can then be verified using linear matrix conditions finally for this class of systems we present a tracking controller that asymptotically stabilises a given hybrid reference trajectory and we illustrate our results with an example

shifting representation search for hybrid flexible flowline problems this paper considers the hybrid flexible flowline scheduling problem with a set of additional restrictions and generalizations that are common in practice these include precedence constraints sequence dependent setup times time lags machine eligibility and release times there are many potential solution representations for this problem ranging from simple and compact to more complex and complete typically when choosing the degree of detail of the solution representation a tradeoff can be found between efficiency of the algorithm and the size of the search space several adaptations of existing methods are introduced memetic algorithm iterated local search iterated greedy as well as a novel algorithm called shifting representation search srs this new method starts with an iterated greedy algorithm applied to a permutation version of the problem and at a given time switches to an iterated local search on the full search space as far as we know this shift of the solution representation is new in the scheduling literature experimental results and statistical tests clearly prove the superiority of srs compared with classical and existing methods

nondispersive radial solutions to energy supercritical non linear wave equations with applications in this paper we establish optimal pointwise decay estimates for non dispersive compact radial solutions to non linear wave equations in 3 dimensions in the energy supercritical range as an application we show for the full energy supercritical range in the defocusing case that if the scale invariant sobolev norm of a radial solution remains bounded in its maximal interval of existence then the solution must exist for all times and scatter

iterated greedy for the maximum diversity problem abstract the problem of choosing a subset of elements with maximum diversity from a given set is known as the maximum diversity problem many algorithms and methods have been proposed for this hard combinatorial problem including several highly sophisticated procedures by contrast in this paper we present a simple iterated greedy metaheuristic that generates a sequence of solutions by iterating over a greedy construction heuristic using destruction and construction phases extensive computational experiments reveal that the proposed algorithm is highly effective as compared to the best so far metaheuristics for the problem under consideration

structural properties of a class of linear hybrid systems and output feedback stabilization in this paper we deal with the problem of output feedback stabilization for a class of linear hybrid systems this problem is addressed by characterizing the structural properties of such a class of systems namely reachability controllability stabilizability observability constructibility and detectability are framed in terms of algebraic and geometric conditions on the data of the system two canonical forms recalling the classical kalman decompositions with respect to reachability and observability are given by taking advantage of this characterization duality between control and observation structural properties is established and necessary and sufficient conditions for the existence of a linear time invariant output feedback compensator are stated compared with previous results no assumption is needed on the plant about minimum phaseness relative degree or squareness

lmis for constrained polynomial interpolation with application in trajectory planning we consider an open loop trajectory planning problem for linear systems with bound constraints originating from saturations or physical limitations using an algebraic approach and results on positive polynomials we show that this control problem can be cast into a constrained polynomial interpolation problem admitting a convex linear matrix inequality lmi formulation

asymptotic tracking of periodic trajectories for a simple mechanical system subject to nonsmooth impacts an infinitely rigid mass is considered which moves on a plane under the action of proper control forces within a closed region delimited by an infinitely massive and rigid circular barrier a suitably amended tracking problem for a class of periodic trajectories involving an infinite number of nonsmooth impacts between the mass and the barrier is formally stated and solved

conditions of cayley s type for ellipsoidal billiard the billiard system within an ellipsoid in three dimensional space is considered we describe periodical trajectories of that mechanical system deriving analytical condition of cayley s type for generalized poncelet s theorem using methods of algebrogeometric integration

iterated greedy local search methods for unrelated parallel machine scheduling abstract this work deals with the parallel machine scheduling problem which consists in the assignment of n jobs on m parallel machines the most general variant of this problem is when the processing time depends on the machine to which each job is assigned to this case is known as the unrelated parallel machine problem similarly to most of the literature this paper deals with the minimization of the maximum completion time of the jobs commonly referred to as makespan c max many algorithms and methods have been proposed for this hard combinatorial problem including several highly sophisticated procedures by contrast in this paper we propose a set of simple iterated greedy local search based metaheuristics that produce solutions of very good quality in a very short amount of time extensive computational campaigns show that these solutions are most of the time better than the current state of the art methodologies by a statistically significant margin

a blowing up wave equation with exponential type nonlinearity and arbitrary positive energy abstract we consider in two space dimensions the nonexistence of global solutions to the class of klein gordon equations t t u u u f a u t x 0 t we give sufficient conditions on the data such that the solution of the above klein gordon equation blows up in finite time

geometric tools for solving the fdi problem for linear periodic discrete time systems this paper studies the problem of detecting and isolating faults in linear periodic discrete time systems the aim is to design an observer based residual generator where each residual is sensitive to one fault whilst remaining insensitive to the other faults that can affect the system making use of the geometric tools and in particular of the outer observable subspace notion the fault detection and isolation fdi problem is formulated and necessary and solvability conditions are given an algorithmic procedure is described to determine the solution of the fdi problem

global well posedness and scattering for the defocusing energy supercritical cubic nonlinear wave equation abstract in this paper we consider the defocusing cubic nonlinear wave equation u t t u u 2 u 0 in the energy supercritical regime in dimensions d 6 with no radial assumption on the initial data we prove that if a solution satisfies an a priori bound in the critical homogeneous sobolev space throughout its maximal interval of existence that is u l t h x s c h x s c 1 then the solution is global and it scatters our analysis is based on the methods of the recent works of kenig and merle 2008 21 and killip and visan 2010 26 27 treating the energy supercritical nonlinear schrodinger and wave equations