hub location as the minimization of a supermodular set function this paper highlights how a general class of hub location problems can be modeled as the minimization of a real valued supermodular set function well known problems such as uncapacitated hub location p hub median and hub arc location among others are shown to be particular cases of this class two integer programming formulations are introduced and compared one uses path based variables frequently employed in hub location whereas the other exploits properties of supermodular functions in addition several worst case bounds for a greedy and a local improvement heuristic are obtained for the general class and for some particular cases in which sharper bounds can be devised computational experiments are performed to compare both formulations when used with a general purpose solver computational results obtained on benchmark instances confirm the superiority of the supermodular formulation

polygonal homographic orbits of the curved n body problem in the 2 dimensional n body problem n 3 in spaces of constant curvature 6 0 we study polygonal homographic solutions we first provide necessary and sufficient conditions for the existence of these orbits and then consider the case of regular polygons we further use this criterion to show that for any n 3 the regular ngon is a polygonal homographic orbit if and only if all masses are equal then we prove the existence of relative equilibria of non equal masses on the sphere of curvature 0 for n 3 in the case of scalene triangles such triangular relative equilibria occur only along fixed geodesics and are generated from fixed points of the sphere finally through a classification of the isosceles case we prove that not any three masses can form a triangular relative equilibrium

finite time boundary stabilization of general linear hyperbolic balance laws via fredholm backstepping transformation this paper is devoted to a simple and new proof on the optimal finite control time for general linear coupled hyperbolic system by using boundary feedback on one side the feedback control law is designed by first using a volterra transformation of the second kind and then using an invertible fredholm transformation both existence and invertibility of the transformations are easily obtained

phase space structure and regularization of manev type problems phase space structure and regularization of manev type problems florin diacu a vasile mioc b cristina stoica c a department of mathematics and statistics university of victoria victoria canada v8w 3p4 b astronomical institute of the romanian academy astronomical observatory cluj napoca str cire silor 19 3400 cluj napoca romania c institute for gravitation and space sciences laboratory for gravitation str mendeleev 21 25 bucharest romania

state and output feedback boundary control for a coupled pde ode system abstract this note is devoted to stabilizing a coupled pde ode system with interaction at the interface first a state feedback boundary controller is designed and the system is transformed into an exponentially stable pde ode cascade with an invertible integral transformation where pde backstepping is employed moreover the solution to the resulting closed loop system is derived explicitly second an observer is proposed which is proved to exhibit good performance in estimating the original coupled system and then an output feedback boundary controller is obtained for both the state and output feedback boundary controllers exponential stability analyses in the sense of the corresponding norms for the resulting closed loop systems are provided the boundary controller and observer for a scalar coupled pde ode system as well as the solutions to the closed loop systems are given explicitly

saari s conjecture for the collinear n body problem in 1970 don saari conjectured that the only solutions of the newtonian n body problem that have constant moment of inertia are the relative equilibria we prove this conjecture in the collinear case for any potential that involves only the mutual distances furthermore in the case of homogeneous potentials we show that the only collinear and non zero angular momentum solutions are homographic motions with central configurations

experiments in quadratic 0 1 programming we present computational experience with a cutting plane algorithm for 0 1 quadratic programming without constraints our approach is based on a reduction of this problem to a max cut problem in a graph and on a partial linear description of the cut polytope

compensating the distributed effect of a wave pde in the actuation or sensing path of mimo lti systems abstract the problem of compensation of infinite dimensional actuator or sensor dynamics of more complex type than pure delay was solved recently using the backstepping method for pdes in this paper we construct an explicit feedback law for a multi input lti system which compensates the wave pde dynamics in its input and stabilizes the overall system our design is based on a novel infinite dimensional backstepping forwarding transformation we illustrate the effectiveness of our design with a simulation example of a single input second order system in which the wave input enters the system through two different channels each one located at a different point in the domain of the wave pde finally we consider a dual problem where we design an exponentially convergent observer that compensates the distributed effect of the wave sensor dynamics

boundary observer design for hyperbolic pde ode cascade systems the paper presents an observer design for a class of hyperbolic pde ode cascade systems with a boundary measurement the cascade systems consist of coupled pdes featuring one rightward and one leftward convecting first order transport pdes and a set of odes which enter the pdes through the left boundary of the systems the design which is based on the volterra integral transformation relies only on a single sensor at the right boundary of the system the observer consists of a copy of the plant plus output injection terms both in the pdes and the odes the observer is constructed in a collocated setup which means both sensing and actuation are located at the same boundary the observer gains are computed analytically by solving goursat type pdes in terms of bessel function of the first kind the observer design is tested against a field scale flow loop test experiment in stavanger by statoil oil company the results show that the observer converges to the actual values and that the design can be used as a process monitoring tool in oil well drilling

triple collision in the quasi homogeneous collinear three body problem abstract we generalize and improve the result of f diacu j differential equations 128 1996 58 77 concerning the dynamics of three points particles moving on the line under the influence of a quasihomogeneous potential w u v where u and v are homogeneous functions of degree a and b respectively for b 2 we found a set of positive measure of collision orbits that do not tend to form asymptotically a central configuration

on the anisotropic manev problem we consider the manev potential given by the sum between the inverse and the inverse square of the distance in an anisotropic space i e such that the force acts differently in each direction using mcgehee coordinates we blow up the collision singularity paste a collision manifold to the phase space study the flow on and near the collision manifold and find a positive measure set of collision orbits besides frontal homothetic frontal nonhomothetic and spiraling collisions and ejections we put into the evidence the surprising class of oscillatory collision and ejection orbits using the infinity manifold we further tackle capture and escape solutions in the zero energy case by finding the connection orbits between equilibria and or cycles at impact and at infinity we describe a large class of capture collision and ejection escape solutions

central configurations and homographic solutions for the quasihomogeneous n body problem for the n body problem given by quasihomogeneous force functions of the form c1 ra c2 rb c1 c2 real and 0 a b we prove that the simultaneous and extraneous central configurations are the only types of central configurations then we focus on attractive attractive force functions c1 and c2 positive and analyze the connection between central configurations and homographic solutions namely we extend the classical lagrange s theorem a solution is homographicif and only if the bodies form equivalent central configurations for all times to attractive attractive quasihomogeneous problems and give sufficient conditions for the construction of homographic solutions

central configurations and total collisions for quasihomogeneous n body problems abstract we consider n body problems given by potentials of the form r a r b with a b constants 0 a b to analyze the dynamics of the problem we first prove some properties related to central configurations including a generalization of moulton s theorem then we obtain several qualitative properties for collision and near collision orbits in the manev type case a 1 at the end we point out some new relationships between central configurations relative equilibria and homothetic solutions

comet and hill type periodic orbits in restricted n 1 body problems abstract we consider the planar restricted n 1 body problem where the interaction potential between the particle and the primaries is taken to be a finite sum of terms of the form distance with 0 the primaries are assumed to be in a relative equilibrium that is they form a uniformly rotating rigid configuration we show two results first if the infinitesimal particle is far from the primaries and the long range dominant term r of the potential is such that 0 and 2 then there exist two one parameter families of large nearly circular periodic solutions these solutions called comet solutions are elliptic and kam stable for 2 and unstable for 2 second if the infinitesimal particle is close to one of the primaries and the short range dominant term r of the potential near that primary is such that 0 and 2 then there exist two one parameter families of nearly circular periodic solutions called hill solutions that encircle the nearby primary for 2 these orbits are unstable the methodology applied involves appropriate symplectic scalings poincare s continuation method and averaging theory the kam stability of the comet periodic orbits is decided by verifying arnol d s non degeneracy conditions

compensating actuator and sensor dynamics governed by diffusion pdes for possibly unstable ode systems with actuator delay predictor based infinite dimensional feedback can compensate for actuator delay of arbitrary length and achieve stabilization we extend this concept to another class of pde ode cascades where the infinite dimensional part of the plant is of diffusive rather than convective type we derive predictor like feedback laws and observers with explicit gain kernels the gain kernels involve second order matrix exponentials of the system matrix of the ode plant which is the result of the second order in space character of the actuator sensor dynamics the construction of the kernel functions is performed using the continuum version of the backstepping method robustness to small perturbations in the diffusion coefficient is proved

linear stability of relative equilibria in the charged three body problem a relative equilibrium is a periodic orbit of the n body problem that rotates uniformly maintaining the same central configuration for all time in this paper we generalize some results of r moeckel and we apply it to study the linear stability of relative equilibria in the charged three body problem we find necessary conditions to have relative equilibria linearly stable for the collinear charged three body problem for planar relative equilibria we obtain necessary and sufficient conditions for linear stability in terms of the parameters masses and electrostatic charges in the last case we obtain a stability inequality which generalizes the routh condition of celestial mechanics we also proof the existence of spatial relative equilibria and the existence of planar relative equilibria of any triangular shape

backstepping boundary control for first order hyperbolic pdes and application to systems with actuator and sensor delays abstract we consider a problem of boundary feedback stabilization of first order hyperbolic partial differential equations pdes these equations serve as a model for physical phenomena such as traffic flows chemical reactors and heat exchangers we design controllers using a backstepping method which has been recently developed for parabolic pdes with the integral transformation and boundary feedback the unstable pde is converted into a delay line system which converges to zero in finite time we then apply this procedure to finite dimensional systems with actuator and sensor delays to recover a well known infinite dimensional controller analog of the smith predictor for unstable plants we also show that the proposed method can be used for the boundary control of a korteweg de vries like third order pde the designs are illustrated with simulations

homographic solutions of the curved 3 body problem abstract in the 2 dimensional curved 3 body problem we prove the existence of lagrangian and eulerian homographic orbits and provide their complete classification in the case of equal masses we also show that the only non homothetic hyperbolic eulerian solutions are the hyperbolic eulerian relative equilibria a result that proves their instability

super central configurations of the n body problem in this paper we consider the inverse problem of central configurations of the n body problem for a given q q1 q2 qn rd n let s q be the admissible set of masses by s q m m1 mn mi r q is a central configurationfor m for a given m s q let sm q be the permutational admissible set about m m1 m2 mn by sm q m m s q m m and m is apermutation of m here q is called a super central configuration if there exists m such that sm q is nonempty for any q in the planar four body problem q is not a super central configuration as an immediate consequence of a theorem proved by macmillan and bartky permanent configurations in the problem of four bodies trans am math soc 34 838 1932 the main discovery in this paper is the existence of super central configurations in the collinear three body problem we proved that for any q in the collinear three body problem and any m s q sm q has at most one element and the detailed classification of sm q is provided

backstepping based estimation of thermoacoustic oscillations in a rijke tube with experimental validation we investigate the state observer design problem for thermoacoustic instabilities in a rijke tube using an infinite dimensional perspective the observer whose design is based on the backstepping methodology with volterra and full integral terms consists of a copy of the linearized plant model plus output injection terms and relies only on a single boundary acoustic pressure sensor the exponential convergence in the l 2 sense of the observed error dynamics is proved and the analytic expression of the observer gains are derived explicitly the results are tested in an experimental rijke tube prototype in order to illustrate the effectiveness of the method

brief paper stabilization of linear strict feedback systems with delayed integrators the problem of compensation of input delays for unstable linear systems was solved in the late 1970s systems with simultaneous input and state delay have remained a challenge although exponential stabilization has been solved for systems that are not exponentially unstable such as chains of delayed integrators and systems in the feedforward form we consider a general system in strict feedback form with delayed integrators which is an example of a particularly challenging class of exponentially unstable systems with simultaneous input and state delays and design a predictor feedback controller for this class of systems exponential stability is proven with the aid of a lyapunov krasovskii functional that we construct using the pde backstepping approach

optimal toll design a lower bound framework for the asymmetric traveling salesman problem we propose a framework of lower bounds for the asymmetric traveling salesman problem tsp based on approximating the dynamic programming formulation with different basis vector sets we discuss how several well known tsp lower bounds correspond to intuitive basis vector choices and give an economic interpretation wherein the salesman must pay tolls as he travels between cities we then introduce an exact reformulation that generates a family of successively tighter lower bounds all solvable in polynomial time we show that the base member of this family yields a bound greater than or equal to the well known held karp bound obtained by solving the linear programming relaxation of the tsp s integer programming arc based formulation

the boolean quadric polytope some characteristics facets and relatives we study unconstrained quadratic zero one programming problems havingn variables from a polyhedral point of view by considering the boolean quadric polytope qpn inn n 1 2 dimensions that results from the linearization of the quadratic form we show that qpn has a diameter of one descriptively identify three families of facets of qpn and show that qpn is symmetric in the sense that all facets of qpn can be obtained from those that contain the origin by way of a mapping the naive linear programming relaxation qpnlp of qpn is shown to possess the trubin property and its extreme points are shown to be 0 1 2 1 valued furthermore o n3 facet defining inequalities of qpn suffice to cut off all fractional vertices of qpnlp whereas the family of facets described by us has at least o 3n members the problem is also studied for sparse quadratic forms i e when several or many coefficients are zero and conditions are given for the previous results to carry over to this case polynomially solvable problem instances are discussed and it is shown that the known polynomiality result for the maximization of nonnegative quadratic forms can be obtained by simply rounding the solution to the linear programming relaxation in the case that the graph induced by the nonzero coefficients of the quadratic form is series parallel a complete linear description of the associated boolean quadric polytope is given the relationship of the boolean quadric polytope associated to sparse quadratic forms with the vertex packing polytope is discussed as well

lagrange pizzetti theorem for the quasihomogeneous n body problem we consider the n body problem given by quasihomogeneous force functions of the form c1 r a c2 r b c1 c2 a b positive constants and a b and address the fundamentals of homographic solutions generalizing techniques of the classical n body problem we prove that if the homographic solution is not flat then it is homothetic if the homographic solution is flat then it is planar using them we prove an analogue of the lagrange pizzetti theorem for quasihomogeneous potentials

the global flow of the manev problem the manev problem a two body problem given by a potential of the form a r b r2 where r is the distance between particles and a b are positive constants comprises several important physical models having its roots in research done by isaac newton we provide its analytic solution then completely describe its global flow using mcgehee coordinates and topological methods and offer the physical interpretation of all solutions we prove that if the energy constant is negative the orbits are generically precessional ellipses except for a zero measure set of initial data for which they are ellipses for zero energy the orbits are precessional parabolas and for positive energy they are precessional hyperbolas in all these cases the set of initial data leading to collisions has positive measure

finiteness of polygonal relative equilibria for generalised quasi homogeneous n body problems and n body problems in spaces of constant curvature we prove for generalisations of quasi homogeneous n body problems with centre of mass zero and n body problems in spaces of negative constant gaussian curvature that if the masses and rotation are fixed there exists for every order of the masses at most one equivalence class of relative equilibria for which the point masses lie on a circle as well as that there exists for every order of the masses at most one equivalence class of relative equilibria for which all but one of the point masses lie on a circle and rotate around the remaining point mass the method of proof is a generalised version of a proof by j m cors g r hall and g e roberts on the uniqueness of co circular central configurations for power law potentials

control of homodirectional and general heterodirectional linear coupled hyperbolic pdes research on stabilization of coupled hyperbolic pdes has been dominated by the focus on pairs of counter convecting heterodirectional transport pdes with distributed local coupling and with controls at one or both boundaries a recent extension allows stabilization using only one control for a system containing an arbitrary number of coupled transport pdes that convect at different speeds against the direction of the pde whose boundary is actuated in this paper we present a solution to the fully general case in which the number of pdes in either direction is arbitrary and where actuation is applied on only one boundary to all the pdes that convect downstream from that boundary to solve this general problem we solve as a special case the problem of control of coupled homodirectional hyperbolic linear pdes where multiple transport pdes convect in the same direction with arbitrary local coupling our approach is based on pde backstepping and yields solutions to stabilization by both full state and observer based output feedback and trajectory tracking problems

backstepping pde design a convex optimization approach backstepping design for boundary linear partial differential equation pde is formulated as a convex optimization problem some classes of parabolic pdes and a first order hyperbolic pde are studied with particular attention to nonstrict feedback structures based on the compactness of the volterra and fredholm type operators involved their kernels are approximated via polynomial functions the resulting kernel pdes are optimized using sum of squares decomposition and solved via semidefinite programming with sufficient precision to guarantee the stability of the system in the mathcal l 2 norm this formulation allows optimizing extra degrees of freedom where the kernel pdes are included as constraints uniqueness and invertibility of the fredholm type transformation are proved for polynomial kernels in the space of continuous functions the effectiveness and limitations of the approach proposed are illustrated by numerical solutions of some kernel pdes

near collision dynamics for particle systems with quasihomogeneous potentials abstract we study collision and ejection orbits of 3 particle systems having the potential w u v where u and v are homogeneous functions of degree a and b respectively with 1 a b we show that for b 2 collision and ejection orbits tend to form asymptotically a central configuration for the case b 2 which corresponds to maneff s gravitational law we find a set of collision and ejection orbits reaching the triple collision manifold without asymptotic phase this set contains an uncountable union of manifolds and has positive measure within the set of all rectilinear solutions

the data correcting algorithm for the minimization of supermodular functions the data correcting dc algorithm is a recursive branch and bound type algorithm in which the data of a given problem instance are heuristically corrected at each branching in such a way that the new instance will be as close as possible to polynomially solvable and the result satisfies a prescribed accuracy the difference between optimal and current solution in this paper the dc algorithm is applied to determining exact or approximate global minima of supermodular functions the working of the algorithm is illustrated by an instance of the simple plant location spl problem computational results obtained for the quadratic cost partition problem qcp show that the dc algorithm outperforms a branch and cut algorithm not only for sparse graphs but also for nonsparse graphs with density more than 40 often with speeds 100 times faster

parameter estimation and non collocated adaptive stabilization for a wave equation subject to general boundary harmonic disturbance this paper is concerned with the parameter estimation and asymptotic stabilization of a 1 d wave equation that is subject to general harmonic disturbances at the controlled end and suffers from instability at the other end first we design an adaptive observer in terms of measured position and velocity we then adopt the backstepping method for infinite dimensional systems to design an observer based output feedback law the resulting closed loop system is shown to be asymptotically stable and the estimates of the parameters converge to the unknown parameters

the maximum capture problem with random utilities problem formulation and algorithms abstract a model for the optimal location of new facilities in a competitive market is introduced under the hypothesis that customers behavior can be modeled by random utility functions it means that the company that wished to locate uses a random utility model to forecast the market share of a location therefore the company cannot forecast the behavior of every customer in a deterministic fashion but is able to embed him by a probability distribution three formulations are proposed to compute upper bounds of the objective function and compared in a numerical simulation a branch and bound method is developed and tested on examples with up to 50 potential locations and a variable neighborhood search heuristic is proposed to solve larger instances

output feedback adaptive control of a wave pde with boundary anti damping abstract we develop an adaptive output feedback controller for a wave pde in one dimension with actuation on one boundary and with an unknown anti damping term on the opposite boundary this model is representative of a torsional stick slip instability in drillstrings in deep oil drilling as well as of various acoustic instabilities the key feature of the proposed controller is that it requires only the measurements of boundary values and not of the entire distributed state of the system our approach is based on employing riemann variables to convert the wave pde into a cascade of two delay elements with the first of the two delay elements being fed by control and the same element in turn feeding into a scalar ode this enables us to employ a prediction based design for systems with input delays suitably converted to the adaptive output feedback setting the result s relevance is illustrated with simulation example

backstepping stabilization of a linearized ode pde rijke tube model abstract the problem of boundary stabilization of thermoacoustic oscillations in the rijke tube is investigated using the backstepping method as a first step this work only considers the full state design this system consists of a vertical tube open at both ends and a heater placed in the lower half of the tube to study this problem we consider that the mathematical model takes the form of 2 2 linear first order hyperbolic partial differential equations pdes with a point source term induced by the dirac delta distribution on the right hand side plus the coupling of an ordinary differential equation ode and control input at one boundary condition the presence of the dirac delta distribution implies that the system solution has a discontinuity on a point of the domain but is continuous everywhere else we use a coordinate transformation to rewrite the equations into a system of four transport pdes convecting in opposite directions and to translate the discontinuity to the boundary conditions then a full state feedback backstepping controller is designed to exponentially stabilize the origin however the model is non strict feedback making unfeasible the use of standard backstepping designs this issue is tackled by formulating a well posed and invertible integral transformation with volterra and fredholm terms that maps the rijke system into a target system with desirable stability properties an exact piecewise differentiable expression for the kernels of this transformation is found allowing us in turn to derive an explicit feedback control law simulation results are presented to illustrate the effectiveness of the proposed control design

on the stability of tetrahedral relative equilibria in the positively curved 4 body problem abstract we consider the motion of point masses given by a natural extension of newtonian gravitation to spaces of constant positive curvature in which the gravitational attraction between the bodies acts along geodesics we aim to explore the spectral stability of tetrahedral orbits of the corresponding 4 body problem in the 2 dimensional case a situation that can be reduced to studying the motion of the bodies on the unit sphere we first perform some extensive and highly precise numerical experiments to find the likely regions of stability and instability relative to the values of the masses and to the latitude of the position of the three equal masses then we support the numerical evidence with rigorous analytic proofs in the vicinity of some limit cases in which certain masses are either very large or negligible or the latitude is close to zero

maximizing a submodular function by integer programming polyhedral results for the quadratic case abstract we give a new mixed integer programming mip formulation for the quadratic cost partition problem that is derived from a mip formulation for maximizing a submodular function several classes of valid inequalities for the convex hull of the feasible solutions are derived using the valid inequalities for the node packing polyhedron facet defining conditions and separation algorithms are discussed and computational results are reported

compensating the distributed effect of diffusion and counter convection in multi input and multi output lti systems compensation of infinite dimensional input or sensor dynamics in siso lti systems is achieved using the backstepping method for mimo lti systems with distributed input or sensor dynamics governed by diffusion with counter convection we develop a methodology for constructing control laws and observers that compensate the infinite dimensional actuator or sensor dynamics the explicit construction of the compensators are based on novel transformations which can be considered of backstepping forwarding type of the finite dimensional state of the plant and of the infinite dimensional actuator or sensor states based on these transformations we construct explicit lyapunov functionals which prove exponential stability of the closed loop system or convergence of the estimation error in the case of observer design finally we illustrate the effectiveness of our controller with a numerical example

existence of a lower bound for the distance between point masses of relative equilibria for generalised quasi homogeneous n body problems and the curved n body problem we prove that if for relative equilibrium solutions of a generalisation of quasi homogeneous n body problems the masses and rotation are given then the minimum distance between the point masses of such a relative equilibrium has a universal lower bound that is not equal to zero we furthermore prove that the set of such relative equilibria is compact and prove related results for n body problems in spaces of constant gaussian curvature

stability in a rhomboidal 5 body problem with generalized central forces we consider a system of five mass points r1 r2 r3 and r4 with masses m1 m2 m and m3 m4 m moving about a single massive body r0 with mass m0 at its center which is assumed to be the origin of the coordinates system we assume that the central body r0 makes a generalized force on the four mass points and that such a force is generated by a manev s type potential i e characterized by a potential of the form 1r er2 on the other hand is assumed that the attraction between the bodies r1 r2 r3 and r4 is of the newtonian type this model represents several cases for instance when the central body is a spheroid or a radiating source first we prove the existence of three different relative rhomboidal solutions and its central configuration is as follows 1 the rhombus is a square and all primaries have equal masses 2 the rhombus is not a square but all masses are equal and 3 the rhombus is not a square and the pairs of primaries have different masses the first two cases present two pa

boundary control of an anti stable wave equation with anti damping on the uncontrolled boundary abstract much of the boundary control of wave equations in one dimension is based on a single principle passivity under the assumption that control is applied through neumann actuation on one boundary and the other boundary satisfies a homogeneous dirichlet boundary condition we have recently expanded the scope of tractable problems by allowing destabilizing anti stiffness a robin type condition on the uncontrolled boundary where the uncontrolled system has a finite number of positive real eigenvalues in this paper we go further and develop a methodology for the case where the uncontrolled boundary condition has anti damping which makes the real parts of all the eigenvalues of the uncontrolled system positive and arbitrarily high i e the system is anti stable exponentially stable in negative time using a conceptually novel integral transformation we obtain extremely simple explicit formulae for the gain functions for the case with only boundary sensing available at the same end with actuation we design backstepping observers which are dual to the backstepping controllers and have explicit output injection gains we then combine the control and observer designs into an output feedback compensator and prove the exponential stability of the closed loop system

maximization of submodular functions theory and enumeration algorithms abstract submodular functions are powerful tools to model and solve either to optimality or approximately many operational research problems including problems defined on graphs after reviewing some long standing theoretical results about the structure of local and global maxima of submodular functions cherenin s selection rules and his dichotomy algorithm we revise the above mentioned theory and show that our revision is useful for creating new non binary branching algorithms and finding either approximation solutions with guaranteed accuracy or exact ones

maximizing a class of submodular utility functions given a finite ground set n and a value vector a in mathbb r n we consider optimization problems involving maximization of a submodular set utility function of the form h s f left sum i in s a i right s subseteq n where f is a strictly concave increasing differentiable function this utility function appears frequently in combinatorial optimization problems when modeling risk aversion and decreasing marginal preferences for instance in risk averse capital budgeting under uncertainty competitive facility location and combinatorial auctions these problems can be formulated as linear mixed 0 1 programs however the standard formulation of these problems using submodular inequalities is ineffective for their solution except for very small instances in this paper we perform a polyhedral analysis of a relevant mixed integer set and by exploiting the structure of the utility function h strengthen the standard submodular formulation significantly we show the lifting problem of the submodular inequalities to be a submodular maximization problem with a special structure solvable by a greedy algorithm which leads to an easily computable strengthening by subadditive lifting of the inequalities computational experiments on expected utility maximization in capital budgeting show the effectiveness of the new formulation

output feedback stabilization of an unstable wave equation with general corrupted boundary observation we consider boundary output feedback stabilization for an unstable wave equation with boundary observation subject to a general disturbance we adopt for the first time the active disturbance rejection control approach to stabilization for a system described by the partial differential equation with corrupted output feedback by the approach the disturbance is first estimated by a relatively independent estimator it is then canceled in the feedback loop as a result the control law can be designed almost as that for the system without disturbance we show that with a time varying gain properly designed the observer driven by the disturbance estimator is convergent and that all subsystems in the closed loop are asymptotically stable in the energy state space we also provide numerical simulations which demonstrate the convergence results and underline the effect of the time varying gain estimator on peaking value reduction

central configurations with a quasihomogeneous potential function for the classical n body problem if the masses are paced at rest in the configuration that is central then the masses will tend to the origin and result in a simultaneous collision a winter the analytical foundations of celestial mechanics 1st ed princeton university press princeton 1941 however if the potential is quasihomogeneous in nature that is the potential is of the form u v w where w i jamimjrij and v i jbmimjrij then we will dramatically get different results this paper determines the orbits that will result when the potential function is quasihomogeneous it also shows when there existences a relative equilibrium solution for the regular n gon configuration this is one half of perko s theorem for a homogeneous potential finally we show the existence of a central configuration which is not central for either w or v this configuration is the placement of two mutual equal pairs of masses placed at the vertices of a square this shows that the reverse implication of perk