stabilization of a second order ode heat system coupling at intermediate point this paper considers the stabilization of a second order ode heat system coupling at an intermediate point under natural and checkable assumptions which is motivated by the thermoelastic coupling physics arising in microelectromechanical systems mems a novel backstepping transformation form is proposed in this work and the feedback gain for the lumped parameter component is constructed using the eigenvector of coefficient matrix in the ode system then we prove the existence of smooth kernels with second order continuously derivative for the forward and inverse transformations in the backstepping feedback control law design at the same time we show that the forward and inverse transformations are mutually invertible transformation pair finally the effectiveness of the stabilization feedback controller design is shown with some numerical examples

cusp size bounds from singular surfaces in hyperbolic 3 manifolds singular maps of surfaces into a hyperbolic 3 manifold are utilized to find upper bounds on meridian length l curve length and maximal cusp volume for the manifold this allows a proof of the fact that there exist hyperbolic knots with arbitrarily small cusp density and that every closed orientable 3 manifold contains a knot whose complement is hyperbolic with maximal cusp volume less than or equal to 9 we also find particular upper bounds on meridian length l curve length and maximal cusp volume for hyperbolic knots in s 3 depending on crossing number particular improved bounds are obtained for alternating knots

optimal control of a class of linear hybrid systems with saturation we consider a class of first order linear hybrid systems with saturation a system that belongs to this class can operate in several modes or phases in each phase each state variable of the system exhibits a linear growth until a specified upper or lower saturation level is reached and after that the state variable stays at that saturation level until the end of the phase a typical example of such a system is a traffic signal controlled intersection we develop methods to determine optimal switching time sequences for first order linear hybrid systems with saturation that minimize criteria such as average queue length worst case queue length average waiting time and so on first we show how the extended linear complementarity problem elcp which is a mathematical programming problem can be used to describe the set of system trajectories of a first order linear hybrid system with saturation optimization over the solution set of the elcp then yields an optimal switching time sequence although this method yields globally optimal switching time sequences it is not feasible in practice due to its computational complexity therefore we also present some methods to compute suboptimal switching time sequences furthermore we show that if there is no upper saturation then for some objective functions the globally optimal switching time sequence can be computed very efficiently we also discuss some approximations that lead to suboptimal switching time sequences that can be computed very efficiently finally we use these results to design optimal switching time sequences for traffic signal controlled intersections

exponential stabilization of the semilinear heat equation with nonlocal boundary conditions abstract the present work is devoted to the problem of boundary stabilization of the semilinear 1 d heat equation with nonlocal boundary conditions the stabilizing controller is finite dimensional linear given in an explicit form involving only the eigenfunctions of the laplace operator with nonlocal boundary conditions

heat equation with memory lack of controllability to rest abstract we prove that the one dimensional heat equation with memory cannot be controlled to rest for large classes of memory kernels and controls the approach is based on the application of the theory of interpolation in paley wiener spaces

bc opt a branch and cut code for mixed integer programs a branch and cut mixed integer programming system called bc opt is described incorporating most of the valid inequalities that have been used or suggested for such systems namely lifted 0 1 knapsack inequalities 0 1 gub knapsack and integer knapsack inequalities flowcover and continuous knapsack inequalities path inequalities for fixed charge network flow structure and gomory mixed integer cuts the principal development is a set of interface routines allowing these cut routines to generate cuts for new subsets or aggregations of constraints

closed form boundary state feedbacks for a class of 1 d partial integro differential equations in this paper a problem of boundary stabilization of a class of linear parabolic partial integro differential equations p i des in one dimension is considered using the method of backstepping avoiding spatial discretization required in previous efforts the problem is formulated as a design of an integral operator whose kernel is required to satisfy a hyperbolic p i de the kernel p i de is then converted into an equivalent integral equation and by applying the method of successive approximations the equation s well posedness and the kernel s smoothness are established it is shown how to extend this approach to design optimally stabilizing controllers an adaptation mechanism is developed to reduce the conservativeness of the inverse optimal controller and the performance bounds are derived for a broad range of physically motivated special cases feedback laws are constructed explicitly and the closed loop solutions are found in closed form a numerical scheme for the kernel p i de is proposed its numerical effort compares favorably with that associated with operator riccati equations

on mapping class groups of contractible open 3 manifolds let w be an irreducible eventually end irreducible contractible open 3 manifold other than r 3 and let v be a good exhaustion of w let h w v be the subgroup of the mapping class group h w which is eventually carried by v this paper shows how to compute h w v in terms of the mapping class groups of certain compact 3 manifolds associated to v the computation is carried out for a genus two example and for the classical genus one example of whitehead for these examples h w h w v

numerical experience with lower bounds for miqp branch and bound the solution of convex mixed integer quadratic programming miqp problems with a general branch and bound framework is considered it is shown how lower bounds can be computed efficiently during the branch and bound process improved lower bounds such as the ones derived in this paper can reduce the number of quadratic programming qp problems that have to be solved the branch and bound approach is also shown to be superior to other approaches in solving miqp problems numerical experience is presented which supports these conclusions

the volume of hyperbolic alternating link complements if a hyperbolic link has a prime alternating diagram d then we show that the link complement s volume can be estimated directly from d we define a very elementary invariant of the diagram d its twist number t d and show that the volume lies between v 3 t d 2 2 and v 3 10t d 10 where v 3 is the volume of a regular hyperbolic ideal 3 simplex as a consequence the set of all hyperbolic alternating and augmented alternating link complements is a closed subset of the space of all complete finite volume hyperbolic 3 manifolds in the geometric topology

boundary state feedback exponential stabilization for a one dimensional wave equation with velocity recirculation abstract in this paper we consider boundary state feedback stabilization of a one dimensional wave equation with in domain feedback recirculation of an intermediate point velocity we firstly construct an auxiliary control system which has a nonlocal term of the displacement at the same intermediate point then by choosing a well known exponentially stable wave equation as its target system we find one backstepping transformation from which a state feedback law for this auxiliary system is proposed finally taking the resulting closed loop of the auxiliary system as a new target system we obtain another backstepping transformation from which a boundary state feedback controller for the original system is designed by the equivalence of three systems the closed loop of original system is proved to be well posed and exponentially stable some numerical simulations are presented to validate the theoretical results

mpc for discrete event systems with soft and hard synchronization constraints discrete event systems with only synchronization and no concurrency also known as timed event graphs or max linear systems have been studied by several authors the synchronization constraints that arise in these discrete event systems are hard i e they cannot be broken under any circumstances in this paper we consider a more extended class of discrete event systems with both hard and soft synchronization constraints i e if necessary some synchronization conditions may be broken but then a penalty is incurred we show how the model predictive control mpc framework which is a very popular controller design method in the process industry can be extended to this class of discrete event systems in general the mpc control design problem for discrete event systems with soft and hard synchronization constraints leads to a non linear non convex optimization problem we show that the optimal mpc strategy can also be computed using an extended linear complementary problem

hyperbolic knots spanning accidental seifert surfaces of arbitrarily high genus a method for constructing hyperbolic knots each of which bounds accidental incompressible seifert surfaces of arbitrarily high genus is given

hyperbolic structures on 3 manifolds i deformation of acylindrical manifolds this is the first in a series of papers showing that haken manifolds have hyperbolic structures this first was published the second two have existed only in preprint form and later preprints were never completed this eprint is only an approximation to the published version which is the definitive form for part i and is provided for convenience only all references and quotations should be taken from the published version since the theorem numbering is different and not all corrections have been incorporated into the present version parts ii and iii will be made available as eprints shortly

a census of cusped hyperbolic 3 manifolds the census provides a basic collection of noncompact hyperbolic 3 manifolds of finite volume it contains descriptions of all hyperbolic 3 manifolds obtained by gluing the faces of at most seven ideal tetrahedra additionally various geometric and topological invariants are calculated for these manifolds the findings are summarized and a listing of all manifolds appears in the microfiche supplement

compensating a string pde in the actuation or sensing path of an unstable ode how to control an unstable linear system with a long pure delay in the actuator path this question was resolved using predictor or finite spectrum assignment designs in the 1970s here we address a more challenging question how to control an unstable linear system with a wave partial differential equation pde in the actuation path physically one can think of this problem as having to stabilize a system to whose input one has access through a string the challenges of overcoming string wave dynamics in the actuation path include their infinite dimension finite propagation speed of the control signal and the fact that all of their infinitely many eigenvalues are on the imaginary axis in this technical note we provide an explicit feedback law that compensates the wave pde dynamics at the input of an linear time invariant ordinary differential equation and stabilizes the overall system in addition we prove robustness of the feedback to the error in a priori knowledge of the propagation speed in the wave pde finally we consider a dual problem where the wave pde is in the sensing path and design an exponentially convergent observer

degree one maps between geometric 3 manifolds let m and n be two compact orientable 3 manifolds we say that m n if there is a degree one map from m to n this gives a way to measure the complexity of 3 manifolds the main purpose of this paper is to give a positive answer to the following conjecture if there is an infinite sequence of degree one maps between haken manifolds then eventually all the manifolds are homeomorphic to each other more generally we prove a theorem which says that any infinite sequence of degree one maps between the so called geometric 3 manifolds must eventually become homotopy equivalences

the generalized linear complementarity problem and an algorithm to find all its solutions motivated by a number of typical applications a generalization of the classicallinear complementarity problem is presented together with an algorithm to determine the complete solution set the algorithm is based on the double description method for solving linear inequalities and succeeds in describing continuous as well as unbounded solution sets

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

three dimensional manifolds kleinian groups and hyperbolic geometry 1 a conjectural picture of 3 manifolds a major thrust of mathematics in the late 19th century in which poincare had a large role was the uniformization theory for riemann surfaces that every conformai structure on a closed oriented surface is represented by a riemannian metric of constant curvature for the typical case of negative euler characteristic genus greater than 1 such a metric gives a hyperbolic structure any small neighborhood in the surface is isometric to a neighborhood in the hyperbolic plane and the surface itself is the quotient of the hyperbolic plane by a discrete group of motions the exceptional cases the sphere and the torus have spherical and euclidean structures three manifolds are greatly more complicated than surfaces and i think it is fair to say that until recently there was little reason to expect any analogous theory for manifolds of dimension 3 or more except perhaps for the fact that so many 3 manifolds are beautiful the situation has changed so that i feel fairly confident in proposing the

sutured manifold hierarchies essential laminations and dehn surgery x0 introduction a compact orientable surface f with nonnegative euler characteristic is either a sphere a disk a torus or an annulus if a 3 manifold m contains such an essential surface then it is said to be reducible reducible toroidal or annular respectively any such surface can be used to decompose the manifold further into simpler manifolds we say that m is a simple manifold if it has no such surfaces a simple manifold is expected to have a nice geometric structure if m has nonempty boundary then the geometrization theorem of thurston for haken manifolds says that m with boundary tori removed admits a nite volume hyperbolic structure with totally geodesic boundary when m has no boundaries thurston s geometrization conjecture asserts that m is either hyperbolic or is a seifert b er space with orbifold a sphere with at most 3 cone points suppose t is a torus boundary component of m we use m to denote the manifold obtained by dehn lling on t so that the slope on t bounds a disk in the dehn lling solid torus when m e k is the exterior of a knot k in s 3 denote m by k and call it the manifold obtained by surgery on the knot k it is well known that if m is simple then there are only nitely many dehn llings on t which produce non simple manifolds if m 1 and m 2 are non simple manifolds then the geometric intersection number between 1 and 2 denoted by 1 2 is proved to be at most 8 by gordon gor1 there are 10 dieren t cases according to the types of nonnegative euler characteristic surfaces in m i in many cases the upper bounds for 1 2 have been established see table 0 1

boundary feedback stabilization of an unstable heat equation in this paper we study the problem of boundary feedback stabilization for the unstable heat equation ut x t uxx x t a x u x t this equation can be viewed as a model of a heat conducting rod in which not only is the heat being diffused mathematically due to the diffusive term uxx but also the destabilizing heat is generating mathematically due to the term a u with a 0 we show that for any given continuously differentiable function a and any given positive constant l we can explicitly construct a boundary feedback control law such that the solution of the equation with the control law converges to zero exponentially at the rate of l this is a continuation of the recent work of boskovic krstic and liu ieee trans automat control 46 2001 pp 2022 2028 and balogh and krstic european j control 8 2002 pp 165 176

least area incompressible surfaces in 3 manifolds let m be a riemannian manifold and let f be a closed surface a map f f m is called least area if the area of f is less than the area of any homotopic map from f to m note that least area maps are always minimal surfaces but that in general minimal surfaces are not least area as they represent only local stationary points for the area function the existence of least area immersions in a homotopy class of maps has been established when the homotopy class satisfies certain injectivity conditions on the fundamental group 18 17 in this paper we shall consider the possible singularities of such immersions our results show that the general philosophy is that least area surfaces intersect least meaning that the intersections and self intersections of least area immersions are as small as their homotopy classes allow when measured correctly one should note that evidence supporting this view had been found by meeks yau in their embedding theorems for minimal disks and 2 spheres 13 143 our main result asserts that if a least area immersion is homotopic to an embedding then it has no self intersections which clearly exemplifies the above philosophy the precise result is the following

backstepping observers for a class of parabolic pdes in this paper we design exponentially convergent observers for a class of parabolic partial integro differential equations p i des with only boundary sensing available the problem is posed as a problem of designing an invertible coordinate transformation of the observer error system into an exponentially stable target system observer gain output injection function is shown to satisfy a well posed hyperbolic pde that is closely related to the hyperbolic pde governing backstepping control gain for the state feedback problem for several physically relevant problems the observer gains are obtained in closed form the observer gains are then used for an output feedback design in both collocated and anti collocated setting of sensor and actuator the order of the resulting compensator can be substantially lowered without affecting stability explicit solutions of a closed loop system are found in particular cases

word hyperbolic dehn surgery in the late 1970 s thurston dramatically changed the nature of 3 manifold theory with the introduction of his geometrisation conjecture and by proving it in the case of haken 3 manifolds 23 the conjecture for general closed orientable 3 manifolds remains perhaps the most important unsolved problem in the subject a weaker form of the conjecture 19 deals with the fundamental group of a closed orientable 3 manifold it proposes that either it contains z z as a subgroup or it is word hyperbolic in the sense of gromov 11 word hyperbolic groups are precisely those groups which satisfy a linear isoperimetric inequality they are of fundamental importance in geometric group theory and have very many useful properties

stabilization of linear heat equation with a heat source at intermediate point by boundary control in this paper the stabilization of a linear heat equation with a heat source at intermediate point is discussed applying the backstepping method firstly we prove the existence of kernels in the forward and inverse transformation by some special techniques secondly we obtain the exponential stability with any prescribed decay rate of a closed loop system finally the effectiveness of the explicit feedback stabilization controller design is illustrated with some numerical examples