area preserving surface diffeomorphisms we prove some generic properties for cr r 1 2 area preserving diffeomorphism on compact surfaces the main result is that the union of the stable or unstable manifolds of hyperbolic periodic points are dense in the surface this extends the result of franks and le calvez 10 on s2 to general surfaces the proof uses the theory of prime ends and lefschetz fixed point theorem

a classification of minimal sets of torus homeomorphisms we provide a classification of minimal sets of homeomorphisms of the two torus in terms of the structure of their complement we show that this structure is exactly one of the following types 1 a disjoint union of topological disks or 2 a disjoint union of essential annuli and topological disks or 3 a disjoint union of one doubly essential component and bounded topological disks moreover in case 1 bounded disks are non periodic and in case 2 all disks are non periodic this result provides a framework for more detailed investigations and additional information on the torus homeomorphism allows to draw further conclusions in the non wandering case the classification can be significantly strengthened and we obtain that a minimal set other than the whole torus is either a periodic orbit or the orbit of a periodic circloid or the extension of a cantor set further special cases are given by torus homeomorphisms homotopic to an anosov in which types 1 and 2 cannot occur and the same holds for homeomorphisms homotopic to the identity with a rotation set which has non empty interior if a non wandering torus homeomorphism has a unique and totally irrational rotation vector then any minimal set other than the whole torus has to be the extension of a cantor set

a classification of minimal sets for surface homeomorphisms we classify minimal sets of closed and oriented hyperbolic surface homeomorphisms by studying the connected components of their complement this extends the classification given by jager et al mat z 274 1 2 405 426 2013 in the torus the classification being sensitive to global topology striking differences with the toral case arise we also show that the given classification can be strengthened when considered for non wandering conservative systems and in the homotopy class of pseudo anosov maps

on the design of stabilizing compensators via semi infinite optimization the authors derive a modified nyquist stability test which makes possible the use of semi infinite optimization for the design of stabilizing compensators the test provide a simple necessary and sufficient condition of exponential stability and is computationally well conditioned computational aspects of the derived stability test are discussed and a design example is given

regular article a fast adaptive multipole algorithm in three dimensions we present an adaptive fast multipole method for the laplace equation in three dimensions it uses both new compression techniques and diagonal forms for translation operators to achieve high accuracy at a reasonable cost

aperiodic invariant continua for surface homeomorphisms we prove that if a homeomorphism of a closed orientable surface s has no wandering points and leaves invariant a compact connected set k which contains no periodic points then either k s mathbb t 2 or k is the intersection of a decreasing sequence of annuli a version for non orientable surfaces is given

a theory of pseudoskeleton approximations abstract let an m n matrix a be approximated by a rank r matrix with an accuracy e we prove that it is possible to choose r columns and r rows of a forming a so called pseudoskeleton component which approximates a with o e r m n accuracy in the sense of the 2 norm on the way to this estimate we study the interconnection between the volume i e the determinant in the absolute value and the minimal singular value r of r r submatrices of an n r matrix with orthogonal columns we propose a lower bound better than one given by chandrasekaran and ipsen and by hong and pan for the maximum of r over all these submatrices and formulate a hypothesis on a tighter bound

a fast high order algorithm for the solution of surface scattering problems basic implementation tests and applications we present a new algorithm for the numerical solution of problems of acoustic scattering by surfaces in three dimensional space this algorithm evaluates scattered fields through fast high order solution of the corresponding boundary integral equation the high order accuracy of our solver is achieved through use of partitions of unity together with analytical resolution of kernel singularities the acceleration in turn results from use of a novel approach which based on high order two face equivalent source approximations reduces the evaluation of far interactions to evaluation of 3 d fast fourier transforms ffts this approach is faster and substantially more accurate and it runs on dramatically smaller memories than other fft and k space methods the present algorithm computes one matrix vector multiplication in o n6 5logn to o n4 3logn operations where n is the number of surface discretization points the latter estimate applies to smooth surfaces for which our high order algorithm provides accurate solutions with small values of n the former more favorable count is valid for highly complex surfaces requiring significant amounts of subwavelength sampling further our approach exhibits super algebraic convergence it can be applied to smooth and nonsmooth scatterers and it does not suffer from accuracy breakdowns of any kind in this paper we introduce the main algorithmic components in our approach and we demonstrate its performance with a variety of numerical results in particular we show that the present algorithm can evaluate accurately in a personal computer scattering from bodies of acoustical sizes of several hundreds

fast directional multilevel algorithms for oscillatory kernels this paper introduces a new directional multilevel algorithm for solving n body or n point problems with highly oscillatory kernels these systems often result from the boundary integral formulations of scattering problems and are difficult due to the oscillatory nature of the kernel and the non uniformity of the particle distribution we address the problem by first proving that the interaction between a ball of radius r and a well separated region has an approximate low rank representation as long as the well separated region belongs to a cone with a spanning angle of o 1 r and is at a distance which is at least o r 2 away from from the ball we then propose an efficient and accurate procedure which utilizes random sampling to generate such a separated low rank representation based on the resulting representations our new algorithm organizes the high frequency far field computation by a multidirectional and multiscale strategy to achieve maximum efficiency the algorithm performs well on a large group of highly oscillatory kernels our algorithm is proved to have o n log n computational complexity for any given accuracy when the points are sampled from a two dimensional surface we also provide numerical results to demonstrate these properties

state space design of low order stabilizers an algorithm is presented for stabilizing a linear multivariable system with a controller of fixed dynamic order this is an output feedback stabilization problem the algorithm attempts to solve this by a sequence of approximate pole assignment problems the approximation is driven by the optimization of an objective function consisting of a weighted sum of the condition number of the closed loop eigenvectors and the norm of the difference between the computed and actual equivalent state feedback controls

a parallel directional fast multipole method this paper introduces a parallel directional fast multipole method fmm for solving n body problems with highly oscillatory kernels with a focus on the helmholtz kernel in three dimensions this class of oscillatory kernels requires a more restrictive low rank criterion than that of the low frequency regime and thus effective parallelizations must adapt to the modified data dependencies we propose a simple partition at a fixed level of the octree and show that if the partitions are properly balanced between p processes the overall runtime is essentially mathcal o n log n p p by the structure of the low rank criterion we are able to avoid communication at the top of the octree we demonstrate the effectiveness of our parallelization on several challenging models

linearization of conservative toral homeomorphisms we give an equivalent condition for the existence of a semi conjugacy to an irrational rotation for conservative homeomorphisms of the two torus this leads to an analogue of poincare s classification of circle homeomorphisms for conservative toral homeomorphisms with unique rotation vector and a certain bounded mean motion property for minimal toral homeomorphisms the result extends to arbitrary dimensions further we provide a basic classification for the dynamics of toral homeomorphisms with all points non wandering

strictly toral dynamics this article deals with nonwandering e g area preserving homeomorphisms of the torus mathbb t 2 which are homotopic to the identity and strictly toral in the sense that they exhibit dynamical properties that are not present in homeomorphisms of the annulus or the plane this includes all homeomorphisms which have a rotation set with nonempty interior we define two types of points inessential and essential the set of inessential points operatorname ine f is shown to be a disjoint union of periodic topological disks elliptic islands while the set of essential points operatorname ess f is an essential continuum with typically rich dynamics the chaotic region this generalizes and improves a similar description by jager the key result is boundedness of these elliptic islands which allows among other things to obtain sharp uniform bounds of the diffusion rates we also show that the dynamics in operatorname ess f is as rich as in mathbb t 2 from the rotational viewpoint and we obtain results relating the existence of large invariant topological disks to the abundance of fixed points

parametric lq control the parametric linear quadratic plq control problem is considered for discrete time stochastic systems the control problem consists of a non linear optimization problem in the parameters of a linear regulator results on global convergence and on rate of convergence are given for the linear descent mapping method for solving the optimal regulator parameter values furthermore a non linear mapping method based on the solution of a generalized discrete riccati equation is given the plq control problem is a useful extension of the optimal output feedback problem with applications to the design of low order regulators decentralized control and adaptive control

wideband fast kernel independent modeling of large multiscale structures via nested equivalent source approximation we propose a wideband fast kernel independent modeling of large multiscale structures we employ a nested equivalent source approximation nesa to compress the dense system matrix the nesa was introduced by these authors for low and moderate frequency problems smaller than a few wavelengths here we introduce a high frequency nesa algorithm and propose a hybrid version with extreme wideband properties the equivalent sources of the wideband nesa wnesa are obtained by an inverse source process enforcing equivalence of radiated fields on suitably defined testing surfaces in the low frequency region the nesa is used unmodified with a complexity of mathcal o n in the high frequency region in order to obtain a fixed rank matrix compression we hierarchically divide the far coupling space into pyramids with angles related to the peer coupling group size and the nesa testing surfaces are defined as the boundaries of the pyramids this results in a directional nested low rank fixed rank approximation with mathcal o n log n computational complexity that is kernel independent overall the approach yields wideband fast solver for the modeling of large structures that inherits the efficiency and accuracy of low frequency nesa for multiscale problems numerical results and discussions demonstrate the validity of the proposed work

fast directional algorithms for the helmholtz kernel this paper presents a new directional multilevel algorithm for solving n body or n point problems with highly oscillatory kernels we address the problem by first proving that the interaction between a ball of radius r and a well separated region has an approximate low rank representation as long as the well separated region belongs to a cone with a spanning angle of o 1 r and is at a distance which is at least o r 2 away from the ball based on this representation our algorithm organizes the high frequency computation using a multidirectional and multiscale strategy our algorithm is proved to have an optimal o nlogn computational complexity for any given accuracy when the points are sampled from a two dimensional surface

a kernel independent adaptive fast multipole algorithm in two and three dimensions we present a new fast multipole method for particle simulations the main feature of our algorithm is that it does not require the implementation of multipole expansions of the underlying kernel and it is based only on kernel evaluations instead of using analytic expansions to represent the potential generated by sources inside a box of the hierarchical fmm tree we use a continuous distribution of an equivalent density on a surface enclosing the box to find this equivalent density we match its potential to the potential of the original sources at a surface in the far field by solving local dirichlet type boundary value problems the far field evaluations are sparsified with singular value decomposition in 2d or fast fourier transforms in 3d we have tested the new method on the single and double layer operators for the laplacian the modified laplacian the stokes the modified stokes the navier and the modified navier operators in two and three dimensions our numerical results indicate that our method compares very well with the best known implementations of the analytic fmm method for both the laplacian and modified laplacian kernels its advantage is the relative simplicity of the implementation and its immediate extension to more general kernels

the design of optimal output regulators for linear multivariable systems with constant disturbances a method recently developed for solving the output regulator problem is extended to linear systems with constant disturbances the design of static and low order dynamic regulators for linear systems based on the use of projective controls is reviewed first the proposed method determines through a unified procedure the order and the parameters of the compensator together with the feedback parameters this methodology is then applied to systems with external disturbances and various control structures incorporating integral action are investigated in the light of the proposed methodology

the optimal projection equations for fixed order dynamic compensation first order necessary conditions for quadratically optimal steady state fixed order dynamic compensation of a linear time invariant plant in the presence of disturbance and observation noise are derived in a new and highly simplified form in contrast to the pair of matrix riccati equations for the full order lqg case the optimal steady state fixed order dynamic compensator is characterized by four matrix equations two modified riccati equations and two modified lyapunov equations coupled by a projection whose rank is precisely equal to the order of the compensator and which determines the optimal compensator gains the coupling represents a graphic portrayal of the demise of the classical separation principle for the reduced order controller case

a characterization of annularity for area preserving toral homeomorphisms we prove that if an area preserving homeomorphism of the torus in the homotopy class of the identity has a rotation set which is a nondegenerate vertical segment containing the origin then there exists an essential invariant annulus in particular some lift to the universal covering has uniformly bounded displacement in the horizontal direction

computational methods for parametric lq problems a survey iterative methods for finding the optimal constant feedback gains for parametric lq problems notably for optimal constant output feedback problems are surveyed the connections of several methods to loss function expansions are discussed with important implications to the understanding of their convergence properties especially the descent anderson moore method levine athans like methods and the newton method are considered convergence results are also included the initialization problem and the output feedback stabilization problem are also discussed furthermore it is shown that the concepts and methods surveyed in this paper are useful in solving many realistic generalized parametric lq problems as well notably so called robust parametric lq problems

controller reduction by component cost analysis component cost analysis 1 is used to develop a method for controller reduction the reduction of the controller is based upon the participation of the controller states in the value of a quadratic performance metric the controller states which have the smallest contribution to the performance metric are truncated to produce the reduced controllers an error index is defined to evaluate the reduced controller compared to the optimal lqg controller and bounds on this index are derived a numerical example is included to illustrate the procedure

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

forcing theory for transverse trajectories of surface homeomorphisms this paper studies homeomorphisms of surfaces isotopic to the identity by means of purely topological methods and brouwer theory the main development is a novel theory of orbit forcing using maximal isotopies and transverse foliations this allows us to derive new proofs for some known results as well as some new applications among which we note the following we extend franks and handel s classification of zero entropy maps of mathbb s 2 for non wandering homeomorphisms we show that if f is a hamiltonian homeomorphism of the annulus then the rotation set of f is either a singleton or it contains zero in the interior proving a conjecture posed by boyland we show that there exist compact convex sets of the plane that are not the rotation set of some torus homeomorphisms proving a first case of the franks misiurewicz conjecture we extend a bounded deviation result relative to the rotation set to the general case of torus homeomorphisms

transitivity of generic semigroups of area preserving surface diffeomorphisms we prove that the action of the semigroup generated by a cr generic pair of area preserving diffeomorphisms of a compact orientable surface is transitive

optimal low order controller design via lqg like parametrization abstract a new lqg like parametrization scheme is introduced for low order controller design descent based design methodologies are developed for optimizing an h 2 cost with respect to the controller design parameters in this case the reduced order regulator and estimator gain matrices in a modified version the reduced order model of the plant is also updated numerical experiments using large space structure models show the efficacy of this approach