goal oriented adaptivity in control constrained optimal control of partial differential equations dual weighted goal oriented error estimates for a class of pointwise control constrained optimal control problems for second order elliptic partial differential equations are derived it is demonstrated that the constraints give rise to a primal dual weighted error term representing the mismatch in the complementarity system due to discretization the paper also contains a posteriori error estimators for the l 2 norm of the error in the state and in the adjoint state

godement jacquet l functions and full theta lifts we relate poles of local godement jacquet l functions to distributions on matrix spaces with singular supports as an application we show the irreducibility of the full theta lifts to mathrm gl n mathrm f of generic irreducible representations of mathrm gl n mathrm f where mathrm f is an arbitrary local field

a posteriori error control for distributed elliptic optimal control problems with control constraints discretized by hp finite elements abstract a distributed elliptic control problem with control constraints is considered which is formulated as a three field problem and consists of two variational equations for the state and the co state variables as well as of a variational inequality for the control variable two discretization approaches with h p finite elements are discussed in the first discretization approach all variables state co state and control are discretized a semi smooth newton method is introduced for solving the resulting algebraic system in the second discretization approach only the state and the co state variables are discretized whereas the control is determined by projection a simple fixed point scheme is presented for the iterative solution of this approach the main focus of the paper is on the derivation of reliable and efficient a posteriori error estimates which enables h p adaptive mesh refinements in particular the estimates can be applied to the iteration solutions so that they can be used as a stopping criterion of the iterative solution schemes in several numerical experiments the order of convergence of the adaptive discretization approaches and the efficiency as well as the reliability of the a posteriori error estimates are studied

higher order fem for the obstacle problem of the p laplacian a variational inequality approach abstract we consider higher order finite element discretizations of a nonlinear variational inequality formulation arising from an obstacle problem with the p laplacian differential operator for p 1 we prove an a priori error estimate and convergence rates with respect to the mesh size h and in the polynomial degree q under assumed regularity moreover we derive a general a posteriori error estimate which is valid for any uniformly bounded sequence of finite element functions all our results contain the known results for the linear case of p 2 we present numerical results on the improved convergence rates of adaptive schemes mesh size adaptivity with and without polynomial degree adaptation for the singular case of p 1 5 and for the degenerated case of p 3

rapidly decreasing functions in reduced algebras of groups let r be a group we associate to any length function l on r the space h r of rapidly decreasing functions on r with respect to l which coincides with the space of smooth functions on the k dimensional torus when r zk we say that r has property rd if there exists a length function l on r such that h r is contained in the reduced c algebra c r of r we study the stability of property rd with respect to some constructions of groups such as subgroups over groups of finite index semidirect and amalgamated products finally we show that the following groups have property rd 1 finitely generated groups of polynomial growth 2 discrete cocompact subgroups of the group of all isometries of any hyperbolic space

k theorie bivariante pour les algebres de banach et conjecture de baum connes je suis parvenu dans ma these a construire une k theorie bivariante pour les algebres de banach cela m a permis de demontrer la conjecture de baum connes pour les groupes de lie semi simples et les groupes reductifs p adiques ainsi que pour les sous groupes discrets de type fini de sl 3 f avec f une extension finie de q p et pour les sous groupes discrets cocompacts de sp n 1 sl 3 r et sl 3 c j ai aussi demontre une conjecture analogue a la conjecture de baum connes pour les algebres l 1 et plus generalement toutes les bonnes completions des sous groupes fermes des groupes de lie semi simples et des groupes reductifs p adiques

error estimates for spectral approximation of elliptic control problems with integral state and control constraints abstract the goal of this paper is to investigate the legendre galerkin spectral approximation of elliptic optimal control problems with integral state and control constraints thanks to the appropriate base functions of the discrete spaces the discrete system is with sparse coefficient matrices we first present the optimality conditions of the control system then a priori and a posteriori error estimates both in h 1 and l 2 norms are derived some numerical tests indicate that the spectral accuracy can be achieved and the proposed method is competitive for solving control problems

a posteriori error analysis of optimal control problems with control constraints we derive a unifying framework for the a posteriori error analysis of control constrained linear quadratic optimal control problems we consider finite element discretizations with discretized and nondiscretized control a fundamental error equivalence drastically simplifies the a posteriori error analysis for optimal control problems it basically remains to apply error estimators for the linear state and adjoint problem we give several examples including stabilized discretizations and investigate the quality of the estimators and the performance of the adaptive iteration by selected numerical experiments

asymptotic behavior of matrix coefficients of admissible representations introduction 869 1 generalities on reductive groups 873 2 the infinitesimal cartan decomposition 876 3 the t radial components 880 4 differential equations satisfied by sphereical functions 885 5 asymptotic behavior of spherical functions on a 888 6 asymptotic behavior of spherical functions along the walls of a 892 7 leading characters and growth estimates on the group 898 8 admissible representations and their matrix coefficients 906 appendix 917

convergence of a finite element approximation to a state constrained elliptic control problem we consider an elliptic optimal control problem with pointwise state constraints the cost functional is approximated by a sequence of functionals which are obtained by discretizing the state equation with the help of linear finite elements and enforcing the state constraints in the nodes of the triangulation the corresponding minima are shown to converge in l 2 to the exact control as the discretization parameter tends to zero furthermore error bounds for the control and the state are obtained in both two and three space dimensions finally we present numerical examples which confirm our analytical findings

adaptive finite element methods for optimal control of partial differential equations basic concept a new approach to error control and mesh adaptivity is described for the discretization of optimal control problems governed by elliptic partial differential equations the lagrangian formalism yields the first order necessary optimality condition in form of an indefinite boundary value problem which is approximated by an adaptive galerkin finite element method the mesh design in the resulting reduced models is controlled by residual based a posteriori error estimates these are derived by duality arguments employing the cost functional of the optimization problem for controlling the discretization error in this case the computed state and costate variables can be used as sensitivity factors multiplying the local cell residuals in the error estimators this results in a generic and simple algorithm for mesh adaptation within the optimization process this method is developed and tested for simple boundary control problems in semiconductor models

adaptive finite element approximation for distributed elliptic optimal control problems in this paper sharp a posteriori error estimators are derived for a class of distributed elliptic optimal control problems these error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems and are implemented in the adaptive approach our numerical results indicate that the sharp error estimators work satisfactorily in guiding the mesh adjustments and can save substantial computational work

connected lie groups and property rd for a locally compact group property rd gives a control on the convolution norm of any compactly supported measure in terms of the l 2 norm of its density and the diameter of its support we give a complete classification of those lie groups with property rd

asymptotic relative efficiency of survival tests with covariates summary comparison of survival for two groups of patients when adjusting for covariates is a standard problem in clinical trials in this paper the general life table models developed by cox 1972 and the stratified log rank test mantel haenszel 1959 peto peto 1972 are compared an analytical expression and numerical results for the asymptotic relative efficiency of the two tests are given when there is no censoring stratification on the covariates is asymptotically as efficient as the test arising from cox s model provided i there is no treatment effect ii the covariates are balanced across treatment groups and iii the hypotheses underlying cox s model are satisfied however if the proportional hazard model does not hold for the covariates then cox s model leads to a biased estimate of the difference between the two treatments

pointwise a posteriori error control for elliptic obstacle problems we consider a finite element method for the elliptic obstacle problem over polyhedral domains in d which enforces the unilateral constraint solely at the nodes we derive novel optimal upper and lower a posteriori error bounds in the maximum norm irrespective of mesh fineness and the regularity of the obstacle which is just assumed to be holder continuous they exhibit optimal order and localization to the non contact set we illustrate these results with simulations in 2d and 3d showing the impact of localization in mesh grading within the contact set along with quasi optimal meshes

the role of the ramanujan conjecture in analytic number theory we discuss progress towards the ramanujan conjecture for the group gln and its relation to various other topics in analytic number theory

sample size considerations for the evaluation of prognostic factors in survival analysis when the role of a new prognostic factor is investigated careful planning of an appropriate study is required this includes an assessment of the power of the study in terms of sample sizes an adequate analysis of the independent prognostic effect of a new factor has to be adjusted for the existing standard factors with survival time as endpoint this will usually be done with the cox proportional hazards model sample size and power formulae in survival analysis have been developed by schoenfeld for randomized treatment comparisons in the analysis of prognostic factors the covariates included are expected to be correlated with the factor of primary interest in this situation the existing sample size and power formulae are not valid and may not be applied in this paper schoenfeld s formula is first extended to the situation where a correlated factor is included in the analysis the validity of the resulting approximate asymptotic formula is investigated for its asymptotic behaviour by numerical integration and for its finite behaviour by simulation second an approximate formula for sample size and power is provided to detect an interaction between the interesting and a second correlated factor this extends the formula for independent effects finally the approach is illustrated by an example on the prognostic impact of dna ploidy and other factors in advanced ovarian cancer

on the discrete series of generalized stiefel manifolds a study of the discrete series of generalized stiefel manifolds is made using the oscillator representation new infinite families of such discrete series are constructed

counting lattice points for a locally compact second countable group g and a lattice subgroup we give an explicit quantitative solution of the lattice point counting problem in general domains in g provided that i g has finite upper local dimension and the domains satisfy a basic regularity condition ii the mean ergodic theorem for the action of g on g holds with a rate of convergence the error term we establish matches the best current result for balls in symmetric spaces of simple higher rank lie groups but holds in much greater generality a significant advantage of the ergodic theoretic approach we use is that the solution to the lattice point counting problem is uniform over families of lattice subgroups provided they admit a uniform spectral gap in particular the uniformity property holds for families of finite index subgroups satisfying a quantitative variant of property we discuss a number of applications including counting lattice points in general domains in semisimple s algebraic groups counting rational points on group varieties with respect to a height function and quantitative angular or conical equidistribution of lattice points in symmetric spaces and in affine symmetric varieties we note that the mean ergodic theorems which we establish are based on spectral methods including the spectral transfer principle and the kunze stein phenomenon we formulate and prove appropriate analogues of both of these results in the set up of adele groups and they constitute a necessary step in our proof of quantitative results in counting rational points

radial rapid decay property for cocompact lattices abstract we study haagerup inequality for radial functions on uniform lattices in semisimple lie groups with respect to riemannian metrics and in some case to word metrics in particular we extend the swiatkowski valette results to any lattice acting properly and essentially transitively on classical buildings

subconvex equidistribution of cusp forms reduction to eisenstein observables let traverse a sequence of cuspidal automorphic representations of gl2 with large prime level unramified central character and bounded infinity type for g gl1 pgl2 let h g denote the assertion that subconvexity holds for g twists of the adjoint l function of with polynomial dependence upon the conductor of the twist we show that h gl1 implies h pgl2 in geometric terms h pgl2 corresponds roughly to an instance of arithmetic quantum unique ergodicity with a power savings in the error term h gl1 to the special case in which the relevant sequence of measures is tested against an eisenstein series

strong haagerup inequalities for free r diagonal elements abstract in this paper we generalize haagerup s inequality u haagerup an example of a nonnuclear c algebra which has the metric approximation property invent math 50 1978 1979 279 293 on convolution norm in the free group to a very general context of r diagonal elements in a tracial von neumann algebra moreover we show that in this holomorphic setting the inequality is greatly improved from its original form we give combinatorial proofs of two important special cases of our main result and then generalize these techniques en route we prove a number of moment and cumulant estimates for r diagonal elements that are of independent interest finally we use our strong haagerup inequality to prove a strong ultracontractivity theorem generalizing and improving the one in p biane free hypercontractivity comm math phys 184 1997 457 474

a posteriori error control of h p finite elements for variational inequalities of the first and second kind in this paper residual based a posteriori error estimates for variational inequalities including those of the second kind are proposed the variational formulation and its discretizations are considered in an abstract framework of general banach spaces the main idea is to express the residual in terms of some lagrange multipliers which can be obtained for instance by some post processing the residual itself is defined for an arbitrary element of the trial space the error of this element and of the solution of the variational inequality is then estimated by the dual norm of the residual plus some computable remainder terms this concept is applied to a variety of frictional contact problems such as signorini and obstacle problems as well as to the bingham fluid problem the applicability of the estimates is confirmed by several numerical experiments in particular the general framework allows for the discretization with h p adaptivity which leads to nearly exponential convergence rates in most cases

best possible rates of distribution of dense lattice orbits in homogeneous spaces this paper establishes upper and lower bounds on the speed of approximation in a wide range of natural diophantine approximation problems the upper and lower bounds coincide in many cases giving rise to optimal results in diophantine approximation which were inaccessible previously our approach proceeds by establishing more generally upper and lower bounds for the rate of distribution of dense orbits of a lattice subgroup in a connected lie or algebraic group g acting on suitable homogeneous spaces g h the upper bound is derived using a quantitative duality principle for homogeneous spaces reducing it to a rate of convergence in the mean ergodic theorem for a family of averaging operators supported on h and acting on g in particular the quality of the upper bound on the rate of distribution we obtain is determined explicitly by the spectrum of h in the automorphic representation on l 2 g we show that the rate is best possible when the representation in question is tempered and show that the latter condition holds in a wide range of examples

biorthogonal basis functions in hp adaptive fem for elliptic obstacle problems abstract in this paper the discretization of a non symmetric elliptic obstacle problem with h p adaptive h 1 conforming finite elements is discussed for this purpose a higher order mixed finite element discretization is introduced where the dual space is discretized via biorthogonal basis functions the h p adaptivity is realized via automatic adaptive mesh refinement based on a residual a posteriori error estimation which is also derived in this paper the use of biorthogonal basis functions leads to unilateral box constraints and componentwise complementarity conditions enabling the highly efficient application of a quadratically converging semi smooth newton scheme which can be modified to ensure global convergence h p adaptivity usually implies meshes with hanging nodes and varying polynomial degrees which have to be handled appropriately within the h 1 conforming finite element discretization this is typically done by using so called connectivity matrices in this paper a procedure is proposed which efficiently computes these matrices for biorthogonal basis functions finally the applicability of the theoretical findings is demonstrated with several numerical experiments

mixed finite element methods for two body contact problems this paper presents mixed finite element methods of higher order for two body contact problems of linear elasticity the discretization is based on a mixed variational formulation proposed by haslinger et al which is extended to higher order finite elements the main focus is on the convergence of the scheme and on a priori estimates for the h and the p method for this purpose a discrete inf sup condition is proven which guarantees the stability of the mixed method numerical results confirm the theoretical findings

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

a posteriori error estimates for hp finite element solutions of convex optimal control problems in this paper we present a posteriori error analysis for hp finite element approximation of convex optimal control problems we derive a new quasi interpolation operator of clement type and a new quasi interpolation operator of scott zhang type that preserves homogeneous boundary condition the scott zhang type quasi interpolation is suitable for an application in bounding the errors in l 2 norm then hp a posteriori error estimators are obtained for the coupled state and control approximations such estimators can be used to construct reliable adaptive finite elements for the control problems

a geometric criterion for the boundedness of characteristic classes we show that for a connected lie group g the linearity of its radical sqrt g that is of its biggest connected normal solvable subgroup is a necessary and sufficient condition for the boundedness of all borel cohomology classes of g with integer coefficients and that the linearity of sqrt g is also equivalent to a large scale geometric property of g involving distortion

functions on symmetric spaces and oscillator representation in this paper we study the l 2 functions on u 2n o 2n and mp n r we relate them using the oscillator representation we first study some isometries between various l 2 spaces using the compactification we defined in h he an analytic compactification of the symplectic group j differential geom 51 1999 375 399 these isometries were first introduced by betten and olafsson in f betten g olafsson causal compactification and hardy spaces for spaces of hermitian type pacific j math 200 2

finite element approximation of elliptic control problems with constraints on the gradient we consider an elliptic optimal control problem with control constraints and pointwise bounds on the gradient of the state we present a tailored finite element approximation to this optimal control problem where the cost functional is approximated by a sequence of functionals which are obtained by discretizing the state equation with the help of the lowest order raviart thomas mixed finite element pointwise bounds on the gradient variable are enforced in the elements of the triangulation controls are not discretized error bounds for control and state are obtained in two and three space dimensions a numerical example confirms our analytical findings

efficient and reliable a posteriori error estimators for elliptic obstacle problems a posteriori error estimators are derived for linear finite element approximations to elliptic obstacle problems these estimators yield global upper and local lower bounds for the discretization error here discretization error means the sum of two contributions the distance between continuous and discrete solution in the energy norm and some quantity that is related to the distance of continuous and discrete contact set moreover the local error indicators in the interior of the discrete contact set reduce to quantities that measure only data resolution

exponential convergence of hp finite element discretization of optimal boundary control problems with elliptic partial differential equations we investigate the numerical solution of boundary control problems with elliptic partial differential equations by the hp finite element method we prove exponential convergence with respect to the number of unknowns for an a priori chosen discretization here we have to prove that derivatives of arbitrary order of the solution belong to suitably chosen weighted sobolev spaces this result relies on the assumption that the number of switching points of the optimal control is finite numerical experiments confirm the theoretical findings

adaptive finite elements for elliptic optimization problems with control constraints in this paper we develop a posteriori error estimates for finite element discretization of elliptic optimization problems with pointwise inequality constraints on the control variable we derive error estimators for assessing the discretization error with respect to the cost functional as well as with respect to a given quantity of interest these error estimators provide quantitative information about the discretization error and guide an adaptive mesh refinement algorithm allowing for substantial saving in degrees of freedom the behavior of the method is demonstrated on numerical examples

a posteriori error estimates of higher order finite elements for frictional contact problems abstract in this paper a posteriori estimates are derived for higher order finite element methods and frictional contact problems the discretization is based on a mixed approach where the geometrical and frictional constraints are captured by lagrange multipliers the use of higher order polynomials leads to a certain non conformity in the discretization which requires special attention in the error analysis as a main result an error estimation is proposed which consists of the dual norm of a residual plus some computable remainder terms the residual is estimated by well known a posteriori error estimates for variational equations the remainder terms represent typical sources resulting from the non conforming mixed discretization numerical experiments confirm the applicability of the a posteriori estimates to adaptive mesh refinements

on the pair correlation density for hyperbolic angles we prove a conjecture of boca popa zaharescu on the density function for the pair correlation of hyperbolic angles in a growing orbit of a discrete lattice in psl2 r

a posteriori error estimates for optimal control problems with state and control constraints we discuss the full discretization of an elliptic optimal control problem with pointwise control and state constraints we provide the first reliable a posteriori error estimator that contains only computable quantities for this class of problems moreover we show that the error estimator converges to zero if one has convergence of the discrete solutions to the solution of the original problem the theory is illustrated by numerical tests

on solid ergodicity for gaussian actions we investigate gaussian actions through the study of their crossed product von neumann algebra the motivational result is chifan and ioana s ergodic decomposition theorem for bernoulli actions chifan and ioana 2010 4 that we generalize to gaussian actions theorem a we also give general structural results theorems 3 4 and 3 8 that allow us to get a more accurate result at the level of von neumann algebras more precisely for a large class of gaussian actions x we show that any subfactor n of l x containing l x is either hyperfinite or is non gamma and prime at the end of the article we show a similar result for bogoliubov actions

uniform pointwise bounds for matrix coefficients of unitary representations on semidirect products abstract let k be a local field of characteristic 0 and let g be a connected semisimple almost k algebraic group suppose rank k g 1 and is an excellent representation of g on a finite dimensional k vector space v we construct uniform pointwise bounds for the k finite matrix coefficients restricted on g of all unitary representations of the semi direct product g v without non trivial v fixed vectors these bounds turn out to be sharper than the bounds obtained from g itself for some cases as an application we discuss a simple method of calculating kazhdan constants for various compact subsets of the pair g v v

exotic crossed products and the baum connes conjecture we study general properties of exotic crossed product functors and characterise those which extend to functors on equivariant c algebra categories based on correspondences we show that every such functor allows the construction of a descent in kk theory and we use this to show that all crossed products by correspondence functors of k amenable groups are kk equivalent we also show that for second countable groups the minimal exact morita compatible crossed product functor used in the new formulation of the baum connes conjecture by baum guentner and willett 4 extends to correspondences when restricted to separable g c algebras it therefore allows a descent in kk theory for separable systems

superconvergence properties of optimal control problems an optimal control problem for a two dimensional 2 d elliptic equation is investigated with pointwise control constraints this paper is concerned with discretization of the control by piecewise constant functions the state and the adjoint state are discretized by linear finite elements approximations of the optimal solution of the continuous optimal control problem will be constructed by a projection of the discrete adjoint state it is proved that these approximations have convergence order h2

strong solidity of group factors from lattices in so n 1 and su n 1 abstract we show that the group factors l where is an icc lattice in either so n 1 or su n 1 n 2 are strongly solid in the sense of ozawa and popa 2010 13 this strengthens a result of ozawa and popa 2010 14 showing that these factors do not have cartan subalgebras

coupling regularization and adaptive hp bem for the solution of a delamination problem in this paper we couple regularization techniques with the adaptive hp version of the boundary element method hp bem for the efficient numerical solution of linear elastic problems with nonmonotone contact boundary conditions as a model example we treat the delamination of composite structures with a contaminated interface layer this problem has a weak formulation in terms of a nonsmooth variational inequality the resulting hemivariational inequality is first regularized and then discretized by an adaptive hp bem we give conditions for the uniqueness of the solution and provide an a priori error estimate furthermore we prove the very first a posteriori error estimate for the nonsmooth variational problem utilizing a novel mixed regularized formulation thus enabling hp adaptivity various numerical experiments illustrate the behavior strengths and limitations of the proposed high order approximation scheme